Colloidal particles effective attractive interactions

In extensively deionized suspensions, tliere are experimental indications for effective attractions between particles, such as long-lived void stmctures [89] and attractions between particles confined between charged walls [90]. Nevertlieless, under tliese conditions tire DLVO tlieory does seem to describe interactions of isolated particles at tire pair level correctly [90]. It may be possible to explain tire experimental observations by taking into account explicitly tire degrees of freedom of botli tire colloidal particles and tire small ions [91, 92]. 

It is important to note that the concept of osmotic pressure is more general than suggested by the above experiment. In particular, one does not have to invoke the presence of a membrane (or even a concentration difference) to define osmotic pressure. The osmotic pressure, being a property of a solution, always exists and serves to counteract the tendency of the chemical potentials to equalize. It is not important how the differences in the chemical potential come about. The differences may arise due to other factors such as an electric field or gravity. For example, we see in Chapter 11 (Section 11.7a) how osmotic pressure plays a major role in giving rise to repulsion between electrical double layers here, the variation of the concentration in the electrical double layers arises from the electrostatic interaction between a charged surface and the ions in the solution. In Chapter 13 (Section 13.6b.3), we provide another example of the role of differences in osmotic pressures of a polymer solution in giving rise to an effective attractive force between colloidal particles suspended in the solution. 

In paper [2.12] it is shown that the van der Waals interactions between two particles can be decreased if they are covered with layers that have a Hamaker constant which is near to that of the suspending liquid. It is also suggested that, at sufficiently high concentrations, the collective behavior of the colloidal particles can generate repulsion when the pairwise interactions are attractive. These two effects are suggested to be responsible for the kinetic stability of the system, and a methodology for achieving kinetic stability is provided. 

An attractive interaction arises due to the van der Waals forces between molecules of colloidal particles. Depending on the nature of dispersed particles, the Keesom forces (or the dipole-dipole interaction), the Debye forces (or dipole-induced dipole interaction), and the London forces (or induced dipole-induced dipole interaction) may contribute to the van der Waals interaction. First, the van der Waals interaction was theoretically computed using a method of the pairwise summation of interactions between different pairs of molecules of the two macroscopic particles. This method called the microscopic approximation neglects collective effects, and, as a consequence, misrepresents the Hamaker constant. For many problems of a practical use, however, specific features of the total interaction are determined by a repulsive part, and such an effective, gross description of the van der Waals interaction may often be accepted [3]. The collective effects in the van der Waals interaction have been taken into account in the calculations of Lifshitz et al. [4], and their method is known in the literature as the macroscopic approach. 

Figure 2.3a is purely a sketch. The exact interaction potential between n-butylammonium-substituted clay plates (or other charged colloidal particles) in solution must incorporate many effects, such as the size of the small ions and the molecular degrees of freedom of the solvent, that are beyond the scope of either the coulombic attraction theory or DLVO theory. However, whatever the complicated functional dependence, the curve must comprise two states of equal thermodynamic potential. Somehow, the valleys in VT, the total potential, must be of equal depth. As discussed previously, in Figure 2.3b we see that the DLVO theory can never account for this experimentally proved phenomenon. 

Most food systems are of a colloidal as well as a polymeric nature. The presence of a nonadsorbing polymer in a skim milk dispersion induces an effective attraction between the casein particles, called depletion interaction, resulting in phase separation at sufficiently high polymer concentration. Tuinier et al. (2003) discussed the influence of colloid-polymer size ratio, polymer concentration regime, size, poly-dispersity and charges in colloid/biopolymer mixtures, demonstrating the challenging complexity of the subject. 

Increased depletion attraction. The presence of nonadsorbing colloidal particles, such as biopolymers or surfactant micelles, in the continuous phase of an emulsion causes an increase in the attractive force between the droplets due to an osmotic effect associated with the exclusion of colloidal particles from a narrow region surrounding each droplet. This attractive force increases as the concentration of colloidal particles increases, until eventually, it may become large enough to overcome the repulsive interactions between the droplets and cause them to flocculate (68-72). This type of droplet aggregation is usually referred to as depletion flocculation (17, 18). 

The existence of short-range attractive interactions between particles leads to a much richer phase behavior, as illustrated in Fig. 3. This situation can be achieved by adding a nonadsorbing polymer to the suspensions, which induces an effective depletion attraction between the particles [105]. Such polymer-colloid mixtures can be viewed as model systems of complex fluids and are involved in many practical... 

Colloidal particles are subjected to a number of attractive and repulsive forces and the stability of dispersions depends on the interplay of these various forces. The van der Waals attractive forces between particles have their origin in the electron wave fluctuations and are usually effective at close ranges. Electrical double layer interactions stem from the presence of ionized species at the interface and are effective at distances proportional to the double layer thickness for the given... 

The van der Waals attraction between two atoms or molecules is relatively short range, extending only over a few-tenths of a nanometre. For colloidal particles, however, each atom or molecule of one particle attracts every atom in the other particle. Typically, a colloidal particle is composed of 10 -10 atoms. The net effect of adding all of the myriad of possible atomic interactions is to generate a long range attraction between the particles that is of considerable strength. 

A more satisfactory method for calculating the attraction between colloidal particles is the macroscopic continuum theory due to Lifshitz (Lifshitz, 1956 Dzyaloshinskii et al., 1961) and subsequently elaborated by Ninham and coworkers (Mahanty and Ninham, 1976). This expresses the interaction in terms of the bulk dielectric properties of the two colloidal particles. The power of the Lifshitz formalism lies in its ability to encompass all many-body interactions to deal properly with the effects of intermediate substances (here the microscopic method is quite vague) and to include contributions from all resonant electronic and molecular frequencies. Its disadvantage lies in the dramatic increase in the complexity of the calculations, although such computations are readily performed with the aid of a digital computer. 

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