Glassy Dynamics Research Articles

Cooperative strings and glassy dynamics in various confined geometries.

Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, by canceling and restarting any cooperative-chain realization reaching the boundary with a smaller number of steps than the bulk cooperativity, we account for a purely attractive substrate, and explore the impact of the latter in the previous geometries.

The interplay between the fragility and mechanical properties of styrene–butadiene rubber composites with unmodified and modified sago seed shell powder

AbstractReinforcing rubber with natural fillers from agrarian wastes is a new area of interest in developing rubber composite technologies. Lignocellulosic material from sago seed shell is one of the important promising natural fillers having 37% cellulose used to reinforce styrene–butadiene rubber (SBR) for enhancing its mechanical properties. Moreover, chemically or physically modified natural fillers play a significant role in enhancing the properties of SBR like morphological, thermal, and electrical characteristics. In this investigation, the changes encountered in molecular mobility, glassy dynamics, thermal stability, flexibility, and tensile strength of SBR on reinforcing with unmodified and modified sago seed shell powder were studied using broadband dielectric spectroscopy (BDS) in conjunction with thermogravimetric analysis, and mechanical properties. BDS has been successfully employed to investigate the relaxation phenomena and glass/rubbery transition in SBR, as well as its composites with unmodified and modified sago seed shell powder over the frequency (10−1 to 107 Hz) and wide temperature range (−100 to 150°C). Experimental data were analyzed in terms of electric modulus formalism and were suited well with the Havriliak Nigami equation. The incorporation of filler and its nature (unmodified or modified it with polyaniline, PANI) greatly influenced the morphological pattern, miscibility, and mode of interaction with the rubber matrix of SBR, which owed a path to diverse charge transport mechanism in the composites. The mechanical properties of all the composites were in good correlation with the steepness index obtained from BDS. The tensile strength, tear strength, and hardness of SBR increased slightly on loading with unmodified cellulose, whereas with modified cellulose causes substantial enhancement in its tensile strength.

Polyvinylidene difluoride-based composite: glassy dynamics and pretransitional behaviour

This paper presents results of broadband dielectric spectroscopy studies in the composite system for which particularly strong interactions between polyvinylidene difluoride (PVDF: ferroelectric polymer, TC = 453−473 K) matrix and barium strontium titanate (BST) ferroelectric micro-particles can be expected. For PVDF the super-Arrhenius (SA) dynamics, associated with segmental motions freezing at the glass temperature Tg = 235 K, is evidenced. The addition of BST particles qualitatively changes dynamics, converting the SA-type behaviour in PVDF to the clear Arrhenius one in BST/PVDF composite. The latter crossovers to the relaxor-type SA dynamics on cooling, exactly at the glass temperature of PVDF. The preliminary model explaining such unique behaviour is proposed. For the consistent portraying of the SA evolution of primary relaxation times in PVDF and BST/PVDF, the activation energy index analysis was carried out and the new equation, entropy and symmetry controlled, is introduced. Studies are accomplished by the analysis of the ferroelectric-paraelectric transition in PVDF and for the composite system. They led to the discovery of the strong pretransitional anomaly of dε∕dT, extending even to the vicinity of the room temperature, The semi-discontinuous nature of melting in PVDF and its composites, with the discontinuity metric △T ≈ 20 K is suggested.Graphical abstract

Role of many-body correlation in slow dynamics of glass-forming liquids: intrinsic or perturbative

Upon cooling or densification, a supercooled liquid shows drastic slowing down toward its glass-transition point. The physical mechanism behind this slow glassy dynamics has been a matter of discussion for a long time, but there has still been no consensus on its origin. Recently, we have found that for systems mainly interacting with steric repulsions, glassy structural order (or, angular order) generally develops upon cooling and its correlation length, , grows as ( is the bare correlation length, T is the temperature, T0 is the hypothetical ideal glass transition, and d is the spatial dimensionality). This ordering is difficult to detect by two-body density correlation since it is a consequence of sterically-induced (entropically-driven) many-body correlation that lowers local free energy. Interestingly, the power-law growth of with the exponent of 2/d is reminiscent of the Ising criticality. We also find that the structural relaxation time diverges as (: the microscopic relaxation time, K is a fragility index, is the Boltzmann constant), suggesting that glass transition is a consequence of Ising-like criticality with growing activation energy. Unlike ordinary critical phenomena, the activation energy of particle motion increases in proportion to the root of the correlation volume of , implying that the particle motion is strongly correlated in that volume. This relation indicates that the impact of spatial fluctuations of the order parameter on slow dynamics is not perturbative but intrinsic. Although we need further study to confirm our claim, we hope that the discussion in this article would provide a good starting point for further consideration of the physical nature of glass transition.

Slow dynamics of supercooled hydration water in contact with lysozyme: examining the cage effect at different length scales

ABSTRACT We study by computer simulation the dynamics of hydration water in solution with lysozyme upon approaching the glassy state of water. We calculate the self-density correlation function at different wavelengths to test the Mode Coupling Theory (MCT) of glassy dynamics at different length scales. The results show a strict and clear relation of the behaviour of the structural relaxation with the cage effect. We find a good agreement with the predictions of the MCT in the short and medium scale range, while at increasing length scales the interaction of water molecules with the protein's substrate induces deviations from the MCT behaviour, as found in previous studies. Besides at low temperatures the slow dynamics deviates from MCT due to hopping processes, similar to the bulk, as witnessed by a crossover from a fragile behaviour to a strong behaviour. We show that this deviation is evident at all length scales. Interestingly, we find that in the fragile region the confining cage decreases in radius with temperature while in the strong region it appears stable.

Phase separation in a two-dimensional binary colloidal mixture by quorum sensing activity.

We present results from Langevin dynamics simulations of a glassy active-passive mixture of soft-repulsive binary colloidal disks. Activity on the smaller particles is applied according to the quorum sensing scheme, in which a smaller particle will be active for a persistence time if its local nearest neighbors are equal to or greater than a certain threshold value. We start with a passive glassy state of the system and apply activity to the smaller particles, which shows a nonmonotonous glassy character of the active particles with the persistence time of the active force, from its passive limit (zero activity). On the other hand, passive particles of the active-passive mixture phase separate at the intermediate persistence time of the active force, resulting in the hexatic-liquid and solid-liquid phases. Thus, our system shows three regimes as active glass, phase separation, and active liquid, as the persistence time increases from its smaller values. We show that the solidlike and hexatic phases consisting of passive large particles are stable due to the smaller momentum transfer from active to passive particles, compared to the higher persistence time where the positional and orientational ordering vanishes. Our model is relevant to active biological systems, where glassy dynamics is present, e.g., bacterial cytoplasm, biological tissues, dense quorum sensing bacteria, and synthetic smart amorphous glasses.

Glass transition temperature of single-chain polystyrene particles end-grafted to oxide-coated silicon.

A method based on the PeakForce QNM atomic force microscopic (AFM) adhesion measurement is employed to investigate the glassy dynamics of polystyrene (PS) single-chain particles end-grafted to SiO2-Si substrates with different diameters, D0, of 3.4 nm-8.8 nm and molar masses, Mn, of 8-123 kg/mol. As temperature was increased, the adhesion force, Fad, experienced by the AFM tip on pulling off the single chains after loading demonstrated a stepwise increase at an elevated temperature, which we identified to be Tg based on previous works. Our result shows that Tg of our grafted single chains increases with Mn in a manner consistent with the Fox-Flory equation, but the coefficient quantifying the Mn dependence of Tg is only (36 ± 6)% the value of bulk PS. In addition, the value of Tg in the Mn → ∞ limit is about 25 °C below the bulk Tg but more than 15 °C above that of (untethered) PS nanoparticles with D0 ≈ 100 nm suspended in a solution. Our findings are consistent with Tg of our single chains being dominated by simultaneous effects of the interfaces, which depress Tg, and end-grafting, which enhances Tg. The latter is believed to exert its influence on the glass transition dynamics by a mechanism reliant on chain connectivity and does not vary with chain length.

Glassy Dynamics in an Intrinsically Disordered Protein

Intrinsically disordered proteins (IDPs) are characterized by their extreme conformational flexibility which gives them unique functional advantages, such as acting as entropic springs in the cytoskeleton. Here, we investigate the dynamic mechanical properties of a model IDP derived from neurofilament tail domains. We use a single-molecule manipulation technique, magnetic tweezers, to force the protein out of equilibrium and observe the relaxation of its end-to-end extension. We observe that the protein's extension decreases logarithmically for hours. We explain our results in terms of a phenomenological model, originally developed for bulk glassy systems, that assumes the total extension change is the sum of many independent structural transitions. Such a model makes sense for bulk measurements but is surprising to observe in a single molecule. Yet, the model accounts for our observation of a nonmonotonic (Kovacs) relaxation when subjecting the protein to a multi-step force protocol. This memory effect is an unambiguous signature that many independent and parallel structural transitions are contributing to the overall dynamic mechanical properties of the IDP. This is fundamentally different from previous examples of glassy behavior in folded proteins which rely on a heterogenous population of folded states. To our knowledge, this is the first reported example of this type of glassiness in proteins.

Fractons from confinement in one dimension

Recent work has shown that two seemingly different physical mechanisms, namely fracton behavior and confinement, can give rise to non-ergodicity in one-dimensional quantum many-body systems. In this work, we demonstrate an intrinsic link between these two mechanisms by studying the dynamics of one-dimensional confining theories, such as a U(1) gauge theory and a quantum Ising model. We show that, within certain parameter regimes, these models exhibit effective fracton dynamics, characterized by immobility of stable single-particle excitations and free motion of dipolar bound states. By perturbatively integrating out the linearly confining field, we obtain an effective fracton Hamiltonian for the confined charges which exhibits conservation of dipole moment. We discuss an intuitive understanding of these results in terms of the motion of the confining strings, leading to potential extensions to higher dimensions. We thereby interpret recent observations of nonthermal eigenstates and glassy dynamics in confining theories in terms of corresponding results in the fracton literature.

Attractive versus truncated repulsive supercooled liquids: The dynamics is encoded in the pair correlation function.

We compare glassy dynamics in two liquids that differ in the form of their interaction potentials. Both systems have the same repulsive interactions but one has also an attractive part in the potential. These two systems exhibit very different dynamics despite having nearly identical pair correlation functions. We demonstrate that a properly weighted integral of the pair correlation function, which amplifies the subtle differences between the two systems, correctly captures their dynamical differences. The weights are obtained from a standard machine learning algorithm.

Nanocapillary confinement of imidazolium based ionic liquids.

Room temperature ionic liquids are salts which are molten at or around room temperature without any added solvent or solution. In bulk they exhibit glass like dependence of conductivity with temperature as well as coupling of structural and transport properties. Interfaces of ionic liquids have been found to induce structural changes with evidence of long range structural ordering on solid-liquid interfaces spanning length scales of 10-100 nm. Our aim is to characterize the influence of confinement on the structural properties of ionic liquids. We present the first conductivity measurements on ionic liquids of the imidazolium type in single conical glass nanopores with confinements as low as tens of nanometers. We probe glassy dynamics of ionic liquids in a large range of temperatures (-20 to 70 °C) and nanopore opening sizes (20-600 nm) in silica glass nanocapillaries. Our results indicate no long range freezing effects due to confinement in nanopores with diameters as low as 20 nm. The studied ionic liquids are found to behave as glass like liquids across the whole accessible confinement size and temperature range.

A simple mean-field model of glassy dynamics and glass transition.

We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.

Glass forming liquids in a quenched random potential.

The response of a model two-dimensional colloidal glass former to an externally imposed spatially random potential, which acts as a quenched disorder, is investigated using numerical simulations, motivated by recent experiments and also mean field predictions. The external potential induces the onset of the glassy dynamics at increasingly smaller field roughness, with increasing packing fraction of the particulate assembly, and the existence of aging processes within the glassy regime is also observed. Furthermore, along the axis of increasing field roughness, the dynamical slowdown is not correlated to the hexatic order within the supercooled regime.

Observation of soft glassy behavior in a magnetic colloid exposed to an external magnetic field.

We provide the first experimental evidence for soft glassy behavior in a sterically stabilized magnetic colloid (ferrofluid) of relatively low volume fraction (φ = 0.037) when a uniform magnetic field is applied at a sufficiently high rate (fast quench). Fast magnetic-field quenches favor structural arrest of field-induced aggregates, owing to insufficient time to settle into lower energy states, thereby pushing the system to a frustrated metastable configuration like a repulsive glass. Brownian dynamics simulations are used to show that the polydisperse ferrofluid (as in experiments) forms thick ropes aligned along the field direction, while a monodisperse ferrofluid does not. The simulations show that there is practically no ordering of the thin, monodisperse chains, while the thick, polydisperse ropes show positional ordering with a typical center-center separation between the particles in different ropes of about 0.39μm. As a consequence of structural arrest, the ferrofluid exhibits aging with broken time-translational invariance, a hallmark of glassy dynamics. The superposition of strain and creep compliance curves obtained from rheological measurements at different waiting times in the effective time domain corroborates the soft glassy behavior when exposed to a magnetic field applied at a fast ramp rate.

Progress towards a phenomenological picture and theoretical understanding of glassy dynamics and vitrification near interfaces and under nanoconfinement.

The nature of alterations to dynamics and vitrification in the nanoscale vicinity of interfaces-commonly referred to as "nanoconfinement" effects on the glass transition-has been an open question for a quarter century. We first analyze experimental and simulation results over the last decade to construct an overall phenomenological picture. Key features include the following: after a metrology- and chemistry-dependent onset, near-interface relaxation times obey a fractional power law decoupling relation with bulk relaxation; relaxation times vary in a double-exponential manner with distance from the interface, with an intrinsic dynamical length scale appearing to saturate at low temperatures; the activation barrier and vitrification temperature Tg approach bulk behavior in a spatially exponential manner; and all these behaviors depend quantitatively on the nature of the interface. We demonstrate that the thickness dependence of film-averaged Tg for individual systems provides a poor basis for discrimination between different theories, and thus we assess their merits based on the above dynamical gradient properties. Entropy-based theories appear to exhibit significant inconsistencies with the phenomenology. Diverse free-volume-motivated theories vary in their agreement with observations, with approaches invoking cooperative motion exhibiting the most promise. The elastically cooperative nonlinear Langevin equation theory appears to capture the largest portion of the phenomenology, although important aspects remain to be addressed. A full theoretical understanding requires improved confrontation with simulations and experiments that probe spatially heterogeneous dynamics within the accessible 1-ps to 1-year time window, minimal use of adjustable parameters, and recognition of the rich quantitative dependence on chemistry and interface.

Glassy dynamics of a model of bacterial cytoplasm with metabolic activities

Recent experiments have revealed that cytoplasms become glassy when their metabolism is suppressed, while they maintain fluidity in a living state. The mechanism of this active fluidization is not clear, especially for bacterial cytoplasms, since they lack traditional motor proteins, which can cause directed motions. We introduce a model of bacterial cytoplasm focusing on the impact of conformational change in proteins due to metabolism. In the model, proteins are treated as particles under thermal agitation, and conformation changes are treated as changes in particle volume. Simulations revealed that a small change in volume fluidizes the glassy state, accompanied by a change in fragility, as observed experimentally.

A localization transition underlies the mode-coupling crossover of glasses

We study the equilibrium statistical properties of the potential energy landscape of several glass models in a temperature regime so far inaccessible to computer simulations. We show that unstable modes of the stationary points undergo a localization transition in real space close to the mode-coupling crossover temperature determined from the dynamics. The concentration of localized unstable modes found at low temperature is a non-universal, finite dimensional feature not captured by mean-field glass theory. Our analysis reconciles, and considerably expands, previous conflicting numerical results and provides a characteristic temperature for glassy dynamics that unambiguously locates the mode-coupling crossover.

Structural order as a genuine control parameter of dynamics in simple glass formers

Glass transition is characterised by drastic dynamical slowing down upon cooling, accompanied by growing spatial heterogeneity. Its rationalisation by subtle changes in the liquid structure has been long debated but remains elusive, due to intrinsic difficulty in detecting the underlying complex structural ordering. Here we report that structural order parameter characterising local packing capability can well describe the glassy dynamics not only macroscopically but also microscopically, no matter whether it is driven by temperature or density. A Vogel-Fulcher-Tammann (VFT)-like relation is universally identified between the structural relaxation time and the order parameter for supercooled liquids with isotropic interactions. More importantly, we find such an intriguing VFT-like relation to be statistically valid even at a particle level, between spatially coarse-grained structural order and microscopic particle-level dynamics. Such a unified description of glassy dynamics based solely on structural order is expected to contribute to the ultimate understanding of the long-standing glass-transition problem.

Tracer transport in attractive and repulsive supercooled liquids and glasses.

The transport of small penetrants through disordered materials with glassy dynamics is encountered in applications ranging from drug delivery to chemical separations. Nonetheless, understanding the influence of the matrix structure and fluctuations on penetrant motions remains a persistent challenge. Here, we use event-driven molecular dynamics to investigate the transport of small, hard-sphere tracers embedded in matrices of square-well particles. Short-range attractions between matrix particles give rise to reentrant dynamics in the supercooled regime, in which the liquid's relaxation time increases dramatically upon heating or cooling. Heating results in a "repulsive" supercooled liquid where relaxations are frustrated by steric interactions between particles, whereas cooling produces an "attractive" liquid in which relaxations are hindered by long-lived interparticle bonds. Further cooling or heating, or compression, of the supercooled liquids results in the formation of distinct glasses. Our study reveals that tracer transport in these supercooled liquids and glasses is influenced by the matrix structure and dynamics. The relative importance of each factor varies between matrices and is examined in detail by analyzing particle mean-square displacements, caging behavior, and trajectories sampled from the isoconfigurational ensemble. We identify features of tracer dynamics that reveal the spatial and temporal heterogeneity of the matrices and show that matrix arrest is insufficient to localize tracers.

Absence of finite temperature phase transitions in the X-Cube model and its [formula omitted] generalization

We investigate thermal properties of the X-Cube model and its Zp “clock-type” (pX-Cube) extension. In the latter, the elementary spin-1/2 operators of the X-Cube model are replaced by elements of the Weyl algebra. We study different boundary condition realizations of these models and analyze their finite temperature dynamics and thermodynamics. We find that (i) no finite temperature phase transitions occur in these systems. In tandem, employing bond-algebraic dualities, we show that for Glauber type solvable baths, (ii) thermal fluctuations might not enable system size dependent time autocorrelations at all positive temperatures (i.e., they are thermally fragile). Qualitatively, our results demonstrate that similar to Kitaev’s Toric code model, the X-Cube model (and its p-state clock-type descendants) may be mapped to simple classical Ising (p-state clock) chains in which neither phase transitions nor anomalously slow glassy dynamics might appear.