London energy forces

Among all the low energy interactions, London dispersion forces are considered as the main contributors to the physical adsorption mechanism. They are ubiquitous and their range of interaction is in the order 2 molecular diameters. For this reason, this mechanism is always operative and effective only in the topmost surface layers of a material. It is this low level of adhesion energy combined with the viscoelastic properties of the silicone matrix that has been exploited in silicone release coatings and in silicone molds used to release 3-dimensional objects. However, most adhesive applications require much higher energies of adhesion and other mechanisms need to be involved. 

Matsui75) has computed energies (Emin) which correspond to the minimal values of Evdw in Eq. 1 for cyclodextrin-alcohol systems (Table 2). Besides normal and branched alkanols, some diols, cellosolves, and haloalkanols were involved in the calculations. The Emi values obtained were adopted as a parameter representing the London dispersion force in place of Es. Regression analysis gave Eqs. 9 and 10 for a- and P-cyclodextrin systems respectively. 

As shown by Fowkes (1968) the interfacial energy between two phases (whose surface tensions - with respect to vacuum - are y1 and y2) is subject to the resultant force field made up of components arising from attractive forces in the bulk of each phase and the forces, usually the London dispersion forces (cf. Eq. 4.2) operating accross the interface itself. Then the interfacial tension (energy) between two phases y12 s given by... 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

The size of macromolecules gives them their unique and useful properties. Size allows polymers to act more as a group so that when one polymer chain moves, surrounding chains are affected by that movement. Size also allows polymers to be nonvolatile since the secondary attractive forces are cumulative (e.g., the London dispersion forces are about 8 kJ/mol of repeat units), and, because of the shear size, the energy necessary to volatilize them is greater than the energy to degrade the polymer. 

The over-riding significance of gas-phase measurements is that in the gaseous state the contributions of electrostatic and even of London dispersion forces can be reasonably estimated this allows of more significant comparison with the observed AH values. At this point it may be appropriate to emphasize the variation in AH with the medium in which it is observed. If the free energy increase (AG) attending the dissociation of the dimer were to vary with the dielectric constant (D) according to... 

Solutions of nonpolar solutes in nonpolar solvents represent the simplest type. The forces involved in solute-solvent and solvent-solvent interactions are all London dispersion forces and relatively weak. The presence of these forces resulting in a condensed phase is the only difference from the mixing of ideal gases. As in the latter case, the only driving force is the entropy (randomness) of mixing. In an ideal solution (AW, = 0) at constant temperature the free energy change will be composed solely of the entropy term ... 

Ionic radii are discussed thoroughly in Chapters 4 and 7. For the present discussion it is only necessary to point out that the principal difference between ionic and van der Waals radii lies in the difference in the attractive force, not the difference in repulsion. The interionic distance in UF, for example, represents the distance at which the repulsion of a He core (Li+) and a Ne core (F ) counterbalances the strong electrostatic or Madelung force. The attractive energy for Lt F"is considerably over 500 kJ mol"1 anti the London energy of He-Ne is of the order of 4 kJ mol-1. The forces in the LiF crystal are therefore considerably greater and the interioric distance (201 pm) is less than expected for the addition of He and Ne van der Waals radii (340 pm). 

Typical potential energy curves for the interaction of two atoms are illustrated in Figure 11.3. There is characteristically a very steeply rising repulsive potential at short interatomic distances as the two atoms approach so closely that there is interpenetration of their electron clouds. This potential approximates to an inverse twelfth-power law. Superimposed upon this is an attractive potential due mainly to the London dispersion forces. This follows an inverse sixth-power law. The total potential energy is given by... 

There are two types of solute-solvent interactions which affect absorption and emission spectra. These are universal interaction and specific interaction. The universal interaction is due to the collective influence of the solvent as a dielectric medium and depends on the dielectric constant D and the refractive index n of the solvent. Thus large environmental perturbations may be caused by van der Waals dipolar or ionic fields in solution, liquids and in solids. The van der Waals interactions include (i) London dispersion force, (ii) induced dipole interactions, and (iii) dipole-dipole interactions. These are attractive interactions. The repulsive interactions are primarily derived from exchange forces (non bonded repulsion) as the elctrons of one molecule approach the filled orbitals of the neighbour. If the solute molecule has a dipole moment, it is expected to differ in various electronic energy states because of the differences in charge distribution. In polar solvents dipole-dipole inrteractions are important. 

The London dispersion forces are present and important in most adsorption processes and in adhesive interactions between dissimilar materials. The free energy of interaction per unit area between materials 1 and 2 in contact is where W 2 -s... 

With the exception of highly polar materials, London dispersion forces account for nearly all of the van der Waals attraction which is operative. The London attractive energy between two molecules is very short-range, varying inversely with the sixth power of the intermolecular distance. For an assembly of molecules, dispersion forces are, to a first approximation, additive and the van der Waals interaction energy between two particles can be computed by summing the attractions between all interparticle molecule pairs. 

Experimentally, one of the main methods of distinction between the Forster and Dexter mechanisms in an energy transfer is a study of the distance dependence of the observed process. From Equation (2.32) it is evident that the rate of dipole-induced energy transfer, kfen/ decreases as d 6. This is typical of dipolar interactions and is reminiscent of the distance dependence of other such mechanisms, e.g. London dispersion forces. Therefore, the Forster mechanism can operate over large distances, whereas, in contrast, the rate of Dexter energy transfer, kden, falls off exponentially with distance. 

Release of high-energy water Release of conformational strain Van der Waals forces Hydrogen bonding London dispersion forces Dipole-dipole interaction... 

See R. H. French, "Origins and applications of London dispersion forces and Hamaker constants in ceramics," J. Am. Ceram. Soc., 83, 2117-46 (2000) K. van Benthem, R. H. French, W. Sigle, C. Elsasser, and M. Rtihle, "Valence electron energy loss study of Fe-doped SrTiOs and a E13 boundary Electronic structure and dispersion forces," Ultramicroscopy, 86, 303-18 (2001), and the extensive literature cited therein. Energy E" in those papers is written as hco" here. 

In a thick film, the molecules located at its free surface do not sense the presence of the substrate. In contrast, in a thin film they do interact with the substrate. For the majority of the molecules of a thick film, the range of the interaction forces is smaller than the thickness of the film. In contrast, it is larger for the molecules of a thin film. As a result, the free energy of a thin film depends on its thickness. Considering, for illustrative purposes, London dispersion forces between molecules, the following expression is obtained for the interaction... 

For the calculation of the magnitude of the London dispersive force in one mole, the quantity hv in Eq. (9) may be regarded as being energy-equivalent and is sometimes approximated by the first ionization potential, /... 

In the case where Li is formamide (subscript F) and liquid L2 is n-alkanes (H), the term yFp may be neglected since the surface free energy of n-alkanes consists of only the London dispersive force, as seen in Table 3. Therefore, we may rewrite Eq. (38) as... 

Computations were carried through for values of 0.05 < 0 < 0.95 in increments of 0.05 unit, with C — 2, 3, 4, and 5. It was assumed that lateral interactions were due to attractive van der Waals-London dispersion forces, where the leading term in the energy expansion varies with distance as r-1/6 with R = V2 one finds C = C1/8. Calculations were also carried out in the Fowler-Guggenheim approximation this simply requires the determination of the zero-order inputs Po(a 0), Pj(b °K and P/P°. The results are exhibited in Figures 2 and 3 the broken curves refer to isotherms calculated according to Equations 22 and 23. 

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