Effective interactions between grafted nanoparticles in a polymer matrix

Abstract

Molecular dynamics simulations were used to delineate the separation dependent forces between two polymer-grafted nanoparticles in a polymer melt, the associated potential of mean force (PMF), and the molecular origins of these forces. The nanoparticle radius (=5, in units of the size of the chain monomers) and grafted brush length (=10) were held constant, while the grafting density and the polymer matrix length were varied systematically in a series of simulations. We first show that simulations of a single nanoparticle do not reveal any signatures of the expected autophobic dewetting of the brush with increasing polymer matrix length. In fact, density distributions of the matrix and grafted chains around a single nanoparticle appear to only depend on the grafting density but not on the matrix chain length in the regime where autophobic dewetting is expected, i.e., when the matrix chain length is equal to or longer than the graft chain length. We thus conjecture that two nanoparticle simulations might be more illuminating in these situations. Indeed, the calculated forces between two nanoparticles in a melt show that increasing the matrix chain length from 10 to 70 causes the inter-nanoparticle potential of mean force (PMF) to go from purely repulsive to attractive with a well depth on the order of kBT. These results are purely entropic in origin and arise from a competition between brush-brush repulsion and an attractive inter-nanoparticle interaction caused by matrix depletion from the inter-nanoparticle zone. The matrix-induced Asakura-Oosawa type inter-nanoparticle attraction, which dominates at intermediate nanoparticle separations especially in the case of long matrix chains, is thus implicated as the essential player in the autophobic dewetting phenomenon, which drives phase separation in these situations.