Dichotomous collective proton dynamics in ice
Dichotomous collective proton dynamics in ice
复制标题
DOI：
10.1103/physrevb.57.234
复制
发表时间：
1998
影响因子：
3.7
通讯作者：
A. Zolotaryuk;A. Savin;E. Economou
中科院分区：
文献类型：
--
作者：
A. Zolotaryuk;A. Savin;E. Economou
基于二维（2D）非线性晶格模型研究了冰中的集体质子动力学，该模型考虑了氢键网络中质子转移的二分分支。该模型的要点是方形质子晶格的网络拓扑满足3D冰晶结构的Bernal-Fowler冰规则。该模型被认为是标准一维耦合双阱振荡器模型的直接扩展，该模型由离散非线性 Klein-Gordon 方程描述为二维，同时施加冰规则。这种在冰约束下的概括已被证明是独特的。建立了边界条件和拓扑电荷之间的关系（如高斯定律）。对于具有非零拓扑电荷和在其边界上随机选择的理想冰构型的方形冰晶格的任何域，扩展的正 $({\mathrm{H}}_{3}{\mathrm{O}}^{+})$ 和负 $({\mathrm{OH}}^{\mathrm{\ensuremath{-}}})$ 离子缺陷用二维矢量拓扑孤子来描述。二维扭结和反扭结的定义是使用高斯定律给出的。二维冰模型的各向异性推广和适当的数值方案使我们能够研究二维孤子的动力学特性，并与相应的一维解进行比较。特别是，与一维情况相反，非零 Peierls-Nabarro 浮雕的存在已被证明在所有情况下都存在，即使位点间质子-质子相互作用无限强，因此自由的二维孤子动力学在冰晶中是不可能的。另一方面，我们对二维冰晶格热化的研究清楚地证明了氢键的协同作用在缺陷对 ${\mathrm{H}}_{3}{\mathrm{O}}^{+}$ 和 ${\mathrm{OH}}^{\mathrm{\ensuremath{-}}}$ 的成核和动力学中的关键作用，$解释了从冰物理实验数据中已知的它们非常低的密度。
The collective proton dynamics in ice is studied on the basis of the two-dimensional (2D) nonlinear lattice model which takes the dichotomous branching of proton transfers in hydrogen-bonded networks into account. The essential point of this model is that the network topology of the square proton lattice satisfies the Bernal-Fowler ice rules of the 3D ice crystal structure. The model is considered as a straightforward extension of the standard 1D coupled double-well oscillator model described by the discrete nonlinear Klein-Gordon equation to two dimensions while imposing the ice rules. This generalization under the ice constraints has been shown to be unique. A relation between the boundary conditions and topological charge (like Gauss' law) is established. For any domain of the square ice lattice with nonzero topological charge and an ideal ice configuration chosen randomly on its boundary, the extended positive $({\mathrm{H}}_{3}{\mathrm{O}}^{+})$ and negative $({\mathrm{OH}}^{\mathrm{\ensuremath{-}}})$ ionic defects are described in terms of 2D vector topological solitons. The definition of the 2D kinks and antikinks is given by using Gauss' law. An anisotropic generalization of the 2D ice model and an appropriate numerical scheme allows us to study the dynamical properties of the 2D solitons in comparison with the corresponding 1D solutions. Particularly, contrary to the 1D case, the existence of a nonzero Peierls-Nabarro relief has been proved to exist in all cases, even if intersite proton-proton interactions are infinitely strong, so that the free 2D soliton dynamics is impossible in the ice crystal. On the other hand, our studies of the thermalization of the 2D ice lattice clearly demonstrate the crucial role of the cooperativity of hydrogen bonding in the nucleation and dynamics of the defect pairs ${\mathrm{H}}_{3}{\mathrm{O}}^{+}$ and ${\mathrm{OH}}^{\mathrm{\ensuremath{-}}},$ explaining their very low density known from experimental data in ice physics.