Application of the extended RSA models in studies of particle deposition at partially covered surfaces

This paper reviews the application of the extended random sequential adsorption (RSA) approaches to the modeling of colloid-particle deposition (irreversible adsorption) on surfaces precovered with smaller particles. Hard (noninteracting) particle systems are discussed first. We report on the numerical simulations we performed to determine the available surface function, jamming coverage, and pair-correlation function of the larger particles. We demonstrate the effect of the particle size ratio and the small particle surface coverage. We found that the numerical results were in reasonable agreement with the formula stemming from the scaled-particle theory in 2D with a modification for the sphere geometry. Next, we discuss three approximate models of adsorption allowing electrostatic interaction of colloid particles at a charged interface, employing a many-body superposition approximation. We describe two approaches of the effective hard-particle approximation next. We demonstrate the application of the effective hard-particle concept to the bimodal systems and present the effect of electrolyte concentration on the effective particle size ratio. We present the numerical results obtained from the theoretical models of soft-particle adsorption at precovered surfaces. We used the effective hard-particle approximation to determine the corresponding simpler systems of particles, namely the system of hard spheres and the system of hard discs at equilibrium. We performed numerical computations to determine the effective minimum particle surface-to-surface distance, available surface function, jamming coverage, and pair-correlation function of the larger particles at various electrolyte ionic strengths and particle size ratios. The numerical results obtained in the low-surface coverage limit were in good agreement with the formula stemming from the scaled-particle theory with a modification for the sphere geometry and electrostatic interaction. We compared the results of numerical computations of the effective minimum particle surface-to-surface distance obtained using the 2D, 3D, and curvilinear trajectory model. The results obtained with the 3D and curvilinear trajectory models indicate that large-particle/substrate attractive interaction significantly reduces the kinetic barrier to large, charged-particle adsorption at a surface precovered with small, like-charged particles. The available surface function and jamming-coverage values predicted using the simplified 3D and the more sophisticated curvilinear trajectory models are similar, while the results obtained with the 2D model differ significantly. The pair-correlation function suggests different structures of monolayers obtained with the three models. Unlike the three models of the electrostatic interaction, both effective hard-particle approximations give almost identical results. Results of this research clearly suggest that the extended RSA approaches can fruitfully be exploited for numerical simulations of colloid-particle adsorption at precovered surfaces, allowing the investigation of both hard and soft-particle systems.     

High density silver nanoparticle monolayers produced by colloid self-assembly on polyelectrolyte supporting layers

A stable silver nanoparticle suspension was synthesized via the reduction of silver nitrate using sodium borohydride and sodium citrate. The particle's shape and size distribution were measured by various methods. The electrophoretic mobility measurements revealed that the zeta potential of particles was highly negative, increasing slightly with the ionic strength, from -52 mV for I=10(-5) M to -35 mV for I=3×10(-2) M (for pH=5.5). The zeta potential of mica modified by the adsorption of cationic polyelectrolytes: PEI and PAH was also determined using the streaming potential measurements. The modified mica sheets were used as substrates for particle monolayers formed via colloid self assembly. The kinetics of this process, proceeding under diffusion-controlled transport conditions, was quantitatively evaluated by a direct enumeration of particles using the AFM and SEM techniques. Both the kinetics of particle deposition and the maximum surface concentration were determined. From the slope of the initial deposition rates, the equivalent diameter of particles was determined to be 16 nm, in agreement with previous measurements. Based on this finding, an efficient method of determining particle size in suspension was proposed. It was also demonstrated that for higher ionic strengths, the maximum coverage of particle monolayers on PAH modified mica exceeded 0.39. The kinetic data were quantitatively interpreted in terms of the random sequential adsorption (RSA) model using the effective hard particle concept.     

Adsorption and desorption of colloidal particles on glass in a parallel plate flow chamber—Influence of ionic strength and shear rate

The adsorption and desorption rates of 736 nm diameter polystyrene particles on glass were studiedin situ using a parallel plate flow chamber and automated image analysis. Adsorption and desorption rates were measured simultaneously during deposition, enabling the determination of initial deposition rates, blocked areas per particle, desorption rate coefficients, and the number of adhering particles in the stationary state. Deposition experiments were done from suspensions with different potassium nitrate concentrations (1, 10 and 50 mM) and at varying shear rates (15 to 200 s^–1). The initial deposition rate, the desorption rate, the blocked area per particle and the number of adhering particles in the stationary state showed major variations with the shear rate and the ionic strength of the suspension. At low ionic strength, the number of adhering particles showed an oscillatory behavior in time, presumably due to a varying interaction between particle and collector surface. Blocked areas, determined from deposition kinetics, ranged 705 to 2374 cross-sections at low ionic strength, and from 10 to 564 at high ionic strength and corresponded well with those estimated from local pair distribution functions which were obtained from an analysis of the spatial arrangement of the adhering particles.     

A novel equation of state for the prediction of thermodynamic properties of fluids

This work proposes a new equation of state (EOS) based on molecular theory for the prediction of thermodynamic properties of real fluids. The new EOS uses a novel repulsive term, which gives the correct hard sphere close packed limit and yields accurate values for hard sphere and hard chain virial coefficients. The pressure obtained from this repulsive term is corrected by a combination of van der Waals and Dieterici potentials. No empirical temperature functionality of the parameters has been introduced at this stage. The novel EOS predicts the experimental volumetric data of different compounds and their mixtures better than the successful EOS of Peng and Robinson. The prediction of vapor pressures is only slightly less accurate than the results obtained with the Peng-Robinson equation that is designed for these purposes. The theoretically based parameters of the new EOS make its predictions more reliable than those obtained from purely empirical forms.     

Comparison of general rate model with a new model--artificial neural network model in describing chromatographic kinetics of solanesol adsorption in packed column by macroporous resins

Herein, two models, the general rate model taking into account convection, axial dispersion, external and intra-particle mass transfer resistances and particle size distribution (PSD) and the artificial neural network model (ANN) were developed to describe solanesol adsorption process in packed column using macroporous resins. First, Static equilibrium experiments and kinetic experiments in packed column were carried out respectively to obtain experimental data. By fitting static experimental data, Langmuir isotherm and Freundlich isotherm were estimated, and the former one was used in simulation coupled with general rate model considering better correlative coefficients. The simulated results showed that theoretical predictions of general rate model with PSD were well consistent with experimental data. Then, a new model, the ANN model, was developed to describe present adsorption process in packed column. The encouraging simulated results showed that ANN model could describe present system even better than general rate model. At last, by using the predictive ability of ANN model, the influence of each experimental parameter was investigated. Predicted results showed that with the increases of particle porosity and the ratio of bed height to inner column diameter (ROHD), the breakthrough time was delayed. On the contrary, an increase in feed concentration, flow rate, mean particle diameter and bed porosity decreased the breakthrough time.     

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.     

Solvation forces in ionic and neutral liquids: A density functional approach

The solvation forces between two planar charged surfaces in ionic solutions, corresponding to charged and neutral hard spheres representing the ions and the solvent, respectively, are studied here using a weighted density functional theory for inhomogeneous Coulomb systems developed by us recently. The hard sphere contributions to the one-particle correlation function are evaluated nonperturbatively using a position-dependent effective density, while the electrical contributions are obtained through a perturbative expansion around this weighted density. The calculated results on the solvation forces between two charged hard walls compare well with available simulation results for ionic systems. For a neutral system, the present results show good agreement with the experimentally observed oscillating forces for two mica surfaces in octamethylcyclotetrasiloxane. The present approach thus provides a direct route to the calculation of interaction energies between colloidal particles.     

The equation of state of isotropic fluids of hard convex bodies from a high-level virial expansion

We have calculated virial coefficients up to seventh order for the isotropic phases of a variety of fluids composed of hard aspherical particles. The models studied were hard spheroids, hard spherocylinders, and truncated hard spheres, and results are obtained for a variety of length-to-width ratios. We compare the predicted virial equations of state with those determined by simulation. We also use our data to calculate the coefficients of the y expansion [B. Barboy and W. M. Gelbart, J. Chem. Phys. 71, 3053 (1979)] and to study its convergence properties. Finally, we use our data to estimate the radius of convergence of the virial series for these aspherical particles. For fairly spherical particles, we estimate the radius of convergence to be similar to that of the density of closest packing. For more anisotropic particles, however, the radius of convergence decreases with increased anisotropy and is considerably less than the close-packed density.     

Hydrolytic stability of nano-particle polyurethane dispersions: Implications to their long-term use

Nano-particle segmented polyurethane anionomer dispersions with ions either on the soft segment or on the hard segment were synthesised using 2,2-bis(hydroxymethyl) propionic acid and 5-sodiosulfo-1,3-benzenedicarboxylic acid as ionic centre. The resulting polyurethane dispersions were characterized for their particle size, reduced viscosity and hydrolytic stability in the presence of the aqueous phase during storage. At similar ionic contents, the polyurethanes that contain ionic groups on their soft segment had smaller particle sizes than those that contain ionic groups on the hard segment due to the effectiveness of the sulphonate ionic groups incorporated in the former. The reduced viscosity of the anionomers in dimethylformamide (DMF) showed typical polyelectrolyte effect that can be eliminated by the addition of LiBr. The hydrolysis study conducted over 2-years indicated that polyurethanes in which the ions were located on the hard segment had better hydrolytic stability in aqueous environment than those with ions located on the soft segment. We attributed this due to the fact that unsolvated hydrophobic polyester segments were packed in the interior of the particles while the strongly hydrated urethane segments with mutually repelling carboxylate ions were situated on the outside surface of the particles. The polyester groups prone to hydrolytic attack were thus protected against hydrolysis as effectively as in the dry solid form.     

Scaled particle theory for hard sphere pairs. I. Mathematical structure

We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g(r). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper.     

Effect of depletion interactions on transport of colloidal particles in porous media

The influence of depletion interactions on the transport of micrometer-sized, negatively charged polystyrene latex particles through porous media was studied by analysis of particle breakthrough curves as a response to short-pulse particle injections to the inlet of a packed column of glass beads. The column outlet latex particle concentration profiles and the total amount of particles exiting the column were determined as a function of the concentration of small, silica nanoparticles in the solution and the bulk flow rate. Because of similar charges, the silica particles do not adsorb to either the latex particles or glass beads and thus induce an attractive depletion force between the latex particles and glass bead collectors. The total column outlet latex particle amount was calculated by integrating the measured breakthrough concentration curve and compared to the known amount of injected particles at the column inlet. It was found that the particle recovery was a decreasing function of the silica nanoparticle concentration and the carrier fluid residence time, and an increasing function of the velocity in the bed. In addition, removing the silica nanoparticles from the flowing solution caused a second outlet peak to appear, suggesting that some of the polystyrene particles were captured in secondary energy wells. The experimental data were interpreted using the predicted potential energy profile between a single particle and a glass bead, which was assumed to consist of electrostatic, van der Waals, and depletion components. The results indicate that secondary energy wells significantly affect particle transport behavior through porous media.     

Origin of de-swelling and dynamics of dense ionic microgel suspensions

A direct consequence of the finite compressibility of a swollen microgel is that it can shrink and deform in response to an external perturbation. As a result, concentrated suspensions of these particles exhibit relaxation dynamics and rheological properties which can be very different with respect to those of a hard sphere suspension or an emulsion. We study the reduction in size of ionic microgels in response to increasing number of particles to show that particle shrinkage originates primarily from steric compression, and that the effect of ion-induced de-swelling of the polymer network is negligible. With increasing particle concentration, the single particle dynamics switch from those typical of a liquid to those of a super-cooled liquid and finally to those of a glass. However, the transitions occur at volume fractions much higher than those characterizing a hard sphere system. In the super-cooled state, the distribution of displacements is non-gaussian and the dependence of the structural relaxation time on volume fraction is describable by a Volger-Fulcher-Tammann function.     

Formation of multilayered structures in the layer by layer deposition of colloid particles

Theoretical calculations of particle film formation in the layer by layer (LbL) self-assembling processes have been performed according to the generalized random sequential adsorption (RSA) scheme. The first (precursor) layer was generated using the standard RSA scheme pertinent to homogeneous surface. Formation of the consecutive layers (up to twenty) was simulated for two kinds of particles of equal size. The interaction of two particles of different kind resulted in irreversible and localized adsorption upon contact, whereas particles of the same kind were assumed to interact via the hard potential (no adsorption possible). Using this algorithm particle coverage (2D density) and volume fraction (3D density) were calculated as well as the film thickness as a function of the number of layers. Additionally, the structure of the film was quantitatively characterized in terms of the 2D and 3D pair correlation functions. The simulations revealed that particle concentration distribution in the film was more uniform for low precursor layer density than for higher density, where well-defined layers of closely packed particles appeared. It was also predicted theoretically that the averaged value of particle volume fraction in the uniform film region was rho(LbL)=0.42, which is very close to the maximum packing density equal to 0.382 predicted from the 3D RSA model. On the other hand, the roughness of the film was the lowest at the highest precursor layer density. It was shown that for low precursor layer density the film thickness increased with the number of layers in a nonlinear way. However, for high precursor layer density, the film thickness increased linearly with the number of layers and the average layer thickness was close to the hexagonal layer thickness equal to 1.73a p. It was concluded that our theoretical results can be effectively exploited for interpretation of the LbL processes involving colloid particles and polyelectrolytes.     

Crystallization kinetics of thermosensitive colloids probed by transmission spectroscopy

The kinetics of crystallization of poly-N-isopropylacrylamide (PNIPAM) particles has been investigated using the UV-visible transmission spectroscopy. Since the particle size decreases with the increase in temperature, microgel dispersions of different volume fractions have been obtained by varying the temperature of a single sample. It is found that the rates of the change in crystallinity, the average crystallite size, and the number density of crystallites at the most rapid stage over a certain time interval at various temperatures can be described by the power-law relations. At 19 degrees C, the PNIPAM system behaves as a hard sphere system under microgravity. The hard sphere theory based on Monte Carlo simulation has been used as a reference point to compare with conventional hard spheres, soft spheres, and PNIPAM spheres.     

Influences of colloidal stability and electrokinetic property on electrodialysis performance in the presence of silica sol

Negatively charged silica sol is known to lead to fouling of anion exchange membranes during electrodialysis (ED) as a result of its deposition on the membrane surface. It is known that the fouling potential is related to the physical and electrochemical properties of the silica particles as well as those of the anion exchange membranes. In this study, the properties of the silica sol were characterized in terms of its particle size, turbidity, and zeta potential in order to predict their effects on the electrodialysis performance. In the stability of colloidal particles, the critical coagulation concentrations of silica sol were determined as functions of ionic strength, cation species, and solution pH. In the electrodialysis of NaCl solution containing silica sol with various concentrations of CaCl(2), the colloidal behavior related to deposition and transport was examined during and after electrodialysis. The electrodialysis experiments clearly showed that the deposition and transport of silica sol during electrodialysis were related to the colloidal stability of dispersion.     

SANS and SAXS analysis of charged nanoparticle adsorption at oil-water interfaces

A systematic study of the adsorption of charged nanoparticles at dispersed oil-in-water emulsion interfaces is presented. The interaction potentials for negatively charged hexadecane droplets with anionic polystyrene latex particles or cationic gold particles are calculated using DLVO theory. Calculations demonstrate that increased ionic strength decreases the decay length of the electrostatic repulsion leading to enhanced particle adsorption. For the case of anionic PS latex particles, the energy barrier for particle adsorption is also reduced when the surface charge is neutralized through changes in pH. Complementary small-angle scattering experiments show that the highest particle adsorption for PS latex occurs at moderate ionic strength and low pH. For cationic gold particles, simple DLVO calculations also explain scattering results showing that the highest particle adsorption occurs at neutral pH due to the electrostatic attraction between oppositely charged surfaces. This work demonstrates that surface charges of particles and oil droplets are critical parameters to consider when engineering particle-stabilized emulsions.     

Cationic and anionic poly(N-isopropylacrylamide) based submicron gel particles: electrokinetic properties and colloidal stability

A cationic and an anionic poly(N-isopropylacrylamide) (poly(NIPAM)) microgel latex were synthesized via batch radical polymerization under emulsifier-free conditions. The hydrodynamic properties, colloidal stability, and electrokinetic characteristics of these two samples were studied. The hydrodynamic particle size variation was discussed by considering the effect of salinity and temperature on the shrinkage of the thermally sensitive polymer domains. The colloidal stability also depended on temperature and electrolyte concentration. A stability diagram with two well-defined domains (stable and unstable) was obtained. The flow from one domain to the other was fully reversible due to the peculiar (de)hydration properties of the polymer. The electrokinetic behavior, which depends on electrical and frictional properties of the particles, was analyzed via electrophoretic mobility measurements. Results were discussed by considering both the particle structure dependence on temperature and salinity, and the electric double layer compression. In addition, the electrophoretic mobility data were analyzed using Ohshima's equations for particles covered by an ion-penetrable surface charged layer, as well as using another simpler equation for charges located on a hydrodynamic equivalent hard sphere. Differences between the properties of both latexes were justified by the presence of a hydrophilic comonomer, aminoethyl methacrylate hydrochloride (AEMH), in the cationic microgel.     

Breakdown of colloid filtration theory: role of the secondary energy minimum and surface charge heterogeneities

The mechanisms and causes of deviation from the classical colloid filtration theory (CFT) in the presence of repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions were investigated. The deposition behavior of uniform polystyrene latex colloids in columns packed with spherical soda-lime glass beads was systematically examined over a broad range of physicochemical conditions, whereby both the fluid-phase effluent particle concentration and the profile of retained particles were measured. Experiments conducted with three different-sized particles in a simple (1:1) electrolyte solution reveal the controlling influence of secondary minimum deposition on the deviation from CFT. In a second series of experiments, sodium dodecyl sulfate (SDS) was added to the background electrolyte solution with the intent of masking near-neutrally charged regions of particle and collector surfaces. These results indicate that the addition of a small amount of anionic surfactant is sufficient to reduce the influence of certain surface charge inhomogeneities on the deviation from CFT. To verify the validity of CFT in the absence of surface charge heterogeneities, a third set of experiments was conducted using solutions of high pH to mask the influence of metal oxide impurities on glass bead surfaces. The results demonstrate that both secondary minimum deposition and surface charge heterogeneities contribute significantly to the deviation from CFT generally observed in colloid deposition studies. It is further shown that agreement with CFT is obtained even in the presence of an energy barrier (i.e., repulsive colloidal interactions), suggesting that it is not the general existence of repulsive conditions which causes deviation but rather the combined occurrence of "fast" and "slow" particle deposition.     

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.