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Optical dynamics of molecular aggregatesde Boer, Steven

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. .

OPTICAL DYNAM-ICS

MOLECULAR AGGREGATES - . -

STEWEN .-- . - DE BOER

OPTICAL DYNAMICS

OF

MOLECULAR AGGREGATES

OPTICAL DYNAMICS OF MOLECULAR AGGREGATES

ter verkrijging van het docforaat in de Wiskunde e l Natuurwetenschappen aan de Rijksuniversiteit Gmningen

OP g-g de Rector Magnificum Dr. L.J. Engels in het openbaar te verdedigen op

vrijdag 22 februari 1W1 des namiddags te 2.45 uur precies

STEVEN DE BOER

geboren op 11 juli 1961 te Dalfsen

druk: wibm disaartatiedrukkerij. h e h d

Promotor: Prof. Dr. D. A. Wiersma

Here's the physicist Working in the Fermi Lab

T090-ni-yi-ight The lights burn In the night

They burn every night And around every bend There comes no end

Around the bend, no end

David Thomas

Chapter 1 Time resolved spectroscopy of molecular aggregates 1 1.1 Molecular aggregates 2 1.2 Picosecond lasers 3 1.3 Sumaary 4 References 6

Chapter 2 Theory of aggregate excitations 2.1 Introduction 2.2 Coupled chromophores

2.2.1 Dimer model 2.2.2 Aggregates

2.3 Optical lieshape of molecular excitons 2.3.1 Exciton-phonon coupling 2.3.2 Influence of site inhomogeneity 2.3.3 Aggregate superradiance and dephasing 2.3.4 Polarons and self-trapping

References ?

Chapter 3 Experimental considerations 3.1 Introduction 3.2 Pump/probe spectroscopy

3.2.1 Theoretical background 3.2.2 Experimental setup

3.3 Accumulated photon echoes 3.3.1 Stochastic accumulated echoes 3.3.2 AOM effects

3.4 High frequency modulated detection 3.5 Time correlated single photon counting (TCSPC) 3.6 Computer control and analysis 3.7 Absorption and emission spectroscopy 3.8 Sample preparation and handling References

Chapter 4 Dephasing of a molecular exciton: PIC 4.1 Introduction 4.2 Dephasing in glasses 4.3 Accumulated echo measurements

4.3.1 b w temperature decay 4.3.2 Temperature dependence 4.3.3 Bottleneck dynamics 4.3.4 Trapping measurements 4.3.5 Other PIC aggregates

4.4 Discussion and summary References

Chapter 5 Superradiance in PIC aggregates 5.1 Introduction 5.2 Steady-state fluorescence

5.2.1 Spectra 5.2.2 Trapping

5.3 Time-reaolved fluorescence 5.3.1 Low temperature decay 5.3.2 Fluorescence depolarization 5.3.3 Temperature dependence 5.3.4 Trapping

5.4 Diecussion and summary 5.4.1 Aggregate ebe 5.4.2 Temperature dependence 5.4.3 Summary

References

Chapter 6 Picosecond pump/probe and time correlated single photon counting experiments on TPY aggregates: excitons and polarone

6.1 Introduction 6.2 Summary of the theoretical concept 6.3 Results

6.3.1 Spectra of monomers aggregates 6.3.2 Pump/probe experiments 6.3.3 Homogeneous lineshape 6.3.4 Monomer properties 6.3.5 TCSPC results

6.4 Diecuesion and summary Acknowledgments References

Chapter 7 Spectra and dynamics of 'I'D aggregates 7.1 Introduction 7.2 Results and discussion Ref erences

cwwTER1

Time resolved spectroscopy of molecular aggregates

11 Molecular aggregate6

1.3 Summary

References

1.1 Molecular aggregates

Condensed phase molecular spectroscopy is concerned with the study of molecular energy states. In solids the interaction between the molecules under study and their environment is important. In a molecular crystd this environment consists of identical molecules, which are ordered perfectly. Two situations are important; one can study the molecule of interest as a pure crystal [1,2], in which every molecule is surrounded by identical neighbors, or a as guest molecule in a crystal- of a different compound [3]. When comparing the excited state of a molecule in a pure crystal with the excited state of a molecule which is isolated, a striking difference is encountered. The state formed after optical excitation of a single molecule is confined to that molecule. The excited state of a molecule in a pure crystal is often delocabed, which means that not a single molecule is excited, but a whole array of molecules. This type of excitation is called exciton [4].

Molecular aggregates represent a situation intermediary between isolated molecules and pure crystals. As such they offer the opportunity to acquire insight in the processes of localization and delocalization of molecular excited states. The spectroscopy of molecular aggregates has been an important topic in molecular spectroscopy (51.

The interactions of the electronic excited state with the environment can be studied using steady state absorption and emission spectroscopy. An absorption spectrum, for example, gives the position and the linewidth of an optical transition. This linewidth contains a contribution from relaxation (homogeneous linewidth), and a contribution which is caused by the statistical fluctuations of the environment of the different molecules (inhomogeneous linewidth). Stated differently, both static and dynamic interactions determine the steady state optical spectra.

Time resolved spectroscopy gives information about the dynamics of the interaction of the molecule with the host environment. The relaxation of an optically excited molecule consists of two processes: relaxation to other states characterized by a population lifetime TI, and pure dephasing process with a lifetime c. Examples of the first process are fluorescence and radiationless relaxation. Optical excitation of a molecule can be treated as driving an optical oscillator to a higher energy level. The disturbances of this optical oscillator that change the phase but not the energy state are d e d pure dephasing. The host environment of the excited molecule is the source of these disturbances. Both static and time resolved spectroscopies of molecular aggregates are the subject of this thesis.

The concept of the molecular exciton dates back to the work of Frenkel [6], and has been applied to many problems in molecular spectroscopy [7]. The coupling of the molecular excited states leads to formation of molecular exciton bands. The oscillator strength is renormalized, and drastic changes occur in the spectrum upon the coupling of the molecules. The simplest molecular exciton is the dimer. Such a dimer state is formed when the electronjc excited states of two molecules mix into a plus and a minus combination. An interesting question is whether the dimer state is a true two-molecule state, or a one molecule state that hops from

1. Time resolved s~ectrosco~v of molecular anerenates

molecule 1 to 2 181. Dimer exciton bands are formed in isotopically mixed crystals. It turns out that the main factor determining the lineshape is the scattering of the exciton, either by impurities or by crystal phonons PI.

When more than two molecules are coupled together a band of molecular exciton states is formed. Some molecular crystale and molecular aggregates exhibit a strong anisotropy of the coupling between the molecules, leading to low dimensional excitations. The salient feature of one and two dimensional molecular excitons is the projection of the combined oscillator strength of the monomers on juet a few exciton states. These particular exciton states acquire a large transition dipole moment. The radiative rate of a transition is proportional to the square of the transition dipole moment, so aggregation leads to very high radiative rates. Thi effect is called superradiance.

The main part of the studies on molecular excitons in molecular crystals has been done on triplet excitons [10,11]. Triplet states of chromophores generally have sinall transition moments, whereas singlet excited states couple much stronger to applied optical fields. Molecules in the triplet atate are in general not coupled as strongly as in the singlet state. As a result, the triplet exciton bandwidth is generally of the order of a few cm-', wherem the bandwidth of a singlet exciton can easily be 1000 cm". The key parameter determining the delocalization of an exciton in both cases is the ratio of the spread of the site inhomogeneity (a) to the exciton bandwidth (B). A delocalized triplet exciton can be observed in highly perfect crystab, which have very emall site inhomogeneitiea. Molecular aggregates are not as perfectly ordered a s molecular crystals. The strong coupling between unite, however, allows for the observation of delocalized exciton states.

The study of singlet excitons is complicated by the fact that the high oscillator strength per unit volume for these transitions in molecular crystals leads to polariton formation upon optical absorption. A polariton is a mixed photon-exciton state which is formed when the coupling of the molecular statea to the optical field is very strong. A recent study on naphthalene single crystals [12] shows that their optical propertie$ are indeed governed by polaritons. The transition moment per unit volume in such a pure crystal can be very high. The characteristic length of an excitation process is the wavelength of the exciting light (b,). The low dimensionality of molecular aggregates leads to a low tramition dipole moment per unit volume (#Aa&,.), and polariton formation can be excluded. As such, molecular aggregate offer an unique possibility to study singlet molecular excitons.

The development of lasers has opened new possibilities for the spectroscopic study of molecules. Using narrow band continuous light sources, lineshapes and thus dephasing can be studied in the frequency domain. Another line in the development of lasers has led to pulsed lasers. Both relaxation and dephasing of collections of optically excited chromophores can be studied in the time domain with the help of pulsed

lasers. Sequences of coherent pulses generate a variety of effects like, for example, coherent Raman scattering [13], and photon echo phenomena 1141. Incoherent dynamica can be probed as well. In thia caee the laser pulses serve to generate a non-equilibrium population whose relaxation can be followed in time. This relaxation can be monitored by either another laser pulse, ss in pump/probe spectroecopy, or by fast electronic detection, ae in time resolved photon counting.

The so called continuous wave modelooked laser has supported the development of time resolved apectroacopy. In this laser the gain is modulated at s frequency which is the same as the inverse round trip time of the light. Only during the short period that the gain is larger thsn one the light will be amplified. The resulting output is a train of pubes at exlctly the round tfip frequency. The pulse lengths that can be produced depend on the actual goin and 106s media in the laser. The pulse lengths vary from 100 picoseconds (1 ps = 10-l2 second) in scowto-optically modelocked crrgon-ion lasers to aa short as 6 ferntoseconds [15] (1 fs = l(Tw second) in colliding pulse modelocked (a) dye ~~eel-l3.

Most lasing media have only a liited spectral width where a high gain is found. For exam@, an argon laser only operates at a number of wavelengths. This pogee severe limitations on the applicability of lasers for 8pectroscopy. The invention of the dye laser has solved this problem. Organic dye molecules and some inorganic s y s k q have very broad emission spectra (>1000~m'~) and can ahow laser action in broad ranges. The technical progress in the past three decpAes since the invention of the laser, has led to lasers that cover most of the ultra-violet, visible and infra-red parts of the electromagnetic spectrum.

1.3 summary

The subject of this thesis is the spectroscopy and dynamics of molecular aggregatee in amorphous matr ia . Aggregates of three different molecules were studied. The molecules are depicted in Fig. (1.1). Supersaturated solutions of these molecules show aggregate formation. Aggregation is a proceaa similar to precipitation of a solution. The loss of entropy in such a precipitation process is compensated by the g& in enthalpy. Molecular aggregates in solutions thus represent a metastable thermodynamic state. The o r g a t i o n of aggregates in solution can be fixed by rapid cooling or rapid mlvent evaporation.

The molecules were selected because of the dramatic changes occurring in the absorption spectra upon formation of aggregates. The aggregates show absorption bands that are shifted to lower energy by more than 1000 cm-l, with respect to the monomer transition. The dynamics of the optical excitations that are formed after absorption of a photon by these aggregates is the main topic of this thesis.

In Chapter 2 an overview is given of the concept of the spectroscopy of excitons in molecular aggregates. Starting from a description of dimers, the energy level structure of exciton bands is developed. The interaction of the exdtons with the lattice modes of the environment, the so-called phonons, is also treated.

1. Time resolved S~ectroscoDY of molecular annrenates

I I (PIC)

Figure 1.1 . From top to bottom: pseudo-iso-cyanhe (PIC), a thiapyrilium dye ( T W ) , and a thiacyanine dye (TD). The first tsoo molecules are charged positivdy and are accompanied by a negative counter ion. The last molecule is an i n t d salt.

In Chapter 3 the experirnena methods are described. The time scale of the radiative and dephaaing d y n d c a of molecular excitons ranges typically from 1 ps to 100 ps. The dynamic8 was studied by time resolved fluorescence, pump/probe spectroscopy, and accumulated echo spectroscopy, which have the time resolution that is required. In this chapter the steady state spectroscopy and the preparation of the aggregate samples are described as well.

Chapter 4 deals with the dephasing of PIC aggregates in water/ ethylene glycol mixtures. These aggregates exhibit very narrow absorption lines (=30 cm-') in solid solution. The dephasing time is related to the

homogeneous width of the transition. At 1.5 kelvin (1.5K) the homogeneous width is about 1 cm-'. At temperatures of about 100 K the dephaaing time is much shorter and the linewidth is determined by this dephaaing time.

Ln Chapter 5 the radiative properties of PIC aggregates are studied. The key result is the observation of a fading of the superradiant effect at higher temperatures. This show that the the radiative coupling of the monomer units is less effective at higher temperatures. Possible reasons for this decoupling are discussed.

The excitations of W Y aggregates that are treated in Chapter 6 differ dramatically from the excitons observed in PIC aggregates. The delocalized e~ci~bt ion is coupled strongly to lattice phonons. A model is proposed that explains the observations in terms of a self-trapping process of the exciton.

Finally, in Chapter 7, a preliminary report is given of results from experiments on aggregates of the thiacyanine dye TD. These aggregates exhibit a number of features that indicate superradiant exciton behavior comparable to PIC aggregates.

References

1. R. Hochstrasser, Ann. Rev. Phys. Chem. 17, 457 (1966). 2. C.W. Robinson, Ann. Rev. Phys. Chem. 21, 429 (1970). 3. W.H. Hesselink and D.A. Wienrma, in "Modern Problems in Condensed

Matter Sciences", vol 4, "Spectroscopy and Excitation Dynamics of Condensed Molecular System", eds. V.M. Agranovich and A.A. Maradudin (North-Holland, haterdam, 1983).

4. A.S. Davydov, "Theory of molecular excitons" (Plenum Press, New York, 1971).

5, see for example: "Organic Molecular Aggregates", e d ~ . P. Reineker, H. Haken, and H.C. Wolf, Springer Ser. SolidState Sciences, vol. 49 (Springer, Berlin, 1983). J.I. Frenkel, Php. Rev. 57, 17 (1931), Phys. Rev. 17, 1!276 (1931).

7. see for example: ''Modem Problems in Condensed Matter Sciencesn, vol 2, "Excitons", eds. V.M. Agranovich and A.A. Maradudin (North-Holland, Amterdaq, 1982).

8. R. Silbey, Arm. Rev. Phys. Chem. 27, 203 (1976). 9. D.M. Burland and A.H. Zewail, "Coherent Rocessee in Molecular

Crystals", Advances in Chemical Physics vol. m, pg. 369, eds, I. Prigogine and S.A. Rice (Wiley, New York, 1979).

10. R.M. Hochstrasser in "Triplet Exciton Statea of Molecular Crystals", Iqt. Rev. of Science, Physical Cheanistry, Ser.2, Vol. 3, ed. D.A. Ramsey (Butterworks, London, 1976).

11. J.F.C. van Kooten, A.J. van Strien and J. Schmidt, Chem. Phys. Lett. SO, 95 (1982). A.J. van Strien, R. Silbey and J. Schmidt, Mol. Phys. 48, 151 (1982).

12. S.H. Stevenson, M.A. Connolly and C.J. Small, Chem. Phys. 128, 157 (1988).

1. Time resolved s~ectrosco~v of molecular anmenates

13. A. Szabo, Phys. Rev. B 11, 4512 (1975). 14. I.D. Abella, N.A. Kurnit and S.R. Hartmann, Phys. Rev. Lett. 13, 567

(1964), Phys. Rev. 141, 391 (1966). 15. R.L. Fork, C.H. Brito Cruz, P.C. Becker and C.V. Shank, Opt. Lett.

12, 483 (1986).

Theory of aggregate excitations

2.1 Introduction

2.2 Coupled chromophoree

2.2.1 Dher model

2.2.2 Aggregates

2.9 Optical m h a p e of molecular excitons

2.3.1 Rtciton-phonon coupling

2.3.2 Influence of site inhomogeneity

2.3.3 Aggregate superradiance and dephasing

2.3.4 Polarons and self-trapping

References

2.Theorv of annrenate excitations

2.1 Introduction

In closely packed s t r u c t u r ~ like molecular crystals and aggregates, the coupling between molecules can lead to delocalization of the excited state of molecules. The delocalized excitation is called Frenkel exciton [I], and it is the main entity in the description of spectra and dynamics of optical excitations in molecular solide.

The concept of a delocalized excitation in a molecular solid has been used extensively to explain the anomalous spectral properties of coupled chromophores. Fiirster [2] considered the excitation transport, and ~oyozawa [3] extended the theory for excitation-phonon interaction. On the basis of the theoretical foundations refinements have been made [4] to describe the transfer of excitons in solids.

Whether or not an extended state is formed depends, on the size of the intermolecular coupling (B) relative to the site energy differences, the so called site inhomogeneity (A). The molecular coupling must overcome these energy differences. In Sect. (2.2), starting from a model system which consists of two coupled chromophores, the strong and intermediate coupling cases will be treated. The treatment founded on the work of Davydov [5] and Kasha [6] offers an interpretation for the observed spectra of aggregated molecules.

In the strong coupling caae a band of delocalized states is formed. Along with the formation of this exciton band, the oscillator strength of the transitions is redistributed. For one and two dimensional excitons, some band states acquire a very large oscillator strength. The radiative liietime, which is inversely proportional to the transition moment squared, is shortened for these optically dowed states.

The final section of this chapter deals with the coupling of the exciton states to lattice vibrations (phonons). The coupling between the aggregate exciton and the aggregate phonons determines the lineshape and the linewidth of the exciton transition. It will be shown that both exciton scattering and self-trapping are dependent on the strength of the exciton-phonon coupling.

2.2 Coupled chromophores

2.2.1 Dimer model

In order to obtain a better understanding of the spectra and dynamics of molecular aggregates it is useful to first consider two monomers coupled by an interaction J. The Hsmiltonian for this system looks like:

where the subscripts refer to the individual molecules 1 and 2. The one-molecule Hmiltonians are diagonal with ground state electronic eigenfunctions and !P2, and energies El and Ez. Provided the dimer is bound by weak van der Waals forces, the combined ground state function reads:

The ground state energy of the dimer will contain the sum of the one-molecule energies and an interaction term D,

which describes the binding energy or, alternatively, the van der Waals energy of the dimer. The excited state dimer wavefunction ia a linear combination of singly excited states:

The asterisk denotes which molecule is in the excited state. The coeff.icienta a1 and 42 can be found by solving the eigenvalue problem H !Pdk = E !P;* The solutions are:

Y+ = 2-1'2(@:92t (2.5a)

!P- = 2A1'2(!P:!P2 - !Pl!P:) . (2.5b)

with eigenvalues x

The wavefunctions are the in-phase and out-of-phase combinations of the two possible excited state configurations. In fact the site basis (Yl,P2) has been transformed into a dimer basis (!P+,!P-). The dimer excited state energy contains a* term ,!?, which is the single molecule excited state energy, a term D , which is the aforementioned van der Waals shift, now of the excited state, and an integral term. The integral is called dimer splitting or exciton splitting (B), and is a result of the excitation transfer induced by the coupling term J.

The energy levels are depicted )in Fig. (2.1). It is possible now to write down an expression for the energy differences of the possible transitions in the dimer:

The first term of Eq. (2.8) is simply the single molecule excited state energy, the second term denotes the difference of the van der Waals shifta and is generally not very large. Two questions need to be answered still; what is the origin of the coupling, and what is the transition

2. Theory of anmenate excitations 11

probability between the ground state and the dimer levels. The excited state of a molecule can be seen as an oscillating charge

distribution. When an optical field is applied to an unexcited molecule, this charge distribution can resonate with the field, which leads to absorption of energy. An identical molecule, which is close to an excited molecule, can also resonate with the oscillating charge distribution of the excited molecule. This last resonance cauaes the coupling of molecular excited states. The two resonance processee are governed by the same molecular properfy: the transition moment between molecular 'ground and excited states. The transition moment can be limited to the point dipole-dipole interaction term of a a multiple expansion. In this case the interaction is reduced to two oscillating dipoles next to one another. The magnitude of the interaction is determined by the geometry of the problexb, and by the relative phases of the oscillators. The simplified exciton splitting has the form of the dipole-dipole intiiraction energy:

-

In the case where the two transition moments are parallel and equal in magnitude the expression for B becomes:

Here 0 denotes the angle between the l i e connecting the chromophores and the direction of the transition moments. For example when the transition momenta are aligned head to tail this angle is zero degrees.

In Table (2.1), three special cases are summarized with parallel in-phase transition moments. From the table it can be seen that the energy for the card pack dimer (8=90°) is increased by pa/?, the energy for the head to tail dimer (8=0°) on the contrary, is lowered by -2pa/P. The energy change is zero at the so called "magic angle". If one realizes that the oscillating' electric field has a characteristic length of one wavelength, which is much larger than the diner separation, one concludes that the constituting monomers experience the same field. The component

Table 2.1 parallel dimers

dimer type

t +

\ %

+a.

0 (degrees)

90

54.7

o

B

cca/r3 0

- 2 2 1 ~ ~

of the combined transition moments that is in phase with the field carries double oscillator strength, refative to the monomer, whereas the out-of-phase component clrrriea none. The @-phase dime state is called superradiant becaw it carries double oscillator strength, and .is the main entity for the understanding of the radiative properties of aggregates.

In real dimers other arrangements of transition moments than petallel exist. In that case the full expression of Eq. (2.9) muat be evaluated, which results in two &tea that both carry nonzero oscillator strength. The energy splitting of the two states is determined by the actual geometry of the dimer and the direction of the transition moment. For example, when the transition moments are perpendicular, the interaction energy B is zero; and both dimer statee have equal transition moment. The only dimer feature that is apparent in this case is the van der Waals term.

In constructing this dimer model some relevant interactions have not been taken in account as, for example, differences in the static energies of the monomers at site 1 and site 2. Another neglected factor is the coupling of the electronic excitation to low frequency vibrational modes of the dimer. Despite thew omissions the model explaine some of the most striking phenomena in the spectroscopy of dirners.

2.2.2 Aggregates

The concept of the dimer can be extended to the case where N, the number of coupled monomer units, is very large. As in the dimer cake, the excitation is a co11ective one, extending over all units. In order to extend the dimer paradigm to the case for large N, the whole assembly is assumed to be smaller than the wavelength of the exciting optical field. The approximate size of a dye molecule is 0.5 nanometer. Combining this with a typical visible wavelength of 500 nanometer the linear extension can be thousand units. I will show that the energy levels and the transition moments, together giving rise to the abeorption spectrum, do not change eignific~tly upon going from amall to large aggregates. In Sect. (2.3) it will be shdwn that the radiative dynamics are more sensitive to the aggregate size.

The approach is the same as for the dimer case, s tar th i with single particle Hmiltonians and coupling terms:

When one asaumes that the binding forces between the constituting monomers are weak and no electron delocalhtion takes place in the ground state, the ground state wavefunction is a product of single particle wavefunctions:

2. Theorv of anscreeate excitations 13

The aggregate ground state energy contains a van der Waals term, D,

Considering excited state wavefunctions, these are again linear combinations of singly excited wavefunctions such as:

where the label a refers to the molecule that is excited. The. linear combinations are:

Aa in the dirner case the basis has been transformed from site oriented wavefunctions into aggregate oriented ones. Instead of considering a long chain with one unit excited, the whole aggregate ia involved. The key parameter characterizing the excitation is not the label of the excited molecule, n, but the k-value, denoting the state of the whole aggregate. In order to complete the picture we have to consider the transition moments and the energies of the aggregate levels.

The interaction term J,, in Eq. (2.11) is often limited to the so- called nearest neighbor terms. The coupling J , in that approximation only has nonzero values for adjoining sites, nan+l. The neglect of other coupling terms is justified by the 119 behavior of the coupling, for example, the nan+2 term originates from a pair with distance 2r, resulting in an interaction that is one eighth of the nearest neighbor term. The interaction of the monomers is assumed to be represented by dipole-dipole coupling. Using cyclic boundary conditions for the chain (circular aggregate), the energies of the band levels can be expressed as:

where k takes the values 0 to N, and B is the binding energy. It is evident from this last equation that the width of the exciton band for large aggregates equals 4B. The bandwidth is twice as large as for the h e r , reflecting the extra energy lowering as a result of extra delocalization. The dependence of the bandwidth on N is weak. For a cyclic aggregate of ten units the bandwidth is only ten percent smaller than for an infinitely long aggregate.

For an aggregate consisting of parallel units, the k=O state carries all of the oscillator strength. That state can be envisioned as the in-phase combination of all separate transition dipole moments. Whether the allowed state is at the bottom of the band or at the top of the band depends on the actual alignment. The head to tail aggregate absorbs at the low energy side of the band, whereas the card pack aggregate absorbs at the high energy side. Historically, the two cases mentioned are

referred to as J- and H-bands [?I, respectively.

Figure 2.1 E w g y levels of a single chromophore (left) tnd an aggregate consisting of chrwphores (right). T k tenns fl and D denote the van dm W d s shift in ground and excited states. The coupling J leads to a banti of ex& stdas Qeith totd width 48. The anows indicste the dloroed optied trcnrsftiow.

The transition dipoles need not be parallel and can be organized in pain, a situation that is commonly encountered. In this case both extremes of the exciton band acquire oscillator strength. The relative polarizations of the two transitions are perpendicular. From Fig. (2.2) it can be seen that the total transition dipole depends on the inclination angle and the direction of the total transition dipole depends on the relative phases. There is no necessity for the resultant total transition moment to be either parallel or perpendicular to the axis of the aggregate.

Figure 2.2 Exciton band for an aggregate with inclined transition moments. The phase of the transition dipoles is indicated by the direction of the small arrows. The top of the exdon band can be reached with light that is polarized vertically relative to the aggregate axis, whereas the bottom of the band can be reached by horixontally polarized light.

In the preceding sections on dirners and aggregates the basic factors determining the delocalization of excitation have been discussed. Though

2. Theorv of anmenate excitations 15

many factors were ignored, the description offers a model for aggregate excitations. This model will often be referred to in the rest of this thesis. The key elements of the model are the weak van der Waals binding of the units, and the excitation transfer in the excited state. The weak binding implies that no delocalization takes place in the ground state. Only the excited state basis must be transformed into a delocalized one.

One of the most interesting results is the direct link between energy levels and transition moments. The transition dipole moments are directly linked to the obaerved abeorption strength. The comparison of monomer, diier, and aggregate absorption spectra with each other provides information about interaction and delocalization of the excited state.

The total oscillator strength does not change upon the coupling of monomer units, because N participating units carry 1/N part of the total excitation. The tramition moment of the optically allowed aggregate state, however, is enhanced by a fador \lEj. This last enhancement drastically changes the radiative properties of the aggregate, as will be shown in Sect. (2.3). The treatment of transition dipoles which can add up, only works as long as the transition dipoles stay in phase, which means that no dephasing of the transitions of the units inside the aggregate should occur. If the transition dipoles do dephase, the radiative properties of the aggregate will change. The description of aggregates in the above way is therefore called coherent. The incoherent description is used for cases where the correlation between the monomers is totally lost. The transfer term in that last limit only results in a random hopping of the excitation.

2.9 Optical lineshape of molecular excitona

2.9.1 Ekciton-phonon coupling

The treatment of the previous section leads to a description in terms of a band of energy levels and delocalized exciton wavefunctions. The goal of this section is to identify the factors that determine the dynamics of the delocalized excitation. The term dynamics refers to both the dephasing rate of the optical excitation and to the lifetime of that excitation.

The linewidth of a transition to a pure isolated exciton k-state is determined solely by lifetime broadening (T,). When the influence of other molecular degrees of freedom is incorporated in the model, other factors determine the optical properties as well. The Hamiltonian of Eq. (2.11) can be extended with terms accounting for the coupling of the delocalized excitation to low frequency lattice modes (phonons) [8,9]. The total Hamiltonian takes the following form:

The terms HWo is the aggregate Hamiltonian that was previously used. The terms in that Hamiltonian are made more explicit using creation and annihilation operators:

In this equation en is the single particle (monomer) energy, directly related to the single particle Hamiltonian &. The term D is the van der Waals shift that was also previously encountered. This shift ie now characterized by a parameter R, and must be evaluated at the equilibrium position R=O, because the phonon modes modify the dietancee between monamers, and coneequently also the coupling of the monomer wavefunctions. 4 and a,, are the Boee creation and annihilation op-erators that create or m a t e an excitation on a site with label n. It is important to realize that these operatom are stridly site based. The intersite coupling term J is, like D, characterized by the equilibrium value at R=O. The eummation extends over all sites for which npm, but is often limited to nearest neighbor interaction, m==n*l.

The phonon W t o n i a n is given by:

The creation and annihilation operators b: and b9 refer to phonons with wavevector q and frequency w,,. The important difference relative to the electronic excitations created by h, is that the phonons are delocalized lattice excitations with a wavevector instead of excitations localized on a particular site. The phonon Harniltonian gives the energy of the phonon, without mixing electronic and lattice motions.

The two exciton-phonon coupling terms are the ones that are relevant for dephasing and localization of the exciton. The expression for the first coupling term is:

This term represents the influence of the phonons on the coupling between sites. The summation extends over the two different site indices (n and m), and is comected to the intersite coupling tern J . Actually, this contribution can be treated aa the change of the intersite coupling caused by interaction with lattice modes. F stands for the coupling strength of the phonons with respect to the intersite interaction.

The second exciton-phonon term ~ ( ~ 1 , describeg the change of the energy on one particular site n cawed by interaction with phonons:

The electronic creation and annihilation operators now refer to the same site n. This term can be envisioned as a change of the van der Waals shift term D. x is the coupling strength for this particular part of the exciton phonon interaction.

The two exciton-phonon terms can be differentiated by the noted local and intersite character. H(') can be named the intersite term and H ( ~ )

2. Theorv of anmenate excitations

can be named the local term. The effect of the two parts of the exciton-phonon coupling is quite different. The local part (H@)) describes the fluctuation of the site energy caused by phonons. From theoretical work [9] it can be concluded that this last term lea& to fluctuations of the energy of the exciton states. The states do not mix as a result of the coupling and the lineshape is not influenced. The intersite term does have an effect on the exciton states, the term causes the scattering of exciton k-states by phonons. The modulation of the coupling between the units mediated by the intersite coupling term mixes the pure exciton states, and causee k to k' scattaring.

The scattering of the exciton state as described by the intersite term ( ~ ( l ) ) is essentially a lifetime limiting or TI process. A scattering event always leads to a change of the exciton state. For an infinite circular aggregate only the transition to one k-state is optically allowed. After excitation this initially prepared state scatters from k to k' and from k' to k" and so *on. Be- there are many k-states accessible, it is not likely that an exciton returns to the initially prepared state. The homogeneous line shape of the exciton state therefore reflects the rate a t which the optically allowed level is depopulated caused by the interaction with phonons.

The influence of the the local exciton-phonon term (tit2)) modifies the zero-order wavefunctions. The new basis set consists of mixed exciton-phonon states, the so-called polaron states. A polaron is an exciton that is accompanied by a phonon induced deformation.

The behavior of an excitation will differ dramatically depending on which of the two exciton-phonon coupling terms dominates. In the limit where the intersite terms are negligible, a polaron is formed. If the local term can be ignored the excitation is better described as an exciton state that is scattered by phonons (wq,q) at certain times, changing the exciton k-state from k to ktq.

The equations above follow from a perturbative approach, considering linear exciton-phonon coupling only. The resulting eigenstates are exciton k-states. A different approach to the interaction of the exciton with the lattice modes ie the so called Haken-Strobl model [lo]. Zn this model the phofions are not treated explicitly, but handled together with all other lattice modes as random fluctuations of E and 3. The principal rermlts of Haken and Strobl [lo] are:

Here the brackets denote averaging over time, and yl, and yg,, are the associated with the rate of the fluctuations of local energies and intersite couplings respectively. The total homogeneous linewidth of the exciton transition assuming nearest neighbor interaction only, is expressed as:

r , = Tloc+ Tint . (2.28)

The importance of this result ia that the linewidth contains a contribution caused by the local energy fluctuation of Eq. (2.22). In the linear exciton-phonon coupling model the only preaas that influences the linewidth is the scattering to other k-staW. In the HakenStrobl model this scattering is incorporated in the term yi,. The local fluctuation leads to a contribution to the linewidth of tks exciton that ie not accompanied by a change of state, in other words, a pure dephasing process. This dephaaing process has consequences for the radiative behavior a s will be shown in Sect. (2.3.3).

The incorporation of lattice motions into the description of excitons is necessary in order to understand the shape of exciton lines. If one considers linear exciton-phonon coupling only, the two extreme caees are an exciton scattered by phonons, and a polaron, depending on the magnitudes of the coupling terms. The interaction with phonons in this approximation does not lead to pure dephesing. Starting from the Haken-Strobl model 'the pure dephasing of the exciton transition can be understood. Equivalent to the local energy fluctuation formaJim (Eq. (2.22), one can evaluate higher order exciton-phonon coupling terms of the Hamiltonians Eq. (2.20) and Eq. (2.21).

2.3.2 Influence of site inhomogeneity

The basic exciton Hamiltonian Eq. (2.11) incorporates the coupling term J,, that no matter how d, totally delocalizes the excited state wavefunction. This fact is caused by the identity of all single particle Hamiltonians H,, for a l l monomers that form the aggregate. The resulting energy levels are sharply defined, and the width of the transitions is only determined by lifetime broadening. In m a t liquids and solids the width of tramitions of dopant molecules ia determined predominantly by site to site energy differences. If these energy differences change rapidly as in room temperature liquids, a time dependent description must be adopted. The site energies in that limit are characterized by time correlation functions. In solids at low temperature the correlation time is infinite. This means that the site contribution to the total energy is static.

The static site energy 4, can directly be incorporated in the aggregate Hamiltonian:

In general the inhomogeneities are distributed randomly, according to a Gaussian distribution with width o.

Noninteracting monomers have an absorption spectrum centered around the eigenvalue of &, with the aforementioned width o. When the monomers combine to aggregates, different situations arise depending on the relative sizes of the coupling 3 and the spread of the inhomogeneity.

2. Theory of anerenate excitations 19

Without inhomogeneity delocalization will occur, independent of the size of the coupling. Introducing the site dependent energy 4 leads to a competition between this energy and the site to site coupling. A large inhomogeneity totally inhibits any delocalization, whereas a- small inhomogeneity leads to almost total delocrrlization.

When the coupling tenn is large enough to overcome the inhomogeneities, the linewidth of the aggregate changes drastically. The excitation extends over a large number of units and consequently the inhomogeneity that can be assigned to the total excitation is some average of the monomer inhomogeneities. This effect is known as exchange narrowing, or motional narrowing. Knapp [ll] has considered aggregates with a Gaussian spread of the site inhomogeneity. In that limit the linewidth scales with the root of N. The scaling with the root of N indicates that the inhomogeneities average quadratically, and that the resulting absorption line has the root-mean-square value as compared to monomer. ~uadratic averaging can be anticipated because the coupling term that connects neighboring sites must overcome energy differences 4-4+1, where the deltas are distributed according to a Gaussian. For cases where the coupling J and the inhomogeneity o are comparable, the narrowing effect ie less pronounced.

Knapp [ll] especially considered the effect of intersite correlation of the energies in the aggregate. It is plausible that two monomers which are next to each other in an aggregate have comparable environments. The linewidth in that case does not scale with the root of N, but contains an extra variable p that gives the amount of intersite correlation. Summarizing, the aggregate linewidth in the strong coupling limit -(JwA) reads:

and with implementation of correlation,

where p=O implies no correlation and @=1 infinite correlation. The treatment shows that in the limit of infinite correlation of inhomogeneities the monomer linewidth is recovered.

2.3.3 Aggregate superradiance and dephasing

For the analysis of the optical dynamics of molecular aggregates it is important to know the connection between the radiative properties of the monomer units and the aggregate as a whole. An exciton can show N-fold enhancement of the radiative rate. This full enhancement is not reached when the interactions with the host environment of the exciton are incorporated. In Sect. (2.2) it was shown that for an infinite circular aggregate only one k-state carries oscillator strength. The transition dipole moment of this exciton level is enhanced by a factor fl, and since the radiative rate is proportional to the square of the transition

moment, that rate is enhanced by a factor N. This phenomenon is the superradiant enhancement.

Grad et al. [12] made the f i s t attempt to describe interaction of this superradiant exciton with the environment. The interaction of the exciton and the lattice modes was modeled according to the HakenStrobl model, ignoring the intersite (scattering) term. An effective W t o n i a n is formulated that contains the damping of the excitation explicitly in the form of an imaginary part:

The most important point is that the superradiant damping (r) of the aggregate is much smaller than the coupling energy B of the monomers. For example, the radiative lifetime of an aggregate excitation can be of the order of tens of picoseconds (approximately 1 an-' in energy units), and the exciton coupling strength can be 1000~n-~ . The fluctuations introduced by the environment Eq. (2.22) compete with the radiative decay, without affecting the delodization of the excitation.

The approach outlined here was extended by Spano and Mukeel (131 using a Liouville operator method. Their result can be summarized as follows. Homogeneous dephasing is caused by fluctuations:

aa in the HakenStrobl model. The damping of the excitation is in direct competition with the superradiant decay,

Next to the acceleration of the superradiant decay expressed in Eq. (2.32), another decay process with a time constant much longer than the monomer decay results from the treatment. Upon going to the limit of fast dephasing ( rdc9N7) , the decay of the superradiant exciton coneista of a fast initial component determined by the dephasing, and a slow decay determined eventually by the monomer rate y.

A last remark should be made about the nature of the dephasing. The term dephasing aa it is used here refers to the fluctuations of the monomer transition frequencies. The dephasing of the optically allowed exciton which is probed by homogeneous linewidth measurements is connected to this monomer dephasing, but it is not necessarily the m e .

2.3.4 Polarons and self-trapping

In Sect. (2.3.1) it was shown that in the approximation of linear exciton-phonon coupling two coupling terms exist. The intersite coupling term leads to scattering of the phonon and the local coupling term leads to a new mixed state: the polaron. The delocalization of a molecular exciton is counteracted by the presence of site inhomogeneities. The coupling of units must overcome the random energy differences, JBA. In this limit a delocalized exciton is formed which leads to motional

2. Theory of anmenate excitations 21

narrowing of the absorption lineshape. If the local exciton-phonon coupling term (Eq. (2.21)) dominates the Hamiltonian can be transformed to [14,16]:

where 4 and A,, refer to polaron creation and annihilation operators. An important difference relative to the exciton ia the lowering of the energy expressed by the term CqIdJ%w. This means that because of exciton-phonon coupling the energy I. fowered by a certain amount. Another difference is the change of the intersite coupling J; the local lattice distortion at site n will reduce that coupling. As long as this renormalized coupling ia larger than the inhomogeneity, a delocalized polaron is the eigenstate of the coupled system. However, when the reduction of the intersite coupling is very large and that coupling can no longer overcome the inhomogeneity, trapping will occur.

In Fig. (2.3) the situation ia sketched for the active phonon coordinate. The coupling between units leads to the formation of a band of exciton states. The excitation will be delocalized as long as the bandwidth is larger than the inhomogeneity. The coupling with the lattice phonone leads to energy stabilization (Cqlfl12~q) along the phcnon coordinate. The reduction of the coupling between the sites to J is indicated by the d bandwidth of the deformed state.

I phonan coordinate

Figure 2.3 Schenaatic energy potentid for e x d o n and polaron states. On optied excitation an exciton ( E ) is formed, the deformcrtion dong the phonon coordinate leads to a new energy minimum ( P ) . The presence of an energy b a w ( B ) depends on the actual -try of the system.

The actual dynamical behavior of the initially formed excitation depends on the system studied. Theoretical work by Raahba [16,17] on the

barrier formation in the process of self-trapping indicates that for one dimensional excitom no barrier is found. For pure electronic self-trapping the stability criterion for the free exciton state reads:

2d (lid-I) - 2

g < l . (2.34) R

Here d denotes the dimensionality, N is the number of participating monomers, and g is the coupling strength. When N is large the inequality always holde for d=3. This implies that a stable free exciton state exists next to the self-trapped state. The two s t a h are separated by a barrier. In the case of a one dimensional exciton aystam, the free exciton is unstable, indicating the absence of a barrier. The local exciton-phonon interaction in a one dimensional system will always lead to an exciton which relaxes to a trapped state. For the d-2 case the formation of a barrier depends on the size of the coupling strength.

In low dimensional molecular systems a barrier can be present that is caused by motions of the molecules in the lattice. In that case self-trapping is not an electronic effect but is caused by changes in the lattice. For example, the excitation can become localized in a one dimensional chain when an exited state dimer (excimer) is formed. The motion of the moleculed can involve a repulsive energy that is not c o ~ e c t e d to the energetics of the polaron iteeli. The repulsive energy term leads to the formation of a barrier for self-trapping.

References

J.I. Frenkel, Phys. Rev. 37, 17 (1931),)Phys. Rev. 17, 1276 (1931). Th. Forster, Ann. Physik, 2, 55 (1948), Th. Forster, in: "Modern Quantum Chemistryn, vol. 3, pg 93, ed. 0. Sinanoglu (Academic Press, New York). Y. Toyozawa, Rog. Theor. Phys. 20, 53 (1958). K. Lindenberg and B.J. West, Phys. Rev. Lett. 61, 1370 (1983). A.S. Davydov, "Theory of moleculaz excitonsn (Plenum Press, New York, 1971). M. Kasha, H.R. Rawls and M. Ashraf El-Bayoumi, Pure Appl. Chem. 11, 371 (1965). The terminology for the bands in dye eolutiona is not based on a strict system: M-band stands for Molecular or Monomer absorption, D-band refers to Dimer absorption, H-band refers to Hypochromic (blue shifted) absorption, and J-band refers to Jelley, one of the discoverers of aggregate bands in pseudo-iso-cyanine. In some German publications the term S-band or S-aggregates can be encountered, here S refers to Scheibe who independently from Jelley aleo described the aggregate band in pseudo-iso-cyanine. H. Friihlich, Roc. Roy. Soc. A 2l6, 291 (1952). D.M. Burland and A.H. Zewail, "Coherent Processes in Molecular Crystalsn, Advances in Chemical Physics vol. XL, pg. 369, eds, I. Rigogine and S.A. Rice (Wiey, New York, 1979). H. Haken and G. Strobl, 2. Phys. 282, 135 (1973).

2. Theory of annrenate excitations 23

11. E.W. Knapp, Chem. Phys. 85, 73 (1984). 12. J. Grad, C. Hernandez and S. Mukamei, Phys. Rev. A 37, 3835 (1988). 13. F.C. Spano and S. Mukamel, J. Chem. Phys. 91, 683 (1989). 14. T. Holstein, Ann. Phys. fi 8, 325 (1959). 15. M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa and E. Hanamura,

"Excitonic processes in solidsn ($pringer, Berlin, 1986). 16. E.I. Raahba, J. Molecular Electronics 4, 149, (1988). 17. E.I. Raahba, in: "Excitonsn, eds. E.I. Rashba and M.D. Sturge, pg.

543 (North-Holland, hterdam, 1982).

Experimental con6identiono

3.1 Introduction

3.2 Pump/probe spectroscopy

3.2.1 Theoretical background

3.2.2 Experimental setup

3.3 Accumulated photon echoes

3.3.1 Stochastic accmulated echoes ,-

3.3.2 AOM effects

3.4 High frequency modulated detection

3.6 Tlme correlated single photon counting (TCSPC)

3.6 Computer control and analysis

3.7 Absorption and emission spectroscopy

3.8 Sample preparation and handling

References

3.1 Introduction

In order to study the spectroscopy of molecular aggregates in the time domain, picosecond techniques must be used. The dephasing and fluorescence lifetimes range from I p (picosecond) to about 500 ps. An excitation source with a pulse width of about 1 ps is necessary in order to resolve the dynamics of processes with the quoted lifetimes.

The main portion of the experimental work presented in this thesis has been done using a so-called synchronously pumped modelocked picosecond dye laser. Such a laser can routinely produce 3 to 4 pa pulses in most of the visible and near infra-red pa- of the optical epectrum. The pulse from the laser is split into two parts that follow different optical paths. The two parts of the pulse are recombined in the sample, allowing for the detection of transient absorption changes. This pump/probe spectrometer uses the same design as Hesselink [I] in the f ist accumulated photon echo experiments [2]. Molenkamp [3] dedicated the apparatus fully to the generation and detection of accumulated echoes. The proposed changes to improve the detection sensitivity [3] have been applied, and have extended the sensitivity of the apparatus. The experimental complications of picosecond spectroscopy will be discussed in Sect. (3.2) through Sect. (3.4), along with a dewription of the measured nonlinear optical regponse6.

A modification of the laser and the addition of several electronics modules allowed us to do time correlated single photon counting experiments. This long established technique [4] has gained new impetus from the commercial availability of microchannel plate (MCP) photomultipliers with rise times as short as 100 ps. Combining these with appropriate fast electronics results in approximately 50 ps responses to ultrashort pulse excitation. The signal to noise ratio is determined by the number of detected fluorescent photons, and so just depends on collection time. The noise statistics follow a Poisson distribution, so the achievable extremely good signal to noise ratio allows for reliable data analysis by reconvolution fitting down to decay values of 10 ps. In Sect. (3.5) this technique is further explained.

In Sect. (3.6) the data collection and data analysis using microcomputers is described. The apparatus had already been automated in the past [3], using the first generally available microcomputer; the APPLEII. The need for more and faster data handling, together with reliability problems caused by the aging of the APPIE has made us discard this computer. The widely used IBM personal computer technology was chosen as replacement. New programs have been written both for data acquisition and analysis.

Sect. (3.7) and Sect. (3.8) describe the spectroscopical and chemical techniques that are used for the experiments. The preparation of aggregated samples of the dyes under study is rather delicate. Details concerning concentrations and cooling of the solutions can be found in the last section.

3.2 PumpJprobe spectroscopy

3.2.1 Theoretical background

A block diagram of the transient absorption or pump/probe experiment is shown in Fig. (3.1). An intense pulse of light (partially) excites the sample. Considering the optical absorbers aa a collection of a two level systems, the laser pulse induces the tranefer of population from the electronic ground state to the excited state. Since the absorption coefficient is proportional to the population difference of the two levels, this implies that the absorption is reduced after the passage of the pump pulse through the ample. The reduction of the absorption is measured by the probe pulse that arrives after a variable delay.

Figure 3.1 Layout of the basic pumplprobe experiment: the probe pulse reads the remaining sample absorption at time T after the passage of the pwnp pulse. The change of the probe pulse transmission AI is recorded by the detector (DET).

Ideally both pulses should have negligible duration compared with the dynamics under study, and have no relative timiig jitter. These conditions cannot always be fulfilled. A more complete description of the induced absorption change [5] must be used:

Here a(t) is the absorption at time t, IpornP(t) is the temporal profile of the pump pulse, and R(t) is the molecule response function of interest. The change of transmission is measured by the probe pulse:

and

3. Emerimental considerations n

where r is the time delay between pump and probe pulses. In all practical caees we follow AI as a funpion of r. The dependence on t is integrated by the slow optical detector.

This result shows that the measured signal is the impulse response R ( t ) of the chromophore, convoluted with the intensity correlation of the l a e r pulse G(t) .

In practical situations often only one laser is used. The output pulse is split in two parts, the weaker delayed part is used as probe, the stronger part is used as pump pulse.

In addition to the coupling of the intensities of the pulses, also the coupling of the fields must be taken into account. This will re@ in the so called coherent artifact. The effect of the pulses has to be expressed in terms of the change of the third order nonlinear polarization [6] . The effect of three fields on a medium possessing a finite third order nonlinear polarbability is expressed as:

Here X(=) represents the time dependent nonlinear susceptibility tensor, and E is a component of the field E inducing the third order polarization change in P(". The subscripts i , j ,k,l refer to the axes of the spatial coordinate system. The time dependent X(3) tensor is a generalization of a frequency domain concept. It has been shown that this generalization is not without complications [7]. These complications are caused by the explicit time ordering of the interactions in a time dependent description. In a frequency domain description the permutations of all interactions have to be taken into account. Strictly speaking, the frequency domain and time domain description of the nonlinear susceptibility are not connected by a Fourier transform. For the description of pump/probe spectroscopy however, the third order nonlinear polarization as given in Eq. (3.6) is sufficient. Expressions for g3) have been given [6] but these expressions are not amenable to computation because of the complexity of the large number of terms. The usual

approach is to isolate the relevant terms, without requiring knowledge of all of the resonances and damping parameters.

The first assumption is that the electric field E(r,t) is quasi monochromatic. The second assumption is that the field is incident in the form of a pulse that has a temporal profile that changes much more slowly than the inverse frequency of the field. This slowly varying envelope approximation (SVE) cleatly holds in the case of picosecond pulses. In femtosecond nonlinear spectroscopy a breakdown of the approximition is expected, a 6 femtosecond pulse [8] in the visible part of the spectrum only consists of 3 optical cycles.

The expression for the field is:

The time averaged intensity change of the probe now becomes:

In case of pump/probe spectroscopy the relevant relaxation is the population relaxation. The phase relaxation that describes the loss of coherence by the ensemble of absorbers is considered to be very fast. In this limit the expressiop for the bleaching can be simplified, just using one response function R(t) which describJes the population decay,

In the pump/probe geometry in some casea the same source is used to generate both of the required pulses. The incident electric fleld is treated as a combination of plane waves with wavevectors kmP and kF&.

Inserting a field of the form of Eq. (3.10) in the expression for the transmission change leads to:

J "d td t s~ ; ( t - r )~~( t ) 2 1 1 2 ( t - t s ) ~ I ( t 9 ) ~ l ( t s - ~ ) . (3.11)

The superscripts of the response function denote that a discrimination must be made concerning the time order of the interactions. denotes the response caused by an interaction of the form two times the pump field followed by two times the probe field. In this way the first part of Eq. (3.11) reproduces Eq. (3.4), and just gives the desired decay function convoluted with the intensity autocorrelation of the incident fields. The extra term is the result of an interaction where the pump and probe field coupled directly. It has the form of the field

3. Emrimental considerations 29

autocorrelation and is called the "coherent artifactn. It must be stressed that the coherent coupling of the field is not directly connected to dephasing of ,the optical oscillators. The source of the artifact is the absorption bleaching response R ( t ) , without dependence on the dephasing time. In experimental situations where the exciting laser pulses are not perfectly modelockad, the artifact appears as a spike at r=O.

Before turning to the experimental realization of pump/probe experiments two more problems must be addreeeed: the stochastic field response and the depolarization behavior. An exactly transform limited pulse is characterized by the exact correspondence of intensity and electric field autocorrelation. Whether or not it is possible to make transform limited pulses 4epends on a number of experimental parameters like laser loss and gain, and cavity stability. In most cases the limit of perfect pulses will be not reached, and fluctuations in the optical fields will be unavoidable, giving rise to different field and intensity autocorrelation functions. These autocorrelation functions can be recorded by noncollinear second harmonic generation (141. For example, in FQ. (3.2.c) a poorly modelocked pulse is shorn ("PNssian helmet"), together with two traces showing better correspondence of field and intensity autocorrelation traces.

probe delay bs)

Figure 3.24, b and c Noncollinear autocorrelation traces of laser pulse from a synchronously pumped dye laser. In a) the pulse is nearly perfectly modelocked, in b) the aUocmelation trace starts to exhibit wings, indicating the presence of extra frequency components, in the pulse spectrum and in c) the autocmlotirm consists of two easily discernible parts: a field and an intensity part.

The spike in Fig. (3.2.c) is given by terms containing ~E*(t)E(t-r) l~, and the background by terme containing ll(t)I(t-?)I. In recent publications the effect of extremely incoherent pulses was treated both theoretically and experimentally [9-121. The field from the l&er is treated as consisting of random field fluctuations as in a thermal source (stochastic fields). In m e techniques that study dephasing this offers the advantage of increased time resolution, as for example the stochastic accumulated echo (Sect. (3.3)). Since the pump/probe technique relies on the intensity correlation (the background in Fig. (3.2~)) transform

limited pulses seem to be optimal. Morita has shown that this is not always true. For random fields Eq. (3.11) must be averaged over the fluctuations and turns into:

where the brackets denote the averaging. The f i t two terms in Eq. (3.12) originate from the intensity term in Eq. (3.11), the last tern derive from the coherent artifact term in Eq. (3.11). The f i s t term is the background of the autocorrelation convoluted with the response and the third term is the coherent artifact. Next to these familiar tertns two new ones are introduced that are caused by the fluctuating character of the fields. The fourth term is the coherent contribution that lasts for the total pulse time, and does not contain information about material dynamics. The second term contains dynamical information: it is the field cross-correlation convoluted with the decay function. When lasers are used that are very incoherent (pulse width rp much larger than the field correlation time T,), and the relevant dynamics are much faster than the envelope, the second term leads to a decaying contribution to the coherent artifact. Since the correlation time T, of the pulses can be much shorter than the pulse time rp this can offer great advantages when studying fast dynamics. One important drawback however must be noted: the relative intensities of the coherent spike (term 3) and the decaying part (term 2) are determined by the ratio of the decay time of R and the correlation time of the fluctuating field 7,. To obtain reliable results the correlation time must be about a factor of three 'shorter than the decay time. This requires knowledge of the time scale of the dynamics before doing the experiment. Better applications of stochastic fields will be treated in Sect. (3.3).

When polarized laser light is used, the interpretation of pump/probe data is more complicated [13]. Exciting an ensemble of chromophores with a polarized laser pulse will induce an anisotropy in the absorption profile. The chromophores that have transition moments aligned parallel to the polarization of the field will have the greatest probability of getting excited. The ones that have perpendicular transition moments will not be excited at all. Robing this anisotropic excitation with polarized light will only give the desired decay response, as long as the directions of the transition moments do not change during the measuring period. In general the molecule and/or the electron distribution do change position. Studying the depolarization provides relevant information about the interaction of the chromophore and its environment. A method is needed to separate the depolarization response p ( t ) from the excited state decay response R(t).

3. Emrimental considerations 31

Consider an ensemble of molecules partially excited by a x-polarized pump pulse. The molecules are randomly oriented, but x-polarized light will be absorbed prefereptially by those molecules having their transition moments oriented in the %-direction. A non-random distribution of orientations of the excited molecules will be the result. The excited molecules will relax to the ground state according to R(t), and the distribution of excitation will change according to p(t). The decay response R(t) is of the form:

Here NU(:) is the timedependent excited state population projected on one of the Cartesian axes. Probing the sample with light polarized parallel and perpendicular to the pump implies detecting NI and N, respectively. R(t) can be recovered by adding them according to Eq. (3.13). Another possibility is to choose the relative angle between pump and probe in such a way that the terms are measured in a weight according to Eq. (3.13). This magic angle can be found when one realizes that the parallel excitation is proportional to the cosine aquared of the angle between polarization and transition vectors, whereas the perpendicular excitation is proportional to the sine squared. Now the probe must detect the contributions in the weight 1:2, this implies cos2(a)/sin2((ar = 112; or = 54.7O.

In addition to measuring the pure decay function function it is also possible to measure the pure orientation4 relaxation p(t),

Here the difference in parallel and perpendicular excited state population is normalized to the total excited state population. In the case where the transition moment is fixed in space, as in a low temperature glass, p(t) has the value 215 (because of isotropic symmetry the ratio Nn to N, is 3). If the transition moment can change its spatial direction p(t) decreases from 215 to 0. Even if the molecule is fixed in a matrix p(t) can change because of electronic redistribution over the molecule, or transfer of excitation to other molecules.

Fig. (3.1) shows that a pair of pulses, having pulse lengths that are short compared to the dynamical constants under study with an adjustable optical delay, is required to perform a pump/probe experiment. In order to produce pulses of less than a nanosecond, one relies on mode locking techniques (141. In a modelocked laser the balance of gain and loss is varied periodically, which lead to pulse formation. The variation of the gain is achieved either by an optical modulator in the cavity (active

modelocking) or a saturable absorber in the cavity (passive modelocking). In the work presented here the firat method is used. In a modelocked argon lseer ionized argon gae is the gain medium, and an acousto-optic modulator is the loss device. The modulator "opens" at a frequency which is exactly the inverse of the round trip time, v=c/2L, where c ie the speed of light in the medium and L is the length of the cavity. The match of the modulation frequency to the inverae round trip time enables repetitive amplification of a pulse after one or more round trips. The output of the laser consists of a continuous train of pulse! with a width of approximately 100 ps, and with a repetition rate of about 94.4 MHz. The length of the dye laser is matched to the length of the pump-laser in order to benefit once more from synchronous gain modulation by repetitive amplification. This synchronous pumping scheme ("sync pump dye lasern) can produce wavelength tunable p d e a shorter than one picosecond. In Table (3.1) the laser system is specified.

laser-type

Ar-ion Coherent Innova 99

dye laser '1-35% Coherent 590/599

The argon laser was modified to match the length imposed by the available modelocking crystal. A new output coupler assembly was made and inserted in the cavity, and the modelocking crystal holder waa mounted on the end plate.

Diffetent laser dyes have to be used to cover the whole wavelength range cited in Table (3.1). The optimal concentration of dye is determined by the absorption coafficient of the dye. The absorption in the dye jet is increased to !W%, by increasing the dye concentration while monitoring the tranemiasion of the pump light through the jet [15]. The output coupling percentage of the dye laaer is chosen as high as possible, still meeting minimum power requirements (stable operation is possible above 10 mW). High output coupling turns out to be the key parameter for good short pulse performance. A wide variety of partially transmitting optics was used: Ar- and Kr-laser mirrors, and many different dye laser mirrors. Some of these are planar, other ones are curved, but that does not cause optimization problems [16]. The output coupler is selected by a trial and error substitution procedure.

In Fig. (3.3) the complete experimental apparatus is shown. The output beam of the dye laser, consisting of a 94.4MI-h pulse train, is split in two beams by a beam splitter. The experiments on TPY-aggregates (Chapter 6) were done with two dye lasers at different wavelengths (50% of the pump beam was sent into another dye laser parallel to the one in Fig. (3.3)). One of the two beams passes a variable delay (MD) consisting

3. Emrimental considerations 33

of a retro-reflector on a cart, which can be moved on a rail. The precision of the translation is 1.5 /wn. Since light travels 0 . 3 m in 1 picosecond, moving a few crn generally is sufficient for scanning the time range of interest. Behind the sample the pump beam is blocked, and the probe transmission is monitored. This optical design allows for simultaneous detection of signal and pulse characteristics. KnowiZlg the particular pulse autocorrelation associated with an experiment reduces the uncertainty in the fitting procedure.

Figure 3.3 Picosecond pumplprobe and accumulated echo setup. The'output of the dye laser is split into pump and probe beanas, a d recombined in the sample ( s ) and a frequency doubling crystal (FD). The signal and the atctocorrelatiun are demodulated simultaneously, and the traces are stored in a microcomputer.

The low peak power, high repetition rate pulses induce only small (1@ to relqtive transmission changes. The quasi-continuous character of the beams however, allow for the use of sophisticated modulation techniques. In our pump/probe experiments the probe beam is modulated a t audio frequencies (100Hz to MM Hz) by a mechanical light chopper (PAR 191, CHOP in Fig. (3.3)). The pump beam is modulated at a radio frequency (20.060MHa), by a standing wave modulator (W, Intra-action SWM 102). Since the bleaching signal is proportional to the product of pump and probe intensities, modulated at 200 Hz and 20 MHz rapectively, the signal will be modulated at 20 MHz * U)O Hz.

A low noise silicon p-i-n diode (ECC SCD100) detects the change of the transmission. The electrical output is filtered and amplified, and fed into a radio (Drake R7) that handles the electrical signal the same way as AM antenna input. The output of the radio is a 200Hz audio signal, which can actually be heard from the speaker. The low frequency is demodulated by a lock-in amplifier (LIA, EGG PAR 128A), and the resulting DC signal is fed into the microcomputer. The photomultiplier' (PMT)

response is too slow to detect the 20MHz modulation. Actually, it is not the PMT itself but the load network of the PMT that limits the time response. The output is fed directly into another lock-in, without high frequency demodulation. The benefit of this complicated modulation scheme is the use of the gap in the noise spectrum in the frequency band from 3MHz to 30 MHz in modelocked dye laeers [17]. The minimum detectable signal modulation, d / Z , can be as low as 10" compared to 5x104 (3) in the apparatus that did not use high frequency modulation. In Sect. (3.4) more details will be given on the operational principles of the radio detection.

When the same laser Is ueed for the generation of both-pump and probe, an extra acousto-optic modulator (AOM, SORO) is used. This device launches a travelling wave into a crystal. Scattering a laser pulse from the travelling refractive index gating gives rise to a phase shift of the light. Since the driving frequency is not slaved to the modelocking frequency, the relative phase shift for consecutive p u l q is essentially random. Grating =,cumulation can no longer occur: the signal is "clean", not buried in large accumulated coherent artifacts. I refer to Sect. (3.3) for further details.

3.3 Photon echoes

3.3.1 Stochastic accumulated echoes

In the treatment of pump/probe spectroscopy in the previous section, it was stated that the absorbers were assumed to have no phase memory (or equivalently T,=O). When this condition does not hold, other third order nonlinear effects can occur. The particular kind of nonlinear phenomenon used most frequently for the work presented in this thesis is the photon echo. The use of photon echoes for the determination of dephasing times has been fruitful (18-201. Especially the accumulated photon echo has proved to be a relatively simple and reliable technique for the study of the dephasing of chromophores in various solid environments [3].

Photon echo spectroscopy gives information about the homogeneous optical lineshape of chromophores. For chromophores in solid environments the observed linewidth can be separated into three components. The first contribution can be assigned to the lifetime of the excited state (T,), which may be converted into a linewidth via the uncertainty relation L EAT>^&. The second contribution is caused by the dephasing (Tz) of the ensemble of absorbera. These first two terms generally lead to Lorentzian contributions to the total linewidth. The last term is the inhomogeneity. It represents the spread of the transition energies of the absorbers caused by the different local environments for the different absorbers. Since inhomogeneity is caused by statistical spread of single molecule energies, the inhomogeneous contribution is generally considered to lead to a Gaussian distribution of the transition frequencies.

When two pulses in the pump/probe geometry (Fig. (3.1)) are combined with zero time delay, interference of the fields leads to a gating. Both fields are idetltical except for a wavevector difference of k,,-k*, which is exactly the difference that characterizes the intensity gatmg.

3. Emerimental considerations 35

A sample placed in this spatial grating wil l be excited at the positions of the maxima, and coneequently an absorption grating in the sample will be formed. When the two fielde are given a relative time delay, the grating formation will depend on the value of the dephasimg the. Very rapid dephasing (T2aro where r, is the electric field correlation time) will lead to a reapom which is limited by the field correlation time, and is related to the coherent artifact d k u s d in Sect. (3.2). In the opposite limit of no dephasing the situation is more complex. After application of the firat field the individual absorbers will oscillate collectively. Because of the fact that the oscillatom have different inhomogeneous offset frequenciee A, inhomogenema dephaaing wi l l occur. The interaction of the second field incident with the oscillators wi l l now lead to formation of a grating which is dependent on both the wavevector difference and the inhomogeneoua offset [I]:

Here p is the excitation parameter, proportional to the population differemce of the ground and excited statea after the application of the two excitation fields. Ihe odllatory term both contains a frequency grating term (AT), and a spatial gratlng term (ah). Analogous to light 6cattering from a spatial grating, scattering can also occur from the frequency grating, giving rise to time delayed scattering: the photon echo.

It ie important to realize that the grating formation depend on the correlation of the fields and not on the correlation of the intensities f21,22]. Interference of optical fields occurs within the coherence time of the fields. Some yeam ago it was shown independently by Hartmann [ll] and Morita [lo] that photon echoes can be generated with incoherent sources. They were the first to use the correlation time of exciting source, and their work formed the basm for other v&te of correlation --PY.

Accumulated photon echoes are a result of the formation of a population grating deecribed by Eq. (3.15). The salient feature of the accumulated echo is the build-up of the gating by many pulse pairs. The build-up is posaible as long as the decay of the grating is slower than the repefition time of the pulses. In Fig. (3.4) the sequence of pulses is shown. The repetition rate is determined by the modelocking frequency of the laser (94.4 MHz, 10.2 na pulse separation). Whem the ground state recovery is faster than Ions, as in most dye molecules, no accumulation can take place. In a large number of different molecules however, intersystem crossing to a triplet sbte can take place. The population grating of the excited state decays to some extent (determined by the intersystem crowing yield) into that triplet state. Only the grating in the ground state remaine, but that is sufficient to generate an echo s i d . "

From the accumulated grating, echoes are generated by the pump pulse of the next cycle of the laser, as indicated in Fig. (3.4). The echo generated has the same wavevector as the probe pulse and is exactly time coincident with that probe pulse. Now as in the case of pump/probe experiments, the polarization interacts with the field, leading to an

intensity change as in Eq. (3.8). This process was named heterodyne beating, after the use of that term in radio technology. However, heterodyne beating refers to mixing a signal at frequency w, with a carrier at frequency w2 and consequently detectin# the beat frequency w,fwz. In the sense of creating an interference of the third order nonlinear polarization P(=) at frequency w with the probe field 8 also at w, it is better to use the term homodyne detection.

t

Figure 3.4 The sce~nuCbteQ eeho sypmee is a continuous repetition of the pwnplprolic sqtkmm Wh& the d c p b i n g ' t i n e T , is larger than the pulse length mi' a long heti bottkm& wrfets, an accwnulated photon echo is generated. The umwvekbrs of the p&ts must be matched, which kads to two distinguishahk echo dinctiqw. The downward dinetion corresponds to the side scattered echo (p ropor tW to P) hnd the upward darectfmr mtspards tq the homqdyne echo (q PxE).

, '

The accumulatidn of the grating is governed by the correlation of the optical fields, so the time resolution in the measurement is determined by the field corr&lation rime r,. In oner nonlinear optical techniques that depend -on the fieid correlation such 'as self-diffraction or CARS, interfering eignals exist that are caused by contributions from the intensity correlation. In the case of acciunulated echoes the long period between grating generating pulse pairs Lesds to a decay of all populatiom atid coherencee, and the only remaining contribution is the gating that was generated during the t h e interval 7. The accumulated echo is lane off the few casea that allow for the use of corr'elation spectrdmpy without introducing new ambiguities in the signal characteristics.

The experiment is performed according exactly to the scheme which was outlined in Sect. (3.2.2) for pumpJprobe spectroecopy. The echo has exactly the same wavevector as the probe pulse, and the signal is detected as a change in the probe transmission. The discrimination between pump/probe and echo aignala is made on the basis of the response to incoherent excitation; in that case the pumpfprobe signal grows with the intensity correlation (the broad background in Fig. (3.2c)), whereas the echo grows with the field correlation (the spike in Fig. (3.2~)).

3.3.2 Acousto-Optic Modulator effects

In Sect. (3'2) I stated that a travelling wave modulator scrambles the

3. Experimental considerations 37

phase of light fields, and ia used to discriminate accumulated from single pulse events. I will show why a standing wave modulator 'can be used for modulation of accumulated photon echo signals and a travelling wave modulator cannot.

An acousto-optic modulator is a piece of glass or quartz brought into oscillation by a transducer. A sinusodal voltage is applied to this transducer. Longitudinal compression waves are sent into the material, where they form a grating in the index of refraction. An light wave that is incident on the grating will diffract. In Fig. (3.5) the situation is depicted; only the maxima of the grating are indicated.

Figure 3.5 A light wave is W e n t at a Bragg angk BB Behoeen the arrival of the pulses the grating moues a distance ad, UIis shift is directly converted ink, a change of the relative phase difference #,, by an amount adlA.

Diffraction only occurs at a specific angle, the Bragg angle, which is defined by:

In Eq. (3.16) Lt is the wavelength of the index grating and is given by the speed of m d divided by the driving frequency. The reflections from plane6 that are one acoustic wavelength apart have a phase difference of 2r. If the maxima of the index grating shift by a distance ad, the phase of the light will shift by an amount &/A. A travelling acoustic wave thus gives rise to a time dependent phase shift of the light [23]:

An alternative way of stating this is that the frequency of the travelling wave is added to the optical frequency, which means that the optical frequency of the diffracted light ,is shifted by an amount v-. For a standing wave modulator no tihe dependent phase shift occurs since the maxima of a standing wave are 'fixed a t a position in -

space. The time dependent phase shifting of the light has consequences for

the purnp/probe spectrometer of Fig. (3.3). The picosecond pulse is split, so the probe is an image of the pump. The pump pulse is diffracted in the travelling wave modulator TWM. The pulse lasts only for picoseconds, so the travelling grating is "frozen" at a particular PI, and the pump pulse

is phaae-shifted by that amount. Focusing the pump and probe in the sample implies that the experiment is done with a relative phase difference A@. For a pump/probe experiment this phase difference poses no problem; the probe can be delayed relative to the pump by many picoseconds, or thousands of optical cycles. A phase shift of n only implies an extra delay of 1 femtosecond. A similar argument shows that the two pulse echo is also not affected.

The accumulated echo experiment however, is seriouely disturbed by this pluw shifting. For accumulation to oc"c, the grating term of Eq. (3.15) must be comtant during the preparation period. That is, the relative phases of the pump and probe must be constant during the full accumulation period. However, we saw that the phase of the pump pulse is modulated by the driving frequency of the travelling wave modulator. For example the pulses have a repetition frequency of 94.4 MHz and the modulator is driven at 200MHz. This implies a phase shift between consecutive pump pulses of (200/94)x% is 4.2373~. Since this clearly is not a multiple of %, the accumulation efficiency will be strongly reduced.

The inhibition of accumulation by a travelling wave modulator was discovered by Heeselink [I]. The increase in signal sensitivity by application of high frequency modulation allows for the parallel detection of single pulse effects and accumulated effects, without the need for amplifying the laser pulses. The inhibition of accumulation by a travelling wave modulator can be used for the clear discrimination of the different effects.

3.4 High frequency modulated detection

The main improvement of the accumulated echo setup relative the old situation [3], waa the application of high frequency modulation techniques [24-271. I will d k m why high frequency modulation ia so helpful, and I will explain a few technological radio tricks. For a thorough dbcwion of the modulation and detection scheme I refer to the work of van Exter [28]

Accumulated echo spectroscopy is a nonlinear technique with a signal strength that is proportional to the square of the applied intensities (S= 12). When the intensities fluctuate by a certain fraction, the signal strength will fluctuate approximately twice as much (aS /S=2d/ I ) . This fact imposes the need for atable lasers and sensitive detection. The signal is measured on a large background of the probe intensity, so lock-in detection is the method of choice. Detecting with a lock-in amplifier is done by modulating the signal component at a frequency vd and not the background, the small (AC) signal component is amplified by

'.- the lock-in. Narrow band filtering around ud assures that only the noise in the frequency band around v d is detected along with the detected signal.

The simplest way is to modulate the pump beam at v, and the cross modulation of the probe intensity ia detected. The major disadvantage of this approach is that any scattered light from the pump beam is indistinguishable from the signal. Modulating the probe beam aa well, at

3. Exwrimental considerations 39

a different frequency v,, offem the opportunity to detect the signal term at frequencies vlfvz. The scattered light from the pump Jxam is modulated at ul and can be filtered out by the lock-in amplifier. The double modulation scheme can easily be realized by double light choppers which include all necessary frequency mixing electronics. Double modulation allows for stray-light free detection; the noise level is limited by the laser noise in the bandwidth around the signal modulation frequency v,*v,.

The only choice that has to be made are the actual modulation frequencies. It is clear that the lowest possible noise in the signal is found at a frequency where the laser noise is at a minimum. Baer and Smith [17] measured the noise spectrum of a modelocked picosecond dye laser pumped by an Ar-ion laser, and found that there are many acoustic disturbances at low frequencies (Hz to Hz). The noise intensity gradually decreases at higher frequencies and reaches the so called shot-noise limit at 3MHz. This shot-noise limit is reached when the noise is the result of the quantum statistics of the light: the fluctuation in the number of photons is the root of the total number of photons. The noise level stays low until 40 MHz, being the modelocking frequency of the dye laser. The conclusion is that the best choice is to modulate the signal at a frequency between 3 MHz and 30 MHz.

A number of schemes have been proposed to realize the double high frequency modulation [24-271. The problem was the detection of small signals modulated at MHz frequencies. A simple lock-in amplifier does not work above 100 kHz, and a high frequency lock-in is expensive. The use of a commercial long distance (DX) radio overcomes this problem [28]. The first design used single dde band demodulation. This demodulation implies that the radio is tuned to the carrier frequency (20MHz) and demodulates the audio frequency (200Hz). In this design, the internal oscillator has to be disconnected and an external carrier has to be supplied. A more simple way is to use amplitude demodulation (AM detection). In the AM mode the signal input is split in two parts, one of which is amplified until saturation. The saturated signal is used as a carrier wave, so frequency locking is always guaranteed.

The effectiveness of the radio detection approach is illustrated by the fact that the intensity stabilizer used previously in the optical apparatus could be discarded. In the old modulation scheme with just one light chopper, the stabilizer was essential to detect signals of about one part in thousand relative to the probe intensity. In the n w high frequency modulation scheme detection of signal strength of one part to ten million is achievable. One must realize that since the signal intensity is the product of pump and probe intensities the probe noise at 2QOHz will still be present in the signal. However, the noise must be evaluated relative to the signal strength: the signal is as stable as the laser. In the old modulation scheme, where the noise of the whole probe intensity was detected. The noise in the large nonmoduleted background already exceeded the signal at the quoted signal strength of one part in thousand.

In Fig. (3.6) the detection electronics have been drawn schematically. The photodiode is part of a resonance loop, in order to increase the load of the diode. A diode is a current source, so the load has to be as large

.as possible without limiting the frequency response. The 50 ohm input impedance of the amplifier is increased to 600ohm, so a twelve fold increase in signal is achieved relative to direct input in the amplifier. A high quality preamplifier is used to match signal levels to the radio sensitivity. A emall amount of carrier wave is added to linearize the response of the radio. The radio demodulates the 20 MHz carrier wave and the resulting 200 Hz signal is detected by the lock-in amplifier.

Figdre 3.6 Schematic representation of the electronics necessary to detect the high frequency modulated signal. The photocurrent generated in the photodiode is fed through a resonance loop consisting of a coil, a capacitor and the input impedance of the amplifier [28]. A small portion of the modulator driving frequency is fed in a ftytuency doubler ( F D ) that provides the undulated carrier necessary for the denwdulglion by the radio.

In the case of pump/probe experiments the improvement is obvious, but a few remarks concerning the detection of accumulated echo signals must be made. A serious complication in the detection of accumulated echoea is the incoherent accumulated bleaching caused by bottleneck filling, leading to a bleaching not dependent on the time delay between the pulses. This effect dways accompanies the accumulation [I] and gives rise to a constant background in the signal detection. Molenkamp [3] proposed to use an intricate four beam design to separate the background from the signal. He reasoned that the extra complication of the optical design would be compensated by increased signal to noise. When I installed the high frequency modulation it turned out that the extra beams were obsolete. The reason for this fact is the slow dynamics of the bottleneck, which is not modulated at 20MHz, because the dynamics occurs at millisecond to microsecond time scales. All detection electronics are only sensitive at 20 MHz so no bottleneck effect is observed.

To summarize the advantages of high frequency modulated detection: 1) improved sensitivity for pump/probe spectroscopy,

3. kerimental considerations

2) laser intensity stabilization is rendered obsolete, 3) the saturated background of the accumulated echo is not detected.

3.6 Time correlated single photon counting (TCSPC)

The radiative lifetime of allowed transitions of dye molecules is several nanoseconds; for example, Rhodamine-6G has a decay time of 3ns [13]. Rhodamine-6G has a high quantum yield for &ion so the fluorescence decay is almost the same as the radiative lifetime. For other dye molecules with comparable radiative lifetimes the quantum yield is smaller than 1, and consequently the fluorescence lifetime is shorter than the radiative lifetime,

where #I is the quantum yield for emission. Aggregate excitations show fluorescence lifetimes considerably shorter than the monomer radiative lifetimes, because of radiative coupling (Sect. (2.2)). In order to obtain reliable results on radiative dynamics a time resolved experiment must be performed.

Three ways to achieve the resolution needed are: direct detection, fluorescence upconversion [29-311 , and photon counting [4]. Direct detection of fluorescence implies monitoring the response of a fast photodiode or a streak camera which is illuminated by the fluorescence. The resolution ia limited by the speed of the detector and can be less than 5 ps. Fluorescence upconversion uses a part of the exciting laser pulse to gate the emission. The gating pulse is delayed relative to the exciting pulse. The emission and the delayed gating pulse are focused in a nonlinear crystal, and the upconverted fluorescence is 'detected. Scanning the delay gives the desired fluorescence curve. The !resolution is only limited by the pulse length of the exciting laser, so even femtosecond resolution is possible [31]. I used the third method: time resolved photon counting. The time interval between the exciting pulse and the emitted photon/ is measured very accurately (within 10 picoseconds). Repeating this "single photon experimentv many times gives the statistical distribution of arrival times. This distribution is just the decay function.

The advantage of the TCSPC technique is the use of very low light levels, less than one emitted photon per exciting pulse is sufficient. The signal to noise ratio is only limited by the statistics of the photons, and longer photon collection times give better signal to noise. The other two detection techniques need many more emitted photons, on the order of lo0 (0.1 nJ in the visible range of the spectrum). Strong exciting pulses are needed. The signal to noise ratio ia rather poor, since pulse to pulse intensity fluctuations cannot be avoided. In one case though the upconversion technique is superior; when the decay is shorter than 10 ps upconversion is the only reliable technique.

The recent availability of ultrafast photomultipliers has extended the possibilities of TCSPC. In these photomultipliers the electron avalanche occurs in short channels, which are only microns wide. The resulting

electron pulse is much shorter than that of the conventional design, because of the smaller spread in transit times. The risetime of the used Hamamatsu microchannel plate (Me) is 190 ps. With the help of a constant fraction discriminator the triggering can be precise to 5 0 p . The apparatus is shown in Fig. (3.7).

Figure 3.7 Basic time correlated single photon counting setup [34,35]. The dye laser is equipped with a cavity dwnper that lowers the repetition rate of the pulses. The pulse is split into a trigger puke for the diode ( P D ) , and an exciting pulse that is focused in the sample. A monochromator removes unwrued resonant scattering, and the photons are detected by a microchannel plate (MCP). The time difference of the electronic pulses (indiccrted by dashed lines) is measured by the combincrtion of a time to amplitude converter (TAC) and a multichannel analyzer (MCA).

The laser system consists of a modelocked argon-ion laser which pumps a synchronously pumped dye W r . The repetition frequency of the dye laser is lowered by a Spectra Physics 452 cavity dumper. Thia device allows for the build-up of high intra cavity power levels. Every N-th pulse that passes is deflected out of the cavity, where N is an integer from the series 20, 100, 200, 1000, et cetera. The lowering of the laser pulse repetition rate is necessary in order to prevent pile-up effects in the electronics. The output of the laser is split into a trigger pulse directed to a fa& photodiode (Telefunken BPW28), and an exciting pulse directed to the sample (S). The fluorescent emission is collected either under a 90 degree angle as shown, or along with the exciting beam. A color filter absorbs the scattered laser light. The emission is directed through a grating monochromator (Jarrell-Ash 0.5m), that serves to filter out the unwanted spectral area. A grating monochromator should have low dispersion in order to avoid unwanted transit time spread [32].

The fluorescence is diffused a t the output slit by a roughened glass plate and hits the photocathode of the M C P (Hamamatsu R1564U-01 [34]).

3. Experimental considerations 43

The photocathode is sensitive at wavelengths from 350 nm to 850 m. The anode pulse lasts for half a nanosecond and has a peak voltage of 10mV. The constant fraction discriminator needs a pulse of a least 100 mV, so amplification is needed. Two cascaded broad band amplifiers are used (Mini-Circuits ZFL-2000). The amplification bandwidth is lOMHz to 2 GHz in order not to loose any Fourier components of the signal. These Fourier components stretch this range because of the low repetition frequency of the photons on one hand, and the steep flanks of the pulses on the other hand. The amplified pulse is fed into one of the units of the quadruple constant fraction discriminator (Tennelec 455). The discriminator is needed to circumvent triggering problems associated with pulse height variations. The photodiode pulse is fed into another unit of the discriminator. The time difference between the two output pulses of the discriminator now contains the relevant information about the arrival time of the fluorescent photon after the excitation by the laser pulse.

Depending on the emission yield one counts either forward or reverse. Forward counting implies using the diode pulse as a start trigger, reverse implies starting on the emitted photon. The last way offers a higher collection efficiency at the cost of a reduction of the signal to noise ratio. The cavity dumper can be operated now at 4.7 MHz instead of 94 kHz in the forward mode. The two limits are set by the input characteristics of the discriminator and the time to amplitude converter.

time Ips)

Figure 3.8 Instrument response function with a width of 75 ps, measured from scattered laser light. The trigge~ pulses (94Mz) preceded the photon pulses ("fonwrd counting"). The width is redwed to 45ps when a prism monochromator is used instead of a grating monochromator.

The time difference is accurately converted into a pulse height by a time to amplitude converter (Ortec 457 TAC). The pulse height is measured by an analog to digital converter. Coupled to the TAC is a buffer that increments the proper memory position (Ortec 917 multi channel buffer). The electronics can work without the computer, which can even be switched off during the collection time. The advantage of the stand alone multi channel analyzer over the computer plug-in boards is evident; the

apparatus is more mobile, and computer failure does not destroy data. The main task of the computer is the graphic representation of the data, provided in scaled form by the micro-processor of the buffer.

The result of this elaborate scheme is shown in Fig. (3.8). Here the so called instrument response is shown. This is the response of the detection system to a laser pulse that has a width of a 5ps. If fluorescence is detected, this response is convolved with the decay function. The instrument response function shows a tail caused by imperfect operation of the cavity dumper. The laser pulses vary in intensity, md this variation is detected by the fast photodiode. The width of the instrument response is lees than 50ps [35] without monochromator. The experiments quoted in this thesis were performed with the grating monochromator, where the reaponse lengthens to 70 ps. The use of a prism monochromatmr and further optimization [36], recently improved the width of the system reeponse to about 45ps. The resolution of decay parameters can be a factor of five better because the noise in the data is only statistical. Fast decay8 can be fitted in a convolute and cbmpare procedure, provided the signal to noise ratio is high enough.

3.6 Computer control and analysis

Experimental research is no longer done without support from automated equipment. Large amounts of data must be acquired, represented and fitted. The ideal situation would be that representation and fitting can be performed during data acquisition, and no time is lost on trivial data handling.

Great progress in the achievements of personal computers was made in the last decade. The APPLEXI computer that was operating the set-up in the past [3] has been replaced by a more powerful IBM PC/AT compatible computer. A slight change has been made in the way the computer is connected to the setup. No home built interfaces are used inside the computer anymore, as it turned out that these interfaces were the main source of problems in the APPLGII. This choice was made easy by the availability of cheap standard interface cards. The necessary connecting electronics are mounted in a separate box. In Fig. (3.9) basic scheme is shown.

The input/output card (110) handles all digital information, such as pulses to the delay stage and inputs from a digital counter. The -analog to digital converter (ADC) card reads the output of the lock-in amplifiers. The serial interface finally (RS232), connects to modern measuring devices that have some form of microprocessor control themselves, such as the multichannel buffer.

New software to use the possibilities offered by the large increase in computing power was written in our group [37]. The main part of the software consists of a new operating system shell, that is completely managed by pull down menus. Within this environment relatively small subroutines perform the specific tasks associated with a particular experiment [37].

Three programs must be mentioned: STAP, MCA and RAMAN. The first program controls pump/probe and accumulated echo experiments. It moves

3. Emerirnental considerations 45

the mechanical delay, and it stores the values from the lock-in amplifiers. The operation of the stepper motor is well developed. The backlash is compensated, and acceleration and speed can be adjusted. The collected signal traces together with experimental information can be stored on disc in the form of text files. The MCA program emulates a standard multi channel analyzer, and includes features like automatic scaling and automatic timing. Commercially available MCA programs are mostly specialized on nuclear experiments, instead of time resolved fluorescence. This fact makes the program better than commercial ones for this application. The RAMAN program scans a monochromator lineatly either in wavelength or wavenumber. At the same time it reads the counter that monitors the number of Raman (or fluorescent) photons. These three programs allow for total digital storage of all data. However, in practice X-Y chart recorders were frequently used in steady state emission and absorption spectroscopy.

Figure 3.9 Connections of the personal computer to the peripherals. The serial interface i s connected directly to the measurement equipment, whereas some extra electronics i s necessary for the ADC and 110 cards.

An attached printer prints the experimental traces and relevant settings on a sheet of paper, so the data are directly accessible. It is also possible to process the traces to make them of presentation quality (vide infra).

Fitting data both has been done both on a VAX 11/750 computer, which is connected to the PC via a serial link, and on the PC itself. Because the echo decays of PIC aggregates turned out to be nonexponential, the standard linear least squares fitting procedures did not work [38]. The fluorescence decay data from the photon counting must be analyzed by reconvolution, which is not possible in "normal" least squares fitting. This limitation was overcome by implementing a nonlinear least squares fitting method using the Marqhart-Levenberg algorithm [39,40] . Arbitrary functions can be used in this iterative method. Reconvolution fitting of (multi) exponential as opposed to non-exponential decays was performed by the method outlined by Grinvald [41]. The algorithm is very efficient: when one starts with reasonable starting values four or five iterations generally suffice.

3.7 Absorption and emission spectroscopy

Relevant information about aggregates can be obtained from absorption and emission spectra. The characterization of samples prior to doing time resolved experiments was done by steady state spectroscopy. Some general methods can be indicated.

The absorption spectra were recorded mostly using light from a tungsten filament lamp of 150 W. A few milliwatts of light intensity are sufficient for any absorption spectrum, so strong attenuation is necessary. Fluorescence excitation was mostly done by laser light, of either 514 nm argon-ion wavelength, or a tunable wavelength from a dye laser. For excitation spectra the light of the tungsten lamp was predispersed in a scanning monochromator, The resulting monochromatic light is used for fluorescence excitation.

After collimation the fluorescent emission is then focused on the entrance slit of a Spex1704 314 m monochromator. The resolution of the monochromator ranges from 0.5 cm-I to 15 cm-l, depending on the slit widths. The detectors used were photomultiplier tubes and photodiodes. For low light levels photomultipliers are the detectors of choice, the actual type of photomultiplier depends on the particular application. The red sensitive, low dark current tubes were only used in critical circumstances. More simple tubes were used for routine measurements. The photocurrent from the photomultiplier was converted into a voltage and consequently amplified. The amplifier was either a home-built stable DC amplifier, or a PAR128A lock-in with comparable signal-to-noise c~acter is t ics . The photodiode used to detect transmitted light was the silicon p-i-n diode of the Spectra-Physics power meter. The output of the amplifier was fed into a Hewlett-Packard chart recorder, and recorded on paper.

In a few cases integrated equipment was used. The Cary W-VIS spectrometer was adapted to house a small cryostat, so some low temperature measurements were possible. The Spectroscopy I n s t r ~ e n t s / Princeton Instruments Optical multichannel analyzer (OMA) was used on some occasions. The apparatus is ideal from a technological viewpoint. However, a bad integration of the detector with the necessary computer software limited its use during my experiments.

5.8 Sample preparation and handling

The aggregates that were studied formed from saturated monomer solutions. The equilibrium was shifted towards aggregation, by lowering the temperature, or by evaporating the solvent, or by increasing the concentration of anions. Most experiments were done at low temperatures where the systems are in the solid phase. Freezing the solutions is necessary in order to prevent any changes of the aggregates. In this section I will discuss some details of the kinetics of aggregate formation, preparation of solutions, and cryogenic sample handling.

Ever since Scheibe and Jelly published their separate papers [42,43] describing the formation of a narrow aggregate band in aquous PIC solutions, researchers have been interested in the process of the

3. Emerimental considerations 47

aggregation. For the PIC case Scheibe himself was involved in settling most open questions, almost 40 years after his first paper was published [44]. The main elements in the description were: precipitation-like formation, a minimum stable aggregate size of seven units, and attachment of counterions to the aggregate. Rom osmometry and spectrometry it was concluded that aggregates behave like a heterogeneous equilibrium as that of any salt, with a eolubility product constant [Pict]x[X-] in the order of lo4 a t room temperature (X- can be Cl-, Br-, I-, F-, Sa- , 003-). The enthalpy of solvation for PIC-chloride aggregates was determined to be M kJ/mol. A nucleation step in the formation was identified; seven units are necessary to form a stable aggregate. One can imagine that the positively charged PIC cations show repulsive interactions. From oarnometry it was concluded that most anions are bound to the aggregate. All of the observations show that the PIC aggregates are a stable phase between the solvated and the precipitated salt. Other dye molecules that form aggregates sometimes precipitate after standing for some time.

PIC solutions for low temperature measurements were prepared from ethylene glycol (Merck p.a.) and triply distilled water, mixed in a 1:l ratio. This mixture was chosen for two reasons, the first being the extremely narrow J-bands that form a t low temperature (451, ryld the second that the mixture has good glass forming properties. The concentrations were IX~O-~M for PIC-Cl, 5~10-~M for PIGBr, and 2x10JM for PIGI. In the room temperature solutions no aggregate formation occurred, showing that the solubility products are much higher than for aqueous solutions. Upon cooling the solutions to 77K aggregation occurred. The extinctions reach values of over 10SM-lcm-l, so short path lengths of about 1 0 p have to be used in order to keep the optical density below 1. Putting a small drop of solution between thin microscope glass plates gives rise to appropriate optical densities. The glass plates are mounted on a copper sample holder that is inserted in a conduction type cryostat that is at liquid nitrogen temperature (77 K).

The solvation product can be used to force aggregation by adding extra salt to the solutions. This scheme was used to make room temperature photon counting measurements on PIC water solutions. A mixture of 3x10-'M PIC-CI and 0.2M KCI in water was gently heated to 50°C in order to get a monomer solution. The mixture was subsequently cooled to 20°C. A normal optical cuvette with a path length of 0.2 mm could now be used, without obtaining optical densities that were too high.

The experiments on TPY aggregates were done on samples of the dye in a polycarbonate matrix. The polycarbonate (PC) is rigid at room temperature, which facilitates handling. Solutions were made of 8 percent PC and 2.3 percent TF'Y-perchlorate (both by weight) in dimethylformamide. The solution was filtered carefully through a cellulose filter with pores of 0.2 jun. A drop of the solution was applied on a clean glass plate, and the glass plate was spun at a final speed of about 700 revolutions per minute for 45seconds in a spincoat apparatus. The resulting polymer films varied in thickness from 1 to 4 p, and had workable optical densities ranging from 0.1 to 1.0, depending on the precise procedures [46]. The films are blue and show the same spectrum as a dilute solution, implying that the dye is not aggregated. Aggregation is induced by exposing the films to saturated dichloromethane vapor. The polymer matrix

absorbs this vapor and the dye can associate, possibly enhanced by polymer crystallization which forces the dye molecules to move. Within thirty seconds the color of the film changes from blue to green. The f i s are dried and stored under vacuum in the dark until use. Polycarbonate is the only polymer in which TPY shows this strong aggregation, other polymers that can be spin coated like polymethylmethacrylate (PMMA) and poly(viny1 alcohol) (WA) showed no aggregation. With the spincoat procedure also PIC aggregate films were made, P I C 4 in PVA, PIGBr and PIG1 in polycarbonate [47].

Samples of the thiacyanine dye (TD) aggregate8 were prepared aceording to a procedure similar to the one used with PIC. Solutions of 1 ~ 1 0 - ~ M TD in waterfethylene glycol 1:l were made, KC1 was added to a concentration of 0.1 M. At room temperature a color change from deep purple to bluish purple could be observed upon adding the salt. A drop was put between glass plates that were mounted on a sample holder.

The cooling process in the cryostat ia rather critical. Immersing the solution samples of PIC and TD in liquid nitrogen does not result in aggregate formation, because cooling is too fast. The samples should be cooled to about -30°C for aggregation to take place, and after that cooled rapidly to below the solidification temperature at around -60°C. Putting samples in a conduction cryostat that is held a t 80 to 100 K is sufficient to obtain the mentioned cooling conditions. In other cryostats procedures have to be adapted to meet aggregation and glass forming requirements.

Standard procedures are used to fill the cryostat with liquid helium in order to cool it down from 77 K to 1.5K in about 45 minutes. The temperature is increased from 1.5 to 4.2 K by varying the helium pressure in the secondary helium .reservoir. For temperatures above 4.2K the sample can be heated by a resistor that is mounted on the sample holder. The thermal stability of the sample during a measurement is at its best when the whole cryostat slowly heats up without using any extra heating.

A small liquid nitrogen cryostat was used for some measurements inside the Cary W/VIS absorption spectrometer, and also for some time resolved fluorescence experiments.

PIGbromide was obtained from Exciton, PIC-iodide was obtained from Kodak, and PIC-chloride was prepared from the bromide salt by ion exchange over a column. TF'Y in the form of the perchlorate and tetrafluoroborate salt was a gift of OcC Nederland. The thiacyanine dye was donated by Polaroid USA.

References

1. W.H. Hesselink, Thesis University of Groningen, The Netherlands (1980).

2. W.H. Hesselink and D.A. Wiersma, Phys. Rev. Lett. 43, 1991 (1979). 3. L.W. Molenkamp, Thesis University of Groningen, The Netherlands

(1985). 4. W.R. Ware, in 'Time-Resolved Fluorescence Spectroscopy in

Biochemistry and Biologyn, eds. R.B. Cundall and R.E. Dale (Plenum Press, New York, 1983).

3. Ex~erimental considerations 49

5. Z. Vardeny and J.Tauc, Opt. Comm. 39, 396 (1981). 6. Y.R. Shen, "The Principles of Nonlinear Opticsn (Wiley, New York,

1984) 7. Y.J. Yan and S. Mukamel, J. Chem. Phys. 89, 5160 (1988), R. Boyd and

S. Mukamel, Phys. Rev. A 29, 1973 (1984). 8. R.L. Fork, C.H. Brito-Cruz, P.C. Becker and C.V. Shank, Opt. Lett.

12, 483 (1987). 9. A. Asaka, M. Nakatsuka, M. Fujiwara and M. Matsuoka, Phys. Rev. A 29,

2286 (1982). 10. N. Morita and T. Yajima, Phys, Rev. A SO, 2525 (1984). 11. R. Beach and S.R. Hartmann, Phys. Rev. Lett. 63, 663 (1984). 12. M. Tomita and M. Matsuoka, J. Opt. Soc. Am. B 3, 560 (1986). 13. see: C.R. Fleming, "Chemical Applications of Ultrafast Spectroscopyn

(Oxford University Press/ Clarendon Ress, New York, 1986). 14. see: A.E. Siegman, "Lasersn (University Science Books, Mill Valley

USA, 1986). 15. Coherent Inc. "Dye laeer fact sheet". 16. J.J. Korperhoek, Research report, University of Groningen, (1990),

J.J. Korpershoek, E.W. Castner and D.A. Wiersma, Opt. Comm. 78, 90 (1990).

17. T.M. Bear and D.D. Smith. in "Ultrafast Phenomena IV", pg 96 (Springer, Berlin, 1984).

18. W.H. Hesselink and D.A. Wiersma, in "Modern Problems in Condensed Mattern, Vol 4, pg 249, Eds V.M. Agranovich and A.A. Marudin (North-Holland, Amsterdam, 1983).

19. L.W. Molenkamp and D.A. Wiersma, J. Chem. Phys. 80, 3054, (1984). 20. W.H. Hesselii and D.A. Wiersma, J. Chem. Phys. 76, 4192 (1981). 21. J.C. Fujirnoto and T.Yee, ID33 J. Quantum Electr. 22, 1215 (1986). 22. V.L. Vinetskii, N.V. Kukharev, S.G. Odulov and M.S. Soskin, Sov.

Phys. Usp. 22, 742 (1979). 23. M.J. Ehrlich, L.C. Phillips and J.W. Wagner, Rev. Sci. Instrum. 69,

2390 (1988). 24. J.P. Heritage, Appl. Phys. Lett. 34, 470 (1979). 25. Z.D. Popovic and E.R. Menzel, Chem. Phys. lett. 46, 537 (1977). 26. P. Bado, S.B. Wilson and K.R. Wilson, Rev. Sci. Instrum. 53, 706

(1982). 27. L. Andor, A. Liirincz, J. Siemion, D.D. Smith and S.A. Rice, Rev. Sci.

Instrum. 65, 64 (1984). 28. M. van Exter and A. Lagendijk, Rev. Sci. Instrum. 67, 390 (1986). 29. C.R. Fleming, S.H. Courtney and M.W. Balk, J. Stat. Phys. 42, 83

(1976). 30. E.W. Castner Jr., B. Bachi, M. Maroncelli, S.P. Webb, A.J. Ruggiero

and G.R. Fleming, Ber. Bunsenges. Phys. Chem. 92, 363 (1988). 31. M.A. Kahlow, W Jarzeba, T.P. DuBruil and P.F. Barbara, Rev. Sci.

Instrum. 69, 1098 (1988). 32. D. Bebelaar, Rev. Sci. Instrum. 50, 1629 (1980). 33. M. Chang, S.H. Courtney, A.J. Cross, R.J. Gulotty, J.W. Petrich and

G.R. Fleming, Anal. Instrum. 11, 433 (1985). 34. D. Bebelaar, Rev. Sci. Instrum. 67, 116 (1986). 35. K. Koyama, H. Kume and D. Fatlowitz, "Application of MCP-PMTs to Time

Correlated Single Photon Counting and Related Procedures", Hamamatsu

Photonics K.K., Technical Information, No. ET-O3/0(=r 1987. 36. K.E. Drabe and J. Terpstra, private communication. 37. All programs were written by F. de Haan, information concerning these

excellent programs can be obtained from: F. de Haan, Department of Physical Chemistry, Nijenborgh 16, 9747 AG Croningen.

38. D.V. O'Connor, W.R. Ware and J.C. Andre, J. Phys. Chem. 83, 1333 (1979).

39. P.R. Bevington, "Data Reduction and Error Analysis for the Physical Sciences" (McGraw-Hill, New York, 1969).

40. W.H. Press, B.P Flannery, S.A. Teukolsky and W.T. Vetterling, recipes, the Art of Scientific Computing" (Cambridge Press, Cambridge, 1986).

41. A. Grinvald, Anal. Biochem. 76, 260 (1976), A. Crinvald and 1.2. Steinberg, Anal. Biochem. SQ, 583 (1974).

42. G. Scheibe, Angew. Chem. 49, 563 (1936), Angew. Chem. 50, 51 (1937), Angew. Chem. 50, 212 (1937).

43. E.E. Jelley, Nature 138, 1009 (1936), Nature 139, 631 (1937). 44. E. Daltrozzo, G. Scheibe, K. (3echwind and F. Hrrimerl, Photogr. Sci.

Eng. 18, 441 (1974). 45. W. Cooper, Chem. Phys. Lett. 7, 73 (1970). 46. W. van Veenen, Research Report University of Groningen (1988). 47. M. Bosma, Research Report University of Groningen (1987).

Dephasing of a molecular exciton: PIC

4.1 Introduction

4.2 Dephasing in glasses

4.3 Accumulated echo measurements

4.3.1 Low temperature decay

4.3.2 Temperature dependence

4.3.3 Bottleneck dynamics

4.3.4 Trapping measurements

4.8.6 Other PIC aggregates

4.4 Discussion and summary

References

4.1 Introduction

Molecular exciton transitions have attracted much attention in the past [I-41. Intriguing aspects of the spectroscopy are the shape and the position of the exciton transition. These aspects were studied using steady state optical spectroscopy. From time resolved optical spectroscopy information is obtained about the relaxation dynamics of the exciton transitions. The results of time resolved spectroscopy can also be used to elucidate frequency domain properties such as 'optical

, lineshapes. In a number of molecular crystals triplet excitona are observed [2].

Examples are the work on triplet excitons in dibromonaphthalene, tetrachlorobenzene and naphthalene [3,4]. The width of these triplet exciton bands (4 times the coupling B) is quite mall ( a few an-'), caused by the small interaction of triplet states. Singlet excitons, which have a much larger bandwidth, are not often observed in molecular crystals because of the occurrence of polariton effects 151.

The so called J-aggregate of pseudo-iso-cyanine [6,7] plays the role of model system for studies of molecular exciton behavior in spectroscopy. -The discovery that this compound form stable aggregates in the liquid phase datea back to 1936. From fluorescence quenching experiments Scheibe found that the excitation was delocalid over many units 181. The J-aggregate has drawn continuous attention ever since its discovery. Three main reasons can be given for the continuing attention.

The thermodynamics and kinetics of aggregate formation in saturated solutions has been the subject of extensive studies [9,10]. Especially the determination of the number of monomers present in an ~ggregate has attracted attention. The second reason is the sensitization behavior of aggregates in photographic emulsions [ll-131. Commercially used photographic materials are mainly silver halide crystallites. These compounds absorb in the blue and ultraviolet parts of the spectrum. In order to make the silver halide sensitive in the rest of the visible spectrum, dyes are coated on the crystallites. The dye molecules absorb quanta of light, and the molecules become electronically excited. The excitation is then transferred to the crystallite. Aggregation often occurs on the surface of the crystallites, so knowledge of aggregate properties is necessary. Narrow and intense aggregate bands also offer the possibility to make wavelength specific layers. Another advantage is presented by the large red shift of the absorption on aggregation; dyes sensitive to red light always have been scarce.

Next to the the11nodynamics of aggregation and the sensitizing properties, the spectroscopy of molecular aggregates is intriguing as well. After optical excitation an molecular exciton is formed. The work on pure and impurity doped molecular crystals shows that the exciton concept is very useful for the description of molecular states and energy transport phenomena.

The theoretical framework developed for the description of molecular excitons can be applied to the aggregates of PIC. The narrow absorption profile, with a width of 190 cm-I for PIC aggregates in water at room temperature, has been the subject of many studies [15-221. It was shown

4. Devhasin~: of a molecular exciton: PIC 53

that a small number of coupled units (about 5) is sufficient to explain the positions of the bands in the absorption spectrum (23-251. The reduced width of the J-band was explained in terms of motional narrowing of the transition. Motional narrowing can be considered as an averaging process, where the site-dependent energy terms 4, belonging to the monomers, are averaged to an effective inhomogeneity. How to extract information about the delocalization from static and dynamic spectroscopy will be shown in this and the following chapters.

The system that is studied most extensively in this thesis -is the PIGbromide salt in a 1:l mixture of water and ethylene glycol as solid solution at low temperatures (glass state). This system has two distinct features as compared to water solutions. The first one is the observation of two separate J-bands (see Fig. (4.1)). The second feature is the extreme narrowing that is observed; the linewidth is only 30cm-'. Cooper [26,!27], who first made this solid solution already noted that the energy splitting between the two peaks is most probably cawed by the occurrence of different conformers. My work substantiates this claim.

670 679 M O

wavelength hn)

Figure 4.1 The two absorption bands of pseudo-iso-cyanine aggregates in a solid solution of tuaEerlethylene glycol 1:l at 1.5 K. The width of the bands is much smdler than the width of the monomer absorption in the s a w nurtrir (see M). The absorption band at the loaacr wavelength is called "blue bandn, whereas the higher wavelength band is called "red band".

PIC aggregates represent an example of a delocalized exciton, which means that the coupling between the molecular units (B) is larger than the spread of the inhomogeneity (a). The homogeneous lineshape is studied as function of temperature. The results from this study show that the delocalized exciton is not subject to dephasing at 1.5K. At higher temperature. the k-state is scattered by phonon modes of the aggregate.

The subject of this chapter is the dephasing dynamics of the aggregate excitation. The measured dephasing time T, is directly connected to the homogeneous part of the linewidth, rh. The data indicates that dephasing up to 70 K is governed by a 10 cm-' phonon. Above 70 K faster

dephasing caused by a contribution of a higher energy process is observed.

The results on the PIC aggregates will be pr-ted in Sect. (4.3). Subjects are the nonexponential echo decays, the temperature dependence of the dephaeing, and $he bottleneck dynaadc8. I also report measurements of the PIC aggregate8 with molecules added that act as a trap for the excitation. In Sect. (4.2) a short summaxy on models to describe the dephasing of chromophores in amorphous matrices is given.

4.2 Dephasing in gbesee

The properties of amorphous and crystalline materials show clear differences. For example, the heat capacity a t low temperature in crystala obeys the Debye P law [28], whereas amorphous materials show deviations from that law. The differences are caused by the absence of translational order in glaeaes, and the fact that glaeeee are not in a thermodynamic equilibrium state. The optical dephasing behavior of chromophores embedded in crystals and glasses differs as well @9]. In mixed molecular crystals exponential activation of the dephasing is observed [30], indicating that a low frequency lattice mode governs the dephasing. In glasses power law activation (F) is observed, which is interpreted in terms of a so called two level system (TLS) model [31]. The TIS model is used to describe other physical properties of glasses as well.

Dephasing of electronic excitations of chromophores in mixed molecular crystals can be described excellently by uncorrelated phonon scattering [ref]. The salient feature, of the model is the singling out of one phonon, which is strongly coupled to the electronic transition. The particular phonon mode either is a crystal phonon with a strong interaction, or a libration. Libration is the name for the motion of a guest molecule in the cage of the host crystal, for example a hindered rotation of the guest molecule. Uncorrelated phonon scattering is a limiting case of the theory by De Bree and Wierma [32], where the important phonon has different energies in ground and excited states. In case the phonon energies are nearly the same, the so called exchange limit is reached. In mixed molecular crystals the exponential activation of the dephasing, which indicates uncorrelated phonon scattering is observed.

In the limit of uncorrelated phonon scattering the pure dephasing is activated biexponentially:

where is the pure dephasing time, r3 and 7, are the local phonon lifetima and n(e,,) and n(e,,)- represent the Bose-Einstein population factors for local phonon energies e, and The dependence of the dephasing on temperature is given by the population factor:

4. De~hasinn of a molecular exciton: PIC

and by the temperature dependence of the phonon lifetimes r(T). The experimentally observed dephaaing characteristic of single exponential activation is recovered when kT a e, and when the phonon lifetimes are not temperature dependent. The term n(e) in that case reduces to the exponent (the Boltzmann factor). For measurements over large temperature ranges the full expression has to be used.

A TLS can be considered as consisting of two conformations of the environment around the guest molecule. The two conformations are separated by an energy barrier. A TIS can flip by tunneling through the barrier. In case this TLS has a different energy for the molecular ground and excited etatea, this flipping process leads to dephasing. In contrast to librations the TIS's cannot be observed as separate peaks in an absorption spectrum. They only influence the optical lineshape of the guest molecules.

TIS's with a whole range of different energies are thought to exist, caused by the many different arrangements of the disordered glass. The temperature dependence of the dephasing is caused by this distribution of TIS level splittings. In order to explain the low temperature activation of the dephasing a TLS density of states, D, is invoked that looks like:

where p is the exponent of the density of states. At temperatures above 5 K an exponentially activated contribution is observed [33]. This shows that an other mode of the glass, possibly an optical phonon is contributing to the optical dephasing at higher temperatures.

Next to the distribution of splittings, a distribution of flipping rates is thought to exist [34]. A direct observation of the dephasing time, as in a two pulse photon echo experiment, measures these flipping rates. The exponentiality of the decays can be explained from a distribution of flipping rates P, which is proportional to the inverse of the rates R, P ( R ) ccR-l. Such a distribution suggests that many flipping rates are present, ranging from the dephasing rate (about 1012s-1) down to very slow changes (about 1 s-I). When the linewidth is measured at a large delay time after the initial excitation, a larger part of the rate distribution influences the measurement. The difference of the dephasing time as reported from two pulse photon echo and holeburning experiments shows this evolution of the linewidth with time [34]. From the evolution of the linewidth with time, information is obtained about the distribution of TZS flipping rates.

4.3 Accumulated echo measurements

4.3.1. Low temperature decay

In Fig. (4.2) accumulated echo traces of the red and blue sites of

PIGbromide aggregates at 1.5K are depicted. The excitation was performed with stochastic light pulses which covered a spectral region larger than the width of the J-band. This scheme gives rise to the averaging of the properties of all ,aggregates present in the inhomogeneous profile. The decay cannot be fitted with a single exponent. A good fit can be obtained by introducing a second decay component, or by using a Kohlrausch decay function, exp[(- t /~)~] . The Kohlrausch decay function (351 is intended to describe a process in which a whole distribution of decays is present. The parameter T is related to the average decay, and CY is related to the width of the distribution. *

probe delay bJ Figure 4.2 The accumulated echo decay of the red site (top) and the blue site (bottom) of PIC-bromide aggregates at 1.5 K, using stochastic pulses. The biexponentid decay parameters are 8 ps/25 ps with weights 0.610.4 for the red site, and 7 psi20 ps toith weights 0.710.3 for the blue site.

The nonexponentiality of the echo decay could indicate that the homogeneous lineshape is not Lorentzian. However, exciting the aggregates with a narrow bandwidth laser (smaller than the absorption bandwidth), one observes different decay parameters at the high and low energy sides of the absorption profile. Varying the central frequencies of such a narrow band laser leads to the echo decay parameters as a function of the position in the inhomogeneous band. The echo decay is slightly longer when the low energy edge of the J-band is excited. In terms of the result of biexponential fitting, an increase of the weight of the slowest component is observed. When the high energy edge of the J-band is excited, the fast component gets more weight. At all frequencies the decay is nonexponential. This observation suggests the presence of a distribution of different excitons having different dephasing times (T,) . Varying the excitation frequency implies that a different part of this

4. De~hasint? of a molecular exciton: PIC 57

distribution ie observed. In Tables (4.1) and (4.2) the wavelength dependence of the echo decay of PIC-bromide and PIC-iodide aggregate6 is given.

Table 4.1 Data on wavelength dependence of PIGBr at 1.5 K

I I I I I a) one J-band is observed, absorption maximum at 576.3 nm -

I

Table 4.2 Data on wavelength dependence of PIG1 at 1.5 K

Different batches of samples do show somewhat different decay properties. The reason for this effect is the "dynamical" preparation of the aggregates. Formation of aggregates occurs during cooling after insertion of a solution sample into a cold cryostat. The cooling speed depends on the temperature at which the cryostat is held, and on the conduction of heat away from the sample. The low temperature decays reflect the variation of the preparation of the samples. No universal values for the parameters (decay constants and weights) can be found. The magnitude of the variations however, is not very large. For example, the initial component varies horn 6 to 9 ps and the tail varies from 20 to 30 ps. The very high sensitivity that can be achieved in the accumulated echo measurements, allows for very precise fitting of the data. Within a

wavelengthC

576.3' 575.5" 574.8' 574.1a 573.4a

570.3: 569.7, 569.0b 565.5

wavelengtha

579.3 578.7 578.0 577.3 576.0 574.7 572.7

a) red site A,-= 576.0 nm, b) blue site A,-= 570.3 nm c) wavelength in nanometers d) the total decay function is defined as Cppxp(-t/ri)

T ? ' ( ~ )

8 8 5 8 6

7 7 5 5

w ': 0.4 0.5 0.5 0.3 0.1

0.7 0.7 0.8

'4 d

0.6 0.5 0.5 0.7 0.9

0.7 0.7 0.8 1

T ? ~ ' ( ~ S )

12 12 10 8 5 3 2

r?"' PS

25 23 22 25 30

20 21 17

WI

0.7 0.7 0.4 0.8 0.7 1 1

Ta WY (PI

35 33 32 32 14

w2

0.3 0.3 0.6 0.2 0.3

series of scans on one sample accuracies of better than 1 ps are easily achievable. The sample dependent decay behavior supports an interpretation in terms of a distribution of aggregates with different dephasing times. Apparently, the actual distribution is the result of the preparation procedure.

Recently Hirschmann and Friedrich [36] performed holeburning experiments on PIGiodide aggregates in waterlethylene glycol. The extrapolated hole width they find is 0.36 cm-I. This holewidth can be converted into a dephasing time of 58 pa. In Table (4.3) the observed quantities of holeburning and echo spectroscopy are related to the dephasing time Tz.

Table 4.3 relation echo and holeburning parameters

A 58ps dephasing time would lead to an accumulated echo decay time of 29 pa. This fits nicely to the slow component in the echo decay, but apparently no trace of the fast component is found in holeburning.

technique

r 2 pulse echd Acc. 3PSEQ Holeburnin8

4.5.2. Temperature depeniience

When the temperature is increased above 1.5 K a very small decrease of the echo decay time is observed in the temperature region up to 10K. From 10K to 100 K a steady decrease of the echo decay with temperature is observed, indicating a decrease of the dephasing time. At 100 K the echo decay is so short (less than 1 ps), that reliable echo measurements are hard to make. Recently the temperature region from 100 K to 200 K was analyzed by linewidth and lineshape rneaeurements by Fidder et al. [37]. The linewidth increases in this region also indicating a decrease of the dephasing time.

The normal approach for analyzing the temperature dependence is to fit the dephasing time (T,) and subtract the lifetime (TI) in order to get a set of pure dephasing times (c) as a function of temperature. In case of PIC aggregates this approach is not straightforward.

The decays are nonexponential so fitting a single T, is not possible. An average decay constant could be used, in order to approximate the decay with a single exponential. It turns out however, that in this way the tail of the decay is neglected. This tail gives information about the onset of the dephasing, especially at temperatures around 10K. At least two decay constants have to be used.

The dephying time is the reciprocal sum of a lifetime (TI) and a pure dephasing (T,) contribution:

measured signal curve

a) observed decay time is T b) observed holewidth is rWe

exp( - t / ~ ' ) e V ( - t / ~ " ) rhde = 2 4 , 0 m o ~

dephasing time

Tz = 47' T, = 27" Tz = 2/(xcr,e )

where the TI contribution is temperature independent, and the T.2 contribution is temperature dependent. The emission lifetime can be determined from time resolved fluorescence measurements (see Chapter 5), and is 70 ps for the red and 45 ps for the blue site. These lifetimes show that at 1.5 K the relation T,=2T1 does not hold. This does however not imply that a pure dephasing contribution in Eq. (4.5) is present. Recently performed resonance Raman scattering have shown that the pure dephasing time goes to zero at 1.5K [37]. The echo decay is not temperature dependent up to 7 K, showing that the pure dephasing contribution is very mnaU at these temperatures.

From the observation of a dephasing time shorter than the lifetime it is clear that an extra term must be included to describe J-aggregate dephasing. The fluorescence lifetime turns out to be temperature dependent, so in principle that should be incorporated a s well. In fact the fluorescence lifetime is constant up to 60 K, and gets longer at higher temperatures, so no influence is expected on the shortening-of the dephasing time. I aesume that a modified description can be used for the dephasing time of the aggregate:

The term T,(T-o) is used to indicate that a difference between the measured T2 and 2T1 exists.

The echo decay is now described by a response function R(~,T) where the temperature dependence is explicit,

When a distribution of aggregates exists, with different values for T2, the decay function looks like:

where the summation over i refers to the separate components in the total decay and wi is the weight of a component. The assumption isathat the pure dephasing time ia the same for all aggregates: G~(T)=T~(T). The pure dephasing term can then be taken out of the summation in Eq. (4.8), and the temperature dependent part is separated from the T=OK decay. Actually, an arbitrary function which matching the low temperature decay will do, as long as the pure dephasing is assumed to be equal for all

aggregates, and is described by an exponential term. The procedure to extract pure dephasing times from the data is to find

the best multiexponential fit for 1.5K data, and then record the changes with temperature. A biexponential fit was sufficient for a good description of the decay. In general the fit parameters of several scans were averaged. The scans a t higher temperature can be fitted to the average of the low temperature scans. Any temperature dependent variation is ascribed to the term preceding the summation in Eq. (4.9).

The summation in Eq. (4.9) describes the low temperature decay and is held fixed in the fitting procedure. In Fig. (4.3) the result of this procedure is shown.

1- 1 5 10 100 5 10 100

temperature, EK) temperawe 00

Figure 4.3 Dephasing as a function of temperature for PIC-bromide aggregates. The left (right) graph shm the data of the red (blue) site and a fit to exponential activation with parameters 10 n - I and 30 ps (10 cm-I and 40 ps).

The fits shown in Fig. (4.3) are curves based on exponential activation of the pure dephasing rate. For both the red and the blue site of PIC the energy of activation is 10cm-l. Exponential activation indicates that a low energy mode is governing the dephasing, as in the uncorrelated phonon scattering limit of the De BreeIWiersma theory. Even though the aggregate is embedded in a glassy environment, a single energy value is needed to describe the activation of the dephasing.

On the basis of the data of Fig. (4.3) a description in terms of glass dynamics cannot be ruled out. As was shown by Fayer [34], many glass systems show the characteristic power law activation up to a temperature of only 5 or 1DK. For pentacene in PMMA and polystyrene we found a crossover temperature close to 4 K [33]. The influence of glass dynamics in PIC aggregates cannot be observed in this temperature region by means of echo methods, because of the extremely short low temperature decay of the echo. Above the crossover temperature both dephasing models predict an exponential activation. Support for the uncorrelated phonon scattering

4. De~hasinn of a molecular exciton: PIC 61

model is given by Raman to fluorescence yield measurements of Fidder et al. [37], which show a pure dephasing contribution which goes to zero below 4K. This observation indicatea that the pure dephasing rate approaches zero, as expected in a pseudo local phonon description. I therefore conclude that the dephasing is governed by a low frequency, mode. Fluorescence line narrowing and holeburning spectroscopy do not exhibit a distinct loan-' mode. An option is that not an isolated mode is present, but a band of optical phonon states. The 10 an-' frequency thus r e p m n t a the gap of the optical phonon band.

From holeburning measurements Riedrich et al. reported a different value of 27 an-' for the frequency of the local phonon for PIC-iodide aggregates in waterlethylene glycol [36]. The main cause for the factor of three difference could be the short T, at 1.5 K. A reliable determinbtion of the pure dephasing contribution below 10 K ki difficult, because in that temperature region the pure dephasing time is much larger than the T 2 ( ~ - o ) contribution. A good determination of the activation energy cannot do without measurements in the region where kT < e, and e = hw*, that is below 14 K for a phonon of 10 an-'. Accumulated echo measurements are very sensitive, and allow for the analysis of nonexponential decays. In holeburning experiments one has to extrapolate to zero hole depth, and a non-lorentzian shape of the burned hole might not be noticed. For PIC-iodide aggregates the frequency is determined to be 102: cm-l, on the basis of the echo measurements.

Above 70 K the temperature dependence changes. The echo data already indicate the change, and linewidth measurements [37] clearly show that the slope is much steeper. The data indicate an exponential activation with an activation energy of about 300 an-'. The temperature range is large (100K) but only represents a factor of two change of temperature. This fact makes it hard to deduct reliable values for the dephasing parameters. It is clear however, that the change at 70K indicates that another mechanism governs the dephasing at elevated temperatures.

4.3.3. Bottleneck dynamics

Accumulated photon echoes can only be generated when a bottleneck state exists that atores population for a period much longer than the repetition period of the exciting laser. Information about the bottleneck state can be obtained from accumulated echo measurements. Both the energy level structure and the lifetime of the relevant state influence the echo decay. From the signal intensities 'the lifetime of the bottleneck state of PIC-bromide aggregates can be deduced. However, no definite conclusions can be drawn about the nature of the state.

The maximum intensity of the echo signal indicates how much of the population grating is stored in the ground state. The signal intensity can be related to the absolute amount of stored population via the "modulation depthn of the signal. This depth is the change of probe transmission and [38] is proportional to the population change. For PIC aggregates at low temperature the relative amount of population (ANIN) stored in the bottleneck is -2~lO-~. No dependence of the modulation depth on the laser intensity is found at pulse energies higher than 6 pJ.

Thia means that the bottleneck M saturated at these very low intensities. Only at excitation energiea lower than 6 jd the bottleneck is not eaturated and the relative amount of stored population is proportional to the used intensity. The saturated modulation depth is equal to the relative- number of accessible bottleneck states, so the number of bottleneck states must be 2 ~ 1 0 - ~ N, or equivalentlx, one bottleneck state exists for every five hundred delocalization areas on an aggregate.

In Sect. (3.3.2) I pointed out that diffraction from a travelling wave inhibits the formation of an accumulated grating. However, an echo effect

, can still be observed of two consecutive pulse pairs. A three pulse stimulated echo (3PSE) L observed, which can be detected according to the homodyne detection scheme (Sect. (3.3)). In general the 3PSE is too mall to be detected without the use of amplified pulses. However, in the case of PIC-aggregates the nonlinear optical response is large enough to allow for detection of the 3PSE. The 3PSE signal also shows saturation but at much higher p u k energies. In Fig. (4.4) the amount of population contributing coherently to the signal is depicted, for accumulated and non-accumulated signals.

pulse energy (J)

Figure 4.4 The modulation depth of the accumulated echo as a function of pulse energy. The top trace represents the accurnuluted 3PSE whereas the bottom trace represents the non-accumulated 3PSE. The bends in the-curves indicates the point mhen the modulation depth is saturated cmpletely.

From the figure, it can be seen that the accumulation amplifies the signal by a factor of 30. This factor is deduced from the ratio of the saturation energie8 (note that the X-axh is logarithmic). Thia gives the accumulation enhancement factor y directly, without any assumptions about the level dynamics. A second observation is that the saturated 3PSE signal is smaller by a factor 4, as compared to the saturated accumulated echo signal. This effect can be understood in terms of the phase shift between consecutive pulse pairs. In Sect. (3.3.2.) the phase shift was determined to be 4.24n, leading to a effective shift of 0.24s between the polarization H3) and the readout field E. The signal is proportional to

4. De~hasine of a molecular exciton: PIC

the cosine of the phase shift, so the signal is expected to be reduced to cos(0.24~) =0.73. This decrease does not cover the whole difference of accumulated and non-accumulated signals. A possible cause for the remaining discrepancy can be an error in the determination of the mode locking and modulation frequencies. Any anharmonicitiee in the driving RF could alos further degrade the signal intensity. My conclusion is that homodyne three pulse stimulated echoes can be observed from J-aggregates. The saturation of the accumulated and non-accumulated signals, indicatee an enhancement of a factor 30, from which the bottleneck lifetime can be determined to be 30~10.6 ns n 305 ns.

More information about the bottleneck state can be obtained by studying the signal intensity as a function of temperature. The results for the red site of PIC-aggregates are presented in Fig. (4.5). Following Molenkamp [39] the logarithm of the ratio [I(O)- I(T)]/I(O) is plotted against inverse temperature. Exponential activation of the signal decrease leads to a straight line in such a plot. The deactivation energy of the bottleneck state is only 3.5 cm-I. The same analysis for the blue site gives an even smaller value of 1.9 cm-I. These very mall activation energies show that the bottleneck state is only weakly binding. This binding energy is not necessarily the depth of the trap state below the exciton band. A small deactivation energy is also posaible when the trap state is deep. ,

Figure 4.5 Normalized echo intensity of the red and blue sites.

The bottleneck state is most probably a long lived trap state on the aggregate. A triplet bottleneck can be excluded on the basis of the lifetime deduced from the saturation experiments. Friedrich et al. [40] recently reported a triplet excitation spectrum from very concentrated samples. However, the lifetime they report (in the order of milliseconds) does not match the bottleneck lifetime. The saturation of the- signal modulation depth proves that a very limited amount of states is involved. Therefore I feel it is plausible to conclude that a trap state on the aggregate serves as the bottleneck state. The average lifetime of the bottleneck states is 300ns, as found from the grating saturation. The very small deactivation energy shows that these trap states are not strongly binding.

4.3.4 Trapping experiment6

Thiacyanine dye TD interacts with PICLaggregates [41] on silver halide crystals. In PIGaggregates in water/ethylene glycol a new trap emission band is formed a t 608nrn with a width of 150 cm-I. The integrated &ion is much larger than can be anticipated from the absorption profile of TD. The reeulta show that a t a mixing ratio of one molecule TD to five hundred molecules PIC already a substantial shortening of the echo decay is. observed.

In Fig. (4.6) four echo decay curves of PIC/TD mixture8 are shown. It ' can be seen that at a ratio of 500:l the decay of the red site shows a fast initial component, not present in the 1000:l and pure PIC mixtures. When the decay traces are analyzed it turns out that next to the shortening of the initial component also the longer tail is shortened. The same analysis of the blue site of PIC aggregates already shows a detectable shortening at the lowest mixing ratio of 1000:l.

-10 0 10 20 30 40

probe delay (ps)

Figure 4.6 Echo decays of aggregates taith traps attached, PIC (solid line), mixture 1000:l (short dash), mixture 500:l (long dash), mixture 250: 1 (dots).

The samples were prepared in one batch, all under exactly the same conditions. Small differences of the decay traces can unambiguously be asgigned to trapping. Assllming that the TD molecules have the same probability as a single PIC molecule to be attached to an aggregate, the mixing ratios in solution represent the molecular ratio within the aggregate. This implies that one trap molecule on thousand PIC molecules already influences the dephasing time, thus giving a direct proof for the extension of the aggregate excitation.

From the fluorescence yield of the mixed samples one can estimate the range over which the exciton moves. I will discuss these emission data in the next chapter. The connection between the trapping as seen in dephasing measurements, and as seen in incoherent fluorescence will also be discussed there.

4. De~hasinn of a molecular exciton: PIC

4.3.5 Other PIC systems

PIC aggregates can form in many different environments, and with different counterions. The original mixture where Scheibe and Jelly found aggregation was PIGchloride in water. It was shown that aggregates form on silver halide crystals [41]. Later Cooper [26] found extremely narrow J-bands in 1:l water/ethylene glycol mixtures. A systematic survey of counter ion effects was performed by Daltrozzo et al [26]. The layer-forming properties of PIC on crystals were exploited by Kuhn and coworkers [42], using a derivative of PIC with one or two octadecyl groups instead of the ethyl groups. This PIC derivative forms aggregated Langrnuir-Blodgett monolayers. PIC aggregates can also be formed in polymer hosts.

The echo experiments were repeated with different host materials and different counterions. In Table (4.4) the steady state spectra are summarized.

Table 4.4 Absorption and emission of PIC aggregates at 1.5 K

The absorption maxima are found in a relatively narrow region around 575 nm. This means that the energy of the allowed exciton transition is not strongly dependent on the environment. Clearly this is the result of the averaging of the matrix properties by the delocalized excitation. The width of the J-band is dependent on the actual system that is studied. The motional narrowing [25] of the absorption line is less effective for the iodide salt in waterlethylene glycol, and for the polymer mixtures, relative to the bromide salt in waterlethylene glycol. The energy difference between of the absorption and emission maxima, the Stokes shift, is zero for the waterlethylene glycol mixtures. The polymer samples do show a small Stokes shift, showing that a relaxation of the lattice accompanies the fluorescent emission.

For all of the mixtures accumulated echoes could be generated. The first trend evident from Table (4.5) is the faster decay observed at the

PIC-Cl/WE b r

PIC-Br/W b r

P IGI /W 1 PIGCI/PVA I PIC-Br/PC

PIC-I/PC

a) absorption width of the J-band b) absorption to emission shift c) WE is waterlethylene glycol, PVA is poly(viny1 alcohol), and PC is

polycarbonate

569.4 574.9 570.3 576.0 576.3 569.3 576.6 581.3

35 40 30 30 65 110 190 180

-0 FJO -0 -0 nrO - 45 60

blue site for those systems exhibiting two sites. The second trend is the shortening of the dephasing time upon going to stiffer matrices. Especially polywbonate is known to partially crystallize under conditions where aggregation occurs. In polycarbonate aggregation is "forcedw by the matrix. The aggregates can be expected to show less long-range order, and larger interaction with the matrix. Poly(viny1 alcohol) has more flexible chains and behaves more like a glassy matrix. A last point that has to be mentioned, is the "coherent spike" that is observed in the polycarbonate samples. The peak intensity of this spike is comparable to the echo decay. The spike indicates that a fraction of the aggregates is coupled so strongly to lattice phonons that coherence is lost immediately.

Table 4.5 Echo decay parameters of PIC

I s m I 4-7~) I Wl

The analysis of the temperature dependence of the dephasing can be done in the same way as for PIC-Br in Sect. (4.3.2). I want to stress once more that different samples can lead to different decay parameters. However, if the whole temperature run can be performed on one sample, and preferably on one spot in that sample, the interpretation of the measurements can be straightforward.

PIC-CI/WE(r) (b)

PIC-Br/WE(r) (b)

PIC-I/WE PIC-CI/WA PIC-Br/PC BIGI/PC

Table 4.6 Dephasing parameters PIC aggregates

8.5 8 8 7

8.5 6 3 2

'abbreviations: see previous

I

E: is the activation energy T is the phonon lifetime

system e (cm-l)

4. De~hasinn of a molecular exciton: PIC 67

The numbers in Table (4.6), both the parametera and the errors, are derived from a simple graphical procedure. The f i data are plotted in a double logarithmic way. A seriee of calculated pure dephasiig times versus temperature traces with different values for the parameters is compared with the data, and the best one is picked. A sensible estimate of the error is also made in the same way. Although the procedure might seem backward, a more sensible result is reached in this manner than by extensive computer fitting. For PIC-iodide aggregates in plycarbonate the low temperature decay is too short to allow for determination of the temperature dependence.

For most aggregate systems the same 10 cm'' activation energy is found. ThEs result supports the interpretation that the dephasing is activated by a low energy mode of the aggregate itself. When modes of the amorphous environment would be involved, a dependence on the host parameters would be expected. The only system showing a deviating activation energy is PIC-chloride in waterlethylene glycol. It is clear that for large aggregates the counterions must be bound to the aggregate, otherwk repulsive Coulomb interactions would dietort the aggregate. A dependence on the counterion can therefore be anticipated. However, if the deviation of PIC-chloride aggregates would be based on a counterion effect, a deviation would also be expected for PIC-chloride aggregates in PVA.

The values of the lifetime of the active mode ( 7 ) is very similar for the different aggregated mixtures. A value is 20 ps for inferred from the data. The similarities of the results for different environments of the PIC aggregate ehow that the averaging of the interaction of the exciton with the host environment is almost complete.

4.4 Discussion and summary

In Chapter2 it was shown that the optical lineshape must be interpreted in terms of a delocalized exciton coupled to lattice phonons. The exciton-phonon coupling consists of an intersite coupling term causing scattering of the exciton (~('1, between site n and m) and a contribution causing local deformation ( ~ ( ~ 1 , on site n). The fluorescent emission from the J-band has a very high quantum yield with very little vibrational (or phonon) structure, and is resonant with the absorption. Clearly, the lattice does not relax after the optical excitation, which m e ! that the exciton state is not. coupled to a lattice deformation. The conclusion can be drawn that the local deformation contribution to the exciton-phonon coupling is negligible. The remaining contribution is the intersite coupling term:

where a: and h, respectively, create and annihilate an electronic excitation at site n (m) and b: and bp create and annihilate phonon with wavevector q. The k to k' scattering described by this exciton-phonon

coupling term is always state changing, which means that the lifetime T1 is influenced and not the pure dephasing. It must be mentioned that this T I is the time during which the exciton is in the initially excited state. It is not the radiative relaxation to the ground state. As was shown in Chapter 2, pure dephasing (Tz) processes are not described by the linear coupling term. Higher order coupling terms must be evaluated to explain pure dephasing.

The low temperature accumulated echo decay of PIC aggregates can be excellently described by two exponents. A t the peak of the red site the fast component is 8 ps, and the slow component is 25 to 30ps. The homodyne accumulated echo measures T2/2, so the dephasing times T , are twice these measured times. The deviating dephasing times found from holeburning could be caused by the selection of aggregates participating in the experiment. I already showed that accumulated photon echo is generated in a fraction (~xIO-~) of the aggregates. Photo-physical holeburning in the same way selects only that part of the aggregates that have a nearby trap state. The absorption spectra of PIC iodide aggregates presented in ref. [36] exhibit two J-bands. However, the. close resemblance of the PIC bromide and PIC iodide aggregate dephasing parameters (Table (4.5)), leads to the conclusion that these different absorption spectra do not explain the discrepancy.

The low temperature dephasing does not match the fluorescence decay time of 70 ps, but is considerably shorter. If the relation ~T,(T-o) =TI (see Eq. (4.6)) holds, the low temperature accumulated echo measures Tl directly. As a result, the decay times cited in Table(4.5) can be compared directly to the fluorescence decay time. Since no residual pure dephasing process is found (371, a definite discrepancy between low temperature dephasing time and the fluorescence lifetime exists.

An explanation for the short dephasing time can be given when one considers the aggregate exciton state. From a perturbative approach is follows that the zero order states are exciton k-states. For a linear chain of identical chromophores not all oscillator strength is in the k=O exciton level. Actually, only a circular 1 D this total projection of oscillator strength occurs. If the aggregate is linear, boundary effects lead to a transfer of oscillator strength occurs to k#O levels. Spano and Mukarnel [43] have shown that site inhomogeneity also leads to transfer of oscillator strength to higher exciton states. In such a perturbative model, the higher k-states in PIC aggregates will definitely have oscillator strength, because they are finite and noncircular. The J-band should now be seen as a band of optically allowed k-states, which a different transition probability.

When the site inhomogeneities are very large, the perturbative viewpoint must be abandoned. One only considers a number of coupled units with a random spread. Numerical calculations [44] have shown that the randomness of the site potential leads to pinning of the delocalized excitation. This resulting delocalized state can not be labelled with a k-value, because the wavefunction shows a distinct maxima at well determined sites. A the spread of the sizes of the delocalization areas will be the result, leading to a distribution of states with different transition probabilities to the ground state.

The noted differences of the transition probabilities have different

4. De~hasing of a molecular exciton: PIC

consequences for echo and fluorescence spectroscopy. The echo will probe the exciton states in proportion to the transition moments. The exciton states with a large transition moment, and thus a short lifetime, will contribute strongly to the echo. In the fluorescence experiment the ahregates are excited at much higher energies in vibronic bands. The J-band exciton states will be populated in a way differing from a direct excitation of the J-band. States with small transition moments can also be populated. The resultant average fluorescence lifetime is much longer than the echo lifetime.

The question that remains to be answered is why the J-band absorption spectrum is asymmetric. The homogeneous bandwidth is -1 cm-l, whereas the total width is -30 cm-l, with a Gaussian tail at the low energy side and a more or less Lorentzian tail at the high energy side. This asymmetric shape is characteristic for other molecular aggregates as well [42]. Excitation wavelength dependent dephasing times are recor-ded a t different positions in the absorption band. Especially for PIC-iodide that did not show a blue site in the samples studied, the wavelength dependence is evident. At the extreme low energy side (579 nm) the decay shows a 12 ps initial component and a 35 ps slow component. The decay at the absorption maximum (577 nm) is faster (see Table (4.2)), and at the extreme high energy side (574 nm) a 3 ps decay is found. This frequency dependence shows that different states are probed.

Explanations starting frdm exciton-phonon Hamiltonian like Eq. (2.20) have been given. In such a model, the motional narrowing of the absorption shape leads to a Gaussian spread exciton energies. The high energy Lorentzian tail reflects the lifetime broadening of the higher exciton states, which show an increased scattering probability. The high energy tail would be homogeneously broadened. On the basis of the homogeneous linewidth measurements this interpretation can be excluded. The measured homogeneous width is much smaller than the absorption bandwidth. As was already noted [45], this scattering model could hold a t elevated temperatures (for PIC aggregates that would be above 70K).

Starting from a model which only incorporates inhomogeneity, the asymmetric shape can be calculated [44]. Numerical diagonalization of a Hamiltonian incorporating diagonal disorder only, reproduces the basic features of the absorption band shape. At low temperatures the absorption lineshape is better interpreted in terms of such a model.

The aggregate should be considered to consist of different delocalization areas with different energies. The regions are bounded by relatively small local inhomogeneities, which could be crossed by the exciton. A t low temperatures the dephasing is determined by the amount of oscillator strength present in the transition. The nonexponential echo decay reflects the existence of states with different oscillator strength. Only the high energy tail of the J-band is subject to phonon scattering, which explains the shortening of the dephasing time upon going to higher energy in the band.

The main conclusions on the dephasing of PIC aggregates are: 1) the echo decay at 1.5 K is non-exponential with time constants of 8 to 25ps, because of the distribution of different exciton states within the J-band, 2 ) the difference between the dephasing time and the fluorescence

lifetime a t low temperatures must be attributed to the difference between direct excitation of the exciton state and population relaxation to this state, 3) the dephasing up to 70 K is activated by a pseudo local mode with an energy of 10 cm-I and a lifetime of 20 to 30 ps for different PIC aggregate systems, 4) the bottleneck state is saturated at ~xIO-~ relative population, indicating trapping of some of the excitons in a state with a lifetime of about 300 ns.

References

1. R.M. Hochstrasser, Triplet Exciton States of Molecular Crystals, Int. Rev. of Sience, Physical Chemistry, Ser.2, Vol. 3, ed. D.A. Ramaey (Butterworks, London 1976).

2. R. Silbey, Ann. Rev. Phys. Chem. 27, 203 (1976). 3. J.F.C. van Kooten, A.J. van Strien and J. Schmidt, Chem. Phys. Lett.

SO, 95 (1982), A.J. van Strien, R. Silbey and J. Schmidt, Mol. Phys. 46, 151 (1982).

4. D.M. Burland and A.H. Zewail, Coherent Processes in Molecular Crystals, Advances in Chemical Physics vol. XL, pg. 369, eds, I. Prigogine and S.A. Rice (Wiley, New York, 1979).

5. S.H. Stevenson, M.A. Connolly and G.J. Small, Chem. Phys. 128, 157 " (1988).

6. G. Scheibe, Angew. Chern. 49, 563 (1936), Angew. Chem. 60, 51 (1937), Angew. Chem. SO# 212 (1937).

7. E.E. Jelley, Nature 138, 1009 (1936), Nature 139, 631 (1937). 8. G. Scheibe, A. Schontag and F. Katheder, Die Naturwissenschaften 39,

499 (1939). 9. For a review see: A.H. Herz, Photogr. Sci. Eng. 18, 323 (1974), A.H.

Herz, Advances in Colloid and Interface Science 8, 237 (1977). 10. E. Daltrozzo, G, Scheibe, K. Gschwind and F. Haimerl, Photogr. Sci.

Eng. 18, 441 (1974). 11. P.B. Gilman Jr., Photogr. Sci. Eng. 18, 418 (1974). 12. A.A. Muenter and W. Cooper, Phdogr. Sci. Eng. 20, 117 (1976). 13. W. Cooper and A.A. Muenter, Photogr. Sci. Eng. 20, 121 (1976). 14. M. Tanaka, N. Nakazawa, I. Tanaka and H. Yamashita, Chem. Phys. 97,

457 (1985). 15. V. Czikkely, H.D. Forsterling and H. Kuhn, Chem. Phys. Lett. 6, 11

(1970). 16. H.J. Nolte, Chem. Phys. Lett. 31, 134 (1975). 17. F. Fink, E. Klose, K. Teuchner and S. DWe, Chem. Phys. Lett. 46,

548 (1977). 18. S.K. Rentsch, R.V. Danielius, R.A. Gadonas and A. Piskarskas, Chem.

Phys. Lett. 84, 446 (1981). 19. B. Kopainsky, J. Hallermeier *and W. Kaiser, Chem. Phys. Lett. 87, 7

(1982). 20. Z.X. Yu, P.Y. Lu and R.R. Alfano, Chim: Phys. 70, 289 (1983). 21. D.V. Brurnbaugh, A.A. Muenter, W. Knox, G. Mourou and B.

4. De~hasine of a molecular exciton: PIC

Wittrnershaus, J. Lumin. 31, 783 (1984). 22. A.S.L. Comes and J.R. Taylor, J. Photochem. 92, 325 (1986). 23. P.O.J. Scherer and S.F. Fischer, Chem. Phys. 86, 269 (1984). 24. E.W. Knapp, P.O.J. Scherer and S.F. Fischer, Chem. Phys. Lett. 111,

481 (1984). 25. E.W. Knapp, Chem. Phys. 85, 73 (1984). 26. W. Cooper, Chem. Phys. Lett. 7, 73 (1970). 27. W. Cooper, Photogr. Sci. Eng. 17, 217 (1973). 28. C. Kittel, Introduction to Solid State Physics (Wiley, New York). 29. W.H. Hesselink and D.A. Wiersma, J. Chem. Phys. 73, 648 (1980). 30. W.A. Philips, J. Low Temp. Phys. 7, 351 (1972). 31. P.W. Anderson, B.I. Halperin, C.M. Varma, Philos. Mag. 26, 1 (1972). 32. P. De Bree and D.A. Wiersma, J. Chem. Phys. 70, 790 (1979).

P. De Bree, Thesis University of Gronbgen, The Netherlands (1981). 33. H. Fidder, S. De Boer and D.A. Wiersma, Chem. Phys. 139, 317 (1989). 34. C.A. Walsh, M. Berg, L.R. Narashiman and M.D. Fayer, J. Chem. Phys.

86, 77 (1987). L.R. Narashiman, K.A. Littau, D.W. Pack, Y.S. Bai, A. Elschner and M.D. Fayer, Chem. Reviews, t o be published.

35. R. Richert, Chem. Phys. 122, 455 (1988). 36. R. Hirschmann and J. Friedrich, J. Chem. Phys. 81, 7988 (1989). - 37. H. Fidder, J. Knoester and D.A. Wiersma, Chem. Phys. Lett. 17l, 529

(1990). 38. W.H. Hesselink, Thesis University of Groningen, The Netherlands

( 1980). 39. L.W. Molenkamp, Thesis University of Groningen, The Netherlands

(1985). 40. G. Gradl, J. Friedrich and E. Daltrozzo, J. Phys. Chem. 94, 2301

(1990). 41. A.E. Rosenoff, K.S. Norland, A.E. Ames, V.K. Walworth and G.R. Bird,

Photogr. Sci. Eng. 12, 185 (1968). 42. D. M6bius and H. Kuhn, Isr. J. Chem. 18, 375 (1979). 43. J. Grad, G. Hernandez and S. Mukamel, Phys. Rev. A 37, 3835 (1988),

F.C. Spmo and S. Mukamel, J. Chem. Phys. 01, 683 (1989). 44. D.A. Wiersma and H. Fidder, private communication. 45. M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa and E. Hanamura,

"Excitonic processes in solidsn (Springer, Berlin, 1986).

Superradiance Sn PIC aggregates

5.1 Introduction

5.2 Sfeady-sfate flu~res~em

6.2.1 Spectra

5.2.2 Trapping

6.3 Time-resolved fluorescence

6.3.1 Low temperature decay

p 3 . 2 Fluorescence depolarhtion

5.3.3 Temperature dependence

5.3.4 Trapping

5.4 Discussion and summary

6.4.1 Aggregate slze

5.4.2 Temperature dependence

5.4.3 Summary

References

5. Su~erradiance in PIC anerenates 73

6.1 Introduction

In molecular aggregates superradiance is caused by the collective oscillation of the the transition moments of many separate monomers. In semiconductor syeteme superradiance is encountered in the case of confined excitons. In semiconductors the electron and hole have a large average diatance (Wannier exciton) [I], as compared to the Frenkel exciton found [2,3] in molecular solids. Confining the electron and the hole to a amall volume increases the radiative rate, aa observed in multiple quantum well structures (MQWS) 14-61 and microclusters (7-91.

The radiative behavior of PIC aggregates (10,111 must be interpreted in terms of delocalized molecular exciton states. The aggregates show strong radiative enhancement, motional narrowing, and resonant fluorescence. The study of the radiative properties gives information about the extent of the radiative enhancement, and about the factors influencing that enhancement. In the preceding chapter I described the optical dephasing behavior of PIC aggregates. In this chapter the low temperature radiative proprties are treated together with the temperature dependence of the superradiant lifetime.

The changes of the width of the steady state absorption spectra, and the radiative enhancement can be used to estimate the extent of the delocalization [12,13]. Recent studies using picosecond fluorpxnce techniques have led to a better understanding of the radiative properties of a number of molecular excitons, as found in molecular aggregates and polysilanes [14]. From these studies it is clear that the delocalization is limited by the inhomogeneities of the environment.

The delocalized exciton state can be seen as an array of chromophores that oscillate in phase. Dephasing will lead to a reduction of the superradiative enhancement [15]. Experimental evidence which suggests a connection between dephasing dynamics and radiative dynamics was presented recently [16]. A model was presented that connects the two kinds of dynamics. The dephasing dynamics and radiative dynamics of PIC aggregates shows the s h e trend: a decrease of radiative rate is correlated to an increcrse of the dephasing rate.

After we proposed a connection between dephasing and superradiative lifetime for PIC aggregates, Minami and coworkers [17] have reported the same effect in a MQWS. Despite the large differences between the excited states of semiconductors and molecular aggregates, the radiative behavior can be explained by the same model.

Next to the results of time resolved and steady state fluorescence spectroscopy on PIC aggregates I will present fluorescence data of PIC aggregates with trap molecules added. Together with the dephasing behavior and the emission behavior the steady state spectroscopy completes the picture of the coherently delocalized molecular exciton of PIC aggregates.

5.2 Steady state fluorescence

6.2.1. Spectra

In Fig. (5.1) the absorption spectrum of PIC-bromide aggregates at 80 K is depicted. The absorption spectrum shows the two prominent J-bands at wavelengths of 571 m and 576 nrn (Fig. (5.2)). The higher energy region of the spectrum is structured as well, although this structure is not as sharp as the J-ban&. Fiecher and Scherer [18] have studied the absorption spectrum of PIC, and reproduced most features of the epectrum with a relatively simple aggregate model. A circular aggregate consisting of only 5 or 6 units is sufficient to explain the1 position of the J-band. From studies on dimerized PIC solutions the molecular coupling (B) of the unite was determined to be 630 cm-l, and the van der Waals shift (D) 1M) cm-I [19], for PIC aggregates in water. The total exciton bandwidth (W) equals four tipea the molecular coupling (Wr4B). The absorption at higher energy is a combination of absorption by the upper exciton level (k= r ia) , and of vibronic activity of the lower exciton level (k = 0). The relative absorption strength of the two exciton band edges is almost equal, as determined from streaming solutions. The transition dipole moment of the sharp J-bands is oriented along the axis of the aggregate, whereas the intensity around 20000 cm-I originates from a perpendicularly polarized transition.

400 450 S m 860 600

wavelength (nrn)

Figun 5.1 The optical absorption spectrum of PIC aggregates in a 1:l waterlethylene glycol mixture at 80 K . The dashed line shows the spectrum of a solution in the same solvent. Note that this last spectrum has been scaled d m , and that the total oscillator strength does not change upon aggregation.

The width of the absorption profile of the J-bands in waterlethylene glycol is only 30 cm-l, whereas the inhomogeneous width of the monomer absorption is about 1000 cm-l. This reduction of the inhomogeneous width is caused by motional narrowing. The factor of 35 reduction shows that extensive delocalization occurs 1201.

5. Su~erradiance in PIC anmenates 75

Exciting the aggregates with 514.5 nm argon-ion laser light gives rise to a fluorescence epectrum consisting of the two J-bands, exactly rwnant with the absorption and with very little vibrational structure (see Fig. (5.2)). The resonant emission is almo8t atom-like, without influence of the molecular degrees of freedom. A remarkable fact is the absence of vibrational structure in the emission, deapite the presence of vibrational structure in absorption. Apparently, the relative displacement between the ground state potential and excited state potential is negligible. This can be understood on the basis of the delocalization. The extended electronic states have only small amplitudes at the separate monomers, therefore they do not distort the nuclear framework of these monomers to a large extent. The presence of vibrational structure in the absorption spectrum must be the result of a strong anharmonicity of the excited state potential.

565 570 575 580 wavelength (nrn)

Figure 5.2 The absorption (top) and emission (bottom) spectra of the J-band regton of the spectra of PIC aggregates at 1.5 K . The shapes of the emission bands arc the same as the absorption except for a difference in rciative intensity and a s d l deviation of the short wavelength tail.

The 514.5 nm excited emission intensity of the blue J-band is reduced relative to the red band. In Fig. (5.3) the excitation spectra are shown for the two bands. The spectra have the same shape, but show a shift of 150~m-~, which is exactly equal to the separation of the two J-bands. The wavelength of the argon line is indicated by an arrow. The absorption of the aggregates that emit at the wavelength of the blue emission band is somewhat smaller. This fact largely explains the mismatch between absorption and emission intensities for the blue and the red band.

One last aspect of the emission spectrum that must be noted is the influence of residual monomers. Aggregation will never be complete,

because of the formation kinetics. When aggregation proceeds, the monomer concentration drops and consequently the aggregation rate drops. PIC monomers show a broad emission spectrum with a maximum at 580 nrn [21], overlapping the aggregate bands. However, when an excitation wavelength is used of 570 nm, only J-band ernhion is observed. For most time resolved experiment6 an excitation wavelength is used such that also some monomers are excited, therefore the monomer decay has to be taken into account when one analyw the results of the experiments.

4 # ) 0 5 1 0 ~ ~ 6 4 0 ~ 6 # 0

wavelength h)

Figure 5.3 Excitation spectra of blue (dashed) and red (drawn line) J-bands. The detection wavelength was set at the maximum of the respective emission bands. The relative shift of the spectra is 150 em-'.

5.2.2 Emission trapping

In Sect. (4.3.4) I showed that the presence of the thiacyanine dye TD shortens the dephasing time of PIC aggregates. At a mixing ratio as large as 500 to 1 the red site showed shortening of the dephasing time at 1.5K. The influence of the 'I'D molecule on the fluorescence behavior was studied as well. In the steady state emission spectrum a band is found at 608nm. This band can be assigned to trap h i o n as substantiated by two observations, 1) the 608nm band is not present in the emission spectrum of TD monomer solutions, and 2) the emission yield from the trap band is over thousand times higher than would be expected from relative absorptions of PIC and TD at the excitation wavelength. In Fig. (5.4) the spectra of PIC/"ID mixtures with a ratio of lo3 (top) and lo5 (bottom) at 80 K are shown. The two traces are taken from a concentration series

'.- ranging from pure PIC aggregates to mixtures with a loa ratio. Two trends in this aeries are illustrated in Fig. (5.4); the increase of the trap emission with increasing trap concentration, and the loss of intensity of the 571 nm J-band emission with decreasing mixing ratio.

At a mixing ratio of lo3 the integrated trap emission is already three times larger than the J-band emission. The analysis of such trapping data in terms of a size of the delocalization area is very difficult, because

5. Su~t?ITadiZmce in PIC w e n a t e s 77

there are many unknown factora. When one aasumea F6rster transfer, the trapping probability depends on the overlap of the aggregate emission with the 'ID absorption. The narrow J-bands lead to a small overlap, and consequently to a mall transfer probability. The fact that, despite this reduction of the transfer probability, trapping is so prominent seem8 to make it obvious to conclude that the excitation must have a non-negligible amplitude on at lwt thousand monomer sites. In the Discussion I will address the question which information on the exciton size can be obtained from trapping measurements. [22] ,

In order to check the trapping mechanism, the spectra were also recorded at 4.2 and 143 K. The ratios of J-band to trap emission do not change significantly at t h e this temperature range. This indicates that trapping ia not activated, implying that trapping by the TD molecule is barrierlea The absence of a barrier means that an excitation which is formed near a TD molecule "fallsn into a trap.

>, + .- a,

5 + C .-

6 .- a, U).

5

6,S.l. Low hmperature decay

I /v Y

I"

In Fig. (5.5) the fluorescence decay of the red site (576 nrn) of PIC aggregates is shown, the aggregates were excited by a 545 run 5 ps laser

\,

560 580 600 620 640 660 680

wavelength (m)

Figure 5.4 Emission spectra of aggregated samples of PICITD mixtures excited at 545nm at 80 K . The top trace represents a 103:1 ratio, the bottom trace a 105:1 ratio. The bottom trace is indistinguishable from a pure aggregated PIC sample.

pulse. Iterative deconvolution of the instrument response function, gives two decay parameters, 70 ps and 1.7 m. The second component has a small weight, and is caused by residual monomers. The fast decay represents the aggregate superradiant decay. The decay of the 571 nm band is faster and has a time constant of 45 ps. Apart from the two picosecond decays no further decay processes could be identified from the emission in the 565 to 585 nm region.

0 500 loo0 1500 2000

time (ps)

Figure 5.5 Time resolved fluorescence decay of the red site of PIC aggregates at 1.5 K . The dashed curve gives the instrument response.

The quantum yield for emission was not determined directly, but can be estimated. For the relaxation rate of an arbitrary excited state, the following relations hold:

where S. is the pure radiative rate, k, is the nonradiative rate, kc is the fluorescence total rate of the excited state, and #fl ie the emiesion yield. The total decay rate is the same as fluorescence rate observed in the photon counting experiment. For the monomer of PIC the pure radiative rate can be calculated by integration of the oscillator strength using the Strickler-Berg relation (231. Dorn and Miiller [21] calculated 7, =(A;)-'= 3.7 ns. The lifetime of the background emhion is 1.7 ns, and so the monomer quantum yield can be calculated to be 0.46. In case of an exciton many monomer units are coupled together, and the radiative rate increases. The processes that cause nonradiative relaxation in the monomer will lead to nonradiative relaxation of the exciton as well, with the ssme rate as for the monomer. The enhancement of the radiative rate,

5. Suoerradiance in PIC aggregates 79

while at the same time the nonradiative rate stays constant, will lead to an increase of the quantum yield for emission. For PIC this is actually observed in the case of aggregated monolayer samples [24], where the quantum yield is almost unity. Assuming that for solid aolution samples the same phenomenon occurs, I interpret the fluorescence decay time as purely radiative:

At low temperatures the radiative rate of J-aggregates is enhanced by a factor of 53 and 82 for the red and blue sites respectiveiy. In Sect. (5.4) the relation between the superradiative enhancement and the size of the aggregates will be made clear.

6.3.2 Fluorescence depolarization

The decay of the fluorescence polarization ratio p(t) (see Sect. (3.3)) was determined from a series of experiments. p(t) waa found to be equal to zero within experimental accuracy. The estimated resolution of the experiment is 20 ps so this implies that the polarhation ratio decays with a time constant of less than 20 ps. Depolarization of the emission occurs when the transition dipole moment vectors of the excited molecules change direction. An example is the rotation of excited molecules in solution, which randomizes the direction vectors of the excited molecules. Such a rotation is clearly not possible for an aggregate in a solid matrix at 1.5 K. A reorganization of the initially e ited state can rtlso lead to depolarization. For an aggregate one c think of transfer of the excitation into differently oriented regions.

=1: At 1.5 K the depolarization time must be shorter than 20 ps, with no

residual long time polarization memory. At room temperature the initial polarization ratio is p(t=O) =0.3 inatead of the maximum value of 0.4 [25], as measured in pump/probe spectroscopy. This shows that only one quarter of the excitons depolarizes rapidly. A smaller fraction (one eighth) depolarizes with a time constant of 50 ps. The remainder of the aggregates (about 60%) doe.. not depolarize within the fluorescence lifetime. The photon counting experiments presented here, on the comparable room temperature samples do show depolarization, with a somewhat larger constant (100 ps), and a smaller depolarization ratio at long times, Am). One should realize that different states are excited in these two kinds of experiments. In a photon counting experiment a mixture of k-states is excited, according to the oscillator strength and the vibronic activity of these k-states. The initially prepared state relaxes rapidly, thereby partially losing the polarization. The fraction of initially excited states which is vibronically allowed via the k=O state is expected to relax while maintaining polarization memory, corresponding to a p(m) larger than zero. In this way the high doo) at room temperature can be explained. However, the rapid and total depolarization a t 1.5K can not be explained on the basis of excitation of different states alone.

I

6.3.3 Temperatun, dependem

In Fig. (5.6) the fluorescence decays of the red band of PIC aggregates for a number of different temperatures are shown. The trend is immediately clear; the decay time increases with temperature. This contradicts the general rule that a t higher temperatures the nonradiative rate will be higher, caused by thermal motions. Consequently the emission decay time, in general, decreases with temperature. The increase of the decay time with temperature is large; from 70 p8 at 1.5K to 400 ps at 180 K. i

0 lo00 2000 3000

time (ps)

Figure 5.6 Flwescence decays of the red site of PIC aggregates at 4.2 K (drawn line), 90 K (short dash), and 180 K . The time constants of the fast component are 70 ps, 110 ps and 400 ps, respectively.

In Fig. (5.7) a plot is presented of the fluorescence decay times ver~us temperature for both J-bands. The decay does not change upon going from a temperature of 1.5K to a temperature of 50K. From 50 K up to about 190K the measured decay time increases steadily. At still higher temperatures the waterlethylene glycol matrix does not remain rigid. The chromophores can move, giving rise to changes in the aggregate. When the solution liquefies a rapid precipitation occurs, and the aggregate absorption spectra change. The aggregation number changes, which might influence the character of the optical excitation. Therefore I will not consider higher temperatures. The blue aggregate band is also shown in the Fig. (5.7), and exhibits the same behavior.

The relative quantum yields of the two bands do not show large variations. Based on the reasoning of Sect. (5.3.1.) I will assume the absolute quantum yield to be close to unity. The increase of the emission lifetime thus reflects a decrease of the radiative rate. The coupling of the monomers into a superradiant aggregate clearly is disturbed. Possible mechanisms for the decoupling will be discussed in Sect. (5 .4) .

Figure 5.7 Fluorescence lifetime versus temperature for the ~ e d site (0) and blue site (A)of PIC aggregates an wderlethylene glycol 1 : 1 .

At room temperature no aggregates are formed in waterlethylene glycol mixtures. In aqueous solution aggregation can be observed in the presence of certain anions [26], for example KCI (see Sect. (3.8)). The aggregates formed in these solutions show a 400ps fluorescence decay time, in agreement with the transient absorption results of Sundatriim et id. The decay time is similar to the decay time found at 190 K for PIC aggregates in solid solution. However, at room temperature the depolarbation is much dower than at 1.5 K, showing that a different regime of excitation delocalization is reached in the liquid solution at roomtemperature.

The transient absorption experiments [25] clearly show that exciton annihilation occurs when high intensity pulses are used. Fluorescence measurements by means of photon counting can be performed at arbitrarily low intensities and thus do not suffer from decay distortion by annihilation.

6.3.4 Trapping

The spectra presented in the Sect. (5.2.2) indicate that the addition of a molecule TD causes transfer of the aggregate excitation to that molecule. I studied the transfer rate by time resolved photon counting. A shortening of the aggregate emission lifetime is observed at 576 nm, and a long lived trap emission a t 608 nm. The dynamics of the filling of the trap state proved to be too fast to be resolvable.

I propose a simple model for the description of the energy transfer. The exciton is coherently delocalized over a number of units. Trapping will occur if a trap molecule is within the delocalization area. -If the aggregate excitation is confined in a region without a trap, the

aggregate will emit undisturbed. The increase of the number of traps has two effects: the trapping rate kh. will increase, and the total fraction of excitons subject to trapping will also get larger.

The decay of the aggregate emission can be used to clarify the trapping dynamics. In Table (5.1) the data on the aggregate decay are summarized. The table shows that at all mixing ratios studied some normal (non trapped) aggregate emission with the characteristic lifetime of pure PIC aggregates is observed. However the major part of the aggiegates shows very fast emission, caused by excitation transfer. The initial decay can be interpreted as the time constant of the energy trapping process.

Table 5.1 Trapping of aggregate emission at 143 K mix. ratio4 b b

ktmn,fer ")tm,UferC

a) mixing ratio defined as number of PIC monomers to TD monomers b) in units of s-l, determined from initial and residual decay components a t 576 nm, the excitation wavelength was 545 nm C) total multiexponential decay is defined as R(t) = &wiexp(-kit)

I must note that the transfer times (l/kh.) are close to the resolution of the experiment. Especially for the case of one trap to hundred PIC monomers the fast emission is almost instrument-response limited. The emission at 608 nm shows the characteristics of trap emission, at a mixing ratio as high as 10000. A decay component of 5 ns is found, which ia much longer than the 1.7 ns PIC monomer decay. Interpretation of the emission at 608 nrn is complicated by the fact that the decay of isolated TD molecules also shows a component of about 2 ns. Attempts to fit the rising edge of the the trap emission did not give reliable results, therefore I will concentrate on the decay of the J-band fluorescence.

The experiments were repeated at 82 K and 4.2 K. Except for the change of the superradiant decay (see previous section), no major differences were found. The transfer rate and the weight of the transfer component seem to be totally temperature independent. I already stated that the ratios of the J-band to trap band emission showed no temperature dependence over the range studied.

The salient feature of the data presented in Table (5.1) is the variation of the weight of the the fast emission in the J-band. This weight is directly proportional to the amount of aggregates susceptible to trapping. Already a t a mixing ratio of 10000 to 1 one half of the excitons undergo trapping, at a mixing ratio of 100 to 1 trapping is almost complete. In all samples a normal J-band emission can be found, be

5. Su~erradiance in PIC a n e r a 83

it with a mall weight. The deviation of the superradiant decay in the 100 to 1 samples could be caused by the trap emission which already accounts for SO percent of e total emission at 576 nm (not shown). The remnant J-band mimion in 2 icates that a fraction (1-wCr) of the excitone is not connected to a trap, and the decay of the J-band fluorescence is described as:

where

and xr, and x, are the fraction8 of aggregates that are trapped and emit superradiantly, respectively. x, and r, still depend on the mixing ratio.

Two conclusions can be drawn from these trapping results. The first one is concerned with the size of exciton. A t a mixing ratio of 1000:1, 80% of the excitations is trapped proving that within the fluorescence lifetime of 70 ps the exciton has a nonzero probability at 1000 sites. An unknown factor, which remains to be settled, is whether the exciton moves or not. Knowledge about the motion of the exciton and the trapping probability are needed to make the size estimate more exact. The second conclusion is that excluded regions exist for the excitons. The temperature independence of the trapped fraction can only be understood if the excitons me confined to regions on the aggregate. When there is no trap molecule within such a region a normal fluorescent exciton decay is observed.

5.4 Discussion and summary

The two main subjects I want to address in this discussion are 1) the information concerning the number of coupled monomers obtainable from (time resolved) spectroscopy, and 2) the temperature dependence of the superradiance.

5.4.1 Aggregate s h

The determination of the size of the aggregate and the size of the delocdization area has been subject of intense debate. For PIC aggregates the reports vary from anywhere between 4 and 40000 units [25,26]. It is necessary to try to bring some order in this jungle of numbers. This can be done by making an explicit distinction between three relevant quantities, all of which have been interpreted as aggregate size in previous publications. These quantities are: the delocalization area (the size of the exciton), the domain (the region over which the exciton moves), and the physical size of the aggregate (the number of monomers constituting one aggregate).

The delocalization area is the area over which the transition' dipole

moments are coupled together, and the coupled transition dipole moment of the aggregate state determines the radiative enhancement. Two important fadom are the intermolecular coupling B, and the inhomogeneous width a (u is defined as the l/e width of the inhomogeneous .profile g(v) a exp(-v2/u2)). In the cam of absence of dephasing (at T=OK) and negligible site inhomogeneity, o/B= 0, the superradiant rate simply ecales with N, the number of coupled monomers,

where is the aggregate radiative rate and the is the monomer radiative rate. Starting from a perturbative approach, the resulting k=O exciton state carries all oscillator strength, in the case of a circular aggregate (see Chapter 2). For a linear aggregate a redistribution of omillator strength occurs, and a scding factor has to be introduced. Other scaling factors must be used to account for the amount of d a t o r strength "lostn to the vibronic absorption, and for the relative orientation of the transition moments.

The radiative enhancement, L, is given by:

For the red site of PIC aggregates L F e s the value 53. How does this number relate to the size of the delocalization area? It is the minimum size of the delocalization area necessary to explain the increase -of the radiative rate. The transition moments of a t least 53 molecules have to be coupled together. Other factors such as inhomogeneity and lattice vibrations will reduce the effectiveness of the coupling, and lead to a larger value for the number of coupled monomers, N.

The first factor is the fraction of the total exciton oscillator strength present in the J-band. This can easily be determined from absorption spectra. For experiments on streaming samples it was shown [19] that the J-band has a transition moment along the aggregate, a m y h g about 50 percent of the oscillator strength. The perpendicular component carries the other 50 percent of the oscillator strength, which means that the molecular transition dipole moments are not parallel but have a large angle of inclination. Since only one half of the oscillator strength is concentrated in the k=O level, the radiative enhancement will also be reduced by that factor.

A peculiarity of PIC aggregates is the absence of vibrational structure in the emission spectrum, as was discussed before. For the evaluation of the superradiance only the transition moment between the k-0 aggregate level and the vibrationless electronic ground state plays a role. In fact only the oscillator strength of the J-band itself should be used to determine the radiative enhancement. From the work of Fischer I181 it follows that about half of the k - 0 oscillator strength intensity is found in vibronic transitions. In order to correct for this -factor, the value for the number of monomers involved has to be multiplied by a factor of two.

5. Su~erradia~ce in PIC anmenates

Site inhomogeneity also reduces the radiative enhancement 120). For PIC monomers in solution the inhomogeneous width is about 1000 cm-I full width half maximum, corresponding to o = 600 cm-l. This leads to o/B = 1, so '

no extensive delocalization is expected. However, the value for u ie determined from a monomer solution. The site energy spread within the aggregate is much smaller. Numerical simulations for small aggregate sizes (small means that the aggregate size determines the size of the delocalization area) show that the value of o/B=l leads to a significant reduction of the enhancement, and consequently to a much larger N to explain the value of L. Recent numerical simulations by Fidder [27] show that a value of a/B=O.l corresponding to a site energy spread of the units in the aggregate of Wan-' leads to reasonable values for the radiative enhancement. Another result of the calculations is that for large aggregates a limiting value for the delocalization area is reached. This maximum size only depends on o/B [n]. Both the numerical approach for mall and large aggregates show that inhomogeneity reduces the radiative enhancement. Since the aggregate is ordered, it can be expected that the inhomogeneities in an aggregate are correlated. In the limit of infinite correlation the full superradiant enhancement (Eq. (5.6)) is recovered.

The last factor that is involved when relating the radiative enhancement to the number of involved monomers is the amount of oscillator strength in higher k-states. For a circular aggregate without inhomogeneity all oscillator strength is concentrated in the k=O level. For a linear aggregate only 81 percent are found in the k = 0 level and the other 19 percent are found in higher exciton states.

The procedure to estimate the size (number of participating monomers) of the superradiant excitation consists of the following steps: 1) determine the pure radiative rate of aggregate and monomer in order to calculate the enhancement L, 2) estimate the geometrical factor (cos2a) in order to determine the total oscillator strength in the k=O level, 3) determine the exciton bandwidth (B) and the inhomogeneity (a). These three points can be put in a simple formula:

where 0.81 is a reduction factor because of the linear geometry, and fd and fw are the reduction factors caused by vibronic mixing and inhomogeneity. Assuming absence of inhomogeneity (fid = I), and taking the geometric factor as 0.5, the m i n i number of participating monomers can be calculated to be 265 units for the red site of PIC aggregates. The blue site of PIC aggregates shows a fluorescence decay of 45 ps. The same reasoning aa for the red site gives a lower limit of N=410.

The motional narrowing effect of the absorption lineshape can also be used to make an estimate of the size of the delocalization area as was shown in Chapter 2. The reduction of the inhomogeneous width with a factor 35 leads to an estimate of thousand coupled units. Non-negligible correlation of inhomogeneity leads to a higher estimate. If the correlation length is a few units, the observed line narrowing can be

reproduced, but only when assuming a larger number of coupled monomers (N). Since the environment of neighboring molecules in the aggregate wil l be very similar some correlation of inhomogeneity is expected, B = exp( - 1/C) > 0 [ref], where lo is the number of monomers over which the correlation extends. The superradiant rate has a complicated dependence on the inhomogeneity. The numbers of 250 and 400 units are valid in case of absence of inhomogeneity w total correlation of inhomogeneity. The reason behind this fact is that the collective resonance of the monomers ie moat effective in case of abeence of energy differences between monomers, oo a= 0 w ,9 11. The latter condition however, ie not realietic becauee in that limit no motional narrowing is observed.

An estimate for the site inhomogeneity in the aggregate is alBwO.1. Clearly, this does not represent the limit of negligible inhomogeneity. A nonzero correlation length lo will increase the number of coupled monomers needed to explain the observed superradiant enhancement. These two facts make it hard to get a precise value for the inhomogeneous reduction factor, f* However, it may be clear that the number of coherently coupled monomers for PIGbromide aggregates in a water/ethylene glycol matrix at 1.5K is considerably larger than the minimum number. A value of 500 units does not seem unreasonable.

The spectroscopy of mixed PIC/TD samples can be used to estimate the size of the domain over which the exciton can move. The interpretation of excitation trapping is complicated by the lack of information about the percentage of TI) molecrllee which are is bound to the PIC aggregates. The most important parameter in the trapping process is the trapping rate k,. This rate is dependent on the number of traps, and the interaction strength of these traps with the exciton. Time resolved fluorescence of the J-band emission shows that the trapping rate is about 4x1010 s-I = (a5 pa)-'. The trapping can be ascribed to those excitons that are formed in the vicinity of a TD molecule. On the basis of the time resolved tkapping experiments it can be concluded that the domain size must extend over thousands of units. A precise determination is not possible because of the unknown binding propertiea and the unknown coupling of aggregate and trap state. The shortening of the dephasing time of mixed aggregates that was described in Chapter 4 can be explained by the same trapping mechanism. In those experiments a detectable shortening of the echo decay at 1.5K was observed in samples with a mixing ratio of 1000:l. A trapping rate of (25ps)-I is sufficient to explain that shortening. The shortening of the dephaeing time therefore can be assigned to the same energy transfer process that leads to emission trapping.

The number of 50000 units coupled units that waa proposed for PIC aggregates a t room 9 p e r a t u r e in solution refers to the delocalization domain [25]. In these experiments the exciton annihilation behavior was studied. From the fluorescence lifetime of 400 ps and the narrowing of the aggregate band, assuming unity quantum yield for emission, the delocahation can be estimated to be in the order of 50 units. The experhmtal results can be explained by an exciton with a delocalization area of 50 units, which can move over a domain of 50000 units. This rapidly moving small exciton is clearly different from the low temperature exciton studied in this work. This low temperature exciton

5. Su~erradiance in PIC anmenates 87

can be estimated to be delocalized over about 500 sites and the domain size is much smaller than 50000.

6.4.2 Temperature dependence

Up to 50 K the fluorescence decay time does not change, but above that temperature an increase approximately linear with temperature is observed (see Fig. (5.7)), reflecting an increase of the radiative lifetime. From the considerations above it follows that the radiative rate is proportional to the number of coupled chromophore units. An increase of the radiative lifetime (decrease of the radiative rate) would imply a decrease of the size of the delocalization area. However, it was shown recently that at higher temperatures the radiative enhancement can be reduced, without reduction of the delocalization area [15].

The linear relation of temperature and radiative lifetime for aggregates in El-films has been suggested before by Kuhn and Mobius [22]. Their conclueion was based on careful steady state energy transfer measurements, without direct evidence from time resolved data. Recently, studies of the radiative behavior of GaAs/AlGaAs Multiple Quantum Well Structures (MQWS) again showed a linear relationship of the radiative lifetime and the temperature [16]. Very recently, a report has been given of the same phenomenon in a GaSe quantum well [17]. What do these widely different systems have in common? In all cases the electronic excitation is confined, and oscillator strength of a large volume is projected into only a small number of states. These confined states all show incresed radiative rates.

The increase of the superradiant emission lifetime with tempbrature was proposed by Kuhn on the basis of trapping experiments. The yields of trapped and non-trapped emission were analyzed starting from the aesumption of rapidly moving excitons which average the interaction with the traps. For excitons on PIC aggregates this assumption does not hold: a fraction the excitons can be trapped, and the remaining fraction cannot reach a trap. In the Kuhn model all excitons are susceptible to trapping, and the temperature dependence is assigned to an increase of the superradiant rate combined with a constant trapping rate. PIC aggregate excitana show an increase of the radiative rate, as can be concluded from direct rate meaeurernents. The ratio of the emission yields in trapping experiments however, does not show any temperature dependence, because of the presence of a non-trapped aggregate fraction. Studying the time resolved trapping dynamics of mixed B-layers should clarify whether or not the decrease of emission ratio really reflects a decrease of the superradiative rate. At present there is reason to believe that the assumption of a freely moving excitbn through the whole LB-layer does not hold.

Feldmann et al. [16] were the first to propose a correlation between the homogeneous width and the measured lifetime. In Fig. (5.8) for PIC aggregates both the dephasing times (T,) and the radiative lifetimes are depicted. Below 50 K the change of the dephasing time is not followed by the superradiant decay time. Above that temperature however, thk correlation is evident.

Figure 5.8 Dephasing rate and fluorescence lifetime of the red site of PIC aggregates 0s a function of temperature in one figure. The similarity of the two sets of dots .'points suggests a connection between homogeneous linemidth and radiative decuy time. J

In order to gain further understanding of the emission properties a thermalized distribution of ideal 1-D excitons is assumed. This assumption is justified by the fact that the excitation occurs in vibronic k=O levels and k=n/a levels. The relaxation through the band will guarantee that the optically allowed levels will not be populated coherently and that the resulting distribution will be more or less thermal. For a circular aggregate where only the k=O exciton carries oscillator strength a t T SO, all population will relax to the lowest k-state and the full superradiant rate (Ny) will be observed. At higher temperatures dephasing will occur, with the reeult that the different k-etates will be mixed. In the high temperature limit the scattering to other exciton states will be much faster than the radiative rate, leading to an equilibrium distribution over the exciton states at all times. Because only a fraction of the population is found in the optically allowed state, the full superradiative rate is not observed.

For a ideal 1-D exciton in the high temperature limit, the superradiative rate is directly proportional to the Bolt!zmann population factor of the k=O level. It is therefore essential to incorporate the density of states of the excitons. Since the energies of a linear chain are distributed according to cos(lrk/N), the density of states at the bottom of the band can be approximated as n ( & ) d ~ a I/*. For example for N = 265 and B = 630 cm-I the level spacing of the bottom k-states is only about 0.05 cm-'. The density of states of a 1-D exciton decreases at for energies just above the k = 0 state, so the population of the k = 0 state will decrease only slowly with temperature. A density of states that

5. Su~erradiance in PIC anmenates 89

increasee (at least linearly) would be necerrsary to provide an acceptable match to the data.

At this point I want to $scum the radiative behavior of a MQWS as found by Feldmann and coworkers. The oadlator strength of an exciton in a semiconductor is determined by the overlap of electron and hole. Thie means that a large exciton has a small transition dipole moment, and vice versa. If such an exciton is confined by the geometry of the MQWS, the exciton will be squeezed in one dimension, and the overlap of electron and hole will increase. The larger overlap leads to a larger transition dipole and thus to faster (superradiant) decay.

The exciton in the GaAslAlGaAs MQWS show the same linear increase of radiative lifetime with teunperature aa PIC aggregates. The decay rate is assumed to be proportional to the population of the optically allowed energy level (k=O). The width of the exciton absorption is determined by the dephasing that is governed by the interaction with phonona. An increase of the temperature leads to a broader exciton line. At the same time higher states will be populated thermally. When this thermd population of phonon statea will be broader than the exciton line (kT>rh), k-statea outside the optically allowed transition will be populated. The superradiant decay wil l be slowed in proportion .to the population of the emitting exciton level [28].

The loas of population to higher non-superradiant levels is determined by the density of etatea of the exciton band. For a 2-D exciton this density of etatea is constant. This means that at a given increase of the thermal energy AT, the same amount of new states becornea available, or directly related to that fact, that the temperature dependence of the radiative lifetime is linear.

The experiments on layered GaSe by Minami and coworkers do show also this behavior. In this compound quasi 2-D excitons exist, because of the confinement inside the crystal layere. The homogeneous line was measured directly, using two pulse photon echoes. The results completely agree with the experiments cited on the MQWS, showing the generality of the approach. It is interesting that for GaSe excitons, just like PIC aggregates, a plateau in the temperature dependence is observed. Only above 25 K the linear increase of the radiative lifetime is observed.

The following model emerges for the relation between radiative lifetime and dephasing. The initially excited state relaxes to a thermal equilibrium. A t TPOK the pure exciton state will be populated, leading to the full auperradiant decay rate. At higher temperaturea dephasmg wil l set in, leading to comanmication between different k-states. In the limit where the line broadening is larger than the thermal energy (rh(T) > K T ) , the radiative rate will be reduced in proportion to the homogmeou width. In the w i t e limit of small broadening (rh(P) <kT) the rate will be reduced according to the Boltpnann population factor, including the deneity of stabse.

The excitons in PIC aggregates are an example of 1-D delocalization. However, other (molecular) degrees of freedom could be involved, for example vibrations, to explain the deviation from a 1-D density of states necessary to explain the linear temperature dependence. Another interesting point is that a t low temperatures a plateau is observed, indicating that a relatively large (tens of cm-l) energy has to be

present before reduction of superradiance sets in. The change of the radiative rate is not the result of a reduction of

the delocalization area, but is caused by scattering of the exciton to non-emitting k-etatea. A of the excitation area is only expected when the site inhomogemeities insidt the aggregate would change (a relative to B), and not for changea of the homogeneous width (rh relative to kT).

5.4.3 Summary

In this chapter I have shown that PIC aggregates ehou a superradiant decay, that ie about 53 times (red site) and 82 timea (blue site) faster than the monomer decay a t low temperaturee. Since the amount of oscillator strength in the aggregatf, band is a fraction of the totid oscillator strength, it must be concluded that the number of coupled molecules must be much larger than the radiative enhancement. Minimum numbers of coupled unita are 265 and 410 for the red and blue sites respectively. Considering site-inhomogeneity l& to even larger numbers necessary to explain the radiative enhancement.

The results cannot be directly applied to room tempi?rature J-aggregates in solution. The 400 p fluorescence decay indicates that even at room temperature considerable delocalization of the aggregate excitation occurs. TQe $low depolarization of the fluorescence however, shows that the initially formed excitatipn is confined to a well defined (oriented) part of the aggregate.

An increase of the superradiant lifetime of PIC aggregates in solid solutions with temperature is observed. This effect is attributed to the removal of population from the superradiant state. The linear dependence of the superradiant Metime on temperature is also found from recent measurements on confined excitations. Further experimental and theoretical developments must clarify the background of this universal behavior.

C. Kittel, Introduction to Solid State Physics, Wiley, New York. J. Renkel, Phys. Rev. 37, 12'76 (1931). A.S. Davydov, "Theory of Molecular Excitons" (McGraw-Hill, New York, 1962). R. Dmgle, in "Festkiirperprobleme: Advances in Solid State physics", vol 16, ed. H.J. Queieser (Pergamon/Vieweg, Braunschweig, 1975). D.S. CXlemla, S. Schmitt-Rink and D.A.B. Miller, in "Nonlinear Optical Properties of Semiconductors", ed. H. Haug (Academic Press, New York, 1987). E. Hanamura, Phys. Rev. B 38, 1228 (1988). R. Roeetti, J.L. Ellison, J.M. Gibson and L.E. Brus, J. Chern. Phys. 80, 4464 (1984). J. Warnoch and D.D. Awschalom, Phys. Rev. B 32, 5529 (1985). E. Hanamura, Phys. Rev. B 37, 1273 (1988).

3. S-ce in PIC annrenateg 91

10. C. Scheibe, Angew. Chem. 49, 563 (1936), Angew. Chem. 50, 51 (1937), Angew. Chem. 50, 212 (1937).

11. E.E. Jelley, Nature 138, 1009 (1936), Nature 139, 631 (1937). 12. E.W. Knapp, Chem. Phys. 86, 73 (1984). 13. S. De Boer, K.J. Vink and D.A. Wienana, Chem. Phys. Lett. 137, 99

(1987). 14. Y. Ohsako, J.R.G. Thorne, C.M. Wp, J.M. Zeigler and R.M.

H o c h s t r ~ , J . Phya. Chem. 93, 4408 (1989). Y.R. Kim, M. Lee, J.RG. Thome, R.M. Hochstraaeer and J.M. Zeigler, Chem. Phys. Lett. 145, 75 (1988).

15. J. Grad, C. Hernandez and S. Mukamel, Phys. Rev. A 37, 3835 (1988), F.C. Spano and S. Mukamel, J. Chem. Phys. 91, 683 (1989).

16. J. Feldmann, G. Peter, E.O. Gobel, P. Dawson, K. Moore, C. Foxon and R.J. Elliot, Phys. Rev. Lett. 59, 2337 (1987).

17. F. Minami, A. Hasegawa, S. Asaka and K. Inoue, J. Lumin. 45, 409 (1990).

18. P.O.J. Scherer and S.F. Fischer, Chem. Phys. 88, 269 (1984). 19. B. Kopainsky, J. Hallermeier and W. Kaiser, Chem. Phys. Lett. 87, 7

(1982). 20. E.W. Knapp, Chem. Phys. 86, 73 (1984). 21. H. Dorn and A. Miiller, Chem. Phys. Lett. 130, 426 (1986). 22. D. M6bius and H. Kuhn, Isr. J. Chem. 18, 375 (1979). 23. S.J. Strickler and R.A. Berg, J. Chem. Phys. 37, 814 (1962). 24. H. Dorn and A. Miiller, Appl. Phys. B 43, 167 (1987). 25. V, Sundstr6m, T. Gillbro, R.A. Gadonm and A. Piskarskas, J. Chem.

Phys. 89, 2754 (1988). 26. E. Daltroszo, C, Scheibe, K. Cgchwind and F. Haimerl, Photogr. Sci.

Eng. 18, 441 (1974). 27. D.A. Wiersma and H. Fidder, private communication. 28. H. Fidder, J. Knoester and D.A. Wiema, Chem. Phys. Lett. 171,

529 (1990). 29. E. Michelbacher, 2. Naturforsch. lla, 790 (1969).

Picosecond pumpfprobe and time comlated single photon ooMflns experhenfa on TPY aggregafes.. excitons and pol='om

6.1 Intraduction

6.2 Polaron concept

6.3 Results

6.3.1 Spectra of monomere and aggregate8

6.3.2 Pwnp/probe experimenfe

6.3.3 Homogemow l h ~ b p e

6.3.4 Monomer propertie8

6.3.6 TC,SPC reeulb

6.4 Discussion and emunary

Rderences

6. TPY-annrenates. Excitons and Polarons

6.1 Introduction

It was recognized early that adequate descriptions of optical excitations in solids must incorporate the influence of the coupling of the optical excitations to phonons [1,2]. Without exciton-phonon coupling the zero order state ia an exciton, with exciton-phonon coupling this changes. As was shown in Chapter2, in particular limits the. mixed excitation is best described as a polaron. A polaron is an electronic excitation which drags a lattice deformation along with it. Polaron states are wed to explain the spectroscopy of polymers and semiconductors [3-51. In a number of molecular systems, the energy gain which is the result of the mixing of exciton and phonon states can be so large that self-trapping can take place. Self-trapping of excitations has been obeerved in pyrene and perylene [%I. The self-trapping in crystals of the last two compounds is the result of excited state dimerization (excimer formation) in the lattice. A related form of self-trapping has been found in Wolffram's red salt, a quasi one-dimensional platinum salt (71. The pure electronic self-trapping effect has been observed in some alkali halides [8].

The J-aggregates of PIC that were discussed in the preceding chapters are an example of strong coupling of the excited states of the monomers. The exciton that is formed is coupled only weakly to the lattice. The TPY aggregates, which are eubject of this chapter, show strong coupling of the monomer excited states, but the excited states also show strong coupling to the lattice. The coupling to the lattice has a profound effect on the spectroscopy. The optical absorption spectrum of TPY aggregates is shifted strongly relative to the monomer spectrum. However, no large motional narrowing effect is observed, and no resonant aggregate emission is found.

The study of molecular aggregates that exhibit strong exciton-phonon coupling is relevant to the study of photobiological systems. The coupling of chromophores in antenna complexes and reaction centers is strong, and "aggregate" states are formed. However, the absorption bands are very broad, and only a ranall amount of emission ia observed. The reaeon for this fact is that low frequency modes of the protein networks surrounding the antenna complexes couple to the extended exciton states [9,10]. The strong chnwophore coupling in photosynthetic systems only leads rapid transfer of energy to acceptor molecules, and does not not lead to an incream of the radiative rates. The energy transfer is neceesary to inhibit radiative relaxation of the initially excited molecule.

The aggregate studied in this chapter is TPY (the structure is shown in Fig. (1.1)) in polycarbonate. A strongly enhanced optical frequency doubling efficiency was reported by Wang [ll]. The high doubling efficiency shows that the molecules are ordered in the aggregates. At first we thought that in TPY aggregates a more extensive delocalization than in PIC aggregates might occur. This turned out not to be true but a number of other phenomena was encountered.

The first report on TPY aggregates dates back to work of Dulmage et . [12]; they studied the light-induced conduction properties of

aggregated samples. In the course of that work the structure of a model system was resolved by X-ray diffraction [13,14], showing that TPY aggregates consist of layers of molecules. More recently Marchetti et al. [15] made a study of the DC Stark effect and tried to interpret their data in terms of aggregate layers which interact strongly. The crystal and aggregate spectra have been interpreted by Young et d.[16]

The present chapter consists of a eummary of the concepts of exciton-phonon coupling presented in Chapter 2, followed by the results of time reaolved experiments, and the discussion of the dynamics of TPY aggregates. I will show that the optical excitation which is formed initially is a polaron. This polaron is a delocalized aggregate state, extending over many molecular units. From pump/probe spectroscopy it can be concluded that the polaron excitation relaxes rapidly to a localized state of lower energy. The transfer can be understood from a model involving self-trapping of the extended state. The interpretation is complicated by the occurrence of Fiirster energy transfer between different aggregates.

6.2 Polaron concept

The energy of an aggregate exciton contains a static and a dynamic contribution. The static contribution is caused by the local energy differences, 4, which are the reault of the different orientations of the molecules around the exciton. The dynamic part of the coupling either leads to scattering of the exciton, which is accompanied by either a change of state, or leads to an energy change of the excitation.

The basic Hamiltonian for a molecular exciton interacting with phonons is (see Sect. (2.3)):

The first summation over the sites n represents the exciton term including inhomogeneity. The exciton-phonon coupling is split in a transfer term which describes the influence of the phonon interaction on the delocdhation over the ~ites, and a local term which describes the changes at site n. Finally a phonon term ia present to include the phonon energies. A delocalized state exists when the transfer term J,,,,, leads to an intermolecular coupling, B, which is larger than the spread of the site inhombgeneitiee a (this spread is defined as the l / e half width of the distribution of site energies 4). Two limiting cases of the exciton-phonon coupling are dominant intersite transfer, and a dominant local deformation. In the former case the resultant state can be described as an exciton scattered by phonons. When the latter (local) exciton-phonon term is dominant a potential deformation occurs along the phonon coordinate, resulting in a polaron state.

Self-trapping of a delocalized state can occur in the limit where the coupling of the units is large enough to overcome the inhomogeneities, B>a. This condition implies that the state which is formed after optical excitation is a delocalized exciton or polaron. The extent ~f the

6. TPY-aggregates. Excitona and Polarow 95

relaxation of thia delocabed state dong the deformation coordinate will determine the chatacter of the final state. Only in the limit where the relaxation energy ie larger than the bandwidth of the d e l w state self-trapping can occur. A transition of the delocalized aggregate state into the localized self-trapped state is accompanied by the collapse of the extended state into a single molecule state. Static and dynamic spectroscopies reflect the transition between these two regimes.

8.3.1 Spectra of monomers and aggregates

In Fig. (6.1) the absorption and emission spectra of 'IPY monomers and aggregates are depicted. In the monomer spectra (left side of Fig. (6.1)) no sharp features are 0bSe~ed in either absorption or emission. The shape of the monomer absorption spectrum deviatea slightly from a Gaussian of width of 3000 an''. Thia width is extraordinarily large for a dye molecule in polymer matrix. Therefore a large fraction of the width may be caused by vibmnic activity. The monomer fluoreecence maximum shows a large shift relative to the absorption maximum, indicating that the excited state relaxes strongly. The pure electronic transition can be estimated to be located a t the low energy side of the abrp t ion at about 620 nm (16100 an-').

4QO#K)aoo7ooemwo ~ s o a s a o 7 0 0 0 9 0 0

wavelength (nm)

Figure 6.1 Absorption (dram line) and emission (dashed) spectra of TPY monomers ( l e f t ) and aggregates (right) at 80 K.

The absorption spectrum of the aggregated sample differs markedly from the monomer spectrum. A ~trongly red-ehifted absorption is observed at 685 m (14800 cm-l) with a broad tail at 1500 a" higher energy. Aesuming that the coupled molecular transition dipoles form a linear chain, the optically allowed state ie the k = 0 exciton level. The aggregate absorption is red-shifted by more than 1500 a - I relative to the monomer. The shift is the sum of a van der Waals shift and a monomer coupling term. When, as for PIC aggregates, the red shift is dominated by the intermolecular coupling, this coupling must be about 700cm-I, and

the total exciton bandwidth (48) must be 2800 cm'l. Although a large red shift is observed, no strong narrowing effect is obeerved. The width of the exciton absorption b 1700 un-l, similar to isolated dye molecules in polymer matrices. No la,@ amount of oscillator strength is present in the top of the exciton band [12], therefore it can be concluded that significant narrowing of the !absorption profile does not occur.

The large red shift of the aggregate emission relative to the absorption implies that the aggregate excited state which is prepared after absorption relaxes strongly. TPY and PIC aggregates show comparable coupling strengths ( B ) and monomer inhomogeneities (0) . The absence of motional narrowing and resonant emission in TPY is caused by strong coupling of the exciton to the lattice.

0.3.2 Pump / probe experiments

By pump/probe experiments the change of the absorption coefficient of the sample is detected a t short time delays after the passage of a pump pulse through the sample. Mapping the absorption change as a function of time and excitation wavelength gives information about the transient abeorption spectrum.

The pump and probe pulse can either come from the same h e r , or from two different lasers. In the former case the time resolution is better, because it is determined by the intensity autocomkrtfon. In the latter case the time resolution is determined by the intensity crosscorrelation. In general the time jitter between pulses of two different synchronously pumped dye-lasers completely determines the crosscorrelation. The autocorrelation1 function of the pulses used was typically 4 ps wide, whereas the crosscorrelation was about 15 p. The advantage of using two different lasers is the separate tunability of the puhp and probe wavelengths. The fastest experimental way to achieve the wavelength scan is to use a continuum probe and optical multichannel detection. Scanning two lasers is more time consuming but leads to the same results. I

In Fig. (6.2) a result of a single laser pump/probe experiment is shown. The two transients are responses a t different wavelengths. The upper trace was detected at the maximum of the aggregate absorption (680nm) and can be fitted with a decay component of 45ps and a component of about 3.5 ns (the total trace is not shown). The lower trace has been measured with pump and probe wavelengths of 670 nm. At this wavelength the bleaching grows with the same time constant of 45 pe to and after that decays with a time constant of about 3.5 ns. The long component is not easily measured because of the impractical long optical path length differences nece8w-y for those experimente. - The metuured pump/probe did not show any depolatization at the temperatures considered (1.5 to 80 K). Within the experimental error the po lka t ion ratio p(t) (88% Sect. (3;2)) was coneta&. Some initial depolarization may occur, but the value of p(t) was close to 0.4, which is the theoretical maximum for a random sample.

The two-color pump/probe experiments were done in two ways. First the pump wavelength was varied, and the probe wavelength was held fixed. Independent of the pump wavelength the same transient response was found.

6. TPY - ~ e n a t e s : Ex- - 97

When the reverse experiment is performed, pump wavelength fixed and probe variable, the transient spectrum is recorded. The pump was tuned to the maximum of the absorption around 680 nm, and the probe was scanned from 625 to 705 nm. A8 can be seen from Fig. (6.2) the 45pe fast component and the slow component behave differently. The fast component changes from a bleaching into an increased absorption at around 675 nm, while the slow component changea at 665 nm. In Fig. (6.3) the tranemission changes are plotted as function of the probe wavelength. It must be noted that the zero crossing points of the two curves are located a t positions in the absorption band close to the maximum, and do no coincide with the edge of the absorption band. The increased absorption at wavelengths shorter than 665nm, shows that a t these wavelengths the transition strength between the initially excited state and higher states is larger than between the excited state and the ground state.

probe delay bs)

Figure 6.2 Pwnplprobe measurements of TPY aggregates an a polycarbonate mat* at 1.5 K. The top trace was recorded at a 'u~ouelength for pump and probe of 680 nm, the middle trace at 670 nna. The bottom trace (dashed) is the pulse autocornlath.

The two time constants, 45 ps and 3.5 ns are present in all decays at different wavelengths. This statement does of course not hold for the respective zero-crossing points, but the growth dynamics of the signal at 670nm in Fig. (6.1) can definitely be fitted with the same time constants as the decay at 680 nm.

The main portion of the experiments was performed at a temperature of 80K. At this temperature kT is in the order of 55 an-', which might influenw the dynamics. However, the experiments that were performed at 4.2K gave the same results for the kinetic constants, showing that the obeerved processes are not energy activated. One difference must be noted: the zero crossing point for the transient absorption shifted to somewhat longer wavelengths (3 to 4nm). This observation can be explained by thermal population of ground state levels at higher temperatures.

- wavelength (nm)

Figure 6.3 Relative bleaching as function of the wavelength of the probe pulse, ( A ) is the fast 45 ps component, a d (0) is the 3.5 ns component. Note that a negative bleaching is the same as an increased absorption.

In the femtosecond laser lab a series of experiments on TPY was performed [la), using a colliding pulse modelocked (CPM) laser, which has a pulsewidth of 50 fs. Fast transients were found but turned out to be very intensity dependent. Analysis in terms of biexcitonic annihilation model [21] proved to be fruitful. Apparently too many excitations are made on one aggregate, and "collisions" can take place. The remedy for this problem is the lowering of the peak intensity of the pulses used, at the expense of the signal-to-noise ratio. The pulse intensities used in the femtosecond experiments, about 300 to 6000CcJ/cm2 per pulse, are about two orders of magnitude higher than the picosecond pulse intensities of 5 to 20 pJ/an2. The intensity dependence of the picosecond pump/probe transients was checked, and no effect was found. Besides the 45ps transient no fast transients which can be assigned to free excitons were found wing BM laser laser pulses.

6.3.3 Homogeneous lineshape

Rom the transient spectrum depicted in Fig. (6.3) it can be inferred that a pulse with a well determined wavelength bleaches the whole band. Such a time-reaolved holeburning experiment shows that the "homogeneousn lineshape b very broad (-1000 m'l) at 80 K. No narrow zero phonon line (2PL) feature is present, because either when pump and probe pulses have the same wavelength or when wavelengths differing about 5 nm are used, the holedepth is the same. Experiments performed at liquid helium temperatures give the same results. This behavior resembles that of some chromophores in glasses [17], where the chromophore transition and the

6. TPY - a w a t e s : Excitons and Polarom 09

motions of the matrix are coupled strongly. In thew systems most absorption is found in phonon-coupled transitions. In a standard stesdy state holeburning experiment no permanent hole was found. This could mean that the efficiency for permanent holeburning ia very low. However, the wide band muat be bleached as a whole, therefore only a very d effect is expected at the burn wavelength..

In Fig. (6.4) a stochastic accumulated echo trace is shown, together with the autocorrelation trace. The intensity used in the experiments was ten times smaller than in the pump/probe experiments. The strength of the accumulated signal is large, 80 large that reliable pump/probe measurements around t=O could only be made with the traveling wave modulator in one of the bssms (see Sect. (3.3)). The echo response (top trace of Fig. (6.4)) resembles the field correlation (bottom trace of Fig. (6.4)). This observation leads to the conclusion that the dephasing time T,, must be much shorter than the field-correlation width of the exciting light pulses. Othemhe the echo trace should show a decaying tail at t>O.

probe delay (ps)

F i g u n 6.4 Response of T W aggregates at 1.5 K to stochastic excitation ( top) . The center wavelength of the exciting light was 680 nm, the fW correlation is s k in the bottom trace. The width of the intensity cornlotion in this expetinent tws about 20 ps.

The absence of a decaying echo signal shows that the oscillator strength is dispersed over phonon-coupled states. The echo decay reflects the Fourier transform of the lineshape: the very fast decay is related to a very broad "homogeneousn line. If some of the oscillator strength is present in the zero phonon line, a component with a normal decay can also be observed. Actually, for some dye molecules complex beating decays are obeerved, in which case the decay traces can be Fourier transformed to the quasi-homogeneous lineghape [17].

6.3.4 Monomer pmpertiea

In Sect. (6.3.1) the abeorption and d i o n spectra were presented. The radiative lifetime of the TPY monomer can be detadned from the absorption spectrum using the Strickler-Berg relation [20]. Dulmage et al. [12] calculated a value of 8ne for the radiative lifetime from the absorption spectrum. Nonradiative proceases are expected to shorten the fluore8cence lifetime to less than 8.0 ns.

In our previous publication on aggregates of TPY, (191 some preliminary time resolved fluorescence results with nanosecond resolution were presented. These preliminary photon counting measurements on TPY monomers yielded a 1.5 ns decay time [19]. The reinvestigation with the new time resolved fluorescence setup showed that the radiative dynamics is more complicated. The fluorescence decaya turned out to be concentration dependent, and strongly nonexponential. However, in low concentration samples TPY in PMMA, the decay was exponential with a 4 ns time constant. Low concentration TPY samples in glycerol showed a 3.5 ns decay time. The quantum yield for radiative emission can be deduced from the ratio of the fluorescence lifetime and the purely radiative lifetime, and is about 0.5.

For concentrated samples transfer of energy between monomers occurs. For example, a concentration dependent red-shift of the emission, and concentration dependent decays are observed. In those concentrated samples a 300 ps pump/probe transient was detected [19]. We tentatively assigned the discrepancy of absorption recovery and emission lifetime to dipolar relaxation of the matrix around the excited molecule. However, on the basis of the better fluorescence data, the 300ps decay must be assigned to energy transfer. I t presents an average of the transfer time of the excitation. The signal-to-noise ratio of the pump/probe data is not good enough to allow for biexponential fitting, so a real match to the emission data is hard.

I conclude that the radiative lifetime of the TPY monomer is 8 ns. In PMMA and glycerol the ernhion lifetime is 4 ns, leading to a quantum yield of 0.5. I aasume that these numbers also hold for TPY in polycarbonate.

8.3.6 Time Correlated Sfngle Photon Counting retsulta

In Fig. (6.5) three fluorescence decay traces are shown, recorded at wavelengths corresponding to three different positions in the fluorescence spectrum of TPY aggregates. The top trace is representative for the broad structureless emission detected from 600 to 700 nm. The middle trace belongs to the short wavelength side of the band centered at 750 nm, while the bottom trace was detected a t the long wavelength side of the 750 nm band. On inspection, it is clear that the traces shown present totally different regimes. The h i o n band from 600 to 700 nm originates from residual monomer

in the aggregated samples. The the-resolved data show the same fluorescence decay time of 3.5 ns in the wavelength region from 600 to

- 6. TPY -tea: Excitone and Polat~na

700 nm. This long lifetime and the high yield for emission exclude the possibility of vibronic emission of aggregates. The emhion spectrum matchea that of the monomer, and the lifetime is close to 4 M found for TPY monomer in PMMA. When the excitation wavelength WAS varied while monitoring the &ion at 700 nm, the relative weight of the 3.5 ns

1 component decreased from 0.17 with 585 nm excitation to 0.05 with 650 nm excitation. This show that the slow -on in the specified wavelength region follows that of the monomer.

time (ns) Figure 6.5 Fluorescence decays of TPY aggregates at 80 K at three different wavelengths indicated in the figure. See text for expklmcrtion.

A ranall component with a very short lifetime (about 30 ps) is observed at 690 nm, a wavelength corresponding to the onset of the emission band centered at 750 m. A t longer wavelengths the weight of the fast campnent rapidly inmeases,- relative 6 the 3.5m component, Upon manning to longer wavelengths the average initial decay constant gets larger. The word "averagen haa to be used because the initial decays are strongly nonexponential. Since the fluorescence decay traces appear to be the sum of many (more than three) exponentiala I will not strese the qwthat ive r d t e too much.

At 700nm the initial decay lengthem to 150ps, and the -weight increase8 aa well. Upon sh'dting the detection to even longer wavelengths, the decay times get longer. This trend continues up to 775nm where the initial decay ie about 0.911s and the residual long component is 2.4 ne. The lengthening of the initial decay time indicates that transfer of energy towards aggregates absorbing a t lower energy take8 place. Energy transfer shows up from a longer risetime of the low energy emission. The first 500 ps of the aggregate emission detected at 800 nrn was compared to the emission of Styryl9 dye, in order to estimate

the risetime. The result is that the growth of the emission signal of the aggregates is slower than that of %he dye. The time constant of the growth of the aggregate emission is about 50 ps. The nonexponentiality of the decays, together with incomplete knowledge of the instrument response of the detection, do not allow for more precise determination of the risetime.

As was mentioned earlier most cited data were taken at 77 K or a few degrees above. Fluorescence decay traces recorded at 4.2 K gave the same results. ' he onset of the fast component is also found at 690 nm, the values of the decay parameters with biexponential fitting are the same. Room temperature experiments give ambiguous results. The 3.5 ns component that is observed at low temperature is not present any more. The background decay has shortened very much leaving a combination of fast picosecond decays. I conclude that the dynamics are not temperature dependent up to 77K. Above that temperature the dynamics change, p&ibly caused by increasing nonradiative relaxation.

To summarize the observations: 1) in the 600 to 700nm region a 3.5ns decay process cause by residual monomers is observed, 2) beyond 690nm a fast aggregate decay is present which starts off with a 30 ps decay time at 690 nm and lengthens to about 1.5 ns (as an average for the biexponential decay) at 800 nm.

6.4 Discussion

In this section I will first discuss the physical shape of the aggregates of TPY. Thereafter I will show that the spectroscopy of TPY aggregates can be explained on the basis of a model involving strong exciton-phonon which leads to self-trapping of the delocalized excitation.

The physical structure of the aggregate of 'IPY has been studied by Dulmage et al., using X-ray diffraction. They prepared single crystals of TPY mixed with a compound that resembles the repeating unit in the polymer polycarbonate. The moat simple way of describing the structure of the model system is that layers of IPY are separated by layers of polymer precursor. Neighboring TPY layers are connected via an invemion operation, which means that the center of a stack of layers is a center of symmetry. The separate layers of IPY consist of string8 of molecules stacked side-to-aide.

Requency doubling experiments performed by Wang showed strong enhancement caused by aggregation of TPY in polycarbonate. Since no frequency doubling is possible in inversion symmetric media, the X-ray structure of the model seems to be in conflict with the structure of the aggregate in polycarbonate. However, it is possible that the larger disorder in the real aggregate allows for some enhancement of the doubling efficiency. Small regions of single layers or odd number TPY stacks could contribute strongly to the frequency doubling.

The layered aggregate model was also used by Marchetti et al. [15] to explain their DC Stark effect experiments. In those experiments the energy changes which are the result of the interaction of an external

static field and the permanent molecular dipole moment is probed. In case of aggregate9 the permanat dipole moment of the whole aggregate layer is involved. They conclude that the interaction energy between molecules neighboring layers is 450 cm'l.

The close resemblance of the spectra of TPY aggregates in I polycarbonate and TPY aggregates in the polymer precursor is convincing

evidence that the aggregate consists of layers of molecules. However, the extension of the ordered region in the TPY aggregate cannot be deduced directly. The microecope photographa presented by Wang 1111 indicate long-range ( p n ) structural order. Photogapha of the samples used in this work show much lees structure. The aggregates are barely resolvable in optical microscopy, and can be seen aa beady grains. Apparently, the addition of large quantities of plasticiaer in the samples of Wang changoa the aggregation process. Marchetti et al. [IS] noted that aggregates also exist in the "homogeneous phaseu, which means that the aggregate9 are smaller than can be obeerved using optical microscopes.

The aggregation energy shift ia large indicating that the coup-hg of the molecular states is large. Despite the large coupling no strong motional nwrowing effect of the exciton absorption line is observed. If one realizes thet a part of the width of the monomer aborption line must be assigned to vibronic activity, hardly any narrowing is observed. Clearly, the narrowing is counteracted by another effect. The packing of the TPY molecules in the layers lead to chaine of molecules with relatively small distances in one direction. A one dimensional character of the resulting aggregate excitation can therefore be anticipated. Spectra of the model system [13] showed that all oscillator strength should be assigned to the lower k=O state of the exciton band. This would imply that individual transition dipole moments are oriented head-to-tail.

A one dimensional exciton can show a strong enhancement of the radiative rate. The delocalization of the excitation can lead to resonant emission. In TPY aggregates no resonant emission is found: the aggregate emission shows a large shift relative to the absorption. Together with the obeervation of very short dephasing times, and the bleaching of the whole absorption band in pump/probe spectra, the large shift shows that the delocalized aggregate excitation is strongly coupled to the lattice. Pure exciton states are not observed in any of the experiments. The fact that an strongly shifted aggregate band is observed, however, proves that a delocabed aggregate state exista.

The zero-order description of the aggregates excitation is not an exciton in a well defined k-state but an exciton coupled to lattice modes. This coupled state is red shifted with respect to the monomer, because of the intermoleculw coupling. The k=O oscillator strength is &pawl over many mixed exciton-phonon modes, leadiig to a large "homogeneousu width, which ,is found in transient spectra and accumulated echo experiments. The initially formed optical excitation is best described as a polaron. The large shift of the emission relative to the absorption shows that the local deformation term of the aggregate Hamiltonian is dominant (see Sect. (2.3)).

From DC Stark effect experiments an interaction between dye layers, which are separated by a polymer layer, of 450 cm-I was inferred. This

coupling is very large when compared with the estimated 700 cm-I coupling between molecule8 within a single layer (B). The displacement of the spectrum of the exciton-phonon state relative to the pure exciton used in their analysis, could explain the large value of the interlayer coupling.

The time resolved results must be interpreted in terms of the polaron model. From pump/probe spectroscopy it is clear that two kinds of dynamics are present. On one haqd, a fast (45 pe) temperature transient is observed. On the other hand we see an approximately 3.5 ns transient. The spectrally resolved reeponaem of the fat% decaying specie8 and the slow decaying speciea (Fig.(6.3)) are very similar except for a shift of 5 nm (120 cm-I). The similarity of the spectral response shows that the excited states involved have the same absorption spectrum. This fact suggests that the two species represent different states on one energy potential. The time resolved fluorescence traces show no resonant 45 ps component cawed by direct emission of a extended (auperradiant) polaron. Throughout the 600 to 700 nm region a 3.5 ns component is observed, which is cwaed by residual monomera in the aggregated samplea. A very fast (k30 ps) component can be seen at 690 nm, at the edge of the absorption, but no fast emiasion is seen that is resonant with the absorption. The fast emission at 690 nm must originate from a phonon relaxed state.

The absence of a resonant 45p component indicates that no superradiant extended state exists, l i e the one found in PIC aggregates. It is pomible that a small fraction of the fast emission around 700nm arises-from the remnant of such a state. It does however only represent a very mall fraction of the total emission.

Since the total rate out of the initially formed state (this rate is observed in pump/pro%e responses and ia (45 ps)-I) is:

and the superradiant emission yield ie:

the emission yield of a superradiant state is proportional to the ratio of the nonradiative transfer time to the radiative lifetime. The emission yield of the fast polaron emission is negligibly small MI the "superradiant" decay time has to be large. The conclusion can be drawn that no direct polaron emission is, seen in the fluorescence spectra of TPY aggregates. The observed 45 p dynamics are totally determined by the transfer rate out of the initially prepared delocalized aggregate state.

In the region of 750 to 800 nm a biexponential decay is observed, with components of 0.9 ns and 2.4 ns. These times indicate that the relaxed state is not superradiant, but resemble the 3.5 ns monomer emission. I propose that this slow decay process should be interpreted in the polaron model. After optical absorption a polaron state is formed. From the absence of direct emission one can infer that this delocalized state relaxes strongly. The relaxation inhibite the fast emission that would be expected from a delocalized polaron. After 45 ps the delocalized polaron is self-trapped at a lattice site. The observation of equal trapping

6. TPY-annrenates: Excitone and P o w 105

times at 4 and 77 K suggests that the trapping is not activated, and is either the result of tunneling or a barrierlese transition.

In some molecular system like pyrene and a-perylene (61 self-trapping occurs caused by molecular excimer formation. Such an excimer formation process is special case of self-trapping. Vesy short-lived delocabd polaron emission is observed, together with much longer lived

I self-trapped emission. Recently evidence for self-trapping was reported for a quasi one dimensional platinum salt [7]. In this last case Stokes shifted self-trapped emission is observed together with small quantities of free exciton emission. This assignment was substantiated by time-resolved data The authors claim that in thie case the formation of the d-trapped sfate is barrierless. No barrier is expected for true electronb u i or two-dimensional self-trapping proceesea [2]. TPY aggregates show the same nonactivated d i o n behavior.

In the spectral range from 690 nm to 775 nm a distribution of emission lifetimes is observed. The wavelength and concentration dependent decay constants indicate excitation transfer, cawed by hopping of the trapped excitation towards lower energy. The formed trapped state can communicate with many sites around it, and energy transfer occurs, until no more sites are available. The transfer rate obeys the Forstar equation:

where fd(v) represents the fluorescence profile of the donor, E,(u) is the absorption profile of the acceptor, and r is the distance between donor and acceptor. The energy transfer rate is proportional to r4, so only molecules a t short distances contribute. In the highly concentrated TPY samples many molecules are available a t short distanceg. The initially excited molecuIe located a t the high energy side of the emission band rapidly transfers the excitation to a lower energy molecule. The result is lifetime shortening at the high energy Bide and lifetime lengthening at the low energy side of the band, together with a slowing of the rising edge of the fluorescence time profile. These effect can be observed both in TPY monomer and TPY aggregate in polycarbonate samples. It is clear however, that the interpretation of the aggregate emission is complicated by the energy transfer.

The t r a d e r of the self-trapped excitation to other sites also explains the striking difference of depolarization found in pump/probe and fluoregcence experiments. In the pump/probe experiments no initial depolarization is observed whereas the emission shows rapid depolarization. The pump/probe response consists solely of a transfer to a self-trapped state. The emission in contrast comes from the trapped state after several hop to other sites have taken place. In the hopping process the polarization memory is loat.

In thia chapter I have shown that the optical excitation in TPY aggregates is an example of strong coupling of the exciton exciton and phonons. The initially formed state is better described by a new quasi-particle called polaron. The experimental results show that the extended polaron states evolves into a localized state. This can be explained on the basis of self-trapping of self-trapping of the

excitation. The initially formed delocalized state rapidly relaxes, without showing radiative relaxation. The delocalized state is self-trapped with a time-constant of 45pe. The trapped state has a lifetime of about 2 na. Further investigations should focus on either amaller aggregates, in order to separate energy-transfer effects, or on different host systems for the TPY-aggregate.

Acknowledgments

I thank Wim van Veenen for the preparation of the aggregate samples. Mr. Meiborg was so kind to spend some time on the phase-contrast microscopy, and produced some excellent photographs. The TPY dye was kindly donated by Ocd-van der Grinten N.V.

1. Y. Toyazawa, Rog. Theor. Phya. 20, 53 (1958). 2. M. Ueta, H. Kanzaki, K. Kobayashi, Y. Toyozawa and E. Hanamura,

Excitonic proceases in solids (Springer, Berlin, 1986). 3. E.I. Rashba, J. Mol. Electronics 4, 149 (1988). 4. M.J. Rice and S.R. Phillpot, Phys. Rev. Lett. 58, 937 (1987). 5. C. Kollmar, W. Riihle, J. Frick, H. Six1 and J.U. von Schiitz, J. Chem.

Phys. 89, 55 (1988). 6. H. Port, R. Seyfang and H.C. Wolf, J. Phys. C 46, 391 (1985). 7. H. Tanino, W.W. Riihle, and K. Takahashi, Phys. Rev. B 38, 12716

(1988). 8. C.B. Lu&&ik, in: Excitone, eds. E.I. Rashba and M.D. Sturge

(North-Holland, Ameterdam, 1982). 9. S.R. Meech, A.J. Hoff and D.A. Wiersrna, Chem. Phys. Lett. 121, 287

(I=). 10. D. Tang, R. Jankowiak, C.J. Small and D.M. Tide, Chem. Phys. 131, 99

(1987). 11. Y. Wag, Chem. Phys. Lett. l26, 209 (1986). 12. W.J. Dubage, W.A. Light, S.J. Marino, C.D. Salzberg, D.L. Smith, and

W.J.Staudenmayer, J. Appl. Phys. 49, 5543 (1978). 13. P.M. Borsenberger, A. Chowdry, D.C. Hoesterey, and W. Mey, J. Appl.

Phys. 49, 5SS5 (1978). 14. W. Mey, E.I.P. Walker, and D.C. Hoesterey, J. Appl. Php. 50, 8090

(1979). 15. A.P. Marchetti, M. S c o d a v a , and R.H. Young, J. Chem. Phys. 89,

1827 (1988). 16. R.H. Young, A.P. Marchetti and E.I.P. Newhouse, J. Chem. Phys. 91,

5743 (1989). 17. S. Saikan, T. Nakabayashi, Y. Kanematsu and A. Imaoka, J. Chem. Phys.

88, 4609 (1988).

18. E.W. Castner and J. Terptra, unpublished results. 19. S. De Boer and D.A. Wierema, Chem. Phya. 131, 135 (1989). 20. S.J. Strickler and R.A. Berg, J. Chem. Phys. 37, 814 (1962). 21. V. Sundatrtim, T. Gillbro, R.A. Cadom, and A. Piskarskas, J. Chem.

Phys. 88, 2754 (1988).

c3wPmu7

Spectra and dynamip of 'I'D aggregate8

7.1 Introduction

7.2 Results and diecusaion

References

7. S m t r a and dvnamia of ID 109

7.1 Introduction

Besides PIC a number of compounds have been found that exhibit stable aggregation in solution. The review articlee by Herr [1,2] list a large number of aggregate forming solutions. A far larger number of dyes show aggregation in heterogeneous environment, for example, on surfaces and m polymers. Another category of dyes, mostly with long alkyl side chains, forms aggregates in Langmuir-Blodgett (LB) monolayers.

Aggregates in solution do show less dieorder than the above cited heterogeneous systems, because they are formed close to thermodynamic equilibrium. For dyes bound to surfaces the situation is quite different. The largest interaction is between the dye molecule and the surface where it is bound to. Since the dye molecules cannot move freely over the surface, the aggregation does not give rise to the same lofig range order. In LB-layers the strongest interaction is between the dye molecules. In these IB-layers the size of the ordered range can be very large, dependinn on the frequency of stackinn errors in the layer.

-~orne-classes of dye molecules edbit aggregation solution, -as for example some carbocyanines, benzimidazolocarbocyanines, and thiackbocyanines. All the& dyes have in common that they consist of two planar aromatic groups connected by a conjugated link. This leads to the possibility of stacking these relatively flat molecules. The dyes also share the feature that they are ionic, so a (delocalized) charge is present on the molecule.

The thiacarbocyaaine dye that is the subject of this chapter (hereafter named 'ID) is depicted in Fig. (1.1). The tendency of the compound to aggregsta on silver halides was established by Rosenoff et d. [S]. The authors showed that the molecule both forms aggregates by itself, and that the molecule connecta to PIC aggregatee. The trapping of PIC aggregate excitation by TD was treated in Chapter 4 and Chapter 5. A structurally cloaely related thiacarbocyanine dye molecule forms aggregatea in water solution [I], and it turned out that TD aggregates could be formed in 0.1 M KC1 water/ethylene glycol solutione. The high anion concentration shifts the aolution equilibrium towards aggregation.

The spectroscopic properties of TD aggregates resemble those of PIC aggregates. For example a strong narrowing (about 1000 cm-I to 275 cm-l) is found for the atmoption, the aggregate band is ahifted over a large distance (2500m-l) relative to the monomer and a fast fluorescence decay is observed (90 ps). Although these spectroscopic properties were not studied as extensively as in the case of PIC aggregates, I want to preeent the results. These results show the applicability of concepts developed for PIC aggregates to another molecular aggregate system.

7.2 Results and Discussion

In Fig. (7.1) the absorption spectra of TD monomers and aggregates ate depicted. The monomer absorption peaks at 570 nm whereas the maximum of the aggregate absorption is at 665nm. The aggregate absorption is strongly red shifted relative to the monomer band (~2500 cm-I), showing

that a large intermolecular coupling (B) between units exists. For the related thiacyanine dye [I] the maximum of the aggregate absorption is found at 630 nm, and the absorption has a much larger width. An aggregate abeorption a t 630nm is aleo found m TD solutions, but this "630 nm aggregaten is a precursor to precipitation. Solutions exhibiting this abeorption all show decoloration upon atanding. The solutions with a band at 665nm are much more stable, and good optical quality glaee samples can easily be made.

wavelength (nm) Figun 7.1 The opticcrl absorption spectra of TD monomer (dashed) and aggregate (line) d 80 K in wuterldhylene glycol 1:l. The aggregate spectrum is obtained after addition of KC1 to the solution up to a concentration of 0.1 M.

The emiesion spectrum of TD aggregates at 1.5 K consists of one line only, resonant with the absorption. From Fig. (7.2) it can be seen that the extinction is maximal at 662 nm and the width is 12 nm (275 cm-I). The emiesion spectrum shows a maximum at 665 nm, but remarkably the width is only 5 nm (115 an-'). I will qeturn to this asymmetry shortly.

The fluorescence decay as measured at the emission maximum at 80K is W10ps. A t the high energy tail of the fluorescence spectrum the decay time is shorter, about 70 pe.

Attempts to measure the accumulated echo decay were not successful, possibly caused by the absence of a bottleneck state. In the course of these attempts incoherent transients could be observed. At sufficiently high intensity levels pump/probe responses could be detected. The response is an increased absorption that decays with a time constant of 15ps. This indicates that the transition to higher exited stafea has more transition strength than the one back to the ground state. At 1.5 K a much slower transient absorption decay ia observed, with a time constant of about 100 ps. Relative to the emission experiments high intensity pulses were needed to observe the transient absorption. Typically a lOpJ pulse was focused through a 5 0 p pinhole,

7. S~ectra and dvnamica of TD anmenates 111

corresponding to 0.5pJ/an2 per pulse. It was checked that the 15p decay did not depend on the excitation intensity, within signal-to-noise limitations.

ill 2 ill SE t! 9 - Y-

wavelength (nm)

Figure 7.2 The absorption spectrum (dashed) and the emission spectrum (line) of the a g p g a t e band of TD aggregates. Note the difference of the l*hs.

Aggregates of TD are sensitive to the application of too high light intensities. Continuous illumination gives rise to a photoproduct that can be characterized by pump/probe responses. Ae the increased absorption fades, (z multi-component bleaching arises, consisting of a pulse limited (-5 ps) component, a 150 ps component and a long lived ns component with weights of 0.6, 0.2 and 0.2 respectively. Although this photochemistry complicates the experiments, it is not directly relevant to the exciton dynamic6 and will not be pursued any further.

The aggregates of TD show clear fektures of exciton behavior. The motional narrowin of the aggregate transition is evident. The absorption width of 2 7 5 ~ n - ~ is at least four times smaller than the monomer (FWHMu1000 an-'). The width of the emhion line (115 an-') may be closer to the intrinsic inhomogeneous width of the exciton transition, leading to a motional narrow' factor of nine. The quadratic scaling of the motional narrowing [4] eads to a minimum delocalization over about 80 units.

"f The narrowed emission line together with the absence of vibrational

structure is intriguing. It shows that a part of the oscillator strength is present in states that relax within the radiative lifetime. The question is which kind of states is involved: or phonon sideband states or extended exciton k-states.

When a phonon sideband is involved the asymmetry of absorption and emission needs explation. The displacement of the excited state potential relative to the ground state must be very small, and the vibrational ground state potential must be harmonic, as was previously

encountered in the caae of the vibronic activity of PIC aggregates. The amall displacement can be understood because the excitation is delocalized, and each molecule carriea a mall part of the total excitation.

0 50

time (ps)

Figwe 7.3 The pumplptobe response of TD aggregates at 80 K . The top trace represents the increased absorption that is observed after the pump pulse has passed the sample. The bottom trace is the autocornlation of the pulse wed.

The relaxation can also be explained when the aggregate band is not treated as a strict exciton state, without any site dependence in the k-states [S]. The band could comist of different states on one aggregate bounded by random site energy fluctuations. The states with a the higher energy can relax into states with a lower energy. When the relaxation of the upper states is faster than the radiative relaxation, a narrow emiesion peak at the low energy side absorption profile is observed [6,71-

At low temperatures the decay of the increased absorption is 100 ps, within experimental error the same as the 80K fluorescence decay. At 80 K the transient absorption is much faster than the fluorescence, 15 ps versus 90 pa. The fast decay of the transient absorption can be explained by relaxation of the exciton state. The 15 ps decay thus represents the relaxation of the excited states towards thermal equilibrium. At low temperatures the initially prepared state does not relax so rapiay and the transient absorption just reflects the exciton radiative decay.

The asymmetry of absorption and emhion spectra is also observed in PIC aggregates. Further work is neceesary in order to clarify the causes of this intriguing phenomenon.

The radiative enhancement for the aggregates of TD is close to 100. This number can be inferred from the 90 pa fluoreecence lifetime at 80 K and the fluorescence lifetime of the monomer. The monomer shows a double exponential decay with decay constants of 1.8 ns and 9.7 ns and weights

7. S w t r a and dvnamics of TD anerenates 113

of 0.3 and 0.7 respectively. For moet dye molecules nonradiative processes will lead to a quantum yield lower than unity. Therefore it is a reasonable assumption that the radiative lifetime of 'Ill monomer is 10 ns, a factor of 100 slower than the aggregate. The quantum yield of the aggregate fluorescence is an unknown factor, but that yield will not be lower than the monomer yield, so the enhancement of a factor-of 100 seems to be a reasonable estimate.

On the basis of the experiments on the TD aggregate the following conclusions can be drawn: 1) The aggregate band of the thiacyanine dye TD is the result of the coherent coupling of at least 100 monomers. 2) The narrowing of the emission relative to the absorption can be explained by relaxation of different states on a single aggregate, W i n g to fast transient absorption responses. The experiments show the clear similarity of the behavior of the aggregates of TD and PIC.

References

A.H. Herz, Advances in Colloid and Interface Science 8, 237 (1977). A.H. Herz, Photogr. Sci. Eng. 18, 323 (1974); Errata ibid. 18, 667 (1974). A.E. Rosenoff, K.S. Norland, A.E. Amea, V.K. Walworth and C.R. Bird, Photogr. Sci. Eng. 12, 185 (1968). E.W. Knapp, Chem. Phys. 86, 73 (1984). J. Knoester, private communication. H. Fidder, J. Knoester and D.A. Wiersma, Chem. Phys. Lett. 171,.529 (1990). D.A. Wiersma and H. Fidder, private communication.

De optische eigenschappen van geaggregeerde moleculen verschillen sterk van gehleerde moleculen. Het in dit proefschrift beachreven werk is een ond&zoek naar de statische en dynamische aepecten van de optische spectroscopie van een drietal verschillende moleculaire aggregeten. In de optieche absorptie- en emissieepectra van aggregerende oplocrsingen treden grote verschuivingen op. Dae vmhuivingen geven bijvoorbeeld 'aanlei- ding tot kleurveranderingen van geaggregeerde opSo88ingen. Het samenbin- den VM moleculen tot aggregafen leidt klaarblijkelijk tot de vorming van nieuwe electronische toestanden, die over meerdere moleculen verdeeld zijn. Deze gedelocati8eerde erciton toeartiinden gedragen zich geheel: an- dere dan geisoleerde moleculaire toestanden. De optische dynamica van exciton toestanden in moleculaire aggregaten is het onderwerp van dit proefschritt. De tijdschaal waarop de relevante processen zich af~pelen wordt gemsten in picamonden (1 picoaeconde is 0.000000000001 seconds). Experimentele studie van exciton dynamica vereist een voldoend hoge tijdsresolutie om de processen te volgen. Daartoe worden h e r s gebruikt die puleen met een tijdsduur van ongeveer een picoseconde leveren.

De moleculen waarvan de aggregaten bestudeerd zijn behoren tot de kleuretofmoleculen. Dergelijke moleculen vinden toepaseing in bijvoor- beeld fotografbche lagen en in pigmenten. Een gemeenschappelijke eigen- schap van veel van deze moleculen is dat ze bestaan uit een of meer vlak- ke aromatieche ringsystemen. In aggregaten kunnen deze vlakke moleculaire systemen ordelijk gestapeld worden. Op deze manier onetaan ketens of lagen van zwak gebonden moleculen. Indien nu 66n molecuul in een aggre- gaat optiech aangeslagen wordt, kan de gevormde excitatie zich vrijelijk bewegen over het geordende aggregaat: de optische excitatie ia gedeloca- liseerd.

Voor de studie van de optische dynamica van gedelocaliieerde toestan- den zijn een aantal spectroscopische technieken beschikbaar. Mn gebruik- te techniek is de detectie van het fluorescentie verval van de aangesla- gen toestand. Door de aggregaten met een korte puls optisch aan te slaan, en daarna het gdmiteerde licht tijdsopgelost te detecteren, is het moge- lijk vervalprocessen te meten. Een andere techniek die gebruikt wordt is de "pump/proben techniek waarbij 6611 korte puls gebruikt wordt om de aggregaten aan te slaan, en een andere puls gebruikt wordt om de optische toestand van de aggregaten uit te lezen. Door het tijdsverschil tussen de pulsen te variiSren kunnen weer vervalprocessen gemeten worden. Fluores- centie en pump/probe spectroscopie leveren elkaar aanvullende informatie. Een ander spectroscopisch effect dat gebruikt is de geaccumuleerde echo. Hierbij wordt niet het verval van het exciton maar de verstoring van de excitonovergang door omgevingstrillingen gemeten, een proces dai defase- ring genoemd wordt. In het geval van gedelocalierde aggregaat excita- ties blijkt dat de omgevingstrillingen, die voor geisoleerde moleculen alleen de defasering behvloeden, ook de stralende vervalprocessen veran- deren.

In hoofdstuk 1 wordt een algemene inleiding gegeven aangaande exciton toestanden in moleculaire aggregaten, en aangaande de experimentele me- thoden die worden gebruikt. Voorts bevat dit hoofdstuk ook nog een korte samenvatting van het proefschrift.

In hoofdstuk 2 wordt het concept van een gedelocaliseerde toestand nader onderbouwd. Uitgaande van een moleculair aggregaat van slech'ts twee moleculen, het dirneer, worden de dominerende aapecten van de spectrosco- pie van moleculaire aggregaten geidentiiiceerd. Het blijkt dat de koppe- ling tussen de geExciteerde toestanden van de afmnderlijke moleculen de delocalisatie bepaald.

In hoofst.uk 3 worden de experimentele methoden van het dynamisch epec- troscopisch ondermk beschreven. De gebruikte meetoptelling bestaande uit lasers en deteddeapparatuur wordt beechreven. Ook worden er enige beschouwingm gewijd aan de fpische achtergrond van de gebruiLte meetme- thoden. E& paragrsaf van dit hoofdst.uk ie gewijd aan de fyeisch- cheunjsche aspecten van de aggreg&ie van moleculen in oplodngen

Hoofdstuk 4 W e l t het defaseringegedrag van optiech gaciteerde aggregaten van pseudo-iso-cyanine mleculen. Deze aggregaten hebben een z&n markant absorptie spectrum dat bestaat uit twee d e banden. Door middel van geaccumuleerde echo spectroecopie verkregen gegevene worden gebruikt om de interratie van de opthche excitatie met de rooetertril- lingen te beechrijven.

In hoofdstuk 5 wordt het fluoreacentieverval van de aggregaat excita- tie beachreven v w r PIC aggregaten. Ook wordt hier de vraag over hoeveel moleculen de aggregast excitatie zich uitstrekt behandeld.

De aggregaten van een thiapyrilium kleurstof, TPY, zijn het onderwep van hoofdstuk 6. In een aantal opzichten lijken de ptische eigenschappen E van TPY aggregaten sterk op die van PIC, echter de oppeling van de exci- tatie in TPY met de rooetertrillingen is vele malen aterker. De eigen- echappen van deze aggregaten zijn bestudeerd met pump/probe en fluores- centie spectroscopic.

In het korte laatste hoofdstuk worden resultaten gepreaenteerd van spectroecopische metingen aan het derde moleculaire aggregaat, dat van de thiacyanine kleuratof TD. Hierbij wordt de verbinding gelegd naar het model dat gebruikt wordt om de optische dynamica van PIC aggregaten te beschrijven.

De afgelopen 5 jaar heb ik de picoseconde spectroscopie van molecu- laire aggregaten beoefend samen met een aantal mensen, die gedurende die jaren ook enige tijd de kelder van het chemisch laboratorium bevolkten. Dit proefschrift kan niet besloten worden zonder diegenen te bedanken die bijgedragen hebben aan de totstandkoming ervan.

Allereerst wil ik mijn promotor, Douwe Wiersrna danken voor de prettige samenwerking in de afgelopen jaren. Zijn imrner aanwezige enthousiasme en de grote inzet hebben mij sterk gestimuleerd.

Karel Drabe wil ik danken voor de perioden die we samen in het lab hebben doorgebracht. Mijn interesse voor alles wat met de generatie en de detectie van fotonen te maken heeft, is voor een groot deel terug te voeren op die eamenwerkig. Laurens Molenkamp dank ik voor de introductie in picoseconde lasertechnieken.

Stephen Meech is acknowledged for the period which we worked together in the basement. Especially the training in intensive and time consuming experiments has been of great we to me.

De steun van Willem Zevenberg en Bert van Dammen is in de afgelopen jaren onontbeerlijk geweeet. Voor elk optredend probleem was altijd snel een optimale oplowing te vinden.

Henk Fidder heeft een aandeel gehad in een groot deel van het hier gepresenteerde werk. Ik wil hem danken voor de vele uren die we samen besteed hebben aan de spectroscopie van moleculaire aggregaten. De kri- tische inbreng tijdens het schrijven van dit proefschrift waardeer ik zeer .

Kees Vink, Wi van Veenen en Egbert Lenderink dank voor de samenwer- king. De uitstekende computer programma's van Foppe de Haan hebben mij enorm geholpen bij het uitvoeren en analyseren van experimenten.

Ed Castner en Egbert Lenderink dank ik voor het nauwgezet controleren van het manuscript op "spelling and style".

Verder wil ik nog alle post-doc's, promovendi en studenten van de groepen Wiersma, Kommandeur, Duppen en Jonkman danken voor de samenwer- king in de aflopen jaren. '"t lab heeft mij altijd een prettige werk- omgeving geboden. Voor de vele gesprekken over andere zaken dan aggrega- ten en picoseconden dank ik iedereen die na het onvermijdelijke vrijdagse b e m k san het stamcaf4 de binnenstad van Croningen nog wist de vinden.

Tot slot wil ik Wilma bedanken voor haar steun in de afgelopen jaren. Meer in het bijzonder wil ik haar danken voor het verdragen van de span- ning die het schrijven van een proefschrift, blijkbaar onvermijdelijk, oproept.

Maastricht, december 1990

Het in deze dissertatie gepresenteerde werk is mogelijk gemaakt door de shun van de stichting Scheikundig Onderzoek Nederland (SON), en is gefinancierd door de Nederlandse Organisatie voor Wetenschappelijk Onder- zoek (NWO). Deze laatste organisatie dank ik ook voor de ondersteuning gedurende de 4-jarige periode die ik bij NWO als werknemer in dienst ben geweest.

De Rijksuniversiteit Croningen dank ik voor het gebruik van de univer- sitaire faciliteiten gedurende mijn onderzoek en voor de ondersteuning rondom de voorbereiding van het verdedigen van dit proefschrift.

Shell Nederland B.V. dank ik voor de reisdonatie die het het mij moge- lijk gemaakt heeft het "Dynamical Processes '89" congres in Athens (V.S.) te bezoeken.