Evaluation of glassy-state dynamics from the width of the glass transition: Results from theoretical simulation of differential scanning calorimetry and comparisons with experiment

Abstract

The purpose of this study is to investigate the quantitative relationship between the width of the glass transition, ΔTg, and glass fragility or activation energy for structural relaxation. The ultimate objective is the estimation of structural relaxation time as a function of temperature from the width of the glass transition region, allowing characterization of glass dynamics by a single simple measurement. The Moynihan correlation indicates that activation energy for structural relaxation should be inversely proportional to the width of the glass transition, but recent experimental studies suggest this relationship is a poor approximation for glasses of pharmaceutical interest. The present study is an effort to better understand the validity of the Moynihan correlation by selected experimental studies and a theoretical analysis of those factors that impact the glass transition width. Experimental data for glass transition widths for (poly)vinylpyrrolidone, sucrose, and trehalose are obtained using a variety of procedures, and relaxation time data are obtained using the thermal activity monitor. The theoretical analysis begins by simulating the temperature dependence of the heat capacity by breaking the cooling and heating scans into a large number of temperature steps followed by isothermal holds, during which relaxation of the material is calculated. Here, the modified VTF equation is used for relaxation time and the generalized Kohlraush-Williams-Watts stretched exponential function is used to describe the relaxation kinetics. Simulations are performed for materials of varying fragility and varying “stretched exponential” constants, β, and the width of the glass transition region, ΔTg, is evaluated from the simulated heat capacity versus temperature curves as one would do with experimental data. Agreement between the theoretical simulations and experimental ΔTg data is excellent. The simulations demonstrate that although the Moynihan correlation is not valid for variable β, a modification of the Moynihan correlation which includes variation in β is a good approximation. Thus, an estimate of fragility may be obtained from glass transition width data provided an estimate of β is available. Furthermore, it is shown that a first approximation for β may be obtained from the magnitude (i.e., height) of the differential scanning calorimetry thermal overshoot. We also find that using the modified VTF equation to evaluate the temperature dependence of the structural relaxation time at the glass transition, and integrating this expression to lower temperatures, it is possible to obtain an evaluation of the relaxation time constant, τβ, in the glass at any temperature, using only the ΔTg and β values obtained from a single differential scanning calorimetry scan. These estimated time constants correlate very well with the values directly measured with the thermal activity monitor.