Adhesive Hard Sphere Research Articles

Features of Fluid Mixtures of Adhesive Charged Hard Spheres

In a fluid mixture system (FMS) containing adhesive charged hard spheres (ACHSs) and ionic species, a state in which an ACHS is contacted by other ACHSs can significantly contribute to the thermodynamics, so that the mean number < N 00 > of the nearest neighors of each ACHS is remarkable. This mean number < N 00 > have been examined with the thermodynamics. The mean number < N 00 > and the electrostatic contributions to the thermodynamics can be described using four dimensionless parameters, when the size of the ionic species can be neglected. As a result, it is found that < N 00 > and the electrostatic contributions, which are evaluated in an FMS where ACHSs dispersed with pointlike-ionic species are highly charged, can be equivalent to those evaluated in another FMS where ACHSs dispersed with pointlike-ionic species are no highly charged.

Mathematical comment on adhesive hard sphere models for fluids

A mathematical discussion is provided on the relationship between Baxter's adhesive hard sphere fluid and the hard sphere Yukawa fluid with sufficiently strong and short range attractive Yukawa tails. It is proved that the Percus-Yevick approximate solution of the Ornstein-Zernike equation for the former fluid can be included mathematically in the generalized mean-spherical approximation solution with the Yukawa closure, and the equivalence conditions of both solutions are presented.

Mathematical comment on adhesive hard sphere models for fluids

Mathematical comment on adhesive hard sphere models for fluids

Phase behavior of small attractive colloidal particles.

The crystallization boundaries of small, attractive particles are found to be identical when interactions are modeled as adhesive hard spheres. Based on experimental results and the attraction range, we conclude that solubility is insensitive to interaction details and various colloidal particles will only display equilibrium colloidal fluid and colloidal crystal equilibrium phases. This study provides a basis for the observations of George and Wilson [Acta Crystallogr. D 50, 361 (1994)] who suggest using second virial coefficient measurements to identify protein crystallization conditions.

Interactions and Phase Behavior of Nanosized Particles

As the concentration of silicotungstate particles (SiW12O404-) is increased at fixed background electrolyte concentration, the suspension separates into a dense, crystalline colloidal phase in equilibrium with a dilute colloidal liquid. The solubility of the particles ranges from 2.67 to 0.2 g/mL as the background 1:1 electrolyte concentration increases from 0 to 5 M. The second virial coefficient of suspensions of silicotungstate particles is a decreasing function of electrolyte concentration and, if interpreted in terms of square well or adhesive hard sphere pair potentials, suggests the particles' feel attractions are on the order of 0−2kT at the phase boundary. Despite attractions of sufficient strength, colloidal gas/colloidal liquid phase transitions are not observed. These results are interpreted as indicating particles feel an attraction with an extent which is much smaller than the core particle diameter.

Static structure factor and collective diffusion of globular proteins in concentrated aqueous solution

We report our measurement of the time average and the temporal autocorrelation function of the intensity of light scattered by the highly monomeric globular protein, bovine γII-crystallin, in aqueous solution as a function of wave number q, protein volume fraction φ, and temperature T. The time average intensity data is used to obtain the q→0 limit of the static structure factor S(φ,T), as a function of φ and T. We show that S(φ,T) may be well characterized by modeling the proteins as interacting through the Baxter adhesive hard sphere pair interaction potential. The temporal autocorrelation function data is used to determine the collective diffusion coefficient D̃(φ,T) of the proteins as a function of φ and T. We then obtain the experimental hydrodynamic factor H̃(φ,T)≡S(φ,T)[D̃(φ,T)/D0(T)], where D0(T) is the diffusion coefficient of the individual proteins in the φ→0 limit. We find that H̃ exhibits a different φ-dependence at low (φ≤0.016) and high (φ≳0.02) protein volume fractions. In the low φ domain our data for H̃ are consistent with the theoretical result for the collective diffusion in the q→0, t→0 limit. However, for φ≳0.02 we find a deviation from single exponential decay in the autocorrelation functions, and an unexpected, large change in the slope of the H̃ vs φ relation. This crossover at such low φ suggests the existence of a heretofore unappreciated length scale in the dynamics of colloid solutions. Clearly, further theoretical insights are required to understand the origin of this crossover behavior.

Solution of the associative Percus-Yevick approximation for the multicomponent mixture of dimerizing hard spheres with surface adhesion

An analytical solution of the two-density Ornstein-Zernike equation closed by the associative Percus-Yevick approximation for the multicomponent mixture of dimerizing adhesive hard spheres (DAHS) is obtained in closed form. This is the generalization of the previous solution for the one-component DAHS model, which has been proposed for the description of protein effect on the properties of reverse micelles. Although the solution is illustrated by its application to the structure of the two-component model, it can be easily utilized for the arbitrary number of components.

Structure of colloidal dispersions with an attractive primary minimum and far-field repulsion in the pair-potential: Adhesive-hard-sphere and random-phase approximations

An analytical method to estimate the static structure factors of charged dispersions dominated by the presence of primary minima in the interparticle potentials is presented. the near-field attraction is approximated by square-well potentials and the far-field repulsion by Yukawa tails. Analytical representation of the structure factor is obtained for the square-well/Yukawa (SWY) dispersions using an adhesive-hard-sphere (AHS) reference and random-phase approximation (RPA). The accuracy of the AHS + RPA combination in predicting structure factors of SWY fluids is examined using Monte Carlo simulations for the SWY fluids over a range of conditions. The results show that AHS + RPA describes the structure factors very well at low to moderately high volume fractions when the range of the square-well potential is less than 10% of the particle diameter and that of the Yukawa tail is sufficiently large. At high volume fractions the AHS + RPA results agree well with those of simulations in the low- q region, but deviate appreciably in the high- q region. At low volume fractions, the model can be applied to even relatively long-ranged Yukawa repulsive interactions. These results provide an unambiguous test of the AHS + RPA model. The AHS + RPA model has been found to describe small-angle neutron scattering intensities of a micellar system consisting of cationic dodecyl tributylammonium bromide surfactant in water and D 2O reasonably well.

Linear viscoelasticity in dispersions of adhesive hard spheres

The viscoelastic behavior of concentrated dispersions of adhesive hard spheres was investigated. By changing the temperature, the interaction potential of the particles was varied from a hard sphere repulsion to a strong attraction. Using torsion resonators and a nickel tube resonator the complex viscosity was measured in the frequency range 70–250 000 Hz. The results were described on the basis of a simple mechanical model in terms of a series of relaxation times and a single relaxation strength. The temperature dependence of the longest relaxation time and the relaxation strength indicated that the system undergoes a kinetic transition with decreasing temperature. The transition could be identified with the percolation threshold. Above the transition temperature where the dispersion is in a stable, fluid state, linear viscoelastic behavior is observed. Below the percolation threshold but still in the one-phase region, nonlinear viscoelasticity was measured, even at the smallest strains.

Adhesive-hard-sphere approximation for the structure of square-well fluids: application to colloidal dispersions

The accuracy of the adhesive-hard-sphere (AHS) model in representing structure factors of the short-range square-well potentials is examined by comparing theoretical predictions with Monte Carlo simulations for the square-well fluids over a range of conditions. We show that the analytical solution for the structure factors of the AHS model can be used to describe structure factors of the square-well potential adequately at low to moderate volume fractions (ϕ < 0·26) when the range of the square-well potential is less than 20% of the particle diameter and the magnitude of the contact potential is less than 3. At low values of the width of the square well (less than 5% of the particle diameter), the AHS model can be applied to even larger values of the contact potential and to higher volume fractions. We also show that the AHS model can be used to describe accurately structure factors of the non-ionic micro-emulsions and inverted micellar systems containing sodium bis 2-ethylhexyl-sulphosuccinate (aerosol-O...

Stability diagrams for colloidal dispersions with attractive interactions: An analytical approximation

We show that a single-parameter, adhesive-hard-sphere (AHS) model can be used to estimate, analytically, the stability diagrams for colloidal dispersions interacting through fairly long-range attractive forces. The use of the model is illustrated for polymer-induced depletion interactions. Analytical expressions are given for the static structure factors, pressures and chemical potentials in terms of the adhesiveness parameter of the AHS model. The adhesiveness parameter is obtained as a function of the relevant parameters appropriate for the actual interaction forces using the second virial coefficient (which can be measured experimentally using scattering techniques). It is shown that both upper-critical and lower-critical stability domains can be predicted, in addition to static structure factors. The results presented are consistent with the predictions based on more elaborate statistical mechanical theories.

Freezing of adhesive hard spheres.

A theoretical study of the freezing of adhesive hard spheres within the generalized-effective-liquid approximation has been performed. The liquid-solid phase diagram exhibits most of the trends observed for simple liquids. There is, however, no triple point because the solid phase becomes mechanically unstable iii the region where the liquid-solid transition crosses the percolation transition. A useful closed-form expression for the free energy of the fluid phases is also given.

Changes in milk on heating: viscosity measurements

SummarySkim milk was heated at 85 °C for different holding times. As a result of such heating, whey proteins, in particular β-lactoglobulin, denatured and associated with casein micelles. This led to an increase in size of the casein micelles but also to a different interaction between them. Both these changes could be described by using a quantitative model which was developed for the viscosity of so-called adhesive hard spheres. We applied the model successfully to skim milk and were able to describe on a quantitative basis the changes due to the heat treatment of milk. It was shown that after heating the casein micelles became larger and acquired a mutual attraction. The unfolding of the whey proteins and their subsequent association with the casein micelles appeared to be responsible for these changes. How this reaction influences the fouling of heat exchangers is discussed.

The Turbidity of Renneted Skim Milk

The turbidity of skim milk dispersions was measured in a spectrophotometer at four different wavelengths and at various dilutions. After adding rennet to milk the transmission (∼exp(-turbidity)) of the samples decreases gradually. This decrease in transmission, which depends on the volume fraction of the micelles and the wavelength of the light used, is caused by the interactions between the micelles. During the renneting the interactions change from repulsive to attractive and can be characterized by the second osmotic virial coefficient. Before the rennet is added to the milk the casein micelles can be characterized as hard spheres for which B′ 2 = 4 V HS, where V HS is the (excluded) volume of a hard sphere. Renneting causes the casein micelles to lose their colloidal stability and B′ 2 decreases strongly. The micelle interaction can be described by the so-called adhesive hard sphere model, also called the "sticky" sphere model. A theory is presented which quantitatively describes the changes in transmission on renneting in the initial stages.

The shear‐distorted microstructure of adhesive hard sphere dispersions: A small‐angle neutron scattering study

In a small‐angle neutron scattering experiment, we measured the shear‐distorted microstructure of a concentrated model dispersion of adhesive hard spheres in the low shear rate regime (Pe≤1) using a couette shear cell. The nonequilibrium structure factor was probed in the velocity–vorticity plane. By changing the temperature, the interaction potential of the particles was varied from a hard sphere repulsion to a strong attraction. The particle distribution which is isotropic at rest, is anisotropically disturbed by the shear flow. At high temperatures, the dispersion is effectively a hard sphere system. In this case the main distortion of the scattering pattern is in the direction of the fluid flow, the shear flow shifts the first maximum in the structure factor toward smaller scattering angles. In the vorticity direction, no significant distortion of the equilibrium structure is observed. Qualitative agreement is found with theoretical predictions for the shear‐distorted structure factor. With decreasing...

Spinodal decomposition in a sterically stabilized colloidal silica dispersion following from quench experiments

Time-resolved light scattering at different quench depths is used to elucidate the kinetics of phase separation in a sterically stabilized colloidal dispersion with volume fractions up to 0.25 near the critical volume fraction and in the off-critical range. The early stage of spinodal decomposition is explicable in terms of the linearized Cahn-Hilliard theory. The late stage follows the power law relation with exponents close to 1 and - 1 3 predicted by the cluster theory of Binder and Stauffer. The trend of self-similarity is also observed in our experiments. The obtained spinodal curve following from the quench experiments are compared to the theory of adhesive hard spheres. The agreement between the experimental curve and the theoretical one is quite reasonable. Our contribution to this special issue of Advances in Colloid and Interface Science is dedicated to professor Overbeek on the occasion of his eightieth birthday in 1991. Stability (caused by electrostatic or steric interactions) in colloidal systems played a central part in his field of research. His enthusiasm and interest in a wide area of the physical chemistry of colloids and surfaces have stimulated many of us in our field of research. We hope that this paper will please him.

Pulse-induced critical scattering on sterically stabilized colloidal silica dispersions

Pulse-induced critical scattering (PICS) is used to explore the onset of phase separation in sterically stabilized colloidal silica dispersions up to high volume fractions of about 0.30. PICS proves to be a very useful technique in measuring spinodals of these silica systems, while operating in the metastable region of the phase diagram. The obtained spinodal curves are compared with the theory of adhesive hard spheres. The agreement between the experimental curves and the theoretical ones is quite reasonable.

Solvation interactions in colloidal dispersions using the adhesive hard sphere model

Colloidal particles dispersed in a liquid are modelled by a binary mixture of large spheres in a “solvent” of small spheres; so the discrete nature of the solvent molecules is explicitly taken into account. It is shown in the Percus-Yevick approximation that, following the adhesive hard sphere model, the effective repulsion between the large particles decreases by increasing the stickness between the solvent molecules (simulation of a “poor” solvent). The isothermal osmotic compressibility goes to infinity when the adhesive strength between the solvent becomes very high and phase separation may occur. By increasing the stickness between the solvent and large solute particles the effective repulsion between the solute particles increases, which can be interpreted as a better solvation of the particles.

The rheology of adhesive hard sphere dispersions

The influence of an attractive interparticle potential on the rheology of a sterically stabilized silica dispersion was investigated. Using a marginal solvent, there was an effective attraction between the particles which depended on the temperature. Three experiments in which different properties of the dispersion were probed showed that a square well model can be used to describe the temperature dependence of the pair potential. The turbidity of a dilute dispersion was measured as a function of the volume fraction and the temperature. Using dynamic light scattering techniques, the effect of the strength of the interparticle attraction on the diffusion coefficient was investigated. Furthermore, the steady shear viscosity was measured as a function of the volume fraction and the temperature. A microscopic theory for the low shear viscosity of a semidilute dispersion of adhesive hard spheres was successfully used to determine the interaction parameters. Viscosity measurement on dense suspensions showed that while the system is still in the one-phase state, temporal aggregates are formed by the interparticle forces which are disrupted by both shear and Brownian motion of the particles. The shear thinning behavior of a concentrated dispersion of adhesive hard spheres scales in a dimensionless shear stress. This group is the ratio of the forces, arising from the shear and the interparticle potential.

A turbidity study on colloidal silica particles in concentrated suspensions using the polydisperse adhesive hard sphere model

A new type of analysis of turbidimetric measurements is proposed for concentrated sterically stabilized colloidal dispersions. It is applied to dispersions of silica spheres, coated with stearylalcohol in aromatic solvents up to high volume fractions of 0.30–0.40. Baxter’s polydisperse adhesive hard sphere model is used to explain the results. Influence of diameter, stickiness, and polydispersity in diameter on turbidity will be discussed. Model calculations fit the experimental curves very well up to high volume fractions and from the data it can be concluded that there exists a small attraction between the particles.