London-van der Waals constant

Similarly, the interaction energy V(h) between two parallel dissimilar plates 1 and 2 per unit area in a vacuum, which have molecular densities N and N2, London-van der Waals constant Cj and C2, and thicknesses d and 2. respectively, can be obtained from Eq. (4.11)... 

On the basis of a sufficient number of calculations of W, we constructed a series of curves giving the values of potential and concentration of 1 — 1 valent electrolyte (for a given London-Van der Waals constant), for which the stability-ratio W just reaches the value lO , or in other words just sufficient to make a diluted sol passably stable. The figures 43 and 44 show for two values of A, (10 and 2 10 ), X — pQ curves separating stability- from instability-regions. 

Interaction of two spherical particles with radius a — 10 cm electrolyte x 10 London-Van Der Waals constant A = surface... 

Table 4 gives some experimentally determined yalucs of the radius of interaction R as compared with the radius of the primary particles, ft, for rapid coagulations. With a London-Van Der Waals constant of 1 or 2 R is expected to be 3 or 4 Experimentally the ratio Rtri is found between 2 and 3 showing that there is an attraction with a range of about one particle radius though perhaps somewhat smaller than the calculated one. 

Interactions between a solute and a solvent may be broadly divided into three types specific interactions, reaction field and Stark effects, and London-van-der-Waals or dispersion interactions. Specific interactions involve such phenomena as ion pair formation, hydrogen bonding and ir-complexing. Reaction field effects involve the polarization of the surrounding nonpolar solvent by a polar solute molecule resulting in a solvent electric field at the solute molecule. Stark effects involve the polarization of a non-polar solute by polar solvent molecules Dispersion interactions, generally the weakest of the three types, involves nonpolar solutes and nonpolar solvents via snap-shot dipole interactions, etc. For our purposes it is necessary to develop both the qualitative and semiquantita-tive forms in which these kinds of interactions are encountered in studies of solvent effects on coupling constants. 

The repulsive force depends on the double layer potential and thickness, the particle radius and the dielectric constant of the medium, whereas the attractive force arises from retarded London/van der Waals forces. 

For a typical experimental hydrosol critical coagulation concentration at 25°C of 0.1 mol dm-3 for z = 1, and, again, taking if/d = 75 mV, the effective Hamaker constant, A, is calculated to be equal to 8 X 10 20 J. This is consistent with the order of magnitude of A which is predicted from the theory of London-van der Waals forces (see Table 8.3). 

Dispersion. Dispersion or London-van der Waals forces are ubiquitous. The most rigorous calculations of such forces are based on an analysis of the macroscopic electrodynamic properties of the interacting media. However, such a full description is exceptionally demanding both computationally and in terms of the physical property data required. For engineering applications there is a need to adopt a procedure for calculation which accurately represents the results of modem theory yet has more modest computational and data needs. An efficient approach is to use an effective Lifshitz-Hamaker constant for flat plates with a Hamaker geometric factor [9]. Effective Lifshitz-Hamaker constants may be calculated from readily available optical and dielectric data [10]. 

Hamaker Constant In a description of the London-van der Waals attractive energy between two dispersed bodies, such as droplets, the Hamaker constant is a proportionality constant characteristic of the droplet composition. It depends on the internal atomic packing and polarizability of the droplets. 

Figure 5.18 gives an impression of the agreement between theory and experiment. choosing representative parameter values. The London-Van der Waals component was computed from the Lifshits theory, as described in sec. 1.4.7. For water and silica the Hamaker constants are similar, as a result these forces do not contribute substcuitially, except at very low h, where 77... 

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