“Inner clocks” of glass-forming liquids

Abstract

Providing a physically sound explanation of aging phenomena in non-equilibrium amorphous materialsis a challenging problem in modern statistical thermodynamics. The slow evolution of physical propertiesafter quenches of control parameters is empirically well interpreted via the concept of material time (orinternal clock), based on the Tool-Narayanaswamy-Moynihan (TNM) model. Yet, the fundamental reasonsof its striking success remain unclear. We propose a microscopic rationale behind the material time onthe basis of the linear laws of irreversible thermodynamics and its extension that treats the correspondingkinetic coefficients as state functions of a slowly evolving material state. Our interpretation is based onthe recognition that the same mathematical structure governs both the Tool model and the recently devel-oped non-equilibrium extension of the self-consistent generalized Langevin equation theory (NE-SCGLE),guided by the universal principles of Onsager's theory of irreversible processes. This identification opensthe way for a generalization of the material-time concept to aging systems where several relaxation modeswith very different equilibration processes must be considered, and partially frozen glasses manifest theappearance of partial ergodicity breaking, and hence materials with multiple very distinct inner clocks.

Size dependent vitrification in metallic glasses

“…This outcome makes the SAP a suitable candidate as the atomic mechanism assisting vitrification at low cooling rates. On more theoretical frameworks, the presence of different equilibration mechanisms can be derived on the base of the self-consistent Langevin equation 73 and the random first order transition (RFOT) theory 74 .…”

Physical aging and vitrification in polymers and other glasses: Complex behavior and size effects

“…111 Self-consistent Langevin equation also predicts the existence of several relaxation modes active in glass equilibration. 160 A recent theoretical development describes relaxation by means of non-Markovian models as a mixture of open and close regions. 161 On lowering the temperature, the presence of open regions with mildly activated relaxation time, and closed regions with the typical super-Arrhenius temperature dependence of the α relaxation are in qualitatively agreement with the two steps recovery of equilibrium in the glassy state.…”

Non-Equilibrium View of the Amorphous Solidification of Liquids with Competing Interactions

“…[68], the time-dependent NESF S(k; t) is given by S(k; t) = S * (u(t)), where the function S * (u) is defined in Eq. ( 18), and with the variable u(t) being the "material" time u(t) ≡ t 0 b(t ′ )dt ′ [65]. Before discussing the structural aging described by the full t-dependence of S(k; t), however, it is useful to consider its stationary, long-time asymptotic limit S a (k) ≡ lim t→∞ S(k; t), given by…”

“…[60], which proposed a farfrom-equilibrium extension of the Onsager theory of irreversible processes [61,62] and the Onsager-Machlup theory of thermal fluctuations [63,64], leading to the general theory of irreversible processes in liquids, referred to as the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory [1]. This more general approach contains as a particular case the original equilibrium SCGLE theory, which is thus enriched by the non-equilibrium kinetic perspective required to describe non-stationary processes [65].…”