Spatial correlations in the dynamics of glassforming liquids: experimental determination of their temperature dependence

Short-Time Beta Relaxation in Glass-Forming Liquids Is Cooperative in Nature

Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. Using molecular dynamics simulations for three model glass-forming liquids, we show that the short-time β relaxation is cooperative in nature. Using finite-size scaling analysis, we extract a growing length scale associated with beta relaxation from the observed dependence of the beta relaxation time on the system size. We find, in qualitative agreement with the prediction of the inhomogeneous mode coupling theory, that the temperature dependence of this length scale is the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time α-relaxation regime.

Length scales in glass-forming liquids and related systems: a review

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.

Ionic liquids and their bases: Striking differences in the dynamic heterogeneity near the glass transition

Ionic liquids (ILs) constitute an active field of research due to their important applications. A challenge for these investigations is to explore properties of ILs near the glass transition temperature Tg, which still require our better understanding. To shed a new light on the issues, we measured ILs and their base counterparts using the temperature modulated calorimetry. We performed a comparative analysis of the dynamic heterogeneity at Tg for bases and their salts with a simple monoatomic anion (Cl(-)). Each pair of ionic and non-ionic liquids is characterized by nearly the same chemical structure but their intermolecular interactions are completely different. We found that the size of the dynamic heterogeneity of ILs near Tg is considerably smaller than that established for their dipolar counterparts. Further results obtained for several other ILs near Tg additionally strengthen the conclusion about the relatively small size of the dynamic heterogeneity of molecular systems dominated by electrostatic interactions. Our finding opens up new perspectives on designing different material properties depending on intermolecular interaction types.

Electron Correlation Microscopy: A New Technique for Studying Local Atom Dynamics Applied to a Supercooled Liquid

Electron correlation microscopy (ECM) is a new technique that utilizes time-resolved coherent electron nanodiffraction to study dynamic atomic rearrangements in materials. It is the electron scattering equivalent of photon correlation spectroscopy with the added advantage of nanometer-scale spatial resolution. We have applied ECM to a Pd40Ni40P20 metallic glass, heated inside a scanning transmission electron microscope into a supercooled liquid to measure the structural relaxation time τ between the glass transition temperature T g and the crystallization temperature, T x . τ determined from the mean diffraction intensity autocorrelation function g 2(t) decreases with temperature following an Arrhenius relationship between T g and T g +25 K, and then increases as temperature approaches T x . The distribution of τ determined from the g 2(t) of single speckles is broad and changes significantly with temperature.

Protein dynamics: from rattling in a cage to structural relaxation

We present an overview of protein dynamics based mostly on results of neutron scattering, dielectric relaxation spectroscopy and molecular dynamics simulations. We identify several major classes of protein motions on the time scale from faster than picoseconds to several microseconds, and discuss the coupling of these processes to solvent dynamics. Our analysis suggests that the microsecond backbone relaxation process might be the main structural relaxation of the protein that defines its glass transition temperature, while faster processes present some localized secondary relaxations. Based on the overview, we formulate a general picture of protein dynamics and discuss the challenges in this field.

Correlation between crystalline order and vitrification in colloidal monolayers

We investigate experimentally the relationship between local structure and dynamical arrest in a quasi-2d colloidal model system which approximates hard discs. We introduce polydispersity to the system to suppress crystallisation. Upon compression, the increase in structural relaxation time is accompanied by the emergence of local hexagonal symmetry. Examining the dynamical heterogeneity of the system, we identify three types of motion: 'zero-dimensional' corresponding to β-relaxation, 'one-dimensional' or stringlike motion and '2D' motion. The dynamic heterogeneity is correlated with the local order, that is to say locally hexagonal regions are more likely to be dynamically slow. However, we find that lengthscales corresponding to dynamic heterogeneity and local structure do not appear to scale together approaching the glass transition.

Method for estimating the cooperativity length in polymers

The problem of estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymeric melts from an analysis of the α-process in ordinary relaxation experiments is addressed. The mechanism whereby a CRR changes its configuration is viewed as consisting of two distinct steps: a reduced number of monomers reaches initially an activated state, allowing for some local rearrangement; then, the subsequent regression of the energy fluctuation may take place through the configurational degrees of freedom, thus allowing for further rearrangements on larger length scales. The latter are indeed those to which the well-known Donth's scheme refers. Local readjustments are described in the framework of a canonical formalism on a stationary ensemble of small-scale regions, distributed over all possible energy thresholds for rearrangement. Large-scale configurational changes, instead, are described as spontaneous processes. Two main regimes are envisaged, depending on whether the role played by the configurational degrees of freedom in the regression of the energy fluctuation is significant or not. It is argued that the latter case is related to the occurrence of an Arrhenian dependence of the central relaxation rate. Consistency with Donth's scheme is demonstrated, and data from the literature confirm the agreement of the two methods of analysis when configurational degrees of freedom are relevant for the fluctuation regression. Poly(n-butyl methacrylate) is chosen in order to show how CRR size and temperature fluctuations at rearrangement can be estimated from stress relaxation experiments carried out by means of an atomic force microscopy setup. Cases in which the configurational pathway for regression is significantly hindered are considered. Relaxation in poly(dimethyl siloxane) confined in nanopores is taken as an example to suggest how a more complete view of the effects of configurational constraints would be possible if direct measurements of temperature fluctuations were combined with the proposed analysis.

Structural heterogeneities at the origin of acoustic and transport anomalies in glycerol glass-former

By means of large scale molecular dynamics simulations, we explore mesoscopic properties of prototypical glycerol glass-former above and below the glass transition. The model used, in excellent agreement with various experimental techniques, permits to carefully study the structure and the vibrational dynamics. We find that a medium range order is present in glycerol glass-former and arises from hydrogen bond network extension. The characteristic size of the structural heterogeneities is related to the anomalous properties of acoustic vibrations (Rayleigh scattering, "mode softening," and Boson Peak) in the glassy state. Finally the characteristic size of these heterogeneities, nearly constant in temperature, is also connected to the cross-over between structural relaxation and diffusion in liquid glycerol.

Mobility restrictions and glass transition behaviour of an epoxy resin under confinement

Confinement can have a big influence on the dynamics of glass formers in the vicinity of the glass transition. Already 40 to 50 K above the glass transition temperature, thermal equilibration of glass formers can be strongly influenced by the confining substrate. We investigate the linear thermal expansion and the specific heat capacity cp of an epoxy resin (diglycidyl ether of bisphenol A, DGEBA) in a temperature interval of 120 K around the glass transition temperature. The epoxy resin is filled into controlled pore glasses with pore diameters between 4 and 111 nm. Since DGEBA can form H-bonds with silica surfaces, we also investigate the influence of surface silanization of the porous substrates. In untreated substrates a core/shell structure of the epoxy resin can be identified. The glass transition behaviours of the bulk phase and that of the shell phase are different. In silanized substrates, the shell phase disappears. At a temperature well above the glass transition, a second transition is found for the bulk phase - both in the linear expansion data as well as in the specific heat capacity. The cp data do not allow excluding the glass transition of a third phase as being the cause for this transition, whereas the linear expansion data do so. The additional transition temperature is interpreted as a separation between two regimes: above this temperature, macroscopic flow of the bulk phase inside the porous structure is possible to balance the mismatch of thermal expansion coefficients between DGEBA and the substrate. Below the transition temperature, this degree of freedom is hindered by geometrical constraints of the porous substrates. Moreover, this second transition could also be found in the linear expansion data of the shell phase.

Exploring the glass transition region: crowding effect, nonergodicity and thermorheological complexity

Thermorheological complexity in polystyrene near the glass transition point has been created through Monte Carlo simulations.

Nonlinear dynamic response of glass-forming liquids to random pinning

We use large scale computer simulations of a glass-forming liquid in which a fraction c of the particles has been permanently pinned. We find that the relaxation dynamics shows an exponential dependence on c. This result can be rationalized by assuming that the configurational entropy of the pinned liquid decreases linearly upon increasing of c. This behavior is discussed in the context of thermodynamic theories for the glass transition, notably the Adam-Gibbs picture and the random first order transition theory. For intermediate and low temperatures we find that the slowing down of the dynamics due to the pinning saturates and that the cooperativity decreases with increasing c, results which indicate that in glass-forming liquids there is a dynamic crossover at which the shape of the relaxing entities changes.

Variation of the dynamic susceptibility along an isochrone

Koperwas et al. showed in a recent paper [Phys. Rev. Lett. 111, 125701 (2013)] that the dynamic susceptibility χ4 as estimated by dielectric measurements for certain glass-forming liquids decreases substantially with increasing pressure along a curve of constant relaxation time. This observation is at odds with other measures of dynamics being invariant and seems to pose a problem for theories of glass formation. We show that this variation is in fact consistent with predictions for liquids with hidden scale invariance: Measures of dynamics at constant volume are invariant along isochrones, called isomorphs in such liquids, but contributions to fluctuations from long-wavelength fluctuations can vary. This is related to the known noninvariance of the isothermal bulk modulus. Considering the version of χ4 defined for the NVT ensemble, data from simulations of a binary Lennard-Jones liquid show in fact a slight increase with increasing density. This is a true departure from the formal invariance expected for this quantity.

Probing cooperative liquid dynamics with the mean square displacement

Literature data for picosecond mean square displacements show that the anharmonicity explains only about half of the fragility (with different fractions for different glass formers). The other half must be ascribed to the Adam-Gibbs mechanism of a growing cooperatively rearranging region. One can measure both influences separately by a simultaneous measurement of liquid and crystal in the coexistence region.

Analytical theory of effective interactions in binary colloidal systems of soft particles

While density functional theory with integral equations techniques are very efficient tools in the numerical analysis of complex fluids, analytical insight into the phenomenon of effective interactions is still limited. In this paper, we propose a theory of binary systems that results in a relatively simple analytical expression combining arbitrary microscopic potentials into effective interaction. The derivation is based on translating a many-particle Hamiltonian including particle-depletant and depletant-depletant interactions into the occupation field language, which turns the partition function into multiple Gaussian integrals, regardless of what microscopic potentials are chosen. As a result, we calculate the effective Hamiltonian and discuss when our formula is a dominant contribution to the effective interactions. Our theory allows us to analytically reproduce several important characteristics of systems under scrutiny. In particular, we analyze the following: the effective attraction as a demixing factor in the binary systems of Gaussian particles, the screening of charged spheres by ions, which proves equivalent to Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, effective interactions in the binary mixtures of Yukawa particles, and the system of particles consisting of both a repulsive core and an attractive/repulsive Yukawa interaction tail. For this last case, we reproduce the "attraction-through-repulsion" and "repulsion-through-attraction" effects previously observed in simulations.

Two glass transitions of polyurea networks: effect of the segmental molecular weight

Polymer-nanoparticle composites (PNCs) play an increasing role in technology. Inorganic or organic nanoparticles are usually incorporated into a polymer matrix to improve material properties. Polyurea is a spontaneously occurring PNC, exhibiting a phase segregated structure with hard nanodomains embedded in a soft (elastically compliant) matrix. This system shows two glass transitions at Tg1 and Tg2. It has been argued that they are related to the freezing of motion of molecular segments in the soft matrix (usual polymer α-glass transition at Tg1) and to regions of restricted mobility near the hard nanodomains (α'-process) at Tg2, respectively. We present detailed dynamic mechanical analysis (DMA) measurements for polyurea networks with different segmental lengths l(c) (2.5, 12.1, 24.5 nm) of the polymer chains, i.e. different volume fractions ϕ(x) (0.39, 0.12, 0.07) of the hard domains. The two glass transitions show up in two distinct peaks in tan δ at Tα and Tα'. Analysing the data using a Havriliak-Negami term for the α- and α'-relaxation, as well as Vogel-Fulcher dependencies for the corresponding relaxation times, it is found that the α-glass transition at Tg1 increases strongly (up to ΔT = 70 K) with increasing ϕ(x), whereas the α'-transition at Tg2 remains unchanged. At ϕ(x)(c) ≈ 0.19 the two curves intersect, i.e. Tg1 = Tg2. This value of ϕ(x)(c) is very close to the percolation threshold of randomly oriented overlapping ellipsoids of revolution with an aspect ratio of about 1 : 4-1 : 5. We therefore conclude that around 19% of the hard nanodomains polyurea changes from a system of hard nanoparticles embedded in a soft matrix (ϕ(x) ≤ ϕ(x)(c)) to a system of soft domains confined in a network of percolated hard domains at ϕ(x) ≥ ϕ(x)(c).

Strong dynamical heterogeneity and universal scaling in driven granular fluids

Large-scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor S(4)(q,t). Both cases, elastic (ϵ=1) and inelastic (ϵ<1) collisions, are studied. As the fluid approaches structural arrest, i.e., for packing fractions in the range 0.6≤ϕ≤0.805, scaling is shown to hold: S(4)(q,t)/χ(4)(t)=s(qξ(t)). Both the dynamic susceptibility χ(4)(τ(α)) and the dynamic correlation length ξ(τ(α)) evaluated at the α relaxation time τ(α) can be fitted to a power law divergence at a critical packing fraction. The measured ξ(τ(α)) widely exceeds the largest one previously observed for three-dimensional (3d) hard sphere fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, χ(4)(τ(α))≈ξ(d-p)(τ(α)), with an exponent d-p≈1.6. This scaling is remarkably independent of ϵ, even though the strength of the dynamical heterogeneity at constant volume fraction depends strongly on ϵ.

Dynamic correlations and heterogeneity in the primary and secondary relaxations of a model molecular liquid

Molecular dynamics simulations were carried out on a series of Lennard-Jones binary mixtures of rigid, asymmetric, dumbbell-shaped molecules. Below an onset temperature, the rotational and translational dynamics split into the slow structural α relaxation and a higher-frequency Johari-Goldstein β relaxation. Both processes are dynamically heterogeneous, having broad distributions of relaxation times. However, only the α relaxation shows strong dynamic correlations; correlations at the β time scale are weak, in particular for molecules having shorter bonds. Despite the close connection between the two processes, we find no correlation between the α and β relaxation times of individual molecules; that is, a molecule exhibiting slow β motion does not necessarily undergo slow α dynamics and likewise for fast molecules. However, the single-molecule α relaxation times do correlate with both the α and β relaxation strengths.

Dynamics and thermodynamics of polymer glasses

The fate of matter when decreasing the temperature at constant pressure is that of passing from gas to liquid and, subsequently, from liquid to crystal. However, a class of materials can exist in an amorphous phase below the melting temperature. On cooling such materials, a glass is formed; that is, a material with the rigidity of a solid but exhibiting no long-range order. The study of the thermodynamics and dynamics of glass-forming systems is the subject of continuous research. Within the wide variety of glass formers, an important sub-class is represented by glass forming polymers. The presence of chain connectivity and, in some cases, conformational disorder are unfavourable factors from the point of view of crystallization. Furthermore, many of them, such as amorphous thermoplastics, thermosets and rubbers, are widely employed in many applications. In this review, the peculiarities of the thermodynamics and dynamics of glass-forming polymers are discussed, with particular emphasis on those topics currently the subject of debate. In particular, the following aspects will be reviewed in the present work: (i) the connection between the pronounced slowing down of glassy dynamics on cooling towards the glass transition temperature (Tg) and the thermodynamics; and, (ii) the fate of the dynamics and thermodynamics below Tg. Both aspects are reviewed in light of the possible presence of a singularity at a finite temperature with diverging relaxation time and zero configurational entropy. In this context, the specificity of glass-forming polymers is emphasized.

Waxing and waning of dynamical heterogeneity in the superionic state

Using molecular dynamics simulations of UO2-a type II superionic conductor-we identify a well-defined onset of dynamic disorder (Tα), which is remarkably correlated to a nontrivial advance of dynamical heterogeneity (DH). Quantified by the correlations in the dynamic propensity and van Hove self-correlation function, the DH is shown to grow with increasing temperature from Tα, peak at an intermediate temperature between Tα and Tλ-the superionic transition temperature-and then recede. Surprisingly, the DH attributes are not uniform across the temperatures-our investigation shows a low temperature (αT) stage DH, which is characterized by weak correlations and a plateaulike period in the correlations of the propensity, and a high temperature (λT) stage DH with strong correlations that are analogous to those in typical supercooled liquids. Our work, which has rigorously identified the onset of superionicity, gives a different direction for interpreting scattering experiments on the basis of statistical, correlated dynamics.

Dynamic length scales in glass-forming liquids: an inhomogeneous molecular dynamics simulation approach

In this work, we numerically investigate a new method for the characterization of growing length scales associated with spatially heterogeneous dynamics of glass-forming liquids. This approach, motivated by the formulation of the inhomogeneous mode-coupling theory (IMCT) [Biroli, G.; et al. Phys. Rev. Lett. 2006 97, 195701], utilizes inhomogeneous molecular dynamics simulations in which the system is perturbed by a spatially modulated external potential. We show that the response of the two-point correlation function to the external field allows one to probe dynamic correlations. We examine the critical properties shown by this function, in particular, the associated dynamic correlation length, that is found to be comparable to the one extracted from standardly employed four-point correlation functions. Our numerical results are in qualitative agreement with IMCT predictions but suggest that one has to take into account fluctuations not included in this mean-field approach to reach quantitative agreement. Advantages of our approach over the more conventional one based on four-point correlation functions are discussed.

Effect of temperature and density fluctuations on the spatially heterogeneous dynamics of glass-forming Van der Waals liquids under high pressure

In this Letter, we show how temperature and density fluctuations affect the spatially heterogeneous dynamics at ambient and elevated pressures. By using high-pressure experimental data for van der Waals liquids, we examine contributions of the temperature and density fluctuations to the dynamics heterogeneity. We show that the dynamic heterogeneity decreases significantly with increasing pressure at a constant structural relaxation time (isochronal condition), while the broadening of the relaxation spectrum remains constant. This observation questions the relationship between spectral broadening and dynamic heterogeneity.

Microscopic calculation of the free energy cost for activated transport in glass-forming liquids

Activated transport in liquids--supercooled liquids in particular--occurs via mutual nucleation of alternative, aperiodic minima of the free energy. Xia and Wolynes [Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000)] have made a general argument that at temperatures near the ideal glass transition, the surface penalty for this kind of nucleation is largely determined by the temperature and the logarithm of the size of the vibrational fluctuation of rigid molecular units about the local minimum. Here, we independently show how to estimate this surface tension and, hence, the activation barrier for the activated transport for several actual liquids, using their structure factors and knowledge of the finite-frequency elastic constants. In this estimate, the activation free energy, while depending on the configurational entropy, also depends on the elastic modulus as in the "shoving" models. The resulting estimates are however consistent with the estimate provided by Xia and Wolynes' argument near the glass transition and, in addition, reflect the barrier softening effects predicted earlier for fragile substances.

Polymer unfolding and motion synchronization induced by spatially correlated noise

The problem of a spatially correlated noise affecting a complex system is studied in this paper. We present a comprehensive analysis of a two-dimensional model polymer chain, driven by the spatially correlated Gaussian noise, for which we have varied the amplitude and the correlation length. The chain model is based on a bead-spring approach, enriched with a global Lennard-Jones potential and angular interactions. We show that spatial correlations in the noise inhibit the chain geometry dynamics, enhancing the preservation of the polymer shape. This is supported by the analysis of correlation functions of both the module length and angles between neighboring modules, which have been measured for the noise amplitude ranging over three orders of magnitude. Moreover, we have observed the correlation length dependent bead motion synchronization and the spontaneous polymer unfolding, resulting from an interplay between chain potentials and the spatially structured noise.

Finite-size effects in the dynamics of glass-forming liquids

We present a comprehensive theoretical study of finite-size effects in the relaxation dynamics of glass-forming liquids. Our analysis is motivated by recent theoretical progress regarding the understanding of relevant correlation length scales in liquids approaching the glass transition. We obtain predictions both from general theoretical arguments and from a variety of specific perspectives: mode-coupling theory, kinetically constrained and defect models, and random first-order transition theory. In the last approach, we predict in particular a nonmonotonic evolution of finite-size effects across the mode-coupling crossover due to the competition between mode-coupling and activated relaxation. We study the role of competing relaxation mechanisms in giving rise to nonmonotonic finite-size effects by devising a kinetically constrained model where the proximity to the mode-coupling singularity can be continuously tuned by changing the lattice topology. We use our theoretical findings to interpret the results of extensive molecular dynamics studies of four model liquids with distinct structures and kinetic fragilities. While the less fragile model only displays modest finite-size effects, we find a more significant size dependence evolving with temperature for more fragile models, such as Lennard-Jones particles and soft spheres. Finally, for a binary mixture of harmonic spheres we observe the predicted nonmonotonic temperature evolution of finite-size effects near the fitted mode-coupling singularity, suggesting that the crossover from mode-coupling to activated dynamics is more pronounced for this model. Finally, we discuss the close connection between our results and the recent report of a nonmonotonic temperature evolution of a dynamic length scale near the mode-coupling crossover in harmonic spheres.

Adam-Gibbs relation for glass-forming liquids in two, three, and four dimensions

The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in two, three, and four spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in three and four dimensions. But in two dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.

Measurement of the four-point susceptibility of an out-of-equilibrium colloidal solution of nanoparticles using time-resolved light scattering

The spatial fluctuations of the dynamics of a colloidal system composed of nanoparticles are probed by a novel experimental setup, which combines homodyne and heterodyne dynamic light scattering focused onto a micron-sized volume via a microscope objective. The technique is used to measure the four-point susceptibility of an aging colloidal suspension, revealing a breakdown of the Gaussian approximation for the correlation function of the scattered electromagnetic field. The deviation from the Gaussian approximation increases with waiting time as the system evolves toward an arrested phase, signaling the gradual emergence of higher-order nontrivial dynamic correlations.

Manifestations of dynamical facilitation in glassy materials

By characterizing the dynamics of idealized lattice models with a tunable kinetic constraint, we explore the different ways in which dynamical facilitation manifests itself within the local dynamics of glassy materials. Dynamical facilitation is characterized both by a mobility transfer function, the propensity for highly mobile regions to arise near regions that were previously mobile, and by a facilitation volume, the effect of an initial dynamical event on subsequent dynamics within a region surrounding it. Sustained bursts of dynamical activity-avalanches-are shown to occur in kinetically constrained models, but, contrary to recent claims, we find that the decreasing spatiotemporal extent of avalanches with increased supercooling previously observed in granular experiments does not imply diminishing facilitation. Viewed within the context of existing simulation and experimental evidence, our findings show that dynamical facilitation plays a significant role in the dynamics of systems investigated over the range of state points accessible to molecular simulations and granular experiments.