Nonequilibrium Thermodynamics of Glasses

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When investigating glasses, nonequilibrium phenomena are ubiquitous. Even if there was a glassy equilibrium state, the occurrence of enormously large relaxation times would force us to deal with the nonequilibrium approach to such an equilibrium state, or with nonequilibrium phenomena taking place during and on top of that approach. We hence apply the modern framework of nonequilibrium thermodynamics to find out whether we might be able to raise our level of understanding of glasses, both from the conceptual and from the practical points of view.

Non-affine deformation of inherent structure as static signature of cooperativity in supercooled liquids

As a first step, we have looked for a static signature of the cooperative and heterogeneous dynamics of liquids approaching the glass transition. When a liquid is cooled down to its glass transition temperature, particle motion slows down enormously and becomes highly cooperative: the more the system becomes glassy, the more the relaxation requires cooperative rearrangements of a large number of particles. Experimental and theoretical investigations as well as simulation results on dynamical heterogeneities strongly support the presence of cooperatively rearranging regions of growing size. Whether and how the onset of such cooperative dynamics can take place without any apparent or straightforward connection to structural changes, is actually one of the great unsolved problems of soft condensed matter physics (See article in New York Times).

It was already known that the accessible potential energy surface qualitatively changes in the supercooled liquids, due to the presence of local minima, or inherent structures (IS). When the system enters the supercooled regime, the presence of local minima turns out to be extremely important and to produce complex trajectories in the potential energy landscape: the time evolution of the system samples the basins associated to the local minima, or groups of such basins, on a relatively short time scale, whereas transitions between different groups of basins separated by major energy barriers take a much longer time and imply a slow, aging process, during which the system is out-of-equilibrium.

Our novel perspective, based on our general framework of nonequilibrium thermodynamics, relates the response of a glassy system to an applied deformation to the corresponding change of its IS. We have therefore studied the response of IS in supercooled liquids by numerical simulations of model glass formers subject to static shear deformations combined with local energy minimizations.

Nonaffine rearrangements  
Figure 1. Nonaffine rearrangements after shear deformation as a static signature of glassy behavior: large localized rearrangements in the melt (left) versus small spatially correlated rearrangements (strongly amplified for visibility) near the glass transition (right). The color code indicates the propensity of particles to motion, a property calculated from the dynamics, which displays strong heterogeneities in the supercooled regime.

For small amplitude of deformation, the nonaffine part of the response of IS reveals the presence of large cooperative and heterogenous domains. The presence of such collective rearrangements in the IS response is strongly evocative of the cooperativity characterizing the dynamics, and it is in fact observed in the same range of temperatures. On this basis, we proposed that these nonaffinely rearranging regions are the IS counterpart of the cooperatively rearranging regions observed so far only in the dynamics.

Mismatch vectors
Figure 2. Left: Average degree of correlation C(r) of the direction of the mismatch vectors for a pair of particles separated by a distance r (in particle diameter units) at different temperatures, showing the presence of extended spatial correlations in the supercooled regime. Right: Distributions f(C(r)) of degree of correlation between particles at a distance r=5, significantly widening in the supercooled regime.

Future work

Work in progress and future developments include the devising, on the basis of these new structural information, of the slow variables needed for a nonequilibrium thermodynamic description of glasses; the investigation of direct correlations between the IS cooperative domains and dynamical heterogeneities; a deeper understanding of whether and how these features of the IS of the supercooled liquid may be connected to the mechanical properties of the amorphous solid.

Related publications

  1. Hans Christian Öttinger, Nonequilibrium thermodynamics of glasses, Phys. Rev. E, 74 (2006) 011113.
  2. Emanuela Del Gado, Patrick Ilg, Martin Kröger and Hans Christian Öttinger, Non-affine deformations of inherent structure as signature of cooperativity in supercooled liquids, Phys. Rev. Lett. 101 (2008) 095501.
  3. Majid Mosayebi, Emanuela Del Gado, Patrick Ilg, Hans Christian Öttinger, Probing a critical length scale at the glass transition, Phys. Rev. Lett. 104 (2010) 205704.
  4. Majid Mosayebi, Emanuela Del Gado, Patrick Ilg, Hans Christian Öttinger, Deformation of inherent structures to detect long-range correlations in supercooled liquids, J. Chem. Phys. 137 (2012) 024504, 1-11.
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