Montrol-Scher model

Scheller reaction Schercamox DML Schercamox DMM Schercomid Schercomid CME Schercotaine Schereowet Scher-Montroll model Schetty-Pfeiffer ligands Schiff base Schiff bases... 

Dispersive transport in PVC was investigated. The results of Pfister and Griffits obtained by the transit method are shown in Fig. 6. The hole current forms at temperatures > 400 K clearly show a bend corresponding to the transit time of the holes. At lower temperature the bend is not seen and transit time definition needs special methods. The pulse form shows the broad expansion during transition to the opposite electrodes. This expansion corresponds to the dispersive transport [15]. The super-linear dependence of the transit time versus sample thickness did not hold for pure PVC. This is in disagreement with the Scher-Montroll model. There are a lot of reasons for the discrepancy. One reason may be the influence of the system dimensions. It is quite possible that polymer chains define dimension limits on charge carrier transfer. 

In polymers, it is always observed that a packet of carriers spreads faster with time than predicted by Eq. (30). Thus, the spatial variance of the packet yields an apparent diffusivily that exceeds the zero-field diffusivity predicted by the Einstein relationship. Further, the pholocurrent transients frequently do not show a region in which the photocurrent is independent of time. As a result, inflection points, indicative of the arrival of the carrier packet at an electrode, can only be observed by plotting the time variance of the photocurrent in double logarithmic representation. The explanation of this behavior, as originally proposed by Scher and Lax (1972, 1973) and Scher and Montroll (1975), is that the carrier mean velocity decreases continuously and the packet spreads anomalously with time, if the time required to establish dynamic equilibrium exceeds the average transit time. Under these conditions, the transport is described as dispersive. There have been many models proposed to describe dispersive transport. Of these, the formalism of Scher and Montroll has been the most widely used. 

A key prediction of the Scher-Montroll model is that the photocurrent transients will decay as... 

The Scher-Montroll model has been widely used to describe dispersive transport phenomena in polymers as well as the chalcogenide glasses. For a review, see Scher et al. (1991). 

Pfister (1977) measured hole mobilities of TPA doped PC. Figure 51 shows the temperature dependencies for different concentrations. The field was 7.0 x 105 v/cm. The concentration is expressed as the weight ratio X of TPA to PC. The mobilities were thermally activated with activation energies that increase with decreasing TPA concentration. The concentration dependence was described by the lattice gas model with a wavefunetion decay constant of 1.3 A. Figure 52 shows the field dependencies at different temperatures for X - 0.40. The solid lines were derived from the Scher-Montroll theoiy (1975) using the listed parameters. Pfister concluded that the theoiy provides a self-consistent interpretation of all experimental observations if field-induced barrier lowering and temperature-dependent dispersion are formally introduced into the expression for the transit time. 

Crisa (1983) measured hole. mobilities of a mixture of 2,5-bis(4-diethylaminophenyl)-l,3,4-oxadiazole and a polyester. The time, thickness, and field dependencies of the photocurrent transients agreed with predictions of the Scher-Montroll model (1975). According to the model, the transit time scales with thickness and field as (L/E)l/a. The experimental value of a was 0.80. The study of Crisa, and later work by Bos and Burland (1987), are the only literature references to polymers where the scaling relationships predicted by Scher and Montroll have been observed over a range of thicknesses and fields. 

N-isopropylcaibazole (NIPC) was studied as a model for the monomer repeat unit of PVK by Mort et al. (1976). The concentration dependence was described by a wavefunction decay constant of 1.5 A, compared to 1.2 A for PVK (Gill, 1972). Composite plots of the logarithm of the photocurrent versus the logarithm of time were universal when normalized to the transit time. The activation energy was 0.1 eV smaller than for PVK. The results were described by the Scher-Montroll model (1975). 

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