(248c) Efficient Sampling of Many-Body Coarse-Grained Potential of Mean Force for Polymer-Grafted Nanoparticles through Non-Equilibrium Forward-Reverse Path Integral.

Polymer-grafted nanoparticles (PGNs) can self-assemble superlattices with intricate crystal symmetries beyond simple crystal structures such as simple cubic or face-centered cubic crystals. Alongside the recent advancements in synthesizing these PGNs to understand their complex crystal assembly, computer simulations pave the way for comprehensively investigating assembly of these complex crystal systems. However, PGNs have a large number of associated high degrees of freedom, making simulation studies of the sluggish assembly kinetics computationally expensive. The Coarse-Graining (CG) method mitigates this issue by treating a nanoparticle and its surrounding polymer complex environment as a single “virtual-particle”, greatly reducing the degrees of freedom by treating inter-particle interactions via a Coarse-Grained Potential of Mean Force (CGPMF). Yet, the non-negligible many-body effect emerging at the thick grafting layer regime greatly complicates the coarse graining process. In this study, we combine techniques introduced in Kostzin et al. [1] and Zhou et al. [2] to enable computationally efficient generation of robust CGPMFs for PNGs. Our approach entails non-equilibrium forward-reverse path integral sampling with carefully chosen reaction coordinates, through the steered molecular dynamics (SMD). We validate our technique by comparing resulting two-body PMFs against those obtained from umbrella sampling method. Furthermore, we demonstrate the calculation of two and three-body CGPMFs, which, when combined, approximate the full many body CGPMFs. Additionally, our technique can be applied to consider up to four-body CGPMFs. Ultimately, our technique offers an efficient and reliable route for coarse-graining the PGNs, thereby extending the achievable simulation timescales.

[1] Kosztin, Ioan, Bogdan Barz, and Lorant Janosi. "Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski’s equality." The Journal of chemical physics 124, no. 6 (2006).

[2] Zhou, Yilong, Sigbjørn Løland Bore, Andrea R. Tao, Francesco Paesani, and Gaurav Arya. "Many-body potential for simulating the self-assembly of polymer-grafted nanoparticles in a polymer matrix." npj Computational Materials 9, no. 1 (2023): 224.