  Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover
from single file diffusion to normal diffusion as the channel becomes wide
enough for particles to hop past each other. In the crossover regime, where
hopping events are rare, the diffusion coefficient in the long time limit can
be related to a hopping time that measures the average time it takes a particle
to escape the local cage formed by its neighbours. In this work, we show that a
transition state theory that calculates the free energy barrier for two
particles attempting to pass each other in the small system isobaric ensemble
is able to quantitatively predict the hopping time in a system of
two-dimensional soft repulsive discs [$U(r_{ij})=(\sigma/r_{ij})^{\alpha}$]
confined to a hard walled channel over a range of channel radii and degrees of
particle softness measured in terms of $1/\alpha$. The free energy barrier
exhibits a maximum at intermediate values of $\alpha$ that moves to smaller
values of $1/\alpha$ (harder particles) as the channel becomes narrower.
However, the presence of the maximum is only observed in the hopping times for
wide channels because the interaction potential dependence of the kinetic
prefactor plays an increasingly important role for narrower channels. We also
begin to explore how our transition state theory approach can be used to
optimize and control dynamics in confined quasi-one-dimensional fluids.
