Rough hard spheres treatment of tracer diffusion of each component in two-component liquid systems

The rough hard spheres treatment of diffusion is extended to cover tracer diffusion of both species in five two-component organic liquid systems. Self-consistent results are obtained for the factor expressing coupling of translational-rotational motion and reasonable agreement is found where comparisons can be made with mutual diffusion data.     

Molecular dynamics study of the effect of atomic roughness on the slip length at the fluid-solid boundary during shear flow

A systematic study into the effect of solid roughness on the slip boundary condition during shear flow is presented. Atomic roughness is modeled by varying the size and spacing between solid atoms at constant packing fraction while the interaction parameters and the thermodynamic state of the fluid are kept constant. It is shown that the fluid structure as manifest in the amplitude of the density oscillations increases with increasing smoothness of the surfaces. The fluid-solid slip length is shown to exhibit nonmonotonic behavior as the solid structure is varied from smooth to rough. Slip occurs for both smooth and rough surfaces, and stick occurs only for surfaces commensurate with the fluid.     

A Model for Calculating Electrostatic Interactions between Colloidal Particles of Arbitrary Surface Topology

A numerical model for calculating the electrostatic interaction between two particles of arbitrary shape and topology is described. A key feature of the model is a generalized discretization program, capable of simulating any desired analytical shape as a set of flat, triangular elements. The relative sizes of the elements are adjusted using a density function to better match the desired shape and the spatial variation of the electrical surface properties on each particle. The distribution of either surface potential or surface charge density is then calculated using a boundary element approach to solve the linearized Poisson-Boltzmann equation. Example interaction energy profiles are calculated for three different types of roughness-bumps, pits, and surface waves. It is found that the interaction energy between rough particles remains different from that between two equivalent smooth spheres at all separations, even for gap widths much larger than either the solution Debye length or the characteristic roughness size. This behavior at large gap widths arises from the nature of the decay of the electric potential away from each particle. In addition, the magnitude of the roughness effect is found to depend greatly on the size and shape of the nonuniformity as well as the electrostatic boundary conditions. For example, for a sphere containing asperities of height equal to 0.2 times the particle radius, the interaction energy can be as much as 50% greater than that between two equivalent spheres under the condition of constant surface potential. At constant surface charge density, the ratio of the interaction energies between rough and smooth spheres was found to either diverge or become zero as contact between the two particles is approached, depending on the nature of the roughness. Changes of this magnitude could clearly have a substantial impact on the stability behavior of a dispersion of such particles. Copyright 2001 Academic Press.     

Mesoscopic model for diffusion-influenced reaction dynamics

A hybrid mesoscopic multiparticle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum, and energy so that hydrodynamic effects are fully taken into account. Reactive and nonreactive interactions with catalytic solute particles are described by full molecular dynamics. Results are presented for large-scale, three-dimensional simulations to study the influence of diffusion on the rate constants of the A + C <==> B + C reaction. In the limit of a dilute solution of catalytic C particles, the simulation results are compared with diffusion equation approaches for both the irreversible and reversible reaction cases. Simulation results for systems where the volume fraction phi of catalytic spheres is high are also presented, and collective interactions among reactions on catalytic spheres that introduce volume fraction dependence in the rate constants are studied.     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

Influence of boundaries of nanoporous crystals on molecular exchange under the conditions of single-file diffusion

We study the tracer exchange of molecules between the phase adsorbed in one-dimensional channels and the surrounding gas phase by molecular dynamics simulations. Under the conditions of single-file diffusion, a novel boundary effect is observed. The shape of the tracer-exchange concentration profiles deviates from those obtained under the conditions of normal diffusion. Compared to the profiles for normal diffusion, which correspond to the same degree of exchange, the equilibrium concentration is reached faster at the boundaries and slower in the middle part of the channel in the case of single-file diffusion. This boundary effect is observed for the system neopentane in AlPO4-5 (which was chosen as a reference system), as well as for modified systems. The effect can be understood considering two diffusion mechanisms which occur in parallel. First, the diffusion of the whole chain of particles, that is, the center-of-mass diffusion, obeying the laws of normal diffusion. Second, the individual movement of the particles relative to the center of mass of the chain. The second mechanism admits additional displacements which, on average, lead to an accelerated exchange of the marginal particles.     

Transport properties of the rough hard sphere fluid

Results are presented of a systematic study of the transport properties of the rough hard sphere fluid. The rough hard sphere fluid is a simple model consisting of spherical particles that exchange linear and angular momenta, and energy upon collision. This allows a study of the sole effect of particle rotation upon fluid properties. Molecular dynamics simulations have been used to conduct extensive benchmark calculations of self-diffusion, shear and bulk viscosity, and thermal conductivity coefficients. As well, the validity of several kinetic theory equations have been examined at various levels of approximation as a function of density and translational-rotational coupling. In particular, expressions from Enskog theory using different numbers of basis sets in the representation of the distribution function were tested. Generally Enskog theory performs well at low density but deviates at larger densities, as expected. The dependence of these expressions upon translational-rotational coupling was also examined. Interestingly, even at low densities, the agreement with simulation results was sometimes not even qualitatively correct. Compared with smooth hard sphere behaviour, the transport coefficients can change significantly due to translational-rotational coupling and this effect becomes stronger the greater the coupling. Overall, the rough hard sphere fluid provides an excellent model for understanding the effects of translational-rotational coupling upon transport coefficients.     

Prediction of collective diffusion coefficient of bovine serum albumin in aqueous electrolyte solution with hard-core two-Yukawa potential

A new method to predict concentration dependence of collective diffusion coefficient of bovine serum albumin (BSA) in aqueous electrolyte solution is developed based on the generalized Stokes-Einstein equation which relates the diffusion coefficient to the osmotic pressure. The concentration dependence of osmotic pressure is evaluated using the solution of the mean spherical approximation for the two-Yukawa model fluid. The two empirical correlations of sedimentation coefficient are tested in this work. One is for a disordered suspension of hard spheres, and another is for an ordered suspension of hard spheres. The concentration dependence of the collective diffusion coefficient of BSA under different solution conditions, such as pH and ionic strength is predicted. From the comparison between the predicted and experimental values we found that the sedimentation coefficient for the disordered suspension of hard spheres is more suitable for the prediction of the collective diffusion coefficients of charged BSA in aqueous electrolyte solution. The theoretical predictions from the hard-core two-Yukawa model coupled with the sedimentation coefficient for a suspension of hard spheres are in good agreement with available experimental data, while the hard sphere model is unable to describe the behavior of diffusion due to its neglect of the double-layer repulsive charge-charge interaction between BSA molecules.     

Structure factors in granular experiments with homogeneous fluidization

Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2D fluidized granular experiment, with packing fractions φ ∈ [10%, 40%]. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the "bath" temperature T(b), depending on shaking parameters, and the "granular" temperature T(g) < T(b), which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with φ, after proper rescaling with the mean free path.     

Tracer diffusion in colloidal gels

Computer simulations were done of the mean square displacement (MSD) of tracer particles in colloidal gels formed by diffusion or reaction limited aggregation of hard spheres. The diffusion coefficient was found to be determined by the volume fraction accessible to the spherical tracers (phi a) independent of the gel structure or the tracer size. In all cases, critical slowing down was observed at phi a approximately 0.03 and was characterized by the same scaling laws reported earlier for tracer diffusion in a Lorentz gas. Strong heterogeneity of the MSD was observed at small phi a and was related to the size distribution of pores.     

Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.     

Diffusion-controlled reactions: hydrodynamic interaction between charged, uniformly reactive spherical reactants

In this work, different models of hydrodynamic interaction (HI) are examined in the diffusion-controlled reaction between uniformly reactive charged spherical particles. In addition to Oseen "stick" and "slip" models of HI, one is considered that accounts for the disturbance of fluid flow by the ions around one reactive partner as they interact with a neighboring reactive species. This interaction is closely related to the "electrophoretic effect" in electrokinetics and can be described by a fairly simple electrophoretic, or E-tensor. These models are applied to the electron-transfer quenching reaction of Ru(bpy)3(2+) and methyl viologen (MV2+) over a wide range of NaCl concentrations (Chiorboli, C. et al., J. Phys. Chem. 1988, 92, 156). The back reaction is also considered. From a comparison of the salt dependence of the model and experimental rates, it is concluded that the "E-tensor" model works best and ignoring HI altogether works worst. The Oseen "stick" and "slip" models fall between these.     

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.     

Toward realistic modeling of dynamic processes in cell signaling: quantification of macromolecular crowding effects

One of the major factors distinguishing molecular processes in vivo from biochemical experiments in vitro is the effect of the environment produced by macromolecular crowding in the cell. To achieve a realistic modeling of processes in the living cell based on biochemical data, it becomes necessary, therefore, to consider such effects. We describe a protocol based on Brownian dynamics simulation to characterize and quantify the effect of various forms of crowding on diffusion and bimolecular association in a simple model of interacting hard spheres. We show that by combining the elastic collision method for hard spheres and the mean field approach for hydrodynamic interaction (HI), our simulations capture the correct dynamics of a monodisperse system. The contributions from excluded volume effect and HI to the crowding effect are thus quantified. The dependence of the results on size distribution of each component in the system is illustrated, and the approach is applied as well to the crowding effect on electrostatic-driven association in both neutral and charged environments; values for effective diffusion constants and association rates are obtained for the specific conditions. The results from our simulation approach can be used to improve the modeling of cell signaling processes without additional computational burdens.     

Structure and dynamics of short chain molecules in disordered porous materials: a molecular dynamics simulation study

The static and dynamic properties of short polymer chains in disordered materials are studied using discontinuous molecular dynamics simulations. The polymers are modeled as chains of hard spheres and the matrix is a collection of fixed hard spheres. The simulations show that the chain size is a nonmonotonic function of the matrix concentration for all polymer concentrations. The dependence of polymer diffusion D on the degree of polymerization N becomes stronger as the matrix concentration is increased. At high matrix concentrations we observe a decoupling between translational and rotational diffusion, i.e., the rotational relaxation time becomes very large but the translational diffusion is not affected significantly. We attribute this to the trapping of a small number of polymers. Under these conditions the polymer chains diffuse via a hopping mechanism.     

Attraction-driven disorder in a hard-core colloidal monolayer

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.     

Drag and Torque on Clusters of N Arbitrary Spheres at Low Reynolds Number

Hydrodynamics of particle clusters suspended in viscous fluids is a subject of considerable theoretical and practical importance. Using a multipole expansion of the flow velocity in a series of spherical harmonics, Lamb's fundamental solution of the Stokes flow outside a single sphere is generalized in this work to the case of N nonoverlapping spheres of arbitrary size with slip boundary conditions. The expansion coefficients are found by transforming the boundary conditions to the Lamb form and by transforming the spherical coordinates and solid spherical harmonics centered at different spheres. The problem is reduced to the solution of the linear system of equations for the expansion coefficients, which is carried out numerically. Based on the developed theory, the relation between the hydrodynamic and gyration radius of fractal-like aggregates with different structure is established. In another application, an asymptotic slip-regime dependence of the aggregate hydrodynamic radius on the Knudsen number and the number of particles is found by performing calculations of drag forces acting on the gas-borne fractal-like and straight chain aggregates. A good agreement is shown in comparing predictions of the described theory with available experimental and theoretical results on motion of various small sphere clusters in viscous fluid. Copyright 2000 Academic Press.     

Theoretical approaches of stability ratio on concentrated colloidal dispersed system

In the theory dealt with in this article, it is assumed that colloidal particles are smooth rigid spheres, their collisions are instantaneous, the probability of multiple encounter is negligible, and the increase of the probability of collisions depends on the radial distribution function in local equilibrium. A simple formula is obtained for the stability ratio in highly concentrated colloid. Good correspondence between theoretical predictions and experiments is shown.