Slow flocculation

Van der Woude, J.H.A. Rijnbout, J.B. De Bmyn, P.L. (1984 a) Formation of colloidal dispersions from supersaturated iron(III) nitrate solutions. IV. Analysis of slow flocculation of goethite. Colloids Surfaces 11 391-400... 

A relatively recent development is the exploitation of w/c microemulsions for the synthesis of metallic and semiconductor nanoparticles. By reducing silver nitrate, Ji et al. (1999) were able to harvest silver nanoparticles from a w/c microemulsion. Analysis of the plasmon resonance peak at 400 nm indicated that samples collected at intervals of 20 and 10 min were 4 nm in diameter. A subsequent decrease in the intensity of the plasmon band, over a period of 1 h, was attributed to the slow flocculation of nanoparticles. 

It tlocs can interpenetrate to some extent after contacting, the floe becomes denser and Df increases to Df 2.0-2.2, which corresponds to slow flocculation, or reaction-limited aggregation. ... 

Gjnax < 5 IcT then flocculation will occur. Two types of flocculation kinetics may be distinguished (i) fast flocculation with no energy barrier and (ii) slow flocculation, where an energy barrier exists. 

The slow flocculation kinetics was investigated by Fuchs [13], who related the rate constant k to the Smoluchowski rate by the stability constant W,... 

The stabihty of the latexes was determined by determining the critical coagulation concentration (ccc) using CaClj. Although the CCC was low (0.0175-0.05 mol dm ), it was higher than that for the latex prepared without surfactant The subsequent addition of INUTEC SPl resulted in a large increase in the CCC, as illustrated in Figure 17.2, which shows log W-log C curves (where W is the ratio between the fast flocculation rate constant to the slow flocculation rate constant, referred to as the stability ratio) at various additions of INUTEC SPl . 

The rate constant k of slow flocculation is usually related to the rapid rate constant k (the Smoluchowski rate) by the stabihty ratio W,... 

Stability in colloidal dispersions is defined as resistance to molecular or chemical disturbance, and the distance the system is removed from a reference condition may be used as a measure of stability. The stability can be analyzed from both energetic and kinetic standpoints. The kinetic approach uses the stability ratio, as a measure of the stability. W is defined as fhe ratio of the rate of flocculation in the absence of any energy barrier to that when there is an energy barrier due to adsorbed surfactant or polymer. These processes are referred to as rapid and slow flocculation with rate constants kj and kg, respectively, such that W = kjlk. The stability of colloidal suspensions can be evaluated using various techniques. In practice, two methods are mainly used sedimentation and rheology measurements. 

For polyelectrolytes, attachment resistance is not restricted to densely covered surfaces, because long-range electrostatic interactions come into play. Obviously, a polyelectrolyte chain will be repelled by a surface that carries a (net) charge of like sign this situation is analogous to that of colloidal particles in water, for which the DLVO theory is the generally accepted way to calculate the interaction, and the Von Smoluchowsky-Fuchs theory [23,24] provides the framework to calculate the resistance in the rate of (slow) flocculation. 

As far as conditioning is concerned, in the case of slow flocculation, controlled conditioning is necessary. If the conditioning is weak, the flocculation rate will be slow, but on the other hand intense conditioning can result in fast relative motion of particles which is also unfavorable for their attachment to each other. 

Among the primary collision mechanisms is Brownian flocculation, also termed perikinetic flocculation, which dominates for submicrometer particles at relatively high number densities. The second principal collision mechanism is that of velocity gradient flocculation, also termed orthokinetic flocculation, which dominates for particles of micrometer size and larger. Evidently, the presence of any stabilizer in the solution will reduce the number of particle encounters and subsequent floccing, as discussed in the last section, resulting in slow flocculation. In our discussion we shall separate the transport and stability problems by assuming that the suspension is completely destabilized, so flocculation occurs on encounter rapid flocculation). Our concern here is with the effect of the particle motion alone on the number of encounters between the suspended particles. 

Figure 5.2 presents a similar plot for a poly(methyl methacrylate) latex sterically stabilized in n-heptane by poly(12-hydroxystearic acid). In this instance, however, the reduction in the solvency of the dispersion medium for the stabilizing moieties was achieved by adding a miscible nonsolvent (specifically ethanol) to the dispersion medium (Napper, 1968a). Flocculation was again accompanied by an abrupt increase in turbidity when a certain volume fraction of ethanol was added to the ra-heptane. In this instance, it was possible to observe the slow flocculation of the latex particles (i.e. flocculation apparently in the presence of a small repulsive potential energy barrier at a rate slower than that predicted by Smoluchowski, 1917). It is, however, usually diflicult to detect such slow flocculation because of the sharpness of the transition from stability to flocculation for stericaUy stabilized dispersions. 

Given the appropriate potential energy diagrams from the DLVO theory, the stability ratio may be calculated by graphical or numerical integration and then compared with experimental values of W=kyk, the ratio of the experimental rate constants for rapid and slow flocculation. Such a comparison is a severe test of the applicability of theory to experiment, and the observed deviations, although often not appreciable, reflect the assumptions and approximations which are necessary in the calculation of the potential energy terms. An advanced treatment of these issues will be found in Russel et al.- . 

Flocculation is a kinetic process and the rate at which a colloidal suspension flocculates forms one of its most important characteristics. Smoluchowski (1917) distinguished between rapid flocculation and slow flocculation and developed a theory based on the rate of collision between the particles (2). Rapid flocculation is considered to take place in the absence of a potential barrier and is limited only by the rate of diffusion of the particles towards one another. The flocculation time, defined as the time tia required for the number of particles to be reduced by one-half of the initial value is given by... 

For slow flocculation in the presence of a potential barrier, analysis leads to... 

The effect of the non-ionic surfactant Ci2E6 on the stability of polystyrene latex as a function of electrolyte concentration and pH is shown in Fig. 9.12. At a constant surfactant concentration at pH 4.6 the value of log decreases gradually with increasing concentration of lanthanum nitrate until a concentration is reached where the curve becomes parallel to the concentration axis. This corresponds to the region of rapid flocculation. The portion below the critical concentration for rapid flocculation is the region of slow flocculation. The plots in Fig. 9.12 have been normalized to show more clearly the effect of increasing... 

Recently, the use of microemulsions in supercritical CO2 to produce nanoparticles has received considerable attention (240,246-249). Since conventional hydrocarbon surfactants for oil/water systems often exhibit low solubilities in CO2 and are therefore incapable of solubilizing a significant amount of water (250,251), surfactants with fiuorinated tails have been used for the formation of water-in-C02 microemulsions (251-254). Perfluoropolyether (PFPE) is a popular and commercially available fiuorinated surfactant. Wai and coworkers prepared silver nanoparticles via chemical reduction in a microemulsion of water in supercritical CO2 with PFPE (247). A slow flocculation of the nanoparticles was... 

The flocculation values are usually determined for a certain slow flocculation, but it is not known by what factor this flocculation is slower than the ideal rapid one ... 

A flocculation value gives only one rather arbitrary set of corresponding values of the rate of flocculation and the concentration of electrolyte. A further test of the theory of the stability can be obtained by examining the concentration dependence of the rate of flocculation. It has been described in Ch. VIL P 283 how the rate of slow flocculation can be related to the form of the potential curve representing the interaction of two particles. This relation has already been used in the construction of Figs. 3 and 4, p. 305 of this chapter. 

The retardation factor W, giving the ratio between the rates of rapid flocculation (no interaction) and slow flocculation for an energy of interaction V, is given by cq. (36) ofCh. VII, p. 285. 

Fig. 11 shows the results of these calculations plotted in a log W log r diagram It is remarkable that in the tnajor region of slow flocculation the relation between log W and log c is ncarly linear. 

It occurs preferentially, although perhaps not exclusively, in systems with elongated (flat or long) particles. It is explained either by a certain slowness of gel formation, which may be based upon the analogue of slow flocculation (see chapter VII, 2 and 3, p. 283 ff.) or upon the rareness of encounters between particles due to slow BROWNian motion. 

This equation, which describes the experiments very well (see Fig. 11) resembles the equation derived by Reerink for slow flocculation (sec chapter VIII, 5, p. 319) except that Reerink finds log c instead of c. For the very small range of concentrations covered in Fig. 11... 

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