Forces between Colloidal Particles

3 FORCES BETWEEN COLLOIDAL PARTICLES 3.3.1 Van der Waals Forces 

Van der Waals forces result from attractions between the electric dipoles of molecules, as described in Section 1.2. Attractive van der Waals forces between colloidal particles can be considered to result from dispersion interactions between the molecules on each particle. To calculate the effective interaction, it is assumed that the total potential is given by the sum of potentials between pairs of molecules, i.e. the potential is said to be pairwise additive. In this approximation, interactions between pairs of molecules are assumed to be unaffected by the presence of other molecules i.e. many-body interactions are neglected. The resulting pairwise summation can be performed analytically by integrating the pair potential for molecules in a microscopic volume dVi on particle 1 and in volume dVi on particle 2, over the volumes of the particles (Fig. 3.1). The resulting potential depends on the shapes of the colloidal particles and on their separation. In the case of two flat infinite surfaces separated in vacuo by a distance h the potential per unit area is 

Here Ah is the Hamaker constant which determines the effective strength of the van der Waals interaction between colloid particles. It is noteworthy that the attractive potential between colloid particles falls off much less steeply than the dispersion interaction between individual molecules (Eq. 1.4). Thus, long-range forces between colloidal particles are important for their stability. 

For two spherical particles of radius R, where the interparticle separation is small h R), the Derjaguin approximation can be used to relate the potential between two curved surfaces to that between two flat surfaces. It is found that Eq. (3.1) is modified to 

It is important to note that Eqs. (3.1) and (3.2) apply to colloidal particles in a vacuum. If there is instead a liquid medium between the particles, the van der Waals potential is substantially reduced. The Hamaker constant in these equations is then replaced by an effective value. Consider the interaction between two colloidal particles 1 and 2 in a medium 3. If the particles are far apart, then effectively each interacts with medium 3 independently and the total Hamaker constant is the sum of two particle-medium terms. However, if particle 2 is brought close to particle 1, then particle 2 displaces a particle of type 3. Then particle 1 is interacting with a similar body (particle 2), the only difference being that molecules of particle 2 have been replaced by those of medium 3. Thus the potential energy change associated with bringing particle 2 close to particle 1 in the presence of medium 3 is less than it would be in vacuo. The effective Hamaker constant is thus a sum of particle-particle plus medium-medium contributions. 

---

Li Y Q, Tao N J, Pan J, Garcia A A and Lindsay S M 1993 Direct measurement of interaction forces between colloidal particles using the scanning force microscope Langmuir 9 637... 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

The introduction of long-range interaction forces between colloidal particles can produce well dispersed or aggregated systems under... 

The theoretical study (2,3) of this interface is made inherently difficult by virtue of the complex, many-body nature of the interaction potentials and forces involving surfaces, counterions, and water. Hence, many models of the interfacial region explicitly specify the forces between colloidal particles or between solutes, but few account for the many-body interaction forces of the solvent. 

When two similarly charged colloid particles, under the influence of the EDL, come close to each other, they will begin to interact. The potentials will detect one another, and this will lead to various consequences. The charged molecules or particles will be under both van der Waals and electrostatic interaction forces. The van der Waals forces, which operate at a short distance between particles, will give rise to strong attraction forces. The potential of the mean force between colloid particle in an electrolyte solution plays a central role in the phase behavior and the kinetics of agglomeration in colloidal dispersions. This kind of investigation is important in these various industries ... 

Kallmann and Willstatter (1932) calculated van der Waals force between colloidal particles using the summation procedure and suggested that a complete... 

Bradley (1932) independently calculated van der Waals forces between colloidal particles. 

Under what conditions are colloids stable Explain qualitatively (with schematic diagrams) the forces between colloidal particles. How does the force of repulsion between them vary with concentration As the concentration of the colloid increases, there is the tendency to coagulate and in fact the critical concentration for coagulation gets less as the valence of the ions present increases (Schulze-Hardy rule). Give a detailed, although qualitative, rationalization of this law. (Bockris)... 

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. 

A whole range of phenomena in interface science revolve around the effect of surface forces. Many practical applications in colloid science come down to the problem of controlling the force between colloidal particles, between particles and surfaces, and between two surfaces. For this reason scientists have devoted considerable effort to understanding surface forces and being able to influence them. 

A1 hydroxide are known to act as binding agents and induce flocculation [33], In all cases, eluent electrical conductivity values (EC), and therefore ionic strength, remained low (50-100 tS cm-1) during the course of the leaching experiment, suggesting that the electrochemical conditions were not conducive for adequate suppression of the thickness of the double layer that would sufficiently reduce the electrostatic repulsive forces between colloid particles and cause flocculation [34],... 

There are five possible types of force between colloidal particles ... 

In this chapter, the theories as well as the experimental justification for the mechanism of stabilization and destabilization of colloidal dispersions are outlined. Interacting forces between colloidal particles are analyzed and an overview of experimental methods for assessing the dispersion and relevant properties is given. The stabilization and flocculation of dispersions in the presence of surfactants and polymers is discussed in the last two sections. 

Kralchevsky, PA. and Nagayama, K., Capillary forces between colloidal particles, Langmuir, 10, 23, 1994. 

The intention in this section is to define key concepts and terms detailed descriptions of the forces between colloidal particles are in standards texts (8, 9). 

The phenomena described above have been known for a long time indeed, Newton reported on the black spots in soap films. In the past 25 years, however, these thin, liquid structures have become a subject of intensive scientific studies. One of the main reasons is that the interaction forces between colloidal particles suspended in a liquid are of the same nature as those operating in soap films. Because the film geometry is well defined (i.e., a thin, flat liquid sheet, macroscopic in lateral extension), it is an attractive experimental subject for studying these forces, in particular with optical means. 

In 1932 Kallmann and Willstatter" and also Bradley recognized that attractive forces between colloidal particles would emerge from a pairwise summation of dispersion forces between atoms. This was further investigated theoretically by Hamaker and de Boer. For a flat geometry, two half-spaces separated by a gap of thickness h, this leads to the form... 

Given that there exist strong, long ran attractive forces between colloidal particles, it follows that in order to impart colloid stability, it is necessary to provide a long range repulsion between the particles. This repulsion must be at least as strong as, and comparable in range to, the attractive interaction. 

Since the beginning of colloids science, however it is also known that the agglomeration of colloids and dispersed particles can be prevented or controlled by stabilization [8]. The attractive interactions between the colloidal particles, caused by van-der-Waals forces, need to be compensated by repulsive interactions. The latter can be based either on electrostatic repulsion due to same-sign surface charges (electrostatic stabilization), or on repulsion via a polymer shell formed through adsorption of polymers to the particle surface (steric stabilization, in presence of polyelectrolytes termed electrosteric stabilization due to additional charged-induced repulsion) [9, 10]. The stabilization by control of the interaction forces between colloidal particles has been in the focus of extensive research efforts. Already... 

Just as the pressure of an atomic gas is affected by the interaction between the atoms, the physical properties of a colloidal dispersion depend on the potential of mean force between colloidal particles. An extended law of corresponding states has been conjectured [15] stating that knowledge of the potential of mean force between spherical colloidal particles enables to predict the phase diagram (topology). Hence, one may therefore expect similarities between the phase diagrams of atomic and colloidal systems. 

In the above descriptions we concentrated on situations where a polar background solvent was implicitly assumed. In apolar solvents double layer repulsion is diflhcult to achieve because dissociation, leading to charged surface groups, is less likely to occur and it becomes essential to stabilize colloids with polymers as to prevent instabilities. In the first decades after the establishment of the DLVO theory most papers on forces between colloidal particles focused on Van der Waals and double layer interactions. Forces of other origin such as polymeric steric stabilization [17], depletion [40] or effects of a critical solvent mixture [41] gained interest at a later stage. 

In this book depletion in colloidal dispersions is a central theme. As we saw in Sect. 1.2.5 depletion effects in colloidal dispersions are caused by an unbalanced force. From a physics point of view the depletion force between colloidal particles... 

Liang, Y, N. Hilal, P. Langston, and V. Starov. 2007. Interaction forces between colloidal particles in liquid Theory and experiment. Advances in Colloid and Interface Science 134-135 (October 31) 151-166. doi 10.1016/j.cis.2007.04.003. 

At the times when DLVO theory was developed, the direct measurement of forces between colloidal particles and surfaces in solution was not possible, and the macroscopic observation of colloidal stability was the only experimental reference data. With increasing technological advancement, setups have been developed for the direct observation of such forces The surface force apparatus (SFA) allows for the measurements of forces between surfaces in solution [6], and with an atomic force microscope (AFM), forces on a colloidal particle can be detected [7]. It is a major success that DLVO theory predicts forces that agree nicely with the measured forces for large particle separations (more than 3-10 nm), but at the same time, it is obvious that in the regime of short particle separations, not aU effects are captured by DLVO. When the barrier for coagulation occurs at such low separations, the DLVO prediction for colloidal stability is not accurate (Fig. 2). 

Five types of forces between colloidal particles may be identified (i) repulsive forces, from the overlap of electrical double-layers (ii) dispersion forces, from long-range van der Waals attraction between molecules in neighbouring particles (iii) steric forces, from interaction of macromolecules adsorbed at the particle surface (iv) structural and Brownian forces, from interaction with solvent molecules of the dispersion medium and (v) hydrodynamic forces. 

---