Transport in disordered systems

A different approach to transport in disordered systems has been developed by considering the excitation dynamics of random one-dimensional chains (Alexander et al. [1981]). Such a system may be represented by a master equation of the form... 

One of the most powerful theoretical tools to account for charge carrier transport in disordered systems is provided by the percolation theory as described in numerous monographs (see, for instance, [15, 18]). According to the percolation theory, one has to connect sites with fastest transition rates in order to fiilfil the condition that the average number Z of connected bonds per site is equal to the so-called percolation threshold Be. In the three-dimensional case this threshold is [15,41,42] ... 

This method has been successfully applied to the theoretical description of hopping transport in doped crystalline semiconductors [15] and also in disordered materials with exponential DOS [43], A treatment of charge transport in disordered systems with a Gaussian DOS in the framework of the percolation theory can be found in [34, 35, 44]. However, this theory is not easy for calculations. Therefore it is desirable to have a more transparent theoretical description of transport phenomena in disordered systems with a Gaussian DOS. In the next section we present such an approach based on the well-approved concept of the transport energy (TE). This concept was successfully applied earlier to describe transport phenomena in inorganic disordered systems with exponential DOS [28-30]. We show below how this concept works in both cases for exponential and for Gaussian DOS functions. 

Johansson, A. and Stafstrom, S., Interchain charge transport in disordered rt-conju-gated chain systems, Phys. Rev. B, 66, 085208, 2002. 

If it is nonresonant, the transfer is accompanied by vibrational excitations in order to ensure energy conservation. A transfer time is clearly defined. Most importantly, the spectrum of the individual chromophore is not changed. In disordered systems, stochastic energy transport is always accompanied by fluorescence depolarization. 

We dedicate here a limited space to these aspects of theoretical and computational description of hquids because this chapter specifically addresses interaetion potentials and because other approaches will be used and described in other chapters of the Handbook. Several other approaches have the QM formulation more in the background, often never mentioned. Such models are of a more classical nature, with a larger phenomenological character. We quote as examples the models to describe light diffraction in disordered systems, the classical models for evaporation, condensation and dissolution, the transport of the matter in the hquid. The number is fairly large, especially in passing to dynamical and... 

Ediger MD, Fayer MD (1984) Electronic excitation transport in disordered finite volume systems. J Phys Chem 88(25) 6108-6116. doi 10.1021/jl50669a012... 

The above qualitative picture is supported by the data of frequency-dependent transport properties. The frequency dependence of conductivity provides another, independent way of determining the effective dimensionality d. In disordered systems the conductivity as a function of frequency usually follows a power law o- o>. Considering that the basic process of conduction is an anomalous diffusion, i.e., a random walk of the charge carriers on a network of effective dimensionality d < d, where d is the space dimension ( = 3 in the present case), the exponent s can be expressed as = 1 - did. This expression with data of conductivity versus frequency given in the literature [106] leads to values for d that agree satisfactorily with those obtained from spin dynamics. 

In the following we consider in parallel the description of the VRH transport in a system with the exponential DOS and that in a system with the Gaussian DOS. We will show that the well-known concepts successfully applied for decades to describe the VRH electrical conduction in the inorganic disordered materials such as... 

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