London interaction potential

TABLE 6.3. Values of the Constants of the Lennard-Jones and London Interaction Potentials and the Interaction Energies at the Distance of Closest Approach of 4 A... 

The total van der Waals interaction potential is obtained by simply adding the individual contributions arising from the Keesom, Debye, and London interactions. Because the radial power-law dependencies of all these interactions vary as 1 /r, the total van der Waals interaction can be expressed simply as... 

Closely related to the London interaction is the dipole-induced-dipole interaction, in which a polar molecule interacts with a nonpolar molecule (for example, when oxygen dissolves in water). Like the London interaction, the dipole—induced-dipole interaction arises from the ability of one molecule to induce a dipole moment in the other. However, in this case, the molecule that induces the dipole moment has a permanent dipole moment. The potential energy of the interaction is... 

Once again, the potential energy is inversely proportional to the sixth power of the separation. Notice that the potential energies of the dipole-dipole interaction of rotating polar molecules in the gas phase, the London interaction, and the dipole-induced-dipole interaction all have the form... 

Cf. also Bernstein, R.B., Ed. "Atom-Molecule Collision Theory" Plenum Press New York and London 1978, with special reference to Schaefer, H.F. Ill Kuntz, P.J. "Interaction Potentials", and the literature quoted. 

FIG. 10.4 A linear arrangement of two dipoles used to define the potential energy in the Schrodinger equation for the London interaction energy. 

The strength of the London interaction depends on the polarizability, a (alpha), the ease with which the electron cloud can be distorted. This dependence is reasonable, because the nuclei in highly polarizable molecules have only weak control over the surrounding electrons, so there can be big fluctuations in electron density and hence large instantaneous partial charges. It turns out that the potential energy of the London interaction varies as the sixth power of the separation of two molecules ... 

An important point to note is that, like the potential energy of dipole-dipole interactions between rotating molecules, the potential energy of the London interaction also decreases very rapidly with distance (as 1/r6 see Fig. 5.1). 

The rate of deposition of Brownian particles is predicted by taking into account the effects of diffusion and convection of single particles and interaction forces between particles and collector [2.1] -[2.6]. It is demonstrated that the interaction forces can be incorporated into a boundary condition that has the form of a first order chemical reaction which takes place on the collector [2.1], and an expression is derived for the rate constant The rate of deposition is obtained by solving the convective diffusion equation subject to that boundary condition. The procedure developed for deposition is extended to the case when both deposition and desorption occur. In the latter case, the interaction potential contains the Bom repulsion, in addition to the London and double-layer interactions [2.2]-[2.7]. Paper [2.7] differs from [2.2] because it considers the deposition at both primary and secondary minima. Papers [2.8], [2.9] and [2.10] treat the deposition of cancer cells or platelets on surfaces. 

Therefore, the molecules moved from the cusp X to the crest Y provide a decrease in the total free energy due to the London interactions. It is true that the molecules below the cusp, A, now have fewer molecules above them than before and this makes their interaction potential less negative, However, the molecules beneath the crest and below the previous planar surface, B, now have a larger number of molecules above them and this makes their interaction potential more negative. It is likely that the last two effects compensate each other. The overall effect of the perturbation on the dispersion interactions is to make the contribution of the latter more negative. The perturbation will grow and... 

Hydrogen bonds" are not due to a separate potential they involve the attraction between an H atom that is covalently bonded to molecule 1 and electronegative atoms (O, N, etc.) in molecule 2 that are between 0.15 nm and 0.25 nm from the H atom. This hydrogen bond interaction is a combination of Keesom, Debye, and London interactions. 

If a gas is brought into contact with a clean metal surface, molecules will absorb on the metal surface. The metal surface itself is characterized by a dipole and a large polarizability. Dipole-dipole and London interactions act between the metal surface and the molecules hence polar and nonpolar molecules and ions may become adsorbed. Physisorption may influence the potential energy drop —etp - Fvac and, hence, the chemical potential with respect to Fyac- The dipole-dipole interactions can lead to a preferential orientation of physisorbed polar molecules such as H2O. 

All three types of polarization interactions—Keesom, Debye, and London—are included in the following formula for the total van der Waals interaction potential between two spherical molecules separated by a distance r ... 

Even though the components of the total interaction potential between such complex adsorbents as solid carbons and a wide range of adsorbates can be grouped in many different ways 315,316], it is convenient and meaningful to consider only the London dispersion (induced dipole) forces and the electrostatic (double-layer) forces [620,621,76,77]. 

As stated above, IGC is possibly the most rapid method for the evaluation of 7 and of a specific interaction parameter, Isp, that qualitatively describes the affinity of the solid surface for non specific interactions. London interactions between two partners are proportional to their polarisabilities, to their molecular ionisation potentials, and to the number of elemental volumes of the two phases in interaction. Hence, taking one partner as a molecular probe allows to detect changes that may occur when, for instance, submitting the other partner to heat treatments or chemical transformations. 

H.C. Hamaker, in 1937, was the first to treat London dispersion interactions between macroscopic objects. He started with the most basic case, to determine the interaction of a single molecule with a planar solid surface. He considered a molecular pair potential and its relation with the molecules present within the solid surface, to derive the total interaction potential by summing the attractive interaction energies between all pairs of molecules, ignoring multibody perturbations. In this way, he built up the whole from the parts. Thus, Hamaker s method is called the microscopic approach. 

Lennard-Jones potential As two atoms approach one another there is the attraction due to London dispersion forces and eventually a van der Waals repulsion as the interatomic distance r gets smaller than the equilibrium distance. A well-known potential energy function to describe this behavior is the Lennard-Jones (6-12) potential (LJ). The LJ (6-12) potential represents the attractive part as r-6-dependent whereas the repulsive part is represented by an r n term. Another often used nonbonded interaction potential is the Buckingham potential which uses a similar distance dependence for the attractive part as the LJ (6-12) potential but where the repulsive part is represented by an exponential function. 

In order to calculate the transfer cross sections of the processes by the PSS method, it is necessary to obtain the interaction potential curves of the system of He + He. The curves are calculated by the usual Heitler-London method. Considering the fact that the cross section will mainly be determined by the interaction at distant nuclear separation, we adopt the single term atomic base wave function of He and He. ... 

Physical adsorption of molecules onto solid surfaces possesses certain similarities to enzyme-substrate binding. The atoms in a solid present a closely packed surface and in some cases, for example graphite, the interatomic distance is similar to that found in covalently bonded molecules. Instead of the normal dependence of the London attractive potential between a pair of molecules there is a r dependence for the interaction between a molecule and a solid. This longer range interaction is the basic reason why gases are adsorbed at pressures lower than those at which they condense to liquids or solids. The differential heat of adsorption is often of the order of twice the heat of condensation of the adsorbed vapour. 

For certain types of gas-surface interactions, it may be useful to view the interaction as between the gas atom and a single surface atom. Weak attractive interaction between a pair of atoms can be due to dispersion forces (London [14, 15]) that represent the interaction of induced fluctuating charge distributions. In addition, molecules that possess permanent dipoles can further polarize each other (Debye [16, 17]) and can have dipole-dipole interactions (Keesom [18, 19]). All these pairwise interaction potentials fall off inversely as the sixth power of the distance. 

The dispersion force is due to induced dipole interaction between atoms or molecules through electron density fluctuations. According to London, the potential energy of interaction London is given by... 

This equation is somewhat similar to that of Girifalco and Good [11], except that these authors used a parameter in the last term (-2 NTy7 ) and did not distinguish between surface tensions resulting from various types of intermolecular forces. The values of were about 0.5 for water-hydrocarbon interfaces. The Berthelot relation in Equation 1 is not exact, as can be shown by the London pair potentials, but is seldom in error by more than 2%, and the geometric mean is applied to only the interacting contributions to the surface tension. 

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