Critical flocculation concentration dispersions

The crucial question is at what value of <)> is the attraction high enough to induce phase separation De Hek and Vrij (6) assume that the critical flocculation concentration is equivalent to the phase separation condition defined by the spinodal point. From the pair potential between two hard spheres in a polymer solution they calculate the second virial coefficient B2 for the particles, and derive from the spinodal condition that if B2 = 1/2 (where is the volume fraction of particles in the dispersion) phase separation occurs. For a system in thermodynamic equilibrium, two phases coexist if the chemical potential of the hard spheres is the same in the dispersion and in the floe phase (i.e., the binodal condition). 

To (obtained from extrapolation of the ascending part of the flow curve) as a function of C. The shear modulus, GQ, measured using the pulse shearometer, is also shown as a function of C in the same figure. A measurable x and GQ is obtained above a critical value of C, which in both cases is -0.22 mol dm 3. As we will see later, this electrolyte concentration should be taken as the critical flocculation concentration (CFC) for the concentrated dispersion. Above the CFC, xg increases rapidly with increasing C whereas G initially increases gradually with increasing C until C = 0.3 mol dm 3, above which there is a more rapid increase of Gq. 

Panayiotopoulos KP, Barbayiannis N, Papatolios K (2004) Influence of electrolyte concentration, sodium adsorption ratio, and mechanical disturbance on dispersed clay particle size and critical flocculation concentration in alfisols. Comm Soil Sci Plant Anal 35 1415-1434... 

As another criterion of stability, a critical flocculation temperature(OFT) was measured. The measurement of CFT was carried out as follows the bare latex suspension was mixed with the polymer solution of various concentrations at 1+8 °C by the same procedure as in the adsorption experiments. Then, the mixture in a Pyrex tube(8 ml, U.0 wt %) was warmed slowly in a water bath and the critical temperature at which the dispersion becomes suddenly cloudy was measured with the naked eye. 

The stability of these dispersions has been investigated. A strong dependence of critical flocculation conditions (temperature or volume fraction of added non-solvent) on particle concentration was found. Moreover, there seems to be little or no correlation between the critical flocculation conditions and the corresponding theta-conditions for the stabilising polymer chains, as proposed by Napper. Although a detailed explanation is difficult to give a tentative explanation for this unexpected behaviour is suggested in terms of the weak flocculation theory of Vincent et al. 

The stability of the various dispersions was assessed and compared by determining the critical flocculation conditions (temperature or volume fraction of added non-solvent for the grafted polymer), as a function of particle concentration. 

It is now well established that the critical flocculation conditions for dispersions with a low particle concentration can be correlated with the 6 conditions of the steric stabilizing moiety in free solution (1). This correlation is only found in systems where desorption of the stabilizer does not occur and where the thickness of the steric barrier is sufficient to completely screen the attractive van der Waals... 

Critical Flocculation Electrolyte Concentration The critical flocculation electrolyte (Na2S0.) concentration was determined by following the average particle size of the dilute dispersion (where the particles were coated with PVA corresponding to the plateau adsorption) as a function of Na2S0 concentration, using a Coulters Nanosizer (Coulters Electronics Ltd) as described before (20). 

Figure 5 shows the variation of Xg with temperature at two C values (0.20 and 0.25 mol dm 3). In both cases Xg is essentially zero until a critical temperature is reached, above which xg increases rapidly with increasing temperature reaching a maximum above which there is a tendency forXg to fall again with further increase in temperature. The critical temperature corresponding to the abrupt increase inTg is 20 and 25°C for C equal to 0.25 and 0.20 mol dm, respectively This temperature may be identified with the critical flocculation temperature (CFT) of the concentrated dispersion. 

The electrostatic repulsion between dispersed particles can be diminished by increasing the concentration of background electrolyte (e.g. NaCl, CaCl2)- Polyvalent ions are more effective than monovalent. There is a critical electrolyte concentration for every system at which flocculation or coalescence takes place. These principles must be taken into account when emulsions have to form in very hard water. 

Scanning electron microscopy (SEM) data for carbon-black compounds and conductive polymer blends [72c], supported by recent transmission electron microscopy (TEM) evaluations [79,80] (shown in Figure 11.39) were made, they also contradict the assumption of a statistical distribution. We find complete dispersion below the critical volume concentration (I) and a sudden stiucture formation ( branched flocculate chains ) at the critical volume concentration. This structural feature remains at higher concentrations. 

Table 12.5. Although the basis of the comparison presented therein is slightly different (per particle vs per doublet), the results predicted by both extreme models are not too widely disparate. The configurational free energy change associated with flocculation can obviously be as large as 10 A T in systems of usual interest. Dilute dispersions are clearly more stable on this basis than more concentrated systems. What this means in terms of the effect on the critical flocculation point depends critically upon the nature of the particular system concerned.

It is obvious that, as with nonaqueous dispersions, the critical polymer concentration required for flocculation decreases with increasing molecular weight. Increasing the temperature rendered the latices more susceptible to flocculation (Fig. 16.6). 

Critical flocculation electrolyte concentration (CFC) of the dilute latex dispersions... 

Two methods were used to establish the critical flocculation electrolyte (KCl or Na2S04) concentration of the dilute latex. In the first method, the turbidity, r, of the dispersion (with mole fraction 0 = 5 x 10 ) was followed as a function of wavelength, X, at various electrolyte concentrations at 25 °C, using an SP 1800 Pye-Unicam Spectrophotometer. Plots of log T versus log A were linear over the wavelength range 400 - 600 nm. The gradient n of such a plot was then plotted versus electrolyte concentration [21]. At the CFC a... 

For conductive fillers (carbon black), Wessling proposed a model explaining a sudden increase of the conductivity at a critical volume concentration of filler, (p rif main aspects of this model consist of the formation of a strongly-adsorbed monolayer of matrix molecules. At the critical point, which is determined by the interfacial energy at the particle/adsorbed shell interphase, the dispersed phase flocculates (separates from the matrix) and forms branched, elongated chains. The process dispersion-flocculation, as a phase transition, seems to be reversible at(p it occurs in the form of an oscil-... 

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