Nurith Schupper

Inverse melting and inverse freezing: a spin model.

Systems of highly degenerate ordered or frozen state may exhibit inverse melting (reversible crystallization upon heating) or inverse freezing (reversible glass transition upon heating). This phenomenon is reviewed, and a list of experimental demonstrations and theoretical models is presented. A simple spin model for inverse melting is introduced and solved analytically for infinite range, constant paramagnetic exchange interaction. The random exchange analogue of this model yields inverse freezing, as implied by the analytic solution based on the replica trick. The qualitative features of this system (generalized Blume-Capel spin model) are shown to resemble a large class of inverse melting phenomena. The appearance of inverse melting is related to an exact rescaling of one of the interaction parameters that measures the entropy of the system. For the case of almost degenerate spin states, perturbative expansion is presented, and the first three terms correspond to the empiric formula for the Flory-Huggins chi parameter in the theory of polymer melts. The possible microscopic origin of this chi parameter and the limitations of the Flory-Huggins theory where the state degeneracy is associated with the different conformations of a single polymer or with the spatial structures of two interacting molecules are discussed.

Direct identification of the glass transition: Growing length scale and the onset of plasticity

Understanding the mechanical properties of glasses remains elusive since the glass transition itself is not fully understood, even in well-studied examples of glass formers in two dimensions. In this context we demonstrate here: i) a direct evidence for a diverging length scale at the glass transition ii) an identification of the glass transition with the disappearance of fluid-like regions and iii) the appearance in the glass state of fluid-like regions when mechanical strain is applied. These fluid-like regions are associated with the onset of plasticity in the amorphous solid. The relaxation times which diverge upon the approach to the glass transition are related quantitatively to the diverging length scale.

Aging and relaxation in glass-forming systems

We propose that there exists a generic class of glass-forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where aging, relaxation, and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to aging occur where the local shear modulus is low (even negative) and result in an increase in the size of local patches of relative order. We examine the aging events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass-forming systems to the reduction in relative volume of the amorphous material which is liquidlike. While we agree with the well-known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulas that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most superexponentially when the temperature is lowered.

Effect of thermal expansion on speckle correlation from surface scattering of a transparent dielectric slab

We study the variation in the back-scattered light from a slab of silicate glass on a change of the glass temperature. Coherent illumination scattered from a ground surface of the glass creates a speckle pattern resulting from the sum of two different scattering events: one originating from the backward scattering from the rough surface, and the second from the forward-scattered light, which is Fresnel reflected from the flat back surface of the slab and rescattered (in the forward direction) by the rough surface. Experimental and theoretical studies show that on heating the glasses, the correlation between the initial and the final speckle patterns oscillates as a function of temperature with a frequency proportional to the thermally induced changes in the optical path in the glass. A measurement of the thermal expansion coefficient α is obtained from the oscillations with 0.01% accuracy, provided that the change in refractive index with temperature is known. The observed slow decrease in the amplitude of the temperature-induced oscillations is in agreement with the theoretical analysis of the effect of uniform thermal expansion of the scattering surface. The surface expansion also results in a damped, slow oscillation of the correlation due to the nonrandom motion of the expanding scatterers, which result in the partial rephasing of the scattered waves when the scatterers move a distance on the order of a wavelength. If the refractive index change with temperature is unknown, the decrease in the amplitude of oscillations can be used to determine α, the thermal expansion coefficient while the oscillations can be used to determine the refractive index change with temperature. The method presented is thus an alternative for measuring the thermal expansion coefficient and the change of index with temperature, and can be applied when dealing with strongly scattering surfaces, where one cannot use the normal fringe method. Different glass thicknesses and sample tilts with respect to the incident laser beam are shown to modify the correlation function.