Polaron mobility in trans-polyacetylene.

Abstract

We present a calculation of the phonon-limited mobility and diffusion coefficient of polarons drifting along a chain in ItransR-polyacetylene for the temperature range 25--300 K. Only scattering by acoustic phonons has been included because the energies of both optical phonons and the polaron's internal degrees of freedom are large compared to ${k}_{B}$T in the range considered. Because the wavelengths of the phonons that dominate the scattering are much longer than the length of the polaron, we treat the scattering by the deformation-potential method. 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\ensuremath{\sim}2.7${v}_{s}$, where ${v}_{s}$ is the velocity of sound, a value obtained from computer simulations for the case of solitons. The constant-mass case is found to become unphysical for T\ensuremath{\gtrsim}75 K because the thermal velocity of the polaron becomes larger than c. The room-temperature mobility of polarons in the model incorporating a maximum velocity is found to be \ensuremath{\sim}3 ${\mathrm{cm}}^{2}$/V s corresponding to a diffusion coefficient of \ensuremath{\sim}0.08 ${\mathrm{cm}}^{2}$/s. The predicted drift mobilities might be observed in photoconductivity measurements at short enough times after creation that the polaron remains on the same chain.