Clarifying the nature of the Johari-Goldstein β-relaxation and emphasising its fundamental importance

Since 1998 the primitive relaxation time tau(0)(T,P) of the Coupling Model (CM) and the Johari-Goldstein (JG) beta-relaxation time tau(JG)(T,P) are shown approximately equal in many glass-formers. The CM relation between tau(0)(T,P) and tau(alpha)(T,P) at anyTandPis exact. Additionally from the CM relation tau(alpha)(T,P)/tau(0)(T,P) isexactlyinvariant to variations ofTandPwhile tau(alpha)(T,P) is kept constant, and tau(0)isexactlya function of rho(gamma)/Tlike tau(alpha). However, since tau(JG)(T,P) approximate to tau(0)(T,P), the exact invariance of tau(alpha)(T,P)/tau(0)(T,P) leads toapproximateinvariance of tau(alpha)(T,P)/tau(JG)(T,P), and tau(JG)isapproximately afunction of rho(gamma)/T. Notwithstanding, the CM prediction of the approximate relations between tau(beta)and tau(alpha)were mistaken asexactrelations by some researchers. In this paper, we remove this misunderstanding by demonstrating via simulations and experiments that the JG beta-relaxation is comprised of processes with different length-scales and degrees of cooperativity, and the process is heterogeneous. The distribution of processes makes tau(JG)(T,P) equivocal, because it is just a single relaxation time used to represent the different processes within the distribution, which may change on varyingTandP, at constant tau(alpha)(T,P). The problem is compounded if the beta-relaxation is not resolved, and fitting procedure used to extract tau(JG)(T,P) and tau(alpha)(T,P). Despite the relations of tau(JG)(T,P) to tau(alpha)(T,P) are approximate, we show these properties of tau(JG)(T,P) are truly remarkable, fundamental, general, and important.