The escape transition of a lattice star polymer grafted in a pore

Abstract Polymers in confined spaces are compressed and have reduced conformational
entropy, and will partially or fully escape from confinement if conditions are suitable. 
This is in particular the case for a polymer grafted in a pore. The escape of the polymer
from the pore may be considered a partial translocation from the pore into bulk solution, 
and the resulting conformational readjustment of the polymer has characteristics 
of a thermodynamic phase transition. In this paper a lattice self-avoiding walk model 
of a star polymer grafted in a pore is examined numerically using the PERM algorithm. 
We show that the arms of the grafted lattice star escape one at a time as the length 
of the pore is reduced, consistent with earlier results in the literature. Critical points 
for the escape transitions are estimated for square and cubic lattice models and we 
also examine various properties of the model as it undergoes the escape transition.