The Interfacial Layers Around Nanoparticle and Its Impact on Structural Relaxation and Glass Transition in Model Polymer Nanocomposites

We quantify the properties of the interfacial layers around bare nanoparticles (NPs) with variable NP diameter in model polymer-NP composites and near the solid substrate and free interfaces of supported thin polymer films using molecular simulations. These interfaces alter both the segmental packing and mobility in an interfacial layer. Variable NP diameter allows us to understand the effect of boundary curvature, where the film sets the limiting value of zero curvature. We find that the interfacial mobility scale \(\xi \) for both NPs and supported films increases on cooling, reaching a scale on the order of a few nanometers at low temperatures, regardless of the polymer-interfacial interaction strength. Additionally, we consider the related problem of the interfacial mobility scale of supported polymer films, which provides an upper limit for the interfacial scale of polymer-NP composites as the particle increases in size to macroscopic dimensions. We also characterize the interfacial density gradient scale \(\xi _\rho \) near the NP surface and find, in contrast to the length scale from dynamics \(\xi \), that \(\xi _\rho \) is even smaller and decreases on cooling in all cases simulated. In other words, the interfaces generally become more sharply defined on cooling. On the other hand, the scale of fluctuations in the interfacial density \(\sigma _{\rho }\) near solid interfaces, which reflects the degree of packing fluctuations, and thus “packing frustration”, grows on cooling and correlates in a near linear fashion with the interfacial mobility scale \(\xi \), although these characteristic thermodynamic and mobility scales have different dependences on the strength of interfacial interaction. Conversely, \(\sigma _{\rho }\) for the free interface in thin films grows on heating, similar to that of \(\xi _\rho \). Having characterized the thickness of interfacial layers from both structure and dynamics, we also examine their effect on the overall relaxation of materials and the glass transition temperature \(T_\mathrm{g}\) based on both thermodynamic and dynamic criteria. In particular, when the interfacial interaction strength is greater than the polymer-polymer interaction strength, a “bound” polymer layer forms near the interface (either the nanoparticle interface or film substrate), giving rise to an additional relaxation process in the self-intermediate scattering function. As a result, we find that \(T_\mathrm{g}\), defined from the gradient in the structural relaxation time, increases monotonically with polymer-interface interaction strength \(\varepsilon \). In contrast, the thermodynamically defined \(T_\mathrm{g}\), defined from “kinks” in the temperature dependence of quasi-thermodynamic properties, is found to saturate to a nearly constant value for \(\varepsilon \) values greater than the polymer-polymer interaction strength since this bound polymer layer effectively “cloaks” the NP or substrate from the unbound polymer from the strong interfacial interactions. Our findings emphasize the quantitative relationship between the interfacial scales in nanocomposites and thin polymer films and show that interfacial effects are rather universal in systems having significantly mobility gradients.