Colloidal Particles In Electrolyte Solution Research Articles

Theory of Charge Regulation of Colloidal Particles in Electrolyte Solutions

We present a theory that enables us to (i) calculate the effective surface charge of colloidal particles and (ii) efficiently obtain titration curves for different salt concentrations. The theory accounts for the shift of pH of solution due to the presence of 1:1 electrolyte. It also accounts self-consistently for the electrostatic potential produced by the deprotonated surface groups. To examine the accuracy of the theory, we have performed extensive reactive Monte Carlo simulations, which show excellent agreement between theory and simulations without any adjustable parameters.

Reentrant crystallization of like-charged colloidal particles in an electrolyte solution: Relationship between the shape of the phase diagram and the effective potential of colloidal particles

The reentrant crystallization of like-charged colloidal particles in electrolyte solutions was studied to clarify the relationship between the shape of the phase diagram and the particle-particle effective potential. Coexisting densities were calculated at various electrolyte concentrations using the thermodynamic perturbation expansion method with effective one-component models. The effective potentials were obtained using an integral equation theory for liquids. Some model effective potentials were examined. The calculated results indicated that the reentrant behaviors of various acidic protein solutions observed in the experiments required not only the nonmonotonic dependence of the short-range attraction on the electrolyte concentration, but also the absence of a long repulsive tail.

Ionic Specificity in Rapid Coagulation of Silica Nanoparticles

The Smoluchowski theory has been widely accepted as the basic theory to estimate the rapid coagulation rate of colloidal particles in electrolyte solutions. However, because the size and specificity of molecules and ions are not taken into account, the theory is applicable only if the particle size is large enough to neglect the effects caused by the structured layers composed of water molecules, ions, and hydrated ions adsorbed on the colloidal surface. In the present study, the rapid coagulation rates of silica nanoparticles in concentrated chloride and potassium solutions were measured by using a low-angle light-scattering apparatus, and the dependence of the experimental value of rapid coagulation rate, KER, on the particle diameter, Dp, and also on the Gibbs free energy of hydration of ions, ΔGhyd, was investigated extensively. The following were found. (1) When the particle size was small enough, the value of KER reduced exponentially not only with the decreasing particle size but also with the increasing value of (-ΔGhyd) of cations (counterions) in the case of chloride solutions and with that of anions (coions) in the case of potassium solutions. (2) Silica nanoparticles of Dp ≲ 70 nm in 1 M KNO3 and KSCN solutions did not coagulate at all, although they coagulated at Dp ≳ 100 nm as in the other potassium solutions. These unexpected phenomena were explained by the proposed mechanisms.

Effective charge saturation in colloidal suspensions

Because micro-ions accumulate around highly charged colloidal particles in electrolyte solutions, the relevant parameter to compute their interactions is not the bare charge, but an effective (or renormalized) quantity, whose value is sensitive to the geometry of the colloid, the temperature or the presence of added-salt. This nonlinear screening effect is a central feature in the field of colloidal suspensions or polyelectrolyte solutions. We propose a simple method to predict effective charges of highly charged macro-ions, that is reliable for monovalent electrolytes (and counterions) in the colloidal limit (large size compared to both screening length and Bjerrum length). Taking reference to the non linear Poisson–Boltzmann theory, the method is successfully tested against the geometry of the macro-ions, the possible confinement in a Wigner–Seitz cell, and the presence of added salt. Moreover, our results are corroborated by various experimental measures reported in the literature. This approach provides a useful route to incorporate the nonlinear effects of charge renormalization within a linear theory for systems where electrostatic interactions play an important role.

Generalizations for the Potential of Mean Force between Two Isolated Colloidal Particles from Monte Carlo Simulations

A substantial amount of experimental and numerical evidence has shown that the Derjaguin–Landau–Verwey–Overbeek theory is not suitable for describing those colloidal solutions that contain multivalent counterions. Toward improved understanding of such solutions, the authors report Monte Carlo calculations wherein, following Rouzina and Bloomfield, they postulate that, in the absence of van der Waals forces, the overall force between two isolated charged colloidal particles in electrolyte solutions is determined by a dimensionless parameter Γ= z 2 l B/ a, which measures the electrostatic repulsion between counterions adsorbed on the macroion surface, where z = counterion valence, l B=Bjerrum length, and a = average separation between counterions on the macroion surface calculated as if the macroion were fully neutralized. The authors find, first, that the maximum repulsion between like-charged macroions occurs at Γ≈0.5 and, second, that onset of attraction occurs at Γ≈1.8, essentially independent of the valence and concentration of the surrounding electrolyte. These observations might provide new understanding of interactions between electrostatic double layers and perhaps offer explanations for some electrostatic phenomena related to interactions between DNA molecules or proteins.

Influence of the Secondary Interaction Energy Minimum on the Early Stages of Colloidal Aggregation

The pair interaction energy of charged colloidal particles in electrolyte solutions can exhibit a large barrier as well as a pronounced secondary minimum. We discuss the effect of a secondary energy minimum on aggregation kinetics by modeling irreversible dimer formation as a two-step process in which charged colloidal particles in electrolyte solutions first aggregate reversibly into the secondary minimum before they can cross the energy barrier. In the classical regime of slow aggregation, the secondary minimum is seen to have a pronounced effect if either the ionic strength of the solution is high (e.g., 0.1 M for particles of 150-nm radius) or particles are large (≥350-nm radius for an ionic strength of 0.01 M). Under these conditions, our calculations predict a transient period of fast aggregation into the secondary minimum followed by slow primary aggregation. The aggregation in this second regime is found to take place at a lower rate than what would be expected in the absence of the secondary minimum or from an earlier linearized model for secondary aggregation. The crossover time between the two regimes strongly depends on the particle size but not on the particle concentration, which however determines the degree of aggregation reached within the fast regime. We also conclude that a previously observed severe discrepancy between measured and predicted aggregation rate constants for submicron particles is not due to the neglect of secondary aggregation in the theoretical treatment.

Symmetrized Poisson-Boltzmann equation for mixtures containing colloidal particles and an electrolyte

The collective interactions among colloidal particles in electrolyte solutions are examined employing a symmetrized Poisson-Boltzmann equation for a mixture consisting of charged colloidal particles and a binary electrolyte solution. This equation is derived by using a virial expansion of the Ornstein-Zernike equation and takes into account the interactions among all the charged species of the system. The particle energy thus obtained is compared with that provided by the Poisson-Boltzmann equation. The pair correlation function of the particles indicates that there are conditions under which the electrostatic interactions among the particles generate an effective attraction.

Osmotic pressure for concentrated suspensions of polydisperse particles with thick double layers

A spherical cell model is used to describe the electrical double layer interaction in concentrated suspensions. The model is used to calculate the osmotic pressure of a system of colloidal particles in electrolyte solution. The model uses the full nonlinear Poisson—Boltzmann equation with constant-potential boundary conditions in spherical coordinates and is therefore not limited to small electrical double layers and small surface potentials. The model, which is applicable to both monodisperse and polydisperse particles, is compared to the pair-potential model of monodisperse systems.

The interaction of two spherical colloidal particles in electrolyte solution. An application of the hypernetted-chain approximation

The hypernetted-chain approximation is solved numerically for a pair of identical spherical colloidal particles immersed in an electrolyte solution. We consider a simple model system where the ions are hard spheres with embedded point charges and the colloidal particles are much larger hard spheres bearing a uniform surface charge distribution. The surface charge density is considered to be constant independent of the particle separation. We obtain the potential of mean force acting between the colloid particles and the structure of the double layer about a single particle. It is found that under some conditions the colloid-colloid interaction is attractive at small separations even in the absence of van der Waals forces. This result should be of interest in the theory of colloidal stability.

Dielectric loss of colloidal particles in electrolyte solution at microwave frequencies

The dielectric loss of aqueous colloidal suspensions of polystyrene particles have been measured for various KCl and LiCl concentrations at a frequency of 10.0 GHz in the temperature range of 0 to 60°C. The dielectric behavior is characterized by the presence of a remarkable thermal anomaly, strongly affected by the ionic species and their concentrations. The results are analyzed in terms of some “mixture equations” and there are suggestions that the water in the double layer exhibits a dielectric constant different from that of the bulk medium.

The solution of a modified Poisson—Boltzmann equation for colloidal particles in electrolyte solutions

The solution of a modified Poisson-Boltzman (PB) equation for the region between two colloidal particles immersed in a 1-1 electrolyte is investigated for low potentials. The practice familiar in the theory of colloidal stability, of replacing the particles by two infinitely thick parallel plates, is employed. Differences between this study and a similar one by Bell and S. Levine include a more rigorous treatment of the “imaging effect,” an avoidance of the iterative assumption of calculating modifications to the PB equation with classical forms for the potential, electric field and volume densities of the ions and a “constant charge” assumption with respect to adsorbed ions and the charge in the plate. Numerical solution shows that contrary to the latter work, with these changes the modifications can significantly effect the magnitude of the force between two particles.

Comparison of Theoretical Equations for Potential Energy of Electrostatic Repulsion of Colloidal Particles at Constant Surface Charge

Recently, derived and relatively simple expressions for the energy of electrostatic repulsion between flat plates and spheres at constant surface charge were compared with the more rigorous expressions of Jones and Levine and of Müller. They are quantitative of the electrostatic barrier to the collision of colloidal particles in electrolyte solutions within the limitation of small surface potentials, ψo < 25mv. They are also useful in the general approximation of colloidal stability of most practical systems, despite the limitations on the validity of the expression at higher surface potentials.

Comment on the Article “On the Theory of the Dielectric Dispersion of Spherical Colloidal Particles in Electrolyte Solution”1

Comment on the Article “On the Theory of the Dielectric Dispersion of Spherical Colloidal Particles in Electrolyte Solution”¹