Mobility and conductivity of ionic and bonded defects in hydrogen-bonded chains with nonlinear interactions

The proton conductivity and the mobility arising from motions of the ionic and bonded defects, in hydrogen-bonded molecular systems are investigated by means of the quantum mechanical method. Our two component model goes beyond the usual classical harmonic interaction by inclusion of a quartic interaction potential between the nearest-neighbor protons. Among the rich variety of soliton patterns obtained in this model, we focus our attention to compact kink (kinkon) solutions to calculate analytically, the mobility of the kinkon-antikinkon pair and the specific electrical-conductivity of the protons transfer in the hydrogen-bonded systems under an externally applied electrical-field through the dynamic equation of the kinkon-antikinkon pair. For ice, the mobility and the electrical conductivity of the proton transfer obtained are about 5.307×10^-7 m²  V^-1  s^-1 and 6.11×10^-4 Ω^-1 m^-1, respectively. The results obtained are in qualitative agreement with experimental data.