London interaction magnitude

The surface free energy of a solid can be described as the sum of the dispersive and specific contributions. Dispersive (apolar) interactions, also known as Lifshitz-van der Waals interactions, consist of London interactions which originate from electron density changes but may include both Keesom and Debye interactions [6, 7]. Other forces influencing the magnitude of surface energy are Lewis acid-base interactions which are generated between an electron acceptor (acid) and an electron donor (base). Details of the widely accepted theoretical... 

LW) interactions refer to the purely physical London s (dispersion), the Keesom s (polar) and Debye s (induced polar) interactions and correspond to magnitudes ranging from approximately 0.1 to 10 kJ/mol (but in rare cases may be higher). The polar forces in the bulk of condensed phases are believed to be small due to the self-cancellation occurring in the Boltzmann-averaging of the multi-body... 

In polyatomic molecules there are separate regions of essentially nonoverlapping electron clouds whose interaction may be treated by London s methods. This was recognized by many authors, but relatively few calculations have emphasized this factor. Indeed sometimes it may have been erroneously dismissed as of negligible magnitude. Bom and Mayer6 Considered London forces in their... 

In order to arrive at a mathematical relationship to describe London forces, we will use an intuitive approach. First, the ability of the electrons to be moved within the molecule is involved. Atoms or molecules in which the electrons are highly localized cannot have instantaneous dipoles of any great magnitude induced in them. A measure of the ability of electrons in a molecule to be shifted is known as the electronic polarizability, a. In fact, each of the interacting molecules has a polarizability, so the energy arising from London forces, Ei, is proportional to a2. London forces are important only at short distances, which means that the distance of separation is in the denominator of the equation. In fact, unlike Coulomb s law, which has r2 in the denominator, the expression for London forces involves r6. Therefore, the energy of interaction as a result of London forces is expressed as... 

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. 

It is of importance for a knowledge of the forces acting between colloidal particles that the greatest distance at which the London forces are still important is not the radius of the atom but in fact of the order of magnitude of the radius of the particle itself, since the interaction between all the atoms in each of the colloidal particles must be summed, and this interaction, therefore, will increase with increasing size of the particles (Hamaker)1. This is quite different from, for example, the interaction between particles with a crystal lattice in which only purely electrostatic forces would act in this case the radius of action remains, even for large particles, of the order of the lattice constant and there is only a question of a surface action. The effect of the more deeply situated parts of the lattice does not appear outside on account of the mutual compensation of the action of the oppositely charged ions. 

A variety of Interaction forces contribute to G(h) and 17(h), each with its own sign, magnitude and typical decay as a function of h. One of them is the London-Van der Wools force, also known as dispersion force, and already described extensively in chapter 1.4. For wetting films G(h) may be positive or negative, depending on the sign of the Hamaker constant examples of which can be found in... 

The relative magnitudes of these three types of interaction can be seen from Table 7.7 for a few simple cases. For a non-polar molecule the London energy is necessarily the only contribution to the lattice energy even for polar molecules ch as NH3 and H2O for which is appreciable, l forms an important part of the lattice energy. Note that these lattice energies are between one and two orders of magnitude smaller than for ionic crystals for example, those of the permanent ... 

Polar molecules have forces between permanent dipoles. With nonpolar molecules London dispersion (or van der Waals ) forces arise between fluctuating dipoles their magnitude is related to molecular polarizability, which generally increases with size. Molecules may also have more specific donor-acceptor interactions including hydrogen bonding. 

As we have seen, London dispersion interactions, Keesom dipole-dipole orientation interactions and Debye dipole-induced dipole interactions are collectively termed van der Waals interactions their attractive potentials vary with the inverse sixth power of the intermol-ecular distance which is a common property. To show the relative magnitudes of dispersion, polar and induction forces in polar molecules, similarly to Equation (78) for London Dispersion forces, we may say for Keesom dipole-orientation interactions for two dissimilar molecules using Equation (37) that... 

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