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Title: Theory of optical transitions in conjugated polymers. I. Ideal systems

Abstract

We describe a theory of linear optical transitions in conjugated polymers. The theory is based on three assumptions. The first is that the low-lying excited states of conjugated polymers are Frenkel excitons coupled to local normal modes, described by the Frenkel-Holstein model. Second, we assume that the relevant parameter regime is ℏω ≪ J, i.e., the adiabatic regime, and thus the Born-Oppenheimer factorization of the electronic and nuclear degrees of freedom is generally applicable. Finally, we assume that the Condon approximation is valid, i.e., the exciton-polaron wavefunction is essentially independent of the normal modes. Using these assumptions we derive an expression for an effective Huang-Rhys parameter for a chain (or chromophore) of N monomers, given by S(N) = S(1)/IPR, where S(1) is the Huang-Rhys parameter for an isolated monomer. IPR is the inverse participation ratio, defined by IPR = (∑{sub n}|Ψ{sub n}|{sup 4}){sup −1}, where Ψ{sub n} is the exciton center-of-mass wavefunction. Since the IPR is proportional to the spread of the exciton center-of-mass wavefunction, this is a key result, as it shows that S(N) decreases with chain length. As in molecules, in a polymer S(N) has two interpretations. First, ℏωS(N) is the relaxation energy of an excited state causedmore » by its coupling to the normal modes. Second, S(N) appears in the definition of an effective Franck-Condon factor, F{sub 0v}(N) = S(N){sup v}exp ( − S(N))/v! for the vth vibronic manifold. We show that the 0 − 0 and 0 − 1 optical intensities are proportional to F{sub 00}(N) and F{sub 01}(N), respectively, and thus the ratio of the 0 − 1 to 0 − 0 absorption and emission intensities are proportional to S(N). These analytical results are checked by extensive DMRG calculations and found to be generally valid, particularly for emission. However, for large chain lengths higher-lying quasimomentum exciton states become degenerate with the lowest vibrational excitation of the lowest exciton state. When this happens there is mixing of the electronic and nuclear states and a partial breakdown of the Born-Oppenheimer approximation, meaning that the ratio of the 0 − 0 to 0 − 1 absorption intensities no longer increases as fast as the IPR. When ℏω/J = 0.1, a value applicable to phenyl-based polymers, the critical value of N is ∼20 monomers.« less

Authors:
 [1];  [1];  [2]
  1. Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ (United Kingdom)
  2. (United Kingdom)
Publication Date:
OSTI Identifier:
22310722
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 16; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ABSORPTION; BORN-OPPENHEIMER APPROXIMATION; CENTER-OF-MASS SYSTEM; COUPLING; DEGREES OF FREEDOM; EMISSION; EXCITATION; EXCITED STATES; EXCITONS; MOLECULES; MONOMERS; POLYMERS; WAVE FUNCTIONS

Citation Formats

Barford, William, E-mail: william.barford@chem.ox.ac.uk, Marcus, Max, and Magdalen College, University of Oxford, Oxford OX1 4AU. Theory of optical transitions in conjugated polymers. I. Ideal systems. United States: N. p., 2014. Web. doi:10.1063/1.4897984.
Barford, William, E-mail: william.barford@chem.ox.ac.uk, Marcus, Max, & Magdalen College, University of Oxford, Oxford OX1 4AU. Theory of optical transitions in conjugated polymers. I. Ideal systems. United States. doi:10.1063/1.4897984.
Barford, William, E-mail: william.barford@chem.ox.ac.uk, Marcus, Max, and Magdalen College, University of Oxford, Oxford OX1 4AU. 2014. "Theory of optical transitions in conjugated polymers. I. Ideal systems". United States. doi:10.1063/1.4897984.
@article{osti_22310722,
title = {Theory of optical transitions in conjugated polymers. I. Ideal systems},
author = {Barford, William, E-mail: william.barford@chem.ox.ac.uk and Marcus, Max and Magdalen College, University of Oxford, Oxford OX1 4AU},
abstractNote = {We describe a theory of linear optical transitions in conjugated polymers. The theory is based on three assumptions. The first is that the low-lying excited states of conjugated polymers are Frenkel excitons coupled to local normal modes, described by the Frenkel-Holstein model. Second, we assume that the relevant parameter regime is ℏω ≪ J, i.e., the adiabatic regime, and thus the Born-Oppenheimer factorization of the electronic and nuclear degrees of freedom is generally applicable. Finally, we assume that the Condon approximation is valid, i.e., the exciton-polaron wavefunction is essentially independent of the normal modes. Using these assumptions we derive an expression for an effective Huang-Rhys parameter for a chain (or chromophore) of N monomers, given by S(N) = S(1)/IPR, where S(1) is the Huang-Rhys parameter for an isolated monomer. IPR is the inverse participation ratio, defined by IPR = (∑{sub n}|Ψ{sub n}|{sup 4}){sup −1}, where Ψ{sub n} is the exciton center-of-mass wavefunction. Since the IPR is proportional to the spread of the exciton center-of-mass wavefunction, this is a key result, as it shows that S(N) decreases with chain length. As in molecules, in a polymer S(N) has two interpretations. First, ℏωS(N) is the relaxation energy of an excited state caused by its coupling to the normal modes. Second, S(N) appears in the definition of an effective Franck-Condon factor, F{sub 0v}(N) = S(N){sup v}exp ( − S(N))/v! for the vth vibronic manifold. We show that the 0 − 0 and 0 − 1 optical intensities are proportional to F{sub 00}(N) and F{sub 01}(N), respectively, and thus the ratio of the 0 − 1 to 0 − 0 absorption and emission intensities are proportional to S(N). These analytical results are checked by extensive DMRG calculations and found to be generally valid, particularly for emission. However, for large chain lengths higher-lying quasimomentum exciton states become degenerate with the lowest vibrational excitation of the lowest exciton state. When this happens there is mixing of the electronic and nuclear states and a partial breakdown of the Born-Oppenheimer approximation, meaning that the ratio of the 0 − 0 to 0 − 1 absorption intensities no longer increases as fast as the IPR. When ℏω/J = 0.1, a value applicable to phenyl-based polymers, the critical value of N is ∼20 monomers.},
doi = {10.1063/1.4897984},
journal = {Journal of Chemical Physics},
number = 16,
volume = 141,
place = {United States},
year = 2014,
month =
}
  • A novel statistical mechanical theory for the order-disorder transformations of conjugated polymers in dilute solution and neat amorphous films is proposed. Single chain configurational statistics and the conformation-dependent polymer-solvent interactions are included in the basic formulation. Abrupt transition phenomena arise from the energetic stabilization of the rod-like conformation via the interaction of the delocalized electrons of the polymer backbone with the surrounding polarizable solvent. The theory is developed in detail for ..pi..-conjugated polymers (polyenes and polydiacetylenes) in dilute solution and makes a significant number of qualitative and quantitative predictions. Available experimental data are consistent with the theoretical picture and amore » variety of additional experiments are suggested to critically test the proposed ideas. The statistical mechanical formalism is generalized to allow for intramolecular hydrogen bonding, polydispersity, solvent mixtures, defect correlations, and substituent disorder. These effects have quantitative consequences but do not change the qualitative physics of the proposed three-dimensional solvation mechanism for the coupled electronic-conformational transitions. Preliminary application of the theory to amorphous films is briefly considered.« less
  • We investigate theoretically and experimentally the effects of (2,5) chemical substitution on the optical absorption in the phenylene-based conjugated polymers. Theoretically, substitution destroys both the charge-conjugation symmetry and spatial symmetry that characterize the unsubstituted materials. Within Coulomb-correlated theoretical models, the effect of broken charge-conjugation symmetry alone on the underlying electronic structure and on the absorption spectrum is rather weak. When both broken spatial symmetry and broken charge-conjugation symmetry are taken into account, a strong effect on the electronic structure of polyphenylene derivatives is found. In spite of the strong effect of the broken symmetries on the electronic structure, the effectmore » on the optical-absorption spectrum is weak. This surprising result is a consequence of the subtle nature of the configuration interaction in the substituted polyphenylenes within Coulomb-correlated models. We demonstrate numerically an approximate sum rule that governs the strength of an absorption band at 3.7 eV in the absorption spectra of poly(para-phenylene vinylene) (PPV) derivatives. Although substitution can make a previously forbidden transition weakly allowed, the latter acquires strength from a {open_quotes}finite-size band{close_quotes} at about the same energy, and not from a higher-energy band at 4.7 eV, as has been previously claimed. It is further predicted that the 3.7-eV band is polarized predominantly along the polymer-chain axis. We have measured the polarization dependence of the optical absorption in an oriented-substituted PPV film. We found that the two lowest-energy absorption bands are polarized predominantly parallel to the chain axis, while the band at 4.7 eV is polarized predominantly perpendicular to the chain axis. These results are in excellent agreement with the theory. {copyright} {ital 1997} {ital The American Physical Society}« less
  • Numerical calculations of the phase behavior and spectroscopic properties of ..pi..-conjugated polymers are presented based on the theory developed in the preceding paper. The specific model studied includes the single chain statistics and the configuration-dependent polymer--solvent interactions. The detailed dependence of the transition temperature and coexistence region on solvent, defect formation energy, chain length, and polydispersity is established. Relevance of the equilibrium calculations to electronic absorption and light scattering measurements is discussed. Experimental implications of the results for the polydiacetylenes, and the effects of system-specific generalizations of the theory, are briefly considered.
  • Finite-temperature extensions of ab initio Gaussian-basis-set spin-restricted Hartree–Fock (HF) and second-order many-body perturbation (MP2) theories are implemented for infinitely extended, periodic, one-dimensional solids and applied to the Peierls and charge-density-wave (CDW) transitions in polyyne and all-trans polyacetylene. The HF theory predicts insulating CDW ground states for both systems in their equidistant structures at low temperatures. In the same structures, they turn metallic at high temperatures. Starting from the “dimerized” low-temperature equilibrium structures, the systems need even higher temperatures to undergo a Peierls transition, which is accompanied by geometric as well as electronic distortions from dimerized to non-dimerized forms. The conventionalmore » finite-temperature MP2 theory shows a sign of divergence in any phase at any nonzero temperature and is useless. The renormalized finite-temperature MP2 (MP2R) theory is divergent only near metallic electronic structures, but is well behaved elsewhere. MP2R also predicts CDW and Peierls transitions occurring at two different temperatures. The effect of electron correlation is primarily to lower the Peierls transition temperature.« less
  • We have studied photogenerated charged excitations in sexithiophene and a variety of {pi}-conjugated polymers by photoinduced absorption (PA) and PA-detected magnetic resonance. We found distinct spin signatures for polarons and bipolarons, which enabled us to separate their contributions to the PA spectrum. In all cases, we find that polarons have two subgap optical transitions, whereas bipolarons have one. Having unambiguously identified the energy levels of polarons and bipolarons, we show that bipolarons are stable photoexcitations, with negative effective correlation energy. {copyright} {ital 1996 The American Physical Society.}