**Using Theory and Simulations To Calculate Effective Interactions in
Polymer Nanocomposites with Polymer-Grafted Nanoparticles**

TB Martin and A Jayaraman, MACROMOLECULES, 49, 9684-9692 (2016).

DOI: 10.1021/acs.macromol.6b01920

Using theory and large-scale simulations, we demonstrate how one can program structure and thermodynamics into polymer-grafted particles filled polymer nanocomposites (PNCs). We simulate varying graft (G) and matrix (M) polymer compositions for varying model graft-matrix bead pairwise interactions, chi(GM), and calculate structural features and the effective graft-matrix interaction parameter, chi(eff)(GM), in the PNC. Varying the graft (G) and matrix (M) polymer compositions provides tunability of morphology (particle dispersion/aggregation) and graft matrix interpenetration at each chi(GM). Thermodynamically, for all composites the chi(eff)(GM) exhibits negative values (effective attraction) at low values of chi(GM), with a sharp transition to positive values (effective repulsion) at large values of chi(GM). The sharp transition in chi(eff)(GM) coincides with the structurally characterized particle dispersion-aggregation transition marked by the onset of upturn in the matrix matrix structure factor at zero wavenumber. Strikingly, regardless of the composition of the graft and matrix chains or the dispersion aggregation transition point, universally, the effective interactions in the PNC at the dispersion- aggregation transition is identical to the analogous athermal PNC.

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