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A recent percolation theory is extended to provide new formulae for the exponent and pre-factor of the average Ohmic hopping conductivity sigma = sigma p exp(-sp) of a 1D hopping system in the variable-range-hopping regime. The formula for sp is in excellent agreement with values calculated in percolation studies but the predicted values of sigma do not fall off with decreasing T as fast as values calculated from Kirchhoff's equations. The temperature dependence of sigma p cannot account for this discrepancy. It is suggested that the extreme fluctuations in the conductivity of the system considered may make the exponent in the average conductivity differ from the percolation value calculated from the average percolation threshold.
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Butcher et al. (1988) studied this question.
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