The Disorder Formalism

This chapter reviews theories proposed to describe charge transport in materials of potential relevance to xerography. The emphasis is on the disorder formalism, polaron arguments, and the Scher-Montroll formalism. These have been the most widely used during the past decade. For reviews, see Silinsh (1980), Movaghar (1987, 1991), Bassler (1993), Silinsh and Capek (1994), and Silinsh and Nespurek (1996). Experimental results are described in the following chapters. 

Due to weak intermolecular coupling, valence and conduction bands of 

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The key parameter of the disorder formalism is the width of the hopping site manifold. There is considerable evidence that a is dependent on the dipole moment of the dopant molecule, as well as the polymer repeat unit, and/or polar additives. This has been described by an argument based on dipolar disorder, originally due to Borsenberger and Bassler (1991). Stated simply, the argument... 

Unlike the Poole-Frenkel effect, the dipole trap argument does not require high concentrations of charged traps. Further, the problem of small distances between the hopping sites relative to the position of the potential energy maxima, which is a major limitation of Poole-Frenkel arguments, is avoided. The model predicts field and temperature dependencies that are similar to the disorder formalism. The dipole trap model and the disorder formalism both lead to activation energies that are temperature dependent. 

For the disorder formalism, Young and Fitzgerald argued that the effect of the polar additives can be described by the expression... 

Hole mobilities of p-diethylaminobenzaldehyde diphenylhydrazone (DEH) doped PC were measured by Schein et al. (1986). The field and temperature dependencies were described as logjU PE1/2 and -(T0/T)2. While the field dependencies could not be described by any existing theory, the temperature dependencies were consistent with the disorder formalism. The field dependencies were further investigated by Schein et al. (1989). The measurements were made over an extended range of fields, 8.0 x 103 to 2.0 x 106 V/cm. The results were compared to predictions of models proposed by Bagley (1970), Seki (1974), Facci and Stolka (1986), and a modified Poole-Frenkel argument due to Hill (1967). The only model that agreed with the results was based on the Poole-Frenkel effect. The authors discounted this explanation for reasons cited in Chapter 7. 

Nishimura et al. (1992) measured hole mobilities for solvent-coated glasses of 4-diphenylaminobenzaldehyde diphenylhydrazone (DPH), 4-diphenylamino-acetophenone diphenylhydrazone (MDPH), and a mixture of DPH and MDPH doped into a PC. The field and temperature dependencies were described by Gill s expressions and the disorder formalism. The Gill expression gave A0 between 0.39 and 0.50 eV, T0 between 387 and 420 K, and nQ between 4.5 x 10-2 and 2.1 x 10-1 cm2/Vs. The disorder formalism gave a between 0.11 and 0.13 eV and n0 between 1.0 x 10-4 and 4.2 x 10-3 cm2/Vs. The higher values of... 

A fundamental prediction of the disorder formalism is that the activation energy is temperature dependent, increasing with decreasing temperature. This... 

At sufficiently low temperatures, dispersive transport is observed in all disordered solids. In most studies, the phenomenon has been attributed to energetic disorder. For a discussion of dispersive transport within the framework of the disorder formalism, see Borsenberger et al. (1993b) and Borsenberger and Bassler (1994). 

T0 A parameter used to describe the temperature dependence of the mobility in the disorder formalism, in K t Time, in s or h... 

Charge carrier drift mobilities of a number of amorphous molecular materials have been determined by a time-of-fhght method, and their electric-field and temperature dependencies have been analyzed in terms of the disorder formalism [56, 57] ... 

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