Fine 3D free energy map of diffusing small molecules in heterogeneous solid media

An efficient free energy calculation method is proposed for diffusing small molecules in heterogeneous solid media, such as polymers and inorganic solids, to obtain fine three-dimensional (3D) free energy maps consisting of one million meshes. The free energy of transfer of molecules from vacuum to individual meshes in the media was calculated according to the Widom equation using a new importance sampling method. The method simultaneously samples configurations of thousands of test molecules, each independently following a single-particle canonical distribution. The sampling was also accelerated using a high-temperature sampling method. The computational cost of the proposed method is considerably lower than that of the conventional particle insertion method, which relies on inefficient random sampling. Here, we demonstrate the present method by applying it to water molecules in polylactic acid and polypropylene, yielding fine 3D free energy maps with a resolution of 0.05 nm. The free energy integrated over the entire simulation cell showed excellent agreement with values independently obtained using the conventional particle insertion method applied to the entire space. The calculated results also showed good correspondence with experimental water absorption rates. The method is expected to facilitate molecular-level studies of absorption mechanisms, including the spatial distribution of absorption sites, their molecular structures, and the corresponding absorption free energies. The resulting maps also provide abundant information on microscopic diffusion mechanisms, such as 3D diffusion pathway networks formed by spatially distributed free energy saddle points connected by slopes from the absorption sites.