The dynamics of freestanding films: predictions for poly(2-chlorostyrene) based on bulk pressure dependence and thoughtful sample averaging†
In this paper we model the segmental relaxation in poly(2-chlorostyrene) 18 nm freestanding films, using only data on bulk samples to characterize the system, and predict film relaxation times (τ) as a function of temperature that are in semi-quantitative agreement with film data. The ability to translate bulk characterization into film predictions is a direct result of our previous work connecting the effects of free surfaces in films with those of changing pressure in the bulk. Our approach combines the Locally Correlated Lattice (LCL) equation of state for prediction of free volume values (Vfree) at any given density (ρ), which are then used in the Cooperative Free Volume (CFV) rate model to predict τ(T, Vfree). A key feature of this work is that we calculate the locally averaged density profile as a function of distance from the surface, ρav(z), using the CFV-predicted lengthscale, Lcoop(z), over which rearranging molecular segments cooperate. As we have shown in the past, ρav(z) is significantly broader than the localized profile, ρ(z), which translates into a relaxation profile, τ(z), exhibiting a breadth that mirrors experimental and simulated results. In addition, we discuss the importance of averaging the log of position dependent relaxation times across a film sample (〈log τ(z)〉), as opposed to averaging the relaxation times, themselves, in order to best approximate a whole sample-averaged value that can be directly compared to experiment.