Drift velocity, electrically charged polymers

Let Uq be the average size of an element of free volume and v the minimum size of the element of free volume required for movement. The probability that an element of free volume permitting movement arises in unit time is then proportional to exp(—u /uq). At each opportunity to move the ion is accelerated in the direction of the applied electrical field and picks up a component of velocity qEx in the direction of the field, where x is the time taken for the move and q is the charge on the ion. The mean drift velocity in the field direction is thus proportional to qExnex —v /vQ), where n is the number of ions per unit volume. For given n the conductivity is thus proportional to exp(—u /Uq). Strictly speaking the constant of proportionality depends on T, but this dependence is small compared with the dependence on T contained in the exponential. The quantity must clearly be proportional to the total fractional free volume Ff, so that the conductivity is proportional to exp(—c/Ff), where c is a constant for the particular polymer and ion. Substitution for Ff from equation (7.33) and rearranging leads finally to the temperature dependence of the conductivity ... 

It should be noted that photocurrents usually observed in organic polymers are small, primarily because of the very low charge-carrier mobilities. The charge drift mobilities// (defined as the velocity per unit electric field) are typically s at the normally used... 

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