Dynamic Length Scale Research Articles

Block Analysis for the Calculation of Dynamic and Static Length Scales in Glass-Forming Liquids

We present block analysis, an efficient method of performing finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves considering blocks of varying sizes embedded in a system of a fixed (large) size. The length scale associated with dynamic heterogeneity is obtained from a finite-size scaling analysis of the dependence of the four-point dynamic susceptibility on the block size. The block size dependence of the variance of the α relaxation time yields the static point-to-set length scale. The values of the obtained length scales agree quantitatively with those obtained from other conventional methods. This method provides an efficient experimental tool for studying the growth of length scales in systems such as colloidal glasses for which performing finite-size scaling by carrying out experiments for varying system sizes may not be feasible.

Glassy swirls of active dumbbells.

Is an active glass different from a conventional passive glass? To address this, we study the dynamics of a dense binary mixture of soft dumbbells, each subject to an active propulsion force and thermal fluctuations. This dense assembly shows dynamical arrest, first to a translational and then to a rotational glass, as one reduces temperature T or the self-propulsion force f. We monitor the dynamics along an iso-relaxation-time contour in the (T-f) plane. We find dramatic differences both in the fragility and in the nature of dynamical heterogeneity, which characterize the onset of glass formation-the activity-induced glass exhibits large swirls or vortices, whose scale is set by activity, and it appears to diverge as one approaches the glass transition. This large collective swirling movement should have implications for collective cell migration in epithelial layers. We construct continuum hydrodynamic equations for the simulated system, and we show that the observed behavior of this growing dynamic length scale can be understood from these equations.

Point-to-set dynamic length scale in binary Lennard-Jones glass-formers.

Our recent molecular dynamics simulation results of binary particle glass-former systems demonstrated that the non-monotonic temperature T-dependence of the point-to-set dynamic length scale ξcdyn in harmonic (HM) systems is not an intrinsic property of bulk liquids but originates from wall effects. We would expect our results to apply equally to other simple models, such as Lennard-Jones (LJ) systems. However, Hocky et al. presented a monotonic T-dependent ξcdyn in a LJ system. Therefore, the present work employs molecular dynamics simulations to investigate the T-dependent behavior of ξcdyn in the LJ system employed by Hocky et al. to clarify our expectation. Results employing a geometry size d that is somewhat smaller than that employed by Hocky et al. reveal that a non-monotonic behavior exists in the LJ system. By varying the value of d, we demonstrate that the formation of a peak in ξcdyn with respect to T in the LJ system is the natural result of wall effects. More importantly, a new non-monotonic behavior is observed, where the temperature at which the ratio of the characteristic time required for the overlap profile of the system to decay to a given value for a point near the wall to the corresponding characteristic time at a point in the center attains a maximum is in good agreement with the temperature Tmax-c at which ξcdyn attains a maximum value, indicating that the non-monotonic behavior of ξcdyn with respect to T is a natural property of liquids in a sandwiched geometry. Furthermore, we find that, contrary to HM systems, where the values of Tmax-c obtained for all values of d considered were greater than the mode-coupling temperature Tc, the value of Tmax-c obtained for LJ systems can be either greater than, equal to, or less than Tc because an HM system has a stronger finite-size effect than that in a LJ system, indirectly implying that the conclusion derived from random first-order transition theory that a dramatic change occurs near Tc bears no necessary relationship with the non-monotonic evolution of ξcdyn with respect to T.

Viscosity of a sheared correlated (near-critical) model fluid in confinement

Second-order phase transitions are characterized by a divergence of the spatial correlation length of the order parameter fluctuations. For confined systems, this is known to lead to remarkable equilibrium physical phenomena, including finite-size effects and critical Casimir forces. We explore here some non-equilibrium aspects of these effects in the stationary state resulting from the action of external forces: by analyzing a model of a correlated fluid under shear, spatially confined by two parallel plates, we study the resulting viscosity within the setting of (Gaussian) Landau–Ginzburg theory. Specifically, we introduce a model in which the hydrodynamic velocity field (obeying the Stokes equation) is coupled to an order parameter with dissipative dynamics. The well-known Green–Kubo relation for bulk systems is generalized for confined systems. This is shown to result in a non-local Stokes equation for the fluid flow, due to the correlated fluctuations. The resulting effective shear viscosity shows universal as well as non-universal contributions, which we study in detail. In particular, the deviation from the bulk behavior is universal, depending on the ratio of the correlation length and the film thickness L. In addition, at the critical point the viscosity is proportional to , where is a dynamic length scale. These findings are expected to be experimentally observable, especially for systems where the bulk viscosity is affected by critical fluctuations.

On the Definition of Marginal Ice Zone Width

AbstractSea ice features a dense inner pack ice zone surrounded by a marginal ice zone (MIZ) in which the sea ice properties are modified by interaction with the ice-free open ocean. The width of the MIZ is a fundamental length scale for polar physical and biological dynamics. Several different criteria for establishing MIZ boundaries have emerged in the literature—wave penetration, floe size, sea ice concentration, etc.—and a variety of definitions for the width between the MIZ boundaries have been published. Here, three desirable mathematical properties for defining MIZ width are proposed: invariance with respect to translation and rotation on the sphere; uniqueness at every point in the MIZ; and generality, including nonconvex shapes. The previously published streamline definition is shown to satisfy all three properties, where width is defined as the arc length of a streamline through the solution to Laplaces’s equation within the MIZ boundaries, while other published definitions each satisfy only one of the desired properties. When defining MIZ spatial average width from streamline results, the rationale for averaging with respect to distance along both MIZ boundaries was left implicit in prior studies. Here it is made rigorous by developing and applying the mathematics of an analytically tractable idealization of MIZ geometry—the eccentric annulus. Finally, satellite-retrieved Arctic sea ice concentrations are used to investigate how well streamline-based MIZ spatial average width is approximated by alternative definitions that lack desirable mathematical properties or local width values but offer computational efficiency.

From Glass Formation to Icosahedral Ordering by Curving Three-Dimensional Space.

Geometric frustration describes the inability of a local molecular arrangement, such as icosahedra found in metallic glasses and in model atomic glass formers, to tile space. Local icosahedral order, however, is strongly frustrated in Euclidean space, which obscures any causal relationship with the observed dynamical slowdown. Here we relieve frustration in a model glass-forming liquid by curving three-dimensional space onto the surface of a 4-dimensional hypersphere. For sufficient curvature, frustration vanishes and the liquid "freezes" in a fully icosahedral structure via a sharp "transition." Frustration increases upon reducing the curvature, and the transition to the icosahedral state smoothens while glassy dynamics emerge. Decreasing the curvature leads to decoupling between dynamical and structural length scales and the decrease of kinetic fragility. This sheds light on the observed glass-forming behavior in Euclidean space.

Nonmonotonic dynamic correlations in quasi-two-dimensional confined glass-forming liquids.

It has been broadly accepted that the behavior of glass-forming liquids, where their relaxation dynamics exhibit a pronounced slowdown as they are cooled toward the glass transition temperature, is caused by the increase in one or more correlation lengths. However, the role of length scales in the dynamics of glass-forming liquids is not clearly established, and past simulation work that suggests a surprising nonmonotonic temperature evolution of spatial dynamical correlations near the mode-coupling crossover temperature has been both questioned and supported by subsequent work. Here, using molecular dynamics simulation, we also show a striking maximum in the dynamic length scale ξ_{c}^{dyn} at a given temperature, but the temperature of this maximum is found to shift as the size of the confined system increases. Furthermore, we find that such a maximum disappears for all geometry sizes considered when a rough wall is replaced with a smooth, hard wall, suggesting that the nature of the nonmonotonic temperature dependence of ξ_{c}^{dyn} does not reflect an intrinsic property of bulk liquids, but originates from wall effects. Our results provide new insights into the dynamics of glass-forming liquids, particularly for quasi-two-dimensional systems.

Make dark matter charged again

We revisit constraints on dark matter that is charged under a U(1) gauge group in the dark sector, decoupled from Standard Model forces. We find that the strongest constraints in the literature are subject to a number of mitigating factors. For instance, the naive dark matter thermalization timescale in halos is corrected by saturation effects that slow down isotropization for modest ellipticities. The weakened bounds uncover interesting parameter space, making models with weak-scale charged dark matter viable, even with electromagnetic strength interaction. This also leads to the intriguing possibility that dark matter self-interactions within small dwarf galaxies are extremely large, a relatively unexplored regime in current simulations. Such strong interactions suppress heat transfer over scales larger than the dark matter mean free path, inducing a dynamical cutoff length scale above which the system appears to have only feeble interactions. These effects must be taken into account to assess the viability of darkly-charged dark matter. Future analyses and measurements should probe a promising region of parameter space for this model.

Experimental Investigation of Cavitation Behind a Circular Cylinder in Cross-Flow

Cavitation behind a circular cylinder is studied with the aid of highly time-resolved images at a constant Reynolds number of 64,000. Apart from recording the overall cavitation activity behind the cylinder, the study also delves into the dynamics of individual cavities. The length of cavity scales with cavitation number and this scaling is similar to the existing results obtained in flow regimes different from that presented here. Dynamics of individual cavities show distinct phases of cavity formation, growth, and collapse. At lower cavitation numbers, cavity collapse was followed by a rebounce. Variation of area normalized by the length of cavity shows self similarity in the growth phase of cavities for different cavitation numbers. Thus, the cavity length is the suitable length scale for dynamics of cavities, at least for the growth phase. The cavity lifetime scales inversely with the square of cavitation number. Dynamics of individual small cavity captured at higher frame rates was found to be similar to that of an isolated bubble. In this case, a rapid collapse follow a more gradual expansion phase, unlike that shown by larger cavities.

Structure and dynamics of a silica melt in neutral confinement.

We analyze the effects of spatial confinement on viscous silica using molecular dynamics simulations. For this purpose, we prepare a silica melt in a cylindrical pore, which is produced by pinning appropriate fractions of silicon and oxygen atoms in a bulk system after an equilibration period. In this way, the structure of the confined silica melt remains unaffected, while the confinement has a strong impact on the dynamics. We find that the structural relaxation of viscous silica is slowed down according to a double exponential law when approaching the pore wall. Moreover, we observe that static density correlations exist in the vicinity of the pore wall. Based on these effects, we determine dynamical and structural length scales of the silica melt. Both length scales show a similar increase upon cooling, with values on the order of the next-neighbor distances in the studied temperature range. Interestingly, we find no evidence that the growth of the length scales is affected by a fragile-to-strong transition of the silica melt. This observation casts serious doubts on the relevance of these length scales for the structural relaxation, at least for the studied glass former.

Interfacial Properties of Polymer Nanocomposites: Role of Chain Rigidity and Dynamic Heterogeneity Length Scale

While it is known that the properties of polymer nanocomposites are largely dominated by the interfacial layer around nanoparticles, the molecular parameters controlling the interfacial layer structure and dynamics remain unknown. In this work we combine small-angle X-ray scattering, differential scanning calorimetry, and broadband dielectric spectroscopy to analyze the dependence of the interfacial layer thickness, lint, on polymer rigidity defined through the characteristic ratio, C∞. This analysis revealed a value of C∞ ∼ 5–7, beyond which lint increases substantially with C∞. Moreover, lint grows upon approaching the glass transition temperature from above, and the rate of this growth seems to correlate with polymer fragility. Most important, our analysis revealed that lint is comparable to the characteristic length scale of dynamic heterogeneities in the studied materials. These results provide new understandings of molecular parameters controlling the interfacial layer and are important not only for the field of polymer nanocomposites but also for the fields of thin polymer films and dynamics of soft matter in general.

Locally favoured structures and dynamic length scales in a simple glass-former

We investigate the static and dynamic properties of a weakly polydisperse hard sphere system in the deeply supercooled state, i.e. at densities higher than that corresponding to the mode-coupling transition. The structural analysis reveals the emergence of icosahedral locally favoured structures, previously only found in trace quantities. We present a new approach to probe the shape of dynamically heterogeneous regions, which is insensitive to particle packing effects that can hamper such analysis. Our results indicate that the shape of the dynamically heterogeneous regions changes only weakly and moreover hint that the often-used four-point correlation length may exhibit a growth in excess of that which our method identifies. The growth of the size of the dynamically heterogeneous regions appears instead to be in line with the one of structural and dynamic propensity correlations.

Waves in Slowly Varying Band-Gap Media

This paper is concerned with waves in locally periodic media, in the high-frequency limit where the wavelength is commensurate with the period. A key issue is that the Bloch-dispersion curves vary with the local microstructure, giving rise to hidden singularities associated with band-gap edges and branch crossings. We suggest an asymptotic approach for overcoming this difficulty, which we develop in detail in the case of time-harmonic waves in one dimension. The method entails matching adiabatically propagating Bloch waves, captured by a two-variable Wentzel--Kramers--Brillouin (WKB) approximation, with complementary multiple-scale solutions spatially localized about dispersion singularities. The latter solutions, obtained following the method of high-frequency homogenization (HFH), hold over dynamic length scales intermediate between the periodicity (wavelength) and the macro-scale. In particular, close to a spatial band-gap edge the solution is an Airy function modulated on the short scale by a standing...

Linking dynamical heterogeneity to static amorphous order

Glass-forming liquids grow dramatically sluggish upon cooling. This slowdown has long been thought to be accompanied by a growing correlation length. Characteristic dynamical and static length scales, however, have been observed to grow at different rates, which perplexes the relationship between the two and with the slowdown. Here, we show the existence of a direct link between dynamical sluggishness and static point-to-set correlations, holding at the local level as we probe different environments within a liquid. This link, which is stronger and more general than that observed with locally preferred structures, suggests the existence of an intimate relationship between structure and dynamics in a broader range of glass-forming liquids than previously thought.

The melting of stable glasses is governed by nucleation-and-growth dynamics.

We discuss the microscopic mechanisms by which low-temperature amorphous states, such as ultrastable glasses, transform into equilibrium fluids, after a sudden temperature increase. Experiments suggest that this process is similar to the melting of crystals, thus differing from the behaviour found in ordinary glasses. We rationalize these observations using the physical idea that the transformation process takes place close to a "hidden" equilibrium first-order phase transition, which is observed in systems of coupled replicas. We illustrate our views using simulation results for a simple two-dimensional plaquette spin model, which is known to exhibit a range of glassy behaviour. Our results suggest that nucleation-and-growth dynamics, as found near ordinary first-order transitions, is also the correct theoretical framework to analyse the melting of ultrastable glasses. Our approach provides a unified understanding of multiple experimental observations, such as propagating melting fronts, large kinetic stability ratios, and "giant" dynamic length scales. We also provide a comprehensive discussion of available theoretical pictures proposed in the context of ultrastable glass melting.

Glasslike behavior of a hard-disk fluid confined to a narrow channel.

Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks that sets in at characteristic packing fraction ϕ(d). Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event-driven molecular dynamics simulations and the time-dependent dynamical length scale has been extracted from them. The dynamical length scale increases with time and, on the equilibration time scale, it is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above ϕ(d). The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer-matrix approach.

Characteristic length scales of the secondary relaxations in glass-forming glycerol.

We investigate the secondary relaxations and their link to the main structural relaxation in glass-forming liquids using glycerol as a model system. We analyze the incoherent neutron scattering signal dependence on the scattering momentum transfer, Q , in order to obtain the characteristic length scale for different secondary relaxations. Such a capability of neutron scattering makes it somewhat unique and highly complementary to the traditional techniques of glass physics, such as light scattering and broadband dielectric spectroscopy, which provide information on the time scale, but not the length scales, of relaxation processes. The choice of suitable neutron scattering techniques depends on the time scale of the relaxation of interest. We use neutron backscattering to identify the characteristic length scale of 0.7 Å for the faster secondary relaxation described in the framework of the mode-coupling theory (MCT). Neutron spin-echo is employed to probe the slower secondary relaxation of the excess wing type at a low temperature ( ∼ 1.13T g . The characteristic length scale for this excess wing dynamics is approximately 4.7 Å. Besides the Q -dependence, the direct coupling of neutron scattering signal to density fluctuation makes this technique indispensable for measuring the length scale of the microscopic relaxation dynamics.

Dynamic Heterogeneity and Cooperative Length Scale at Dynamic Glass Transition in Glass Forming Liquids

Understanding the evolution of the cooperative molecular mobility as a function of time and temperature remains an unsolved question in condensed matter research. However, recently great advances have been made within the framework of the Adam–Gibbs theory on the connection between cooperatively rearranging regions, or dynamic heterogeneities, i.e., domains of the supercooled liquid whose relaxation is highly correlated. The growth of the size of these dynamic domains is now believed to be the driving mechanism for different experimental parameters like relaxation times and viscosity of supercooled liquid approaching the glass transition. Recent studies have shown the evolution of cooperative motions in supercooled liquids using different experimental tools and models. In this work, broadband dielectric spectroscopy and modulated temperature differential scanning calorimetry were carried out on six different amorphous glass-forming systems in order to scan a wide range of relaxation times and temperatures...

Correlation between fragility and cooperativity in segmental dynamics of glass-forming para-substituted polystyrenes

To understand the mechanism of the viscous slowdown in supercooled liquids that is responsible for glass transition, we investigate the interrelation between glass transition temperature Tg, fragility and cooperativity in segmental dynamics. Polymeric glass formers having a similar chemical structure are expected to exhibit clear correlations between the above parameters. In this paper, polystyrene (PS) derivatives possessing various para-substituents are studied using calorimetry with regard to the fragility parameter m, dynamic length scale ξ and the number of cooperatively rearranging segments NCRR at Tg. Positive correlations were revealed for both NCRR(Tg) vs m and ξ3(Tg) vs m. Both fragility and cooperativity were found to increase as the bulkiness of the substituent increases. Wide-angle X-ray scattering measurements revealed that the structural correlation between backbone chains is reduced as the bulkiness increases. This may be responsible for the reduced cooperativity. In contrast, for poly(methacrylic acid ester)s, the relations between the above parameters appeared to be less clear. The clear trend observed for the PS system may be due to the rigidity of the phenylene unit, through which the substituent directly affects the backbone dynamics. The estimated activation energy per segment increased consistently with an increase in the para-substituent’s bulkiness. The relations between glass transition temperature, fragility and cooperativity in segmental dynamics were investigated on polystyrene derivatives possessing various para-substituents using calorimetry. A positive correlation was observed between cooperativity and fragility. Both fragility and cooperativity were found to increase as the bulkiness of the substituent increases. Estimated activation energy per segment increased consistently with an increase in the substituent’s bulkiness.

Dynamic heterogeneity in crossover spin facilitated model of supercooled liquid and fractional Stokes-Einstein relation.

Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.