  The rate of escape of polymers from a two-dimensionally confining potential
well has been evaluated using self-avoiding as well as ideal chain
representations of varying length, up to 80 beads. Long timescale Langevin
trajectories were calculated using the path integral hyperdynamics method to
evaluate the escape rate. A minimum is found in the rate for self-avoiding
polymers of intermediate length while the escape rate decreases monotonically
with polymer length for ideal polymers. The increase in the rate for long,
self-avoiding polymers is ascribed to crowding in the potential well which
reduces the free energy escape barrier. An effective potential curve obtained
using the centroid as an independent variable was evaluated by thermodynamic
averaging and Kramers rate theory then applied to estimate the escape rate.
While the qualitative features are well reproduced by this approach, it
significantly overestimates the rate, especially for the longer polymers. The
reason for this is illustrated by constructing a two-dimensional effective
energy surface using the radius of gyration as well as the centroid as
controlled variables. This shows that the description of a transition state
dividing surface using only the centroid fails to confine the system to the
region corresponding to the free energy barrier and this problem becomes more
pronounced the longer the polymer is. A proper definition of a transition state
for polymer escape needs to take into account the shape as well as the location
of the polymer.
