(119e) Incremental Gauge Cell Monte Carlo Simulation Method for Calculating Chemical Potential of Chain Molecules

Calculation of the chemical potential and free energy of polymer chains in atomistic simulations is a difficult problem. Many approaches have been proposed, all with their caveats. We suggest a new method, based on the chain-incrementing strategy of Kumar et al. [1] and its extension to the gauge cell method. The incremental chemical potential is calculating by adding a single monomer to a test chain and measuring the difference in the chain free energy. As such, the chain chemical potential represents the sum of these incremental values. Introduction of the gauge cell that contains monomers, which are added to or removed from the end of the test chain, provides three main benefits: first, it serves as a measure of the incremental chemical potential, second, it suppresses fluctuations and allows unstable states to be stabilized in the main cell, and third, exchange from main to gauge cell and back facilitates efficient sampling of state space. The method was applied to chains of Lennard-Jones beads with stiff harmonic bonds up to 500 monomers in length. We show that the suggested method quantitatively reproduces the modified Widom particle insertion method, and it is by the order of magnitude more efficient for long chains in terms of the computational time required for the same accuracy of chemical potential calculations. A special attention is paid to the studies of the behavior of single chains in confinements comparable in size with the free chain radius of inertia with and without adsorption potential and at various temperatures. At sufficiently low temperatures, the dependence of the incremental chemical potential on the chain length is superficially similar to adsorption and capillary condensation isotherms of simple Lennard Jones fluids. It reflects monolayer formation on the adsorbing wall with subsequent filling of the pore volume as the chain length increases.  We find that the incremental gauge cell Monte Carlo method is an accurate and efficient technique to calculate the free energy of chain molecules that can be applied for bulk and confined systems that may find practical applications, as shown with several examples of modeling polymer partitioning on porous substrates and dynamics of chain translocation into nanopores.

[1]  Kumar SK, Szleifer I, Panagiotopoulos AZ. Determination of the chemical potentials of polymeric systems from Monte Carlo simulations. Physical Review Letters. 1991;66(22):2935.