Mapping Isobaric Aging onto the Equilibrium Phase Diagram

Nonlinear susceptibilities and higher-order responses related to physical aging: Wiener-Volterra approach and extended Tool-Narayanaswamy-Moynihan models

Large-amplitude thermal excursions imposed on deeply supercooled liquids modulate the nonlinear time evolution of their structural rearrangements. The consequent aftereffects are treated within a Wiener-Volterra expansion in laboratory time that allows one to calculate the associated physical-aging and thermal response functions. These responses and the corresponding higher-harmonic susceptibilities are illustrated using calculations based on the Tool-Narayanaswamy-Moynihan (TNM) model. The conversion from laboratory to material time is thoroughly discussed. Similarities and differences to field-induced higher-harmonic susceptibilities are illustrated using Lissajous and Cole-Cole plots and discussed in terms of aging nonlinearity parameters. For the Lissajous plots, banana-type shapes emerge, while the Cole-Cole plots display cardioidic and other visually appealing patterns. For application beyond the regime in which conventional single-parameter aging concepts work, the Wiener-Volterra material-time-series is introduced as the central tool. Calculations and analyses within this general framework in conjunction with suitable choices of higher-order memory kernels and employing correspondingly extended TNM models yield at least qualitative agreement with recent large-perturbation physical aging experiments. Implications for differential scanning calorimetry and related methods are discussed. The introduced concepts and analyses provide a solid foundation for a generalized description of nonlinear thermal out-of-equilibrium dynamics of glass forming materials, differing from the nonlinear responses known from rheology and dielectric spectroscopy.

Crossing the Frontier of Validity of the Material Time Approach in the Aging of a Molecular Glass

We studied the physical aging of glycerol in response to upward temperature steps of amplitude ranging from 0.3 to 18 K. This was done using a specially designed experimental setup allowing quick heating of a liquid film while measuring the evolution of its dielectric properties. Despite the nonlinear evolution of these observables for large steps, a fictive temperature could be obtained. In the case of moderate step amplitudes, we checked that the material time approach in its simplest form, the single parameter aging (SPA), applies well. The memory kernel extracted from the quasi-linear regime was used to test its frontiers of validity for significant step amplitudes. We showed that the observations deviate from the prediction of the material time framework and of SPA simultaneously. As these approaches link aging to equilibrium dynamics, our results help set the bounds beyond which new theoretical arguments are needed.

Distance-as-time in physical aging

Although it has been known for half a century that the physical aging of glasses in experiments is described well by a linear thermal-history convolution integral over the so-called material time, the microscopic definition and interpretation of the material time remains a mystery. We propose that the material-time increase over a given time interval reflects the distance traveled by the system's particles. Different possible distance measures are discussed, starting from the standard mean-square displacement and its inherent-state version that excludes the vibrational contribution. The viewpoint adopted, which is inspired by and closely related to pioneering works of Cugliandolo and Kurchan from the 1990s, implies a "geometric reversibility" and a "unique-triangle property" characterizing the system's path in configuration space during aging. Both of these properties are inherited from equilibrium, and they are here confirmed by computer simulations of an aging binary Lennard-Jones system. Our simulations moreover show that the slow particles control the material time. This motivates a "dynamic-rigidity-percolation" picture of physical aging. The numerical data show that the material time is dominated by the slowest particles' inherent mean-square displacement, which is conveniently quantified by the inherent harmonic mean-square displacement. This distance measure collapses data for potential-energy aging well in the sense that the normalized relaxation functions following different temperature jumps are almost the same function of the material time. Finally, the standard Tool-Narayanaswamy linear material-time convolution-integral description of physical aging is derived from the assumption that when time is replaced by distance in the above sense, an aging system is described by the same expression as that of linear-response theory.

A density scaling conjecture for aging glasses

The aging rate of glasses has traditionally been modeled as a function of temperature, T , andfictive temperature, while density, ρ, is not explicitly included as a parameter. However, this de-scription does not naturally connect to the modern understanding of what governs the relaxationrate in equilibrium. In equilibrium it is well known that the relaxation rate, γeq , depends on tem-perature and density. In addition a large class of systems obey density scaling which means therate specifically depends on the scaling parameter, Γ = e(ρ)/T , where e(ρ) is a system specificfunction. This paper present a generalization of the fictive temperature concept in terms of a fic-tive scaling paramter, Γfic , and a density scaling conjecture for aging glasses in which the agingrate depends on Γ and Γfic .

Predicting nonlinear physical aging of glasses from equilibrium relaxation via the material time

The noncrystalline glassy state of matter plays a role in virtually all fields of materials science and offers complementary properties to those of the crystalline counterpart. The caveat of the glassy state is that it is out of equilibrium and therefore exhibits physical aging, i.e., material properties change over time. For half a century, the physical aging of glasses has been known to be described well by the material-time concept, although the existence of a material time has never been directly validated. We do this here by successfully predicting the aging of the molecular glass 4-vinyl-1,3-dioxolan-2-one from its linear relaxation behavior. This establishes the defining property of the material time. Via the fluctuation-dissipation theorem, our results imply that physical aging can be predicted from thermal-equilibrium fluctuation data, which is confirmed by computer simulations of a binary liquid mixture.

Isomorph theory beyond thermal equilibrium

This paper generalizes isomorph theory to systems that are not in thermal equilibrium. The systems are assumed to be R-simple, i.e., to have a potential energy that as a function of all particle coordinates R obeys the hidden-scale-invariance condition U(R_a) < U(R_b) ⇒ U(λR_a) < U(λR_b). "Systemic isomorphs" are introduced as lines of constant excess entropy in the phase diagram defined by density and systemic temperature, which is the temperature of the equilibrium state point with the average potential energy equal to U(R). The dynamics is invariant along a systemic isomorph if there is a constant ratio between the systemic and the bath temperature. In thermal equilibrium, the systemic temperature is equal to the bath temperature and the original isomorph formalism is recovered. The new approach rationalizes within a consistent framework previously published observations of isomorph invariance in simulations involving nonlinear steady-state shear flows, zero-temperature plastic flows, and glass-state isomorphs. This paper relates briefly to granular media, physical aging, and active matter. Finally, we discuss the possibility that the energy unit defining the reduced quantities should be based on the systemic rather than the bath temperature.

Fast contribution to the activation energy of a glass-forming liquid

This paper presents physical-aging data for the silicone oil tetramethyl-tetraphenyl trisiloxane. The density and the high-frequency plateau shear modulus [Formula: see text] were monitored following temperature jumps starting from fully equilibrated conditions. Both quantities exhibit a fast change immediately after a temperature jump. Adopting the material-time formalism of Narayanaswamy, we determine from the dielectric loss at 0.178 Hz the time evolution of the aging-rate activation energy. The relative magnitude of the fast change of the activation energy differs from that of the density, but is identical to that of [Formula: see text] In fact, the activation energy is proportional to [Formula: see text] throughout the aging process, with minor deviations at the shortest times. This shows that for the silicone oil in question the dynamics are determined by [Formula: see text] in-as well as out of-equilibrium.

Experimental Evidence for a State-Point-Dependent Density-Scaling Exponent of Liquid Dynamics

A large class of liquids obey density scaling characterized by an exponent, which quantifies the relative roles of temperature and density for the dynamics. We present experimental evidence that the density-scaling exponent γ is state-point dependent for the glass formers tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl ether (5PPE). A method is proposed that from dynamic and thermodynamic properties at equilibrium estimates the value of γ. The method applies at any state point of the pressure-temperature plane, both in the supercooled and the normal liquid regimes. We find that γ is generally state-point dependent, which is confirmed by reanalyzing data for 20 metallic liquids and two model liquids.

Perspective: Searching for simplicity rather than universality in glass-forming liquids

This article gives an overview of experimental results on dynamics in bulk glass-forming molecular liquids. Rather than looking for phenomenology that is universal, in the sense that it is seen in all liquids, the focus is on identifying the basic characteristics, or "stylized facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner.

Perspective: Excess-entropy scaling

This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.

Isomorph theory of physical aging

This paper derives and discusses the configuration-space Langevin equation describing a physically aging R-simple system and the corresponding Smoluchowski equation. Externally controlled thermodynamic variables like temperature, density, and pressure enter the description via the single parameter T_s/T, in which T is the bath temperature and T_s is the "systemic" temperature defined at any time t as the thermodynamic equilibrium temperature of the state point with density ρ(t) and potential energy U(t). In equilibrium, T_s ≅ T with fluctuations that vanish in the thermodynamic limit. In contrast to Tool's fictive temperature and other effective temperatures in glass science, the systemic temperature is defined for any configuration with a well-defined density, even if it is not close to equilibrium. Density and systemic temperature define an aging phase diagram, in which the aging system traces out a curve. Predictions are discussed for aging following various density-temperature and pressure-temperature jumps from one equilibrium state to another, as well as for a few other scenarios. The proposed theory implies that R-simple glass-forming liquids are characterized by the dynamic Prigogine-Defay ratio being equal to unity.

The very long-term physical aging of glassy polymers

The thermodynamic state of polymer glasses aged over 30 years reveals the existence of a metastable state with partial equilibrium recovery.