Particle van der Waals

Gady found that, depending on the charge of the particle, van der Waals forces dominated over the forces associated with electrostatically charged patches when the particle-to-substrate separation was between 3 and 10 nm, depending on the particle charge. In addition, he found that the distance at which the snap-together occurred required that van der Waals forces dominate over electrostatic. In all his measurements, however, a component of the total attractive force, even at close separations, was observed to be electrostatic in nature. 

Following the strategy for extracting small-particle van der Waals interactions from the interaction between semi-infinite media, we can specialize the general expression for ionic-fluctuation forces to derive these forces between particles in salt solutions. Because of the low frequencies at which ions respond, only the n = 0 or zero-frequency terms contribute. In addition to ionic screening of dipolar fluctuations, there are ionic fluctuations that are due to the excess number of ions associated with each particle. 

This interaction is like the first n = 0 term for small-particle van der Waals forces but with ionic rather than retardation screening. In the limit of low salt concentration, Km - 0, it has the familiar l//6 form ... 

Following the Pitaevskii strategy for extracting small-particle van der Waals interactions for the interaction between suspensions, we specialize the general expression for ionic-fluctuation forces to derive forces between cylinders (Level 3). As with the extraction of dipolar forces between rods, consider two regions A and B, dilute suspensions of parallel rods immersed in salt solution interacting across a region of salt solution m (see Fig. L2.19). 

The classical DLVO (Derjaguin-Landau-Verwey-Overbeek) theory (Derjaguin and Landau, 1941 Yerwey and Overbeek, 1948) states that the stability of a colloidal system essentially depends on two independent interactions between colloidal particles van der Waals attractions and electrostatic repulsion ... 

In a random mixture the probability that a sample contains a certain amount of active substance is equal throughout the entire mixture. This probabihty is proportional to the fraction of active substance present in the mixture. Theoretically, this applies only if the particles of the substances in the mixture have the same shape, size and density, and if there are minimal surface forces in action such as moisture, electrostatic charge, or, for small particles. Van der Waals forces. 

The film formation process is extremely complex, and there are a number of theories — or more accurately, schools of theories — to describe it. A major point of difference among them is the driving force for particle deformation surface tension of the polymer particles. Van der Waals attraction, polymer-water interfacial tension, capillary pressure at the air-water interface, or combinations of the above. These models of the mechanism of latex film formation are necessary in order to improve existing waterborne paints and to design the next generation. To improve the rate of film fonnation, for example, it is important to know if the main driving force for coalescence is located at the interface between polymer and water, between water and air, or between polymer particles. This location determines which surface tension or surface energies should be optimized. 

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 adhesion between two solid particles has been treated. In addition to van der Waals forces, there can be an important electrostatic contribution due to charging of the particles on separation [76]. The adhesion of hematite particles to stainless steel in aqueous media increased with increasing ionic strength, contrary to intuition for like-charged surfaces, but explainable in terms of electrical double-layer theory [77,78]. Hematite particles appear to form physical bonds with glass surfaces and chemical bonds when adhering to gelatin [79]. 

The charge on a droplet surface produces a repulsive barrier to coalescence into the London-van der Waals primary attractive minimum (see Section VI-4). If the droplet size is appropriate, a secondary minimum exists outside the repulsive barrier as illustrated by DLVO calculations shown in Fig. XIV-6 (see also Refs. 36-38). Here the influence of pH on the repulsive barrier between n-hexadecane drops is shown in Fig. XIV-6a, while the secondary minimum is enlarged in Fig. XIV-6b [39]. The inset to the figures contains t,. the coalescence time. Emulsion particles may flocculate into the secondary minimum without further coalescence. 

Some studies have been made of W/O emulsions the droplets are now aqueous and positively charged [40,41 ]. Albers and Overbeek [40] carried out calculations of the interaction potential not just between two particles or droplets but between one and all nearest neighbors, thus obtaining the variation with particle density or . In their third paper, these authors also estimated the magnitude of the van der Waals long-range attraction from the shear gradient sufficient to detach flocculated droplets (see also Ref. 42). 

Note that the van der Waals forces tliat hold a physisorbed molecule to a surface exist for all atoms and molecules interacting with a surface. The physisorption energy is usually insignificant if the particle is attached to the surface by a much stronger chemisorption bond, as discussed below. Often, however, just before a molecule fonus a strong chemical bond to a surface, it exists in a physisorbed precursor state for a short period of time, as discussed below in section AL7.3.3. 

The saturation coverage during chemisorption on a clean transition-metal surface is controlled by the fonnation of a chemical bond at a specific site [5] and not necessarily by the area of the molecule. In addition, in this case, the heat of chemisorption of the first monolayer is substantially higher than for the second and subsequent layers where adsorption is via weaker van der Waals interactions. Chemisorption is often usefLil for measuring the area of a specific component of a multi-component surface, for example, the area of small metal particles adsorbed onto a high-surface-area support [6], but not for measuring the total area of the sample. Surface areas measured using this method are specific to the molecule that chemisorbs on the surface. Carbon monoxide titration is therefore often used to define the number of sites available on a supported metal catalyst. In order to measure the total surface area, adsorbates must be selected that interact relatively weakly with the substrate so that the area occupied by each adsorbent is dominated by intennolecular interactions and the area occupied by each molecule is approximately defined by van der Waals radii. This... 

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... 

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

Here we consider the total interaction between two charged particles in suspension, surrounded by tlieir counterions and added electrolyte. This is tire celebrated DLVO tlieory, derived independently by Derjaguin and Landau and by Verwey and Overbeek [44]. By combining tlie van der Waals interaction (equation (02.6.4)) witli tlie repulsion due to the electric double layers (equation (C2.6.lOI), we obtain... 

Hamaker H C 1937 London-van der Waals attraction between spherical particles Physica 4 1058-72... 

Tlic cavity and van der Waals contributions may also be modelled as separate terms. In som implementations an estimate of the cavity term may be obtained using scaled particle theor [Eierotti 1965 Claverie et al. 1978], which uses an equation of the form ... 

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