ANOMALOUS DIFFUSION IN CONFINED MONOLAYER FILMS

A monolayer, solid, epitaxial film confined to a prototypal slit-pore (a monatomic substance constrained between two parallel planar walls o f like atoms) and subjected to a shear strain (created by altering the transverse lateral alignment of the walls) begins to melt if a critic al strain (shear melting point) is exceeded. The resulting 'molten' ph ase exhibits structural disorder characteristic of a liquid yet suppor ts a shear stress. Molecular dynamics and Monte Carlo calculations are used to study self-diffusion in this molten phase as a function of th e excess shear strain above the critical value. Three distinct self-di ffusion time scales are manifest through plots of the mean-square disp lacement (MSD). Over the shortest time scale the MSD can be represente d by a power-law, similar to t(d), where t is time and d is a function of the excess shear strain, varying from 0 for the solid just below t he shear melting point to its Brownian-limit value of 1 for a complete ly liquefied film, having the disorder of a bulk fluid and supporting no shear stress. That d < 1 indicates anomalous (i.e., non-Brownian) s elf-diffusion. The intermediate time scale is characteristic of a stro ngly cooperative process that is spatially non-local and gives rise to anomalous diffusion. Both short and intermediate time scales exceed b y several orders of magnitude typical times after which Brownian diffu sion is observed in dense homogeneous bulk fluids. The persistance of anomalous diffusion is ascribed to severe spatial confinement of the f ilm atoms. The longest time scale corresponds to asymptotic Brownian d iffusion for which d = 1. All results are interpreted in terms of a mo del in which film atoms are diffusing in an effective molecular-scale porous medium generated by the potential field of the wall atoms.