Particle surface DLVO theory

Hence, for two similarly charged surfaces in electrolyte, interactions are determined by both electrostatic doublelayer and van der Waals forces. The consequent phenomena have been described quantitatively by the DLVO theory [6], named after Derjaguin and Landau, and Verwey and Over-beek. The interaction energy, due to combined actions of double-layer and van der Waals forces are schematically given in Fig. 3 as a function of distance D, from which one can see that the interplay of double-layer and van der Waals forces may affect the stability of a particle suspension system. 

The DLVO theory, with the addition of hydration forces, may be used as a first approximation to explain the preceding experimental results. The potential energy of interaction between spherical particles and a plane surface may be plotted as a function of particle-surface separation distance. The total potential energy, Vt, includes contributions from Van der Waals energy of interaction, the Born repulsion, the electrostatic potential, and the hydration force potential. [Israelachvili (13)]. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

In summary, the DLVO theory seems to break down at very close separation where interfacial phenomena such as particle-particle interaction (coagulation) and particle-surface interaction (deposition) are important. 

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.). 

Calculation of Coagulation Rate. Here we discuss an interaction potential of two charged particles in a liquid within a framework of DLVO theory. Following this theory, the overall interaction potential U, of charged spherical particles of the same radius R and surface distance d is a sum of a coulombic repulsive force of charged particles and a van der Waals attractive force given by the equation (28) ... 

Figure 6.11 Gibbs free interaction energy (in units of ki>T) versus distance for two identical spherical particles of R = 100 nm radius in water, containing different concentrations of monovalent salt. The calculation is based on DLVO theory using Eqs. (6.57) and (6.32). The Hamaker constant was Ah = 7 x 10 21 J, the surface potential was set to )/>o = 30 mV. The insert shows the weak attractive interaction (secondary energy minimum) at very large distances.

In an aqueous electrolyte we have spherical silicon oxide particles. The dispersion is assumed to be monodisperse with a particle radius of 1 /rm. Please estimate the concentration of monovalent salt at which aggregation sets in. Use the DLVO theory and assume that aggregation starts, when the energy barrier decreases below 0ksT. The surface potential is assumed to be independent of the salt concentration at -20 mV. Use a Hamaker constant of 0.4 x 10-20 J. 

The role of electrostatic repulsion in the stability of suspensions of particles in non-aqueous media is not yet clear. In order to attempt to apply theories such as the DLVO theory (to be introduced in Section 5.2) one must know the electrical potential at the surface, the Hamaker constant, and the ionic strength to be used for the non-aqueous medium these are difficult to estimate. The ionic strength will be low so the electric double layer will be thick, the electric potential will vary slowly with separation distance, and so will the net electric potential as the double layers overlap. For this reason the repulsion between particles can be expected to be weak. A summary of work on the applicability or lack of applicability of DLVO theory to non-aqueous media has been given by Morrison [268],... 

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. 

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