Does the Naıve Mode-Coupling Power Law Divergence Provide an Objective Determination of the Crossover Temperature in Glass Formation Behavior?

The glass formation temperature range is commonly divided into a weakly supercooled regime at higher temperatures and a deeply supercooled regime at lower temperatures, with a change in the physical mechanisms that govern dynamics often postulated to occur at the crossover between these regimes. This crossover temperature <i>T</i>_c is widely determined based on a fit of relaxation time vs temperature data to a power law divergence form predicted by the naı̈ve mode coupling theory (MCT). Here, we show, based on simulation data spanning polymeric, small molecule organic, metallic, and inorganic glass formers, that this approach does not yield an objective measure of a crossover temperature. Instead, the value of <i>T</i>_c is determined by the lowest temperature <i>T</i>_min employed in the fit, and no regime of stationary or convergent <i>T</i>_c value is generally observed as <i>T</i>_min is varied. Nor does the coefficient of determination <i>R</i>² provide any robust means of selecting a fit range and thus a value of <i>T</i>_c. These results may require a re-evaluation of published results that have employed the fit MCT <i>T</i>_c value as a metric of temperature-dependent dynamics or a benchmark for depth of supercooling, and they highlight a need for the field to converge on a more objective determination of any posited crossover temperature between high and low temperature regimes of glass formation.