Dispersion forces , 230

Much of chemistry is concerned with the short-range wave-mechanical force responsible for the chemical bond. Our emphasis here is on the less chemically specific attractions, often called van der Waals forces, that cause condensation of a vapor to a liquid. An important component of such forces is the dispersion force, another wave-mechanical force acting between both polar and nonpolar materials. Recent developments in this area include the ability to measure... 

To first order, the dispersion (a-a) interaction is independent of the structure in a condensed medium and should be approximately pairwise additive. Qualitatively, this is because the dispersion interaction results from a small perturbation of electronic motions so that many such perturbations can add without serious mutual interaction. Because of this simplification and its ubiquity in colloid and surface science, dispersion forces have received the most significant attention in the past half-century. The way dispersion forces lead to long-range interactions is discussed in Section VI-3 below. Before we present this discussion, it is useful to recast the key equations in cgs/esu units and SI units in Tables VI-2 and VI-3. 

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

The continuum treatment of dispersion forces due to Lifshitz [19,20] provides the appropriate analysis of retardation through quantum field theory. More recent analyses are more tractable and are described in some detail in several references [1,3,12,21,22],... 

A common approach to treating retardation in dispersion forces is to define an effective Hamaker constant that is not constant but depends on separation distance. Lxioking back at Eq. VI-22, this defines the effective Hamaker constant... 

Application of the exact continuum analysis of dispersion forces requires significant calculations and the knowledge of the frequency spectmm of the material dielectric response over wavelengths X = 2irc/j/ around 10-10 nm. Because of these complications, it is common to assume that a primary absorption peak at one frequency in the ultraviolet, j/uv. dominates the dielectric spectrum of most materials. This leads to an expression for the dielectric response... 

A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. 

A thin film of hydrocarbon spread on a horizontal surface of quartz will experience a negative dispersion interaction. Treating these as 1 = quartz, 2 = n-decane, 3 = vacuum, determine the Hamaker constant A123 for the interaction. Balance the negative dispersion force (nonretarded) against the gravitational force to find the equilibrium film thickness. 

Determine the net DLVO interaction (electrostatic plus dispersion forces) for two large colloidal spheres having a surface potential 0 = 51.4 mV and a Hamaker constant of 3 x 10 erg in a 0.002Af solution of 1 1 electrolyte at 25°C. Plot U(x) as a function of x for the individual electrostatic and dispersion interactions as well as the net interaction. 

J, Mahanty and B. W. Ninham, Dispersion Forces, Academic, New York, 1976. 

In order to include other interactions such as dipolar or hydrogen bonding, many semiempirical approaches have been tried [196, 197, 200], including adding terms to Eq. X-45 [198, 201] or modifying the definition of [202, 199]. Perhaps the most well-known of these approaches comes from Fowkes [203, 204] suggestion that the interactions across a water-hydrocarbon interface are dominated by dispersion forces such that Eq. X-45 could be modified as... 

Calculate y for naphthalene assume that it interacts with water only with dispersion forces. 

The most important second-order forces are dispersion forces. London [3, 31, 32] showed that they are caused by a correlation of tlie electron distribution in one molecule with tliat in the other, and pointed out that the... 

Dispersion forces caimot be explained classically but a semiclassical description is possible. Consider the electronic charge cloud of an atom to be the time average of the motion of its electrons around the nucleus. 

McLachlan A D 1963 Retarded dispersion forces between molecules Proc. R. Soc. A 271 387... 

McLachlan A D 1963 Three-body dispersion forces Moi. Phys. 6 423... 

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

We consider first the Maier-Saupe tlieory and its variants. In its original foniiulation, tills tlieory assumed tliat orientational order in nematic liquid crystals arises from long-range dispersion forces which are weakly anisotropic [60, 61 and 62]. However, it has been pointed out [63] tliat tlie fonii of tlie Maier-Saupe potential is equivalent to one in... 

Between any two atoms or molecules, van der Waals (or dispersion) forces act because of interactions between the fluctuating electromagnetic fields resulting from their polarizabilities (see section Al. 5, and, for instance. 

A long range attraction arising from dispersion forces... 

Van der Waals forces involv ing induced dipoles are of ten called London forces or dispersion forces... 

Carbon-fluorine bonds are quite strong (slightly stronger than C—H bonds) and like polyethylene Teflon is a very stable inert material We are all familiar with the most characteristic property of Teflon its nonstick surface This can be understood by com paring Teflon and polyethylene The high electronegativity of fluorine makes C—P bonds less polarizable than C—H bonds causing the dispersion forces m Teflon to be less than those m polyethylene Thus the surface of Teflon is even less sticky than the already slick surface of polyethylene... 

Compared with the alkyl groups of the four just mentioned the presence of sulfur makes the side chain of methionine (R = —CH2CH2SCH3) somewhat more polarizable Greater polarizability leads to stronger dispersion forces... 

Dispersion force (Section 2 17) Attractive force that involves induced dipoles... 

Induced dipole/mduced dipole attraction (Section 2 17) Force of attraction resulting from a mutual and complemen tary polanzation of one molecule by another Also referred to as London forces or dispersion forces Inductive effect (Section 1 15) An electronic effect transmit ted by successive polanzation of the cr bonds within a mol ecule or an ion... 

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