Stability ratio critical coagulation concentration

The principle of this method is that the initial slope (time = zero) of the optical density-time curve is proportional to the rate of flocculation. This initial slope increases with increasing electrolyte concentration until it reaches a limiting value. The stability ratio W is defined as reciprocal ratio of the limiting initial slope to the initial slope measured at lower electrolyte concentration. A log W-log electrolyte concentration plot shows a sharp inflection at the critical coagulation concentration (W = 1), which is a measure of the stability to added electrolyte. Reerink and Overbeek (12) have shown that the value of W is determined mainly by the height of the primary repulsion maximum in the potential energy-distance curve. 

Equation (51) shows that Wis a sensitive function of max, the maximum in the interaction potential, which in turn is a very sensitive function of properties such as p0, electrolyte concentration, and so on. As a consequence, the stability ratio decreases rapidly with, for example, added electrolyte, and the dispersion coagulates beyond a threshold value of electrolyte concentration known as the critical coagulation concentration, as we saw in Section 13.3b.1. 

The sensitivity of the stability ratio to chemical or particle interaction factors can be illustrated by an examination of the model expression for Wn in Eq. 6.75. For example, if temperature and the particle interaction parameters are fixed, then Wn will vary with the concentration, c (also included in /c), of Z-Z electrolyte. At low values of c, k is also small, and the first equality in Eq. 6.75 indicates that Wu will take on its largest values. (Decreasing c also provokes an increase in dm because of Eq. 6.73, but this effect is dominated by that of k.40) Conversely, as c increases, the value of Wu will drop until it achieves its minimum, Wn = 1.0, when Z dm = 2 (Eq. 6.75). At this concentration, termed the critical coagulation concentration (ccc), or flocculation value, the flocculation process has become transport-controlled and therefore is rapid. Thus in general... 

Figure 5, in which the stability ratio is plotted against electrolyte concentration, for cations of valencies 1,2, and 3 and monovalent anions, shows that the critical coagulation concentration increases with decreasing cation valency (Figure 6). This rule is not valid for the critical stabilization concentration.

In this chapter, mathematical procedures for the estimation of the electrical interactions between particles covered by an ion-penetrable membrane immersed in a general electrolyte solution is introduced. The treatment is similar to that for rigid particles, except that fixed charges are distributed over a finite volume in space, rather than over a rigid surface. This introduces some complexities. Several approximate methods for the resolution of the Poisson-Boltzmann equation are discussed. The basic thermodynamic properties of an electrical double layer, including Helmholtz free energy, amount of ion adsorption, and entropy are then estimated on the basis of the results obtained, followed by the evaluation of the critical coagulation concentration of counterions and the stability ratio of the system under consideration. 

LOG MOLAR CONCENTRATION FIGURE 10J29 Colloid stability ratio for different salt concentrations showing the critical coagulation concentration, CCC. Data from Barringer [25]. 

The stabihty of the latexes was determined by determining the critical coagulation concentration (ccc) using CaClj. Although the CCC was low (0.0175-0.05 mol dm ), it was higher than that for the latex prepared without surfactant The subsequent addition of INUTEC SPl resulted in a large increase in the CCC, as illustrated in Figure 17.2, which shows log W-log C curves (where W is the ratio between the fast flocculation rate constant to the slow flocculation rate constant, referred to as the stability ratio) at various additions of INUTEC SPl . 

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