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, tau(21), 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 tau(21) follows a power law as a function of the reduced pore radius for a wide range of particle size ratios with an exponent, alpha, 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 tau(21) through a power law with exponent beta=-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.

Landscapes, dynamic heterogeneity, and kinetic facilitation in a simple off-lattice model.

We present a simple off-lattice hard-disk model that exhibits glassy dynamics. The inherent structures are enumerated exactly, transitions between metabasins are well understood, and the particle configurations that act to facilitate dynamics are easily identified. The model readily maps to a coarse grained dynamic facilitation description.

Calculating the hopping times of confined fluids: two hard disks in a box.

The dynamical transition between the anomalous single file diffusion of highly confined fluids and bulk normal diffusion can be described by a phenomenological model involving a particle hopping time tau(hop). We suggest a theoretical formalism that will be useful for the calculation of tau(hop) for a variety of systems and test it using a simple model consisting of two hard disks confined to a rectangular box with hard walls. In the case where the particles are moving diffusively, we find the hopping time diverges as a power law in the threshold region with an exponent of -(3/2). Under conditions where the particles move inertially, transition state theory predicts a power law behavior with an exponent of -2. Molecular dynamics simulations confirm the transition state theory result for inertial dynamics, while Brownian dynamics simulations suggest the scaling exponent is highly sensitive to the details of the algorithm.

Osmotic force resisting chain insertion in a colloidal suspension.

We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accommodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple scaling arguments. The forces computed in these ways are shown, for nanometer chain and colloid diameters, to be of the order of tens of pN for solution volume fractions of a few tenths. These magnitudes are argued to be important for biophysical processes such as the ejection of DNA from viral capsids into the cell cytoplasm.