Molecular mechanics London dispersion forces

Among all the low energy interactions, London dispersion forces are considered as the main contributors to the physical adsorption mechanism. They are ubiquitous and their range of interaction is in the order 2 molecular diameters. For this reason, this mechanism is always operative and effective only in the topmost surface layers of a material. It is this low level of adhesion energy combined with the viscoelastic properties of the silicone matrix that has been exploited in silicone release coatings and in silicone molds used to release 3-dimensional objects. However, most adhesive applications require much higher energies of adhesion and other mechanisms need to be involved. 

Polarizability is a measure of the ease with which the electrons of a molecule are distorted. It is the basis for evaluating the nonspecific attraction forces (London dispersion forces) that arise when two molecules approach each other. Each molecule distorts the electron cloud of the other and thereby induces an instantaneous dipole. The induced dipoles then attract each other. Dispersion forces are weak and are most important for the nonpolar solvents where other solvation forces are absent. They do, nevertheless, become stronger the larger the electron cloud, and they may also become important for some of the higher-molecular-weight polar solvents. Large solute particles such as iodide ion interact by this mechanism more strongly than do small ones such as fluoride ion. Furthermore, solvent polarizability may influence rates of certain types of reactions because transition states may be of different polarizability from reactants and so be differently solvated. 

As shown above, there have been identified several mechanisms involved in the interactions between atoms and molecules, denominated collectively as the van der Waals forces. In atomic and completely nonpolar molecular systems (hydrocarbons, fluorocarbons, etc.) the London dispersion forces provide the major contribution to the total interaction potential. However, in many molecular systems containing atoms of very different electronegativities and polarizabilities the dipole-dipole (Keesom) and dipole-induced dipole (Debye) forces may also make significant contributions to the total interaction. 

Absorption mechanisms involve secondary molecular forces. Here it is hypothesized that molecules near the interface are attracted to each other by London dispersion forces, dipole-dipole interactions, hydrogen bonding, or other secondary molecular forces. The strength of these forces varies from 0.1 to 10 J/mol. Although most adhesives exhibit some dipole interactions, it is difficult to account for the relatively large strength of many practical joints purely on these secondary molecular forces. 

The Hamaker approach of pairwise addition of London dispersion forces is approximate because multi-body intermolecular interactions are neglected. In addition, it is implicitly assumed in the London equation that induced dipole-induced dipole interactions are not retarded by the finite time taken for one dipole to reorient in response to instantaneous fluctuations in the other. Because of these approximations an alternative approach was introduced by Lifshitz. This method assumes that the interacting particles and the dispersion medium are all continuous i.e. it is not a molecular theory. The theory involves quantum mechanical calculations of the dielectric permittivity of the continuous media. These calculations are complex, and are not detailed further here. 

The selection of the solvent is based on the retention mechanism. The retention of analytes on stationary phase material is based on the physicochemical interactions. The molecular interactions in thin-layer chromatography have been extensively discussed, and are related to the solubility of solutes in the solvent. The solubility is explained as the sum of the London dispersion (van der Waals force for non-polar molecules), repulsion, Coulombic forces (compounds form a complex by ion-ion interaction, e.g. ionic crystals dissolve in solvents with a strong conductivity), dipole-dipole interactions, inductive effects, charge-transfer interactions, covalent bonding, hydrogen bonding, and ion-dipole interactions. The steric effect should be included in the above interactions in liquid chromatographic separation. 

Whereas many scientists shared Mulliken s initial skepticism regarding the practical role of theory in solving problems in chemistry and physics, the work of London (6) on dispersion forces in 1930 and Hbckel s 7t-electron theory in 1931 (7) continued to attract the interest of many, including a young scientist named Frank Westheimer who, drawing on the physics of internal motions as detailed by Pitzer (8), first applied the basic concepts of what is now called molecular mechanics to compute the rates of the racemization of ortho-dibromobiphenyls. The 1946 publication (9) of these results would lay the foundation for Westheimer s own systematic conformational analysis studies (10) as well as for many others, eg, Hendrickson s (11) and Allinger s (12). These scientists would utilize basic Newtonian mechanics coupled with concepts from spectroscopy (13,14) to develop nonquantum mechanical models of structures, energies, and reactivity. 

Adsorption by Dispersion Forces. Occurs via London-van der Waals dispersion forces acting between adsorbent and adsorbate molecules (Figure 2-9). Adsorption by this mechanism generally increases with an increase in the molecular weight of the adsorbate and is important not only as an independent mechanism, but also as a supplementary mechanism in all other types. For example, it accounts in part for the pronounced ability of surfactant ions... 

Dispersion forces arise because of the fluctuations and uncertainties which are fundamental in quantum mechanics. Thus, though the expectation value of a molecular dipole may be zero, the instantaneous value fluctuates about zero because <(x —<(i = <(x > —<( ,> does not vanish. This instantaneous fluctuating dipole can cause polarization effects in a neighbouring molecule in the same way as does a permanent dipole and this leads to an attractive potential varying as Details of the calculation are given by London (1937) and Buckingham (1965) and in standard texts on quantum mechanics and we will not repeat them here. The approximate result found by London was... 

Advantage has been taken of the nanomechanical effects of molecular adsorption, confined to one surface of a microcantilever, to utilize these devices for sensors. Surfiice adsorption can be characterized as either physisorption or chemisorption. Physisorption is a result of among other effects, London-type dispersion forces resulting from an induced d le and induction forces caused by surface electric fields. On the other hand, chemisorption is accompanied by charge transfer between adsorbed molecules and the surfree or the presence of covalent bonds between the adsorbate and the surface atoms. The mechanical... 

In Sections 4.1 and 4.2 we discussed the fact that the electric moments of molecules play an important role in the description of the intermolecular forces between two molecules separated by a large distance. Their contribution to the interaction energy is of purely classical, i.e. electrostatic nature. Here, we want to show now that also the contribution from quantum mechanical dispersion or London forces, i.e. the dispersion energy E, can be related to molecular properties of the two interacting molecules. In particular, we will see that it is related to the frequency-dependent polarizabilities, which is in line with the physical interpretation of the dispersion forces as arising from the interaction of induced dipole moments, which implies that both charge distributions are perturbed by their interaction. 

In molecular crystals, there are two levels of bonding intra—within the molecules, and inter—between the molecules. The former is usually covalent or ionic, while the latter results from photons being exchanged between molecules (or atoms) rather than electrons, as in the case of covalent bonds. The hardnesses of these crystals is determined by the latter. The first quantum mechanical theory of these forces was developed by London so they are known as London forces (they are also called Van der Waals, dispersion, or dipole-dipole forces). 

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