Transport in Trans-polyacetylene

The first highly conducting polymer, polyacetylene with up to ~500 Ω-1 cm-1, was reported ten years ago. Since then, polyacetylene and other polymers in which comparable conductivities have been achieved have been studied intensively. This review is devoted to polyacetylene. It starts with a description of its bonding, band structure, crystal structure and morphology. Basic to the nature of conduction in polymers is the fact, predicted by theory and verified by experiments, that addition of an electron or hole to a polymer chain leads to a characteristic pattern of bond relaxation. The characteristic pattern, which may also be viewed as an excitation of the chain, in polyacetylene may be either a soliton or a polaron, each with an extent of 10 to 20 atoms. As a preliminary to the mathematical description of these excitations, we derive the continuum version of the Hamiltonian introduced by Su, Schrieffer and Heeger, and the equations that result therefrom. From these equations the wavefunctions of the solitons and polarons and their creation energies are obtained. The description of the excit lions is completed with a phenomenological dispersion relation that describes the variation of their masses with velocity. This formalism is then used to derive the diffusion coefficient for neutral solitons. These solitons, present as defects in most pristine, i.e., not deliberately doped, trans-polyacetylene samples, have been shown by nuclear magnetic resonance and other experiments to diffuse fairly rapidly along the chains.