Colloid Interactions DLVO Theory

This procedure defines an effective volume fraction, p — 4 (d/do), where do is the hard-core diameter of the actual system. The softer part of the (repulsive) potential defines the effective diameter d do so that the effective volume fraction can be considerably greater than the actual volume fraction, j). Thus, transitions such as crystalization will occur when 0 = 0.50 the actual volume fraction, 0, can be substantially less than this value if there is an enhancement of d by the soft-core repulsions this enhancement is particularly effective since the effective volume fraction scales as (d/do).  

We first consider the balance of interactions for flat plates. Once this interaction is understood, the interaction between two spheres can be obtained within the Derejaguin approximation the virial coefficient and hence the stability of the system to phase separation can then be determined. 

From Chapter 5, the attractive dispersion forces for two plates separated by a gap D, gives rise to an energy per unit area  

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To what extent can theory predict the collision efficiency factor Two groups of researchers, Derjagin and Landau, and Verwey and Overbeek, independently of each other, have developed such a theory (the DLVO theory) (1948) by quantitatively evaluating the balance of repulsive and attractive forces that interact most effective tool in the interpretation of many empirical facts in colloid chemistry. 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

Verwey, E. J. W., and Overbeek, J. Th. G., Theory of the Stability of Lyophobic Colloids, Elsevier, Amsterdam, Netherlands, 1948. (Another classic reference, by two of the originators of the DLVO theory of colloidal interactions.)... 

A pair of polysaccharide molecules approaching each other in water exerts an interaction potential ( ) that is the algebraic sum of the competing attractive and repulsive forces. integrated over all pairs of molecules, is . This principle is embodied in the Deijaguin-Verwey-Landau-Overbeek (DLVO) theory of colloidal stability (Ross and Morrison, 1988). The equilibrium distance between the molecules is related to c, the volume of the hydrated particles, ionic strength, cosolute, nonsolvent additions, temperature, and shearing. 

When two charged particles immersed in an electrolyte approach each other, the overlap of their ionic atmospheres (the double layers) generates a repulsive force. The traditional Derjaguin—Landau—Verwey—Overbeek (DLVO) theory assumes that the stability of charged colloids is a consequence of a balance between this double layer repulsion and the attractive van der Waals interactions.1... 

When either ion-hydration interaction or ion-dispersion forces were included in the treatment, the results were qualitatively identical to the traditional DLVO theory, which roughly predicts that strongly charged colloidal particles are stable, and weakly charged particles coagulate. Significant quantitative differences, which can account for specific ion effects, could he introduced by either mechanism, when suitable interaction parameters were selected. 

Gouy1 and Chapman,2 who were the first to predict the distribution of electrolyte ions in water around a charged flat surface, demonstrated that the ions form a diffuse layer (the electric double layer) in the liquid near the interface. The interaction between two charged surfaces, due to the overlapping of the double layers, was calculated much later by Deryaguin and Landau3 and Verwey and Overbeek.4 The stability of the colloids was successfully explained by them in terms of a balance between the double layer and van der Waals interactions (the DLVO theory).3 4... 

The strong discrepancy between experiment and the traditional DLVO theory at low ionic strengths (where the latter theory is considered to be accurate) cannot be explained by additional interactions between ions and surfaces, because they are negligible below 0.01 M. Therefore, we are inclined to believe that the structural modification of the adsorbed protein by the addition of a structure breaking ion, such as SCN" is mainly responsible for the quantitative disagreement between experiment and model calculations. The nonuniformity ofthe colloidal particles may be also responsible for the disagreement. 

Most of the water-mediated interactions between surfaces are described in terms of the DLVO theory [1,2]. When a surface is immersed in water containing an electrolyte, a cloud of ions can be formed around it, and if two such surfaces approach each other, the overlap of the ionic clouds generates repulsive interactions. In the traditional Poisson-Boltzmann approach, the ions are assumed to obey Boltzmannian distributions in a mean field potential. In spite of these rather drastic approximations, the Poisson-Boltzmann theory of the double layer interaction, coupled with the van der Waals attractions (the DLVO theory), could explain in most cases, at least qualitatively, and often quantitatively, the colloidal interactions [1,2]. 

The DLVO theory [1,2], which describes the interaction in colloidal dispersions, is widely used now when studying behavior of colloidal systems. According to the theory, the pair interaction potential of a couple of macroscopic particles is calculated on the basis of additivity of the repulsive and attractive components. For truly electrostatic systems, a repulsive part is due to the electrostatic interaction of likely charged macroscopic objects. If colloidal particles are immersed into an electrolyte solution, this repulsive, Coulombic interaction is shielded by counterions, which are forming the diffuse layer around particles. A significant interaction occurs only when two double layers are sufficiently overlapping during approach of those particles. 

A general scheme, based on a rigorous statistical mechanical formulation, for obtaining the interaction between two colloidal particles in a fluid has been outlined. The implementation of the theory is in its early stages. In the DLVO theory and the theory of HLC, it is assumed that the various contributions can be added together. In the MSA, the hard core and electrostatic terms will be additive. However, it is only at low electrolyte concentration that the effect of dipole orientation and the repulsive contribution of the double layer overlap will be additive. There is no reason to believe (or disbelieve) that the van der Waals term should also be additive. 

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