Total dispersion forces

Because alkanes are nearly nonpolar, their physical properties are determined by dispersion forces. The four-C alkanes boil lower than the five-C compounds (Table 15.3). Moreover, within each group of isomers, the more spherical member (isobutane or neopentane) boils lower than the more elongated one ( -butane or ii-pentane). As you saw in Chapter 12, this trend occurs because a spherical shape leads to less intermolecular contact, and thus lower total dispersion forces, than does an elongated shape. 

As already mentioned molecules cohere because of the presence of one or more of four types of forces, namely dispersion, dipole, induction and hydrogen bonding forces. In the case of aliphatic hydrocarbons the dispersion forces predominate. Many polymers and solvents, however, are said to be polar because they contain dipoles and these can enhance the total intermolecular attraction. It is generally considered that for solubility in such cases both the solubility parameter and the degree of polarity should match. This latter quality is usually expressed in terms of partial polarity which expresses the fraction of total forces due to the dipole bonds. Some figures for partial polarities of solvents are given in Table 5.5 but there is a serious lack of quantitative data on polymer partial polarities. At the present time a comparison of polarities has to be made on a commonsense rather than a quantitative approach. 

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. 

Solvatochromic shifts are rationalized with the aid of the Franck-Condon principle, which states that during the electronic transition the nuclei are essentially immobile because of their relatively great masses. The solvation shell about the solute molecule minimizes the total energy of the ground state by means of dipole-dipole, dipole-induced dipole, and dispersion forces. Upon transition to the excited state, the solute has a different electronic configuration, yet it is still surrounded by a solvation shell optimized for the ground state. There are two possibilities to consider ... 

We have now discussed three types of intermolecular forces dispersion forces, dipole forces, and hydrogen bonds. You should bear in mind that all these forces are relatively weak compared with ordinary covalent bonds. Consider, for example, the situation in HzO. The total intermolecular attractive energy in ice is about 50 kj/mol. In contrast, to dissociate one mole of water vapor into atoms requires the absorption of928 kj of energy, that is, 2(OH bond energy). This explains why it is a lot easier to boil water than to decompose it into the elements. Even at a temperature of 1000°C and 1 atm, only about one H20 molecule in a billion decomposes to hydrogen and oxygen atoms. 

The dispersion forces that act between atoms of the noble gases depend on the polarizabilities of their electron clouds. The total electron counts for these atoms are 10 for neon and 54 for xenon. When two atoms approach each other, the smaller electron cloud of neon distorts less than the larger electron cloud of xenon, as a molecular picture illustrates ... 

Dispersion forces increase in strength with the number of electrons, because larger electron clouds are more polarizable than smaller electron clouds. For molecules with comparable numbers of electrons, the shape of the molecule makes an important secondary contribution to the magnitude of dispersion forces. For example. Figure 11-11 shows the shapes of pentane and 2,2-dimethylpropane. Both of these molecules have the formula C5 H12, with 72 total electrons. Notice that 2,2-dimethylpropane has a more compact structure than pentane. This compactness results in a less polarizable electron cloud and smaller dispersion forces. Accordingly, pentane has a boiling point of 36 °C, while 2,2-dimethylpropane boils at 10 °C. 

The dispersion forces in acetone are nearly the same as those in 2-methylpropane, but the addition of dipolar forces makes the total amount of intermolecular attraction between acetone molecules substantially greater than the attraction between molecules of 2-methylpropane. Consequently, acetone boils at a considerably higher... 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

But the overall dispersion force strength also depends on the total number of electrons in the atom or molecule. It is a cumulative effect. Butane contains 14 atoms and 58 electrons, whereas octane has 26 atoms and 114 electrons. The greater number of electrons increases the total number of interactions possible and, since both melting... 

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... 

One conceptually simple remedy for the shortcomings of DFT regarding dispersion forces is to simply add a dispersion-like contribution to the total energy between each pair of atoms in a material. This idea has been developed within localized basis set methods as the so-called DFT-D method. In DFT-D calculations, the total energy of a collection of atoms as calculated with DFT, dft> is augmented as follows ... 

Because the dispersion force acts between neutral molecules it is ubiquitous (compare the gravitational force) however, between polar molecules there are also other forces. Thus, there may be permanent dipole-dipole and dipole-induced dipole interactions and, of course, between ionic species there is the Coulomb interaction. The total force between polar and non-polar (but not ionic) molecules is called the van der Waals force. Each component can be described by an equation of the form V = C/rf, where for the dipole-dipole case n = 6 and C is a function of the dipole moments. Clearly, it is easy to give a reasonable distance dependence to an interaction however, the real difficulty arises in determining the value of C. 

The principal difference in the physical properties of polyethylene and paraffin wax is based on both chain entanglement and total intermolecular dispersion forces per molecule (chain). 

Dispersion forces. These exist between all polar or nonpolar molecules. They result from the attraction between atoms, arising from interaction between small dipoles, induced in one atom by those formed by the nucleus and electrons of the other atom. Dispersion forces constitute a major component of the total intermolecular forces only with nonpolar systems-e.g., benzene and polyethylene or polystyrene. 

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... 

Figure S.3 Potential energies of interaction between two colloidal particles as a function of their distance of separation, for electrical double layers due to surface charge (VolK London-van der Waals dispersion forces (V ), and the total interaction (VT). From Schramm [426], Copyright 2003, Wiley.

The first EOF, which is responsible for 46.1% of the total dispersion, represents the most large-scale mode of the Black Sea main pycnocline response to external forcing (Fig. 9a). The intra-annual variability of the corresponding coefficient (curve 1 in Fig. 9d) shows that the maximal positive (negative) salinity anomalies in the central (near-shore) areas of the Black Sea described by this mode are observed in April, when the main pycnocline dome is especially high. An opposite situation is observed a half-year later, in October, when the dome is most low. The near-shore zones of maximal positive values... 

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 ... 

In the derivation of Eq. (7.3) by Hildebrand only dispersion forces between structural units have been taken into account. For many liquids and amorphous polymers, however, the cohesive energy is also dependent on the interaction between polar groups and on hydrogen bonding. In these cases the solubility parameter as defined corresponds with the total cohesive energy. 

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