Colloid Particle Adsorption on Partially Covered (Random) Surfaces

The random sequential adsorption (RSA) approach was used to model irreversible adsorption of colloid particles at surfaces precovered with smaller particles having the same sign of surface charge. Numerical simulations were performed to determine the initial flux of larger particles as a function of surface coverage of smaller particles θ(s) at various size ratios lambda=a(l)/a(s). These numerical results were described by an analytical formula derived from scaled particle theory. Simulations of the long-time adsorption kinetics of larger particles have also been performed. This allowed one to determine upon extrapolation the jamming coverage θ(l)(infinity) as a function of the lambda parameter at fixed smaller particle coverage θ(s). It was found that the jamming coverage θ(l)(infinity) was very sensitive to particle size ratios exceeding 4. Besides yielding θ(l)(infinity), the numerical simulations allowed one to determine the structure of large particle monolayers at the jamming state which deviated significantly from that observed for monodisperse systems. The theoretical predictions suggested that surface heterogeneity, e.g., the presence of smaller sized contaminants or smaller particles invisible under microscope, can be quantitatively characterized by studying larger colloid particle adsorption kinetics and structure of the monolayer. Copyright 2001 Academic Press.     

Escape from a cavity through a small window: turnover of the rate as a function of friction constant

To escape from a cavity through a small window the particle has to overcome a high entropy barrier to find the exit. As a consequence, its survival probability in the cavity decays as a single exponential and is characterized by the only parameter, the rate constant. We use simulations to study escape of Langevin particles from a cubic cavity through a small round window in the center of one of the cavity walls with the goal of analyzing the friction dependence of the escape rate. We find that the rate constant shows the turnover behavior as a function of the friction constant, zeta: The rate constant grows at very small zeta, reaches a maximum value which is given by the transition-state theory (TST), and then decreases approaching zero as zeta-->infinity. Based on the results found in simulations and some general arguments we suggest a formula for the rate constant that predicts a turnover of the escape rate for ergodic cavities in which collisions of the particle with the cavity walls are defocusing. At intermediate-to-high friction the formula describes transition between two known results for the rate constant: the TST estimation and the high friction limiting behavior that characterizes escape of diffusing particles. In this range of friction the rate constants predicted by the formula are in good agreement with those found in simulations. At very low friction the rate constants found in simulations are noticeably smaller than those predicted by the formula. This happens because the simulations were run in the cubic cavity which is not ergodic.     

Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution

We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap h(0) between the large particle and the wall is assumed to be comparable to the diameter 2a of the smaller particles so there is a length-scale separation between the gap width h(0) and the radius of the large particle b>h(0). We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations h(0), the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For h(0)>a, the resistance coefficient approaches the lubrication value corresponding to a particle moving in a fluid with the effective viscosity given by the Einstein formula.     

Adhesion as an interplay between particle size and surface roughness

Surface roughness plays an important role in the adhesion of small particles. In this paper we have investigated adhesion as a geometrical effect taking into account both the particle size and the size of the surface features. Adhesion is studied using blunt model particles on surfaces up to 10 nm root-mean-square (RMS) roughness. Measurements with particles both smaller and larger than surface features are presented. Results indicate different behavior in these areas. Adhesion of particles smaller than or similar in size to the asperities depend mainly on the size and shape of the asperities and only weakly on the size of the particle. For large particles also the particle size has a significant effect on the adhesion. A new model, which takes the relative size of particles and asperities into account, is also derived and compared to the experimental data. The proposed model predicts adhesion well over a wide range of particle/asperity length scales.     

Mechanical behavior of saturated,consolidated, alumina powder compacts: effect of particle size and morphology on the plastic-to-brittle transition

The effects of particle size and morphology on the mechanical behavior of pressure consolidated, saturated, alumina powder bodies, were determined with uniaxial compression experiments of cylindrical specimens at a fixed displacement rate. Five different α-Al₂O₃ powders, from the same manufacturer, were used. The slurries were dispersed at pH 4 and then either coagulated with additions of NH₄Cl to produce weakly attractive particle networks with short-range repulsive potentials or flocculated at the isoelectric point (iep=pH 9). These slurries were consolidated by pressure filtration using pressures ranging from 2.5 to 150 MPa. Larger particles packed to higher relative densities when compared to smaller particles. Blocky particles packed at a lower relative density when compared to particles with roundish surfaces. Bodies were plastic when consolidated below a critical consolidation pressure; above this pressure, the body was brittle. Bodies formed with large particles were brittle at a lower consolidation pressure. The effect of particle size is discussed with respect to the number of particle–particle contacts per unit volume at a given relative density. Namely, for a given applied pressure, larger forces exist between larger particles because of the smaller number of contacts per unit volume relative to smaller particles.     

A purely geometric derivation of the scaled particle theory formula for the work of cavity creation in a liquid

A very simple statistical geometric approach is devised that allows the derivation of a formula for the work to create a spherical cavity in a liquid consisting of spherical molecules in the small cavity size limit. This formula exactly corresponds to the general expression for the work of cavity creation provided by scaled particle theory. The origin of the success of the present statistical geometric approach needs further insight.     

A study on shear coagulation and heterocoagulation

Coagulation and heterocoagulation of spherical particles in a simple shear flow have been studied by means of trajectory analysis. Effects of particle size and size ratio have been extensively examined. Some new features of shear coagulation and heterocoagulation have been recognized. Primary and secondary shear coagulations differ in many aspects. The nonequatorial effective capture cross-sections can be attributed to the pure secondary shear coagulation. Shear stability can be low at small and large particle size ranges due to secondary and primary shear coagulation, respectively, with a high stability range at medium particle sizes. A second range of high stability may appear at even larger sizes. On the basis of relative coagulation rate, shear heterocoagulation between particles of the same material but different sizes may or may not be favored over the respective homocoagulations. In the case of primary coagulation, the two homocoagulations are favored over the heterocoagulation. The opposite is true in the case of secondary coagulation. In a suspension composed of particle species of different materials and different sizes, if the larger particles are less stable at an assumed same size with the smaller particles, the homocoagulation of the larger species is still favored over heterocoagulation in the case of primary shear coagulation. In the case of secondary shear coagulation, the heterocoagulation may be favored over the homocoagulation of the larger species, if the above mentioned stability difference is not very large, the particle size difference is not small, and the size of the larger particles is within a certain range.     

Distribution kinetics of Ostwald ripening at large volume fraction and with coalescence

Condensation phase transitions from metastable fluids occur by nucleation with accompanying particle growth and eventual Ostwald ripening. During ripening the subcritical particles dissolve spontaneously while larger particles grow and possibly coalesce if their volume fraction is large enough. The classical diffusion-influenced rates are also affected by large particle concentrations and are here described by mass-dependent rates. We represent the kinetics of ripening through growth, dissolution, and biparticle coalescence by a new population dynamics equation for the particle size distribution (PSD). Numerical solutions of the scaled governing equations show that coalescence plays a major role in influencing the PSD when the scaled mass concentration (volume fraction) or number concentration is relatively large. The solution describes the time range from initial conditions to the final narrowing of polydispersity. We show that the time dependence of the average particle mass in the asymptotic period of ripening has a power-law increase dependent on rate expressions for particle growth and coalescence at large values of volume fraction.     

Partial molar volume of n-alcohols at infinite dilution in water calculated by means of scaled particle theory

The partial molar volume of n-alcohols at infinite dilution in water is smaller than the molar volume in the neat liquid phase. It is shown that the formula for the partial molar volume at infinite dilution obtained from the scaled particle theory equation of state for binary hard sphere mixtures is able to reproduce in a satisfactory manner the experimental data over a large temperature range. This finding implies that the packing effects play the fundamental role in determining the partial molar volume at infinite dilution in water also for solutes, such as n-alcohols, forming H bonds with water molecules. Since the packing effects in water are largely related to the small size of its molecules, the latter feature is the ultimate cause of the decrease in partial molar volume associated with the hydrophobic effect.     

High velocity interparticle collisions driven by ultrasound

Ultrasonic irradiation of slurries produces high velocity impacts between solid metal particles that are sufficient to cause interparticle melting. Sonication of 5 mum Zn powder as a slurry in alkanes, for example, produces dense agglomerates 50 mum in diameter consisting of approximately 1000 fused particles. Particle size was found to be the most influential parameter in inducing local melting during interparticle collisions. Ultrasonic irradiation of mixed powders resulted in formation of agglomerates with larger Zn particles "soldered" by the smaller ones. A simple kinematic model of the ultrasound-driven interparticle fusion predicts a melting criterion that is nonmonotonically dependent on particle size and is shown to be in agreement with experiment.     

A second-order Markov process for modeling diffusive motion through spatial discretization

A new "mesoscopic" stochastic model has been developed to describe the diffusive behavior of a system of particles at equilibrium. The model is based on discretizing space into slabs by drawing equispaced parallel planes along a coordinate direction. A central role is played by the probability that a particle exits a slab via the face opposite to the one through which it entered (transmission probability), as opposed to exiting via the same face through which it entered (reflection probability). A simple second-order Markov process invoking this probability is developed, leading to an expression for the self-diffusivity, applicable for large slab widths, consistent with a continuous formulation of diffusional motion. This model is validated via molecular dynamics simulations in a bulk system of soft spheres across a wide range of densities.     

Efflorescence relative humidity for ammonium sulfate particles

The classical homogeneous nucleation theory was employed to calculate the efflorescence relative humidity (ERH) of airborne ammonium sulfate particles with a wide size range (8 nm to 17 microm) at room temperature. The theoretical predictions are in good agreement with the experimentally measured values. When the ammonium sulfate particle is decreased in size, the ERH first decreases, reaches a minimum around 30% for particle diameter equal to about 30 nm, and then increases. It is for the first time that the Kelvin effect is theoretically verified to substantially affect the ERH of ammonium sulfate particles smaller than 30 nm, while the aerosol size is the dominant factor affecting the efflorescent behavior of ammonium sulfate particles larger than 50 nm.     

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.     

Synthesis of Microporous Silica Spheres

Spherical microporous silica powders with a narrow size distribution have been prepared by a precipitation technique involving the hydrolysis reaction of a silicon alkoxide in ethanol. The formation of the important microporosity has been investigated following two templating methods: the co-hydrolysis and condensation of two alkoxides, one of which presents porogen function, and the adsorption of an organic compound (glycerol) as the porogen. In both processes, the organic porogen is removed by a simple calcination. In the first method, the addition of more than 20 mol% of the porogen alkoxide, necessary for generating enough microporosity, disturbs completely the condensation process resulting in microporous, nonuniform silica particles of large size distribution. The best result has been obtained with the glycerol method where submicrometer-sized silica spheres with a very narrow size distribution and about 40 vol% porosity have been synthesized. The presence of glycerol during the synthesis considerably affects the precipitation mechanism, resulting in a larger mean particle size. The use of an aggregative growth model has successfully been employed to explain the effect of the porogen during particle formation. The precipitation mechanism of silica involves the aggregation between particles of similar size until a critical size is reached, resulting in a uniform particle size distribution. In the presence of glycerol, it has been shown that a second aggregative growth between still-nucleating primary particles and large particles occurred with increasing reaction time. This second aggregative growth appears at an intermediate stage of the precipitation process and is due to both the precipitation of smaller primary particles and the destabilization of the colloidal stability of the system. This explains why the final particle size reached in this system is larger compared to silica particles synthesized without glycerol and shows how glycerol is incorporated in the silica particles. The synthesis of silica microporous spheres of narrow size distribution, by varying particle size and porosity, should yield a wide range of aqueous silica slurries for particular chemical mechanical polishing applications. Copyright 2000 Academic Press.     

Dielectrophoresis-based particle exchanger for the manipulation and surface functionalization of particles

We present a microfluidic device where micro- and nanoparticles can be continuously functionalized in flow. This device relies on an element called "particle exchanger", which allows for particles to be taken from one medium and exposed to some reagent while minimizing mixing of the two liquids. In the exchanger, two liquids are brought in contact and particles are pushed from one to the other by the application of a dielectrophoretic force. We determined the maximum flow velocity at which all the particles are exchanged for a range of particle sizes. We also present a simple theory that accounts for the behaviour of the device when the particle size is scaled. Diffusion mixing in the exchanger is also evaluated. Finally, we demonstrate particle functionalization within the microfluidic device by coupling a fluorescent tag to avidin-modified 880 nm particles. The concept presented in this paper has been developed for synthesis of modified particles but is also applicable to on-chip bead-based chemistry or cellular biology.     

The van Hove distribution function for brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self?" component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.     

On the influence of size, zeta potential, and state of motion of dispersed particles on the conductivity of a colloidal suspension

The dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of the dispersed particles is analyzed both theoretically and numerically. It is shown that the simple formula that represents the conductivity as a sum of products: charge times mobility, taken over all the carriers present in the suspension, is only valid for exceedingly low values of the product kappaa. In contrast, the formulation based on the value of the dipolar coefficient of the suspended particles seems to be valid for all the range of particle sizes. This assertion is only true if the dipolar coefficient is calculated taking into account the electrophoretic motion of the particles. For very low values of the product kappaa, the dipolar coefficient of particles free to move can be several orders of magnitude larger than that of immobile particles.     

Use of a Cross-Sectional Model for Determining Rheology in Settling Slurries: Effect of Solvent,Particle Size,and Density

Transport models for partially settling slurries need accurate rheology correlations, particularly describing viscosity relationship to the particle concentration. A method is needed to untangle the effects of settling on apparent viscosity and the real effects of particle concentration on viscosity during rheology measurements. Our approach is based on model inversion of a cross-section model for the vertical particle concentration gradient and the local rheologies in the gap of a Couette type rheometer, established by a balance between gravitational particle settling and shear induced migration of the particles. The Krieger-Dougherty rheology correlation with adjustable parameters has been applied, where the parameters are determined by minimizing the difference between the measured viscosity data and those calculated by the model. Fairly mono-disperse silver coated polystyrene particles with two sizes and densities were used in both the aqueous and oil phase. In the raw data an apparent shear thinning tendency is observed. Through the model inversion process, this is accounted for by the shear dependent settling and the steep increase of viscosity with particle concentration. Maximum packing fraction was obtained through settling experiments. The difference between this value and the maximum packing fraction from the model inversion was less than 3% for oil-based suspensions. The larger difference was found for smaller particle size in water which is attributed to the larger effect of interparticle forces.     

Particle interactions in electrophoresis: I. Motion of two spheres along their line of centers

The electrophoretic motion of two charged colloidal spheres with very thin electrical double layers in a constant applied electric field along their line of centers is considered. The particles may differ in radius and in zeta potential at the surface. The electrostatic and hydrodynamic governing equations are solved in the quasi-steady situation using bipolar coordinates and the electrophoretic velocities of particles are calculated for various cases. The interaction effect between particles can be very significant when the distance between particle surfaces gets close to zero. The particle with smaller zeta potential is speeded up by the motion of the other, which is retarded at the same time by the motion of the former one, if the two spheres have unequal zeta potentials of the same electrical sign. For two particles of different signs in zeta potential, motions of both are hindered by each other. The influence of the interaction between particles in general is stronger on the smaller one than on the larger one. For the special case of two electrophoretic spheres with identical zeta potentials, there is no particle interaction for all particle sizes and separations.     

Relationship between scattered intensity and separation for particles in an evanescent field

We describe measurements of the scattering of visible light from an evanescent field by both spherical particles (R = 1-10 mum) that are glued to atomic force microscopy (AFM) cantilevers, and by sharp tips (R < 60 nm) that were incorporated onto the cantilevers during manufacture. The evanescent wave was generated at the interface between a flat plate and an aqueous solution, and an atomic force microscope was used to accurately control the separation, h, between the particle and the flat plate. We find that, for sharp tips, the intensity of scattered light decays exponentially with separation between the tip and the plate all the way down to h approximately 0. The measured decay length of scattered intensity, delta, is the same as the theoretical decay length of the evanescent intensity in the absence of the sharp tip. For borosilicate particles, (R = 1-10 mum), the scattering also decays exponentially with separation at large separations. However, when the separation is less than roughly 3delta, the measured scattering intensity is smaller in magnitude than that which would be predicted by extrapolating the exponential decay observed at large separations. For these particles, the scattering approximately fits the sum of two exponentials. The magnitude of the deviation from exponential at contact was roughly 10-15% for R = 1 mum particles and about 30% for larger particles and is larger for s-polarized light. Preliminary experiments on polystyrene particles shows that the scattering is also smaller than exponential at small separations but that the deviation from exponential is larger for p-polarized light. In evanescent wave AFM (EW-AFM) the scattering-separation can be calibrated for situations where the scattering is not exponential. We discuss possible errors that could be introduced by assuming that exponential decay of scattering continues down to h = 0.