London s forces

London Bullion Market Association, silver specifications by, 22 649 London coherence length, 23 806 London equations, 23 806 London-Norris equations, 23 845 London penetration depth, 23 805, 806 London s forces, 12 4 15 213 21 602-604 ... 

For more information on the derivation of London s force law for nonpolar atoms or molecules, see J. M. Prausnitz, R. N. Lichtenthaler, and E. G. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed., Prentice Hall, Upper Saddle River, NJ, 1999. 

First attempts to quantitatively estimate stabilizing capabilities of polymers date back to Faraday s time." Steric stabilization becomes probable because spatial dimensions of at least comparatively low-molecular compounds are commensurable with the range of London s forces of attraction or even exceed them. If the diameter of a macromolecule of a linear polymer coincides with the root-mean-square (rms) distance between its ends then the relationship between the mean geometric radius of the particle (r versus polymer molecular mass M can be expressed by the following relationship ... 

There are probably several factors which contribute to determining the endo exo ratio in any specific case. These include steric effects, dipole-dipole interactions, and London dispersion forces. MO interpretations emphasize secondary orbital interactions between the It orbitals on the dienophile substituent(s) and the developing 7t bond between C-2 and C-3 of the diene. There are quite a few exceptions to the Alder rule, and in most cases the preference for the endo isomer is relatively modest. For example, whereas cyclopentadiene reacts with methyl acrylate in decalin solution to give mainly the endo adduct (75%), the ratio is solvent-sensitive and ranges up to 90% endo in methanol. When a methyl substituent is added to the dienophile (methyl methacrylate), the exo product predominates. ... 

London [11] was the first to describe dispersion forces, which were originally termed London s dispersion forces. Subsequently, London s name has been eschewed and replaced by the simpler term dispersion forces. Dispersion forces ensue from charge fluctuations that occur throughout a molecule that arise from electron/nuclei vibrations. They are random in nature and are basically a statistical effect and, because of this, a little difficult to understand. Some years ago Glasstone [12] proffered a simple description of dispersion forces that is as informative now as it was then. He proposed that,... 

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... 

The van der Waals forces for these substances are due mainly to dispersion forces, which decrease with decrease in atomic number for atoms of similar structure. London s calculations (F. London, Z. Physik 63, 245 (1930) have shown the interaction of permanent dipoles to contribute only a small amount to the van der Waals forces for a substance such as hydrogen chloride. 

Kristyan, S., Pulay, P., 1994, Can (Semi)Local Density Functional Theory Account for the London Dispersion Forces , Chem. Phys. Lett., 229, 175. 

Van der Waals forces are derived from the energy of interaction between two molecules, Vss. These can be derived from London s theory as follows ... 

The electron density changes continually, so induced dipoles never last more than about 10-11 s. Nevertheless, they last sufficiently long for an interaction to form with the induced dipole of another nitrogen molecule nearby. We call this new interaction the London dispersion force after Fritz London, who first postulated their existence in 1930. 

As shown by Fowkes (1968) the interfacial energy between two phases (whose surface tensions - with respect to vacuum - are y1 and y2) is subject to the resultant force field made up of components arising from attractive forces in the bulk of each phase and the forces, usually the London dispersion forces (cf. Eq. 4.2) operating accross the interface itself. Then the interfacial tension (energy) between two phases y12 s given by... 

D) Dispersion forces Ever since London s pioneer work in 1930 it has been agreed that dispersion forces contribute to all intermolecular... 

The carbon sheets in graphite are separated by a distance of 335 pm and are held together by only London dispersion forces. Atmospheric gases can be absorbed between the sheets, thus enabling the sheets to easily slide over one another. As a result, graphite has a slippery feel and can be used as a lubricant. Because the sheets are so far apart, it s relatively difficult for an electron to hop from one sheet to the next and the electrical conductivity in the direction perpendicular to the sheets is therefore about 104 times smaller than the conductivity parallel to the sheets. 

The London dispersion forces are present and important in most adsorption processes and in adhesive interactions between dissimilar materials. The free energy of interaction per unit area between materials 1 and 2 in contact is where W 2 -s... 

The term dispersion in dispersion forces comes from an analogy to the refraction (dispersion) of light due to induced dipole interactions. Since London s induced dipole-induced dipole interactions resemble this, the term Dispersion Forces was coined which is unfortunate in that these dispersion forces act against the dispersion of colloidal particles. 

Kristyan S, Pulay P (1994) Can (semi)local density-functional theory account for London dispersion forces, Chem Phys Lett, 229 175-180... 

The application of Walter Heftier and Fritz London s valence bond theory was the first description of the binding forces in the H2 molecule, the simplest neutral molecule. Linus Pauling and John Slater later extended the principles to larger molecules. The key element in their proposal was the synthesis of a bonding wavefunction resulting from a combination of atomic orbitals that link the two atoms in a bond. It was hugely important that this localized approach concurred with the Lewis dot model. For the simplest neutral molecule, H2, the Hamiltonian operator may be written... 

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