Keesom equation

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 ... 

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. 

Permanent dipole/permanent dipole interaction (Keesom equation)... 

In this section we outline the molecular origins of the Debye, Keesom, and London forces and discuss the strengths of these forces relative to each other. In addition, we also outline how macroscopic properties and behavior (such as the heat of vaporization of materials, nonideality of equations of state, and condensation of gases) can be traced to the influence of the above van der Waals forces and illustrate these through specific examples. Another example of the van der Waals forces, namely, the relation between the surface tension (or surface energy) of materials and the London force, is discussed in Section 10.7. 

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

In examining the Debye, Keesom, and London equations we see that (a) they share as a common feature an inverse sixth-power dependence on the separation and (b) the molecular parameters that describe the polarization of a molecule, polarizability and dipole moment, serve as proportionality factors in these expressions. For a full discussion of the experimental determination of a0 and p, a textbook of physical chemistry should be consulted (Atkins 1994). For our purposes, it is sufficient to note that the molar polarization of a substance can be related to its relative dielectric constant e, by... 

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 ... 

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.

Keesom forces, 242 Kelley-Bueche equation, 611 Kerr effect, 299, 349 Kinetic(s)... 

Keesom s formula is also not satisfactory since the term a from Van der Waals equation, which is proportional to e, would then be strongly dependent on temperature, which is not the case. The Debye energy is indeed independent of temperature but is always very small (Table 29). 

Induced Interaction between Two Multipole Systems. Equation (58) defines in general form the classical electrostatic interaction of two electric systems having permanent multipoles and pj" , in conformity with the classical theory of Keesom. In the classical approach also, as shown by Debye and Falkenhagen, one has to take into consideration energies due to interactions between the permanent multipoles of the one system and electric multipoles induced in the other, and vice versa. Restricting the problem in a first approximation to the energy arising from the mutual interaction of dipoles, we can write ... 

In this still relatively simple molecule all pair interactions between the nine H-atoms at the carbons, the H at the hydroxyl, the four carbons and the oxygen, have to be accounted for. Treating the OH-group interaction also via a Lennard-Jones interaction plus an added (ideal) dipole contribution is already an approximation because intermolecular distances are too short to treat dipoles as ideal. In mathematical terms, the expressions derived for Debye- and Keesom-type interactions (1,4,4c) are only first approximations, the more so because the rotation of the dipole is restricted. In practice there is often no alternative than to make clever guesses about the various Uy r) functions. It is always possible to group some types of interaction together, to obtain more detailed expressions for yA. Such an equation for dumb-bell types of molecules have been given by Alejandre et al. ) and by Harris 2). 

Low temperature heat capacity measurements by Anderson 10) y Bronson and MacHattie 42) y Keesom and van den Ende 176) y and Armstrong and Grayson-Smith 16) were used to calculate an entropy and enthalpy at 298 K. of 13.58 e. u. and 1536 cal./gram atom, respectively. From many sources, Kelley 186) derives an equation for the solid heat capacity above 298 K. Kubaschewski and coworkers 206) select 544.5 K. as the melting point and 2600 50 cal./gram atom for the heat of melting. Data on... 

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. 

Waals to include a term a/K in his equation of state. For molecules with a permanent dipole moment (ju) Keesom calculated the mean interaction energy... 

Note that temperature is a parameter of the equation. As the material temperature rises during processing, the value of orientation energy becomes negligible. In a typical system conflicting dipole fields are created which significantly reduce dipole-dipole net interaction. Keesom forces, unlike London forces, do not apply to nonpolar substances because both dipoles, which participate in the interaction, must be permanent dipoles (London forces do not require the presence of permanent dipoles). 

Debye modified the Keesom equation to account for experimental observations. He showed that the energy of interaction was not as greatly reduced by temperature as was predicted by the Keesom equation ... 

These are often called Debye induced dipole interactions. It is interesting to note that the Keesom orientation interaction expression (Equation (37) in Section 2.4.3) may also be obtained from Equation (59) by replacing a with aorien = p2/3kT. This fact also indicates the presence of induction in orientation interactions. Thus, both Keesom and Debye interactions vary with the inverse sixth power of the separation distance and they both contribute to the van der Waals interactions, which we will see in Section 2.6. 

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... 

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