Closure-based density functional theory applied to interfacial colloidal fluids

The behavior of dense colloidal fluids near surfaces can now be probed in great detail with experimental techniques like confocal microscopy. In fact, we are approaching a point where quantitative comparisons of experiment with particle-level theory, such as classical density functional theory (DFT), are appropriate. In a forward sense, we may use a known surface potential to predict a particle density distribution function from DFT; in an inverse sense, we may use an experimentally measured particle density distribution function to predict the underlying surface potential from DFT. In this paper, we tested the ability of the closure-based DFT of Zhou and Ruckenstein (J. Chem. Phys. 2000, 112, 8079-8082) to perform forward and inverse calculations on potential models commonly employed for colloidal particles and surfaces. To reduce sources of uncertainty in this initial study, Monte Carlo simulation results played the role of experimental data. The combination of Rogers-Young and modified-Verlet closures consistently performed well across the different potential models. For a reasonable range of choices of the density, temperature, and potential parameters, the inversion procedure yielded particle-surface potentials to an accuracy on the order of 0.1kT.     

Interfacial colloidal sedimentation equilibrium. II. Closure-based density functional theory

In Part I [R. E. Beckham and M. A. Bevan, J. Chem. Phys. 127, 164708 (2007)], results were presented for the sedimentation equilibrium of concentrated colloidal dispersions using confocal scanning laser microscopy experiments, Monte Carlo (MC) simulations, and a local density approximation perturbation theory. In this paper, we extended the modeling effort on those systems to include nonlocal density functional theory (DFT), which is capable of predicting the microstructure of the sediment at length scales comparable to the colloidal particle dimension. Specifically, we use a closure-based DFT formulation to predict interfacial colloidal sedimentation equilibrium density profiles. The colloid-colloid and colloid-surface interactions were modeled with DLVO screened electrostatic potentials using parameters taken directly from the experimental work. The DFT profiles were compared to the experimental and MC results from Part I. Good agreement was found for relatively dilute interfacial colloidal fluids, but agreement was less satisfactory as interfacial layering became more pronounced for conditions approaching the onset of interfacial crystallization. We also applied DFT in an inverse sense using the measured colloid density profile to extract the underlying colloid-surface potential; this can be thought of as a microscopic analog to the well-known procedure of using the macroscopic (coarse-grained) density profile to extract the osmotic equation of state. For the dilute interfacial fluid, the inverse DFT calculations reproduced the true colloid-surface potential to within 0.5kT at all elevations.     

Interaction between an ion-penetrable particle and a solid particle. II. Criteria for heterocoagulation

The potential energy of the total interaction between two spherical colloidal particles of different nature is calculated, i. e., of an ion-penetrable particle and an ion-impenetrable solid particle having a constant surface potential or constant surface charge density. The criteria for heterocoagulation are derived. The obtained results suggest a possibility of selective coagulation in the mixed system.     

Modification of Surface Forces by Metal Ion Adsorption

Abstract

Sorption of ions may lead to variations in interparticle forces and, thus, changes in the stability of colloidal particles. Chemical interactions between metal ions and colloidal particles modify the molecular structure of the surface, the surface charge, and the electrical potential between colloidal particles. These modifications to the surface and to the electrical double layer due to metal ion sorption are reflected in the interaction force between a particle and another surface, which is measured in this study by atomic force microscopy (AFM). Specifically, AFM is used to investigate the sorption of copper ions from aqueous solutions by silica particles. The influence of metal ion concentration and solution ionic strength on surface forces is studied under transient conditions. Results show that as the metal ion concentration is decreased, charge reversal occurs and a longer period of time is required for the system to reach equilibrium. The ionic strength has no significant effect on sorption kinetics. Furthermore, neither metal concentration nor ionic strength exhibits any effect on sorption equilibria, indicating that for the experimental conditions used in this study, the surface sites of the silica particle are fully occupied by copper ions.     

Synthesis and dispersion of Ni(OH)2 platelet-like nanoparticles in water

Synthesis of nanometric platelet-like Ni(OH)2 particles is described. The role of several experimental parameters on the particle size is investigated. A colloidal dispersion of particles is produced by adsorbing ionizable organic ligands (trisodium citrate) on the particle surface. The stability of this colloidal dispersion and the particle charge density are determined for different citrate ions concentrations.     

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.     

Electrophoretic mobility of a colloidal particle with constant surface charge density

When the electrophoretic mobility of a particle in an electrolyte solution is measured, the obtained electrophoretic mobility values are usually converted to the particle zeta potential with the help of a proper relationship between the electrophoretic mobility and the zeta potential. For a particle with constant surface charge density, however, the surface charge density should be a more characteristic quantity than the zeta potential because for such particles the zeta potential is not a constant quantity but depends on the electrolyte concentration. In this article, a systematic method that does not require numerical computer calculation is proposed to determine the surface charge density of a spherical colloidal particle on the basis of the particle electrophoretic mobility data. This method is based on two analytical equations, that is, the relationship between the electrophoretic mobility and zeta potential of the particle and the relationship between the zeta potential and surface charge density of the particle. The measured mobility values are analyzed with these two equations. As an example, the present method is applied to electrophoretic mobility data on gold nanoparticles (Agnihotri, S. M.; Ohshima, H.; Terada, H.; Tomoda, K.; Makino, K. Langmuir 2009, 25, 4804).     

Effect of colloidal particle size on adsorbed monodisperse and bidisperse monolayers

Coating hydrogel films or microspheres by an adsorbed colloidal shell is one synthesis method for forming colloidosomes. The colloidal shell allows control of the release rate of encapsulated materials, as well as selective transport. Previous studies found that the packing density of self-assembled, adsorbed colloidal monolayers is independent of the colloidal particle size. In this paper we develop an equilibrium model that correlates the packing density of charged colloidal particles in an adsorbed shell to the particle dimensions in monodisperse and bidisperse systems. In systems where the molar concentration in solution is fixed, the increase in adsorption energy with increasing particle size leads to a monotonic increase in the monolayer packing density with particle radius. However, in systems where the mass fraction of the particles in the adsorbing solutions is fixed, increasing particle size also reduces the molar concentration of particles in solution, thereby reducing the probability of adsorption. The result is a nonmonotonic dependence of the packing density in the adsorbed layer on the particle radius. In bidisperse monolayers composed of two particle sizes, the packing density in the layer increases significantly with size asymmetry. These results may be utilized to design the properties of colloidal shells and coatings to achieve specific properties such as transport rate and selectivity.     

Colloidal Interaction at the Air-Liquid Interface

In this paper, we propose a model to analyze the stability of colloidal particles at the air-liquid interface. The proposed model for the colloidal particle interaction considers DLVO interactions and capillary, hydrophobic, and dipolar interactions between the particles. Typical values from the literature were assigned to most parameters included in the model. Numerical computation revealed the most important parameter in determining the total interaction is the density of dipoles at the external surface of the particles. We have found significant differences for the pair potential between hydrophobic and hydrophilic particles. Hydrophobic particles must aggregate in a principal minimum of the interaction potential curve while hydrophilic particles aggregate in a secondary minimum. Copyright 2000 Academic Press.     

Thermal-diffusive behavior of a dilute solution of charged colloids

Thermal diffusion of a dilute solution of charged silica colloidal particles (Ludox) is studied by a holographic grating technique. The Soret coefficient of the charged colloids is measured as a function of the Debye screening length and the surface charge density of the colloids. The latter is varied by means of variation of the pH. The experimental Soret coefficients are compared with several theoretical predictions. The surface charge density is independently obtained from electrophoresis measurements, the size of the colloidal particles is obtained from electron microscopy, and the Debye length is calculated from ion concentrations. The only adjustable parameter in the comparison with theory is therefore the intercept at zero Debye length, which measures the contribution to the Soret coefficient of the solvation layer and possibly the colloid core material.     

Inorganic,polymeric and hybrid colloidal carriers with multi-layer reactive shell

Main experimental approaches for obtaining polymer, inorganic and hybrid colloidal particles as well as the tailored functionalization of their surface by oligoperoxide surfactants (OPS) and metal complexes (OMC) on their basis are discussed in the paper. The methods proposed enable to combine the stage of the formation of colloidal polymer, siliceous, metal and metal-oxide particles with the stage of their surface modification by functional surface-active oligoperoxides, which are sorbed irreversibly. Novel functional particles are studied by chemical, colloidal-chemical, rheological methods and scanning electronic microscopy. The occurrence of metal and metal oxide particle formation in distinct zones correlates well with the particle size distribution. The availability of reactive ditertiary peroxidic fragments on the particle surface as a result of OPS or OMC sorption causes their reliable protection, hydrophobity and ability to form free radicals and participate in elementary stages of radical processes.     

Fast formation of opal-like columnar colloidal crystals

We demonstrate that highly polydisperse colloidal gibbsite platelets easily form an opal-like columnar crystal with striking iridescent Bragg reflections. The formation process can be accelerated by orders of magnitude under a centrifugation force of 900 g without arresting the system in a disordered glassy phase. Using transmission electron microscopy and small-angle X-ray scattering techniques, we find that the forced sedimentation is accompanied by particle size fractionation, leading to inversion of the iridescent colors. The relatively easy self-organization of the polydisperse colloidal particles into opal-like crystals may be explained on the basis of the observed particle fractionation and possibly also on hexatic-like ordering.     

Hofmeister effects in the restabilization of IgG--latex particles: testing Ruckenstein's theory

The hydration interaction is responsible for the colloidal stability observed in protein-coated particles at high ionic strengths. The origin of this non-DLVO interaction is related not only to the local structure of the water molecules located at the surface but also to the structure of those molecules involved in the hydration of the ions that surround the colloidal particles. Ruckenstein and co-workers have recently developed a new theory based on the coupling of double-layer and hydration interactions. Its validity was contrasted by their fitting of experimental data obtained with IgG-latex particles restabilized at high salt concentration. The theory details the important role played by the counterions in the stability at high salt concentrations by proposing an ion pair reaction forming surface dipoles. These surface dipoles are responsible of repulsive interactions between two approaching surfaces. This paper checks the theory with recent data where some ions associated with the Hofmeister series (NO(3)(-), SCN(-) and Ca(2+)) restabilize the same kind of IgG-latex systems by means of hydration forces. Surprisingly, these ions induce stability acting even as co-ions, likely by modifying the water structure at the surface, but not forming surface ion pairs. Therefore, this experimental evidence would question Ruckenstein's theory based on the surface dipole formation for explaining the observed restabilization phenomena.     

Sintered silica colloidal crystals with fully hydroxylated surfaces

Silica colloidal crystals require multiple processing steps before they are useful materials in analytical applications, such as chemical separations, microarrays, sensors, and total internal reflection microscopy. These chemical processing steps include calcination, sintering, surface rehydroxylation, and chemical modification, but these steps have not been fully characterized for colloidal crystals. Silica particles of nominally 200 nm in diameter were prepared, and FTIR, SEM, UV-visible spectroscopy, and refractive index measurements were used to study the changes in chemical composition, particle size, and particle density throughout the process. The final material is shown to be a durable, crack-free crystal of solid particles bearing a fully hydroxylated surface of silanols, which can then be chemically modified.     

Polymer mediated peptide immobilization onto amino-containing N-isopropylacrylamide-styrene core-shell particles

Monodisperse cationic core-shell latex particles have been prepared using a shot polymerization process, with N-(3-aminopropyl)-methacrylamide-hydrochloride (APMH) as the functional monomer. The final latexes were characterized with respect to final polymerization conversion, water soluble polymer formation, particle size and size distribution, surface charge density and electrokinetic properties. Then the covalent grafting of maleic anhydride-alt-methyl vinyl ether (MAMVE) copolymer onto aminated latex particles was investigated. The most efficient conditions to obtain derivatised particles with no alteration of the colloidal stability were to control both polymer amount/latex particles concentration ratio and the mixing method of the two species. The charge inversion of the hydrolysed MAMVE functionalized particles was demonstrated by measuring the electrophoretic mobility as a function of pH. Finally, the covalent binding approach was implemented with peptide-MAMVE conjugates, confirming the great potential of this promising methodology for the preparation of reactive latex particles bearing peptides.     

Confocal microscopy of colloidal particles: towards reliable, optimum coordinates

Over the last decade, the light microscope has become increasingly useful as a quantitative tool for studying colloidal systems. The ability to obtain particle coordinates in bulk samples from micrographs is particularly appealing. In this paper we review and extend methods for optimal image formation of colloidal samples, which is vital for particle coordinates of the highest accuracy, and for extracting the most reliable coordinates from these images. We discuss in depth the accuracy of the coordinates, which is sensitive to the details of the colloidal system and the imaging system. Moreover, this accuracy can vary between particles, particularly in dense systems. We introduce a previously unreported error estimate and use it to develop an iterative method for finding particle coordinates. This individual-particle accuracy assessment also allows comparison between particle locations obtained from different experiments. Though aimed primarily at confocal microscopy studies of colloidal systems, the methods outlined here should transfer readily to many other feature extraction problems, especially where features may overlap one another.     

Wettability of Freon hydrates in crude oil/brine emulsions

The surface energy of petroleum hydrates is believed to be a key parameter with regard to hydrate morphology and plugging tendency in petroleum production. As of today, the surface energy of natural gas hydrates is unknown, but will depend on the fluids in which they grow. In this work, the wettability of Freon hydrates is evaluated from their behavior in crude oil emulsions. For emulsions stabilized by colloidal particles, the particle wettability is a governing parameter for the emulsion behavior. The transition between continuous and dispersed phases as a function of brine volume in crude oil-brine emulsions containing Freon hydrates has been determined for 12 crude oils. Silica particles are used for comparison. The results show that phase inversion is highly dependent on crude oil properties. Based on the measured points of phase inversion, the wettability of the Freon hydrates generated in each system is evaluated as being oil-wet, intermediate-wet, or water-wet. Generation of oil-wet hydrates correlates with low hydrate plugging tendency. The formation of oil-wet hydrates will prevent agglomeration into large hydrate aggregates and plugs. Hence, it is believed that the method is applicable for differentiating oils with regard to hydrate morphology.     

Distribution of colloidal particles in a spherical cavity

The spatial distribution of colloidal particles in a confined space is frequently a key issue to many phenomena of practical significance. This problem is investigated by considering the distribution of colloidal particles in a spherical cavity under the conditions of relatively large cavities, low cavity and colloidal particles potentials, and low monovalent electrolyte and colloidal concentrations. The analytical expression for the particle-cavity pair interaction energy is derived under various surface conditions. The results obtained are used to evaluate the direct correlation functions in the hypernetted chain approximation employed for the resolution of an Ornstein-Zernike equation. For a fixed particle number concentration at the center of a cavity, we make the following conclusions: (i) the spatial distribution of particles increases in an oscillatory manner with the distance away from the cavity surface, (ii) increasing the particle-cavity pair interaction energy has the effect of reducing the free space of particles inside a cavity, and (iii) the greater the pair interaction energy between two particles, the higher the average concentration of particles.     

Analysis of the validity of perturbation density functional theory: based on extensive simulation for simple fluid at supercritical and subcritical temperature under various external potentials

Because of the scarcity of available simulation data for confined hard-core attractive Yukawa model fluid, extensive Monte Carlo (MC) simulation research for this fluid under the influence of various external potentials were carried out. The present MC simulation results were employed to test a performance of the third-order perturbation density functional theory (DFT) based on a high order direct correlation function (DCF) [S. Zhou and E. Ruckenstein, Phys. Rev. E. 61, 2704 (2000)]. It was found that the present perturbation DFT formalism is soundly structured only if the imported second-order DCF is reliable. In this case, the accuracy of the results can be satisfactory or even very high for various types of external potentials. Further, the associated adjustable parameter can be universal, i.e., independent of the particular external field responsible for the generation of a nonuniform density profile. Dependence of both the maintenance of the reliability of the formalism and holding of the universality of the adjustable parameter on the accuracy of the imported bulk second-order DCF can be strengthened by the large difference between the external field investigated and that caused by a single hard wall used for specification of the adjustable parameter. In case the gaseous density in the subcritical region is below the coexistence density, an excellent performance of the present formalism is observed even for the mean spherical approximation's second-order DCF as an input. This advantageous property, combined with the fact that the present formalism needs only the second-order DCF of fluid at the coexistence state as an input, enables the present formalism to be a very good theoretical tool for the investigations of wetting and prewetting transitions.     

Colloidal stability of chitosan-modified poly(methyl methacrylate) latex particles

Experiments of coagulation kinetics were used to study the influence of the electrolyte concentration on the colloidal stability of cationic poly(methyl methacrylate) latex particles with various degrees of chitosan modification. For the chitosan-free latex products prepared by various levels of 2,2′ azobis(2-amidinopropane) dihydrochloride (V-50) at constant pH, the critical coagulation concentration (ccc) increases with increasing V-50 concentration, due to the enhanced particle surface charge density. On the other hand, the chitosan-modified latex products at constant pH do not exhibit very different values of ccc. This result is attributed to the counterbalance between two opposite effects related to the grafted chitosan, that is, the increased particle surface charge density and the enhanced shift of the particle's shear plane toward the aqueous phase with the chitosan content. The ccc of the latex products with various degrees of chitosan modification decreases significantly when the pH increases from 3 to 7. This is because the degree of ionization of the surface amino groups (the particle surface charge density) decreases with increasing pH. As a result, the stability of the colloidal system decreases significantly with increasing pH. The apparent Hamaker constant and diffuse potential were obtained from the coagulation kinetics data. These two parameters along with the zeta potential and particle size data for the latex samples taken immediately after the end of the coagulation experiments were also used to study the effect of ionic strength on the colloidal stability of the latex particles. Received: 10 October 1998 Accepted in revised form: 16 December 1998