Leveraging Modern Computational Tools to Identify the Glass Transition From Noisy Data on Thin Polymer Films

Measurements of the glass transition frequently yield data where the transition manifests as a continuous change in slope from a linear liquid region to glassy region, with Tg often taken as the intersection of two linear fits or from a nonlinear fit to an equivalent functional form. Temperature-dependent film thickness data from ellipsometry is an example. The challenge arises for very thin films where the data are inherently noisier, and interfacial gradients cause significant broadening of the transition. Leveraging state-of-the-art computational tools, we address various inherent drawbacks of the methods commonly used. We compare the use of a Bayesian inference method to rapidly search combined subsets of parameter space relative to a standard nonlinear least squares fit. The Bayesian inference method we developed uses the open-source library PyMC as its backend to rapidly search the parameter space for the values that minimize the error of the model, allowing for efficient fitting while reducing ambiguity in the determination of Tg. We also test a least trimmed squares regression that was designed to isolate linear trends from noisy data, as well as simply a brute-force iterative search of all possible Tg values.