Anomalous diffusion in confined monolayer films

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Abstract
A monolayer, solid, epitaxial film confined to a prototypal slit-pore (a monatomic substance constrained between two parallel planar walls of like atoms) and subjected to a shear strain (created by altering the transverse lateral alignment of the walls) begins to melt if a critical strain (shear melting point) is exceeded. The resulting ‘molten’ phase exhibits structural disorder characteristic of a liquid yet supports a shear stress. Molecular dynamics and Monte Carlo calculations are used to study self-diffusion in this molten phase as a function of the excess shear strain above the critical value. Three distinct self-diffusion time scales are manifest through plots of the mean-square displacement (MSD). Over the shortest time scale the MSD can be represented by a power-law, ∼td , where t is time and d is a function of the excess shear strain, varying from 0 for the solid just below the shear melting point to its Brownian-limit value of 1 for a completely liquefied film, having the disorder of a bulk fluid and supporting no shear stress. That d < 1 indicates anomalous (i.e., non-Brownian) self-diffusion. The intermediate time scale is characteristic of a strongly cooperative process that is spatially non-local and gives rise to anomalous diffusion. Both short and intermediate time scales exceed by several orders of magnitude typical times after which Brownian diffusion is observed in dense homogeneous bulk fluids. The persistance of anomalous diffusion is ascribed to severe spatial confinement of the film atoms. The longest time scale corresponds to asymptotic Brownian diffusion for which d = 1. All results are interpreted in terms of a model in which film atoms are diffusing in an effective molecular-scale porous medium generated by the potential field of the wall atoms.