J. Chem. SOC., Faraday Trans. 2, 1988, 8(3), 239-245

Optical Investigation of Short-chain n-Alkanes Zdzisiaw Biaszczak and Pawei Gauden

Quantum Electronics Laboratory, Institute of Physics, A. Mickiewicz University, Grunwaldzka 6, 60- 780 Pozna6, Poland

An experimental study of the molecular optical anisotropy and non-linear third-order polarizability of short-chain flexible n-alkanes in neat liquids has been carried out. The techniques of optically induced birefringence (optical Kerr effect) and depolarized Rayleigh scattering have been used. For the liquids studies, the molecular optical Kerr constants and Rayleigh coefficients are also given. A linear correlation between the optical Kerr constant and the number of carbon atoms in the alkane molecule has been found.

The linear and non-linear optical properties of organic molecules have long been the subject of experimental and theoretical investigations.' Of particular interest is informa- tion on the conformation of the molecules in the liquid state and also on their interac- tions.2 n-Alkane molecules that can exist in a variety of conformations have proved to be of particular interest as their structure and thermodynamical properties are well known.3 Investigations of these compounds also provide the possibility of performing accurate tests of the bond additivity a p p r ~ a c h . ~ - ~ This simple approach is known to work quite well for the linear polarizability of organic m01ecules,~-~ as well as for the non-linear polarizabilities of simple chain molecule^.^

Of the particularly advantageous non-destructive optical methods we used the optical Kerr effect (OKE) and anisotropic Rayleigh light scattering (ARS). OKE, which is based on the phenomenon of induction, by intense laser light, of optical birefringence in a medium originally macroscopically isotropic,'0 can at present be measured with almost the same accuracy as the intensity of scattered These effects may provide, amongst other things, information regarding conformations of the molecules in the liquid state and their interactions. The purpose of this paper is to present and discuss the results of systematic investigations of OKE and ARS in a series of short-chain n-alkanes. In particular we wanted to study the dependence of these effects on the chain length (i.e. the number of C-C bonds) and to determine the linear and non-linear optical parameters of the molecules.

Theory

The theory of OKE and its relationship with ARS has been presented in a number of papers. 1 0 9 1 3 7 1 4 In view of this we will give only the most important relationships used in this work in the elaboration of our experimental results.

From OKE investigations we determined the optical Kerr constant B,( h a , h i ) which describes the macroscopic properties of the medium. The molecular properties of the medium are described by the molar Kerr constant ,,,Bo(A,, hi) dependent on parameters characterizing the atoms and molecules and on the molecular mechanisms producing birefringence. In the case of dense media the two constants are related as

In this expression, n, and ni are light refractive indices for the analysing (A,) and inducing ( h i ) beams, respectively, and V , is the molar volume.

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240 Optical Investigation of Sh ort-ch a in Alkanes

From the point of view of molecular mechanisms which on a macroscopic scale lead to the appearance of induced birefringence of the medium, the constant ,,,Bo may be written as the sum of two terms:13-15

(2) In this formula describes the contribution to OKE due to deformation of the electron shell of an atom or molecule in an optical field (Voigt effect), while BET represents the contribution to OKE due to orientation (Langevin effect) and redistribu- tion of the atoms and molecules17 in the field. The term B,NL depends on the non-linear properties of the atoms or molecules determined by the second-rank hyperpolarizability tensor capYs, and on intermolecular interactions. For liquids composed of molecules of small permanent electric moments (mainly dipolar and quadrupolar) and of low optical anisotropy, the influence of intermolecular interactions on the constant B:L may be neglected in the first approximation. Then, we can write"

,BO(ha, h i ) = B:L(h, , h i ) + BET(A, , h i ) .

18

BrL( A , , h i ) = ;TNC where c = icaapp.

The constant B:=(A,, hi) can be expressed in general form" as: RT ST N

45 kT B , ( A a , A i ) = - - - T 2 ( h a , h i ) .

(3)

(4)

In the above formula N is the Avogadro number, k the Boltzmann constant, T the absolute temperature, and r the effective optical anisotropy characterizing the molecular optical anisotropy of a molecule immersed in a liquid. Only for dilute gases can we assume that r is equal to the molecular optical anisotropy y of the isolated molecule. In the case of molecules of axial symmetry y = a 3 3 - a 1 1 , where amp is the optical linear polarizability tensor and a = 1/3a,, the mean optical polarizability. However, the influence of the local environment on the optical properties of the molecule increases with increasing density of the medium and is significant in liquid media. This leads, mainly through dipolar interactions (depending on molecular structure), to the formation of regions of short-range ordering and temporary molecular clusters. In this case, the effective optical anisotropy of a molecule with the influence of its nearest surroundings included may differ significantly from that of the isolated molecule.

If the medium is composed of anisotropic molecules (which is the case for short-chain n-alkanes), the main contribution to OKE arises from molecular reorientation and redistribution. Considering only these two phenomena, the effective optical anisotropy may be expressed in the form''

where J A is the parameter of angular correlations for anisotropically polarized molecules and JR is the parameter of bimolecular radial interactions. Taking into account the Voigt effect and maintaining the above assumption as to the properties of the molecules and the interactions between them, we can rewrite eqn (2) in the form

T2(h , , h i ) - ~ ~ y i ( l + J A ) + ( 9 ~ Z a a f + ~ ( ~ ~ l ~ i ~ ~ ~ i + ' * * ) J R ( 5 )

where r 2 ( h a , h i ) given by eqn ( 5 ) is convenient for further numerical calculations. The intensity of light scattered in a medium consists, in general, of two parts: one

isotropic and the other anisotropic. The intensity of the anisotropic component strongly depends on intermolecuiar interactions and the microscopic structure of the medium, as does OKE. The intensity of the anisotropic component of the scattered light of wavelength A, is given by16.20

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Z. Btaszczak and P. Gauden 24 1

where p = N / V is the number of molecules per unit volume. The experimentally determined component If, is the Rayleigh coefficient for horizontally polarized, scattered light when the incident light beam is polarized vertically. All the above considerations and formulae can be applied to calculate the effective optical anisotropy r2(A,). This implies that in ARS the same statistical fluctuations of molecular fields as in OKE are revealed. Once ,Bo is known from OKE studies and r2 from ARS, then eqn (6) allows one to obtain the mean value of the second-rank hyperpolarizability tensor (under the assumption that A, = hi = A, = A ) . This new method of determination of the non-linear contribution to the molecular optical Kerr constant and of determination of c for an anisotropic molecule from OKE and ARS has been proposed in refs (16) and (22). If a medium of anisotropic molecules is considered, we assume only angular interactions occur between the molecules. Then, according to eqn ( 5 ) , the Rayleigh coefficient H , can be rewritten as

The above relation enables us to calculate of the value of the angular correlation parameter J A from anisotropic light scattering data.23

Experiment a1

The type of apparatus used in our OKE investigations has already been described in For the measurements reported in this paper we used a modified version,"

which would allow us to perform precise measurements of Bo in media of low optical anisotropy such as n-alkanes. The effect was induced by a 15 ns (f.w.h.m.) ruby laser pulse ( A i = 694.3 nm, 50 MW cm-') and analysed by means of a C.W. argon laser beam (A, = 488 nm, 100 mV). The measurements were carried out at 20 "C.

In the studies of light scattering our apparatus25 allowed us to determine both the isotropic and anisotropic components of the scattered light by the method of photon counting. As source of light, a krypton laser was used (A, = 676.4 nm). The apparatus was calibrated with benzene using R,,,,,(benzene) = 2.74 x cm-'. All measurements were made at a fixed scattering angle of 90" and a temperature of 21 "C.

The spectrally or analytically pure liquids were produced by International Enzymes Limited. In all experiments the liquids, after having been prepared according to standard procedure," were filtered directly into the sample cells through 0.2 pm MF millipore filters.

Results

Measurements of OKE and ARS were performed for 1 1 short-chain n-alkanes from pentane to hexadecane (excluding tridecane) at room temperature. Additionally, measurement of the light-refractive indices (using a Pulfrich refractometer) and the density of the liquid were carried out. The results are collected in table 1 . From the OKE data we obtained the relative Kerr constants B, referred to benzene,8 defined as B, = ~ a q u i d /BEenzene. The value of B, is, for each liquid, the statistical mean of several measurements calculated by the least-squares method. The error in B, was estimated as not exceeding 5 % . The B, values are also summarized in table 1. In the light scattering study, independent measurements of the anisotropic H , and isotropic V, components of the scattered light (in relation to benzene) were carried out. These data allowed us to determine the depolarization ratio D, of the scattered light for neutral light and the Rayleigh coefficients of isotropic Ri, and anisotropic Ranis light for the liquids studied. The results of our calculations are listed in table 2. The accuracy of these results is estimated at +3%. Using the value of Bo for benzene equal to

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242 Optical Investigation of Short-chain Alkanes

Table 1. Experimental data for the determination the optical Kerr constants (light refraction indices for given A values)

n

liquid 10-20p/cm-3 (694.3 nm) (676.4 nm) (488 nm) d / g cmP3 B,

n-pentane n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane n-tetradecane n-pentadecane n-hexadecane

52.27 46.08 41.10 37.06 33.70 30.90 28.52 26.56 23.14 21.80 20.57

1.3560 1.3727 1.385 1 1.3934 1.4028 1.4075 1.4131 1.4174 1.4246 1.4275 1.4314

1.3560 1.3727 1.3855 1.3958 1.4034 1.4082 1.4135 1.41 86 1.4253 1.4283 1.4325

1.3654 1.3796 1.3952 1.402 1 1.4104 1.4161 1.4215 1.427 1 1.4340 1.4374 1.4408

0.6262 0.6594 0.6838 0.7030 0.7177 0.7301 0.7402 0.751 1 0.7624 0.7689 0.7734

0.125 0.142 0.162 0.173 0.183 0.194 0.208 0.220 0.253 0.263 0.288

Table 2. Experimental Rayleigh scattering results ~ ~ ~~~~

liquid lo6 Hv/cm-' lo6/ Vv/cm-' lo6 R,,/cm-' lo6 R,,,,/cm-' D,,

n-pentane n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane n-tetradecane n-pentadecane n-hexadecane

0.101 0.123 0.130 0.134 0.141 0.147 0.159 0.181 0.226 0.243 0.276

2.842 2.658 2.157 2.243 1.550 1.487 1.440 1.570 1.933 2.292 2.191

1.35 1.24 0.99 1.03 0.70 0.65 0.61 0.66 0.82 0.98 0.9 1

0.22 0.27 0.28 0.29 0.30 0.3 1 0.35 0.40 0.49 0.53 0.60

0.068 0.088 0.113 0.1 13 0.166 0.171 0.200 0.206 0.209 0.192 0.224

Table 3. Optical and molar Kerr constants (in e.s.u.) calculated from OKE and ARS measurements"

liquid

n-pentane n-hexane n-heptane n-octane n-nonane n-decane n-undecane n - d o d e c a n e n-tetradecane n-pentadecane n-hexadecane

7.90 8.97

10.24 10.93 11.57 12.26 13.15 13.90 15.76 16.62 18.20

14.89 18.57 23.06 26.56 30.56 35.19 40.28 45.29 58.03 64.56 74.28

5.05 5.26 7.57 7.80

10.52 13.76 14.03 13.50 12.72 13.05 12.62

9.84 13.31 15.46 18.56 20.04 2 1.43 26.25 3 1.79 45.3 1 51.51 61.66

33.9 28.3 32.8 29.4 34.4 39.1 34.8 29.8 21.9 20.2 17.0

All values are expressed in e.s.u.: 1 e.s.u. = 0.1 11 259 x C' m5 J6.

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2, Blaszczak and P. Gauden 243

Table 4. Molecular parameters calculated from refraction, OKE and ARS studies. The error in a determination did not exceed 2%"

~~~ ~~

liquid a/ cm3 y'/ cm6 r2/ cm' ~ / 1 0 - ~ ~ cm6 erg-' J A

n-pentane n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane n-tetradecane n-pentadecane n-hexadecane

100 118 136 154 174 189 209 226 264 28 1 30 1

9.80 2.4 f 0.2

20.84 3.7 * 0.3 26.82 4.5 f 0.3

4.8 * 0.3 36.12 5.2 f 0.4

6.3 * 0.4 67.54 7.7 f 0.5

10.9 f 0.6 12.4 f 0.7 14.8 f 0.7

16.24 3.2 f 0.2 6.0 f 0.9 6.3 * 0.9 9.0 f 1.4 9.5 f 1.4

-0.76 * 0.08 -0.80 * 0.07 -0.82 f 0.08 -0.83 * 0.07

12.5 f 1.9

16.7 f 2.5

15.1 *2.3 15.5 f 2.3 15.0f 2.3

16.4 f 2.5 -0.86 * 0.08

16.1 f 2.4 -0.89 * 0.08

a Expressed in e.s.u. 1 cm3 = 0.11 1 259 x C2 m2 J-', 1 cm6 = 1.237 86 x C4 m3 J-2

63.2 x e.s.u. (70.15 x 10-'6mV-2),27 the values of Bo for the n-alkanes and the mBo values were calculated. These data are given in table 3.

The results of our ARS studies allowed us to determine numerically the effective optical anisotropy. With the value of r2 available we calculated from the above formulae, the orientational-redistributional part of the molar optical Kerr constant and then its non-linear part (table 3). This subsequently permitted the determination of the mean value of the second-order optical hyperpolarizability. The results obtained are presented in table 4, where the calculated values of JK and a (from molecular refraction measure- ments using the Lorentz-Lorenz equation25), as well as the value of the molecular optical anisotropy y 2 calculated from the relation y2 = 9/2a262 (where the a2 were taken from28) are also given.

Discussion

From the data in tables 1-4 it is evident that the parameters describing the optical properties of the short-chain n-alkanes and the molecular parameters of these compounds dependent on the number of carbon atoms (C-C bonds) in the n-alkane molecule. This is especially visible in the case of the optical and molar Kerr constants, as is illustrated by the linear correlation for all n-alkanes studied in fig. 1 . The other molecular parameters are linearly dependent on the number of carbon atoms in the molecule only for shorter n-alkanes. For longer ones this dependence becomes strongly non-linear as, for example, in the case of the square of the effective optical anisotropy fig. 2), which proves that the ordering of molecules has increased. The values obtained for the effective optical anisotropy are several times lower than their values in the gaseous state and the difference between them increases for longer molecules (table 4). This fact, which is in good agreement with the results obtained by other experimental indicates that the surroundings of the C-C bonds become more isotropic in longer n-alkanes. For the n-alkanes considered here, the contribution of non-linear deformation of the molecules to the optically induced anisotropy amounts to ca. 30% (table 3) . This confirms the results obtained earlier for n-pentane, n-hexane and n-octane reported in ref. (3 1 ) . With increasing chain length the non-linear effects decrease and simultaneously the contribution of molecular orientation increases, as it becomes very clear from n-dodecane onwards. This suggests an increase in intermolecular interactions respon- sible for a stronger screening of the individual molecules from the optical field. Also, the increase in absolute value of the angular correlation parameter of the molecules

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244

220 h

CI wi .- 5 200

B v

180

p 160

cd

C Y wi

2 .; 140 - c.’ CL

120

Optical Investigation of Short-chain Alkanes

6 8 10 12 1L 16

chain length/carbon atoms

Fig. 1. Optical Kerr constant of n-alkane us. the number of carbon atoms.

I , I 1 1 1 1 1 I , , m 0 5 10 15

chain length/carbon atoms

Fig. 2. Dependence of the square of the effective optical anisotropy on the number of carbon atoms in an n-alkane molecule.

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2. Blaszczak and P, Gauden 245

with increasing length of the chain points to an increasing contribution from molecular interactions in longer n-alkanes.

This simple and unambiguous description is complicated by the fact that the molecules of n-alkanes cannot be treated as rigid and moreover, the flexibility increases with growing chain length.

We hope that the information required for a more complete interpretation of the results of our OKE and ARS studies of short-chain n-alkanes as regards conformation and molecular interactions will be provided by the temperature investigation now under way.

We thank Professor Franciszek Kaczmarek for his kind interest and encouragement throughout this investigation. This work was carried out under Research Project CPBP 0 1.063.03.

References

1 D. Chandler, Annu. Rev. Phys. Chem., 1978, 29, 441. 2 A. D. Buckingham and H . Sutter, J. Chem. Phys., 1976,64, 364. 3 J. P. Ryckaert and A. Bellemans, Faraday Discuss. Chem. SOC., 1978, 66, 95. 4 J. P. Hermann and J. Ducuing, J. Appl. Phys., 1974, 45, 5100. 5 J. F. Ward and I . J. Bigio, Phys. Rev. A , 1975, 11, 60. 6. A. D. Buckingham and B. J. Orr, Trans. Faraday Sac., 1969,65,673; Q. Rev., Chem. Soc., 1967,21, 195. 7. C. G. Le Fevre and R. J. W. Le Fevre, Rev. Pure Appl. Chem., 1955, 5, 261. 8 Z. Blaszczak, Acta Phys. Pol. A , 1975, 49, 515. 9 B. F. Levine and C. G. Betha, J. Chem. Phys., 1975, 63, 2666.

10 A. D. Buckingham, Proc. Phys. SOC., London, Sect B, 1956, 69, 344. 11 Z. Blaszczak, Opt. Commun., 1986, 58, 439. 12 I . L. Fabielinskii, Molekularnoye Rasseyaniye Sveta (Izd. Nauka Moskva, 1965), p. 156. 13 S. Kleich, Acta Phys. Pol., 1966, 30; Opto-Electronics 1969, 1, 75. 14 S. Kielich, Molekularna Optyka Nieliniowa (PWN, Warszawa-Poznan, 1977), p. 345 (in Polish). 15 S. Kielich, Proc. Phys. SOC., London, 1967, 90, 847. 16 S. Kielich, J. R. Lalanne and F. B. Martin, J. Phys. (Paris) , 1972, 33, 191. 17. R. W. Hellwarth, Phys. Rev., 1966, 152, 156. 18 A. D. Buckingham and J . A. Pople, Proc. Phys. SOC., London, Sect. A , 1955, 68, 905. 19 S. Kielich and S. Woiniak, Acta Phys. Polon. A , 1971, 39, 233. 20 S. Kielich, J. Chem. Phys., 1967, 46, 4090; Chem. Phys. Lett., 1971, 10, 516. 21 S. Kielich and S. Woiniak, Acta Phys. Polon. A , 1974, 45, 163. 22 S. Kielich, J. R. Lalanne and F. B. Martin, C. R. Seances Acad. Sci., 1971, 272, 731. 23 P. Bothorel, J. Colloid Interface Sci., 1968, 27, 529. 24 2. Blaszczak, Acta Phys. Polon. A, 1984, 66, 657. 25 Z. Blaszczak, Acta Phys. Polon. A , 1985, 68, 629. 26 S. Kielich, Acta Phys. Polon. A , 1960, 19, 149. 27 Z. Blaszczak, Acta Phys. Polon. A , 1987, 71, 601. 28 A. H . Stuart, Molekiilstruktur (Springer-Verlag, Berlin, 1967), p. 417. 29 J. V. Champion, A. Dandridge and G. H. Meeten, Faraday Discuss. Chem. SOC., 1978, 66, 266. 30 B. L. Levine and C. G. Bethea, J. Chem. Phys., 1975, 63, 2666. 31 S. Kielich, J . R. Lalanne and F. B. Martin, IEEE J. Quantum Electron., 1973, 9, 601.

Paper 7/1078; Received 181h June, 1987

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