Particle surface potential

The surface charge density cr of the particle is related to the particle surface potential i/ o obtained from the boundary condition at the sphere surface,... 

Figure 2.14 Measured electrostatic double-layer and van der Waals forces between two surfaces of curved mica of radius 1 cm in (a) water and (b) dilute KNO3 and Ca(N03)2 solutions. The lines are the predictions of the DLVO theory with a Hamaker constant of 2.2 x 10 J in the limits of constant surface charge and constant surface potential here xfrQ = -(j/s, the particle surface potential. (The lines for constant surface charge are slightly higher than those for constant surface potential at small D.) The inset in (b) is the measured force in 0.1 M KNO3, which shows a force minimum at a distance of around 7 nm. Since this minimum in force occurs away from the deep minimum at the surface, it is called a secondary minimum. (From Israelachvili and Adams 1978 and Israelachvili 1992, reprinted with permission from Academic Press.)...

The titania particles precipitate under reaction conditions very similar to those of the silica systems discussed earlier. A critical nucleation concentration of 1.5-3 times [C]eq is measured. This low supersaturation level is not reached until very late in the precipitation reaction (Figure 3). The rate of loss of soluble titania is also independent of the presence of solid surface area. Finally, on the basis of measures of particle surface potentials, nuclei of sizes less than about 20 nm are expected to be unstable and to rapidly aggregate. These results again indicate that during the precipitation of titania, nucleation may occur over much of the reaction period and final particle sizes may be determined by the aggregation of primary particles. These conclusions are supported by the transmission electron microscopy work of Diaz-Gomaz et al. (30). 

Note that the critical concentration of electrolyte at low particle surface potentials (j) strongly depends on C-potential, while it is practically independent of C, at high values of < ) . Besides, the critical concentration does not depend on particles size at a given value of... 

Here i//(r) is set equal to zero at points where the concentration of counterions equals its average value n. An approximate solution to Equation (2.61) for the case of dilute suspensions has been obtained by Imai and Oosawa [64-66] and later by Ohshima [67]. They showed that there are two distinct cases separated by a certain critical value of the particle charge Q, that is, (case 1) the low-charge case and (case 2) the high-charge case. In the latter case, counterions are condensed near the particle surface (counterion condensation). For the dilute case (< < C 1), approximate values of i//(a) and i//(/f) together with the particle surface potential defined by — i//(F) are given below. 

Colloidal particles snspended in a solvent can acquire charge by two ways. The surface groups can dissociate or the ions from solution can bind to the particle surface (Israelachvili, 1992 Russel, 1989 Hunter, 1987). The charge boimd to the particle surface is balanced by a diffuse region of ions in solution, called the diffuse double layer. When two like particles (radius a) approach one another, the double layers overlap and the particles feel a repulsion. Exact analytic expressions for the electrostatic potential energy ( Ve) for all values of the particle surface potential are difficult to compute and therefore analytical approximations or numerical solutions are used. Eor interacting particles with low surface potential e fa/kT < 1), can accurately be calculated using the linear superposition approximation (Israelachvili, 1992 Russel, 1989 Hunter, 1987)... 

A potential is simply the work done in bringing a point charge from infinity to the particle surface. Potentials are always relative to ground (i.e. at an infinite distance from the surface). The surface potential is very important and is approximated by the so-called zeta potential, which can be estimated by (micro)electrophoresis experiments, at least for some special cases (small and large particles via the so-called Hiickel and Smoluchowski equations). In the general case, the zeta potential is calculated from values of the electrophoretic mobility, using graphical solutions or the Henry equation, which requires a correction factor. 

As before for the PM case, a new object at infinite dilution is added to the BO electrolyte in order to mimic colloid-water, solid-water or air-water interfaces. For smooth surfaces, the added particle of radius R keeps its spherical symmetry. The previous electrolyte with Wmax = 4 for water requires one, one, nine projections for surface-cation, surface-anion and surface-water correlations, respectively. The local HNC profiles can be derived in a few seconds from the previously calculated bulk correlations and the imposed particle-surface potentials v jQ r). 

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