Forces between molecules induction

For a pair of identical molecules, it is noted in Eq. (13) that the first term determined with regard to the deformation polarizability is a so-called Debye inductive force , and the second term is generally called a Keesom orientational force between molecules when the dipole moment is considered in the intermolecular attractive system. 

Solvent selectivity is a measure of the relative capacity of a solvent to enter into specific solute-solvent interactions, characterized as dispersion, induction, orientation and coaplexation interactions, unfortunately, fundamental aiq>roaches have not advanced to the point where an exact model can be put forward to describe the principal intermolecular forces between complex molecules. Chromatograidters, therefore, have come to rely on empirical models to estimate the solvent selectivity of stationary phases. The Rohrschneider/McReynolds system of phase constants [6,15,318,327,328,380,397,401-403], solubility... 

Many different types of forces arise from molecule-molecule interaction. They may be electrostatic forces between permanent dipoles, induction forces between a permanent dipole and induced dipoles, or dispersion forces between non-polar molecules, etc. (Prausnitz, U2)). Forces involved in molecule-molecule interaction are known to be short-range in nature. 

The characterization of a solvent by means of its polarity is an unsolved problem since the polarity itself has, until now, not been precisely defined. Polarity can be understood to mean (a) the permanent dipole moment of a compound, (b) its dielectric constant, or (c) the sum of all those molecular properties responsible for all the interaction forces between solvent and solute molecules (e.g., Coulombic, directional, inductive, dispersion, hydrogen bonding, and EPD/EPA interaction forces) (Kovats, 1968). The important thing concerning the so-called polarity of a solvent is its overall solvation ability. This in turn depends on the sum of all-specific as well as nonspecific interactions between solvent and solute. 

Van der Waals postulated that neutral molecules exert forces of attraction on each other which are caused by electrical interactions between dipoles. The attraction results from the orientation of dipoles due to any of (1) Keesom forces between permanent dipoles, (2) Debye induction forces between dipoles and induced dipoles, or (3) London-van der Waals dispersion forces between fluctuating dipoles and induced dipoles. (The term dispersion forces arose because they are largely determined by outer electrons, which are also responsible for the dispersion of light [272].) Except for quite polar materials the London-van der Waals dispersion forces are the more significant of the three. For molecules the force varies inversely with the sixth power of the intermolecular distance. 

When one molecule is polar and the other nonpolar, the polar molecule induces a dipole in the nonpolar one. The two dipoles are again attracted by electrostatic forces, in this case designated as induction forces. These forces are considerably weaker than orientation forces but stronger than the attractive forces between nonpolar molecules. 

Dispersion forces cannot be explained by the magnetic analogy nor by conventional electrostatics. They are weak forces that exist even in mon-oatomic gases that are symmetrical and nonpolar. It is believed that at any particular instant this symmetry is somewhat distorted due to the motion (and position) of the electrons of a given atom, which produces a momentary polarity. This momentary polarity can attract and be attracted by a similar polarity in a neighboring atom or molecule in such a way as to produce a net attraction. As we have already seen, such inductions depend on the polarizability of the molecule or atom. Dispersion forces will always be possible between molecules, but they are the only forces between nonpolar hydrocarbons such as the alkanes. For this reason alkanes are often chosen as the ideal molecules for study or for use as standards. An example of a chromatographic separation in which the only forces are dispersion forces would be the GC separation of alkanes on squalane, a branched paraffin. 

Table 2 contains some typical values for these three van der Waals forces for a few atoms and simple molecules. Beginning with the noble gases that are nonpolar and have no induction or orientation forces, we can see that the polarizability increases as the size increases and that the dispersion forces also increase. The symmetrical molecule hydrogen has no permanent dipole and only a small dispersion force between its molecules. 

For tliis class of mixtures, interactions between molecules of like species are different in kind for the two species. In particular, two molecules of the polar species experience a direct-electrostatic interaction and a (usually weak) induction interaction, in addition to the usual dispersion interaction here, the attractive forces are stronger than would be observed for a nonpolar species of similar size and geometry. Interactionbetween uiihke species, on the other liand, involves only the dispersion and (weak) induction forces. One therefore expects to be positive, only more so than for otlierwise similar NPNP mixtures. Experiment bears tliis out, on average (Fig. 16.5). 

There are no electrostatic or induction forces between spherical molecules, such as argon, and yet there is clearly a long-range attractive force that causes the liquefaction of argon at low temperatures. This is the dispersion energy, the universal long-range force, which appears at second-order perturbation theory as ... 

The van der Waals forces are the interactive forces between dipoles of molecules. The dispersion force, a type of van der Waals force between dipoles that arises from thermal fluctuation or electric field induction, is always present between molecules. The van der Waals forces (FV(jw) between tip and sample can be estimated by the following equation, if we assume the tip is a sphere with radius, R. 

The above expressions were derived for the polarizabilities of molecules in free space or in a dilute gas (mostly air). However, we often encounter molecules interacting in a liquid solvent medium, which reduces the interaction pair potential by around e, or more the extent of this reduction depends on several factors. First of all, the intrinsic polarizability and dipole moment of an isolated gas molecule may be different when it is itself in the liquid state, or alternatively when dissolved in a solvent medium. This is because of the difference in interaction strength and also the separation distance between molecules. Thus, the polarizability values are best determined by experiment. Second, a dissolved molecule can only move by displacing an equal volume of solvent from its path. If the molecule has the same polarizability as the solvent molecules, that is if no electric held is reflected by the molecule, it is invisible in the solvent medium and does not experience any induction force. Thus, the polarizability of the molecule, a, must represent the excess or effective polarizability of a molecule over that of the solvent. Landau and Lifshitz applied a continuum approach and modeled a molecule, i, as a dielectric sphere of radius, ah having... 

If no ion is present in the system (q, = 0) then the above expression gives the sum of the Keesom-dipolar orientation and Debye-induction contributions to the total van der Waals forces between two molecules. A third contribution to van der Waals forces is also present,... 

Intermolecular forces, sometimes called non-covalent interactions, are caused by Coulomb interactions between the electrons and nuclei of the molecules. Several contributions may be distinguished electrostatic, induction, dispersion, exchange that originate from different mechanisms by which the Coulomb interactions can lead to either repulsive or attractive forces between the molecules. This review deals with the ab initio calculation of complete intermolecular potential surfaces, or force fields, but we focus on dispersion forces since it turned out that this (relatively weak, but important) contribution took longest to understand and still is the most problematic in computations. Dispersion forces are the only attractive forces that play a role in the interaction between closed-shell ( 5) atoms. We will see how the understanding of these forces developed, from complete puzzlement about their origin, to a situation in which accurate quantitative predictions are possible. 

Apropos of nomenclature the forces between closed-shell molecules (exchange repulsion, electrostatics, induction, and dispersion) are nowadays usually referred to as van der Waals forces. A stable cluster consisting of closed-shell molecules bound by these... 

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