Dipole–dipole interactions effects on mobility and conductivity of ionic and bonded defects in hydrogen-bonded chains

Abstract

Defect formation and transport in a hydrogen-bonded system is studied via a two-sublattice soliton-bearing one-dimensional model. Our two component model completes and extends our previous study (Tchakoutio Nguetcho and Kofane, 2007; Tchakoutio Nguetcho et al., 2008; Li et al., 2015) made on the dynamics of defects in a quasi-one-dimensional nonlinear model of complex hydrogen bond systems. The inclusion of dipole–dipole interactions provides a new class of differential equations possessing several key parameters and many singular straight lines. In order to evaluate and measure the variations effects on each interaction parameter, we use dynamic system methods to first say what are really the key parameters of the system, and then discuss on phase portraits bifurcations to derive a variety of exotic solutions corresponding to phase trajectories under different parameter conditions. Among the rich variety of soliton patterns obtained, we focus our attention to kink (antikink) solutions. The response of these solitonic defects to an externally applied DC electric field makes this system an excellent model to describe the protonic conductivity in complex hydrogen-bonded networks. Therefore, we evaluate analytically the effect of dipole–dipole interactions on the mobility of the kink–antikink pair and the specific electrical-conductivity of the protons transfer.