Many-Body Potential for Simulating Self-Assembly of Polymer-Grafted Nanoparticles in a Polymer Matrix

Many-body effects (interactions) play a key role in promoting low-dimensional assembly of polymer-grafted nanoparticles (NPs) in polymer melts or at interfaces. However, capturing such interactions in molecular dynamics simulations and understanding their effects on self-assembly remain challenging because explicit modeling of the polymers is highly computationally expensive even using coarse-grained models. In this work, we introduce a general machine learning (ML) approach to develop an analytical three-body potential that can describe the many-body interactions between polymer-grafted NPs in a polymer matrix. Our approach involves the use of permutational invariant polynomials to fit the Morse-transformations of interparticle distances. The developed potential reduces the computational cost by several orders of magnitude and thus allows us to explore NP assembly at large length and time scales. We show that the developed three-body potential can reproduce the previously discovered phases including 1d strings and 2d hexagonal sheet and help discover many interesting phases like network strings, small clusters, and gel phases. The roles of three-body contributions on the formation of those phases are also elucidated. Overall, our work suggests the usefulness of machine learning in dealing with complex problems in polymer nanocomposites and in predicting new types of NP assemblies is promising.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.