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A polymer chain containing $N$ monomers confined in a finite cylindrical tubeof diameter $D$ grafted at a distance $L$ from the open end of the tube mayundergo a rather abrupt transition, where part of the chain escapes from thetube to form a "crown-like" coil outside of the tube. When this problem isstudied by Monte Carlo simulation of self-avoiding walks on the simple cubiclattice applying a cylindrical confinement and using the standardpruned-enriched Rosenbluth method (PERM), one obtains spurious results,however: with increasing chain length the transition gets weaker and weaker,due to insufficient sampling of the "escaped" states, as a detailed analysisshows. In order to solve this problem, a new variant of a biased sequentialsampling algorithm with re-sampling is proposed, force-biased PERM: thedifficulty of sampling both phases in the region of the first order transitionwith the correct weights is treated by applying a force at the free end pullingit out of the tube. Different strengths of this force need to be used andreweighting techniques are applied. Using rather long chains (up to N=18000)and wide tubes (up to D=29 lattice spacings), the free energy of the chain, itsend-to-end distance, the number of "imprisoned" monomers can be estimated, aswell as the order parameter and its distribution. It is suggested that this newalgorithm should be useful for other problems involving state changes ofpolymers, where the different states belong to rather disjunct "valleys" in thephase space of the system.

Escape transition of a polymer chain from a nanotube: how to avoid spurious results by use of the force-biased pruned-enriched Rosenbluth algorithm