Ionic conduction in keratin (wool)

Abstract

Measurements of the conductivity of dry wool (keratin) in vacuo as a function of temperature are described. The dc conductivity is given by σ = σ 0 exp ( — W RT ), with σ 0 = 10.0 (ohm·cm) −1 and W = 23.0 kcal/mole; R is the gas constant and T the temperature in °K. The dc conductivity of wool under ordinary conditions (i.e., when not in vacuo) is determined by its water content in equilibrium with the prevailing relative humidity; the relationship is σ = σ s ( sol| α/ α s ) n , where n = 16.4, α s , is the saturation water content, and σ s , is the saturation conductivity. A model is proposed here to account for these two types of conduction simultaneously. It is based upon the consideration that ionic conduction in solids depends upon the presence of transient defects in concentration proportional to a Boltzmann factor. The additional assumption is made that within each transient defect there is a pattern of discrete sites at which single water molecules can be adsorbed. The index n gives the number of these sites within a transient defect according to the hypothesis. As these patterns are assumed to be characteristic of the material, the defects are described as “transient characteristic defects” (TCD). Hydrated ions within such defects have a very high mobility because “bipedal random walk,” i.e., successive breaking of single hydrogen bonds, is available to them. In the fibrous proteins (and cellulose) the energy W in the Boltzmann factor giving the concentration of TCD depends upon the breaking of hydrogen bonds, which are rather weak; therefore, the concentration of TCD, and their size, may be rather large. The model has implications applicable to properties other than conduction.