Force between two dipoles

Next consider an interactive force between two dipole particles separated by R. The dipole dipole interaction F is given by the following equation [52]. 

Permanent Dipole interactions these are the electrostatic attractive forces between two dipoles, these are responsible for fluromethane s (CH3F) high boiling point (about -15 deg C) compared to Nitrogen (about -180 deg C). 

If the surface dipole is strong and the distance between dipoles small, the repulsive force between two dipoles aligned parallel to each other may be dominant. This is, however, only likely to be the case for ionic adsorption, as in alkali metals adsorbed on transition metals. Despite the relatively weak nature of this interaction for most systems, the importance of dipole—dipole coupling in vibrational spectroscopy is now well established [57]. 

The displacement of charge toward one of the two bonded atoms gives to the pair of atoms a dipole moment, as Fig. 2.4 points out. Such dipole moments within molecules are important contributors to the bonds between the molecules in a liquid or solid. The force between two dipoles varies not only with their separation but also with their relative orientation, as Fig. 2.5 shows. Since favourable relative orientations will afford lower electrostatic energies than unfavourable orientations, the molecules will tend to... 

The strength of a dipole (Fig 1.7) within a bond depends on the relative electronegativities of the atoms composing the bond. Where a molecule contains a dipole, it can interact with other molecules containing a dipole. The force between two dipoles is give by equation 3. 

Dipole moment (Section 1 5) Product of the attractive force between two opposite charges and the distance between them Dipole moment has the symbol p- and is measured in Debye units (D)... 

The MM2 and MM3 force fields use a bond dipole description for E. Tire interaction between two dipoles is given by... 

The frustration effects are implicit in many physical systems, as different as spin glass magnets, adsorbed monomolecular films and liquid crystals [32, 54, 55], In the case of polar mesogens the dipolar frustrations may be modelled by a spin system on a triangular lattice (Fig, 5), The corresponding Hamiltonian consists of a two particle dipolar potential that has competing parallel dipole and antiparallel dipole interactions [321, The system is analyzed in terms of dimers and trimers of dipoles. When the dipolar forces between two of them cancel, the third dipole experiences no overall interaction. It is free to permeate out of the layer, thus frustrating smectic order. 

A dipole-dipole interaction, or Keesom force, is analogous to the interaction between two magnets. For non-hydrogen bonding molecules with fixed dipoles, these interactions are likely to influence the orientation of the molecules in the crystal. This is because, unlike the Debye force which is always attractive, the interaction between two dipoles is only attractive if the dipoles are properly oriented with respect to one another, as is the case with magnets. 

Fig. 6. The potential in the vicinity of a surface when ion-hydration interactions affect the anions (AWa) and the cations (AJTC) The other parameters are cE=0.1 M, iVA=lxi018 sites/m2, /VB=lxi018 sites/m2, H=iCr7 M, Oh=10"7 M, Kc=10 4 Ms ZA=10 4 M, e=80s Am=14.9 As m0=0, w=5 A, and (a) pH=4,pA/ v- =0 (b) pi 1=4, pAlv =—3 Debyes (c) pi 1=10,/ < / =0 (d) pH=10, pc v =3 Debyes. The values ofdo not affect the results plotted in (a) and (b), while the values ofptjz do not afFect the results plotted in (c) and (d). (e) The force between two identical surfaces for the same parameter values as in (a-d). Only the magnitude of the force is strongly dependent on the value of the surface dipoles and ion-hydration forces, but not its functional behaviour.

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. 

The Direct Lattice Sum. Dispersion forces between two atoms can be described by a potential function expressed in terms containing inverse powers of the internuclear separations, s. The simplest function of this sort includes a potential energy of attraction proportional to the inverse sixth power of the separation and a repulsion that is zero at distances of separation greater than a particular value se and infinite at separations less than sc. This is the so-called hard sphere or van der Waals model. Such an approximate potential function can be improved in two respects. Investigations of the second virial coefficient have revealed that the potential energy of repulsion is best described as proportional to the inverse twelfth power of the separation and the term in sr9, which accounts for the greater part of the total attraction potential, due to the attraction of mutually induced dipoles, should have added to it the dipole-quadrupole and quadrupole-quadru-pole attractions, expressed as terms in sr8 and s-10, respectively. The complete potential function for the forces between two atoms is, therefore ... 

As mentioned in the introduction to this chapter, the first theory for condensed phase vdW interactions was due to London [6], who summated dipole interactions to describe the force between two bodies (denoted by subscripts I and 2) interacting via a third medium (subscript 3). Equation (7) describes this relationship for a sphere interacting with a flat surface ... 

The earliest quantitative theory to describe van der Waals forces between two colloidal particles, each containing a statistically large number of atoms, was developed by Hamaker, who used pairwise summation of the atom-atom interactions. This approach neglects the multi-body interactions inherent in the interaction of condensed phases. The modem theory for predicting van der Waals forces for continua was developed by Lifshitz who used quantum electrodynamics [19,20] to account for the many-body molecular interactions and retardation within and between materials. Retardation is a reduction of the interaction because of a phase lag in the induced dipole response that increases with distance. 

Figure 5 Illustration of the forces F and F (Eq. [23]) arising from the interaction between two dipole moments situated at (atomic) site 1 at A + azj and site 2 at B + bz2, where molecules A and B have their centers of mass at A and B, respectively, and the dipoles are parallel to the local axes Zj and Zj, respectively. There is a torque at each center of mass arising from these forces and the dipole-dipole interaction torque (Eq. [24]), which is perpendicular to the plane of the page, if Zj, Z2, and R are all in the plane of the paper. 

Another interaction occurs between dipoles in molecules. Dipoles arise when the electrons of a chemical bond between atoms are not shared equally, thus creating positive and negative charge centers in the molecule. The interaction forces between permanent dipoles of polar molecules depend on the strength of the two dipoles, and decrease with the sixth power of the distance between their centers. Clearly, the dipolar interaction of polymeric adhesives will be strong when they carry polar chemical groups. 

Dipole-dipole forces act between neutral molecules that have permanent dipole moments. They are relatively weak and short ranged the potential energy between two dipoles falls off as... 

The van der Waals (VDW) attractive forces are the principal forces between dry, noncharged spherical aerosol particles [262] and may reduce stability and cause flocculation of suspended particles. The VDW forces arise from the attractive forces between permanent dipoles (Keesom forces), induced dipoles (London forces), and dipole-induced dipoles (Debye forces). For nonpolar or slightly polar compounds, the force of attraction between two particles with diameter d separated by a distance h (where h < d) is ... 

Electrostatic forces between two ions decrease by the factor 1/cP as their separation, d, increases. But dipole-dipole forces vary as l/r/. Because of the higher power of d in the denominator, l/r/ diminishes with increasing d much more rapidly than does l/d. As a result, dipole forces are effective only over very short distances. Furthermore, for dipole-dipole forces, q+ and q represent only partial charges, so these forces are weaker than ion-ion forces. Average dipole-dipole interaction energies are approximately 4 kj per mole of bonds. They are much weaker than ionic and covalent bonds, which have typical energies of about 400 kJ per mole of bonds. Substances in which permanent dipole-dipole interactions affect physical properties include bromine fluoride, BrF, and sulfur... 

A collision between atoms, molecules, or ions is not like one between two hard billiard balls. Whether or not chemical species collide depends on the distance at which they can interact with one another. For instance, the gas-phase ion-molecule reaction CH4+ + CH4 CH5+ + CH3 can occur with a fairly long-range contact. This is because the interactions between ions and induced dipoles are effective over a relatively long distance. By contrast, the reacting species in the gas reaction CH3 + CH3 C2H are both neutral. They interact appreciably only through very short-range forces between induced dipoles, so they must approach one another very closely before we could say that they collide. ... 

Attractive interactions between non-polar residues of the antibody and the antigen are due to dispersion forces (transient mutual perturbation in electron clouds between two residues results in oscillating dipoles). This interactive force decreases with the inverse 7th power of the intermolecular distance until a certain minimum distance (the so-called van der Waals contact distance of about 0.3 to 0.4 nm). Two important characteristics of these forces are that they act, for practical purposes, over small distances only, and their additivity, i.e., the force between two large sites equals the sum of all interactions. A single van der Waals bond accounts for a decrease of only about 4 kJ/mol, which is just slightly more than the average thermal energy of molecules at room temperature (2.5 kJ/mol). 

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