A Bayesian Inference Approach to Accurately Fit the Glass Transition from Noisy Experimental Data

As artificial intelligence (AI) and machine learning frameworks are developed for advanced materials design, automated tools for robustly determining physical properties from experimental data are needed to supply unbiased labeling of training data. One such property is the glass transition temperature Tg, on which many other material properties depend. Even for human experimentalists, identifying Tg from experimental data is nontrivial due to the glass transition manifesting as a continuous change in slope in, for example, film thickness versus temperature data as might be collected via ellipsometry. Fitting such data from thin polymer films, a highly industrially relevant system exhibiting thickness-dependent shifts in Tg, is challenging due to increased noise and a broadening transition with decreasing film thickness. Here we show that Bayesian inference using Hamiltonian Monte Carlo can be applied to nonlinear least-squares fitting of temperature-dependent film thickness data to obtain a robust measure of Tg without the degree of human intervention required with existing fitting methods. We benchmark and contrast this automated-Bayesian approach against existing fitting methods commonly used in the field by using published data from supported polystyrene (PS) and poly(2-vinylpyridine) (P2VP) films collected over a wide range of film thicknesses by ellipsometry.