Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, f (t) = f ₀exp - (t/τ)^β , with the exponent β increasing with the temperature. The relaxation time diverges as an Arrhenius law when T→ 0. Received 24 May 2001 and Received in final form 12 September 2001     

Glassy effects in the swelling/collapse dynamics of homogeneous polymers

We investigate, using numerical simulations and analytical arguments, a simple one-dimensional model for the swelling or the collapse of a closed polymer chain of size N, representing the dynamical evolution of a polymer in a Θ-solvent that is rapidly changed into a good solvent (swelling) or a bad solvent (collapse). In the case of swelling, the density profile for intermediate times is parabolic and expands in space as t ^1/3, as predicted by a Flory-like continuum theory. The dynamics slows down after a time ∝N ² when the chain becomes stretched, and the polymer gets stuck in metastable “zig-zag” configurations, from which it escapes through thermal activation. The size of the polymer in the final stages is found to grow as . In the case of collapse, the chain very quickly (after a time of order unity) breaks up into clusters of monomers (“pearls”). The evolution of the chain then proceeds through a slow growth of the size of these metastable clusters, again evolving as the logarithm of time. We enumerate the total number of metastable states as a function of the extension of the chain, and deduce from this computation that the radius of the chain should decrease as 1/ln(ln t). We compute the total number of metastable states with a given value of the energy, and find that the complexity is non-zero for arbitrary low energies. We also obtain the distribution of cluster sizes, that we compare to simple “cut-in-two” coalescence models. Finally, we determine the aging properties of the dynamical structure. The subaging behaviour that we find is attributed to the tail of the distribution at small cluster sizes, corresponding to anomalously “fast” clusters (as compared to the average). We argue that this mechanism for subaging might hold in other slowly coarsening systems. Received 23 October 2000     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

Vitrification in a 2D Ising model with mobile bonds

A bond-disordered two-dimensional Ising model is used to simulate Kauzmann's mechanism of vitrification in liquids, by a Glauber Monte Carlo simulation. The rearrangement of configurations is achieved by allowing impurity bonds to hop to nearest neighbors at the same rate as the spins flip. For slow cooling, the theoretical minimum energy configuration is approached, characterized by an amorphous distribution of locally optimally arranged impurity bonds. Rapid cooling to low temperatures regularly finds bond configurations of higher energy, which are both a priori rare and severely restrictive to spin movement, providing a simple realization of kinetic vitrification. A supercooled liquid regime is also found, and characterized by a change in sign of the field derivative of the spin-glass susceptibility at a finite temperature. Received 3 August 2000 and Received in final form 9 March 2001     

The ionic transition and the glass transition in ion-conducting glasses

In an ion-conducting glass, there may be the ionic transition which characterizes ‘melting’ of the modifying ions in a similar way as the glass transition characterizes ‘melting’ of the glass network former. The ionic transition can be observed, electrically, by the thermally stimulated depolarization current technique. It is demonstrated that the relaxation time for the ionic transition is the same (near 100 s) with that for the glass transition in so far as the heating/cooling rate lies within, say, 10⁻¹-10⁻⁵ K/s as adopted in our routine works.     

Pulsed dielectric spectroscopy of supercooled liquids

Pulsed dielectric spectroscopy is introduced as a technique for selectively emphasizing specific components of the non-exponential dielectric response of matter. Samples studied include supercooled liquid propanol, propylene carbonate, and poly(lauryl-methacrylate). It is shown that particular sequences of pulses can be used to emphasize the fast response regime, to produce a cross-over or memory effect, or to eliminate the response of selected components. Furthermore, for materials characterized by broad distributions of relaxation times, the technique facilitates the investigation of a relatively narrow band from that distribution. It is also shown that the time domain spectroscopy can be combined with conventional frequency domain techniques to provide the characterization of dielectric response over an extraordinarily broad spectral range.     

Average coordination-number dependence of glass-transition temperature in Ge-In-Se chalcogenide glasses

Twenty-six glassy compositions, belonging to the Ge_xIn₆Se_94-x and Ge_xIn₁₂Se_88-x families of the Ge-In-Se system, were prepared from high purity constiment elements. Differential Scanning Calorimetry (DSC) measurements were carried out on these glasses. The DSC thermograms were used to determine the glass transition temperatures (T _g) for the compositions examined. TheT _g-composition dependence of the Ge_xIn₆Se_94-x family shows a minimum inT _g at a value of the average coordination number, r, equal to 2.4. For both families of the glasses examined, theT _g-r dependence displays maxima at r=2.75 and r=2.83 for Ge_xIn₆Se_94-x and Ge_xIn₁₂Se_88-x families, respectively. These results are interpreted by using the Phillips model of rigidity percolation and Chemically Ordered Covalent Network (COCN) model.     

P-adic numbers and replica symmetry breaking

The p-adic formulation of replica symmetry breaking is presented. In this approach ultrametricity is a natural consequence of the basic properties of the p-adic numbers. Many properties can be simply derived in this approach and p-adic Fourier transform seems to be a promising tool. Received 9 June 1999     

Viscosity of (GeSe2)x(Sb2Se3)1−x undercooled melts

Viscosity of (GeSe₂)_x(Sb₂Se₃)_1−x undercooled melts (x = 0.4-0.8) was measured using parallel-plate method and penetration method. By using these two techniques viscosity of the whole measurable region of undercooled melt and of the part of glass region can be measured. In this relatively broad viscosity interval (seven orders of magnitude) all measured samples show Newtonian behavior and the dependence of their viscosity on temperature can be described by a simple Arrhenius equation. The kinetic fragilities calculated from these dependencies show similar compositional dependence as heat capacity changes at glass transition measured by DSC.