Quantum Theory of Polymers - Uniwersytet...
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Quantum Theory of Polymers
JeanMarie André
EC Socrates Erasmusprogramme
FUNDP, NamurUniversity of Warsaw
Quantum Theory of Polymers
1° Role of a quantum theory of polymers and its relations with photoelectron spectroscopy
2° LCAO Bloch theory for electronic structure analysis of polymers
3° Electronic structure of conducting and semiconducting polymers
4° Examples of applications of LCAO Bloch theory:a) graphite and Boron nitrideb) planar, cyclically belt and Möbius polyacenes
5° Electron transfer in polymers: Marcus classical theory
6° Electron Transfer in polymers: Marcus semiclassical theory
7° Energy transfers in polymers: Förster and Dexter mechanisms
8° Nonlinear optical (NLO) effects in polymers
Methodology
Concepts
Theory at the simple orbital (Hückel) level
Examplified by timely subjects(semi) conducting polymersNonlinear Optics (NLO)Electron and Energy transfer
Combined with personal « trajectory » and « souvenirs »
PS. More examples in the .ppt files
than in the oral lecture
1991
2003
p. 426 et sq.
Quantum Theory of Polymers1° Role of a quantum theory of polymers and its relations with photoelectron spectroscopy
JeanMarie André
FUNDP, NamurUniversita’ degli Studi dell’Insubria, Como
Methane CH4 - 161 °C -182 °CEthane C2H6 H-(CH2-CH2)-H -89 °C - 183 °CPropane C3H8 - 42 °C - 187 °CButane C4H10 H-(CH2-CH2)-(CH2-CH2)-H + 0,5 °C - 138 °CPentane C5H12 + 36 °C - 130 °CHexane C6H14 H-(CH2-CH2)-(CH2-CH2)-(CH2-CH2)-H + 69 °C - 95°CHeptane C7H16 + 98,4 °C - 91 °COctane C8H18 H-(CH2-CH2)4-H + 126,6 °C - 57 °C
PE HDPE 2,000 – 10,000 CH2-CH2 unitsUHMWPE > 100,000 CH2-CH2 units
Criticism against Staudinger’s ideas ( ≅ 1920)
Dear Colleague, Leave the concept of large molecules well alone; Organic molecules with a molecular weight above 5000 do not exist. Purify your products, such as rubber, then they will crystallize and prove to be lower molecular substances. Organic molecules with more than 40 carbon atoms do not exist. Molecules cannot be larger than the crystallographic unit cell, so there can be no such things as a macromolecule
Quoted in: R. Olby, J. Chem. Educ., 47, 168 (1970).
Polypropylene -CH2-CH(CH3)- CH2-CH(CH3)- CH2-CH(CH3)- CH2-CH(CH3)- -CH3
PVC -CH2-CH(Cl)- CH2-CH(Cl)- CH2-CH(Cl)- CH2-CH(Cl)- -Cl
1999 Polyethylene Production Data from C&EN, June 26, 2000
1,30189013,906HDPE
1,8561,59215,681LDPE
Japan**Canada**US*
* millions of pounds** milliers de tons
1999 European polyethylene production
France 2,770 millions of poundsGermany 2,097Italy 2,585U.K. 734
Ethylene C2H4 H-(CH=CH)-H -103,7 °C - 169 °
C
Butadiene C4H6 H-(CH=CH)-(CH=CH)-H - 4,4 °C - 108,9
°C
Hexatriene C6H8 H-(CH=CH)-(CH=CH)-(CH=CH)-H 78 °C - 12 °C
CH4
C2H6
C3H8
C4H10
C5H12
polyethylene
Basis of Bloch theory
ρ r ja =ρ r ∣ f n r ja ∣2
=∣ f n r ∣2
f n r ja =eikja f n r f n¿ r ja =e−ikja f n
¿ r
Consequencesf n r = f n , k r e k =en k
en k =en klg
en k =en −k
First Brillouin Zone
Half first Brillouin zone
Polymer quantum chemistry ≠1D solid state physics
1D periodicity but 3D orbitals
Band structures, density of states and XPS spectra
Band structures, density of states and XPS spectra
Ab initio calculationAndré, Leroy (1968)
ESCA spectrumAndré, Delhalle, Caudano, … (1972)
Angle-resolved ultraviolet photoelectron spectroscopyARUPS
UenoSeki
FujimotoKuramochi
SigitaInokuchi
Physical Review B 41, 1176 (1990)
JMA, Delhalle, …1975
Study of conformationaleffects on XPS valencespectra:
Polyethylene
Study of conformationaleffects on XPS valencespectra:
Polypropylene
JMA, Delhalle, …1979
CH bonds
CC bonds
-CH2 - CH2 - CH2 - CH2 - CH2 - CH2 - CH2 -
Polyethylene
- CH2 - CH(CH3) - CH2 - CH(CH3) - CH2 - CH(CH3) -
Polypropylene
MetalZero Gap
SemiconductorGap < 2 eV
InsulatorGap > 2 eV
Electrical conductivity
In order to have a net electrical current, electrons must jump from filled levels to empty levels across the bandgap (Eg).
If Eg is large, ≥≈ 2 eV → INSULATOR
σRT ≈ 10-10 Ω−1cm-1
≈ 10-10 S.cm-1
Electrical conductivity
For 0 < Eg ≤≈ 2 eV → SEMICONDUCTOR
10-10 ≤ σRT 10≤ 2 S.cm-1
polyacetylene Eg ≈ 1.5 eV σRT ≈ 103 - 105 S.cm-1
Si Eg ≈ 1.1 eV
For Eg = 0 → METAL
Upon applying an external electrical field, few e- at room temperature (RT) have the necessary energy to jump from valence band to conduction band.
Thermal energy : kT (per particle) or RT (per mole)at 300 K kT ≈ 0.025 eV
RT ≈ 0.6 kcal.mol-1
RT ≈ 2.5 kJ.mol-1
σRT 10≤ 2 S.cm-1
Cu σRT ≈ 6 105 S.cm-1
Ag, Au σRT ≈ 106 S.cm-1
Electrical conductivity
Mobility ≈ average speed of diffusion of the charge carriers (cm/s) as a function of applied electric field (V/cm):
m= cm
s V
cm
Dimension analysis:s=
Scm
=1 . cm
=q . m . n
q . m . n=Cb⋅cm2
V . s⋅1
cm3
¿CbV . s
⋅1cm
=1 .cm
R=
Vi
V . sCb
=
s=n⋅m⋅q N = density of charge carriers cm-3
µ = mobility of charge carrier cm2/V.sq = charge Cb
Electrical conductivityBand model ⇔ Hopping model
Band model: . perfectly ordered material. delocalized wave-functions of holes (in VB)and of electrons (in CB) over whole chain and various chains
Hopping model: . charges localized by vibrations on a single chain. charges “hop” from one chain to another
Time of residency of a carrier on a given polymeric unit =
must be less than characteristic time of a vibration ≈ 10-13 s
W(VB or CB) ≤≈ 0.1 eV → band model
t=hW
=23
10−1 5
W eV
W< kTIncoherent motion of localized chargesGeometry relaxation (polarons)Hopping regime controlled by MarcusActivation energy
W>kTExtended coherent electronic statesNo geometry relaxation (vibration=10-13s)Band-like regime
Electronic Structure of Polymers and Molecular Crystals, J. M. André and J. Ladik, Eds., Plenum, New York (1975).
Quantum Theory of Polymers, J. M. André, J. Delhalle, and J. Ladik, Eds., Reidel, Dordrecht (1978).
Recent Advances in the Quantum Theory of Polymers, J. M. André, J. L. Brédas, J. Delhalle, J. Ladik, G. Leroy, and C. Moser, Eds., Springer-Verlag, Berlin (1980).
Quantum Chemistry of Polymers: Solid State Aspects, J. Ladik and J. M. André, Eds., Reidel, Dordrecht (1984).
C. Pisani, R. Dovesi, and C. Roetti, Hartree-Fock Treatment of Crystalline Systems, Springer-Verlag, Berlin (1988).
R. Hoffmann, Solids and Surfaces: A Chemist’s View of Bonding in Extended Structures, VCH, New York (1988).
J. Ladik, Quantum Theory of Polymers as Solids, Plenum Press, New York (1988)
J. M. André, J. Delhalle, and J. L. Brédas, Quantum Chemistry Aided Design of Organic Polymers for Molecular Electronics, World Scientific, Singapore (1991).
J. M. André, D. H. Mosley, M. C. André, B. Champagne, E. Clementi, J. G. Fripiat, L. Leherte, L. Pisani, D. P. Vercauteren, M. Vracko, Exploring Aspects of Computational Chemistry, I. Concepts, II. Exercises, Presses Universitaires de Namur (1997).
Bibliography