Idealized glass transitions for a system of dumbbell molecules

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.

Explicit Analytical Solution for Random Close Packing in d=2 and d=3

We present an analytical derivation of the volume fractions for random close packing (RCP) in both d=3 and d=2, based on the same methodology. Using suitably modified nearest neighbor statistics for hard spheres, we obtain ϕ_{RCP}=0.658 96 in d=3 and ϕ_{RCP}=0.886 48 in d=2. These values are well within the interval of values reported in the literature using different methods (experiments and numerical simulations) and protocols. This statistical derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mechanical rigidity where the finite shear modulus emerges, (ii) the onset of mechanical rigidity marks the maximally random jammed state and dictates ϕ_{RCP} via the coordination number z, (iii) disordered packings with ϕ>ϕ_{RCP} are possible at the expense of creating some order, and z=12 at the fcc limit acts as a boundary condition.

Solvation dynamics in electronically polarizable solvents: Theoretical treatment using solvent-polarizable three-dimensional reference interaction-site model theory combined with time-dependent density functional theory

The theory of solvation structure in an electronically polarizable solvent recently proposed by us, referred to as the "solvent-polarizable three-dimensional reference interaction-site model theory," is extended to dynamics in this study through the combination with time-dependent density functional theory. Test calculations are performed on model charge-transfer systems in water, and the effects of electronic polarizability on solvation dynamics are examined. The electronic polarizability slightly retards the solvation dynamics. This is ascribed to the decrease in the curvature of the nonequilibrium free energy profile along the solvation coordinate. The solvent relaxation is bimodal, and the faster and the slower modes are assigned to the reorientational and the translational modes, respectively, as was already reported by the surrogate theory combined with the site-site Smoluchowski-Vlasov equation. The relaxation path along the solvation coordinate is a little higher than the minimum free energy path because the translational mode is fixed in the time scale of the reorientational relaxation.

Evolutionary drivers of protein shape

Diffusional motion within the crowded environment of the cell is known to be crucial to cellular function as it drives the interactions of proteins. However, the relationships between protein diffusion, shape and interaction, and the evolutionary selection mechanisms that arise as a consequence, have not been investigated. Here, we study the dynamics of triaxial ellipsoids of equivalent steric volume to proteins at different aspect ratios and volume fractions using a combination of Brownian molecular dynamics and geometric packing. In general, proteins are found to have a shape, approximately Golden in aspect ratio, that give rise to the highest critical volume fraction resisting gelation, corresponding to the fastest long-time self-diffusion in the cell. The ellipsoidal shape also directs random collisions between proteins away from sites that would promote aggregation and loss of function to more rapidly evolving nonsticky regions on the surface, and further provides a greater tolerance to mutation.

Coupling and decoupling between translational and rotational dynamics in supercooled monodisperse soft Janus particles

We perform dynamics simulations to investigate the translational and rotational glassy dynamics in a glass-forming liquid of monodisperse soft Janus particles. We find that, with decreasing temperature, the mean-square angular displacement shows no clear plateau in the caging region, in contrast with the apparent caging behavior of translational motion. By defining a reorientational mean-square angular displacement, the caging behavior of rotational motion can be recognized. On approaching the glass transition (decreasing temperature), the coupling between translational and rotational relaxation increases, while the coupling between translational and rotational diffusion decreases, whereas the coupling between translational and reorientational diffusion increases. The strong decoupling between translational and rotational diffusion is due to the suppressed translational mobility but promoted rotational mobility of soft Janus particles. We think that the low-T SE and SED decoupling is mainly attributed to hopping motion of soft Janus particles, whereas the high-T SE and SED decoupling is mainly attributed to collective cage motion of soft Janus particles. Our results demonstrate that interaction anisotropy has a critical effect on the translational and rotational dynamics of soft Janus particles.

Dynamics theory for molecular liquids based on an interaction site model

Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.

Mode-coupling theoretical study on the roles of heterogeneous structure in rheology of ionic liquids

Theoretical calculations of the rheological properties of coarse-grained model ionic liquids were performed using mode-coupling theory. The nonpolar part of the cation was systematically increased in order to clarify the effects of the heterogeneous structure on shear viscosity. The shear viscosity showed a minimum as the function of the size of the nonpolar part, as had been reported in literatures. The minimum was ascribed to the interplay between the increase in the shear relaxation time and the decrease in the high-frequency shear modulus with increasing the size of the nonpolar part of the cation. The ionic liquids with symmetric charge distribution of cations were less viscous than those with asymmetric cations, which is also in harmony with experiments. The theoretical analysis demonstrated that there are two mechanisms for the higher viscosity of the asymmetric model. The first one is the direct coupling between the domain dynamics and the shear stress. The second one is that the microscopic dynamics within the polar domain is retarded due to the nonlinear coupling with the heterogeneous structure.

Are polymers standard glass-forming systems? The role of intramolecular barriers on the glass-transition phenomena of glass-forming polymers

Traditionally, polymer melts have been considered archetypal glass-formers. This has been mainly due to the fact that these systems can easily be obtained as glasses by cooling from the melt, even at low cooling rates. However, the macromolecules, i.e. the structural units of polymer systems in general, are rather different from the standard molecules. They are long objects ('chains') made by repetition of a given chemical motif (monomer) and have intra-macromolecular barriers that limit their flexibility. The influence of these properties on, for instance, the glass-transition temperature of polymers, is a topic that has been widely studied by the polymer community almost from the early times of polymer science. However, in the framework of the glass-community, the relevant influence of intra-macromolecular barriers and chain connectivity on glass-transition phenomena of polymers has started to be recognized only recently. The aim of this review is to give an overview and to critically revise the results reported on this topic over the last years. From these results, it seems to be evident that there are two different mechanisms involved in the dynamic arrest in glass-forming polymers: (i) the intermolecular packing effects, which dominate the dynamic arrest of low molecular weight glass-forming systems; and (ii) the effect of intra-macromolecular barriers combined with chain connectivity. It has also been shown that the mode coupling theory (MCT) is a suitable theoretical framework to discuss these questions. The values found for polymers for the central MCT parameter--the so-called λ-exponent--are of the order of 0.9, clearly higher than the standard values (λ ≈ 0.7) found in systems where the dynamic arrest is mainly driven by packing effects ('standard' glass-formers). Within the MCT, this is a signature of the presence of two competing mechanisms of dynamic arrest, as it has been observed in short-ranged attractive colloids or two component mixtures with dynamic asymmetry. Moreover, recent MD-simulations of a 'bead-spring' polymer model, but including intra-macromolecular potential of different strengths, confirm that the high λ-values found in polymers are due to the effect of intra-macromolecular barriers. Although there are still open questions, these results allow to conclude that there is a fundamental difference between the nature of the glass transition in polymers and in simple (standard) glass-formers.

Molecular dynamics of a model dimerizing fluid

A model dimer forming fluid has been investigated by continuous molecular dynamics simulations. This study emphasizes the volume fraction and temperature dependence of the dynamic properties of the system, including the self and collective diffusion coefficients and the forward and reverse rate constants. The self and collective diffusion coefficients are found to be well described by a monomer fraction controlled interpolation formula. The forward rate constant (dimer formation) is found to be weakly temperature dependent and strongly volume fraction dependent. The opposite holds for the reverse rate constant. The dimer and monomer decay rates are not found to affect the intermediate scattering functions at the conditions studied.

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.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Tagged-particle motion in a dense confined liquid

We investigate the dynamics of a tagged particle embedded in a strongly interacting confined liquid enclosed between two opposing flat walls. Using the Zwanzig-Mori projection operator formalism we obtain an equation of motion for the incoherent scattering function suitably generalized to account for the lack of translational symmetry. We close the equations of motion by a self-consistent mode-coupling ansatz. The interaction of the tracer with the surrounding liquid is encoded in generalized direct correlation functions. We extract the in-plane dynamics and provide a microscopic expression for the diffusion coefficient parallel to the walls. The solute particle may differ in size or interaction from the surrounding host-liquid constituents offering the possibility of a systematic analysis of dynamic effects on the tagged-particle motion in confinement.

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.

Theory of kinetic arrest, elasticity, and yielding in dense binary mixtures of rods and spheres

We extend the quiescent and stressed versions of naïve mode coupling theory to treat the dynamical arrest, shear modulus, and absolute yielding of particle mixtures where one or more species is a nonrotating nonspherical object. The theory is applied in detail to dense isotropic "chemically matched" mixtures of variable aspect ratio rods and spheres that interact via repulsive and short range attractive site-site pair potentials. A remarkably rich ideal kinetic arrest behavior is predicted with up to eight "dynamical phases" emerging: an ergodic fluid, partially localized states where the spheres remain fluid but the rods can be a gel, repulsive glass or attractive glass, doubly localized glasses and gels, a porous rod gel plus sphere glass, and a narrow window where a type of rod glass and gel localization coexist. Dynamical complexity increases with rod length and the introduction of attractive forces between all species which both enhance gel network formation. Multiple dynamic reentrant features and triple points are predicted, and each dynamic phase has unique particle localization characteristics and mechanical properties. Orders of magnitude variation of the linear shear modulus and absolute yield stress are found as rod length, mixture composition and the detailed nature of interparticle attractions are varied. The interplay of total (high) mixture packing fraction and composition at fixed temperature is also briefly studied. The present work provides a foundation to study more complex rod-sphere mixtures of both biological and synthetic interest that include physical features such as interaction site size asymmetry, rod-sphere specific attractions, and/or Coulomb repulsion.

Glassy relaxation and excess wing in mode-coupling theory: the dynamic susceptibility of propylene carbonate above and below T(c)

We explore the possibility of describing experimental susceptibility spectra of the glass former propylene carbonate with a two-component schematic model of mode-coupling theory (MCT) from above the melting point down to temperatures far below the critical temperature of MCT. By introducing a phenomenological time-dependent hopping rate, the spectra are reproduced in the full frequency and temperature range available. Literature data of dielectric susceptibilities and depolarized Brillouin light-scattering spectra are combined with our measurements of photon correlation spectroscopy to cover up to 18 decades in frequency of spectra for two different dynamical variables. A consistent description of all data sets is obtained by adjusting only a few physically motivated parameters. In particular the excess wing or slow β-relaxation commonly observed in the susceptibility spectra can consistently be modeled as originating from a coupling of the individual experimental probe correlator to the collective density fluctuations.

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.

Yielding in dense suspensions: cage, bond, and rotational confinements

The effect of weak particle anisotropy on the onset of fluidity in dense suspensions of glasses of repulsive, weakly attractive and strongly attractive spherical and dumbbell shaped particles is explored. Yield stresses are found to scale with volume fraction showing a divergence at random close packing for all systems. However the onsets of yielding in suspensions of spherical and dumbbell shaped particles are shown to display qualitatively different behaviors. Suspensions of hard spheres exhibit a single yield stress (strain) while suspensions of spheres experiencing short range attractions in dense gels display two yielding events. Double yielding occurs when attractions between particles are only a few kT and the suspensions are sufficiently dense. For dumbbell suspensions, single yielding is observed for hard dumbbell glasses in a region where the glasses are expected to be plastic while double yielding is observed when the particles are expected to have localized centers of mass and localized orientations. Double yielding is also observed for dense dumbbell suspensions that experience attractions while only single yielding events are observed in strongly attractive gels for both dumbbells and spheres. These results are discussed in the light of recent theories and simulations of mechanisms of localization in suspensions of spherical and weakly anisotropic particles.

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 theoretical analysis of transport and relaxation properties of liquid dimethylimidazolium chloride

The mode-coupling theory for molecular liquids based on the interaction-site model is applied to a representative molecular ionic liquid, dimethylimidazolium chloride, and dynamic properties such as shear viscosity, self-diffusion coefficients, reorientational relaxation time, electric conductivity, and dielectric relaxation spectrum are analyzed. Molecular dynamics (MD) simulation is also performed on the same system for comparison. The theory captures the characteristics of the dynamics of the ionic liquid qualitatively, although theoretical relaxation times are several times larger than those from the MD simulation. Large relaxations are found in the 100 MHz region in the dispersion of the shear viscosity and the dielectric relaxation, in harmony with various experiments. The relaxations of the self-diffusion coefficients are also found in the same frequency region. The dielectric relaxation spectrum is divided into the contributions of the translational and reorientational modes, and it is demonstrated that the relaxation in the 100 MHz region mainly stems from the translational modes. The zero-frequency electric conductivity is close to the value predicted by the Nernst-Einstein equation in both MD simulation and theoretical calculation. However, the frequency dependence of the electric conductivity is different from those of self-diffusion coefficients in that the former is smaller than the latter in the gigahertz-terahertz region, which is compensated by the smaller dispersion of the former in the 100 MHz region. The analysis of the theoretical calculation shows that the difference in their frequency dependence is due to the different contribution of the short- and long-range liquid structures.

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.

Coupling and decoupling between translational and rotational dynamics in a supercooled molecular liquid

We use molecular dynamics simulations to investigate the coupling and decoupling between translational and rotational dynamics in a glass-forming liquid of dumbbells. We find that the coupling between the translational (tau_{q;{*}};{C}) and rotational (tau_{2}) relaxation times increases with decreasing temperature T, whereas the coupling decreases between the translational (D_{t}) and rotational (D_{r}) diffusivities. In addition, the T dependence of D_{t} decouples from that of 1/tau_{2}. We show that the decreasing coupling between D_{t} and D_{r} is only apparent due to the inadequacy of the concept of the rotational diffusion constant for describing the reorientational dynamics in the supercooled state. We also argue that the coupling between tau_{q;{*}};{C} and tau_{2} and the decoupling between D_{t} and 1/tau_{2} can be consistently understood in terms of the growing dynamic length scale.

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.

Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres

Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.

Structural and conformational dynamics of supercooled polymer melts: insights from first-principles theory and simulations

We report on quantitative comparisons between simulation results of a bead-spring model and mode-coupling theory calculations for the structural and conformational dynamics of a supercooled, unentangled polymer melt. We find semiquantitative agreement between simulation and theory, except for processes that occur on intermediate length scales between the compressibility plateau and the amorphous halo of the static structure factor. Our results suggest that the onset of slow relaxation in a glass-forming melt can be described in terms of monomer caging supplemented by chain connectivity. Furthermore, a unified atomistic description of glassy arrest and of conformational fluctuations that (asymptotically) follow the Rouse model emerges from our theory.

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.

Dynamics of uniaxial hard ellipsoids

We study the dynamics of monodisperse hard ellipsoids via a new event-driven molecular dynamics algorithm as a function of volume fraction phi and aspect ratio X0. We evaluate the translational D(trans) and the rotational D(rot) diffusion coefficients and the associated isodiffusivity lines in the phi-X0 plane. We observe a decoupling of the translational and rotational dynamics which generates an almost perpendicular crossing of the D(trans) and D(rot) isodiffusivity lines. While the self-intermediate scattering function exhibits stretched relaxation, i.e., glassy dynamics, only for large phi and X(0) approximately 1, the second order orientational correlator C2(t) shows stretching only for large and small X0 values. We discuss these findings in the context of a possible prenematic order driven glass transition.

Statistical-mechanical theory of ultrasonic absorption in molecular liquids

We present results of the theoretical description of ultrasonic phenomena in molecular liquids. In particular, we are interested in the development of a microscopical, i.e., statistical-mechanical, framework capable of explaining the long living puzzle of excess ultrasonic absorption in liquids. Typically, an ultrasonic wave in a liquid can be generated by applying a periodically alternating external pressure with an angular frequency that corresponds to the ultrasound. If the perturbation introduced by such a process is weak, its statistical-mechanical treatment can be done with the use of a linear response theory. We treat the liquid as a system of interacting sites, so that all the response/aftereffect functions as well as the energy dissipation and generalized (wave-vector and frequency-dependent) ultrasonic absorption coefficient are obtained in terms of familiar site-site static and time correlation functions such as static structure factors or intermediate scattering functions. To express the site-site intermediate scattering functions, we refer to the site-site memory equations in the mode-coupling approximation for first-order memory kernels, while equilibrium properties such as site-site static structure factors, and direct and total correlation functions are deduced from the integral equation theory of molecular liquids known as RISM, or one of its generalizations. All of the formalism is phrased in a general manner, hence the results obtained are expected to work for arbitrary types of molecular liquids including simple, ionic, polar, and nonpolar liquids.

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.

Site-site memory equation approach in study of density/pressure dependence of translational diffusion coefficient and rotational relaxation time of polar molecular solutions: acetonitrile in water, methanol in water, and methanol in acetonitrile

We present results of the theoretical study and numerical calculation of the dynamics of molecular liquids based on the combination of the memory equation formalism and the reference interaction site model (RISM). Memory equations for the site-site intermediate scattering functions are studied in the mode-coupling approximation for the first-order memory kernels, while equilibrium properties such as site-site static structure factors are deduced from RISM. The results include the temperature-density (pressure) dependence of translational diffusion coefficients D and orientational relaxation times tau for acetonitrile in water, methanol in water, and methanol in acetonitrile--all in the limit of infinite dilution. Calculations are performed over the range of temperatures and densities employing the extended simple point charge model for water and optimized site-site potentials for acetonitrile and methanol. The theory is able to reproduce qualitatively all main features of temperature and density dependences of D and tau observed in real and computer experiments. In particular, anomalous behavior, i.e, the increase in mobility with density, is observed for D and tau of methanol in water, while acetonitrile in water and methanol in acetonitrile do not show deviations from the ordinary behavior. The variety exhibited by the different solute-solvent systems in the density dependence of the mobility is interpreted in terms of the two competing origins of friction, which interplay with each other as density increases: the collisional and dielectric frictions which, respectively, increase and decrease with increasing density.

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)].

Mode-coupling study on the dynamics of hydrophobic hydration

The molecular motion of water in water-hydrophobic solute mixtures was investigated by the mode-coupling theory for molecular liquids based on the interaction-site description. When the model Lennard-Jones solute was mixed with water, both the translational and reorientational motions of solvent water become slower, in harmony with various experiments and molecular dynamics simulations. We compared the mechanism of the slowing down with that of the pressure dependence of the molecular motion of neat water [T. Yamaguchi, S.-H. Chong, and F. Hirata, J. Chem. Phys. 119, 1021 (2003)]. We found that the decrease in the solvent mobility caused by the solute can essentially be elucidated by the same mechanism: That is, the fluctuation of the number density of solvent due to the cavity formation by the solute strengthens the friction on the collective polarization through the dielectric friction mechanism: We also employed the solute molecule that is the same as solvent water except for the amount of partial charges, in order to alter the strength of the solute-solvent interaction continuously. The mobility of the solvent water was reduced both by the hydrophobic and strongly hydrophilic solutes, but it was enhanced in the intermediate case. Such a behavior was discussed in connection with the concept of positive and negative hydrations.

Molecular dynamics study of orientational cooperativity in water

Recent experiments on liquid water show collective dipole orientation fluctuations dramatically slower than expected (with relaxation time > 50 ns) [D.P. Shelton, Phys. Rev. B 72, 020201(R) (2005)]. Molecular dynamics simulations of extended simple point charge (SPC/E) water show a large vortexlike structure of the dipole field at ambient conditions surviving over [J. Higo, Proc. Natl. Acad. Sci. U.S.A. 98, 5961 (2001)]. Both results disagree with previous results on water dipoles in similar conditions, for which autocorrelation times are a few picoseconds. Motivated by these recent results, we study the water dipole reorientation using molecular dynamics simulations of the SPC/E model in bulk water for temperatures ranging from ambient 300 K down to the deep supercooled region of the phase diagram at 210 K. First, we calculate the dipole autocorrelation function and find that our simulations are well described by a stretched exponential decay, from which we calculate the orientational autocorrelation time t(alpha). Second, we define a second characteristic time, namely, the time required for the randomization of molecular dipole orientation, the self-dipole randomization time t(r), which is an upper limit on t(alpha); we find that t(r) is approximately equal to 5t(alpha). Third, to check if there are correlated domains of dipoles in water which have large relaxation times compared to the individual dipoles, we calculate the randomization time t(box) of the site-dipole field, the net dipole moment formed by a set of molecules belonging to a box of edge L(box). We find that the site-dipole randomization time t(box) is approximately equal to 2.5t(alpha) for L(box) approximately equal to 3 A, i.e., it is shorter than the same quantity calculated for the self-dipole. Finally, we find that the orientational correlation length is short even at low T.

Dynamics in the Presence of Attractive Patchy Interactions

We report extensive Monte Carlo and event-driven molecular dynamics simulations of a liquid composed of particles interacting via hard-sphere interactions complemented by four tetrahedrally coordinated short-range attractive ("sticky") spots, a model introduced several years ago by Kolafa and Nezbeda (Kolafa, J.; Nezbeda, I. Mol. Phys. 1987, 87, 161). To access the dynamic properties of the model, we introduce and implement a new event-driven molecular dynamics algorithm suited to study the evolution of hard bodies interacting, beside the repulsive hard-core, with a short-ranged interpatch square well potential. We evaluate the thermodynamic properties of the model in deep supercooled states, where the bond network is fully developed, providing evidence of density anomalies. Different from models of spherically symmetric interacting particles, the liquid can be supercooled without encountering the gas-liquid spinodal in a wide region of packing fractions phi. Around an optimal phi, a stable fully connected tetrahedral network of bonds develops. By analyzing the dynamics of the model we find evidence of anomalous behavior: around the optimal packing, dynamics accelerate on both increasing and decreasing phi. We locate the shape of the isodiffusivity lines in the (phi - T) plane and establish the shape of the dynamic arrest line in the phase diagram of the model. Results are discussed in connection with colloidal dispersions of sticky particles and gel-forming proteins and their ability to form dynamically arrested states.

Mode-coupling study on the dynamics of hydrophobic hydration II: Aqueous solutions of benzene and rare gases

The dynamic properties of both the solute and solvent of the aqueous solution of benzene, xenon and neon are calculated by the mode-coupling theory for molecular liquids based on the interaction-site model. The B-coefficients of the reorientational relaxation and the translational diffusion of the solvent are evaluated from their dependence on the concentration of the solute, and the reorientational relaxation time of water within the hydration shell is estimated based on the two-state model. The reorientational relaxation times of water in the bulk and within the hydration shell, that of solute, and the translational diffusion coefficients of solute and solvent, are calculated at 0-30 degrees C. The temperature dependence of these dynamic properties is in qualitative agreement with that of NMR experiment reported by Nakahara et al. (M. Nakahara, C. Wakai, Y. Yoshimoto and N. Matubayasi, J. Phys. Chem., 1996, 100, 1345-1349, ref. 36), although the agreement of the absolute values is not so good. The B-coefficients of the reorientational relaxation times for benzene, xenon and neon solution are correlated with the hydration number and the partial molar volume of the solute. The proportionality with the latter is better than that with the former. These results support the mechanism that the retardation of the mobility of water is caused by the cavity formation of the solute, as previously suggested by us (T. Yamaguchi, T. Matsuoka and S. Koda, J. Chem. Phys., 2004, 120, 7590-7601, ref. 34), rather than the conventional one that the rigid hydration structure formed around the hydrophobic solute reduces the mobility of water.