Brownian Dynamics Model of Excited-State Relaxation in Solutions of Conjugated Oligomers

The effects of torsional degrees of freedom on the excited-state relaxation of conjugated oligomers in solution are explored computationally by coupling an exciton model of the oligomer to a Brownian dynamics model of the solvent. The exciton model assigns one torsional degree of freedom to each unit cell, or site, of the oligomer. A simple molecular mechanical form is used for the ground electronic state. The excitation energy is obtained assuming coherent coupling between sites that is proportional to the cosine of the difference in torsional angles. The solvent is characterized by a single parameter, which is equivalent to setting the rotational diffusion time, t rot, of a single unit cell about the oligomer axis in the absence of any internal forces. The relaxation of long oligomers exhibits a fast component, with a time constant that is about 0.025t rot and a slow component that is about 0.15t rot. As the oligomer length is decreased, the time constant for the slow component decreases such that the biexponential behavior smoothly diminishes below 10 unit cells, nearly disappearing by three unit cells. Comparisons of the exciton model, which includes self-trapping, with molecular mechanics and harmonic oscillator models, which do not include self-trapping, show similar behaviors. The double-exponential behavior therefore appears to be a general consequence of the participation of many torsional degrees of freedom in establishing the excitation energy. Because the time scales are relatively independent of the details of the torsional potential, experimental measurements of relaxation due to planarization report primarily on t rot.