The critical flocculation point

The point at which flocculation is first detected on decreasing the solvency of the Aspersion medium for the stabilizing moieties is termed the critical flocculation point (Napper, 1968b) (see Figs 5.1-5.3). The abbreviation CFPT will be used hereafter to denote this point, which in its various manifestations will be central to much of the discussion in this and subsequent chapters. 

As shown in Fig. S.l, sterically stabilized dispersions often display an abrupt transition from long-term (indeed thermodynamic) stability to the onset catastrophic flocculation. Changing the temperature by only a few degrees kelvin is sufficient to transform a very stable dispersion into a flocculated coagulum. This dramatic temperature response contrasts sharply with the more sluggish response to temperature changes exhibited by electrostatically stabilized dispersions. Their stability is normally decreased by heating, as noted by Faraday (1857). 

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When >0.5, becomes negative (attractive) this, combined with the van der Waals attraction at this separation distance, produces a deep minimum causing flocculation. In most cases, there is a correlation between the critical flocculation point and the 0-condition of the medium. A good correlation is found in many cases between the critical flocculation temperature (CFT) and the 0-temperature of the polymer in solution (with both block and graft copolymers the 0-temperature of the stabilising chains A should be considered) [2]. A good correlation was also found between the critical volume fraction (CFV) of a nonsolvent for the polymer chains and their 0-point under these conditions. In some cases, however, such correlation may break down, and this is particularly the case for polymers that adsorb by multipoint attachment. This situation has been described by Napper [2], who referred to it as enhanced steric stabilisation. 

Influence of the system parameters on the critical flocculation point... 

Thermodynamically Limited Steric Stabilization The Identification of the Critical Flocculation Point... 

The dependence of the critical flocculation point on the molecular weight of the stabilizing moieties... 

Note that, as mentioned previously, both and Xz often tend to approach i and i respectively as the 0-point is approached. Accordingly, both free energy terms will approach zero at the 0-point and become negative in slightly worse than 0-solvents. Thus the concentration dependence of x is unlikely to interfere with the expected correlation between the critical flocculation point and the 0-point. This accords with the results of several experiments. 

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.

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). 

This is expected since the extrapolation procedure usually overestimates the yield value. The data of Figs. 3 and 4 show a rapid increase in yield value above a critical PEO concentration, 4. This concentration corresponds to the critical flocculation concentration of the free polymer. However, since the rise in Tg did not occur at a sharp value, the latter was taken as the intersection point at which the extrapolated hprizontal and vertical lines meet. This gave values of 4 of 0.02 0.002, O.OItO.001 and O.OOStO.OOl for PEO with of 20,000, 35,000 and 90,000 respectively. Moreover, the 4p values obtained from the two sets of rheological results were almost the scime within the error of locating p. 

When the electrostatic stabilization of the emulsion is considered, the electrolytes (monovalent and divalent) added to the mixture are the major destabilizing species. The zeta potential of the emulsion particles is a function of the concentration and type of electrolytes present. Two types of emulsion particle-electrolyte (ions) interaction are proposed non-specific and specific adsorption.f H non-specific adsorption the ions are bound to the emulsion particle only by electrical double-layer interactions with the charged surface. As the electrolyte concentration is increased, the zeta potential asymptotes to zero. As the electrostatic repulsion decreases, a point can be found where the attractive van der Waals force is equal to the repulsive electrostatic force and flocculation of the emulsion occurs (Fig. 9A). This point is called the critical flocculation concentration (CFC). 

Plots of log W versus log C are shown in Figure 10.28. The condition log W = 0 [W = 1) is the onset of fast flocculation. The electrolyte concentration at this point defines the critical flocculation concentration (CFG). Above the CFG, W<1 (due to the contribution of van der Waals attractions which accelerate the rate above the Smoluchowski value). Below the GFG, W > 1 and it increases with a decrease... 

Summary of the various critical flocculation points for thermodynamically limited stability... 

We emphasise that both enthalpic and entropic stabilization have been observed in both aqueous and nonaqueous dispersion media. Furthermore all dispersions in principle should be able to be flocculated both by heating and by cooling, if only a wide enough range of temperatures and pressures can be scanned. It is not, however, always possible to observe both critical flocculation points. Sometimes the dispersion medium fre es before flocculation at the LCFT can be reached. Alternatively, it may decompose on heating before the UCFT is reached. 

As Patterson and Delmas (1969) have implied, application of the Euler chain rule in the vicinity of a critical flocculation point (CFT) gives for its pressure dependence... 

The condition x = 0-5 is referred to as the 0-point and denotes the onset of change of repulsion to attraction, i.e. the onset of flocculation. In many cases, there is good correlation between the 0-point and the flocculation point (e.g. the critical flocculation temperature). 

With many systems, good correlation between the flocculation point and the 0 point is obtained [8]. For example, the emulsion will flocculate at a temperature (referred to as the critical flocculation temperature, CFT) that is equal to the 6-temperature of the stabilising chain. The emulsion may flocculate at a critical volume fraction of a non-solvent (CFV) that is equal to the volume of non-solvent that brings it to a 0-solvent. 

Incipient flocculation of sterically stabilized suspensions, i.e. the condition when the chains are in a poor solvent condition, can be investigated using turbidity measurements. The suspension is placed in a spectrophotometer cell placed in a block that can be heated at a controlled rate. From a plot of turbidity versus temperature one can obtain the critical flocculation temperature, which is the point at which there is rapid increase in turbidity. 

The critical factor in the development of the syndrome is the size of the ultrafine zinc oxide particles produced when zinc is heated to temperatures approaching its boiling point in an oxidizing atmosphere." The particles must be small enough (zinc oxide powder is either inhaled or taken orally. Only freshly formed fume causes the illness, presumably because flocculation occurs in the air with formation of larger particles that are deposited in the upper respiratory tract and do not penetrate deeply into the lungs. ... 

The current theories of steric stability (3-6) predict that provided the particles are well-covered and the polymer is well-anchored particles bearing non-ionic polymers should flocculate at or near the 0-point of the stabilising chains. The available experimental date ( 3, 7 9 8) confirm this result in as much as critical flocculation temperatures and pressures have been found to correlate tolerably well with the relevant 0-points for a wide range of systems. Where the correlation has been less than satisfactory the discrepancy has often been understandable in terms of multiple anchoring, selective adsorption of lyophobic blocks, or other specific effects (9, 10). 

The water is actually touching the blade, so the velocity that it attains on contact must be equal to that of the blade. Of course, as it departs, its velocity will be dilferent, but this is not the critical point of power transfer. The blade transfers power to the water while still in contact. Upon detachment, the water parcel that got the power being transferred will then commence expending the power to overcome fluid friction imposed upon it by neighboring parcels this process produces the velocity gradient required for flocculation to occur. 

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