Localization in quasi-one-dimensional systems

A general method for obtaining transfer matrices in quasi-one-dimensional systems is presented. We used the method to study Anderson localization in trans-polyacetylene, polyparaphenylene, polyparaphenylene vinylene, and polythiophene. The electron localization length for the polymers as a function of disorder was calculated from the Lyapunov exponents. The polymers are shown to exhibit different sensitivity to disorder, which could be explained in terms of different dimensionality of the polymeric systems. We also give an explanation to the recently observed differences between electron and hole intrachain mobilities in alkoxy derivatives of polyparaphenylene-vinylene, as being a result of the electron-donating nature of the alkoxy substituents.