Interacting particles in contact

Abstract

The depth of the potential well for contacting particles determines the texture of a floc. This energy can be calculated from the interaction forces between the particles. In electrocratic colloids it depends on the counter-ion valency z, the (local) potential ϕ_δ near the contact point and the curvature of the surfaces in contact. However, it does not depend on the Debye length, 1/κ, which measures the range of the repulsive forces.

At a critical value Z_c for the parameter Z=zeϕ_δ the minimum disappears. For Z < Z_c particles form aggregates when they collide. But for Z > Z_c flocs are unstable: they would repeptize or at least rearrange their texture.

Because the rules of Schulze and Hardy and of Eilers and Korff apply simultaneously it can be derived that ϕ_δ is low (Z < Z_c) and that Z has an equal value in sols when they coagulate at equal rates in electrolytes with different z. This theoretical observation has been verified experimentally. The double-layer potential, ϕ_δ, is indeed inversely proportional to z under such conditions. As a consequence, the parameter γ= tanh (zeϕ_δ/4k_BT), which represents the influence of double-layer potentials in the DLVO theory, becomes a constant for conditions of equal rate. But, unlike the suggestion in the classical theory γ≠ 1, and its value is required to account for experimental observations.

When sols coagulate at the same rate the depth of the potential well for aggregates increases with z. This effect is readily observed, since it is reflected in the texture of the flocs which are formed. Both Z(i.e. ϕ_δ) and z are variables in the coagulation conditions, and can be used to control the porosity of flocs, sediments and materials, which are prepared by sol–gel and related methods.