The Keesom Interaction

The structures of VdW dimers, considered as weakly bounded complexes in which each monomer maintains its original structure (Buckingham, 1982), are studied at low temperatures by sophisticated experimental techniques, such as far infrared spectra, high-resolution rotational spectroscopy in the microwave region, and molecular beams. Distances Re between the centres of mass and bond strengths De at the VdW minimum for some homodimers of atoms and molecules taken from Literature are collected in Table 4.4. 

We notice from the table how large Re and how small De values characterize our VdW dimers with respect to the corresponding values of the chemical bonds reported in Table 2.1 of Chapter 2. The sensibly larger De values observed for the dimers of first-row hydrides (NH3)2, (H20)2, (HF)2, (BeH2)2, (LiH)2 denote formation of a XH—X hydrogen bond, particularly strong in (LiH)2, where it is of the order of a chemical bond. 

The electrostatic energy Ei(es) is zero when averaged over the angles describing the relative orientation of the two interacting molecules. However, Keesom (1921) showed that if two dipolar molecules undergo thermal motions, they attract each other according to  

The Keesom formula (4.70) is easily derived (Magnasco, 2009a) by taking the Boltzmann average of the dipolar interaction over the angles of relative orientation of the two molecules for small values of the dimensionless parameter  

It may be helpful for the reader to recall briefly the derivation of the Keesom formula. 

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The van der Waals force between atoms consists of three different dipole induced forces, the Keesom interaction, the Debye interaction and the London interaction. 

Molecules bearing a permanent-dipole moment Think of the interaction between two fairly strong dipoles, /xc ipoie = 2 D = 2 x 10 18 esu cm, slightly larger than the 1.87-D moment of a water molecule.11 Let this molecule be approximately the size of a water molecule, i.e., 3 A across so that the point-molecule approximation would apply at separations much greater than 3 A. In emits of kT the Keesom interaction is... 

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). 

The Keesom interaction energy for freely rotating dipoles is obtained from an expansion series. That series becomes inaccurate as the interaction energy approaches a value of kT. Calculate the dipole moment at which this occurs at room temperature and a separation distance of 0.28 nm ... 

Orientation Forces. Besides the most basic non-polar interaction, dispersion forces, there are polar interactions between molecules of counterbodies, e.g. the dipole-dipole interaction (Keesom), the dipole-induced dipole interaction (Debye) and hydrogen bonding. The Keesom interaction (orientation) is temperature dependent and the energy is expressed as... 

The van der Waals interaction between molecules is the sum of the Keesom, Debye, and London dispersion interactions. The Keesom interaction describes the average interaction between freely rotating dipoles. The Debye interaction describes the interaction between a molecule with permanent dipole moment and the induced dipole moment of a polarizable molecule. The London dispersion interaction arises from quantum mechanical charge fluctuations. In most cases, the London dispersion interaction gives the largest contribution to the total van der Waals interaction. The van der Waals interaction energy between molecules is proportional to D. ... 

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... 

There are three types of interactions that contribute to van der Waals forces. These are interactions between freely rotating permanent dipoles (Keesom interactions), dipole-induced dipole interaction (Debye interactions), and instantaneous dip le-induced dipole (London dispersion interactions), with the total van der Waals force arising from the sum. The total van der Waals interaction between materials arise from the sum of all three of these contributions. 

It should be noted that, if the medium between the particle and substrate is something other than vacuum and possesses a dielectric constant e, the interaction energy in Eq. 68 is reduced by a factor of Eq. 68, which relates the interaction energy between permanent electric dipoles and their separation distances is known as the Keesom effect. 

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... 

It is clear from Table 1 that, for a few highly polar molecules such as water, the Keesom effect (i.e. freely rotating permanent dipoles) dominates over either the Debye or London effects. However, even for ammonia, dispersion forces account for almost 57% of the van der Waals interactions, compared to approximately 34% arising from dipole-dipole interactions. The contribution arising from dispersion forces increases to over 86% for hydrogen chloride and rapidly goes to over 90% as the polarity of the molecules decrease. Debye forces generally make up less than about 10% of the total van der Waals interaction. 

It should also be noted that contributions to van der Waals interactions from the Keesom effect are likely to be decreased in solids due to the locking in of the... 

Abbreviations are in parentheses. The dd interactions are also known as Keesom interactions di interactions are also known as Debye interactions ii interactions are also known as London or dispersion interactions. Collectively, dd, di and ii interactions are known as van der Waals interactions. Charge transfer interactions are also known as donor-acceptor interactions. 

The dipole-dipole interactions, frequently referred to as Keesom interactions, are historically included in the van der Waals interactions, even though they are purely electrostatic. For molecules that are free to orient themselves, the dipole-dipole interactions must be averaged over the molecular orientations, as the angular dependence of the interaction energy is comparable to the Boltzmann energy kBT (Israelachvili 1992, p. 62). With the averaging of the Keesom... 

This is the dipole-dipole interaction energy, often termed the orientation or Keesom interaction. Notice that it depends on the product of the squares of both dipole moments, but is inversely proportional to distance to the sixth power. This is a very short-range... 

Almost all interfacial phenomena are influenced to various extents by forces that have their origin in atomic- and molecular-level interactions due to the induced or permanent polarities created in molecules by the electric fields of neighboring molecules or due to the instantaneous dipoles caused by the positions of the electrons around the nuclei. These forces consist of three major categories known as Keesom interactions (permanent dipole/permanent dipole interactions), Debye interactions (permanent dipole/induced dipole interactions), and London interactions (induced dipole/induced dipole interactions). The three are known collectively as the van der Waals interactions and play a major role in determining material properties and behavior important in colloid and surface chemistry. The purpose of the present chapter is to outline the basic ideas and equations behind these forces and to illustrate how they affect some of the material properties of interest to us. 

This is the Keesom equation (subscript K) from Table 10.1 it applies to the interaction of two permanent dipoles. 

Note that AvapG encompasses dispersive (i.e., London), dipole-induced dipole (i.e., Debye), and dipole-dipole (i.e., Keesom) contributions (Section 3.2). However, in most organic liquids, dipole interactions are generally of secondary importance. Hence, as a first approximation, we consider only the dispersive interactions. Then we can use the approach described in Section 3.2 to quantify the vdW term (Eq. 3-10, Fig. 3.4). Since lnp, =-AvapG, / i r, we may express Eq. 4-23 as ... 

Two freely rotating dipoles attract each other because they preferentially orient with their opposite charges facing each other. This randomly oriented dipole-dipole interaction is often referred to as the Keesom energy2 ... 

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.

The van der Waals force includes three kinds of dipole-dipole interactions The Keesom, the London, and the London dispersion component. Usually the dispersion interaction dominates. 

Keesom forces are a function of the number and magnitude of a molecule s local dipole moments, but since they are dependent upon the positioning of a molecule with respect to its neighbors, they may not always be strictly additive. Flowever, since the molecules in most crystals are aligned for maximum dipolar interaction, the group interactions are often roughly additive. 

One limitation of the one-solubility parameter model is that it assumes that the solute can only interact with the organic matter through London forces. Although this assumption may be reasonable for SOM, DOM is typically more polar and can participate in other types of van der Waals interactions. These include permanent dipole-induced dipole (Debye) and permanent dipole-permanent dipole (Keesom) interactions in which the degree of binding that occurs depends on the polarizability of the DOM (Gauthier et al., 1987 Uhle et al., 1999). To account for these types of interactions Chin and Weber (1989) segregated the solubility parameter terms into three components to account for all these different types of molecular interactions to... 

This expression shows that the attractive electrostatic interaction, commonly known as the Keesom energy, is inversely proportional to the sixth power... 

This extraction precisely reproduces the same London, Debye, and Keesom interactions, including all relativistic retardation terms that had been effortfully derived in earlier formulations. These interactions are distinguished by whether they involve the interaction of two permanent dipoles of moment //.uipoie, or involve an inducible polarizability aind. A water molecule, for example, has both a permanent dipole moment and inducible polarizability. The contribution of each water molecule to the total dielectric response is a sum of the form of Eqs. (L2.163) and (L2.173) in mks units,... 

An attractive interaction arises due to the van der Waals forces between molecules of colloidal particles. Depending on the nature of dispersed particles, the Keesom forces (or the dipole-dipole interaction), the Debye forces (or dipole-induced dipole interaction), and the London forces (or induced dipole-induced dipole interaction) may contribute to the van der Waals interaction. First, the van der Waals interaction was theoretically computed using a method of the pairwise summation of interactions between different pairs of molecules of the two macroscopic particles. This method called the microscopic approximation neglects collective effects, and, as a consequence, misrepresents the Hamaker constant. For many problems of a practical use, however, specific features of the total interaction are determined by a repulsive part, and such an effective, gross description of the van der Waals interaction may often be accepted [3]. The collective effects in the van der Waals interaction have been taken into account in the calculations of Lifshitz et al. [4], and their method is known in the literature as the macroscopic approach. 

The expression van der Waals attraction is widely used and is here defined as the sum of dispersion forces [9], Debye forces [17] and the Keesom forces [18]. Debye forces are Boltzmann-averaged dipole-induced dipole forces, while Keesom forces are Boltzmann-averaged dipole-dipole forces. The interaction for all three terms decays as 1 /r6, where r is the separation between the interacting particles, and they are combined into one term with the proportionality constant denoted the Hamaker constant. In order to determine the van der Waals force there are at least two approaches, either to calculate the force between two particles assuming that the interaction is additive, (this is usually called the Hamaker approach) or to use a variant of Lifshitz theory. 

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