Tailoring Nanoparticle Orientation in Polymer Matrices via Nonuniform Grafting: Implications for Nanoparticle Dispersions and Self-Assembled Nanocomposite Morphologies

We propose a three-dimensional model implementing a self-consistent field (SCF) mathematical formulation to predict the equilibrium orientation and morphology of grafted nanoparticles (NPs) in a polymer, based on two- and multibody interactions developed among them. First, we investigate the potential of mean force (PMF) between two spherical polystyrene-grafted silica NPs in a polystyrene melt as a function of the matrix-to-grafted chain length ratio and, more importantly, of the distribution of grafting points on their surfaces. While the most common assumption when performing such calculations is an equidistant distribution of grafting points on the surfaces of the NPs, we demonstrate here that the pattern of grafting plays an essential role in the equilibrium orientation and shape assumed by the particles inside the polymer matrix. In equidistant grafting, the role of grafting density is dominant, but, when grafting the chains irregularly, the same number of grafted chains distributed differently can significantly affect the self-assembly tendencies of the particles and the thermodynamic behavior of the composite system. Next, we calculate the free energy of a system of multiple equidistantly grafted nanoparticles exposed to a melt when they are arranged in a simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) lattice as a function of their spatial density. We minimize the free energy with respect to nanoparticle density to impose the condition of thermodynamic equilibrium. Among the three arrangements, the FCC/SC is the most/least stable configuration. The three-dimensional SCF methodology proposed herein addresses all possible degrees of freedom for the molecular-level design of both stable dispersions and self-assembled nanocomposite morphologies with tailor-made properties. It offers a cost-effective approach to creating high-value nanocomposite materials such as polymer-matrix nanocomposites in the rubber industry as well as “particle-solids,” the latter combining toughness with good optical properties.