Glass transition and fragility of nanosized polymeric fibers and spheres predicted from a surface-controlled model

In a previous article, we proposed a surface-controlled cooperatively rearranging region (SCC) model that mimics the segmental dynamics of supercooled liquids, including polymeric materials. By introducing surface/interface effects into the SCC model, the size-dependent dynamics of nanosized polymer materials such as ultrathin films can be predicted. In this study, the SCC model is extended to various nanomaterial geometries, i.e., filled fibers (cylinders), filled spheres, hollow fibers, hollow spheres, core/shell fibers, core/shell spheres, and thin films and spheres embedded in a substrate. We formulated temperature-dependent hole (free-volume) fraction profiles with respect to local position in the nanomaterials, and evaluated the weighted average of the hole fraction to consider the coupled dynamics in nanoconfined systems. The predicted glass transition temperature (Tg) and fragility (m) of filled spheres of polystyrene coincide qualitatively with experimental observations reported in literature. The geometry dependence of the dynamics was also investigated, and it was revealed that Tg(filled sphere)?> Tg(filled fiber)?>?Tg(free-standing film) when compared at the same surface area to volume ratio, whereas for fragility, the opposite trend was found, i.e., m(free-standing film)?>?m(filled fiber)?>?m(filled sphere).