The synergetic theory of the glass transition in liquids

The glass transition is treated as a spontaneous emergence of the shear components of strain and stress elastic fields upon cooling a liquid at a rate exceeding the critical value. The stationary elastic strains and stresses and the effective relaxation time are determined within the adiabatic approximation. It is shown that the glass transition process occurs through the mechanism of a first-order kinetic transition with allowance made for the strain dependence of the shear modulus. The critical cooling rate turns out to be proportional to the thermal diffusivity and unrelaxed shear modulus and inversely proportional to the temperature derivative of the relaxed shear modulus and the square of the heat conductivity length of the sample.     

Theoretical approaches to the glass transition in simple liquids

Theoretical approaches to the development of an understanding of the behaviour of simple supercooled liquids near the structural glass transition are reviewed and our work on this problem, based on the density functional theory of freezing and replicated liquid state theory, are summarized in this context. A few directions for further work on this problem are suggested.     

Dynamics of supercooled liquids and understanding the glass transition

The self-consistent mode coupling theory of glass transition is briefly reviewed. The existance of a temperature T_c, higher than the usual calorimetric glass transition temperature, across which the dynamics of the fluid becomes quite different are indicated through different experimental results. Above T_c the viscosity tends to diverge with a power law while for lower temperature this sharp transition is cutoff. Such changes in the transport properties can be understood from the self-consistent mode coupling theory. The relaxation functions predicted by the mode-coupling theory over different time scales are indicated. The models with proper wave-vector dependence are also discussed.     

Mode-coupling theory of the glass transition for colloidal liquids in slit geometry

ABSTRACT

We provide a detailed derivation of the mode-coupling equations for a colloidal liquid confined by two parallel smooth walls. We introduce irreducible memory kernels for the different relaxation channels thereby extending the projection operator technique to colloidal liquids in slit geometry. Investigating both the collective dynamics as well as the tagged-particle motion, we prove that the mode-coupling functional assumes the same form as in the Newtonian case corroborating the universality of the glass-transition singularity with respect to the microscopic dynamics.     

On the dynamics of liquids in their viscous regime approaching the glass transition

Recently, Mallamace et al. (Eur. Phys. J. E 34, 94 (2011)) proposed a crossover temperature, T(×), and claimed that the dynamics of many supercooled liquids follow an Arrhenius-type temperature dependence between T(×) and the glass transition temperature T(g). The opposite, namely super-Arrhenius behavior in this viscous regime, has been demonstrated repeatedly for molecular glass-former, for polymers, and for the majority of the exhaustively studied inorganic glasses of technological interest. Therefore, we subject the molecular systems of the Mallamace et al. study to a "residuals" analysis and include not only viscosity data but also the more precise data available from dielectric relaxation experiments over the same temperature range. Although many viscosity data sets are inconclusive due to their noise level, we find that Arrhenius behavior is not a general feature of viscosity in the T(g) to T(×) range. Moreover, the residuals of dielectric relaxation times with respect to an Arrhenius law clearly reveal systematic curvature consistent with super-Arrhenius behavior being an endemic feature of transport properties in this viscous regime. We also observe a common pattern of how dielectric relaxation times decouple slightly from viscosity.     

Statistical mechanics of the glass transition in one-component liquids with an anisotropic potential

We study a recently introduced model of one-component glass-forming liquids whose constituents interact with an anisotropic potential. This system is interesting per se and as a model of liquids such as glycerol (interacting via hydrogen bonds) which are excellent glass formers. We work out the statistical mechanics of this system, encoding the liquid and glass disorder using appropriate quasiparticles (36 of them). The theory provides a full explanation of the glass transition phenomenology, including the identification of a diverging length scale and a relation between the structural changes and the diverging relaxation times.     

Direct observation of medium-range crystalline order in granular liquids near the glass transition

Collective behavior of driven granular matter is often strikingly analogous to that of thermal systems. Here we use a vibrated quasi-two-dimensional granular matter as a model system and investigate the mechanism of the liquid-glass transition. We demonstrate by direct observation the existence of long-lived medium-range crystalline order, which is found to be closely related to both dynamic heterogeneity and slow dynamics. Our findings are remarkably similar to recent numerical results on model thermal liquids and thus open an intriguing possibility of understanding the dynamic arrest in both thermal and athermal systems in a unified manner.     

Molecular simulation study of the glass transition in a soft primitive model for ionic liquids

In this paper, we present a molecular dynamics study of the glass transition for a soft-core primitive model for ionic liquids, in which cations are fully flexible chains of tangent soft spherical monomers, being the positively charged monomer at one of the ends of the chain, and anions as charged soft spheres. We have monitored transport coefficients such as the self-diffusion coefficients and the shear viscosity, as well as correlation functions such as the mean-square displacement, the self-intermediate scattering function, and probes of heterogeneous dynamics such as the van Hove distribution function and the four-points susceptibility. The analysis of these properties indicates that, for a given pressure, the glass transition shows a weak temperature dependence on the cation length, occurring first for short-chain than for long-chain ionic liquids.     

Liquid limits: glass transition and liquid-gas spinodal boundaries of metastable liquids

The liquid-gas spinodal and the glass transition define ultimate boundaries beyond which substances cannot exist as (stable or metastable) liquids. The relation between these limits is analyzed via computer simulations of a model liquid. The results obtained indicate that the liquid-gas spinodal and the glass transition lines intersect at a finite temperature, implying a glass-gas mechanical instability locus at low temperatures. The glass transition lines obtained by thermodynamic and dynamic criteria agree very well with each other.     

Phenomenological equations for multicomponent fluids

Ahydrodynamic equation of motion for each component of a multicomponent fluid is derived on the basis of nonequilibrium thermodynamics. Special care has been directed to the choice of state variables. In some limiting cases, this equation leads to customary phenomenological equations, such as the equation for diffusion and the Navier-Stokes equation. The viscosity is a consequence of nonlocal coupling of forces and fluxes. The reciprocity between the linear coefficients is examined closely.     

Heterogeneous dynamics at the glass transition in van der Waals liquids: Determination of the characteristic scale

Recent experiments have demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous. The characteristic size of these heterogeneities has been measured to be a few nanometers at T _g. We extend here a recent model for describing the heterogeneous nature of the dynamics which allows both to derive this length scale and the right orders of magnitude of the heterogeneities of the dynamics close to the glass transition. Our model allows then to interpret quantitatively small probes diffusion experiments. Received 29 March 2002 and Received in final form 11 November 2002 RID="a" ID="a"e-mail: long@lps.u-psud.fr     

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