Pair diffusion in quasi-one- and quasi-two-dimensional binary colloid suspensions

The authors report the results of measurements of the center of mass and relative pair diffusion coefficients in quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D) binary colloid suspensions. The new results extend the findings of similar studies of one-component quasi-one-dimensional and quasi-two-dimensional colloid suspensions. Our principal new finding is that the presence of the smaller diameter component can destroy the oscillatory structure of the separation dependence of the q2D relative pair diffusion coefficient of the large particles even though the oscillatory character of the large particle equilibrium pair correlation function remains prominent, and that no such effect occurs with the q1D suspension. An interpretation of these results is proposed.     

Influence of a depletion interaction on dynamical heterogeneity in a dense quasi-two-dimensional colloid liquid

We report the results of digital video microscopy studies of the large particle displacements in a quasi-two-dimensional binary mixture of large (L) and small (S) colloid particles with diameter ratio sigma(L)/sigma(S)=4.65, as a function of the large and small colloid particle densities. As in the case of the one-component quasi-two-dimensional colloid system, the binary mixtures exhibit structural and dynamical heterogeneity. The distribution of large particle displacements over the time scale examined provides evidence for (at least) two different mechanisms of motion, one associated with particles in locally ordered regions and the other associated with particles in locally disordered regions. When rhoL*=Npisigma(L) (2)/4A< or =0.35, the addition of small colloid particles leads to a monotonic decrease in the large particle diffusion coefficient with increasing small particle volume fraction. When rhoL* > or =0.35 the addition of small colloid particles to a dense system of large colloid particles at first leads to an increase in the large particle diffusion coefficient, which is then followed by the expected decrease of the large particle diffusion coefficient with increasing small colloid particle volume fraction. The mode coupling theory of the ideal glass transition in three-dimensional systems makes a qualitative prediction that agrees with the initial increase in the large particle diffusion coefficient with increasing small particle density. Nevertheless, because the structural and dynamical heterogeneities of the quasi-two-dimensional colloid liquid occur within the field of equilibrium states, and the fluctuations generate locally ordered domains rather than just disordered regions of higher and lower density, it is suggested that mode coupling theory does not account for all classes of relevant fluctuations in a quasi-two-dimensional liquid.     

Schulz distribution function and the polydispersity of the binary suspension of charged macroions

Bidispersity of binary suspensions of charged macroions due to different sizes and charges are reduced into one-component model (OCM) using Schulz distribution function. Ordering in charged macroions has been studied using rescaled mean spherical approximation (RMSA) method with modified Derjaguin, Landau, Verwey and Overbeek (DLVO) potential. The results obtained are compared with the experiment, weight-average and Roger–Young (RY) schemes. It is inferred that Schulz distribution function is a plausible model to average out size and charges of macroions to study the structural behavior of the binary suspension of macroions. An ordering with co-ordination number 12 has been reported in the binary suspension of charged macroions.     

A new model system for diffusion NMR studies of concentrated monodisperse and bidisperse colloids

A method to prepare monodisperse and simultaneously NMR-visible and fluorescent colloidal particles is described, and a systematic approach to obtain spectrally resolved diffusion coefficient for every component in a monodisperse colloidal suspension is presented. We also prepared bidisperse colloidal suspensions, where each colloid component has a distinct NMR spectral signature, and obtained the diffusion coefficients of both colloid species simultaneously in concentrated colloidal suspensions, with volume fractions between 20 and 50%. The colloidal model system developed in this work enables the study of colloidal phase behavior in binary mixtures for different number and size ratios.     

Monte Carlo study of four dimensional binary hard hypersphere mixtures

A multithreaded Monte Carlo code was used to study the properties of binary mixtures of hard hyperspheres in four dimensions. The ratios of the diameters of the hyperspheres examined were 0.4, 0.5, 0.6, and 0.8. Many total densities of the binary mixtures were investigated. The pair correlation functions and the equations of state were determined and compared with other simulation results and theoretical predictions. At lower diameter ratios the pair correlation functions of the mixture agree with the pair correlation function of a one component fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.     

Structure and aggregation of colloids immersed in critical solvents

We consider an ensemble of spherical colloidal particles immersed in a near-critical solvent such as a binary liquid mixture close to its critical demixing point. The emerging long-ranged fluctuations of the corresponding order parameter of the solvent drive the divergence of the correlation length. Spatial confinements of these critical fluctuations by colloidal solute particles, acting as cavities in the fluctuating medium, restrict and modify the fluctuation spectrum in a way which depends on their relative configuration. This results in effective, so-called critical Casimir forces (CCFs) acting on the confining surfaces. Using the available knowledge about CCFs we study the structure and stability of such colloidal suspensions by employing an approach in terms of effective, one-component colloidal systems. Applying the approximation of pairwise additive CCFs we calculate the radial distribution function of the colloids, which is experimentally accessible. We analyze colloidal aggregation due to CCFs and thus allude to previous experimental studies which are still under debate.     

Preparation of stable aqueous suspensions of antimony-doped tin oxide nanoparticles used for transparent and thermal insulation fluorocarbon coating

In order to prepare the highly stable aqueous suspensions of antimony-doped tin oxide (ATO) used for the transparent and thermal insulation fluorocarbon coating, the effect of sodium polyacrylate (PAAS) and polyvinyl alcohol (PVA) on the stability of the suspensions was investigated. The stability and dispersity of the suspensions were characterized using zeta potential analyzer, ultraviolet–visible spectrophotometer, and scanning electron microscope. No sediments were observed after 6-month storage of the ATO suspensions containing 0.1 wt% PAAS and 2.0 wt% PVA. The reason why aqueous suspensions were capable of stabilization was explained from a theoretical perspective. A new model of steric hindrance for colloid particles stabilized by binary dispersant was proposed, which may have positive contribution to other colloid system containing two dispersants. A nano-composite fluorocarbon coating, exhibiting a good thermal insulation and high transmittance, was formed after ATO suspensions were added in fluorocarbon emulsion. The temperature inside the chamber was decreased by 6.0 °C, and 75.0 % visible light rays could pass through the coating.     

Ordering in linear multipolar colloids driven by an external field

An approach to describe a linear multipolar colloid driven by an external field is developed by considering a colloid which in absence of the field is low structured and its coupling potential is axially symmetric. The equilibrium correlation of one component of the orientation tensor, self and collective, is computed up to linear order in density, which can be measured in an appropriate light scattering experiment. The self-correlation is written in terms of the second and fourth order parameters. All the equilibrium quantities are computed up to two-body level. This is done by assuming that the two-body equilibrium density function is given by the Boltzmann distribution, whereas the one-body density function is computed as solution of the equilibrium N-body Smoluchowski equation in the absence of hydrodynamic interactions. These observables, self and collective, as well as the second and fourth order parameters are able to describe when the colloid would evolve to an orientationally ordered phase. Explicit results for the dipole and quadrupole moments are reported. These results predict a different alignment with the external field for each moment. A relationship is provided between second and fourth order parameters, predicting the critical value of the external field in which the colloid goes into an axially symmetric phase.     

Hydrogen-bonded clusters on the vapor/ethanol-aqueous-solution interface

The structure of the vapor/ethanol-aqueous-solution interface has been carefully investigated focusing on an intermolecular hydrogen bond (HB) and molecular clusters bound by HBs. This paper is a continuation of our previous molecular dynamics (MD) study (Langmuir 2005, 21, 10885), and all analysis was performed based on five independent adsorption-equilibrated configurations of a slab of ethanol solution at 298.15 K, where the ethanol mole fraction of the solution, chi(e), is 0.0052, 0.012, 0.024, 0.057, and 0.12, respectively. The geometrical definition of HB enabled the detection of the HB between ethanol-ethanol, ethanol-water, and water-water molecules. The variations of the density of HB and the coordination number of HB across the vapor/solution interface were analyzed. Analysis on the density of HB reveals that a monolayer of adsorbed ethanol can be classified into two parts where ethanol molecules prefer to form HBs with each other and ethanol molecules prefer to form HBs with water molecules. Despite chi(e), the coordination number of ethanol-ethanol HB monotonically increases toward the vapor region, while those of ethanol-water and water-water HBs monotonically decrease. In addition, the variation of the mean size of both ethanol one-component clusters and ethanol/water binary clusters across the interface were analyzed. The mean size of an ethanol one-component cluster and that of an ethanol/water binary cluster are expressed as a maximum at the interface. These behaviors are linked with the size distributions of both one-component and binary clusters. A relatively large system in this calculation also enables detailed discussion about the molar dependency of the bulk structural properties of an ethanol solution.     

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.     

Electron localizability indicator for correlated wavefunctions. III: singlet and triplet pairs

The electron pair density can be decomposed into the symmetric and antisymmetric parts. The antisymmetric component is connected with the probability that two electrons are coupled to a triplet. On the basis of triplet-coupled electrons the electron localizability indicator is defined, describing the correlation of motion of electrons forming a triplet pair. In case of spin-polarized systems the electron localizability indicator for triplet pairs combines the two spin channels together into a single functional.     

Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions

We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the possibility of phase coexistence between two phases of colloidal suspensions, one being rich and the other being poor in colloidal particles. The reliability of this effective approach is discussed.     

Transient ordering in a quasi-two-dimensional liquid near freezing

We report the results of a theoretical study of locally ordered fluctuations in a quasi-two-dimensional colloid fluid. The fluctuations in the equilibrium state are monitored by the aperture cross-correlation function of radiation scattered by the fluid, as calculated from molecular dynamics simulations of near hard spheres with diameter sigma confined between smooth hard walls. These locally ordered fluctuations are transient; their decay can be monitored as a function of the time between the cross-correlated scattered radiation signals, but only the single-time cross-correlated signals are discussed in this paper. Systems with thicknesses less than two hard sphere diameters were studied. For wall separation H in the range 1 sigma/=1.57 sigma, hexagonal fluctuations persist in the dense liquid up to H=1.75 sigma, and fluctuations with square ordered symmetry, that of the solid to which the liquid freezes, only emerge at densities approximately 2% below freezing. For H=1.8 sigma and 1.85 sigma, hexagonal ordered flucuations are no longer found, and the square ordered fluctuations dominate the dense liquid region as the system freezes into a two layer square solid. For H=1.9 sigma and 1.95 sigma, where the liquid freezes into a two layer hexagonal solid, both square and hexagonal ordered fluctuations are observed. At lower densities, the ordered fluctuations only exhibit square symmetry. Hexagonal ordered fluctuations appear at densities approximately 7% below freezing and become more dominant as the density is increased, but the square ordered fluctuations persist until the system is converted into the solid.     

Surface clusters of colloid particles produced by deposition on sites

The possibility of producing surface clusters of well-defined structure formed by colloid particles was analyzed theoretically and experimentally. Theoretical results were derived by performing Monte Carlo-type simulations according to the generalized random sequential adsorption (RSA) mechanism. In these simulations, the jamming coverage of particles adsorbing irreversibly on spherical sites was determined as a function of the particle-to-site size ratio lambda. It was revealed that, by properly choosing lambda, a targeted site coordination can be achieved; for example, there can be one, two, three, and so forth particles attached to one site. The structure of the heterogeneous clusters produced in this way was described in terms of the pair correlation function. It was predicted that the extent of ordering within surface clusters was diminished as the concentration of sites increased. These theoretical predictions were checked by performing deposition experiments of negatively charged polystyrene latex particles (average diameter 0.9 mum) under the diffusion-controlled transport regime. Mica sheets precovered by positively charged polystyrene latex (average diameters 0.45 and 0.95 microm) were used as the substrate surface in these experiments. Positive latex (site) deposition was also carried out under diffusion-controlled transport conditions. The concentration of the sites and the adsorbed particles was determined by direct particle counting using optical microscopy. It was found, in quantitative agreement with theoretical simulations, that the structure of surface clusters produced in this way exhibits a significant degree of short-range ordering. It also was proven experimentally that clusters containing a targeted number of colloid particles (e.g., 2 and 4) could be produced by the deposition procedure.     

Effective interactions in colloid-semipermeable membrane systems

We investigate effective interactions between a colloidal particle, immersed in a binary mixture of smaller spheres, and a semipermeable membrane. The colloid is modeled as a big hard sphere, and the membrane is represented as an infinitely thin surface, which is fully permeable to one of the smaller spheres and impermeable to the other one. Within the framework of the density functional theory, we evaluate depletion potentials and we consider two different approximate theories: the simple Asakura-Oosawa approximation and the accurate White-Bear version of the fundamental measure theory. The effective potentials are compared with the corresponding potentials for the hard, nonpermeable wall. Using statistical-mechanical sum rules, we argue that the contact value of the depletion potential between a colloid and a semipermeable membrane is smaller in magnitude than the potential between a colloid and a hard wall. A heuristic argument is provided that the colloid-semipermeable membrane effective interactions are generally weaker than these near a hard nonpermeable wall. These predictions are confirmed by explicit calculations, and the effect is more pronounced for smaller osmotic pressures. The depletion potential for a colloidal particle inside a semipermeable vesicle is stronger than the potential for the colloidal particle located outside of a vesicle. We find that the asymptotic decay of the depletion potential for the semipermeable membrane is similar to that for the nonpermeable wall and reflects the asymptotics of the total correlation function of the corresponding binary mixture of smaller spheres. Our results demonstrate that the ability of the membrane to change its shape as well as specific interactions constitute an important factor in determining the effective interactions between the semipermeable membrane and the colloidal macroparticle.     

Effect of polymer size and chain length on depletion interactions between two colloids

A density functional theory based on the weighted density has been developed to investigate the depletion interactions between two colloids immersed in a bath of the binary polymer mixtures, where the colloids are modeled as hard spheres and the polymers as freely jointed tangent hard-sphere chain mixtures. The theoretical calculations for the depletion forces between two colloids induced by the polymer are in good agreement with the computer simulations. The effects of polymer packing fraction, degree of polymerization, polymer/polymer size ratio, colloid/polymer size ratio on the depletion interactions, and colloid-colloid second virial coefficient B2 due to polymer-mediated interactions have been studied. With increasing the polymer packing fraction, the depletion interaction becomes more long ranged and the attractive interaction near the colloid becomes deeper. The effect of degree polymerization shows that the long chain gives a more stable dispersion for colloids rather than the short chain. The strong effective colloid-colloid attraction appears for the large colloid/polymer and polymer/polymer size ratio. The location of maximum repulsion Rmax is found to appear Rmax approximately sigmac+Rg2 for the low polymer packing fraction and this is shifted to smaller separation Rmax approximately sigmac+sigmap2 with increasing the polymer packing fraction, where sigmap2 and Rg2 are the small-particle diameter and the radius of gyration of the polymer with the small-particle diameter, respectively.     

Rejection-free Monte Carlo scheme for anisotropic particles

We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed.     

The rheology and microstructure of charged colloidal suspensions

The effects of electric charge interation and particle correlations on suspension rheology are examined. A one-component fluid analysis using a Smoluchowski equation for the equilibrium structure is applied to charged suspensions of spherical colloids under shear. The frequency dependent modulus and viscosity, predicted as functions of particle and added salt concentrations, are compared with published rheological measurements on model suspensions. Recent improvements in the statistical mechanical theories for the equilibrium microstructure, its nonequilibrium deformation, and the bulk shear stresses are included. The direct electrostatic interaction is found to drive the divergence in the shear viscosity near the liquid-solid phase transition. Extensions of the theory predict the elastic modulus of binary mixtures of charged colloids. Estimates of the primary electroviscous effect, hydrodynamic interactions, and errors in the Yukawa limiting form for the potential and applications of asymptotic theories are presented. Predictions for the rheology based on effective hard-sphere models are found to be reasonable when using a parameter fit from the equilibrium phase behavior. Mean-field mode coupling theories predict larger relaxation times than calculated from the Smoluchowski equation (=SE). A study of binary mixing effects on elasticity shows non-ideal behavior. It is noted that equilibrium structural information can be used to resolve discrepancies between the theoretical predictions and the measured rheology.