The Prefactor Mobility

The concentration dependence of the hole mobility of TPM-E doped PS was described by Magin et al. (1996). TPM-E is a moderately polar molecule with a dipole moment of 2.10 Debye. Figure 5 shows the temperature dependencies for 45% TPM-E. The results are similar to those reported for vapor-deposited TPM glasses and doped polymers described previously. The data in Fig. 5 yield n0 = 2.9 x 10-2 cm2/Vs and a = 0.111 eV. For purposes of comparison, Fig. 6 shows the zero-field data of Fig. 5 plotted versus T-l. From these results, it is clear that the temperature dependence cannot be described by an Arrhenius relationship over an extended range of temperatures. A further problem concerning the use of an Arrhenius relationship is the prefactor mobility. At 272 K, the data in Fig. 6 yields a prefactor mobility of 690 cm2/Vs, a value that is difficult to justify. For all concentrations, plots of ft versus (a/kT)2 were linear with slopes between... 

Figure 36 shows the temperature dependencies for different S BA ratios for a field of 2.0 x 10 V/cm. The results yield a between 0.069 and 0.103 eV, increasing with increasing dipole moment. The prefactor mobilities were approximately 1.5 x 10 2 cm /Vs, independent of the polymer. Values of the positional disorder parameter were approximately 2.4, also independent of the polymer. 

Aratani et al. (1996) investigated effects of molecular orbital distributions on hole mobilities of a series of triphenylamine derivatives doped into PC. The results show that the HOMO of the triphenylamine derivatives has essentially no effect on either the width of the DOS or the degree of positional disorder, but has a large effect on the prefactor mobility. Aratini et al. argued that increasing the HOMO distribution on the triphenylamine moiety results in an increase in the wavefunction decay constant. The mobility increases as the fraction of the HOMO electron density distributed on the triphenylamine moiety increases. The ionization potential of the triphenylamine derivatives was found to have little effect on the transport behavior. 

Naito and Kanemitsu (1996) investigated the relationship between the prefactor mobilities, zero-field mobilities, and the glass transition temperatures of OX doped polyarylate (PA), PC, poly(methyl methacrylate) (PMMA), PS, poly(vinyl chloride) (PVC), polyethylene terephthalate) (PET), and poly(vinyl butyral) (PVB), DEH doped PC, 5(p-diethylaminophenyl)-l-phenyl-3-(/ -diethylaminostyryl)-2-pyrazoline (DEASP) doped PS, and DEASP doped PC. OX, DEH, and DEASP are highly polar molecules with similar dipole moments. By modifying the polymer, the glass transition temperature can be varied over... 

The results show that values of jiQ vary over a wide range. This is one of the reasons for the very considerable differences in mobilities of these materials. The prefactor mobility is proportional to the intermolecular transfer integral J as fiQ oc j2t For charge transfer between molecules, J depends on the molecular angular orientations, unless the initial and final states are spherically symmetric. Slowik and Chen (1983) have shown that for carbazole molecules, J may vary by orders of magnitude as the molecular planes are rotated. It is likely that differences in the prefactor mobility are largely due to differences in orientation of the donor molecules. Differences in intersite distances may also contribute to differences in prefactor mobilities. 

For doped polymers, the concentration dependence of the prefactor mobility is usually described by the wavefunction decay constant. Wavefunction decay constants are separately discussed in Section XII G. 

Several explanations have been proposed to describe these effects. Sasakawa and coworkers explained their results by a conformational trap argument (Lange and BSssler, 1982 Zboinski, 1983). Differences in trap densities were proposed as due to differences in rotational mobility of the dopant molecules in various polymers. Borsenberger concluded that the effect of the polymer was largely related to the prefactor mobility. It was argued that the effect of the polymer was related to differences in polymer ionization potentials. 

There is, at present, no realistic theoretical model of the effect of geometrical disorder. A proper model must take into account the complicated orientation dependence of the matrix element (K) [63g], as well as the distribution of positions and orientations of the CTM. The simple treatment adopted by the Gaussian Disorder Model predicts a dependence of the prefactor mobility (//q) on the geometrical disorder parameter Z, namely //q oc exp(i2 ) [63a], and this relationship has been used often to analyze experimental data. The comparison of TTA and TAPC at low concentrations disagrees with this prediction, and it appears to be untenable a priori anyway [60b, 63e]. A worthy challenge for future work will be to construct a model with enough realism to have predictive value. Recent reports indicate progress in this direction [641,o]. 

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