Relation between the alpha-Relaxation and Johari-Goldstein beta-Relaxation of a Component in Binary Miscible Mixtures of Glass-Formers

The coupling model was applied to describe the R-relaxation dynamics of each component in perfectly miscible mixtures A(1-x)B(x) of two different glass-formers A and B. An important element of the model is the change of the coupling parameter of each component with the composition, x, of the mixture. However, this change cannot be determined directly from the frequency dispersion of the R-relaxation of each component because of the broadening caused by concentration fluctuations in the mixture, except in the limits of low concentrations of either component, x -> 0 and x -> 1. Fortunately, the coupling model has another prediction. The coupling parameter of a component, say A, in the mixture determines tau_alpha/tau_JG, the ratio of the alpha-relaxation time, tau_alpha, to the Johari-Goldstein (JG) secondary relaxation time, tau_JG, of the same component A. This prediction enables us to obtain the coupling parameter, n_A, of component A from the isothermal frequency spectrum of the mixture that shows both the alpha-relaxation and the JG beta-relaxation of component A. We put this extra prediction into practice by calculating n_A of 2-picoline in binary mixtures with either tri-styrene or o-terphenyl from recently published broadband dielectric relaxation data of the alpha-relaxation and the JG beta-relaxation of 2-picoline. The results of n_A obtained from the experimental data show its change with composition, x, follows the same pattern as assumed in previous works that address only the alpha-relaxation dynamics of a component in binary mixtures based on the coupling model. There is an alternative view of the thrust of the present work. If the change of n_A with composition, x, in considering the alpha-relaxation of component A is justified by other means, the theoretical part of the present work gives a prediction of how the ratio tau_alpha/tau_JG of component A changes with composition, x. The data of tau_alpha and tau_JG of 2-picoline mixed with tri-styrene or o-terphenyl provide experimental support for the prediction.