Forces of Electrostatic Origin

In most natural colloidal systems and in particular the aqueous solutions, the repulsive interparticle forces are related to the presence of ionised species on the surface of the particles. These surface charges may have various origins  

We thus see one of the practical difficulties in setting up colloidal suspensions the presence of impurities, whose origin and composition are not well known, may seriously influence the surface charge of the partieles. Two paper production units may have to operate with different control settings depending on the hardness of the water (i.e., its calcium ion content). 

One case which is easy to deal with is a plane object, immersed in a solution of some univalent salt. Taking the zero of the potential in the unperturbed regions far from the surface, is described by a simple exponential law  

This general feature of electrostatic effects is valid even if some rather crude assumptions are required to justify the exponential variation of particularly close to the surface. 

As in the case of the van der Waals forces, the electrical energy of a multiparticle system can be worked out for simple geometrical arrangements. The 

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Van der Waals Forces Interatomic and intermolecular forces of electrostatic origin. These forces arise due to die small instantaneous dipole moments of the atoms. They are much weaker than valence-bond forces and inversely proportional to the seventh power of the distance between the particles (atoms or molecules). 

Forces Superimposed on the Coulomb Forces. The discussion has been based on the idea that, superimposed on the electrostatic forces between a pair of ions, there are rather short-range forces of other origin, which may be attractive or repulsive. Consider now what the situation will be if these forces cause the mutual potential energy to fall at short distances, below the value — e2/er that is assumed in the Debye-Hlickel theory. In Fig. 74 let the broken curve be a plot of — e2/er, while the full curve gives the actual potential energy between a certain pair of... 

Subsequently major theoretical advances were made, principally by Mayer, in creating an adequate statistical mechanical theory in which both long-range electrostatic forces and short-range forces of whatever origin were properly considered. 

The aforementioned diffuse-layer and discreteness-of-charge effects have been taken into consideration in the model proposed by Grahame and Parsons [26,250-252]. First, it was assumed (unlike in the Stern model) that the specifically adsorbed ions were located at the distance from the metal surface (in the inner Helmholtz plane ) ensuring their maximum bond strength, owing to the combination of forces of electrostatic and quantum-mechanical origins. It shows the need for the partial or even complete desolvation of the adsorbed species and its deep penetration into the compact layer. The position of this adsorption plane depends on all components of the system, metal, solvent, and adsorbed ion. 

In fact, the predominant forces determining association of amphiphiles in well defined structures (e.g., micellar, cylindrical, lamellar) are the hydrophobic effect, tending to associate chains together, and repulsions between head groups. The latter are of electrostatic origin for ionic surfactants and steric for non-ionic surfactants. These two forces tend respectively to diminish or increase the interfacial area per molecule at the water/chain interface. The result is an optimal interfacial area Uq. 

When two colloidal particles come close to each other, they experience two types of force. The first one, the surface forces of intermolecular origin (the disjoining pressure), which are due to the van der Waals, electrostatic, steric, interactions, for example, have been discussed in Sec. VI. The second type represent the hydrodynamic forces which originate from the interplay of the hydrodynamic flows around two moving colloidal particles or two film surfaces. It becomes important when the separation between the particle surfaces is of the order of the particle radius and increases rapidly with the decrease of the gap width. 

The molecular systems in which the individual parts are held together by forces other than covalent bonds. These include ionic complexes (where the dominant attractive force is of electrostatic origin), complexes with hydrogen bonds, chaige transfer complexes, and true van der Waals molecules for which the dominant attractive contribution is the dispersion energy. 

MMl, MM2, MM3, and MM4 are general-purpose organic force fields. There have been many variants of the original methods, particularly MM2. MMl is seldom used since the newer versions show measurable improvements. The MM3 method is probably one of the most accurate ways of modeling hydrocarbons. At the time of this book s publication, the MM4 method was still too new to allow any broad generalization about the results. However, the initial published results are encouraging. These are some of the most widely used force fields due to the accuracy of representation of organic molecules. MMX and MM+ are variations on MM2. These force fields use five to six valence terms, one of which is an electrostatic term and one to nine cross terms. 

Increased concentration of PSS at 7.0 g/L (1.4 X 10 M) leads to an increase in the force to value seven higher than that between the surfaces of fluorocarbon monolayers alone. The origin of this force is electrostatic in nature. Recharging of the surface by additional adsorption of PSS should occur as shown in Figure 9b. 

Some Basics. The field theory of electrostatics expresses experimentally observable action-at-a-distance phenomena between electrical charges in terms of the vector electric field E (r, t), which is a function of position r and time t. Accordingly, the electric field is often interpreted as force per unit charge. Thus, the force exerted on a test charge q, by this electric field is qtE. The electric field due to a point charge q in a dielectric medium placed at the origin r = 0 of a spherical coordinate system is... 

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