Critical flocculation pressure

Figure 2 The upper critical flocculation temperature is shown plotted against the applied pressure. refers to the PMMA latex while, o refers to the PVAc latex. The solid line represents 9 conditions for a solution of PIB + 2-methylbutane while the dashed line represents the theoretically calculated UCFT as a function of pressure.

It was suggested in a previous publication (9) that flocculation at the UCFT can be ascribed to the free volume dissimilarity between the polymer stabilizing the particle and the low molecular weight dispersion medium. Incorporating this idea in a quantitative way into the theory of steric stabilization allowed for a qualitative interpretation of the experimental data. This idea is further extended to include the effect of pressure on the critical flocculation conditions. 

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). 

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 lower critical solution temperature (LCST) phase behavior exhibited by the nanocrystals is often found for low molecular weight solutes in supercritical fluids (25,26) and also for polymers dissolved in SCFs, and results from compressibility differences between the polymer and the solvent (15). As the temperature increases or the pressure decreases, the solvent prefers to leave the solute to increase its volume and entropy. The same mechanism that governs phase separation in supercritical fluids also drives flocculation of two surfaces with steric stabilizers, as has been shown with theory (22) and simulation (23). 

Finally, we stress that the free volume approach is only applicable to nonpolar systems. Aqueous dispersions fall outside its scope. This is vividly illustrated by the data of Evans et al. (1975), who determined experimentally that d(UCFT)/d7 = — 1 x 10 KPa for latex particles sterically stabilized by poly(oxyethylene) in aqueous 0-43 molal magnesium sulphate solutions. Both the sign and magnitude of this quantity is different from that predicted by free volume theory for the UCFT of non aqueous dispersions. Paradoxically, it falls in line with the predictions, both in sign and magnitude, published by Croucher and Hair (1979) for the pressure dependence of the LCFT of poly(a-methylstyrene) in -butyl chloride. This may be merely coincidental, but the very small pressure dependence exhibited by the UCFT of aqueous sterically stabilized dispersions emphasizes the major differences between the origins of flocculation at the UCI T for aqueous and nonaqueous dispersions. The small pressure dependence observed for aqueous systems is scarcely surprising since the UCFT of an aqueous dispersion occurs far from the critical point of water whereas that for nonaqueous dispersions is quite close to the critical point of the dispersion medium. 

The effect of pressure shown earlier is modified in most industrial flltrations in which cake compressibility usually lies between 0.1 and 0.8. Furthermore, the resistance of the filter reduces the effects of the respective variables. It has been found, however, that an increase in pressure causes a nearly proportionate increase in the flow rate in the filtration of granular or crystalline solids. Flocculent or slimy precipitates, on the other hand, have their filtration rates increased only slightly by an increase in pressure. Some materials have a critical pressure above which a further increase results in an actual decrease in flow rate. 

Figure 7. (a) Schematic illustrating the increase in concentration and expulsion of solvent as surfaces are compressed in the simulations, (b) Pressure-polymer concentration phase diagram. Flocculation of surfaces occurs at the upper critical solution density when the concentration between the surfaces reaches an unstable value (the critical concentration). 

Case (1) represents a phenomenon, referred to as depletion flocculation, produced by addition of free non-adsorbing polymer [38]. In this case, the polymer coils cannot approach the particles to a distance A (which is determined by the radius of gyration of free polymer, Rg), since the reduction of entropy on close approach of the polymer coils is not compensated by an adsorption energy. The suspension particles will be surrounded by a depletion zone of thickness A. Above a critical volume fraction of the free polymer, the polymer coils are squeezed out from between the particles and the depletion zones begin to interact. The interstices between the particles are now free from polymer coils and hence an osmotic pressure is exerted outside the particle surface (the osmotic pressure outside is higher than between the particles), resulting in weak flocculation [4]. A schematic representation of depletion flocculation is shown in Figure 7.35. 

Another method of reducing creaming or sedimentation is to induce weak flocculation in the emulsion system. This may be achieved by controlling some parameters of the system, such as electrolyte concentration, adsorbed layer thickness and droplet size. These weakly flocculated emulsions are discussed in the next section. Alternatively, weak flocculation may be produced by addition of a free (non-adsorbing) polymer. Above a critical concentration of the added polymer, polymer-polymer interaction becomes favourable as a result of polymer coil overlap and the polymer chains are squeezed out from between the droplets. This results in a polymer-free zone between the droplets, and weak attraction occurs as a result of the higher osmotic pressure of the polymer solution outside the droplets. This phenomenon is usually referred to as depletion flocculation [59] and can be applied for structuring emulsions and hence reduction of creaming or sedimentation. 

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