De Gennes Narrowing and Hard-Sphere Approach

Importance of Many Particle Correlations to the Collective Debye-Waller Factor in a Single-Particle Activated Dynamic Theory of the Glass Transition

We theoretically study the importance of many body correlations on the collective Debye-Waller (DW) factor in the context of the Nonlinear Langevin Equation (NLE) single-particle activated dynamics theory of glass transition and its extension to include collective elasticity (ECNLE theory). This microscopic force-based approach envisions structural alpha relaxation as a coupled local-nonlocal process involving correlated local cage and longer range collective barriers. The crucial question addressed here is the importance of the deGennes narrowing contribution versus a literal Vineyard approximation for the collective DW factor that enters the construction of the dynamic free energy in NLE theory. While the Vineyard-deGennes approach-based NLE theory and its ECNLE theory extension yields predictions that agree well with experimental and simulation results, use of a literal Vineyard approximation for the collective DW factor massively overpredicts the activated relaxation time. The current study suggests many particle correlations are crucial for a reliable description of activated dynamics theory of model hard sphere fluids.

Collective Nanoparticle Dynamics Associated with Bridging Network Formation in Model Polymer Nanocomposites

The addition of nanoparticles (NPs) to polymers is a powerful method to improve the mechanical and other properties of macromolecular materials. Such hybrid polymer-particle systems are also rich in fundamental soft matter physics. Among several factors contributing to mechanical reinforcement, a polymer-mediated NP network is considered to be the most important in polymer nanocomposites (PNCs). Here, we present an integrated experimental-theoretical study of the collective NP dynamics in model PNCs using X-ray photon correlation spectroscopy and microscopic statistical mechanics theory. Silica NPs dispersed in unentangled or entangled poly(2-vinylpyridine) matrices over a range of NP loadings are used. Static collective structure factors of the NP subsystems at temperatures above the bulk glass transition temperature reveal the formation of a network-like microstructure via polymer-mediated bridges at high NP loadings above the percolation threshold. The NP collective relaxation times are up to 3 orders of magnitude longer than the self-diffusion limit of isolated NPs and display a rich dependence with observation wavevector and NP loading. A mode-coupling theory dynamical analysis that incorporates the static polymer-mediated bridging structure and collective motions of NPs is performed. It captures well both the observed scattering wavevector and NP loading dependences of the collective NP dynamics in the unentangled polymer matrix, with modest quantitative deviations emerging for the entangled PNC samples. Additionally, we identify an unusual and weak temperature dependence of collective NP dynamics, in qualitative contrast with the mechanical response. Hence, the present study has revealed key aspects of the collective motions of NPs connected by polymer bridges in contact with a viscous adsorbing polymer medium and identifies some outstanding remaining challenges for the theoretical understanding of these complex soft materials.