Critical coagulation concentration Schulze-Hardy rule

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). 

Under what conditions are colloids stable Explain qualitatively (with schematic diagrams) the forces between colloidal particles. How does the force of repulsion between them vary with concentration As the concentration of the colloid increases, there is the tendency to coagulate and in fact the critical concentration for coagulation gets less as the valence of the ions present increases (Schulze-Hardy rule). Give a detailed, although qualitative, rationalization of this law. (Bockris)... 

Critical coagulation concentrations - Schulze-Hardy rule... 

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 from stable dispersion to aggregation usually occurs over a fairly small range of electrolyte concentration. This makes it possible to determine aggregation concentrations, often referred to as critical coagulation concentrations (CCC). The Schulze-Hardy rule summarizes the general tendency of the CCC to vary inversely with the sixth power of the counter-ion charge number (for indifferent electrolyte). 

The transitions from stable dispersion to aggregation just described in terms of the critical coagulation concentrations and the Schulze-Hardy rule, apply best to suspensions in which the particles have only one kind of charge. However, clay particles can carry positive and negative charges at the same time, on different parts of the particle. See Section 5.6.2. 

If an emulsion is stabilized by electrical repulsive forces, then demulsification could be brought about by overcoming or reducing these forces. In this context the addition of electrolyte to an O/W emulsion could be used to achieve the critical coagulation concentration, in accord with the Schulze-Hardy rule. 

Critical Coagulation Concentration (CCC) The electrolyte concentration that marks the onset of coagulation. The CCC is very system-specific, although the variation in CCC with electrolyte composition has been empirically generalized. See also Schulze-Hardy Rule. 

Schulze-Hardy Rule An empirical rule summarizing the general tendency of the critical coagulation concentration (CCC) of an emulsion or other dispersion to vary inversely with the sixth power of the counterion charge number of added electrolyte. See also Critical Coagulation Concentration. 

The minimum concentration of ions needed to produce fast coagulation is called the critical coagulation concentration (c.c.c.). The c.c.c. values usually depend strongly on the counterion charge (Schulze-Hardy rule)238. ... 

The critical coagulation concentrations (c.c.c.) determined turbidimetrically for latex A-2 with NaCl, CaCl2, AlCl3(pH 3), and AlCl3(pH 7) were 180, 18.5, 0.37, and 0.15 mM, respectively (the values for NaCl and CaCl2 were independent of pH). These results do not follow the inverse sixth-power Schulze-Hardy rule derived by Verwey and Overbeek (18, 22) for the dependence of c.c.c. on valence. Instead, the log c.c.c.-log valence plot has a slope of about 3.3. This could indicate a low C potential for this system, since, in the limiting case of low potentials where the Debye-Hiickel approximation applies, the derived dependence is second-power (22) However, more extensive data are required before it can be concluded that this case deviates from the "normal sixth-power Schulze-Hardy rule. 

This expression is the principal result of DLVO theory. The steep r dependence of the critical coagulation concentration has been observed experimentally for strongly charged surfaces and is commonly known as the Schulze-Hardy rule. In the case of weakly charged surfaces, a less steep dependence of the critical coagulation concentration on the valence (z" ) is observed. In fact, it was the empirical dependence of the c.c.c. on the valence established in the course of experimental studies on coagulation that inspired the development of DLVO theory. 

Schulze-Hardy rule and the critical coagulation concentration (CCC)... 

Figure 10.19 The role of salt In colloid stability as described via the Schulze-Hardy rule for dispersions. The critical coagulation concentration (CCC) Is Inversely proportional to z (the exponent 6 Is em average value and a reasonable number to use). This fact leads to the equation in the figure for two salts with different ionic valencies (i.e. onecan calculate the CCC of one salt from CCC of another salt with a different counter-ion valency). In the drawing, the particle is negatively charged (e.g. a Agl particle), K is the counter-ion and NOs is the co-ion...

Further colloid/surfiice chemistry experiments references coagulation kinetics using Agl hydrosol (y.CAem. diSchulze/Hardy rule using Au hydrosol (ibid. 71(1994)624) determination of critical micelle concentration of surfactants using a colorimetric method ri hid.70(1993)254) density gradient columns displaying acid/base and metal ion (V, Cr, Fe, Co, Ni) equilibria (76iV 63(1986)148). 

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