4 - The balance of forces

Summary

Forces in the DLVO theory of colloidal stability

For over 50 years the theory of the stability of colloid suspensions due independently to Deryaguin and Landau and Verwey and Overbeek held centre stage in the field. Following the derivation from quantum mechanics of the attractive force between two molecules, it was a straightforward matter to add these forces up to arrive at a force between two model colloidal particles. This potential of interaction per unit area behaves, for two particles modelled as planar interfaces a distance l apart as, V(l) ≈ −A/(12πl²) where A is the Hamaker constant (see Chapter 2).

The double-layer force of repulsion between the (charged) surfaces behaves at large distances of separation as V(l) ≈ f · exp(−κ_Dl). Here κ_D is the Debye length, which depends on salt concentration, and the prefactor is a complicated function of the surface charge or potential (see Chapter 3). Then a combination of these forces gives rise to a predicted net force of attraction like that shown schematically in Fig. 4.1.

These forces depend on geometry assumed for the particles (see Chapter 2). The insertion of this potential into a theory of coagulation of particles predicted whether the particles would stay in suspension or flocculate. The particles could flocculate into a ‘secondary minimum’, with a barrier usually at l ∼ 1/κ_D.

Or in the absence of such a barrier they could (theoretically) adhere into a deep ‘primary’ minimum at a distance of a few molecular diameters.