Assembly of Polymer-Grafted Nanoparticles Dictates the Topological Constraints on Grafted Chains

The rheological response and polymer dynamics in nanocomposites synthesized from polymer-grafted nanoparticles are significantly influenced by the nanoparticle arrangements. Small-angle X-ray scattering (SAXS) serves as an excellent tool to unearth the spatial arrangements of polymer-grafted nanoparticles. However, despite the good data fits, the density of the grafted polymer obtained from the fit parameters of the commonly used hard sphere model is found to be incorrect for our nanocomposites with different molecular weights (Mw) of the grafted chains. Therefore, the hard sphere model leads to inappropriate quantitative descriptions of nanoparticle assemblies for our nanocomposites. This renders it impossible to quantitatively connect the structural features of nanocomposites to relevant properties, e.g., density, rheological response, and so forth. We analyze SAXS data by accounting for the polymer-induced interactions between the nanoparticles and demonstrate significantly different geometric assemblies in nanocomposites with different Mw. Effects of these nanoparticle arrangements are manifested as different topological and dynamical features of the grafted polymer chains observed by rheology. We show that the unentangled as well as weakly entangled grafted polyisoprene chains exhibit an apparent entanglement plateau in their rheological response. We construct a Rouse mode analysis by selectively altering the mode amplitudes and relaxation times to model the stress relaxation modulus for the pure polymer and nanocomposites. Our analysis elegantly captures the site-dependent topological confinements in ungrafted as well as grafted polymers. While the pure polymers exhibit uniform entanglement tubes, the topological confinements for grafted chains are realized to be nonuniform. Remarkably, the confinement lengths obtained from Rouse mode analysis relate to the nanoparticle assembly and corresponding distances between the nanoparticles from SAXS. Overall, with our Rouse mode analysis of rheology and SAXS results, we are able to establish quantitative relations between the nanoparticle assembly and the polymer structure in the nanocomposites.