Title: Assembly of Polymer-Grafted Nanoparticles in Polymer Matrices
Description: Polymer nanocomposites (PNCs) have found their way into our everyday lives in a long list of applications, including airplane parts and car tires. This is due to their unique properties of combining the strengths of their constituents – elasticity and stiffness – while mitigating their weaknesses – softness and brittleness. In the past few decades, they have generated more interest due to the discovery that the PNCs’ optical, electrical, and a host of other properties can be tuned for specific use by controlling the assembly and dispersion of nanoparticles (NPs) within the host polymer matrix. The grafting of some of the matrix chains onto the surface of the NPs not only improves NP miscibility but also grants an additional handle tocontrol the self-assembly of NPs. However, at present, there remains many open questions in the field of these novel PNCs. For instance, it is commonly believed that long enough matrix polymers of length P will spontaneously dewet a chemically identical polymer layer, comprised of sufficient chains of length N , end-grafted to a flat surface (”brush”).

This entropically driven idea is frequently used to explain experiments in which 10-20 nm diameter polymer-grafted NPs are observed to phase separate from homopolymer matrices for P/N⪆4. At lower grafting densities, these entropic effects are also thought to underpin the self-assembly of grafted NPs into a diverse set of structures. To explore the validity of this picture, a two-pronged approach is used in this thesis, exploring such systems from both a single NP and a multi-NP point of view in order to find novel methods for understanding and controlling NP dispersion in polymers. In each of the chapters, we employ coarse-grained Molecular Dynamics (MD) simulations to understand the self-assembly and dispersion behavior in PNCs, with the experimental analog being primarily polystyrene (PS) grafted silica NPs in PS matrices. We start by investigating the entropic effects of P/N on the brush of a single grafted NP, taking advantage of an indirect umbrella sampling method (INDUS) to quantify matrix density fluctuations.

This method essentially makes use of an external biasing potential to mimic the dewetting of the brush. We find for the first time that entropic P/N effects can be identified at the single NP level and is primarily surface driven. INDUS is later extended to two-body and many-body NP systems, to understand the role of NP surfactantcy in the self-assembly of grafted NPs and create free-energy profiles for a range of inter-NP separations. Finally, results from a comprehensive series of large-scale multi-NP simulations, where we consider NPs in the ≈ 5nm and ≈ 10nm size range. For the smaller NPs, we find no evidence of phase separation even for P/N = 10 in the absence of attractions. Instead, we discover that we are able to recreate most of the experimentally observed structures when allthe polymer chain monomers are equally attractive to each other but repel the NPs. Only when the NPs are in the ≈ 10nm size range that we are able to access the phase separated morphologies. Our results thus imply that experimental situations where the grafting density is low are dominated by the surfactancy of the NPs, which is driven by the chemical mismatch between the inorganic core and the organic ligands (the graft and free chains are chemically identical).

Entropic effects, i.e. the translational entropy of the NPs and the matrix, the entropy of mixing of the grafts and the matrix, and the conformational entropy of the chains appear to thus play a second order effect even in the context of these model systems. Each of these insights provides details around controlling the organization and assembly of NPs in polymers for the purpose of improving their mechanical properties, all while changing the way in which the material is designed.