Landau theory minima

For the minimum in the free energy to correspond to the zero value of q at T > T, T being the stability limit of the isotropic phase, A must be positive, while for a nonzero value of q to correspond to a stable state at T < T, A has to be negative. Therefore, A must vanish at T = T. The simplest choice of A(T) that satisfies these conditions is A(T) = a(T — T ). In practice, the coefficients of higher-order terms are assumed to be temperature-independent, as in the well-known Landau theory. 

In the equation, the first term of the Taylor expansion is zero because the free energy is a minimum at the average value of the order parameter in the parent phase. According to the Landau theory, near a continuous transition, the coefficient J goes to zero as... 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

This presentation forms the basis of the theory of colloid stability due to Deryaguin-Landau-Verwey-Overbeek (DLVO theory) [10]. The Gj-h curve shows two minima and one maximum A shallow minimum (of the order of few kT) units at large separations, which may result in weak and reversible flocculation. A deep primary minimum (several lOOkT units) is seen at short separations - this results in strong flocculation (coagulation). An energy maximum, G ax, at intermediate distances prevents flocculation into the primary minimum. 

---