Aggregation electrolyte concentration

A combination of equation (C2.6.13), equation (C2.6.14), equation (C2.6.15), equation (C2.6.16), equation (C2.6.17), equation (C2.6.18) and equation (C2.6.19) tlien allows us to estimate how low the electrolyte concentration needs to be to provide kinetic stability for a desired lengtli of time. This tlieory successfully accounts for a number of observations on slowly aggregating systems, but two discrepancies are found (see, for instance, [33]). First, tire observed dependence of stability ratio on salt concentration tends to be much weaker tlian predicted. Second, tire variation of tire stability ratio witli particle size is not reproduced experimentally. Recently, however, it was reported that for model particles witli a low surface charge, where tire DL VO tlieory is expected to hold, tire aggregation kinetics do agree witli tire tlieoretical predictions (see [60], and references tlierein). 

Figure 6.9 Influence of electrolyte concentration on colloid stability ( denotes change from a stable to an aggregated state)...

Ion-pair formation (or the formation of triplets, etc.) is a very simple kind of interaction between ions of opposite charge. As the electrolyte concentration increases and the mean distance between ions decreases, electrostatic forces are no longer the only interaction forces. Aggregates within which the ions are held together by chemical forces have certain special features (i.e., shorter interatomic distances and a higher degree of desolvation than found in ion pairs) and can form a common solvation sheath instead of the individual sheaths. These aggregates are seen distinctly in spectra, and in a number of cases their concentrations can be measured spectroscopically. 

Rupture of fractal (flocculated) aggregates of polystyrene latices in simple shear flow and converging flow was studied by Sonntag and Russel (1986, 1987b). For simple shear flow and low electrolyte concentrations, the critical fragmentation number decreases sharply with agglomerate radius (R) as... 

At high electrolyte concentrations of the soil solution, the double layer is compressed so that clay remains flocculated. A decrease in ion concentration, e.g. as a result of dilution by percolating rain water, can result in dispersion of clay and collapse of aggregates. If the exchange complex is dominated by polyvalent ions, the double layer may remain narrow even at low electrolyte concentrations and consequently aggregates remain intact (FAO, 2001). 

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

In addition to its simplicity, such a geometric argument can also be used to predict the changes in the structure of the aggregates as variables such as pH, charge, electrolyte concentration, and chain length of the tail are varied. The importance of the relative effects of the head group area and the size of the tails was first emphasized by Tatar (1955), and the details were developed subsequently by Tanford (1980) and others (see Wennerstrom and... 

External factors that result in a reduction in the hydrophilicity of the head group, such as high neutral electrolyte concentrations, will cause an increase in the aggregation number,... 

C is clearly an important quantity for a latex dispersion since it essentially represents the electrolyte concentration at which complete loss of stability occurs. It may be obtained experimentally by a variety of different methods (14,17, 18,19). It should be noted, however, that since coagulation is a kinetic phenomena time enters as a variable and consequently the various methods may yield somewhat different numerical results. This effect is illustrated by results obtained for the coagulation of polytetrafluoroethylene (PTFE) latices with sodium chloride as a function of pH (19). From Figure 4 it can be seen that different results are obtained according to whether the system was examined after 2 h or 24 h. As expected the results indicate that the state of aggregation is more advanced after 24 h and consequently systems at a lower electrolyte concentration have coagulated. Care must therefore be taken when comparing values... 

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 size and shape of micelles have been a subject of several debates. It is now generally accepted that three main shapes of micelles are present, depending on the surfactant structure and the environment in which they are dissolved, e.g., electrolyte concentration and type, pH, and presence of nonelectrolytes. The most common shape of micelles is a sphere with the following properties (i) an association unit with a radius approximately equal to the length of the hydrocarbon chain (for ionic micelles) (ii) an aggregation number of 50-100 surfactant monomers (iii) bound counterions for ionic surfactants (iv) a narrow range of concentrations at which micellization occurs and (v) a liquid interior of the micelle core. 

There is some experimental evidence that for some colloidal systems, the rate of aggregation has a maximum and then decreases with increasing electrolyte concentration. In the experiment of Alfridsson et al.,2 the rate constant of aggregation for a suspension of charged... 

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