Fitting meaningful model parameters to relevant data is a valuable tool for inferring microstructural information from rheology. In this work, we focus on the asymptotically-nonlinear medium-amplitude oscillatory shear (MAOS) data, the next systematic step after small-amplitude oscillatory shear (SAOS). The first part of this research is composed of new methods development and improvements in current practices for fitting MAOS. We develop a new, faster and material economical technique for MAOS enabling its nontrivial data acquisition much easier. We further propose confidence metrics for validating the single measurements of the new MAOS protocol. We remind the community that an honest uncertainty quantification of fit parameter estimates requires fitting SAOS+MAOS simultaneously. Even then there are subjective choices in fitting, particularly for SAOS data. We demonstrate that fitting with data uncertainty weighted least squares significantly reduces the effects of subjectivity. As a follow up, we provide a methodology for estimating uncertainties in single measurement SAOS data.
In the second part of the research, we apply the ideas of previous part to fit the data on two entangled polyethylene melts: a linear polyethylene melt and its blend with a three-arm symmetric star polymer (5 weight % of star by composition). We show that the simplest model for entangled polymer melts i.e. the Doi-Edwards reptation model is not able to capture the MAOS data of our systems. We then proceed to fit various other sophisticated and mathematically more complex models categorizing them as time-strain separable (TSS) versus non-TSS MAOS models with a discrete or continuous spectrum parameterization for model parameters. We choose the most credible model from among these models using Bayesian information criterion (BIC). The most credible model for the linear polyethylene melt comes out to be a TSS MAOS model with a fractional Maxwellian continuous spectrum parameterization for SAOS, with a single nonlinear parameter whose fit value indicates: (1) a non-negligible polymer chain stretch compared to chain orientation, and (2) that the cross sectional area of the mean field tube around a chain deforms affinely with the average macroscopic deformation. Interestingly for the polymer blend, while the differences in data compared to pure linear melt are minor, they are sufficient to alter the choice of most credible model. For the blend case, the most credible model is still a TSS MAOS model with a fit value of nonlinear parameter that gives the same interpretation for chain stretch and tube deformation, however, the response for SAOS is now best explained by a lognormal continuous spectrum compared to the fractional Maxwell continuous spectrum for the pure linear melt case. This approach of selecting the most credible model for a given dataset has the potential to inform what physics and its governing mathematics might be missing from the well-accepted models
