Nonequilibrium thermodynamics of the soft glassy rheology model

Non-Maxwellian viscoelastic stress relaxations in soft matter

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Thermalization of plastic flow versus stationarity of thermomechanical equilibrium in SGR theory

We discuss issues related to thermalization of plastic flow in the context of soft glassy rheology (SGR) theory. An apparent problem with the theory in its current form is that the stationarity of thermomechanical equilibrium obtained by requiring that its flow rule satisfy detailed balance in the absence of applied deformation requires plastic flow to be athermal. This prevents proper application of SGR to small-molecule and polymer glasses where plastic flow is often well thermalized. Clearly, one would like to have a SGR-like theory of thermalized plastic flow that satisfies stationarity. We discuss reasons why such a theory could prove very useful and clarify obstacles that must be overcome in order to develop it.

Thermalized formulation of soft glassy rheology

We present a version of soft glassy rheology that includes thermalized strain degrees of freedom. It fully specifies systems' strain-history-dependent positions on their energy landscapes and therefore allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characteristics of fully thermal and nearly athermal plasticity by comparing results for thermalized and nonthermalized plastic flow.

Temperature dependence of aging kinetics of hectorite clay suspensions

The aging of salt-free hectorite suspensions with different concentrations (c(L)=2.9, 3.2 and 3.5 wt%) stored for 2 days or 4 days was studied by rheology at different temperatures. The evolution of storage and loss moduli G' and G″ during aging followed aging time-temperature superposition. The temperature dependence of the shift factor a(T), which reflected the aging kinetics, was interpreted by the reaction-limited colloidal aggregation (RLCA) mechanism with counterion condensation in calculating the double-layer interaction of the charged clay particles. Temperature dependence of the plateau modulus and yield stress of the suspension aged for 800 s was modeled with the soft glassy rheology (SGR) theory. The estimated noise temperature x indicated that the sample aged at higher temperature corresponded to a deeper quench in the nonergodic state. Under larger amplitude of oscillatory shear, the suspension exhibited a strain rate-frequency superposition (SRFS). The shearing eliminated the effects of aging and heating.

Nonequilibrium thermodynamics of the shear-transformation-zone model

The shear-transformation-zone (STZ) model has been applied numerous times to describe the plastic deformation of different types of amorphous systems. We formulate this model within the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework, thereby clarifying the thermodynamic structure of the constitutive equations and guaranteeing thermodynamic consistency. We propose natural, physically motivated forms for the building blocks of the GENERIC, which combine to produce a closed set of time evolution equations for the state variables, valid for any choice of free energy. We demonstrate an application of the new GENERIC-based model by choosing a simple form of the free energy. In addition, we present some numerical results and contrast those with the original STZ equations.