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.     

Flow curves of colloidal dispersions close to the glass transition

The flow curves, viz. the curves of stationary stress under steady shearing, are obtained close to the glass transition in dense colloidal dispersions using asymptotic expansions in the schematic -model of mode coupling theory. The shear thinning of the viscosity in fluid states and the yielding of glassy states is discussed. At the transition between fluid and shear-molten glass, simple and generalized Herschel-Bulkley laws are derived with power law exponents that can be computed for different particle interactions from the equilibrium structure factor.     

Phenomenological equations of the glass transition in liquids

The paper presents a theoretical analysis of the glass transition. It is demonstrated that the kinetics of glass transition is described by the following equations: the Maxwell equation of a viscoelastic medium; the equation of elastic relaxation, which, in addition to the usual Debye term, involves a nonlinear term due to the positive feedback between the strain field and temperature; and the equation of specific heat continuity, in which the entropy term includes the contribution of elastic fields and the heat flux contains a term related to external cooling. These equations are analogous to the Lorenz synergetic system, in which the strain plays the role of an order parameter, the conjugate field reduces to elastic stresses, and the temperature is a controlling parameter.     

Dewetting of thin polymer films at temperatures close to the glass transition

We present detailed studies on dewetting of thin polystyrene (PS) films which were deposited onto silicon wafers coated with a polydimethylsiloxane (PDMS) monolayer. Experiments were performed at temperatures close to the glass transition temperature of PS. Several significant deviations from the dewetting behaviour of Newtonian liquids were observed. The length of the PS molecules, and thus the viscosity, turned out to be of minor importance in determining the dewetting velocity, in particular for the later regimes. In stark contrast, the geometry of the drying spot had a striking influence on the dewetting velocity. Initially, dewetting from straight contact lines proceeded faster than the opening of circular holes. At later stages, the process slowed down significantly in both cases. Under the conditions at which our experiments were performed, PS cannot flow like a simple liquid. Thus, the observed dewetting has to be the consequence of plastic deformation induced by capillary forces. Our results indicate that under such conditions the energy dissipation process is strongly affected by geometry, which is not the case for viscous liquids.Received: 1 January 2003, Published online: 14 October 2003PACS: 68.60.-p Physical properties of thin films, nonelectronic - 61.41. + e Polymers, elastomers, and plastics - 68.55.-a Thin film structure and morphology - 83.50.-v Deformation and flow     

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.     

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.     

Translational and rotational diffusion in supercooled orthoterphenyl close to the glass transition

Self diffusion coefficients in supercooled orthoterphenyl (OTP) have been determined down toD _t =3·10^–14 m²s^–1 using a¹H-NMR technique applying static field gradients up to 53T m^–1 In a range of more than two decades theD _t values agree with those of photochromic tracer molecules of the same size determined by forced Rayleigh scattering down to the glass transition temperatureT _g . A change of mechanism is found for translational diffusion atT _c 1.2T _g whereD _t is proportional to the inverse shear viscosity ^–1 atT>T _c butD _t with =0.75 atT<T _c . Rotational correlation times determined by²H-NMR stimulated echo techniques in deuterated OTP remain proportinal to ^–1 down toT _g . Our results are discussed in relation with mode coupling theory and with models of cooperative motion at the glass transition.     

Light scattering and dielectric susceptibility spectra of glassforming liquids

A new method based on a micromechanical sensor has been developed for the investigation of viscosity shear waves in liquids. A number of Newtonian liquids having various molecular properties were tested with the help of a miniaturized sensor oscillating in a liquid. A good experimental confirmation of theoretical predictions was obtained for relatively high viscosities η. On the contrary, a significant discrepancy between the hydrodynamic limit for η → 0, i.e. the “ideal liquid” limit, and the experimental data was observed. In addition, the data shows a discontinuity for different types of liquid molecules of variable polarity.     

Magnetic properties of magnetite thin films close to the Verwey transition

Temperature dependence of the magnetic properties of magnetite thin film across the Verwey transition has been investigated. As the temperature is decreased, the magnetization of the film in a fixed field showed a sharp decrease close to the Verwey transition temperature (T_v). The M–H loops of the film have been recorded at various temperatures below and above T_v. It is found that film does not saturate at any temperature and saturation becomes more difficult below T_v. While cooling through T_v, the extrapolated value of magnetization to infinite field (Q), calculated from the numerical fit 4πM=Q [1−(H*/H)^1/2], does not show a drop, but the coefficient indicating difficulty in saturation (H*) shows a sharp rise as does the coercivity.     

Mechanical properties of thin confined polymer films close to the glass transition in the linear regime of deformation: Theory and simulations

Over the past twenty years experiments performed on thin polymer films deposited on substrates have shown that the glass transition temperature T(g) can either decrease or increase depending on the strength of the interactions. Over the same period, experiments have also demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. A model for the dynamics of non-polar polymers, based on percolation of slow subunits, has been proposed and developed over the past ten years. It proposes a unified mechanism regarding these two features. By extending this model, we have developed a 3D model, solved by numerical simulations, in order to describe and calculate the mechanical properties of polymers close to the glass transition in the linear regime of deformation, with a spatial resolution corresponding to the subunit size. We focus on the case of polymers confined between two substrates with non-negligible interactions between the polymer and the substrates, a situation which may be compared to filled elastomers. We calculate the evolution of the elastic modulus as a function of temperature, for different film thicknesses and polymer-substrate interactions. In particular, this allows to calculate the corresponding increase of glass transition temperature, up to 20 K in the considered situations. Moreover, between the bulk T(g) and T(g) + 50 K the modulus of the confined layers is found to decrease very slowly in some cases, with moduli more than ten times larger than that of the pure matrix at temperatures up to T(g) + 50 K. This is consistent with what is observed in reinforced elastomers. This slow decrease of the modulus is accompanied by huge fluctuations of the stress at the scale of a few tens of nanometers that may even be negative as compared to the solicitation, in a way that may be analogous to mechanical heterogeneities observed recently in molecular dynamics simulations. As a consequence, confinement may result not only in an increase of the glass transition temperature, but in a huge broadening of the glass transition.     

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.     

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.