Volume 138, Issue 12, 28 March 2013
 SPECIAL TOPIC: GLASS TRANSITION


Preface: Special Topic on the Glass Transition
View Description Hide DescriptionThis Special Topic on the Glass Transition contains a perspective article and a collection of original research articles that showcase recent experimental and theoretical advances in the field. This special issue provides a timely discussion of modern developments in our understanding of the behavior of supercooled liquids and amorphous materials, which have implications in diverse fields ranging from biology to materials science.
 Perspective

Perspective: The glass transition
View Description Hide DescriptionWe provide here a brief perspective on the glass transition field. It is an assessment, written from the point of view of theory, of where the field is and where it seems to be heading. We first give an overview of the main phenomenological characteristics, or “stylised facts,” of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner. We describe recent developments, with a particular focus on real space properties, including dynamical heterogeneity and facilitation, the search for underlying spatial or structural correlations, and the relation between the thermal glass transition and athermal jamming. We then discuss briefly how competing theories of the glass transition have adapted and evolved to account for such real space issues. We consider in detail two conceptual and methodological approaches put forward recently, that aim to access the fundamental critical phenomenon underlying the glass transition, be it thermodynamic or dynamic in origin, by means of biasing of ensembles, of configurations in the thermodynamic case, or of trajectories in the dynamic case. We end with a short outlook.
 Articles

Are the dynamics of a glass embedded in its elastic properties?
View Description Hide DescriptionThe low temperature dynamics of glass are critically important for many hightech applications. According to the elastic theory of the glass transition, the dynamics of glass are controlled by the evolution of shear modulus. In particular, the elastic shoving model expresses dynamics in terms of an activation energy required to shove aside the surrounding atoms. Here, we present a thorough test of the shoving model for predicting the low temperature dynamics of an oxide glass system. We show that the nonequilibrium viscosity of glass is governed by additional factors beyond changes in shear modulus.

Are polar liquids less simple?
View Description Hide DescriptionStrong correlation between equilibrium fluctuations under isochoric conditions of the potential energy, U, and the virial, W, is a characteristic of liquids that implies the presence of certain dynamic properties, such as density scaling of the relaxation times and isochronal superpositioning of the relaxation function. In this work we employ molecular dynamics simulations on methanol and two variations, lacking hydrogen bonds and a dipole moment, to assess the connection between the correlation of U and W and these dynamic properties. We show, in accord with prior results of others [T. S. Ingebrigtsen, T. B. Schrøder, and J. C. Dyre, Phys. Rev. X2, 011011 (Year: 2012)10.1103/PhysRevX.2.011011], that simple van der Waals liquids exhibit both strong correlations and the expected dynamic behavior. However, for polar liquids this correspondence breaks down—weaker correlation between U and W is not associated with worse conformance to density scaling or isochronal superpositioning. The reason for this is that strong correlation between U and W only requires their proportionality, whereas the expected dynamic behavior depends primarily on constancy of the proportionality constant for all state points. For hydrogenbonded liquids, neither strong correlation nor adherence to the dynamic properties is observed; however, this nonconformance is not directly related to the concentration of hydrogen bonds, but rather to the greater deviation of the intermolecular potential from an inverse power law (IPL). Only (hypothetical) liquids having interactions governed strictly by an IPL are perfectly correlating and exhibit the consequent dynamic properties over all thermodynamic conditions.

Glass transition of poly(ethylmethacrylate) admixed and bound to nanoparticles
View Description Hide DescriptionThe chain dynamics at the glass transition of poly(ethylmethacrylate) in the bulk is compared to that of mixtures of the polymer with nanoparticles by advanced NMR methods. In order to make the two components compatible, the particles were functionalized with the polymer itself. Particular emphasis is placed on the extended local chain conformations of this polymer accessible by ^{13}C NMR spectroscopy. The isotropization dynamics of these extended conformations is only slightly changed in the mixtures, but is significantly slowed down by attachment of the chains to the nanoparticles themselves. The slowing down is studied at various distances from the nanoparticle and is observed for most of the attached chains segments except for the chain ends. The results are put into perspective to the glass transition in polymers attached to surfaces, thin polymer layers, and the chain dynamics of star polymers.

Modeling the relaxation of polymer glasses under shear and elongational loads
View Description Hide DescriptionGlassy polymers show “strain hardening”: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flowinduced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymerborne stress, slowing the deformation enough for the segmental (or solvent) modes then to revitrify. Here, we present new results for the corresponding behavior under stepstress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a “crinkle factor” describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves nonentropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally, we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.

Higherorder correlation functions and nonlinear response functions in a Gaussian trap model
View Description Hide DescriptionThe fourtime correlation function of a general dynamical variable obeying Gaussian statistics is calculated for the trap model with a Gaussian density of states. It is argued that for energyindependent variables this function is reminiscent of the fourtime functions that have been discussed earlier in the interpretation of the results of fourdimensional NMR experiments on supercooled liquids. Using an approximative relation between the fourtime correlation function and the cubic response function the nonlinear susceptibility is calculated and the results are compared with the corresponding ones resulting from an exact calculation. It is found that the results of the approximation change the qualitative behavior of the modulus of the susceptibility. Whereas in the exact calculation a peak is found in the modulus in most cases, depending on temperature and the additional model parameters no such peak occurs in the approximation. This difference has its origin mainly in an incorrect estimate of the static response. The results are discussed in relation to recent experimental findings.

Multiple length and time scales of dynamic heterogeneities in model glassforming liquids: A systematic analysis of multipoint and multitime correlations
View Description Hide DescriptionWe report an extensive and systematic investigation of the multipoint and multitime correlation functions to reveal the spatiotemporal structures of dynamic heterogeneities in glassforming liquids. Molecular dynamics simulations are carried out for the supercooled states of various prototype models of glassforming liquids such as binary Kob–Andersen, Wahnström, softsphere, and networkforming liquids. While the first three models act as fragile liquids exhibiting superArrhenius temperature dependence in their relaxation times, the last is a strong glassformer exhibiting Arrhenius behavior. First, we quantify the length scale of the dynamic heterogeneities utilizing the fourpoint correlation function. The growth of the dynamic length scale with decreasing temperature is characterized by various scaling relations that are analogous to the critical phenomena. We also examine how the growth of the length scale depends upon the model employed. Second, the fourpoint correlation function is extended to a threetime correlation function to characterize the temporal structures of the dynamic heterogeneities based on our previous studies [K. Kim and S. Saito, Phys. Rev. E79, 060501–R (Year: 2009)10.1103/PhysRevE.79.060501;K.Kim and S.Saito, J. Chem. Phys.133, 044511 (Year: 2010)10.1063/1.3464331]. We provide comprehensive numerical results obtained from the threetime correlation function for the above models. From these calculations, we examine the time scale of the dynamic heterogeneities and determine the associated lifetime in a consistent and systematic way. Our results indicate that the lifetime of the dynamical heterogeneities becomes much longer than the αrelaxation time determined from a twopoint correlation function in fragile liquids. The decoupling between the two time scales is remarkable, particularly in supercooled states, and the time scales differ by more than an order of magnitude in a more fragile liquid. In contrast, the lifetime is shorter than the αrelaxation time in tetrahedral networkforming strong liquid, even at lower temperatures.

Dynamic criticality at the jamming transition
View Description Hide DescriptionWe characterize vibrational motion occurring at low temperatures in dense suspensions of soft repulsive spheres over a broad range of volume fractions encompassing the jamming transition at (T = 0, φ = φ_{ J }). We find that characteristic time and length scales of thermal vibrations obey critical scaling in the vicinity of the jamming transition. We show in particular that the amplitude and the time scale of dynamic fluctuations diverge symmetrically on both sides of the transition, and directly reveal a diverging correlation length. The critical region near φ_{ J } is divided in three different regimes separated by a characteristic temperature scale T ^{⋆}(φ) that vanishes quadratically with the distance to φ_{ J }. While two of them, (T < T ^{⋆}(φ), φ > φ_{ J }) and (T < T ^{⋆}(φ), φ < φ_{ J }), are described by harmonic theories developed in the zero temperature limit, the third one for T > T ^{⋆}(φ) is inherently anharmonic and displays new critical properties. We find that the quadratic scaling of T ^{⋆}(φ) is due to nonperturbative anharmonic contributions, its amplitude being orders of magnitude smaller than the perturbative prediction based on the expansion to quartic order in the interactions. Our results show that thermal vibrations in colloidal assemblies directly reveal the critical nature of the jamming transition. The critical region, however, is very narrow and has not yet been attained experimentally, even in recent specificallydedicated experiments.

Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition
View Description Hide DescriptionThe small wavenumber k behavior of the structure factor S(k) of overcompressed amorphous hardsphere configurations was previously studied for a wide range of densities up to the maximally random jammed state, which can be viewed as a prototypical glassy state [A. Hopkins, F. H. Stillinger, and S. Torquato, Phys. Rev. E86, 021505 (Year: 2012)]10.1103/PhysRevE.86.021505. It was found that a precursor to the glassy jammed state was evident long before the jamming density was reached as measured by a growing nonequilibrium length scale extracted from the volume integral of the direct correlation function c(r), which becomes longranged as the critical jammed state is reached. The present study extends that work by investigating via computer simulations two different atomic models: the singlecomponent Z2 Dzugutov potential in three dimensions and the binarymixture KobAndersen potential in two dimensions. Consistent with the aforementioned hardsphere study, we demonstrate that for both models a signature of the glass transition is apparent well before the transition temperature is reached as measured by the length scale determined from the volume integral of the direct correlation function in the singlecomponent case and a generalized direct correlation function in the binarymixture case. The latter quantity is obtained from a generalized OrnsteinZernike integral equation for a certain decoration of the atomic point configuration. We also show that these growing length scales, which are a consequence of the longrange nature of the direct correlation functions, are intrinsically nonequilibrium in nature as determined by an index X that is a measure of the deviation from thermal equilibrium. It is also demonstrated that this nonequilibrium index, which increases upon supercooling, is correlated with a characteristic relaxation time scale.

Static correlations functions and domain walls in glassforming liquids: The case of a sandwich geometry
View Description Hide DescriptionThe problem of measuring nontrivial static correlations in deeply supercooled liquids made recently some progress thanks to the introduction of amorphous boundary conditions, in which a set of free particles is subject to the effect of a different set of particles frozen into their (low temperature) equilibrium positions. In this way, one can study the crossover from nonergodic to ergodic phase, as the size of the free region grows and the effect of the confinement fades. Such crossover defines the socalled pointtoset correlation length, which has been measured in a spherical geometry, or cavity. Here, we make further progress in the study of correlations under amorphous boundary conditions by analyzing the equilibrium properties of a glassforming liquid, confined in a planar (“sandwich”) geometry. The mobile particles are subject to amorphous boundary conditions with the particles in the surrounding walls frozen into their low temperature equilibrium configurations. Compared to the cavity, the sandwich geometry has three main advantages: (i) the width of the sandwich is decoupled from its longitudinal size, making the thermodynamic limit possible; (ii) for very large width, the behaviour off a single wall can be studied; (iii) we can use “antiparallel” boundary conditions to force a domain wall and measure its excess energy. Our results confirm that amorphous boundary conditions are indeed a very useful new tool in the study of static properties of glassforming liquids, but also raise some warning about the fact that not all correlation functions that can be calculated in this framework give the same qualitative results.

Evolution of the dynamic susceptibility in molecular glass formers: Results from light scattering, dielectric spectroscopy, and NMR
View Description Hide DescriptionAlthough broadly studied, molecular glass formers are not well investigated above their melting point. Correlation times down to 10^{−12} s are easily accessible when studying lowT g systems by depolarized light scattering, employing a tandemFabryPerot interferometer and a double monochromator. When combining these techniques with stateoftheart photon correlation spectroscopy (PCS), broad band susceptibility spectra become accessible which can compete with those of dielectric spectroscopy (DS). Comparing the results with those from DS, optical Kerr effect, and NMR, we describe the evolution of the susceptibilities starting from the boiling point T b down to T g, i.e., from simple liquid to glassy dynamics. Special attention is given to the emergence of the excess wing contribution which is also probed by PCS and which signals a crossover of the spectral evolution. The process is attributed to a smallangle precursor process of the αrelaxation, and the apparent probe dependent stretching of the αprocess is explained by a probe dependent contribution of the excess wing. Upon cooling, its emergence is linked to a strong decrease of the strength of the fast dynamics which is taken as reorientational analog of the anomaly of the DebyeWaller factor. Many glass formers show in addition a slow βprocess which manifests itself rather universally in NMR, in DS, however, with different amplitudes, but not at all in PCS experiments. Finally, a threeparameter function is discussed interpolating τ α(T) from T b to T g by connecting high and lowtemperature dynamics.

Nonexponential nature of calorimetric and other relaxations: Effects of 2 nmsize solutes, loss of translational diffusion, isomer specificity, and sample size
View Description Hide DescriptionCertain distributions of relaxation times can be described in terms of a nonexponential response parameter, β, of value between 0 and 1. Both β and the relaxation time, τ _{0}, of a material depend upon the probe used for studying its dynamics and the value of β is qualitatively related to the nonArrhenius variation of viscosity and τ _{0}. A solute adds to the diversity of an intermolecular environment and is therefore expected to reduce β, i.e., to increase the distribution and to change τ _{0}. We argue that the calorimetric value β ^{cal} determined from the specific heat [C _{ p } = T(dS/dT)_{ p }] data is a more appropriate measure of the distribution of relaxation times arising from configurational fluctuations than β determined from other properties, and report a study of β ^{cal} of two sets of binary mixtures, each containing a different molecule of ∼2 nm size. We find that β ^{cal} changes monotonically with the composition, i.e., solute molecules modify the nanoscale composition and may increase or decrease τ _{0}, but do not always decrease β ^{cal}. (Plots of β ^{cal} against the composition do not show a minimum.) We also analyze the data from the literature, and find that (i) β ^{cal} of an orientationally disordered crystal is less than that of its liquid, (ii) β ^{cal} varies with the isomer's nature, and chiral centers in a molecule decrease β ^{cal}, and (iii) β ^{cal} decreases when a sample's thickness is decreased to the nmscale. After examining the difference between β ^{cal} and β determined from other properties we discuss the consequences of our findings for theories of nonexponential response, and suggest that studies of β ^{cal} may be more revealing of structurefreezing than studies of the nonArrhenius behavior. On the basis of previous reports that β → 1 for dielectric relaxation of liquids of centiPoise viscosity observed at GHz frequencies, we argue that its molecular mechanism is the same as that of the JohariGoldstein (JG) relaxation. Its spectrum becomes broader on cooling and its unimodal distribution reversibly changes to a bimodal distribution, each of β < 1. Kinetic freezing of the slower modes of the bimodal distribution produces a glass. After this bifurcation, the faster, original relaxation persists as a weak JG relaxation at T → T _{ g }, and in the glassy state.

Nonlinear active microrheology in a glassforming softsphere mixture
View Description Hide DescriptionWe present extensive molecular dynamics computer simulations of a glassforming Yukawa mixture, investigating the nonlinear response of a single particle that is pulled through the system by a constant force. Structural changes around the pulled particle are analyzed by pair correlation functions, measured in the deeply supercooled state of the system. A regime of intermediate force strengths is found where the structural changes around the pulled particle are small, although its steadystate velocity shows a strong nonlinear response. This nonlinear response regime is characterized by a forcetemperature superposition principle of a Peclet number and anisotropic diffusive behavior. In the direction parallel to the force, meansquare displacements show anomalous superdiffusion in the long time limit. We analyze this superdiffusive behavior by means of the van Hove correlation function of the pulled particle. Perpendicular to the force, the driven particle shows diffusive behavior for all considered force strengths and temperatures. We discuss the dynamics perpendicular and parallel to the force in terms of effective temperatures.

On the Bauschinger effect in supercooled melts under shear: Results from mode coupling theory and molecular dynamics simulations
View Description Hide DescriptionWe study the nonlinear rheology of a glassforming binary mixture under the reversal of shear flow using molecular dynamics simulations and a schematic model of the modecoupling theory of the glass transition (MCT). Memory effects lead to a historydependent response, as exemplified by the vanishing of a stressovershoot phenomenon in the stress–strain curves of the sheared liquid, and a change in the apparent elastic coefficients around states with zero stress. We investigate the various retarded contributions to the stress response at a given time schematically within MCT. The connection of this macroscopic response to singleparticle motion is demonstrated using moleculardynamics simulation.

Dynamics of thermal vibrational motions and stringlike jump motions in threedimensional glassforming liquids
View Description Hide DescriptionUsing molecular dynamics simulation on a glassforming liquid in three dimensions, we investigate the thermal vibrational motions, the configuration changes caused by stringlike jump motions, and their close correlations. The heterogeneous vibrational motions are visualized in terms of a vibration length S _{ i }(t) defined for each particle i. The structure factor for the inhomogeneity of S _{ i }(t)^{2} is also calculated, which exhibits considerable long wavelength enhancement. By examining the birth times of strings, they are shown to appear collectively and intermittently. We show that particles with larger S _{ i }(t) tend to trigger jump motions more frequently at later times than those with smaller S _{ i }(t). We also show that the particles with fewer bonds tend to have larger S _{ i }(t) and participate more frequently in the stringlike motions.

Geometrical frustration and static correlations in hardsphere glass formers
View Description Hide DescriptionWe analytically and numerically characterize the structure of hardsphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly irrelevant with increasing dimension. We also find the growth in structural correlations to be modest in the dynamical regime accessible to computer simulations.

Can a stable glass be superheated? Modelling the kinetic stability of coated glassy films
View Description Hide DescriptionThe fabrication of ultrastable glass films by vapour deposition and their subsequent frontlike response to annealing are both manifestations of the enhancement of dynamics at the amorphous surface. We use the facilitated kinetic Ising model to model the behaviour of ultrastable amorphous films when a coating is applied that suppresses the dynamics at the film surface. The consequences of this manipulation of the film include glass films that can be heated to temperatures in excess of the glass transition without transforming into the liquid, the possibility of direct visualization of the spatial distribution of intrinsic dynamic heterogeneities, and the possibility of using surface treatment to engineer relaxation of these glass films.

Manipulating the properties of stable organic glasses using kinetic facilitation
View Description Hide DescriptionIn contrast to ordinary glasses, when highly stable organic glasses are annealed at temperatures above T_{g}, they transform heterogeneously into the liquid state by a constant velocity propagating front that initiates at the free surface. The evolution of this growth front has been interpreted as kinetic facilitation, i.e., efficiently packed molecules become unjammed only when mobility is available in adjacent regions. Here we use physical vapor deposition to prepare highly stable glasses of indomethacin in which mobile regions are either added to or eliminated from the samples in an attempt to use the kinetic facilitation concept to manipulate the properties of these materials. The addition of higher mobility layers in the interior of a thin stable glass film or at the substrate surface is shown to initiate new growth fronts, thus demonstrating that kinetic facilitation occurs independently of free surface mobility. Conversely, capping the free surface with a higher T_{g} stable glass stops the growth front, apparently by eliminating surface mobility, thus increasing sample stability by slowing the transformation to the supercooled liquid.

Microrheology of supercooled liquids in terms of a continuous time random walk
View Description Hide DescriptionMolecular dynamics simulations of a glassforming model system are performed under application of a microrheological perturbation on a tagged particle. The trajectory of that particle is studied in its underlying potential energy landscape. Discretization of the configuration space is achieved via a metabasin analysis. The linear and nonlinear responses of drift and diffusive behavior can be interpreted and analyzed in terms of a continuous time random walk. In this way, the physical origin of linear and nonlinear response can be identified. Critical forces are determined and compared with predictions from literature.
