Soliton mobility intrans-polyacetylene

Abstract

We present a calculation of the phonon-limited mobility and diffusion coefficient for solitons drifting along a chain in ItransR-polyacetylene for the temperature range 25–300 K. Only scattering by acoustic phonons is considered because the energies of both optical phonons and the soliton’s internal degrees of freedom are large compared to $k_B$T in the range considered. The scattering is treated by the deformation-potential method because, in the regime where phonons dominate the scattering, their wavelengths are large compared to the length of the soliton. The mobility has been calculated with the effective mass taken as (1) constant and (2) variable, such that there exists a maximum velocity of propagation c. We take c∼2.7$v_s$ where $v_s$ is the velocity of sound. Our calculations show that phonon scattering becomes ineffective for T≲100 K leading to a diffusion coefficient that diverges as T→0, while experimentally it is found to vanish. To account for a diffusion coefficient that vanishes at low T it is necessary to include trapping effects in the model. We find a good fit to the experimental data obtained by magnetic-resonant techniques by introducing traps of 0.01 eV, estimated to be the barrier presented by remanent cis linkages in a ItransR-(CH${)}_x$ chain.