Examining Correlations Between Density and Dynamics in Thin Polymer Films: Modeling Refractive Index Gradients with Ellipsometry

A long standing issue with glassy dynamics in thin polymer films has been the question of whether density and dynamics may be correlated near interfaces. Several recent works have reported large, physically unrealistic density increases (~25%) with decreasing film thickness. Using ellipsometry, we have shown that polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(2-vinyl pyridine) (P2VP) all exhibit similar large increases in refractive index with decreasing thickness, also suggestive of large apparent increases in density. Results were found to be independent of molecular weight, chain connectivity, and substrate surface chemistry [Han et al., J Chem Phys 2020, 153, 044902]. Our investigation concluded these artificially large increases in film properties are likely associated with film inhomogeneities invalidating the common use of homogeneous approximations within layer model analyses. Here we demonstrate that an ellipsometric optical layer model with a depth-dependent gradient in refractive index appears to resolve most of these large, unphysical apparent increases. Modeling thin films with a linear gradient in refractive index n(z) surprisingly finds that PS and PMMA films have opposite trends in n(z), with PMMA films behaving counter to known dynamical gradients.