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 τ hop. We suggest a theoretical formalism that will be useful for the calculation of τ 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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry