Solitonic proton transport in (A−H⋯B−H⋯)n systems

Proton transport along hydrogen-bonded (HB) chains is essential for achieving high electric conductivity in ice crystals and facilitating bioenergetic transport within membrane proteins. Soliton models have been proposed to explain the mechanism of the proton transport, with their dynamics studied both analytically and numerically. In this study, I examine how the soliton dynamics is affected by the asymmetry of double-well potential and the alternative array of two types of heavy ions. As the special cases, the HB chain also contains a symmetric double-well potential and one type of heavy ions. I present a soliton model that has a new interaction between a proton and its neighboring heavy ions, which is valid for the HB chain with an asymmetric double-well potential. A mathematical analysis using a continuum approximation demonstrates that the newly identified interaction produces solitons in the coupled motion of protons and heavy ions. The outcome is influenced by the type of heavy ions involved and the symmetry of the double-well potential. It is also found that the proton transport in the HB chain with two types of heavy ions is represented by solitons with an effective mass of these heavy ions. Furthermore, numerical simulations are performed to examine the stability of solitons in the discretized HB model. They also show a kink-like solution in the HB chain with an asymmetric potential and demonstrate the effects of thermal fluctuations and an electric field on the stability of solitons.