The dielectric properties of humid cellulose

The electrical characteristics of cellophane have been measured at variable moisture contents and temperatures in the frequency range 10−3–105 Hz. The data show very strong dependence on moisture content, which is typical of hydrophilic solids, and exhibit constant phase angles over wide frequency ranges. Complex admittance is proportional to (jω)−(β−1) where ω is the frequency and β ≈ 0.95. We use a model of hopping charge transport to explain the frequency and moisture dependence of the measured spectra. At low frequencies conduction occurs predominantly by phonon-assisted proton hopping between absorbed water molecules, with β dependent on the energetic disorder of the protonic states. The moisture dependence of the conductivity σ is shown to arise from its exponential dependence on the critical percolation distance RC and to have the form exp{−BN−1/3}, where N is the water concentration and B is a constant. This result explains the universally observed logarithmic dependence on N of the low frequency conductivity in hydrophilic solids. The model also explains the characteristic low frequency dispersion observed in solid ionic conductors. In hydrophilic solids in-phase charge transport due to rotating water molecule dipoles increases with frequency and eventually becomes the dominant contribution to the total conductivity.