Universal Relation for Effective Interaction between Polymer-Grafted Nanoparticles

Understanding
the interactions between polymer-grafted nanoparticles
is imperative to predict the macroscale mechanical properties of the
nanocomposites they form. Molecular dynamics simulations capture the
interfacial effects of grafting on structure and mobility, but directly
linking these features to macroscale constitutive relations for nanocomposites
remains challenging. As a step toward addressing this challenge, we
develop a computational framework to predict the effective pairwise
interparticle interactions between polymer-grafted nanoparticles with
different design parameters, that is, polymer chain length, grafting
density, and polymer chemistry. Using coarse-grained molecular dynamics
simulations, we evaluate the potential of mean force between two nanoparticles
by varying their radial distance under uniaxial deformations, from
which an effective interaction can be derived. We find that the repulsive
part of the interaction can be expressed as an exponential repulsion
term, whereas the attractive part is best captured using a sigmoidal
form. The empirical constants of these equations depend linearly on
the chain length and quadratically on the grafting density. To ensure
that the finite rate of deformation does not affect our conclusions,
we also take into account the strain rate dependence of the effective
interaction, using a Cowper–Symonds model to extrapolate the
zero-rate limit of our results. With the development of this interatomic
potential between the nanoparticles, we propose a mesoscopic model
for nanoparticle assemblies that circumvents the need to explicitly
simulate polymer chains, significantly improving the computational
efficiency by extending the spatiotemporal scales by 6–7 orders
of magnitude.