The charge-carrier mobility in disordered organic materials: the long-range one-dimensional diffusion with the memory effect

The transport of charge carriers in disordered organic materials is considered based on the techniques of generalized Langevin equation. We simulate the one-dimensional diffusion of a charge in the ensemble of molecular chains interacting with the acoustic phonon subsystem of bulk environment. The random local charge transitions between chain links are mutually correlated. The full computation of the zero-field charge mobility for the N, N-di(1-naphthyl)-N, N-diphenyl-(1,1-biphenyl)-4,4-diamine (α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-NPD) is performed as an illustration. Several models for the probabilities of local transitions are tested. The individual local diffusion constants are randomly varied along a molecular chain within several orders of magnitude. The stationary diffusion regime establishes for every chain the temperature-dependent partial charge mobility as a frequency-dependent complex-valued response function. It is averaged over the chain ensemble. The computational scheme is simple and efficient. The importance of the memory effect depends on specific properties of a given material. This dependence in terms of the system parameters is discussed.