Slow dynamics of a confined supercooled binary mixture: direct space analysis

Glassy dynamics of water in TIP4P/Ice aqueous solutions of trehalose in comparison with the bulk phase

We perform molecular dynamics simulations of TIP4P/Ice water in solution with trehalose for 3.65 and 18.57 wt. % concentrations and of bulk TIP4P/Ice water at ambient pressure, to characterize the structure and dynamics of water in a sugar aqueous solution in the supercooled region. We find here that TIP4P/Ice water in solution with trehalose molecules follows the Mode Coupling Theory and undergoes a fragile to strong transition up to the highest concentration investigated, similar to the bulk. Moreover, we perform a Mode Coupling Theory test, showing that the Time Temperature Superposition principle holds for both bulk TIP4P/Ice water and for TIP4P/Ice water in the solutions and we calculate the exponents of the theory. The direct comparison of the dynamical results for bulk water and water in the solutions shows upon cooling along the isobar a fastening of water dynamics for lower temperatures, T < 240 K. We found that the counter-intuitive behavior for the low temperature solutions can be explained with the diffusion anomaly of water leading us to the conclusion that the fastening observed below T = 240 K in water dynamics is only fictitious, due to the fact that the density of water molecules in the solutions is higher than the density of the bulk at the same temperature and pressure. This result should be taken into account in experimental investigations which are often carried out at constant pressure.

Deformable hard particles confined in a disordered porous matrix

With suitably designed Monte Carlo simulations, we have investigated the properties of mobile, impenetrable, yet deformable particles that are immersed into a porous matrix, the latter one realized by a frozen configuration of spherical particles. By virtue of a model put forward by Batista and Miller [Phys. Rev. Lett. 105, 088305 (2010)], the fluid particles can change in their surroundings, formed by other fluid particles or the matrix particles, their shape within the class of ellipsoids of revolution; such a change in shape is related to a change in energy, which is fed into suitably defined selection rules in the deformation "moves" of the Monte Carlo simulations. This concept represents a simple yet powerful model of realistic, deformable molecules with complex internal structures (such as dendrimers or polymers). For the evaluation of the properties of the system, we have used the well-known quenched-annealed protocol (with its characteristic double average prescription) and have analyzed the simulation data in terms of static properties (the radial distribution function and aspect ratio distribution of the ellipsoids) and dynamic features (notably the mean squared displacement). Our data provide evidence that the degree of deformability of the fluid particles has a distinct impact on the aforementioned properties of the system.

Protein-Water and Water-Water Long-Time Relaxations in Protein Hydration Water upon Cooling-A Close Look through Density Correlation Functions

We report results on the translational dynamics of the hydration water of the lysozyme protein upon cooling obtained by means of molecular dynamics simulations. The self van Hove functions and the mean square displacements of hydration water show two different temperature activated relaxation mechanisms, determining two dynamic regimes where transient trapping of the molecules is followed by hopping phenomena to allow to the structural relaxations. The two caging and hopping regimes are different in their nature. The low-temperature hopping regime has a time scale of tenths of nanoseconds and a length scale on the order of 2–3 water shells. This is connected to the nearest-neighbours cage effect and restricted to the supercooling, it is absent at high temperature and it is the mechanism to escape from the cage also present in bulk water. The second hopping regime is active at high temperatures, on the nanoseconds time scale and over distances of nanometers. This regime is connected to water displacements driven by the protein motion and it is observed very clearly at high temperatures and for temperatures higher than the protein dynamical transition. Below this temperature, the suppression of protein fluctuations largely increases the time-scale of the protein-related hopping phenomena at least over 100 ns. These protein-related hopping phenomena permit the detection of translational motions of hydration water molecules longly persistent in the hydration shell of the protein.

Dynamics of TMAO and urea in the hydration shell of the protein SNase

Using all-atom molecular dynamics simulations of aqueous solutions of the globular protein SNase, the dynamic behavior of water molecules and cosolvents (trimethylamine-N-oxide (TMAO) and urea) in the hydration shell of the protein was studied for different solvent compositions. TMAO is a potent protein-stabilizing osmolyte, whereas urea is known to destabilize proteins. For molecules that are initially located in successive narrow layers at a given distance from the protein, the mean displacements and the distribution of displacements for short time intervals are calculated. For molecules that are initially located in solvation shells of a given thickness around the protein, the characteristic residence times in these shells are determined to characterize the dynamic behavior of the solvent molecules as a function of the distance to the protein. A combined consideration of these characteristics allows to reveal additional features of the dynamics of the cosolvents. It is shown that TMAO molecules leave the nearest vicinity of the protein faster than urea molecules, despite the fact that the mobility of TMAO molecules, measured by their mean displacements, is lower than that of urea. Moreover, we show that the rate of release of TMAO molecules from the hydration shell is lower in ternary (TMAO + urea + H₂O) solvent mixtures than in the binary ones. This is consistent with a recent observation that the fraction of TMAO near the protein decreases in the presence of urea. From the analysis of the decay of the number of particles initially located in the region of the first peak of the distribution function of solvent molecules around the protein, we estimated that about 20 water molecules and 6-7 urea molecules stay near the protein for more than 1000 ps.

Effect of gold nanoparticles on structure and dynamics of binary Lennard-Jones liquid: direct space analysis

We investigate the static structure and diffusive dynamics of binary Lennard-Jones mixture upon supercooling in the presence of gold nanoparticle within the framework of the mode-coupling theory of the dynamic glass transition in the direct space by means of constant-NVT molecular dynamics simulations. It is found that the presence of gold nanoparticle causes the energy per particle and the pressure of this system to decrease with respect to the bulk binary Lennard-Jones mixture. Furthermore, the presence of nanoparticle has a direct effect on the liquid structure and causes the peaks of the radial distribution functions to become shorter with respect to the bulk binary Lennard-Jones liquid. The dynamics of the liquid at a given density is found to be consistent with the mode-coupling theory (MCT) predictions in a certain range at low temperatures. In accordance with the idealized MCT, the diffusion constants D(T) show a power-law behavior at low temperatures for both types of binary Lennard-Jones (BLJ) particles as well as the gold atoms comprising the nanoparticle. The mode-coupling crossover temperature T(c) is the same for all particle types; however, T(c)=0.4 is reduced with respect to that of the bulk BLJ liquid, and the γ exponent is found to depend on the particle type. The existence of the nanoparticle causes the short-time β-relaxation regime to shorten and the range of validity of the MCT shrinks with respect to the bulk BLJ. It is also found that at intermediate and low temperatures the curves of the mean-squared displacements (MSDs) versus tD(T) fall onto a master curve. The MSDs follow the master curve in an identical time range with the long-time α-relaxation regime of the mode-coupling theory. By obtaining the viscosity, it is observed that the Stokes-Einstein relation remains valid at high and intermediate temperatures but breaks down as the temperatures approach T(c) as a result of the cooperative motion or activated processes.

Glassy dynamics in a confined monatomic fluid

Molecular dynamic simulations of a strongly inhomogeneous system reveals that a single-component soft-sphere fluid can behave as a fragile glass former due to confinement. The self-intermediate scattering function, F(s)(k,t), of a Lennard-Jones fluid confined in slit-shaped pores, which can accommodate two to four fluid layers, exhibits a two-step relaxation at moderate temperatures. The mean-squared displacement data are found to follow time-temperature superposition and both the self-diffusivity and late α relaxation times exhibit power-law divergences as the fluid is cooled. The system possesses a crossover temperature and follows the scalings of mode coupling theory for the glass transition. The temperature dependence of the self-diffusivity can be expressed using the Vogel-Fulcher-Tammann equation, and estimates of the fragility index of the system indicates a fragile glass former. At lower temperatures, signatures of additional relaxation processes are observed in the various dynamical quantities with a three-step relaxation observed in the F(s)(k,t).

Lennard-Jones binary mixture in disordered matrices: exploring the mode coupling scenario at increasing confinement

We present results of molecular dynamics simulations performed on a Lennard-Jones liquid binary mixture confined in matrices of soft spheres at increasing packing fraction. We study the dynamical properties of the liquid at a given density upon supercooling. Our aim is to test the validity of the mode coupling theory in predicting the behaviour of the glass forming liquid when it is under confinement in a disordered matrix. We use two different methods to build up the confining environment. We focus in particular on the behaviour of the single particle density correlators. We find a close agreement with the mode coupling theory at least for all the range of packing fractions examined. Discrepancies between the theory and the computer simulation results can be attributed to hopping effects which are more important at increasing confinement.

Dynamic arrest of colloids in porous environments: disentangling crowding and confinement

Using numerical simulations we study the slow dynamics of a colloidal hard-sphere fluid adsorbed in a matrix of disordered hard-sphere obstacles. We calculate separately the contributions to the single-particle dynamic correlation functions due to free and trapped particles. The separation is based on a Delaunay tessellation to partition the space accessible to the centres of fluid particles into percolating and disconnected voids. We find that the trapping of particles into disconnected voids of the matrix is responsible for the appearance of a nonzero long-time plateau in the single-particle intermediate scattering functions of the full fluid. The subdiffusive exponent z, obtained from the logarithmic derivative of the mean squared displacement, is essentially unaffected by the motion of trapped particles: close to the percolation transition, we determined z approximately = 0.5 for both the full fluid and the particles moving in the percolating void. Notably, the same value of z is found in single-file diffusion and is also predicted by mode-coupling theory along the diffusion-localization line. We also reveal subtle effects of dynamic heterogeneity in both the free and the trapped component of the fluid particles, and discuss microscopic mechanisms that contribute to this phenomenon.

Slow dynamics, dynamic heterogeneities, and fragility of supercooled liquids confined in random media

Using molecular dynamics simulations, we study the slow dynamics of supercooled liquids confined in a random matrix of immobile obstacles. We study the dynamical crossover from glass-like to Lorentz-gas-like behavior in terms of the density correlation function, the mean square displacement, the nonlinear dynamic susceptibility, the non-gaussian parameter, and the fragility. We find the cooperative and spatially heterogeneous dynamics to be suppressed as the obstacle density increases, leading to a more Arrhenius-like behavior in the temperature dependence of the relaxation time. Our findings are qualitatively consistent with the results of recent experimental and numerical studies for various classes of spatially heterogeneous systems. We also investigate the dependence of the dynamics of mobile particles on the protocol used to generate the random matrix. A re-entrant transition from the arrested phase to the liquid phase as the mobile particle density increases is observed for a class of protocols. This re-entrance is explained in terms of the distribution of the volume of the voids that are available to the mobile particles.

Statistical mechanics of homogeneous partly pinned fluid systems

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.

Impact of random obstacles on the dynamics of a dense colloidal fluid

Using molecular dynamics simulations we study the slow dynamics of a colloidal fluid annealed within a matrix of obstacles quenched from an equilibrated colloidal fluid. We choose all particles to be of the same size and to interact as hard spheres, thus retaining all features of the porous confinement while limiting the control parameters to the packing fraction of the matrix, φ(m), and that of the fluid, φ(f). We conduct detailed investigations on several dynamic properties, including the tagged-particle and collective intermediate scattering functions, the mean-squared displacement, and the van Hove function. We show the confining obstacles to profoundly impact the relaxation pattern of various quantifiers pertinent to the fluid. Varying the type of quantifier (tagged-particle or collective) as well as φ(m) and φ(f), we unveil both discontinuous and continuous arrest scenarios. Furthermore, we discover subdiffusive behavior and demonstrate its close connection to the matrix structure. Our findings partly confirm the various predictions of a recent extension of mode-coupling theory to the quenched-annealed protocol.

Single master curve for self-diffusion coefficients in distinctly different glass-forming liquids

An existence of a single master curve for the long-time self-diffusion coefficients D(S)(L)(T) in diversely different glass-forming liquids is predicted over wide temperature T ranges above the glass transition point T(g) by analyzing various experimental and simulation data consistently from a unified point of view based on the mean-field theory recently developed. In order to scale those data appropriately, the power-law dependence of the α- and the β-relaxation times on D(S)(L) is used. Then, it is shown that any equilibrium data for self-diffusion of atom in different systems are all collapsed onto a singular function f(T(f)((α))/T) , where T(f)((α)) is a fictive singular temperature of atom α. Thus, we emphasize that any equilibrium self-diffusion data can be described by a single master curve f(x) above T(g)(>T(f)), while the data out of equilibrium start to deviate from f(x) around T(g).

Mode-coupling behavior of a Lennard-Jones binary mixture upon increasing confinement

Molecular dynamics simulations are performed on a Lennard Jones binary mixture confined in off lattice matrices of soft spheres with increasing radius. We focus on dynamics upon supercooling and in particular on testing the mode coupling theory properties of the confined mixture. Parameters of mode coupling theory in going from bulk to weak confinement, and from weak to strong confinement are extracted from simulations and analyzed. We focus on the study of the behavior of the single particle density correlators. We find that the mode coupling theory retains its validity also in the case of strong confinement, with a reduction of range of validity. The role of hopping is discussed in relation with the differences between the results obtained from the diffusion coefficients and the mode coupling theory predictions.

Single-particle and collective slow dynamics of colloids in porous confinement

Using molecular dynamics simulations, we study the slow dynamics of a hard sphere fluid confined in a disordered porous matrix. The presence of both discontinuous and continuous glass transitions as well as the complex interplay between single-particle and collective dynamics are well captured by a recent extension of mode-coupling theory for fluids in porous media. The degree of universality of the mode-coupling theory predictions for related models of colloids is studied by introducing size disparity between fluid and matrix particles, as well as softness in the interactions.

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass asymmetry

Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio mu, including the limiting case mu = infinity, for different mole fractions x. Within a large range of x and mu the product of the diffusion coefficient of the heavy species D(2) and the total shear viscosity of the mixture eta(m) is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function, and the van Hove correlation function.

Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions

A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its equations, such as the previous ones, reflect the interplay between confinement-induced relaxation phenomena and glassy dynamics through the presence of two contributions in the slow part of the memory kernel, which are linear and quadratic in the density correlation functions, respectively. From numerical solutions for two simple models with pure hard-core interactions, it is shown that two different scenarios result for the diffusion-localization transition depending on the strength of the confinement. For weak confinement, this transition is discontinuous and coincides with the ideal glass transition, such as in one-component bulk systems, while, for strong confinement, it is continuous and occurs before the collective dynamics gets nonergodic. In the latter case, the glass transition manifests itself as a secondary transition, which can be either continuous or discontinuous, in the already arrested single-particle dynamics. The main features of the anomalous dynamics found in the vicinity of all these transitions are reviewed and illustrated with detailed computations.

Mode coupling behavior of a Lennard-Jones binary mixture: a comparison between bulk and confined phases

We present a quantitative comparison at equivalent thermodynamical conditions of bulk and confined dynamical properties of a Lennard-Jones binary mixture upon supercooling. Both systems had been previously found to display a behavior in agreement with the mode coupling theory of the evolution of glassy dynamics. Differences and analogies of behavior are discussed focusing, in particular, on the role of hopping in reducing spatially correlated dynamics in the confined system with respect to the bulk.

Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media

We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical framework, except for a linear contribution to the memory kernel which adds to the usual quadratic term. The coupling coefficients involve structural quantities which are specific of fluids evolving in random environments and have expressions which are consistent with those found in related problems. Numerical solutions for two simple models with pure hard core interactions lead to the prediction of a variety of glass transition scenarios, which are either continuous or discontinuous and include the possibility of higher-order singularities and glass-glass transitions. The main features of the dynamics in the two most generic cases are reviewed and illustrated with detailed computations. Moreover, a reentry phenomenon is predicted in the low fluid-high matrix density regime and is interpreted as the signature of a de-correlation mechanism by fluid-fluid collisions competing with the localization effect of the solid matrix.

Relaxation scenarios in a mixture of large and small spheres: Dependence on the size disparity

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and small particles. Density-density correlators for the small particles become extremely stretched and display logarithmic relaxation by properly tuning the temperature or the wave vector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated with mode coupling transition lines of the types B and A at, respectively, small and very large size disparities. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent mode coupling theory for fluids confined in matrices with interconnected voids [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)].

Anomalous dynamic arrest in a mixture of large and small particles

We present molecular dynamics simulations of the slow dynamics of a mixture of large and small soft spheres with a large size disparity. The dynamics are investigated in a broad range of temperature and mixture composition. As a consequence of the large size disparity, large and small particles exhibit very different relaxation times. As previously reported for simple models of short-ranged attractive colloids and polymer blends, several anomalous dynamic features are observed: (i) sublinear behavior for mean-squared displacements, (ii) concave-to-convex crossover for density-density correlators, by varying the temperature or wave vector, and (iii) logarithmic decay for specific wave vectors of density-density correlators. These anomalous features are observed over time intervals extending up to four decades and strongly resemble predictions of the mode coupling theory (MCT) for state points close to higher-order MCT transitions, which originate from the competition between different mechanisms for dynamic arrest. For the large particles we suggest competition between soft-sphere repulsion and depletion effects induced by neighboring small particles. For the small particles we suggest competition between bulklike dynamics and confinement, respectively induced by neighboring small particles and by the slow matrix of large particles.

Dynamic arrest in a liquid of symmetric dumbbells: Reorientational hopping for small molecular elongations

We present extensive equilibrium and out-of-equilibrium molecular-dynamics simulations of a liquid of symmetric dumbbell molecules, for constant packing fraction, as a function of temperature and molecular elongation. We compute diffusion constants as well as odd and even orientational correlators. The notations odd and even refer to the parity of the order l of the corresponding Legendre l polynomial, evaluated for the orientation of the molecular axis relative to its initial position. Rotational degrees of freedom of order l are arrested if, in the long-time limit, the corresponding orientational l correlator does not decay to zero. It is found that for large elongations translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. On the contrary, the odd rotational degrees of freedom remain ergodic at all investigated temperatures. Hence, in the translationally arrested state, each molecule remains trapped in the cage formed by its neighboring molecules, but is able to perform 180 degrees rotations, which lead to relaxation only for the odd orientational correlators. The temperature dependence of the characteristic time of these residual rotations is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of the type-A transition for the odd rotational degrees of freedom, as predicted by mode-coupling theory for small molecular elongations. This transition is distinct from the type-B transition, associated with the arrest of the translational and even rotational degrees of freedom for small elongations, and with all degrees of freedom for large elongations. Odd orientational correlators are computed for small elongations at very low temperatures in the translationally arrested state. The obtained results suggest that hopping events restore the ergodicity of the odd rotational degrees of freedom at temperatures far below the A transition.

Inherent structures and Kauzmann temperature of confined liquids

Calculations of the thermodynamical properties of a supercooled liquid confined in a matrix are performed with an inherent structure analysis. The liquid entropy is computed by means of a thermodynamical integration procedure. The contributions to the free energy of the liquid can be decoupled also in confinement in the configurational and the vibrational parts. We show that the vibrational entropy can be calculated in the harmonic approximation as in the bulk case. The Kauzmann temperature of the confined system is estimated from the behavior of the configurational entropy.

Liquid-glass transition of a fluid confined in a disordered porous matrix: a mode-coupling theory

We derive an extension of the mode-coupling theory for the liquid-glass transition to a class of models of confined fluids, where the fluid particles evolve in a disordered array of interaction sites. We find that the corresponding equations are similar to those describing the bulk, implying that the methods of investigation which were developed there are directly transferable to this new domain of application. We then compute the dynamical phase diagram of a simple model system and show that new and nontrivial transition scenarios, including reentrant glass transitions and higher-order singularities, can be predicted from the proposed theory.

Slow dynamics of a confined supercooled binary mixture. II. Q space analysis

We report the analysis in the wave vector space of the density correlator of a Lennard-Jones binary mixture confined in a disordered matrix of soft spheres upon supercooling. In spite of the strong confining medium the behavior of the mixture is consistent with the mode-coupling theory predictions for bulk supercooled liquids. The relaxation times extracted from the fit of the density correlator to the stretched exponential function follow a unique power law behavior as a function of wave vector and temperature. The von Schweidler scaling properties are valid for an extended wave vector range around the peak of the structure factor. The parameters extracted in the present work are compared with the bulk values obtained in literature.