Dispersive attractions

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

While the confirmation of the predicted long-range dispersion attraction between surfaces in air has been a major experimental triumph, the forces between particles in solution are of more general interest in colloid and surface chemistry. The presence of a condensed medium between the surfaces... 

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 exchange repulsion and dispersive attraction com bine in what is referred to as a van der Waals term. Sometimes a potential is added to account for hydrogen bonding explicitly while in other situations this is expected to fall out of ordinary electrostatic interactions. 

As has been noticed by Gelbart and Gelbart [7], the predominant orientational interaction in nematics results from the isotropic dispersion attraction modulated by the anisotropic molecular hard-core. The anisotropy of this effective potential comes from that of the asymmetric molecular shape. The coupling between the isotropic attraction and the anisotropic hard-core repulsion is represented by the effective potential... 

In addition to the static induction effects included in I/scf, the hot Drude oscillators give rise to a 1/r6, temperature-dependent, attractive term. This jkg Ta2/r6 term is the classical thermodynamic equivalent of the London quantum dispersive attraction IEa2/r6. It corresponds to a small perturbation to the London forces, because k T is at least two orders of magnitude smaller than the typical ionization energy IE. The smaller the temperature of the Drude motion, the closer the effective potential is to the SCF potential, making Eq. (9-57) independent of mo, the mass of the oscillators. 

The second term in equation (2.55) describes the long range Van der Waals or dispersive (attractive) forces. The first term describes the much shorter range repulsive forces experienced when the electron clouds on two atoms come into contact the repulsion increases rapidly with decreasing distance, with the atoms behaving almost as hard spheres. 

Therefore, there is a certain equilibrium distance r , at which the dispersive-attractive and the repulsive forces balance and the system achieves minimum energy at the minimum of potential curve y(r ). The van der Walls radius, r, for the C-H interaction can be assumed to be about 0.16 nm. 

Dispersion attractions are usually weak, increasing from small to large cations, (of the order of 0.1, 1.0 and 1.5 kcal/mol for Li+, K+ and Cs+, respectively) they slightly favour nitrogen sites over oxygen sites. 

Molecules that have no permanent dipole still have their electrons in movement. Although the time-averaged distribution of electrons is symmetrical, at any instant the electrons are not uniformly distributed, so the molecule has a small instantaneous dipole, p. This instantaneous dipole can polarize electrons in a neighboring molecule, giving a small dipole in the molecules. This is the dispersion attraction responsible for molecules sticking together. These dispersions forces are the weakest of all inter-... 

Van der Waals interactions are composed of dispersive attraction changing as r fi with distance, and repulsion changing as r 12 prevailing when the atoms are close. 

To think about the strength of dispersive attractions, we consider a situation in which a molecule, i, is moved from a gas phase and mixed into (i.e., absorbed by) a liquid made of the substance, 1 ... 

Considering one molecule of i next to one molecule of 1, we have a dispersive attraction energy, Adispg, given by (Israelachvili, 1992) ... 

LONDON FORCES (dispersion) attraction due to induced dipole moments increases with a... 

A fourth potential problem is that HF theory does not model van der Waals attractive interactions between nonbonded molecules. Whereas hydrogen bonding is well represented by the HF-SCF model, weak London dispersion attractions are not. 

Let us look at the benzene-cyclohexane separation more closely as we summarize how GC works. The boiling points of benzene and cyclohexane are nearly the same, 80.1 and 81.4°C respectively. Any GC separation will have to depend on differences in the intermolecular interactions between the stationary phase and these two analytes, both of which are nonpolar hydrocarbons. What differences could be exploited with GC Benzene has a -n-electron cloud, which should make it more susceptible to induction effects and perhaps dispersion attractions (Chapter 3). Therefore we should choose a stationary liquid phase that would accentuate this difference—a polar one also, using the like-dissolves-like rule we might choose an aromatic compound that would interact more with benzene than with cyclohexane. One possible liquid phase that meets these criteria is dinonylphthalate, and it has been used to separate benzene and cyclohexane. The relative retention has been found to be 1.6, which represents a very good separation.1... 

As might be expected, there is a very large variation in the magnitudes of these terms at some normal or standard concentration. Thus, at a monolayer coverage, these terms will have approximate upper limits of 104, 103, 102, and 101 cal. per mole, respectively, when the induced moments are taken into account along with the permanent ones. At low coverages, the relative differences will be even greater, and we may expect to be able to account for the observed interaction heats on the basis of pure dispersion-attraction and simple dipole interactions. 

These temporary dipoles last only a fraction of a second, and they constantly change yet they are correlated so their net force is attractive. This attractive force depends on close surface contact of two molecules, so it is roughly proportional to the molecular surface area. Carbon tetrachloride has a larger surface area than chloroform (a chlorine atom is much larger than a hydrogen atom), so the intermolecular London dispersion attractions between carbon tetrachloride molecules are stronger than they are between chloroform molecules. 

The nonpolar solvation free energy is given by the sum of two terms the free energy to form the cavity in solvent filled by the solute and the dispersion attraction between solute and solvent [65,113]. The nonpolar free energy is written as [27]... 

The forces responsible for physisorption always include the dispersion attractive interactions (which derive their name from the close connection between their origin and the cause of optical dispersion) and the short-range repulsion. These interactions... 

The dispersion attractive interactions were first characterized by London (1930) and arise from the rapid fluctuations in electron density in one atom, which induce an electrical moment in a neighbouring atom. By making use of quantum-mechanical perturbation theory, London arrived at the well-known expression for the potential energy, eD(r), of two isolated atoms separated by a distance r ... 

Atomic repulsion and induced dipole-induced dipole dispersive attraction are typically described by a Lennard-Jones function [16,17] ... 

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