Forces Operating between Colloidal Particles

The stability of lyophobic colloids is governed by long-range forces, that is, forces that operate over a distance of at least a few nanometers. These forces can, in principle, accurately be formulated, provided a well-defined geometry and known composition of the particles and the medium. 

In Sections 13.3.4 and 15.5.2, we already encountered the role of dispersion interaction in, respectively, globular protein structure and protein adsorption. Here, we discuss dispersion forces in somewhat more detail. 

The interaction between two (colloidal) particles may be considered as that between two ensembles of atoms, each containing atoms. As a first approximation. 

Note that in Equation 16.7, Gjjsp(ft) is expressed in energy units, whereas from Equation 16.5, it is obtained as energy per unit surface area. 

It is thus derived that for a given geometry, is determined by the value of A, 

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A is the Hamaker constant (2). In real colloidal systems the particles are suspended in a medium or solvent, in which case an effective Hamaker constant has to be used to describe the force operating between the particles. When two particles 1 and 2 separated by a solvent 3 are at large distances from one another, the interactions are particle-solvent interactions and A 23. When the particles approach one another, particle-solvent and particle-particle interactions must now be considered. The effective Hamaker constant becomes... 

Electrostatic and Dispersion Forces. Several repulsive and attractive forces operate between colloidal species and determine their stability (7,8,10,25, 31,54). In the simplest example of colloid stability, particles would be stabilized entirely by the repulsive forces created when two charged surfaces approach each other and their electric double layers overlap. The overlap causes a Coulombic repulsive force acting against each surface, and that will act in opposition to any attempt to decrease the separation distance. One can thus express the Coulombic repulsive force between plates as a potential energy of repulsion. There is another important repulsive force causing a strong repulsion at very small separation distances where the atomic electron clouds overlap, called the Bom repulsion. 

Similarly, van der Waals forces operate between any two colloidal particles in suspension. In the 1930s, predictions for these interactions were obtained from the pairwise addition of molecular interactions between two particles [38]. The interaction between two identical spheres is given by... 

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 ... 

That is, the potential energy of attraction is identical in the two cases. This is an important result as far as the extension of molecular interactions to macroscopic spherical bodies is concerned. What it says is that two molecules, say, 0.3 nm in diameter and 1.0 nm apart, interact with exactly the same energy as two spheres of the same material that are 30.0 nm in diameter and 100 nm apart. Furthermore, an inspection of Equation (49) reveals that this is a direct consequence of the inverse sixth-power dependence of the energy on the separation. Therefore the conclusion applies equally to all three contributions to the van der Waals attraction. Precisely the same forces that are responsible for the association of individual gas molecules to form a condensed phase operate —over a suitably enlarged range —between colloidal particles and are responsible for their coagulation. 

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. 

To counteract the attractive forces in lyophobic colloids repulsive forces must operate and consequently, the question regarding an overall interaction potential between colloidal particles arises. Equation 31 leads for separation distances close... 

In the past decade, much development has taken place in regard to measuring the forces involved in these colloidal systems. In one method, the procedure used is to measure the force present between two solid surfaces at very low distances (less than micrometer). The system can operate under water, and thus the effect of addictives has been investigated. These data have provided verification of many aspects of the DLVO theory. Recently, the atomic force microscope (AFM) has been used to measure these colloidal forces directly (Birdi, 2002). Two particles are brought closer, and the force (nanoNewton) is measured. In fact, commercially available apparatus are designed to perform such analyses. The measurements can be carried out in fluids and under various experimental conditions (such as added electrolytes, pH, etc.). 

Imagine a suspension of colloidal particles in water. What causes stability, and what, imder changing solution conditions like addition of salt causes flocculation (precipitation of the suspension) Two opposing forces were considered to operate between two such particles. The one, attractive, is the quantum mechanical van der Waals force and treats an intervening liquid as if it has bulk liquid properties up to the interfaces of the particles (theme (i)). The other, repulsive, due to charges formed by dissociation of ionisable surface groups, is electrostatic in origin, and depends on salt concentration. 

Oxides, especially those of silicon, aluminum, and iron, are abundant components of the earth s crust they participate in geochemical reactions and in many chemical processes in natural waters, and often occur as colloids in water and waste treatment systems. The properties of the phase boundary between a hydrous oxide surface and an electrolyte solution depend on the forces operating on ions and water molecules by the solid surface and on those of the electrolyte upon the solid surface. The presence of an electric charge on the surface of particles often is essential for their existence as colloids the electric double layer on their surface hinders the attachment of colloidal particles to each other, to other surfaces, and to filter grains. 

Four main type of forces act between surfaces in liquids van der Waals, electrostatic, solvation (hydration), and steric forces. For a typical colloidal system of rigid particles in water, it is rare for more than two of these forces to be dominating the interaction at any one time. In contrast to this, the forces between highly mobile amphyphific surfaces of fluid bilayers and biological membranes can have all four operating simultaneously, as well as other - more specific -types of interaction. Hydrophobic force can be far stronger than the van der... 

If the relative excess Tj of the free dissolved polymer decreases as the colloidal particles approach (i.e. h decreases), then the sign of (dr2 ydh) must be positive. This implies that /a is positive and a repulsion is operative as the polymer molecules are squeezed out of the space between the particles, just as in the gas/solid case. This is the situation that pertains in the early sta of the close approach of colloidal particles immersed in free polymer solutions. Thus a repulsive force must be operative under those conditions. This is the thermodynamic basis of depletion stabilization. Just as in the solid/gas case, the repulsion can, in one sense, be considered to be of entropic origin. This, however, is far too simplistic a picture. 

Microfiltration (MF) is a membrane filtration in which the filter medium is a porous membrane with pore sizes in the range of 0.02-10 pm. It can be utilized to separate materials such as clay, bacteria, and colloid particles. The membrane structures have been produced from the cellulose ester, cellulose nitrate materials, and a variety of polymers. A pressure of about 1-5 atm is applied to the inlet side of suspension flow during the operation. The separation is based on a sieve mechanism. The driving force for filtration is the difference between applied pressure and back pressure (including osmotic pressure, if any). Typical configurations of the cross-flow microfiltration process are illustrated in Fig. 2. The cross-flow membrane modules are tubular (multichannel), plate-and-frame, spiral-wound, and hollow-fiber as shown in Fig. 3. The design data for commercial membrane modules are listed in Table 1. 

One of the most useful practical operating concepts for membrane processes is that of a critical filtration flux or critical operating pressure. These critical parameters are such that below such critical values rejection will occur and fouling will be minimum, while above these critical values both transmission and fouling may take place. For colloidal particles, the critical values may arise as a balance between the hydrodynamic force driving solutes toward a membrane pore and an electrostatic (electrical double layer) force opposing this motion. 

Attempts to explain the remarkable fact that a gel, which consists mostly of fluid, behaves as a rigid solid and yet retains many properties characteristic of the fluid component (such as compressibility, vapor pressure, and electrical conductivity, which are but little altered), have resulted in many contributions to the colloid chemical literature and numerous hypotheses concerning the nature of gel structure. Most prominent among these (c/. Goodeve, 1939) have been those based on (a) immobilization of solvent through adsorption by the solute, (6) the presence of a three-dimensional network of solute, and (c) the operation of long-range forces between solute particles. Each of these theories may be applicable to some gel systems but not to others. 

In many colloidal systems, both in practice and in model studies, soluble polymers are used to control the particle interactions and the suspension stability. Here we distinguish tliree scenarios interactions between particles bearing a grafted polymer layer, forces due to the presence of non-adsorbing polymers in solution, and finally the interactions due to adsorbing polymer chains. Although these cases are discussed separately here, in practice more than one mechanism may be in operation for a given sample. 

Particle electrophoresis studies have proved to be useful in the investigation of model systems (e.g. silver halide sols and polystyrene latex dispersions) and practical situations (e.g. clay suspensions, water purification, paper-making and detergency) where colloid stability is involved. In estimating the double-layer repulsive forces between particles, it is usually assumed that /rd is the operative potential and that tf/d and (calculated from electrophoretic mobilities) are identical. 

In view of the distance over which electrical double layers extend into the solution, interaction between double layers become effective at a separation between the surfaces of at least a few nanometers. Hence, electrical double layer forces can be considered as long-range forces they operate over distances comparable to those over which dispersion forces between particles of colloidal dimensions reach significant magnitudes. 

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