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

The effect of polymorphism on the structural, dynamic and dielectric properties of plastic crystal water: A molecular dynamics simulation perspective

We have employed molecular dynamics simulations based on the TIP4P/2005 water model to investigate the local structural, dynamical, and dielectric properties of the two recently reported body-centered-cubic and face-centered-cubic plastic crystal phases of water. Our results reveal significant differences in the local orientational structure and rotational dynamics of water molecules for the two polymorphs. The probability distributions of trigonal and tetrahedral order parameters exhibit a multi-modal structure, implying the existence of significant local orientational heterogeneities, particularly in the face-centered-cubic phase. The calculated hydrogen bond statistics and dynamics provide further indications of the existence of a strongly heterogeneous and rapidly interconverting local orientational structural network in both polymorphs. We have observed a hindered molecular rotation, much more pronounced in the body-centered-cubic phase, which is reflected by the decay of the fourth-order Legendre reorientational correlation functions and angular Van Hove functions. Molecular rotation, however, is additionally hindered in the high-pressure liquid compared to the plastic crystal phase. The results obtained also reveal significant differences in the dielectric properties of the polymorphs due to the different dipolar orientational correlation characterizing each phase.

Active dumbbells: Dynamics and morphology in the coexisting region

With the help of molecular dynamics simulations we study an ensemble of active dumbbells in purely repulsive interaction. We derive the phase diagram in the density-activity plane and we characterise the various phases with liquid, hexatic and solid character. The analysis of the structural and dynamical properties, such as enstrophy, mean-square displacement, polarisation, and correlation functions, shows the continuous character of liquid and hexatic phases in the coexisting region when the activity is increased starting from the passive limit.

Peculiar Molecular Shape and Size Dependence of the Dynamics of Fluids Confined in a Small-Pore Metal-Organic Framework

Force-field-based molecular dynamics simulations were deployed to systematically explore the dynamics of confined molecules of different shapes and sizes, that is, linear (CO₂ and N₂) and spherical (CH₄) fluids, in a model small pore system, that is, the metal-organic framework SIFSIX-2-Cu-i. These computations unveil an unprecedented molecular symmetry dependence of the translational and rotational dynamics of fluids confined in channel-like nanoporous materials. In particular, this peculiar behavior is reflected by the extremely slow decay of the Legendre reorientational correlation functions of even-parity order for the linear fluids, which is associated with jump-like orientation flips, while the spherical fluid shows a very fast decay taking place on a subpicosecond time scale. Such a fundamental understanding is relevant to diverse disciplines such as in chemistry, physics, biology, and materials science, where diatomic or polyatomic molecules of different shapes/sizes diffuse through nanopores.

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.

Rotational dynamics of simple asymmetric molecules

Molecular dynamic simulations were carried out on rigid diatomic molecules, which exhibit both α (structural) and β (secondary) dynamics. The relaxation scenarios range from onset behavior, in which a distinct α process emerges on cooling, to merging behavior, associated with two relaxation peaks that converge at higher temperature. These properties, as well as the manifestation of the β peak as an excess wing, depend not only on thermodynamic conditions, but also on both the symmetry of the molecule and the correlation function (odd or even) used to analyze its dynamics. These observations help to reconcile divergent results obtained from different experiments. For example, the β process is more intense and the α-relaxation peak is narrower in dielectric relaxation spectra than in dynamic light scattering or NMR measurements. In the simulations herein, this follows from the weaker contribution of the secondary relaxation to even-order correlation functions, related to the magnitude of the relevant angular jumps.

Observable-dependence of the effective temperature in off-equilibrium diatomic molecular liquids

We discuss the observable-dependence of the effective temperature Teff, defined via the fluctuation-dissipation relation, of an out-of-equilibrium system composed by homonuclear dumbbell molecules. Teff is calculated by evaluating the fluctuation and the response for two observables associated, respectively, to translational and to rotational degrees of freedom, following a sudden temperature quench. We repeat our calculations for different dumbbell elongations ζ. At high elongations (ζ > 0.4), we find the same Teff for the two observables. At low elongations (ζ ⩽ 0.4), only for very deep quenches Teff coincides. The observable-dependence of Teff for low elongations and shallow quenches stresses the importance of a strong coupling between orientational and translational variables for a consistent definition of the effective temperature in glassy systems.

Orientational glass in mixtures of elliptic and circular particles: structural heterogeneities, rotational dynamics, and rheology

Using molecular dynamics simulation with an angle-dependent Lennard-Jones potential, we study orientational glass with quadrupolar symmetry in mixtures of elliptic particles and circular impurities in two dimensions. With a mild aspect ratio (= 1.23) and a mild size ratio (= 1.2), we realize a plastic crystal at relatively high temperature T. With further lowering T, we find a structural phase transition for very small impurity concentration c and pinned disordered orientations for not small c. The ellipses are anchored by the impurities in the planar alignment. With increasing c, the orientation domains composed of isosceles triangles gradually become smaller, resulting in orientational glass with crystal order. In our simulation, the impurity distribution becomes heterogeneous during quenching from liquid, which then produces rotational dynamic heterogeneities. We also examine rheology in orientational glass to predict a shape memory effect and a superelasticity effect, where a large fraction of the strain is due to collective orientation changes.

Characteristics of the Johari-Goldstein process in rigid asymmetric molecules

Molecular dynamics simulations were carried out on a Lennard-Jones binary mixture of rigid (fixed bond length) diatomic molecules. The translational and rotational correlation functions, and the corresponding susceptibilities, exhibit two relaxation processes: the slow structural relaxation (α dynamics) and a higher frequency secondary relaxation. The latter is a Johari-Goldstein (JG) process, by its definition of involving all parts of the molecule. It shows several properties characteristic of the JG relaxation: (1) merging with the α relaxation at high temperature; (2) a change in temperature dependence of its relaxation strength on vitrification; (3) a separation in frequency from the α peak that correlates with the breadth of the α dispersion; and (4) sensitivity to volume, pressure, and physical aging. These properties can be used to determine whether a secondary relaxation in a real material is an authentic JG process, rather than more trivial motion involving intramolecular degrees of freedom. The latter has no connection to the glass transition, whereas the JG relaxation is closely related to structural relaxation, and thus can provide new insights into the phenomenon.

Formation of double glass in binary mixtures of anisotropic particles: dynamic heterogeneities in rotations and displacements

We study glass behavior in a mixture of elliptic and circular particles in two dimensions at low temperatures using an orientation-dependent Lennard-Jones potential. The ellipses have a mild aspect ratio (∼1.2) and tend to align at low temperatures, while the circular particles play the role of impurities disturbing the ellipse orientations at a concentration of 20%. These impurities have a size smaller than that of the ellipses and attract them in the homeotropic alignment. As a result, the coordination number around each impurity is mostly 5 or 4 in glassy states. We realize double glass, where both the orientations and the positions are disordered but still hold mesoscopic order. We find a strong heterogeneity in the flip motions of the ellipses, which sensitively depends on the impurity clustering. In our model, a small fraction of the ellipses still undergo flip motions relatively rapidly even at low temperatures. In contrast, the nonflip rotations (with angle changes not close to ±π) are mainly caused by the cooperative configuration changes involving many particles. Then, there arises a long-time heterogeneity in the nonflip rotations closely correlated with the dynamic heterogeneity in displacements.

Microscopic models of mode-coupling theory: the F12 scenario

We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the F(12) schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation. Depending on the facilitation strength, one observes two distinct dynamical glass transition lines--continuous and discontinuous--merging at a dynamical tricritical-like point with critical decay exponents consistently related by MCT predictions. The mechanisms of dynamical arrest can be naturally interpreted in geometrical terms: the discontinuous and continuous transitions correspond to bootstrap and standard percolation processes, in which the incipient spanning cluster of frozen spins forms either a compact or a fractal structure, respectively. Our cooperative dynamical facilitation picture of glassy behavior is complementary to the one based on disordered systems and can account for higher-order singularity scenarios in the absence of a finite temperature thermodynamic glass transition. We briefly comment on the relevance of our results to finite spatial dimensions and to the F(13) schematic model.

Molecular dynamics simulation of the Johari-Goldstein relaxation in a molecular liquid

Molecular dynamics simulations were carried out to investigate the reorientational motion of a rigid (fixed bond length), asymmetric diatomic molecule in the liquid and glassy states. In the latter the molecule reorients via large-angle jumps, which we identify with the Johari-Goldstein (JG) dynamics. This relaxation process has a broad distribution of relaxation times, and at least deeply in the glassy state, the mobility of a given molecule remains fixed over time; that is, there is no dynamic exchange among molecules. Interestingly, the JG relaxation time for a molecule does not depend on the local density, although the nonergodicity factor is weakly correlated with the packing efficiency of neighboring molecules. In the liquid state the intensity of the JG process increases significantly, eventually subsuming the slower α relaxation. This evolution of the JG motion into structural relaxation underlies the correlation of many properties of the JG and α dynamics.

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.

Kinetic arrest, dynamical transitions, and activated relaxation in dense fluids of attractive nonspherical colloids

The coupled translation-rotation activated dynamics in dense suspensions of attractive homogeneous and Janus uniaxial dicolloids are studied using microscopic statistical mechanical theory. Multiple kinetic arrest transitions and reentrant phenomena are predicted that are associated with fluid, gel, repulsive glass, attractive glass, plastic glass, and novel glass-gel states. The activated relaxation rate is a nonuniversal nonmonotonic function of attraction strength at high volume fractions due to the consequences of a change of the transient localization mechanism from caging to physical bonding.

Activated dynamics in dense fluids of attractive nonspherical particles. I. Kinetic crossover, dynamic free energies, and the physical nature of glasses and gels

We apply the center-of-mass versions of naïve mode coupling theory and nonlinear Langevin equation theory to study how short-range attractive interactions modify the onset of localization, activated single-particle dynamics, and the physical nature of the transiently arrested state of a variety of dense nonspherical particle fluids (and the spherical analog) as a function of volume fraction and attraction strength. The form of the dynamic crossover boundary depends on particle shape, but the reentrant glass-fluid-gel phenomenon and the repulsive glass-to-attractive glass crossover always occur. Diverse functional forms of the dynamic free energy are found for all shapes including glasslike, gel-like, a glass-gel form defined by the coexistence of two localization minima and two activation barriers, and a "mixed" attractive glass characterized by a single, very short localization length but an activation barrier located at a large displacement as in repulsive-force caged glasses. For the latter state, particle trajectories are expected to be of a two-step activated form and can be accessed at high attraction strength by increasing volume fraction, or by increasing attraction strength at fixed high enough volume fraction. A new classification scheme for slow dynamics of fluids of dense attractive particles is proposed based on specification of both the nature of the localized state and the particle displacements required to restore ergodicity via activated barrier hopping. The proposed physical picture appears to be in qualitative agreement with recent computer simulations and colloid experiments.

Glass formation and shear elasticity in dense suspensions of repulsive anisotropic particles

Kinetic vitrification, shear elasticity, and the approach to jamming are investigated for repulsive nonspherical colloids and contrasted with their spherical analog. Particle anisotropy dramatically increases the volume fraction for kinetic arrest. The shear modulus of all systems increases roughly exponentially with volume fraction, and a universal collapse is achieved based on either the dynamic crossover or random close packing volume fraction as the key nondimensionalizing quantity. Quantitative comparisons with recent microscopic theories are performed and good agreement demonstrated.

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.

Theory of coupled translational-rotational glassy dynamics in dense fluids of uniaxial particles

The naïve mode coupling theory (NMCT) for ideal kinetic arrest and the nonlinear Langevin equation theory of activated single-particle barrier hopping dynamics are generalized to treat the coupled center-of-mass (CM) translational and rotational motions of uniaxial hard objects in the glassy fluid regime. The key dynamical variables are the time-dependent displacements of the particle center-of-mass and orientational angle. The NMCT predicts a kinetic arrest diagram with three dynamical states: ergodic fluid, plastic glass, and fully nonergodic double glass, the boundaries of which meet at a "triple point" corresponding to a most difficult to vitrify diatomic of aspect ratio approximately 1.43. The relative roles of rotation and translation in determining ideal kinetic arrest are explored by examining three limits of the theory corresponding to nonrotating, pure rotation, and rotationally ergodic models. The ideal kinetic arrest boundaries represent a crossover to activated dynamics described by two coupled stochastic nonlinear Langevin equations for translational and rotational motions. The fundamental quantity is a dynamic free-energy surface, which for small aspect ratios in the high-volume fraction regime exhibits two saddle points reflecting a two-step activated dynamics where relatively rapid rotational dynamics coexists with slower CM translational motions. For large-enough aspect ratios, the dynamic free-energy surface has one saddle point which corresponds to a system-specific coordinated translation-rotation motion. The entropic barriers as a function of the relative amount of rotation versus translation are determined.

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.

Glassy dynamics and kinetic vitrification of isotropic suspensions of hard rods

A nonlinear Langevin equation (NLE) theory for the translational center-of-mass dynamics of hard nonspherical objects has been applied to isotropic fluids of rigid rods. The ideal kinetic glass transition volume fraction is predicted to be a monotonically decreasing function beyond an aspect ratio of two. The functional form of the decrease is weaker than the inverse aspect ratio. Vitrification occurs at lower volume fractions for corrugated tangent bead rods compared to their smooth spherocylinder analogs. The ideal glass transition signals a crossover to activated dynamics, which is estimated to be observable before the nematic phase boundary is encountered if the aspect ratio is less than roughly 25. Calculations of the glassy elastic shear modulus and absolute yield stress reveal a roughly exponential growth with volume fraction. The dependence of entropic barriers and mean barrier hopping times on concentration for rods of variable aspect ratios can be collapsed quite well based on a difference volume fraction variable that quantifies the distance from the ideal glass boundary. Full numerical solution of the NLE theory via stochastic trajectory simulation was performed for tangent bead rods, and the results were compared to their hard sphere analogs. With increasing shape anisotropy the characteristic length scales of the nonequilibrium free energy increase and the magnitude of the localization well and entropic barrier curvatures decreases. These changes result in a significant aspect ratio dependence of dynamical properties and time correlation functions including weaker intermediate time subdiffusive transport, stronger two-step decay of the incoherent dynamic structure factor, longer mean alpha relaxation time, and stronger wavevector-dependent decoupling of relaxation times and the self-diffusion constant. The theoretical results are potentially testable via computer simulation, confocal microscopy, and dynamic light scattering.

Ideal vitrification, barrier hopping, and jamming in fluids of modestly anisotropic hard objects

Our recent theory for the glassy dynamics of fluids and suspensions of hard nonspherical objects is applied to several modestly anisotropic shapes. The role of bond length and aspect ratio is studied for diatomics, triatomics, and spherocylinders. As spherical symmetry is broken the ideal kinetic glass transition volume fraction of all objects increases linearly with aspect ratio with the same slope, in surprising agreement with the jamming phase diagram of hard granular ellipsoids. The ideal glass boundary of all shapes is a nonmonotonic function of aspect ratio which is also in qualitative accord with the jamming behavior of spherocylinders and ellipsoids. The maximum glass volume fraction shifts to higher values, and larger aspect ratios, as the object becomes smoother. Suggestions for why the nonequilibrium jamming and kinetic ideal glass formation (dynamical crossover) boundaries are similar are advanced. Beyond the ideal glass volume fraction the nonequilibrium free energy acquires a localization well and entropic barrier. Although its form is highly nonuniversal, if different shapes are compared at constant barrier height then a good collapse is found. Collapse of the volume fraction dependence of the barrier height for different shapes is also predicted for modest shape anisotropy, but increasingly fails as the aspect ratio exceeds 2. For a given volume fraction the mean barrier hopping times are nonmonotonic functions of aspect ratio. The functional form of this dependence, and order of magnitude variation with aspect ratio, is distinct for each object.

Ideal glass transitions, shear modulus, activated dynamics, and yielding in fluids of nonspherical objects

An extension of naive ideal mode coupling theory (MCT) and its generalization to treat activated barrier hopping and glassy dynamics in fluids and suspensions composed of nonspherical hard core objects is proposed. An effective center-of-mass description is adopted. It corresponds to a specific type of pre-averaging of the dynamical consequences of orientational degrees of freedom. The simplest case of particles composed of symmetry-equivalent interaction sites is considered. The theory is implemented for a homonuclear diatomic shape of variable bond length. The naive MCT glass transition boundary is predicted to be a nonmonotonic function of the length-to-width or aspect ratio and occurs at a nearly unique value of the dimensionless compressibility. The latter quantifies the amplitude of long wavelength thermal density fluctuations, thereby (empirically) suggesting a tight connection between the onset of localization and thermodynamics. Localization lengths and elastic shear moduli for different aspect ratio and volume fraction systems approximately collapse onto master curves based on a reduced volume fraction variable that quantifies the distance from the ideal glass transition. Calculations of the entropic barrier height and hopping time, maximum restoring force, and absolute yield stress and strain as a function of diatomic aspect ratio and volume fraction have been performed. Strong correlations of these properties with the dimensionless compressibility are also found, and nearly universal dependences have been numerically identified based on property-specific nondimensionalizations. Generalization of the approach to rigid rods, disks, and variable shaped molecules is possible, including oriented liquid crystalline phases.

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)].