Mobility effect positional disorder

A low AH for a cooperative cluster rotation allows excitation of a cluster of atoms from normal to saddle-point positions. Such an excitation may, in turn, lower the energy of the saddle-point sites relative to the normal sites, thus effectively introducing a AHg(T) that collapses in a smooth transition. At temperatures T> T, the mobile ions become disordered over the normal and saddle-point sites. Such a situation appears to be illustrated by stoichiometric LijN and PbFj (Goodenough, 1984). 

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. 

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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