Charge transport positional disorder

Since the early work of Scher and Montroll, there have been many studies of effects of positional disorder on charge transport in disordered solids (Poliak, 1977, 1977a Marshall, 1978, 1981. 1983 Mclnnes and Butcher, 1980 Schirmacher, 1981 Adler and Silver, 1982). These have lied to the general conclusion that while positional disorder can, under some conditions, give rise to dispersive transport, nondispersive transport is almost always attained after a carrier has executed a very few jumps. Hence, dispersive transport occurs over a small fraction of the thickness or at very low temperatures. This leads to the prediction that a transition from nondispersive to dispersive transport occurs within a single transit time or at increasing times with decreasing temperature. 

To analyze the negative field dependence of the mobihty in EHO-OPPE within the Gaussian disorder transport formahsm and to determine the diagonal (energetic) disorder parameter a and the off-diagonal (positional) disorder parameter d, the following relation between the charge mobihty p and the disorder parameters was employed [75] ... 

Fishchuk II, Kadashchuk A, Bassler H, Abkowitz M (2004) Low-field charge-carrier hopping transport in energetically and positionally disordered organic materials. Phys Rev B 70 245212... 

Vs//2. The energetic disorder o can be imderstood as the width of the Gaussian distribution of the density of energy states for the transport sites the positional disorder E can be treated as the geometric randomness arising from structural or chemical defects [28,29]. In essence, only two material parameters, viz., a and E, are used to describe the randomness of the amorphous organic charge transporter. The PF slope, Ppp, is now replaced with P in Equation 3.7, and in the context of the GDM, it is related to the disorders of tire material. From Equations 3.6 and 3.7, o can be determined from the slope of the plot of p(0,T) vs l/T, while E can be determined from the x-intercept of a plot of P vs (cs/k Tf. 

In conclusion, charge transport in amorphous polymers occurs by way of carrier hopping within a positionally random and energetically disordered system of localized states [48]. The dependence of the carrier mobility on diagonal and off diagonal disorder is taken into account by Eq. (2-11) ... 

The o(T) of 2-acrylamido-2-methyl-l-propane-sulfonic acid (AMPSA) samples are shown in Figure 2.6 [38, 39]. These samples show a positive TCR at temperatures above 80 K. Although the o(300 K) of PANI-AMPSA samples is slightly lower with respect to PANI-CSA, its positive TCR is observed down to much lower temperatures. The wet spun PANI-AMPSA fibres have shown an impressive room temperature conductivity of nearly 2000 S cm [40]. The difference in o(300 K) and o(T) between CSA- and AMPSA-doped PANI samples is possibly due to the variations in microstructure and its contribution to disorder-induced localisation. This shows that the charge transport in doped conducting polymers is rather sensitive to slight variations in the morphological features. 

In summary, the conductivity and its temperature dependence in doped (CH), PPV, PPy, PANI and PEDOT samples suggests that by reducing the role of disorder-induced localisation in charge transport, it is possible to observe the intrinsic metallic positive TCR in doped conducting polymers. 

Borsenberger, P. M., Richert, R., and Bassler, H., Dispersive and non-dispersive charge transport in a molecularly doped polymer with superimposed energetic and positional disorder, Phys. Rev. B, 47, 4289, 1993. 

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