Thermodynamic Perturbation Theory for Charged Branched Polymers

Classical density functional theory (DFT) provides a versatile framework to study the polymers with complex topological structure. Generally, a classical DFT describes the excess Helmholtz free energy of nonbonded chain connectivity due to excluded-volume effects and electrostatic correlations using the first-order thermodynamic perturbation theory (referred to as DFT-TPT1). Beyond first-order perturbation, the second-order TPT (TPT2) captures not only the correlations between neighboring monomers but also the interactions within three consecutive monomers, playing a crucial role in describing the polymer topology. However, the numerical implementation of TPT2 is limited by the lack of an effective triple correlation function (CF), especially for charged systems. Here, we propose an effective triple CF and incorporate it into DFT using TPT2 (referred to as DFT-eTPT2) to describe the nonbonded chain connectivity due to excluded-volume effects and electrostatic correlations. Using the data from molecular dynamics simulation as a benchmark, DFT-eTPT2 shows a clear improvement over DFT-TPT1 in predicting the density profiles of both neutral and charged branched polymer brushes, accurately capturing key structural features, such as the significant peaks near the branching point in the density profiles. In short, this work provides a precise and efficient theoretical tool for revealing molecular-level insights into branched polymers and their brushes.