Issue 13, 2010

Nonequilibrium thermodynamics of the Kovacs effect

Abstract

We present a thermodynamic theory of the Kovacs effect based on the idea that the configurational degrees of freedom of a glass-forming material are driven out of equilibrium with the heat bath by irreversible thermal contraction and expansion. We assume that the slowly varying configurational subsystem, i.e. the part of the system that is described by inherent structures, is characterized by an effective temperature, and contains a volume-related internal variable. We examine mechanisms by which irreversible dynamics of the fast, kinetic-vibrational degrees of freedom can cause the entropy and the effective temperature of the configurational subsystem to increase during sufficiently rapid changes in the bath temperature. We then use this theory to interpret the numerical simulations by Mossa and Sciortino (MS, S. Mossa and F. Sciortino, Phys. Rev. Lett., 2004, 92, 045504), who observe the Kovacs effect in more detail than is feasible in laboratory experiments. Our analysis highlights two mechanisms for the equilibration of internal variables. In one of these, an internal variable first relaxes toward a state of quasi-equilibrium determined by the effective temperature, and then approaches true thermodynamic equilibrium as the effective temperature slowly relaxes toward the bath temperature. In the other mechanism, an internal variable directly equilibrates with the bath temperature on intermediate timescales, without equilibrating with the effective temperature at any stage. Both mechanisms appear to be essential for understanding the MS results.

Graphical abstract: Nonequilibrium thermodynamics of the Kovacs effect

Article information

Article type
Paper
Submitted
21 Jan 2010
Accepted
26 Feb 2010
First published
15 Apr 2010

Soft Matter, 2010,6, 3065-3073

Nonequilibrium thermodynamics of the Kovacs effect

E. Bouchbinder and J. S. Langer, Soft Matter, 2010, 6, 3065 DOI: 10.1039/C001388A

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