Axiomatic Theories of Intermediate Phases (IP) and Ideal Stretched Exponential Relaxation (SER)

TL;DR

This paper reviews axiomatic theories explaining the universal occurrence of stretched exponential relaxation (SER) in complex systems like glasses, highlighting the role of shape fractions and models such as Scher-Lax and Phillips.

Contribution

It provides a comprehensive review of axiomatic theories for SER and IP, emphasizing the significance of specific shape fractions and models in complex non-equilibrium materials.

Findings

SER is observed universally in complex glasses and materials.

Specific shape fractions b = 3/5 and 3/7 are confirmed experimentally.

Different b values are observed in dielectric SER with ion conduction due to electric fields.

Abstract

Minimalist theories of complex systems are broadly of two kinds: mean-field and axiomatic. So far all theories of properties absent from simple systems and intrinsic to complex systems, such as IP and SER, are axiomatic. SER is the prototypical complex temporal property of glasses, discovered by Kohlrausch 150 years ago, and now observed almost universally in microscopically homogeneous, complex non-equilibrium materials (strong network and fragile molecular glasses, polymers and copolymers, even electronic glasses). The Scher-Lax trap model (1973) is paradigmatic for electronic SER; for molecular SER Phillips (3RCS 1995) identified two "magic" shape fractions \beta = 3/5 and 3/7, as confirmed by many later experiments here reviewed. In the dielectric SER frequency domain involving ion conduction, there are also special beta values for fused salts and glasses, slightly, but distinguishably, different because of the presence of a forcing electric field.