Hardy-Schulze 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). 

A prediction from DLVO theory can be made by deriving the conditions under which V = 0 and dV/dH = 0. The result is 

It is evident that for high potentials (F —F 1) the CCC varies inversely with z6. Experimental results generally give the same relation with z and calculate back to reasonable values for A. (For lower potentials this also will influence CCC, but for a 

Example. For clay particles in water, assuming that they to act like flat plates, 

100 mV) gives the critical coagulation concentrations in polyvalent metal chlorides as follows  

Examples. For clay particles in water, assuming them to act like flat plates, A = 5xlO °J, C in moll and area of 2500nm, [e f/(5)]/kT = 4 (i.e. K 100 mV) gives the CCCs in polyvalent metal chlorides as follows  

The transitions from stable dispersion to aggregation just described in terms of the CCCs 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 5.7.2). 

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Schottky mechanism Schott nomenclature Schradan [152-16-9] Schreibersite [12424-46-3] Schugi mixer Schulze-Hardy rule Schwann cells Schwarzembergite Schwenzfeier process Science policy... 

When foreign electrolytes which do not react with the soap are present, the ions responsible for bringing about coagulation are the ones with charges opposite in sign to those on the dispersed particle. The effect of the valence of the ion follows the Schulze-Hardy rule for the precipitation of sols by electrolytes wherein the coagulating power of an ion increases considerably with the increasing valence of the ion. 

Schrock alkylidyne catalysts, 26 948-949 Schrodinger s equation, 16 734-735 Schultz-Flory distribution, 20 156 Schultz-Flory equation, 17 714 Schulze—Hardy rule, 7 289, 10 121 Schweizer, M. E., 11 248 Schwenzfeier process, 3 641 Science... 

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). 

After expanding these expressions, as related to h and C, this becomes (Schulze-Hardy Rule for suspensions in water)... 

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)... 

The results in Table 13.1 have been collected for colloids bearing both positive and negative surface charges. One of the earliest (1900) generalizations about the effect of added electrolyte is a result known as the Schulze-Hardy rule. This rule states that it is the valence of the ion of opposite charge to the colloid that has the principal effect on the stability of the colloid. The CCC value for a particular electrolyte is essentially determined by the valence of the counterion regardless of the nature of the ion with the same charge as the surface. The numbers listed in parentheses in Table 13.1 are the CCC values in moles per liter for counterions of the... 

In Chapter 11 (Sections 11.4 and 11.6) we implicitly anticipated that the ion opposite in charge from the wall plays the predominant role in the double layer, the central observation of the Schulze-Hardy rule. This enters the mathematical formalism of the Gouy-Chapman theory in Equation (11.52), in which a Boltzmann factor is used to describe the relative concentration of the ions in the double layer compared to the bulk solution. For those ions that have the same charge as the surface (positive), the exponent in the Boltzmann factor is negative. This reflects the Coulombic repulsion of these ions from the wall. Ions with the same charge as the surface are thus present at lower concentration in the double layer than in the bulk solution. 

Explain the Schulze-Hardy rule. Is it empirical or based on theory ... 

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. 

In the early work of Schulze ( 0, Linder and Picton (2) and Hardy (3) the sensitivity of colloidal dispersions to the addition of electrolytes was clearly demonstrated. Then in 1900 Hardy (4) showed that the stability of sols was connected with the electrophoretic mobility of the particles and he demonstrated, i) that the valency of the ion opposite in charge to that of the sol particles determined the ability of an electrolyte to coagulate a sol and that, ii) the effectiveness of the electrolyte increased rapidly with increase in valency of the counter-ion. These observations formed the basis of the so-called Schulze-Hardy rule. 

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. 

Multivalent ions in starch dispersions, particularly those of aluminum, calcium, sulfate and oxalate, will induce retrogradation due to complexation or competition for water of hydration. The ions can be introduced by hard process water or accumulate by leaching from paper during surface sizing or coating. The destabilizing effect of ions follows the Schulze-Hardy rule. 

I. M. Metcalfe and T. W. Healy, Charge-regulation modeling of the Schulze-Hardy rule and related coagulation effects, Faraday Discuss. Chem. Soc. 90 335 (1990). 

Attempts to utilize traditional DLVO approaches to quantify the Schulze-Hardy Rule have found limited and qualified success [23,59]. Although a qualitative agreement of the predicted dependence of ccc on counterion valence can be demonstrated, non-DLVO forces are typically ignored and analytical solutions of the DLYO equations predict unrealistically large ccc values [23,59]. 

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