Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime

Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum

In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel-Fulcher-Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

Dynamic Heterogeneity at the Interface of an Intrinsically Disordered Peptide

It is believed that water around an intrinsically disordered protein or peptide (IDP) in an aqueous environment plays an important role in guiding its conformational properties and aggregation behavior. However, despite its importance, only a handful of studies exploring the correlation between the conformational motions of an IDP and the microscopic properties of water at its surface are reported. Attempts have been made in this work to study the dynamic properties of water present in the vicinity of α-synuclein, an IDP associated with Parkinson's disease (PD). Room temperature molecular dynamics (MD) simulations of eight α-synuclein_1-95 peptides with a wide range of initial conformations have been carried out in aqueous media. The calculations revealed that due to solid-like caging motions, the translational and rotational mobility of water molecules near the surfaces of the peptide repeat unit segments R1 to R7 are significantly restricted. A small degree of dynamic heterogeneity in the hydration environment around the repeat units has been observed with water near the hydrophobic R6 unit exhibiting relatively more restricted diffusivity. The time scales involving the overall structural relaxations of peptide-water and water-water hydrogen bonds near the peptide have been found to be correlated with the time scale of diffusion of the interfacial water molecules. We believe that the relatively more hindered dynamic environment near R6 can help create water-mediated contacts centered around R6 between peptide monomers at a higher concentration, thereby enhancing the early stages of peptide aggregation.

Construction of a quantitative relation between structural relaxation and dynamic heterogeneity by vibrational dynamics in glass-forming liquids and polymers

The structural relaxation slows down drastically upon approaching the glass transition, accompanied by the significant growth of dynamic heterogeneity. The fundamental question of elusiveness and interest is whether there exists an underlying quantitative relationship between structural relaxation and dynamic heterogeneity. Here, we reveal that b̃ which is related to the reduced mean square displacements to overcome the energy barriers of activated jumps, instead of the kinetic fragility m, is the genuine key parameter connecting dynamic heterogeneity with structural relaxation for varying types of glass formers. Furthermore, based on the dependence of dynamic heterogeneity on the Debye-Waller factor we obtained a direct quantitative relation between dynamic heterogeneity and structural relaxation is built for different glass-forming liquids. More importantly, a scaling collapse of structural relaxation and dynamic heterogeneity is achieved by the important parameter b̃. These results are of fundamental and critical importance for developing a unified theory of glassy dynamics.

Breakdown of the Stokes-Einstein relation in supercooled water: the jump-diffusion perspective

Although water is the most ubiquitous liquid it shows many thermodynamic and dynamic anomalies. Some of the anomalies further intensify in the supercooled regime. While many experimental and theoretical studies have focused on the thermodynamic anomalies of supercooled water, fewer studies explored the dynamical anomalies very extensively. This is due to the intricacy of the experimental measurement of the dynamical properties of supercooled water. Violation of the Stokes-Einstein relation (SER), an important relation connecting the diffusion of particles with the viscosity of the medium, is one of the major dynamical anomalies. In absence of experimentally measured viscosity, researchers used to check the validity of SER indirectly using average translational relaxation time or α-relaxation time. Very recently, the viscosity of supercooled water was accurately measured at a wide range of temperatures and pressures. This allowed direct verification of the SER at different temperature-pressure thermodynamic state points. An increasing breakdown of the SER was observed with decreasing temperature. Increasing pressure reduces the extent of breakdown. Although some well-known theories explained the above breakdown, a detailed molecular mechanism was still elusive. Recently, a translational jump-diffusion (TJD) approach has been able to quantitatively explain the breakdown of the SER in pure supercooled water and an aqueous solution of methanol. The objective of this article is to present a detailed and state-of-the-art analysis of the past and present works on the breakdown of SER in supercooled water with a specific focus on the new TJD approach for explaining the breakdown of the SER.

Nonlinear measurements of kinetics and generalized dynamical modes. I. Extracting the one-dimensional Green's function from a time series

Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion. Here, these ideas are generalized to other observables. A set of correlation functions of nonlinear functions of an observable is used to extract the corresponding Green's function. Although this paper focuses on nonlinear correlation functions of an equilibrium time series, the results are directly connected to other types of nonlinear kinetics, including perturbation-response experiments with strong fields. Generalized modes are defined as the orthogonal polynomials associated with the equilibrium distribution. A matrix of mode-correlation functions can be transformed to the complete, single-time-interval (1D) Green's function. Diagonalizing this matrix finds the eigendecays. To understand the advantages and limitation of this approach, Green's functions are calculated for a number of models of complex dynamics within a Gaussian probability distribution. Examples of non-diffusive motion, rate heterogeneity, and range heterogeneity are examined. General arguments are made that a full set of nonlinear 1D measurements is necessary to extract all the information available in a time series. However, when a process is neither dynamically Gaussian nor Markovian, they are not sufficient. In those cases, additional multidimensional measurements are needed.

Temperature Induced Dynamical Transition of Biomolecules in Polarizable and Nonpolarizable TIP3P Water

Temperature induced dynamical transition (DT), associated with a sharp rise in molecular flexibility, is well-known to be exhibited between 270 and 280 K in glycerol to 200-230 K in hydrated biomolecules and is controlled by diffusivity (viscosity) of the solvation layer. In the molecular dynamics (MD) community, especially for water as a solvent, this has been an intense area of research despite decades of investigations. However, in general, water in these studies is described by empirical nonpolarizable force fields in which electronic polarizability is treated implicitly with effective charges and related parameters. This might have led to the present trait of discovery that DTs of biomolecules, irrespective of the potential functions for water models used, occur within a narrow band of temperature variation (30-40 K). Whereas a water molecule in a biomolecular surface and one in bulk are polarized differently, therefore explicit treatment of water polarizability would be a powerful approach toward the treatment of hydration water, believed to cause the DT manifestation. Using MD simulations, we investigated the effects of polarizable water on the DT of biomolecules and the dynamic properties of hydration water. We chose two types of solutes: globular protein (lysozyme) and more open and flexible RNAs (a hairpin and a riboswitch) with different natures of hydrophilic sites than proteins in general. We found that the characteristic temperature of DT ( T_DT) for the solutes in polarizable water is always higher than that in its nonpolarizable counterpart. In particular, for RNAs, the variations are found to be ∼45 K between the two water models, whereas for the more compact lysozyme, it is only ∼4 K. The results are discussed in light of the enormous increase in relaxation times of a liquid upon cooling in the paradigm of dynamic switchover in hydration water with liquid-liquid phase transition, derived from the existence of the second critical point. Our result supports the idea that structures of biomolecules and their interactions with the hydration water determines T_DT and provides evidence for the decisive role of polarizable water on the onset of DT, which has been hitherto ignored.

Single molecule studies reveal temperature independence of lifetime of dynamic heterogeneity in polystyrene

Polymeric systems close to their glass transition temperature are known to exhibit heterogeneous dynamics that evolve both over time and space, comparable to the dynamics of small molecule glass formers. It remains unclear how temperature influences the degree of heterogeneous dynamics in such systems. In the following report, a fluorescent perylene dicarboximide probe molecule that reflects the full breadth of heterogeneity of the host was used to examine the temperature dependence of the dynamic heterogeneity lifetime in polystyrene at several temperatures ranging from the glass transition to 10 K above this temperature via single molecule microscopy. Contrary to prior reports, no apparent temperature dependence of time scales associated with dynamic heterogeneity was detected; indeed, the probe molecules report characteristic dynamic heterogeneity lifetimes 100-300 times the average alpha-relaxation time (τ_α) of the polystyrene host at all temperatures studied.

Broken detailed balance at mesoscopic scales in active biological systems

Systems in thermodynamic equilibrium are not only characterized by time-independent macroscopic properties, but also satisfy the principle of detailed balance in the transitions between microscopic configurations. Living systems function out of equilibrium and are characterized by directed fluxes through chemical states, which violate detailed balance at the molecular scale. Here we introduce a method to probe for broken detailed balance and demonstrate how such nonequilibrium dynamics are manifest at the mesosopic scale. The periodic beating of an isolated flagellum from Chlamydomonas reinhardtii exhibits probability flux in the phase space of shapes. With a model, we show how the breaking of detailed balance can also be quantified in stationary, nonequilibrium stochastic systems in the absence of periodic motion. We further demonstrate such broken detailed balance in the nonperiodic fluctuations of primary cilia of epithelial cells. Our analysis provides a general tool to identify nonequilibrium dynamics in cells and tissues.

Universal rescaling of flow curves for yield-stress fluids close to jamming

The experimental flow curves of four different yield-stress fluids with different interparticle interactions are studied near the jamming concentration. By appropriate scaling with the distance to jamming all rheology data can be collapsed onto master curves below and above jamming that meet in the shear-thinning regime and satisfy the Herschel-Bulkley and Cross equations, respectively. In spite of differing interactions in the different systems, master curves characterized by universal scaling exponents are found for the four systems. A two-state microscopic theory of heterogeneous dynamics is presented to rationalize the observed transition from Herschel-Bulkley to Cross behavior and to connect the rheological exponents to microscopic exponents for the divergence of the length and time scales of the heterogeneous dynamics. The experimental data and the microscopic theory are compared with much of the available literature data for yield-stress systems.

Time scale of dynamic heterogeneity in model ionic liquids and its relation to static length scale and charge distribution

We find a general power-law behavior: , where ζ_dh ≈ 1.2 for all the ionic liquid models, regardless of charges and the length scale of structural relaxation.

Simple picture of supercooled liquid dynamics: dynamic scaling and phenomenology based on clusters

Although it is now well established that in glassy liquids, slow structural relaxation accompanies a correlated structural rearrangement, the role of such a correlation in the transport anomaly, and thus in the slow dynamics, remains unclear. In this paper, we argue from a hydrodynamic viewpoint that a correlated structure (cluster) with a characteristic size ξ sustains the long-lived stress and dynamically couples with the hydrodynamic fluctuations; therefore, the dynamics of this cluster is the origin of the mesoscopic nature of anomalous hydrodynamic transport. Based on this argument, we derive a dynamic scaling law for τ(α) (or η, where η is the macroscopic shear viscosity) as a function of ξ: τ(α)([proportionality]η)[proportionality]ξ(4). We provide a simple explanation for basic features of anomalous transport, such as the breakdown of the Stokes-Einstein relation and the length-scale-dependent decoupling between viscosity and diffusion. The present study further suggests a different physical picture: Through the coarse graining of smaller-scale fluctuations (</~ξ), the supercooled liquid dynamics can be regarded as the dynamics of normal (cluster) liquids composed of units with a typical size of ξ. Although the correlation length of hydrodynamic transport ξ and the dynamic heterogeneity size ξ(DH), which is determined by the usual four-point correlation function, reflect some aspects of the cooperative effects, the correspondence between ξ and ξ(DH) is not one to one. We highlight the possibility that ξ(DH) overestimates the actual collective transport range at a low degree of supercooling.

Multidimensional Measures of Response and Fluctuations in Stochastic Dynamical Systems

A new class of experiments is proposed which involve multiple measurements combined with multiple perturbations of a nonlinear classical complex system. A family of multipoint n + m - 1 dimensional measures R^(n,m) that provide complimentary information on complex systems is obtained by combining m non linear stimuli and n measurements. They represent the combined effect of causal response and noncausal spontaneous fluctuations. The proposed signals can be measured either in the frequency domain or in the time domain. Generalized fluctuation-dissipation relations which hold in the nonlinear regime restrict the number of independent techniques. Two dimensional correlation plots derived from such measurements can reveal various types of couplings among collective modes.

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

Thermodynamic study of simple molecular glasses: universal features in their heat capacity and the size of the cooperatively rearranging regions

We have obtained some universal thermodynamic properties on glass transitions of molecular liquids. The heat capacity C(p) of glassy propene, which was vitrified by using a vapor-deposition technique, was measured with a newly developed adiabatic calorimeter. Propene has the lowest glass transition temperature (T(g)=56 K), the largest C(p) jump at T(g) (C(p)(lq)/C(p)(gl)~2.5), and the lowest residual entropy (S(res)~Rln2) compared with glass-forming molecules measured before. We have analyzed the present data with other hydrocarbon molecules vitrified by liquid quenching and obtained the following results: (1) The excess heat capacities are scaled well by using a Kauzmann temperature T(K), (2) The size of the cooperative rearrangement region (CRR) frozen at T(g) increases with decreasing the temperature difference between T(g) and T(K) (Kauzmann temperature), and (3) The simpler the molecule is, the larger the frozen CRR becomes. These are all supporting the validity of the Adam-Gibbs theory.

Dynamical heterogeneity in a highly supercooled liquid: consistent calculations of correlation length, intensity, and lifetime

We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length ξ(4), intensity χ(4), and lifetime τ(hetero). We evaluated all three quantities consistently from a single order parameter. In a previous study [H. Mizuno and R. Yamamoto, Phys. Rev. E 82, 030501(R) (2010)], we examined the lifetime τ(hetero)(t) in two time intervals t = τ(α) and τ(ngp), where τ(α) is the α-relaxation time and τ(ngp) is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime τ(hetero)(t), we evaluated the correlation length ξ(4)(t) and the intensity χ({4)(t) from the same order parameter used for the lifetime τ(hetero)(t). We found that as the temperature decreases, the lifetime τ(hetero)(t) grows dramatically, whereas the correlation length ξ(4)(t) and the intensity χ(4)(t) increase slowly compared to τ(hetero)(t) or plateaus. Furthermore, we investigated the lifetime τ(hetero)(t) in more detail. We examined the time-interval dependence of the lifetime τ(hetero)(t) and found that as the time interval t increases, τ(hetero)(t) monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which τ(hetero)(t) plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.

Three-dimensional infrared spectroscopy of isotope-substituted liquid water reveals heterogeneous dynamics

The dynamics of the hydrogen bond network of isotopically substituted liquid water are investigated with a new ultrafast nonlinear vibrational spectroscopy, three-dimensional infrared spectroscopy (3D-IR). The 3D-IR spectroscopy is sensitive to three-point frequency fluctuation correlation functions, and the measurements reveal heterogeneous structural relaxation dynamics. We interpret these results as subensembles of water which do not interconvert on a half picosecond time scale. We connect the experimental results to molecular dynamics (MD) simulations, performing a line shape analysis as well as complex network analysis.

Lifetime of dynamical heterogeneity in a highly supercooled liquid

We numerically examine dynamical heterogeneity in a highly supercooled three-dimensional liquid via molecular-dynamics simulations. To define the local dynamics, we consider two time intervals: τ(α) and τ(ngp). τ(α) is the α relaxation time, and τ(ngp) is the time at which non-gaussian parameter of the Van Hove self-correlation function is maximized. We determine the lifetimes of the heterogeneous dynamics in these two different time intervals, τ(hetero)(τ(α)) and τ(hetero)(τ(ngp)), by calculating the time correlation function of the particle dynamics, i.e., the four-point correlation function. We find that the difference between τ(hetero)(τ(α)) and τ(hetero)(τ(ngp)) increases with decreasing temperature. At low temperatures, τ(hetero)(τ(α)) is considerably larger than τ(α), while τ(hetero)(τ(ngp)) remains comparable to τ(α). Thus, the lifetime of the heterogeneous dynamics depends strongly on the time interval.