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. 

In a number of recent publications (1, 2) microcrystailine cellulose dispersions (MCC) have been used as models to study different aspects of the papermaking process, especially with regard to its stability. One of the central points in the well established DLVO theory of colloidal stability is the critical coagulation concentration (CCC). In practice, it represents the minimum salt concentration that causes rapid coagulation of a dispersion and is an intimate part of the theoretical framework of the DLVO theory (3). Kratohvil et al (A) have studied this aspect of the DLVO theory with MCC and given values for the CCC for many salts, cationic... 

Inert electrolytes, i.e., ions which are not specifically adsorbed, compress the double layer and thus reduce the stability of the colloids (Fig. 7.4). A critical coagulation concentration, Cs or ccc, can be defined (see Eqs. (4) and (5) in Table 7.3) which is independent of the concentration of the colloids (Schulze-Hardy Rule). 

The critical concentration (critical coagulation concentration) is thus found to depend on the type of electrolyte used, as well as on the valency of the counterion. It is seen... 

TABLE 13.1 Critical Coagulation Concentration Values (in Moles Liter-1) for Mono-, Di-, Tri-, and Tetravalent Ions Acting on Both Positive and Negative Colloids (Numbers in Parentheses) and CCC Values Relative to the Value for Monovalent Electrolytes in the Same System (Numbers Outside Parentheses)3... 

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. 

What is the critical coagulation concentration How does it vary with interaction energies ... 

Substitute this in Equation (2) or (3) and solve for the critical coagulation concentration (CCC) ... 

Here, Co(OH)2 represents the solid hydroxide. The solution data show that at pH values of 7.5 and 6.5 the dominant cobalt (II) species is the free (aquo) ion by factors of 100 and 1000 respectively. It is therefore highly unlikely that the coagulation at pH 6.5-7.5 and 10"4Af Co (II) and the reversal of charge can be caused by the free CoOH+ species. If it is caused by polynuclear charged species then the log-linear relationship (9) between the critical coagulation concentration and the valence of the coagulating ion would require a polynuclear species to have a charge of +5 or +6. Such a species has not been identified. (It is of interest to note that if this species did exist it would have to be a compact ion,... 

Critical coagulation concentrations - Schulze-Hardy rule... 

Table 8.1 Critical coagulation concentrations (in millimoles per dm3) for hydrophobic sols 6 (By courtesy of Elsevier Publishing Company)...

The critical coagulation concentration (c.c.c.) of an indifferent (inert) electrolyte (i.e. the concentration of the electrolyte which is just sufficient to coagulate a lyophobic sol to an arbitrarily defined extent in an arbitrarily chosen time) shows considerable dependence upon the charge number of its counter-ions. In contrast, it is practically independent of the specific character of the various ions, the charge number of the co-ions and the concentration of the sol, and only moderately dependent on the nature of the sol. These generalisations are illustrated in Table 8.1, and are known as the Schulze-Hardy rule. 

The transition between stability and coagulation, although in principle a gradual one, usually occurs over a reasonably small range of electrolyte concentration, and critical coagulation concentrations can be determined quite sharply. The exact value of the critical... 

An expression for the critical coagulation concentration (c.c.c.) of an indifferent electrolyte can be derived by assuming that a potential energy curve such as V(2) in Figure 8.2 can be taken to represent the transition between stability and coagulation into the primary minimum. For such a curve, the conditions V = 0 and dV/dH = 0 hold for the same value of H. If Vr and VA are expressed as in equations (8.7) and (8.10), respectively,... 

For a typical experimental hydrosol critical coagulation concentration at 25°C of 0.1 mol dm-3 for z = 1, and, again, taking if/d = 75 mV, the effective Hamaker constant, A, is calculated to be equal to 8 X 10 20 J. This is consistent with the order of magnitude of A which is predicted from the theory of London-van der Waals forces (see Table 8.3). 

Critical coagulation concentrations for spherical particles of a given material should be proportional to e3 and independent of particle size. 

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