Normal and anomalous diffusion in highly confined hard disk fluid mixtures

Monte Carlo simulation is used to study binary mixtures of two-dimensional hard disks, confined to long, narrow, structureless pores with hard walls, in a regime of pore sizes where the large particles exhibit single file diffusion while the small particles diffuse normally. The dynamics of the small particles can be understood in the context of a hopping time, τ21, that measures the time it takes for a small particle to escape the single file cage formed by its large particle neighbors, and can be linked to the long time diffusion coefficient. We find that τ21 follows a power law as a function of the reduced pore radius for a wide range of particle size ratios with an exponent, α, that is independent of the size ratio, but linearly dependent on the Monte Carlo step size used in the dynamic scheme. The mean squared displacement of the small particles as a function of time exhibits two dynamic crossovers. The first, from normal to anomalous diffusion, occurs at intermediate times then the system returns to normal diffusion in the long time limit. We also find that the diffusion coefficient is related to τ21 through a power law with exponent Β=-0.5, as predicted by theory. Finally, we show that particle separation in a binary mixture will be optimal at the pore radius that causes the large particles to undergo their transition from normal to anomalous diffusion.