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Characterizing heterogeneous dynamics at hydrated electrode surfaces
23. Stable hydrogen bond configurations can be generated by tiling the surface with a four-membered unit cell with no net dipole. By lattice symmetry four such tilings exist as shown on the left-hand side of Fig. 2(a). If tiling begins from the bottom left-hand side of the electrode and works up and to the right-hand side each water molecule can be uniquely assigned to one of the four patterns based on the relative orientation of the molecular dipole projected onto the plane parallel to the electrode.
24. Here we use the standard geometric criteria for identifying hydrogen bonds. That is two molecules are considered hydrogen bonded if the O–O distance is less than and the O–H⋅⋅⋅O angle is less than 35°.
25. G. Grimmett and D. Stirzaker, Probability and Random Processes (Clarendon Press, Oxford, 1992), Vol. 2.
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In models of Pt 111 and Pt 100 surfaces in water, motions of molecules in the first hydration layer are spatially and temporally correlated. To interpret these collective motions, we apply quantitative measures of dynamic heterogeneity that are standard tools for considering glassy systems. Specifically, we carry out an analysis in terms of mobility fields and distributions of persistence times and exchange times. In so doing, we show that dynamics in these systems is facilitated by transient disorder in frustrated two-dimensional hydrogen bonding networks. The frustration is the result of unfavorable geometry imposed by strong metal-water bonding. The geometry depends upon the structure of the underlying metal surface. Dynamic heterogeneity of water on the Pt 111 surface is therefore qualitatively different than that for water on the Pt 100 surface. In both cases, statistics of this ad-layer dynamic heterogeneity responds asymmetrically to applied voltage.
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