Collisions, caging, thermodynamics, and jamming in the barrier hopping theory of glassy hard sphere fluids

An ultralocal limit of the microscopic single particle barrier hopping theory of glassy dynamics is proposed which allows explicit analytic expressions for the characteristic length scales, energy scales, and nonequilibrium free energy to be derived. All properties are shown to be controlled by a single coupling constant determined by the fluid density and contact value of the radial distribution function. This parameter quantifies an effective mean square force exerted on a tagged particle due to collisions with its surroundings. The analysis suggests a conceptual basis for previous surprising findings of multiple inter-relationships between characteristics of the transient localized state, the early stages of cage escape, non-Gaussian or dynamic heterogeneity effects, and the barrier hopping process that defines the alpha relaxation event. The underlying physical picture is also relevant to fluids of nonspherical molecules and sticky colloidal suspensions. The possibility of a unified view of liquid dynamics is suggested spanning the range from dense gases to the zero mobility jammed state.     

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 2002, 65, 011106] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also successfully tested against simulations of a hard sphere fluid at relatively low density.     

缔合溶液热力学性质与谱学性质的关联

缔合溶液具有与理想溶液显著不同的热力学和谱学性质,对于热力学和谱学的研究,有助于我们理解缔合溶液的特殊行为.谱学技术中核磁共振(NMR)、红外(IR)和拉曼(Raman)光谱是研究分子间相互作用和溶液结构等微观性质的有效方法,谱学已成为分子热力学研究体系"四面体结构"中的第四个顶点.本文对缔合溶液中热力学(汽液平衡和焓)和谱学(NMR,IR和Raman)联系的最新研究进展进行了综述,着重介绍相关的模型,如化学缔合模型、局部组成(LC)、格子流体氢键(LFHB)理论以及统计缔合流体理论(SAFT).     

Lifetime and strength of adhesive molecular bond clusters between elastic media

With a long-term objective toward a quantitative understanding of cell adhesion, we consider an idealized theoretical model of a cluster of molecular bonds between two dissimilar elastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to obey classical elastic equations whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. Monte Carlo simulations that combine the elastic and stochastic equations are conducted to investigate the lifetime of the bond cluster as a function of the applied load. We show that the interfacial traction is generally nonuniform and for a given adhesion size the average cluster lifetime asymptotically approaches infinity as the applied load is reduced to below a critical value, defined as the strength of the cluster. The effects of elastic moduli, adhesion size, and rebinding rate on the cluster lifetime and strength are studied under strongly nonuniform distributions of interfacial traction. Although overly simplified in a number of aspects, our model seems to give predictions that are consistent with relevant experimental observations on focal adhesion dynamics.     

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.     

Examination of membrane fusion by dissipative particle dynamics simulation and comparison with continuum elastic models

A dissipative particle dynamics model is applied to probe the lipidic membrane fusion. This model is verified by reproducing the lipid phase behavior. The classical stalk model has been visited and modified. The tilt deformation of the lipids and the noncircular shape of the stalk are supported. The stalk is shown to undergo asymmetric expansion to form the trans-monolayers contact (TMC). Unlike previous models, an energy barrier between the stalk and the TMC has been identified, implying that the TMC should be a metastable formation. This shows good agreement with the fusion experiments. Two typical elastic continuum models are compared with our result and possible modifications to the two elastic models are suggested. The effect of spontaneous curvature of lipid on selection of fusion pathway is also examined. It is observed that a bent stalk with pore or an inverted micellar intermediate will have more chance to occur than traditional stalk when the spontaneous curvature of the lipid becomes more negative.     

A microscopic model for the fluctuations of local field and spontaneous emission of single molecules in disordered media.

We develop a microscopic model to describe the observed temporal fluctuations of the fluorescence lifetime of single molecules embedded in a polymer at room temperature. The model represents the fluorescent probe and the macromolecular matrix on the sites of a cubic lattice and introduces voids in the matrix to account for its mobility. We generalize Lorentz's approach to dielectrics by considering three domains of electrostatic interaction of the probe molecule with its nanoenvironment: (1) the probe molecule with its elongated shape and its specific polarizability, (2) the first few solvent shells with their discrete structure and their inhomogeneity, (3) the remainder of the solvent at larger distances, treated as a continuous dielectric. The model is validated by comparing its outcome for homogeneous systems with those of existing theories. When realistic inhomogeneities are introduced, the model correctly explains the observed fluctuations of the lifetimes of single molecules. Such a comparison is only possible with single-molecule observations, which provide a new access to local field effects.     

Influence of deuteration on lithium acetate dihydrate studied by inelastic X-ray scattering, density functional theory, thermal expansion, elastic and thermodynamic measurements

The influence of deuteration on the properties of lithium acetate dihydrate has been investigated by thermal expansion measurements, ultrasound spectroscopy and calorimetry. Inelastic X-ray scattering has been employed to investigate if the low temperature structural phase transition can be detected by a change in the vibrational spectrum. Density functional theory, DFT, calculations have been employed to complement the experimental investigations. The thermal expansion coefficients and the specific heat of the deuterated compound differ significantly from the protonated form. The differences in the elastic stiffness coefficients are just above the detection limit of the technique employed here. Temperature dependent inelastic X-ray spectroscopic measurements show no significant change of the vibrational spectrum when crossing the transition temperature. The DFT calculations show that the methyl group dynamics are best described in the framework of coupled rotators of opposing methyl groups. One of the coupled rotational modes corresponds to a hindered rotator with a barrier of 15 meV, while the other is a free rotator.     

Relationships between miscibility behavior and chemical structure of phospholipids in pseudobinary systems

The influence of chain length differences of cephalines and the influence of the head group methylation on the miscibility behavior of N-methylated phosphatidylethanolamine (PE) mixtures in aqueous dispersions were tested. Nine different phase diagrams were studied by means of differential scanning calorimetry. The phase diagrams of the five pseudobinary cephaline/cephaline/water systems (fatty acid chain length: C _n , n = 12–18) showed that in the high temperature L_α phase all the homologous cephalines were completely miscible. In the low-temperature phase a distinct succession of the phase diagram types was observed according to increasing chain length differences of the PEs: complete miscibilty (C₁₂/C₁₄; C₁₄/C₁₆), peritectic mixing behavior (C₁₂/C₁₆; C₁₄/C₁₈), eutectic mixing behavior (C₁₂/C₁₈). Furthermore four phase diagrams of pseudobinary phospholipid systems consisting of N-methylated PEs with different numbers of methyl groups and a constant length of fatty acid chains were investigated and compared. These four phase diagrams showed phase separations in the low-temperatures phase (gel phase). The width and the concentration range of the miscibility gaps changed systematically with increasing degree of methylation of the head group of the mixing components and are connected with different possibilities of PEs to form hydrogen bridges between the mixture components. Received: 26 August 1999/Accepted: 30 August 1999     

Equation of state and jamming density for equivalent bi- and polydisperse, smooth, hard sphere systems

We study bi- and polydisperse mixtures of hard sphere fluids with extreme size ratios up to 100. Simulation results are compared with previously found analytical equations of state by looking at the compressibility factor, Z, and agreement is found with much better than 1% deviation in the fluid regime. A slightly improved empirical correction to Z is proposed. When the density is further increased, excluded volume becomes important, but there is still a close relationship between many-component mixtures and their binary, two-component equivalents (which are defined on basis of the first three moments of the size distribution). Furthermore, we determine the size ratios for which the liquid-solid transition exhibits crystalline, amorphous or mixed system structure. Near the jamming density, Z is independent of the size distribution and follows a -1 power law as function of the difference from the jamming density (Z → ∞). In this limit, Z depends only on one free parameter, the jamming density itself, as reported for several different size distributions with a wide range of widths.     

Relationships between the particle velocity and introduction of drug-loaded microparticles into the skin in a microparticulate bombardment system

Recently, it has been suggested that a microparticulate bombardment system would be a very useful tool for the delivery of a variety of powdered drugs as an alternative to parenteral injection via a needle. However the relationship between the particle dynamics and introduction into the skin has not been researched using this system. In the present study, we analyzed the velocity of microparticles bombarded by the Helios(TM) gun system under various conditions using particle image velocimetry (PIV). The particle kinetic energy, which depended on the particle velocity and particle mass, was increased with increasing helium pressure and particle size, decreasing bombardment dose, resulting in the increased percentage introduction and relative bioavailability (F(0-24 h)). The particle velocity had a greater influence than the particle mass. Therefore, in order to be the most effective system for introduction into the skin, it is necessary to use a high helium pressure and microparticles of high density. However, it is also necessary to consider the skin damage after bombardment.     

On the thermodynamic and kinetic stability of nonequilibrium systems

A criterion of evolution of nonequilibrium systems in the region of stable states was formulated.     

Direct calculation of solid-vapor coexistence points by thermodynamic integration: application to single component and binary systems

We present a new thermodynamic integration method that directly connects the vapor and solid phases by a reversible path. The thermodynamic integration in the isothermal-isobaric ensemble yields the Gibbs free energy difference between the two phases, from which the sublimation temperature can be easily calculated. The method extends to the binary mixture without any modification to the integration path simply by employing the isothermal-isobaric semigrand ensemble. The thermodynamic integration, in this case, yields the chemical potential difference between the solid and vapor phases for one of the components, from which the binary sublimation temperature can be calculated. The coexistence temperatures predicted by our method agree well with those in the literature for single component and binary Lennard-Jones systems.     

Edge-to-site reduction of Bethe-Peierls approximation for nearest neighbor exclusion cubic lattice particle systems and thermodynamic modeling of liquid silicates

We study an interacting particle system on the simple cubic lattice satisfying the nearest neighbor exclusion (NNE) which forbids any two nearest sites to be simultaneously occupied. Under the constraint, we develop an edge-to-site reduction of the Bethe-Peierls entropy approximation of the cluster variation method. The resulting NNE-corrected Bragg-Williams approximation is applied to statistical mechanical modeling of a liquid silicate formed by silica and a univalent network modifier, for which we derive the molar Gibbs energy of mixing and enthalpy of mixing and compare the predictions with available thermodynamic data.     

Nonequilibrium statistical theory of damage and fracture for glassy polymers, 1. The statistical distribution and evolution of microcracks in glassy polymers

The purpose of this paper is to construct a unified theoretical framework to link micro to macro-mechanical properties of glassy polymers. Starting from a model of microcrack propagation in craze on a mesoscale, the kinetic process of microcrack propagation resulting from fibril breakdown in the crack tip zone is mathematically formulated by a combination of fracture mechanics and fracture kinetics. A microcrack evolution equation involving both the geometric structure parameters of craze and the meso-mechanical quantities is obtained. After solving this evolution equation, a statistical distribution function of microcrack size which evolves with time and the moment generating function of microcrack size are derived. Any-order averaged damage functions can be therefore deduced. Specifically, the analytical expressions of the first-order averaged damage function and its damage rate are presented, which correspond to a similar definition of damage mechanics.     

Interlamellar forces and the thermodynamic characterization of lamellar phospholipid systems

In this review, we summarize a series of experimental studies of the swelling of zwitterionic lamellar phospholipid and phospholipid-cholesterol systems using a novel double twin calorimeter. With this method, one can obtain simultaneous measures of the partial molar free energy and the partial molar enthalpy, and the experimental studies thus provide a complete thermodynamic characterization of the isothermal swelling process. A major finding is that the swelling of lamellar zwitterionic phospholipid systems at higher water contents (> 4 water molecules per lipid) is endothermic. The enthalpy has the opposite sign relative to the free energy, thus demonstrating that the swelling process is entropy driven. The water uptake also triggers a transition from a gel to a liquid crystalline state showing that, at given water content, the swelling pressure is much higher in the liquid crystal than in the gel. When cholesterol is added to the system the liquid ordered phase is formed at all available water contents. In this phase the swelling pressure varies smoothly and takes relatively low values at water contents below two per phospholipid, while it is substantially higher than in the gel phase at higher water contents. Together, these data demonstrate that the swelling pressure is sensitive to the phase state of the lipids. We also describe a series of studies that demonstrate that the addition of a second polar solute to the phospholipid–water system has a remarkably small effect on the swelling behavior when analyzed with respect to solvent volume. The reviewed experimental studies provide a thermodynamic characterization of the swelling of lamellar zwitterionic phospholipid systems that should be encompassed in the mechanistic molecular interpretation of the “hydration force.”