Source of JG-Relaxation in the Entropy of Glass.

Abstract

Intrinsic mobility of the glassy state is known as Johari-Goldstein (JG)-relaxation. Its source is either rotational and translational motions of a small number of molecules or small-angle orientational motion of all molecules, which may include restricted translational motion of part of their flexible segments. We examine the merits of the two views by using the excess entropy, Sexc, the difference between the entropy of a glass and its crystal state. Its value at the glass-forming temperature, Sexc( Tg), is the sum of (1) Sexc from phonons and anharmonic forces and (2) the configurational entropy from (a) the JG-process and, (b) the unfrozen modes of the α-process. If all molecules participated in the JG-process, the minimum configurational entropy from this process would be R ln(2) [= 5.76 J/(mol K)], and [ Sexc( Tg) - Sexc(0 K)] cannot be less than that. Analysis of data for 33 liquid and 3 liquid crystal glasses and 7 orientational glasses shows that its value is less than or comparable to R ln(2) for 10 liquids and 2 orientational glasses. If contributions from (1) and (2b) were known and subtracted from Sexc( Tg), the [ Sexc( Tg) - Sexc(0 K)] value would be less than R ln(2) for more glasses. Cooperative motions to explain our finding and heterogeneous dynamics to explain the broad JG-relaxation spectra would require sufficiently large local mobility regions. We also argue that all molecules cannot participate in small-angle orientational fluctuations, cite evidence against such fluctuations for the JG-process, and note that nucleation and crystallization in a glass structure indicate such regions. After discussing the consequences for the entropy theory, the available NMR studies, the Eshelby inclusions, the potential energy landscape, and the Gardner transition, we conclude that JG-process likely occurs in local regions in internal equilibrium in a glass structure.