LAUSR

ABSTRACT Since 1998 the primitive relaxation time τ 0(T,P) of the Coupling Model (CM) and the Johari-Goldstein (JG) β-relaxation time τJG (T,P) are shown approximately equal in many glass-formers. The CM relation between τ 0(T,P) and τα (T,P) at any T and P is exact. Additionally from the CM relation τα (T,P)/τ 0(T,P) is exactly invariant to variations of T and P while τα (T,P) is kept constant, and τ 0 is exactly a function of ρ γ/T like τα . However, since τJG (T,P) ≈ τ 0(T,P), the exact invariance of τα (T,P)/τ 0(T,P) leads to approximate invariance of τα (T,P)/τJG (T,P), and τJG is approximately a function of ρ γ/T. Notwithstanding, the CM prediction of the approximate relations between τβ and τα were mistaken as exact relations by some researchers. In this paper, we remove this misunderstanding by demonstrating via simulations and experiments that the JG β-relaxation is comprised of processes with different length-scales and degrees of cooperativity, and the process is heterogeneous. The distribution of processes makes τJG (T,P) equivocal, because it is just a single relaxation time used to represent the different processes within the distribution, which may change on varying T and P, at constant τα (T,P). The problem is compounded if the β-relaxation is not resolved, and fitting procedure used to extract τJG (T,P) and τα (T,P). Despite the relations of τJG (T,P) to τα (T,P) are approximate, we show these properties of τJG (T,P) are truly remarkable, fundamental, general, and important.