The van der Waals Attraction

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

The van der Waals attraction arises from tlie interaction between instantaneous charge fluctuations m the molecule and surface. The molecule interacts with the surface as a whole. In contrast the repulsive forces are more short-range, localized to just a few surface atoms. The repulsion is, therefore, not homogeneous but depends on the point of impact in the surface plane, that is, the surface is corrugated. 

The ion that has the greater polarizability (which determines the Van der Waals attraction). 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

The electrostatic repulsive forces are a function of particle kinetic energy (/ T), ionic strength, zeta potential, and separation distance. The van der Waals attractive forces are a function of the Hamaker constant and separation distance. 

The wettiag eaergies give repulsive forces exceeding that of the van der Waals attractive force under certain conditions. The combiaed van der Waals and wettiag force is givea by equatioa 7 ia which h is the distance perpendicular to the iaterface that the particle has moved from its equiHbrium positioa. 

Let us now calculate the three components of the van der Waals attraction by first calculating these interactions between two molecules. Subsequently, the total van der Waals potential between bodies will be determined by assuming that the molecules belong to two different materials and integrating the molecular interactions over the volumes of the materials. 

Since the contributions of the three constiments of the van der Waals attraction are additive, one can consider each contribution separately. This indeed proves to be convenient not only because all the contributions exhibit distinct scaling with the parameters, but each contribution comes to dominate the expansivity at somewhat distinct temperatures. We consider first the ripplon-ripplon attraction. This contribution appears to dominate the most studied region around 1 K. The off-diagonal (flip-flop) interaction between the ripplons has the form... 

The stability of colloids can also be dramatically altered by inclusion of polymeric materials. If the polymer interacts favourably with the particle surfaces, i.e. it adsorbs, then both an increase and a reduction in stability is possible, via modification of the electrostatic interaction of the polymer is charged or a reduction in the van der Waals attraction. 

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

In this category, among the molecular, electrostatic and magnetic interparticle bonds, interest is primarily centered on the van der Waals-type attractive forces that may predominate in the absence of liquid and solid bonds. The force of the van der Waals attraction between two spheres of equal size is (R4)... 

The van der Waals attractive potential [27] increases with an increase in nanopartide radius or with a decrease in center-to-center separation distance between nanoparticles ... 

Two repulsive contributions, osmotic and elastic contributions [31, 32], oppose the van der Waals attractive contribution where the osmotic potential depends on the free energy of the solvent-ligand interactions (due to the solvation of the ligand tails by the solvent) and the elastic potential results from the entropic loss due to the compression of ligand tails between two metal cores. These repulsive contributions depend largely on the ligand length, solvent parameters, nanopartide radius, and center-to-center distance ... 

The increase in the rheological parameters, ri0> G0 and 1(5 with reduction in surface coverage points towards an increase in particle interaction. This could be the result of either flocculation by polymer "bridging" (which is favourable at coverages <0.5) or as a result of coagulation due to the van der Waals attraction between the "bare" patches on the particles. In the absence of any quantitative relationship between interaction forces and rheology, it is clearly difficult... 

As discussed above, the contribution from Gg to the attraction will be significantly larger than the van der Waals attraction. Thus, E may be equated to Gg. Equation (4) may be used to calculate Eg from the measured fg values for the flocculating dispersions. The results are summarized in tables I and II. ... 

Van der Waals forces depend upon the electron density of the atoms. Increasing number of atoms in a molecule increases the van der Waals attractive force. Since the electron number of a neutral atom is equal to its proton number, atoms which have a large proton number have strong van der Waals forces between their molecules. Therefore, van der Waals forces are stronger between molecules with high molecular masses. 

The van der Waal attraction energy, in a first approximation is inversely proportional to the square of the intercolloid distance. 

Polyelectrolytes provide excellent stabilisation of colloidal dispersions when attached to particle surfaces as there is both a steric and electrostatic contribution, i.e. the particles are electrosterically stabilised. In addition the origin of the electrostatic interactions is displaced away from the particle surface and the origin of the van der Waals attraction, reinforcing the stability. Kaolinite stabilised by poly(acrylic acid) is a combination that would be typical of a paper-coating clay system. Acrylic acid or methacrylic acid is often copolymerised into the latex particles used in cement sytems giving particles which swell considerably in water. Figure 3.23 illustrates a viscosity curve for a copoly(styrene-... 

As a result of the nature of the intermolecular interaction giving rise to the van der Waals force, it is active only at very close range. The molecules must approach one another closely before the attraction, which results in sorption, can exert itself. It is generally believed that the force of the van der Waals attraction between two molecules is proportional to the square of the polarizability and varies inversely with the sixth power of the distance between the molecules [65] ... 

Interaction Energy Expressions. Previous papers (8,10,12,13) have used exact sphere-plane interaction energy expressions to approximate the sphere-cylinder Interaction. In this work, these exact expressions were replaced with recently published approximate expressions. For the double layer repulsion, this avoided the inconvenience and Inaccuracy of using tabular values ( ) while for the van der Waals attraction, using the approximate solution simplified the programing task. 

Neumann, A.W., Absolom, D.R., Francis, D.W. and van Oss C.J. (1980). Conversion tables of contact angles to surface tension For use in determining the contribution of the van der Waals attraction or repulsion to various separation processes. Separ. Purif Mech. 9, 69-163. 

---