Implicit Chain Particle Model for Polymer-Grafted Nanoparticles

Matrix-free nanocomposites made from polymer-grafted nanoparticles (PGN) represent a paradigm shift in materials science because they greatly improve nanoparticle dispersion and offer greater tunability over rheological and mechanical properties in comparison to neat polymers. Utilizing the full potential of PGNs requires a deeper understanding of how polymer graft length, density, and chemistry influence interfacial interactions between particles. There has been great progress in describing these effects with molecular dynamics (MD). However, the limitations of the length and time scales of MD make it prohibitively costly to study systems involving more than a few PGNs, even with bead-spring coarse-grained models. Moreover, it remains unclear how to properly address shortcomings of these models in describing the rate-dependent constitutive response of polymers in a chemistry-specific fashion. Here, we address some of these challenges by proposing a new modeling paradigm for PGNs using a strain-energy mapping framework involving potential of mean force (PMF) calculations. In this approach, each nanoparticle is coarse grained into a representative particle with chains treated implicitly, namely, the implicit chain particle model (ICPM). Using a chemistry-specific coarse-grained molecular dynamics (CG-MD) model of poly(methyl methacrylate) as a testbed, we derive the effective interaction between particles arranged in a close-packed lattice configuration by matching bulk dilation and compression strain-energy densities up to failure. We establish an iterative optimization scheme to fine tune PMFs in the ICPM to accurately match the stress-strain behaviors during dilation and compression tests. The strain-rate dependence of the mechanical work done is quantified to reveal that the interparticle potential can be expressed with a strain-rate-dependent energy well depth that culminates in a simple power-law Cowper-Symonds strain hardening model. Given the aggressive degree of coarse graining (∼1:10 000) involved, the scope and limitations of the ICPM are cautiously discussed. Overall, the ICPM increases the computational speed by approximately 5-6 orders of magnitude compared to the CG-MD models. This novel framework is foundational for particle-based simulations of PGNs and their blends and accelerates the understanding and predictions of emergent properties of PGN materials.