London attraction

The ever present dispersion force (London attraction). 

Equations (25)-(28) are widely encountered expressions for the London attraction between two molecules. 

There is an ill-defined boundary between molecular and polymeric covalent substances. It is often possible to recognise discrete molecules in a solid-state structure, but closer scrutiny may reveal intermolecular attractions which are rather stronger than would be consistent with Van der Waals interactions. For example, in crystalline iodine each I atom has as its nearest neighbour another I atom at a distance of 272 pm, a little longer than the I-I distance in the gas-phase molecule (267 pm). However, each I atom has two next-nearest neighbours at 350 and 397 pm. The Van der Waals radius of the I atom is about 215 pm at 430 pm, the optimum balance is struck between the London attraction between two I atoms and their mutual repulsion, in the absence of any other source of bonding. There is therefore some reason to believe that the intermolecular interaction amounts to a degree of polymerisation, and the structure can be viewed as a two-dimensional layer lattice. The shortest I-I distance between layers is 427 pm, consistent with the Van der Waals radius. Elemental iodine behaves in most respects - in its volatility and solubility, for example - as a molecular solid, but it does exhibit incipient metallic properties. 

With the exception of highly polar materials, London dispersion forces account for nearly all of the van der Waals attraction which is operative. The London attractive energy between two molecules is very short-range, varying inversely with the sixth power of the intermolecular distance. For an assembly of molecules, dispersion forces are, to a first approximation, additive and the van der Waals interaction energy between two particles can be computed by summing the attractions between all interparticle molecule pairs. 

In the case of Brownian diffusion and interception, particle capture is enhanced by London attractive forces and reduced by electrostatic double layer repulsive forces. 

Later Tien and Payatakes (15), in their study of the deposition of colloidal particles, developed a mathematical model which included in one expression the contributions by Brownian diffusion, interception with London attraction, and gravitational field. The most general form of their expression is ... 

Fig. 1. Profile of the total energy of interaction between a colloidal particle and the collector surface arising from the double-layer repulsion and London attraction.

Compared to small molecules the description of convective diffusion of particles of finite size in a fluid near a solid boundary has to account for both the interaction forces between particles and collector (such as van der Waals and double-layer forces) and for the hydrodynamic interactions between particles and fluid. The effect of the London-van der Waals forces and doublelayer attractive forces is important if the range over which they act is comparable to the thickness over which the convective diffusion affects the transport of the particles. If, however, because of the competition between the double-layer repulsive forces and London attractive forces, a potential barrier is generated, then the effect of the interaction forces is important even when they act over distances much shorter than the thickness of the diffusion boundary layer. For... 

The process of cell deposition in the presence of repulsive forces may be considered as a two-step sequence. First the cells move, primarily under the action of gravity, to a region very near to the surface. In order to move closer to the surface the particle must experience the energy barrier formed by the electrostatic double-layer repulsions and London attraction. Diffusion of cells over the energy barrier is the second step of the process. If the deposition rate is much smaller than the sedimentation rate the second step... 

The combined effect of attraction and repulsion forces has been treated by many investigators in terms borrowed from theories of colloidal stability (Weiss, 1972). These theories treat the adhesion of colloidal particles by taking into account three types of forces (a) electrostatic repulsion force (Hogg, Healy Fuerstenau, 1966) (b) London-Van der Waals molecular attraction force (Hamaker, 1937) (c) gravity force. The electrostatic repulsion force is due to the negative charges that exist on the cell membrane and on the deposition surface because of the development of electrostatic double layers when they are in contact with a solution. The London attraction force is due to the time distribution of the movement of electrons in each molecule and, therefore, it exists between each pair of molecules and consequently between each pair of particles. For example, this force is responsible, among other phenomena, for the condensation of vapors to liquids. 

In conclusion, we suggest that the ion dispersion forces were ignored by most (but by no means all) electrolyte theories mainly because they are important only for separations between ions smaller than about 5 A, and the interactions at these distances are not well-known. It is hard to believe that at these distances the interactions can be accurately described by a sum between a hard-wall repulsion, a Coulomb interaction, and a London attraction. Even if the latter would be true, a correction in the local dielectric constant (because of incomplete screening by water molecules) would render again the van der Waals interactions negligible, up to distances of the order of ion diameters. 

In the early 1960s, Fowkes [88,89] introduced the concept of the surface free energy of a solid. The surface free energy is expressed by the sum two components a dispersive component, attributable to London attraction, and a specific (or polar) component, y p, owing to all other types of interactions (Debye, Keesom, hydrogen bonding, and other polar effects, as similarly described before in Sec. II. C... 

This Van der Waals-London attraction is always present, also when there is a bond belonging to one of the other main types of the chemical bond. This interaction is always attractive, non-directional (apart from the anisotropy of the polarizability), non-specific, it does not lead to saturation and it acts only over distances of the order of magnitude of the radius of the particle and is dependent on the degree of polarizability of both particles. 

J. Th. G. Overbeek in H. R. Kruyt et al., Colloid Science /, Amsterdam, Houston, New York, London, 1952, p. 264. Thus the Van der Waals-London attraction between glass plates can even be measured in macroscopic experiments (Overbeek and Sparnaay). 

In the tetrahalides of Si, Ti and Ge and in the halides of B, P, Al, with the exception of A1F3 and TiF4, the rise of the boiling point of the fluoride proceeding to the iodide is a direct consequence of the increase of the London attraction, as a result of the increase of the quantity a/r3 from fluorine to iodine. That the boiling point of A1F3 (above 1290°) is so high... 

Jet was at the height of its popularity. A display of Whitby jet at the Great Exhibition of 1851 in London attracted international attention and orders even came in from foreign royalty. 

At the rather large internuclear distance of 5.63a0, the potential energy curve of the He(ls2)-He(ls2) interaction shows a shallow minimum of —33.4 x 10 corresponding to the formation of a so-called Van der Waals bond. This is possible since, at this large distance, the small Pauli repulsion between closed shells is overbalanced by a small London attraction (see Chapter 4). 

The leading term of London attraction has an R 6 dependence on R, the Cg coefficient involving knowledge of the individual nonobservable (i.e., nonmeasurable) contributions from each excited pseudostate to the polarizabilities of A and B, as given by Equations (4.22) and (4.23). 

Salt Structure Coulomb attraction London attraction Born repulsion Zero-point energy U (total) kJ mol" ... 

We can combine the London attractive term with this repulsive term to construct a realistic potential energy function known as the Lennard-Jones... 

Values of e, n and ve and Hamaker constants for two identical types of a material in a vacuum, which are calculated from Equation (567) by taking e3 = 1 and 3 = 1, are given in Table 7.1. Unfortunately, the lack of material constants, such as the dielectric constant, as a function of frequency for most of the substances, and also the complexity of the derived formulae have hampered the general use of the Lifshitz model. However, Lifshitz theory made possible the advent of the first theories on the stability of hydrophobic colloids as a balance between London attraction and electrical double-layer repulsion. Later, these theories were further elaborated by Derjaguin and Landau, and independently by Verwey and Overbeek. The general theory of colloidal stability (which is beyond the scope of this book) is based on Lifshitz theory and has become known as the DLVO theory, by combining the initials of these four authors. 

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