Scalable free energy computation of polymers in explicit solvent using TMMC and pre-generated conformation libraries

We present a novel application of the Transition Matrix Monte Carlo (TMMC) algorithm to compute the relative free energies of polymers in explicit solvents as a function of a selected order parameter. Our method leverages a pre-generated library of polymer conformations in vacuum, coupled with explicit solvent environments using the Growth Expanded Ensemble (GEE) framework. The integration of TMMC within GEE addresses sampling challenges by introducing bias in Monte Carlo simulations while enabling the computation of unbiased probability distributions and relative free energies. A key advantage of our approach is its flexibility-the polymer conformation library can be generated using any sampling technique, including Molecular Dynamics or Monte Carlo simulations, in implicit or explicit solvents and at different temperatures. The method is adaptable to any collective variable (CV) and can be extended to compute free energies as a function of multiple CVs. Furthermore, its parallelizable structure makes it highly scalable on multi-core central processing units and graphics processing unit architectures. To demonstrate its applicability, we apply it to a fully flexible polymer model consisting of Lennard-Jones particles connected via a harmonic potential, immersed in an explicit solvent of Lennard-Jones particles. The relative free energies are computed as a function of the radius of gyration. Results for three different solvents, obtained by varying the polymer-solvent interaction strength, reveal that the polymer preferentially adopts an extended conformation in good solvents and a collapsed conformation in poor solvents, consistent with theoretical expectations. Our method provides a computationally efficient and scalable framework for free energy calculations, with broad applications in polymer physics and macromolecular thermodynamics.