Eur. Phys. J. B 62, 7-14 (2008)
https://doi.org/10.1140/epjb/e2008-00110-5

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

¹ Laboratoire de Mécanique, Département de Physique, Faculté des Sciences, Université de Yaoundé I, B.P. 812, Yaoundé, Cameroun
² International Chair of Mathematical Physics and Applications ICMPA-UNESCO Chair, 072 BP50, Cotonou, Université d'Abomey-Calavi, BP 50, 072 Cotonou, Benin
³ The Abdus Salam International Centre for Theoretical Physics, P.O. Box 586 Strada Costiera, II-34014 Trieste, Italy

Corresponding author: ^a nguetchoserge@yahoo.fr

Received: 5 September 2007
Revised: 12 November 2007
Published online: 12 March 2008

Abstract

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.