A Bayesian\nInference Approach to Accurately Fitting\nthe Glass Transition Temperature in Thin Polymer Films

We present a Bayesian\ninference-based nonlinear least-squares fitting\napproach developed to reliably fit challenging, noisy data in an automated\nand robust manner. The advantages of using Bayesian inference for\nnonlinear fitting are demonstrated by applying this approach to a\nset of temperature-dependent film thickness <i>h</i>(<i>T</i>) data collected by ellipsometry for thin films of polystyrene\n(PS) and poly(2-vinylpyridine) (P2VP). The glass transition experimentally\npresents as a continuous transition in thickness characterized by\na change in slope that in thin films with broadened transitions can\nbecome particularly subtle and challenging to fit. This Bayesian fitting\napproach is implemented using existing open-source Python libraries\nthat make these powerful methods accessible with desktop computers.\nWe show how this Bayesian approach is more versatile and robust than\nexisting methods by comparing it to common fitting methods currently\nused in the polymer science literature for identifying <i>T</i><sub>g</sub>. As Bayesian inference allows for fitting to more complex\nmodels than existing methods in the literature do, our discussion\nincludes an in-depth evaluation of the best functional form for capturing\nthe behavior of <i>h</i>(<i>T</i>) data with temperature-dependent\nchanges in thermal expansivity. This Bayesian fitting approach is\neasily automated, capable of reliably fitting noisy and challenging\ndata in an unsupervised manner, and ideal for machine learning approaches\nto materials development.