Description of a glass transition with immeasurable structural relaxation time

A general problem of studying supercooled liquids and glasses is very long relaxation times that do not allow determining explicitly dynamic characteristics. One of the ways to solve this problem is extrapolating values of some dynamical property (e.g. viscosity) from the temperature range where it can be directly measured (simulated) to the low-temperature region. Such extrapolations are usually contradictory because different fitting functions can give substantially different results. Thus, the development of methods for robust extrapolation is an urgent task especially for molecular dynamic study of glassforming liquids. Here we propose a model-free statistical algorithm for a low-temperature extrapolation of liquid viscosity (diffusion coefficient) and apply it to the problem of determination of glass transition temperature and the temperature Tc where the viscosity formally diverges. Our approach is based on numerical analytical continuation of temperature dependence of the viscosity using Padé approximants and error correction procedures using statistical averaging for the treatment of noisy input data. We tested the method on several glass-forming systems and revealed good stability and predictability. Our extrapolation algorithm is suitable for both numerical and experimental studies of glassformers when it is necessary to descend into the parameter range where structural relaxation times of a liquid are too long to be directly obtained.