Relations of pressure and temperature dependences of the Johari-Goldstein β -relaxation to the α-relaxation: Amorphous polymers

An approximate relation between the Johari-Goldstein (JG) β-relaxation time τJG and the α-relaxation time τα was derived and predicted to be approximately invariant to variations of pressure P and temperature T at constant τα. This prediction was verified in several glass-formers where τα and τJG were determined directly without fitting by empirical procedure. In some polymers including PMMA, 1,4 polybutadiene and polyisoprene, either the JG β-relaxation or the α-relaxation was not resolved at all P and T, and τα and τJG had to be obtained by fitting the spectra by some procedure. Unfortunately, in fitting the spectra, the procedure commonly used allows τα and τJG to vary freely and independently of each other. Consequently, the values of τα and τJG obtained from the fits are artifacts of the inappropriate fitting procedure, and naturally the obtained values can deviate from the predicted relation. The deviations are artificial and cannot be used to test the prediction. Another purpose of the paper is to provide better understanding of the nature of the JG β-relaxation and to elucidate how and when the approximate relation between τα and τJG was found.