Keesom potential

The van der Waals forces between atoms or molecules are the sum of three different forces, all proportional to 1/r , where r is the distance between the atoms or molecules. The corresponding potentials are the orientation or Keesom potential, the induction or Debye potential, and the dispersion or London potential, respectively. For two dissimilar polar molecules, the van der Waals potential is... 

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... 

Keesom relationship phys chem An equation for the potential energy associated with the interaction of the dipole moments of two polar molecules. ka-sam ri la-sh3n,ship ... 

Dividing Equation (34) through by gives the fractional contribution made to the total attraction by the Debye (D), Keesom (K), and London (L) components of potential energy ... 

Keesom, Debye, and London contributed much to our understanding of forces between molecules [111-113]. For this reason the three dipole interactions are named after them. The van der Waals4 force is the Keesom plus the Debye plus the London dispersion interaction, thus, all the terms which consider dipole-dipole interactions Ctotai = Corient+Cind- -Cdisp. All three terms contain the same distance dependency the potential energy decreases with l/D6. Usually the London dispersion term is dominating. Please note that polar molecules not only interact via the Debye and Keesom force, but dispersion forces are also present. In Table 6.1 the contributions of the individual terms for some gases are listed. 

Table 6.1 Contributions of the Keesom, Debye, and London potential energy to the total van der Waals interaction between similar molecules as calculated with Eqs. (6.6), (6.8), and (6.9) using Ctotal = Corient + Cind + Cdisp- They are given in units of 10-79 Jm6. For comparison, the van der Waals coefficient Cexp as derived from the van der Waals equation of state for a gas (P + a/V fj (Vm — b) = RT is tabulated. From the experimentally determined constants a and b the van der Waals coefficient can be calculated with Cexp = 9ab/ (47T21V ) [109] assuming that at very short range the molecules behave like hard core particles. Dipole moments /u, polarizabilities a, and the ionization energies ho of isolated molecules are also listed.

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. 

The effect of the polarisability. and of the ionization potential IP may be directly related to their impact on the energy of the dispersive forces (London, Debye and Keesom) which govern physical adsorption onto activated carbon [4]. The lower positive effect of the molar mass M may be related to the influence of the molecular overcrowding which increases the surface contact with the solid, leading to more intensive interactions. 

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 ... 

Magnasco etal. (2006) recently extended Keesom s calculations up to the R w term, showing that deviations of the Keesom approximation15 from the full series expansion are less important than consideration of the higher-order terms in the R 2n expansion of the intermolecular potential. The validity of the Keesom two-term approximation with respect to the complete series expansion is thus very good, and is best studied by comparing the respective logarithmic derivatives. 

Table 4.6 gives the dimensionless Keesom parameters <% and the T-dependent C2 (/, / ) Keesom coefficients for /, / = 1,2,3 calculated from the electrostatic potentials given in Equations (5.3-5.8) of the next chapter, using the same techniques as we did before for the dipole-dipole term. 

Permanent dipole moment Molecule (D) Polarizability (1 0 24cm3) Ionization potential (eV) London dispersion coefficient (1 0-79J m6) (Equation 80) Keesom polar orientation coefficient (1 0"79J m6) (Equation 86) Debye induced coefficient (1 0-79J m6) (Equation 88)... 

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... 

As we have already discussed in Section 2.5.3 for excess polarizabilities of molecules dissolved in a solvent, and in Section 2.6.4 for van der Waals interactions in a medium, when two molecules 1 and 2 are dissolved in a medium 3, the van der Waals forces between them are reduced because of the dielectric screening of the medium. This reduction is particularly important for liquids with high dielectric constants. The attraction force is decreased by a factor of the medium s er for Keesom and Debye interactions and by a factor of e] for London dispersion interactions. This strong reduction in the attractive pair potential means that the contributions of molecules further apart tend to be relatively minor, and each interaction is dominated only by contributions from its nearest neighbors. 

As we saw in Chapter 2, van der Waals forces consist only of long-range forces the interaction pair potential, V(r), decreases with the inverse sixth power of the distance between molecules, r-6 and the corresponding interaction force, F(r), decreases as r 7. When particle-particle or particle-surface attractions are considered, polar Keesom and Debye... 

D18.4 There are three van der Waals type interactions that depend upon distance as l/r6 they are the Keesom interaction between rotating permanent dipoles, the permanent-dipole-induced-dipole-interaction, and the induced-dipole-induced-dipole, or London dispersion, interaction. In each case, we can visualize the distance dependence of the potential energy as arising from the Mr dependence of the field (and hence the magnitude of the induced dipole) and the Mr3 dependence of the potential energy of interaction of the dipoles (either permanent or induced). 

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 Boltzmann angle-averaged interaction potential is generally referred to as the orientation or Keesom interaction and represents one of the three 6th power of distance relationships involved in the total van der Waals interaction. 

We have seen, now, that there are three types of interactions that can be involved in the total van der Waals interaction between atoms or molecules dipole-dipole (orientational or Keesome), dipole-induced dipole (induced or Debye), and dispersion (London) interactions. The theories for all three interactions are found (to a first approximation) to involve an inverse 6th power of the distance separating the two interacting centers. The total van der Waals interaction potential, Wvdw(r), can then be written as... 

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. 

The basic derivations of the van der Waals forces is based on isolated atoms and molecules. However, in many particle calculations or in the condensed state major difficulties arise in calculating the net potential over all possible interactions. The Debye interaction, for example is non additive so that a simple integration of Equation (4.27) over all units will not provide the total dipole-induced dipole interaction. A similar problem is encountered with the dipole-dipole interactions which depend not only on the simple electrostatic interaction analysis, but must include the relative spatial orientation of each interacting pair of dipoles. Additionally, in the condensed state, the calculation must include an average of all rotational motion. In simple electrolyte solutions, the (approximately) symmetric point charge ionic interactions can be handled in terms of a dielectric. The problem of van der Waals forces can, in principle, be approached similarly, however, the mathematical complexity of a complete analysis makes the Keesom force, like the Debye interaction, effectively nonadditive. 

Polar forces K W ALLEN Nature of Keesom and Debye forces, attraction constants Lennard-Jones potential... 

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