Critical flocculation volume fraction

Flocculated Systems. The viscoelastic responses of flocculated systems are strongly dependent on the suspension structure. The suspension starts to show an elastic response at a critical solid volume fraction of 0ct = 0.05 — 0.07, at which the particles form a continuous three-dimensional network (211-213). The magnitude of the elastic response for flocculated suspensions above 0ct depends on several parameters, such as the suspension structure, interparticle attraction forces and particle size, and shape and volume fraction. Buscall et al. (10) found that the volume fraction dependence of the storage modulus follows a power-law behavior. 

It is usually easier experimentally to specify the critical particle volume fraction rather than the critical particle concentration. Vincent, who has pioneered this approach, usually denotes the critical coagulation particle volume fraction by CF4>. The in Vincent s pseudo-acronym denotes the particle volume fraction whereas the F denotes flocculation, rather than the term coagulation which has been preferred in this text to signify the origin of the attraction. 

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). 

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. 

Figure 3. Critical flocculation temperature (T) versus log (particle volume fraction ) for the two Si02 g PDMS dispersions in bromocyclohexane O, S15/PDMS5 x, S15/ PDHS3.

Figure 4. Critical flocculation solvent composition toluene + n-hexane (v = volume fraction of toluene), versus log (particle volume fraction, (J>) for various SiC -g-PS systems at 24 1°C V, S12/PS13c 0, S12/PS13a ...

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. 

Depletion flocculation is produced by addition of a free nonadsorbing polymer [7]. In this case, the polymer coils caimot approach the particles to a distance A (this is determined by the radius of gyration of free polymer, Rq), as the reduction in entropy on close approach of the polymer coils is not compensated by an adsorption energy. The suspcakesension particles or emulsion droplets will be surrounded by a depletion zone with thickness A. Above a critical volume fraction of the free polymer, the polymer coils wiU be squeezed out from between the particles... 

This is achieved by the addition of free (nonadsorbing) polymer in the continuous phase [26]. At a critical concentration, or volume fraction of free polymer,, weak flocculation occurs as the free polymer coils become squeezed-out from between the droplets. This is illustrated in Figure 10.27, which shows the situation when the polymer volume fraction exceeds the critical concentration. 

For example, the emulsion will flocculate at a temperature (referred to as the critical flocculation temperature CFT) that is equal to the 0-temperature of the stabilising chain. The emulsion may flocculate at a critical volume fraction (CFV) of a nonsolvent, which is equal to the volume of nonsolvent that brings it to a... 

Most colloidal stable suspensions show more or less reversible response to compression and decompression. However, in the case of flocculated suspensions, the compressive properties are irreversible. In concentrated flocculated suspensions, a continuous particle network forms. The particle network can support some stress up to a critical value. Once this critical stress, also called the compressive yield stress Fy, is exceeded, the network consolidates to a higher volume fraction with a higher critical stress. 

Also the effect of block-copolymer surfactants (Synperonic NPE) on the viscosity and stability of suspensions as a function of the PEO chain length is studied [278], The critical volume fraction of coal in suspension and maximum stability were observed for a surfactant with 48 PEO units. At 27 PEO units, flocculation appeared. In the interval from 79 to 174 PEO, desorption resulted leding to an increase in suspension flocculation. Thus, the choice of an optimum PEO content is very important to obtain liquid and stable suspensions, considering the features of the coal nature. 

S.4. Critical flocculation particle volume fraction Theoretical considerations... 

Clarke and Vincent in these studies established the phase diagrams for the free polystyrene-microgel-ethyl benzene systems, two of which are displayed in Fig. 16.2a and b. In all cases, only the stability/instability boun ry is shown. These lines correspond to the locus of the critical volume fraction of free polymer required to induce flocculation (vj ) as a function of the volume fraction of the microgel particles (< 3). 

It is apparent that up to a critical volume fraction Vj of free polymer, the particles displayed long-term stability (1/1F=0). Any further increase in the free polymer concentration resulted in the onset of instability, which was manifested by an increase in l/W. In all cases, however, l/W reached a maximum value and then declined. Flocculation was thus not evident at high concentrations of free polymer. It usually occurred only over a finite range of free polymer concentrations. This lack of flocculation at higher concentrations of free polymer is the phenomenon of depletion stabilization mentioned in the prefatory remarks to this chapter. It will be considered in detail in the next chapter. 

The effect of molecular weight of the free polymer. Figure 16.5 presents the characteristic dependence of the critical volume fraction of free polymer required to induce flocculation as a function of the molecular weight of the added polymer. For the particles stabilized by poly(oxyethylene) 750, two different temperatures (25 °C and 45 °C) are shown. 

Flocculation occurs when the net force between the particles is attractive. At low volume fractions, aggregation results in clusters, or floes, which have a fractal structure (7). For most systems, the properties of the aggregating suspension changes drastically at a certain critical particle concentration, 0g, which corresponds to the formation of a space-filling particle network. In dilute suspensions, at 0 < 0g, suspensions have no yield stress and the discrete clusters will settle more or less independently. Above 0g, the suspension can sustain a stress before yielding the elasticity may be significant, and the rate of settling is very slow. 

As discussed before, addition of free non-adsorbing polymer can produce weak flocculation above a critical volume fraction of the free polymer, This weak flocculation produces a gel structure that reduces sedimentation. As an illustration, results were obtained for a sterically stabilised suspension [using a graft copolymer of poly(methyl methacrylate) with poly(ethylene oxide) side chains] to which hydroxyethyl cellulose with various molecular weights was added to the suspension. The weak flocculation was studied using oscillatory measurements. Figure 7.52 shows the variation of the complex modulus G with p. 

---