The continuous configurational Boltzmann biased direct Monte Carlo method for free energy properties of polymer chains

We develop here a highly efficient variant of the Monte Carlo method for direct evaluation of the partition function, free energy, and other configurational dependent physical properties for long polymer chains. This method (CC–BB) combines continuous configurational biased sampling with Boltzmann factor biased enrichment. To illustrate the efficiency and to validate the bias correction for weighting the torsion and chain enrichments, we applied this model to isolated single chains using a united atom force field. For a 50 monomer polymer chain CC–BB with 400 chains leads to an accuracy of 0.1% in the free energy whereas simple sampling direct Monte Carlo requires about 109 chains for this accuracy. This leads to cost savings by a factor of about 350 000. CC–BB is easily extended to multichain systems, to the condensed state, to more realistic force fields, and to evaluating the mixing free energy for polymer blends.