**Understanding the Effect of Heterogeneous Particle Functionalization on
Graft-Matrix Wetting and Structure in Polymer Nanocomposites Containing
Grafted Nanoparticles Using Multiscale Modeling and Simulation**

U Kapoor and A Kulshreshtha and SC Brown and A Jayaraman, ACS APPLIED POLYMER MATERIALS, 3, 5642-5655 (2021).

DOI: 10.1021/acsapm.1c00953

We use multiscale modeling and simulations to investigate the effect of heterogeneous grafted ligands that vary in chemistry, size, composition, and placement on the dispersion and aggregation of grafted nanoparticles in (matrix) oligomer solutions. Motivated by industrial formulations that contain nanoparticles in complex solutions, such as paints, coatings, varnishes, printing inks, toners, and cosmetics, we study nanoparticles of diameters roughly 10-25 nm grafted with hydrophobic and/or hydrophilic oligomer denoted as "A") and alkanes (denoted as "B") as the model hydrophilic and hydrophobic graft and matrix chain chemistries, respectively. We simulate the A/B-grafted nanoparticles in A/B oligomer solution using coarse-grained (CG) models at two different length scales- "monomer level" and "chain level"; in the "monomer-level" CG model, each CG bead represents a monomer or two in A and B chain chemistries, and in the "chain-level" CG model, each CG bead represents an entire A or B oligomer chain, with bonded and nonbonded interactions for both these generic CG models guided by atomistic simulations of oligomers of poly(ethylene glycol) and alkanes in explicit water. Using the "monomer-level" CG model, we simulate explicit A and B chains in the grafted layer interacting with A or B matrix chains in solution. We find that the graft-matrix wetting increases when the grafted layer is composed mainly of B chains that are shorter, stiffer, and more attractive toward A and B chains than A chains are and when A and B-grafted chains are placed in segregated domains (i.e., patchy arrangement) on the particle. Comparison with analogous systems with only excluded volume interactions shows that the wetting trends with the grafted layer composition and placement are driven primarily by entropic driving forces, with the attractive interactions simply enhancing the entropically-driven grafted layer wetting. Using the "chain-level" CG model, we then simulate multiple grafted particles with particle diameter 10-20 times that of the graft/matrix chain size (i.e., twice the radius of gyration) in solutions containing matrix B chain CG beads. Simulations with this "chain-level" CG model show that when the particle surface is entirely functionalized homogeneously with chain A alone, the attractive A-B interactions and repulsive A-A interactions and particle translational entropy drive the grafted particles to remain dispersed in solutions of B matrix chains. In contrast, when the particle surfaces have heterogeneous functionalization of A and B chains, we observe particle aggregation with specific aggregated morphologies being a function of A and B graft placements. These results from the two different levels of CG models describe the complex balance of enthalpic and entropic driving forces that dictate grafted layer wetting and the dispersion/aggregation of grafted particles within complex formulations.

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