Intrachain exciton dynamics in conjugated polymer chains in solution

Abstract

We investigate exciton dynamics on a polymer chain in solution induced by the Brownian rotational motion of the monomers. Poly(para-phenylene) is chosen as the model system and excitons are modeled via the Frenkel exciton Hamiltonian. The Brownian fluctuations of the torsional modes were modeled via the Langevin equation. The rotation of monomers in polymer chains in solution has a number of important consequences for the excited state properties. First, the dihedral angles assume a thermal equilibrium which causes off-diagonal disorder in the Frenkel Hamiltonian. This disorder Anderson localizes the Frenkel exciton center-of-mass wavefunctions into super-localized local exciton ground states (LEGSs) and higher-energy more delocalized quasi-extended exciton states (QEESs). LEGSs correspond to chromophores on polymer chains. The second consequence of rotations-that are low-frequency-is that their coupling to the exciton wavefunction causes local planarization and the formation of an exciton-polaron. This torsional relaxation causes additional self-localization. Finally, and crucially, the torsional dynamics cause the Frenkel Hamiltonian to be time-dependent, leading to exciton dynamics. We identify two distinct types of dynamics. At low temperatures, the torsional fluctuations act as a perturbation on the polaronic nature of the exciton state. Thus, the exciton dynamics at low temperatures is a small-displacement diffusive adiabatic motion of the exciton-polaron as a whole. The temperature dependence of the diffusion constant has a linear dependence, indicating an activationless process. As the temperature increases, however, the diffusion constant increases at a faster than linear rate, indicating a second non-adiabatic dynamics mechanism begins to dominate. Excitons are thermally activated into higher energy more delocalized exciton states (i.e., LEGSs and QEESs). These states are not self-localized by local torsional planarization. During the exciton's temporary occupation of a LEGS-and particularly a quasi-band QEES-its motion is semi-ballistic with a large group velocity. After a short period of rapid transport, the exciton wavefunction collapses again into an exciton-polaron state. We present a simple model for the activated dynamics which is in agreement with the data.

Non-adiabatic excited state molecular dynamics of phenylene ethynylene dendrimer using a multiconfigurational Ehrenfest approach

“…A number of models, such as Pariser-Parr-Pople, 8 Frenkel exciton, 9 and Frenkel-Holstein, 10 have been used to describe quasi one-dimensional conjugated systems. The real-time Density Matrix Renormalization Group (DMRG) 11 technique is a powerful numerical method for studying these model systems.…”

Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wavefunction

“…In the results presented below, we adopt a variation of this model that is specific to the physics of conjugated polymer systems and similar to that developed by Tozer and Barford to model poly(para-phenylene) chains. 11 In this variation, the monomer excitation energies are all assumed to be identical, given by the parameter ϵ 0 , and the coupling J ij is assumed to be the sum of a through-bond and a through-space contribution. The Hamiltonian of our model is given by…”

“…1 −9 A common solution to the TCP is to force the quantum subsystem to change eigenstates at the crossing point in order to maintain the continuity of the adiabatic wave function. 2,10,11 However, this type of approach necessarily introduces a discontinuous transition in the number of nodes in the adiabatic wave function. In systems that require long time dynamics or that feature multiple trivial crossings, we show that this change in nodal symmetry can lead to inaccurate and inconsistent electronic adiabatic dynamics.…”

“…Changes in wave function character are quantified in a variety of ways, for example, by computing the overlap integral of eigenstates at sequential points in time. 2,10,11,13 Variations of this approach include the consideration of additional factors such as energy gaps between two eigenstates, 1 nonadiabatic coupling vectors, 1,4, 10,14 or differences in calculated surface hopping probabilities. 6 Other methods circumvent the trivial crossing problem by identifying problematic eigenstates and artificially forbidding their occupation.…”

Role of quantum coherence in shaping the line shape of an exciton interacting with a spatially and temporally correlated bath

“…[3][4][5][6][7] In addition to these important systems, the study of excitonic energy transfer in molecular crystals has been a subject of long and sustained interest. Experimentally one studies not only energy transfer dynamics but also optical line shapes in these systems.…”