Glass Transition Line Research Articles

Effect of cross-link density on re-entrant melting of microgel colloids

We investigated concentrated suspensions of newly synthesized highly cross-linked (1:10) polystyrene (PS) microgel particles dispersed in a good, iso-refractive organic solvent that allowed for a detailed study using light scattering techniques. Inducing depletion attraction by addition of non-adsorbing (PS) polymer, we analyzed the re-entrant melting behavior of the particle system. We compared our results with that of previous studies on polystyrene microgel particles with a lower cross-linking ratio (1:50) and on PMMA suspensions. In contrast to the (softer) 1:50 microgels where an unexpectedly huge re-entry effect was found with fluid samples extending up to a volume fraction ϕ≈0.69, the re-entry region here extends only up to ϕ≈0.61 and the attractive glass transition line is found at significantly lower polymer concentrations.Instead we find a closer similarity of the re-entry behavior with that observed for hard sphere-like PMMA particles. Whereas the highest volume fractions up to which fluid states could be observed are comparable, the polymer concentration needed to induce re-entrant melting and the formation of attractive glass is shifted to higher polymer concentrations. While the latter effect may be attributed to the non-ideal behavior of the free polymer, the extension of the fluid region with respect to colloid volume fraction appears to depend sensitively on system details like particle softness or particle size distribution.

Yield stresses and flow curves in metallic glass formers and granular systems

We discuss the concept of a glass transition line in the temperature-shear-stress plane in the context of recent simulation data for a metallic melt and dense-packed granular systems. Analyzing these data within a schematic model of the mode-coupling theory for dense glass formers under shear, values for the critical dynamic yield stress (the stress resulting in the limit of arbitrarily slow shear, at the glass transition) are estimated. We discuss two possible scenarios, that of a continuous rise in the dynamic yield stress at the transition, and that of a discontinuous transition, and discuss the data range that needs to be covered to decide between the two cases. A connection is made to the two commonly drawn versions of the jamming diagram, one convex and one concave regarding to the shape of the solid region.

Connection between slow and fast dynamics of molecular liquids around the glass transition

The mean-square displacement (MSD) was measured by neutron scattering at various temperatures and pressures for a number of molecular glass-forming liquids. The MSD is invariant along the glass-transition line at the pressure studied, thus establishing an "intrinsic" Lindemann criterion for any given liquid. A one-to-one connection between the MSD's temperature dependence and the liquid's fragility is found when the MSD is evaluated on a time scale of ∼4 ns , but does not hold when the MSD is evaluated at shorter times. The findings are discussed in terms of the elastic model and the role of relaxations, and the correlations between slow and fast dynamics are addressed.

Glass transition of binary mixtures of dipolar particles in two dimensions

We study the glass transition of binary mixtures of dipolar particles in two dimensions within the framework of mode-coupling theory, focusing in particular on the influence of composition changes. In a first step, we demonstrate that the experimental system of König et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by point dipoles through a comparison between the experimental partial structure factors and those from our Monte Carlo simulation. For such a mixture of point particles we show that there is always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks. We demonstrate that the predicted plasticization effect is in qualitative agreement with experimental results. Furthermore, also some general properties of the glass transition lines are discussed.

Dynamical study of a polydisperse hard-sphere system

We study the interplay between the fluid-crystal transition and the glass transition of elastic sphere system with polydispersity using nonequilibrium molecular dynamics simulations. It is found that the end point of the crystal-fluid transition line, which corresponds to the critical polydispersity above which the crystal state is unstable, is on the glass transition line. This means that crystal and fluid states at the melting point becomes less distinguishable as polydispersity increases and finally they become identical state, i.e., marginal glass state, at critical polydispersity.

Glass transition and the replica symmetry breaking in vortex matter: MC study

We investigate effects of disorder and thermal fluctuations on the Abrikosov state of type II superconductors applying the Monte Carlo method to Ginzburg–Landau theory to confirm earlier replica calculation. The vortex phase diagram has two transition lines, the melting line and the vortex glass transition lines in both crystalline and homogeneous states. The glass line is always a continuous transition, while the melting line is the first order.

Effect of residual attractive interactions in size asymmetric colloidal mixtures: Theoretical analysis and predictions

We analyze the influence of residual attractions on the static and some dynamic properties of size asymmetric mixtures of "hard-sphere-like" colloids. These attractions, usually neglected in the theoretical analysis, are characterized by a very short range and a moderate strength reflecting the underlying microscopic structure of the colloidal particles. Their effect on the potentials of mean force is analyzed from analytical expressions obtained from low density expansions. The effective potential of the big particle fluid is next considered. An analytical expression is proposed for estimating the deviation with respect to the hard sphere depletion potential. This case is compared to that of mixtures with noninteracting depletants. The important consequences on the binodals and the glass transition lines of the effective fluid are discussed in both cases. This study is next extended to other properties-the specific heat and the low shear viscosity-which incorporate contributions from the two components of the binary mixture.

Development of state diagram of bovine gelatin by measuring thermal characteristics using differential scanning calorimetry (DSC) and cooling curve method

A state diagram of bovine gelatin was developed by measuring the freezing curve, glass transition, unfolding, solids-melting lines, and ultimate maximum-freeze-concentration conditions. The freezing point decreased with the increase of solids; whereas glass transition, unfolding, and solids-melting decreased with the decrease of solids up to solids content 0.84 g/g gelatin and then remained constant. The freezing point, glass transition and solids-melting were modeled by Chen's model based on the Clausius-Clapeyron equation, modified Gordon-Taylor model, and Flory's equation, respectively. The ultimate maximum-freeze-concentration conditions were found as ( T ′ m ) u equal to −11.9 °C and ( T ‴ g ) u equal to −14.9 °C, and the characteristic solids content, X ′ s as 0.80 g/g sample (i.e. un-freezable water, X ′ w = 0.20), respectively. Similarly the value of T g i v (i.e. intersection of vertical line passing through T ′ m and glass transition line) was estimated as 34 °C.

State diagram of dates: Glass transition, freezing curve and maximal-freeze-concentration condition

The state diagram of Deglet Nour dates was developed using freezing curve, glass transition line, and maximal-freeze-concentration condition. Freezing points and glass transition temperature were measured by differential scanning calorimetry (DSC) as a function of water content. Freezing points were fitted to the Clausius–Clapeyron equation adjusted with un-freezable water, and glass transition was fitted to the Gordon–Taylor model. Glass transition decreased with a decrease in solids content, confirming the plasticizing effect of water on date solids. Freezing point data indicated the temperature when ice formed and dates would be most stable in terms of its deterioration if it can be stored below its glass transition. Maximum-freeze-concentration conditions was found as X s ′ (characteristic solids content) = 0.78 g/g sample, with the characteristic temperature as T g ′ (characteristics glass transition) = −48 °C and T m ′ (characteristic end point of freezing) = −38.2 °C. These characteristics indicated that 0.22 g/g sample water in date was un-freezable (i.e. bound with solids or unable to form ice). The developed state diagram can be used in determining the stability of dates during storage as a function of temperature and moisture content. Moreover, it can be used to determine optimum drying and freezing conditions.

Higher-Order Singularities without Glass-Glass Transitions

Within the framework of mode-coupling theory, the glass-transition scenario is investigated for a system of particles interacting with a hard-core repulsion and an additional square-shoulder soft core at larger distances. The static structure is calculated from the potential in Percus-Yevick approximation. For certain widths of the shoulder, the exponent parameter λ along the glass-transition line shows a double peak. At both peaks, λ can reach unity indicating the existence of higher-order glass-transition singularities. It is shown that these higher-order singularities originate from a line of avoided glass-glass transitions.

The elementary softening event in glassy systems in terms of the model of the excited state

The pressure dependence of the glass-transition temperature (glass-transition lines) is described through a relationship similar to the Clausius-Clapeyron equation. The criterion for the glass-liquid transition for polymer and other glasses is calculated. According to the proposed speculations, an elementary softening event in glasses is reduced to the critical deformation of interatomic (intermolecular) linkage, which corresponds to the maximum force of attraction between atoms. A glass (an amorphous polymer) softens when the mean energy of the thermal motion of the kinetic units responsible for the viscous flow is ∼3 times higher than the work of the ultimate deformation of the interatomic bond. The nature of structural changes occurring in the course of critical displacement (excitation) of kinetic units in liquids and glasses is discussed.

Effect of mixing and spatial dimension on the glass transition

We study the influence of composition changes on the glass transition of binary hard disk and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard disks strongly resembles the random close packing diagram. Compared to three dimensions from previous studies, the extension of the glass regime due to mixing is much more pronounced in two dimensions where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size ratio from unity.

Food stability determination by macro–micro region concept in the state diagram and by defining a critical temperature

In the 1950s the concept of water activity was proposed for determining food stability. This concept is now being used although it has some limitations. Indeed, these limitations mean that the concept is not universally applicable and in fact is invalid under certain conditions. In order to address the limitations of the water activity concept, the glass transition concept was proposed in the 1960s, although significant application of the concept only started in the 1980s. Recently, it has become evident that the glass transition concept is also not universally valid for stability determination in all types of foods when stored under different conditions. Currently in the literature the need is emphasized to combine the water activity and glass transition concepts since both concepts could complement each other. The glass transition concept was used to develop the state diagram by drawing another stability map using freezing curve and glass transition line. In this paper an attempt is made to review the published methods used to combine both concepts. These approaches are graphical plot of glass transition conditions and water content as a function of water activity, and macro–micro region concept in the state diagram. In addition, a new approach is proposed in this paper by defining a critical temperature for stability and then relating it with water content, and other hurdles affecting food stability. The water mobility concept is also reviewed to provide another dimension of food stability in order to determine a more complete picture.

Glass transition and state diagram for freeze-dried horse mackerel muscle

Glass transition temperatures of freeze-dried horse mackerel muscle conditioned at various water activities at 25 °C were determined by differential scanning calorimetry (DSC). High moisture content (>0.33 g/g, d.b.) samples obtained by adding liquid water into freeze-dried samples, were also analyzed. The state diagram was composed of the freezing curve and the glass transition line, which were fitted according to Clausius–Clapeyron model and Gordon–Taylor model, respectively. The state diagram yielded maximally freeze-concentrated solutes at 0.786 solids with the characteristic temperature of glass formation being −83.1 °C. The state diagram of horse mackerel muscle developed in this work could be used to predict the stability during frozen storage and in dried conditions as well as in designing drying and freezing processes.

Structure and pinning of the moving vortex matter in type II superconductors

The Martin – Siggia – Rose method is applied to the time dependent Ginzburg – Landau model in the presence of both disorder and thermal fluctuations beyond linear response. This allows calculation of correlators of the order parameter, the critical current as function of magnetic field and temperature and the I-V curves. The static or moving flux line lattice in type II superconductors undergoes a transition into three disordered phases: moving vortex liquid (not pinned), homogeneous vortex glass (pinned) and crystalline Bragg glass (pinned) due to both thermal fluctuations and random quenched disorder. The location of the glass transition line is determined and compared to experiments. The line is clearly different from both the melting line and the second peak line describing the translational and rotational symmetry breaking at high and low temperatures respectively. Applications to thermal transport and Nernst effect are considered.

Phase diagram of vortices in high-Tcsuperconductors with a melting line in the deepHc2region

We use a simple elastic Hamiltonian for the vortex lattice in a weak impurity background which includes defects in the form of integer-valued fields to calculate the free energy of a vortex lattice in the deep H_{c2} region. The phase diagram in this regime is obtained by applying the variational approach of M{\'e}zard and Parisi developed for random manifolds. We find a first-order line between the Bragg-glass and vortex-glass phase as a continuation of the melting line. In the liquid phase, we obtain an almost vertical third-order glass transition line near the critical temperature in the H-T plane. Furthermore, we find an almost vertical second-order phase transition line in the Bragg-glass as well as the vortex-glass phases which crosses the first-order Bragg-glass, vortex-glass transition line. We calculate the jump of the temperature derivate of the induction field across this second-order line as well as the entropy and magnetic field jumps across the first-order line.

Alternative View of Dynamic Arrest in Colloid-Polymer Mixtures

Colloid-polymer mixtures are frequently viewed as an effective one-component fluid (the colloid) with polymer-mediated depletion interactions. This view, together with conventional mode coupling theory, constitutes the current description of the reentrant glass transition experimentally observed in these systems. A more fundamental view is to consider these systems as what they actually are, namely, genuine highly size-asymmetric binary colloidal mixtures. In this Letter we demonstrate that the recently developed multicomponent self-consistent generalized Langevin equation theory of dynamic arrest correctly predicts the observed reentrance in excellent quantitative agreement with the experimental glass transition line of a colloid-polymer mixture. In this scenario the polymer plays a much more active dynamic role than in the conventional one-component description.

Thermal transitions of rice: Development of a state diagram

A state diagram of basmati rice was developed by measuring the glass line; glass transition temperature vs. solids content, freezing curve; initial freezing point vs. solids content and maximally freeze concentrated conditions by using the modulated differential scanning calorimetry (MDSC) method. In addition, a cooling curve method was used to measure the initial freezing point ( T F) and the end point of freezing ( T m ′ ). The glass transition line of the state diagram was modeled using the Gordon–Taylor and linear equations, and the pattern of freezing curve was modeled using the Chen equation which incorporated unfreezable water. The condition of maximal-freeze-concentration corresponded to X s ′ (characteristic solids content) = 0.60 and T m ′ (end point of freezing) = −3.6 °C obtained from freezing curve. The characteristics glass transition T g ′ = −7.1 °C and corresponding solids content X s ″ = 0.66 were obtained by extending the freezing curve up to glass line modeled using linear equation. The T g ′ = −11.6 °C and X s ″ = 0.82 were obtained when the glass line was modeled using Gordon–Taylor equation. Adsorption isotherms of rice were measured at room temperature by isopiestic method and data were modeled with BET and GAB equations. The BET and GAB monolayer values were found as 0.083 and 0.136 kg H 2O/kg dry solids, respectively. The state diagram and water sorption properties of basmati rice can be useful in optimizing the drying and freezing processes as well as studying the physicochemical changes during storage.

Magnetic phase diagram of type-II superconductors: From high Tc to low Tc superconductors

Phase diagram of both high temperature superconductors and low temperature superconductors are studied within the Ginzburg–Landau approach. Due to enhanced thermal fluctuation strength, disorder effects are relatively small in high T c superconductors and consequently can be studied analytically. The vortex glass transition line is different and well separated from both the melting line and from the so-called second peak lines. On contrary, in low temperature superconductors, the disorder effect is dominant, as the thermal fluctuation strength is very small. Peak effect appears due to cross over of the collective pinning region to stronger pinning region. The location of the peak effect is obtained. The disorder and thermal fluctuation effects on structure phase transition are also studied.

Equilibrium and glassy states of the Asakura-Oosawa and binary hard sphere mixtures: Effective fluid approach

Motivated by recent experimental results on model binary colloidal mixtures, especially for the glass transition, we investigate the phase diagram of two models of asymmetric binary mixtures: the hard sphere and the Asakura-Oosawa mixtures. This includes the binodals and the glass transition line, computed in the effective one-component representation using the corresponding potentials of mean force at infinite dilution. The reference hypernetted chain approximation is used for computing the static properties and the glass transition line is computed in the mode coupling approximation. The similarities and the differences between the two models are discussed for different size ratios. It is shown that while both models follow a universal behavior at large asymmetry, the hard sphere mixture model leads to more original results at moderate size ratio. These results show that a modeling beyond generic effective potentials might be necessary for an appropriate description of the complete phase diagram.