Thermodynamics of shear-induced phase transition of polydisperse soft particle glasses

Abstract

The thermodynamics of the shear-induced phase transition of soft particle glasses is presented. Jammed suspensions of soft particles transform into a layered phase in a strong shear flow from a stable glassy phase at lower shear rates. The thermodynamics of the two phases can be computed based on the elastic energy and excess entropy of the system. At a critical shear rate, the elastic energy, the excess entropy, the free energy, the temperature, and the shear stress undergo discontinuous jumps at the phase transitions from the glassy to the layered phase. An effective temperature is defined from the derivative of the elastic energy and the excess entropy. The Helmholtz free energy is constructed using the elastic energy, excess entropy, and derived temperature. At a fixed shear rate, there is no equilibrium between the states. However, at a fixed temperature, the glassy and layered states may coexist, as indicated by the equality of their Helmholtz free energies. While this first-order phase transition is possible, it cannot be observed in simple shear because the stress is the same in both phases at the same temperature. Thus, shear banding cannot be observed in this system. Finally, an equation of state, which relates the shear stress to the excess entropy, is presented. This equation of state shows that all dynamical properties (e.g., shear-induced diffusivity and first and second normal stresses) of these jammed non-Brownian suspensions can be determined solely by measuring the shear stress.