Iterative Integral Equation Analysis to Predict Solvation Thermodynamics in Coarse-Grained Polymer Melts Using MARTINI Models

Predicting the solvation thermodynamics of a solute in polymer melts at a coarse-grained (CG) level is important in diverse fields of macromolecular science. This knowledge supports the development of predictive CG models and the design of novel polymeric materials. However, accurately and efficiently calculating solvation thermodynamics in such complex systems remains a significant challenge. We present an application of the integral equation theory in combination with the iterative Boltzmann inversion (IBI) method to predict the solvation thermodynamics of three small molecules, including water, acetonitrile, and C60, in poly(ethylene glycol) (PEG) melts. To enhance computational efficiency, we further develop an efficient algorithm based on the direct inversion in the iterative subspace (DIIS) to solve the IBI-based integral equations. The analysis is performed within the framework of the MARTINI 3 force field. We demonstrate that our approach accurately incorporates the intrachain pair correlation functions of polymer chains and successfully predicts the liquid structure of PEG melts and solvation thermodynamics of the three molecules through a comparison with molecular dynamics (MD) simulations. We further investigate how the solvation thermodynamics of water depends on the PEG chain length and temperature. The obtained results reveal that PEG melts with longer chains at lower temperature are less favorable solvents for water. Finally, we discuss some necessary improvements and outline potential applications of our approach.