Collective proton transport with weak proton-proton coupling

Abstract

A mechanism based on the peculiar dynamical properties of the hydrogen bond is suggested to describe fast proton transfers in hydrogen-bonded chains with realistic (weak) intersite proton-proton interactions. For this purpose, a two-sublattice model is suggested and studied analytically that admits an exact soliton solution. The solitons, which are topological objects (kinks and antikinks) on the one hand, but dynamical entities (like Boussinesq solitons) on the other hand, are shown to have a sufficiently large width to allow free propagation along the chain.

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“…In this model we consider the one dimensional motion of the proton (H + ) moving in an approximate double Morse potential (as showed in Fig.1) and coupled to a heat bath when the ions (X -) are fixed [6,7]. In these considerations, the Hamiltonian (2.1) can be rewritten in the simple form:…”

“…In Ref, Zolotaryuk, et al [7] the considered model has been used to investigate the proton transport by taking into account the degrees of freedom of the heavy-ion subsystem, where essential ingredients of the models are the realistic anharmonic ion-proton interaction in the HB, the harmonic coupling between the protons in adjacent hydrogen bonds, and thus the harmonic coupling between the nearest-neighbor heavy ions (an isolated diatomic chain with the lowest acoustic band) or instead a harmonic on-site potential for the heavy ions, both providing a bistability of the HB proton. Considering then the insufficiency of the coupled motion of the H and X atoms to lower the barrier enough to provide a free soliton regime, the work of ref [5] was carried out.…”

Discrete kink dynamics in hydrogen-bonded chains: The two-component model

“…The parameter ␤ is adjustable, while the other parameter ␣ can be computed through the equilibrium distance r 0 of a single Morse potential [26,30] using the relation…”

“…The two-dimensional intrabond proton potential V͑u , ͒ is assumed to be a symmetric double-well function (with respect to variable u) of a general form with two minima at ͑u , ͒ = ͑±a ,0͒ (more details on the topology of this potential are given in Ref. [30]). The lattice variables u n and n are defined through the relations…”

“…1. In general, it is not necessary to construct the intrabond proton potential as a sum of two single-well potentials because the equations of motion for the chain can be written in terms of any potential V͑u , ͒ given as a function of the proton displacement u from the middle of the HB bridge and the relative displacement of the ions X + from their equilibrium positions [25,30]. The discrete kink states, their stability and mobility properties have been studied previously [31] in detail, where the heavy ions forming the intrabond proton potential from two Morse potentials were assumed to be fixed.…”