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by relatively strong dipole-dipole interactions which cause the water molecules to become highly organized (Chapter 4). The accumulation and organization of water molecules around solutes are determined by various types of dipole-dipole, dipole-ion, and ion-ion interactions (Chapter 4). The "screening" of electrostatic interactions between charged emulsion droplets is due to the attraction of counterions to the surface of the droplets (Chapters 3 and 7). The conformation and interactions of biopolymers in aqueous solution are governed by electrostatic interactions between the charged groups and the surrounding molecules (Chapter 4). These examples highlight the importance of understanding the origin and nature of electrostatic interactions in food emulsions.

2.3.3. van der Waals Interactions van der Waals forces act between all types of molecular species, whether they are ionic, polar, or nonpolar (Hiemenz 1986, Israelachvili 1992). They are conveniently divided into three separate contributions, which all rely on the polarization of molecules (Figure 2.4):

1. Dispersion forces. These forces arise from the interaction between an instantaneous dipole and a dipole induced in a neighboring molecule by the presence of the instantaneous dipole. The electrons in a molecule are continually moving around the nucleus. At any given instant in time, there is an uneven distribution of

FIGURE 2.4 Schematic representation of van der Waals intermolecular interactions which involve either the electronic or orientational polarization of molecules.

the negatively charged electrons around the positively charged nucleus, and so an instantaneous dipole is formed. This instantaneous dipole generates an electrical field which induces a dipole in a neighboring molecule. Consequently, there is an instantaneous attractive force between the two dipoles. On average, the attraction between the molecules is therefore finite, even though the average net charge on the molecules involved is zero.

2. Induction forces. These forces arise from the interaction between a permanent dipole and a dipole induced in a neighboring molecule by the presence of the permanent dipole. A permanent dipole causes an alteration in the distribution of electrons of a neighboring molecule, which leads to the formation of an induced dipole. The interaction between the permanent dipole and the induced dipole leads to an attractive force between the molecules.

3. Orientation forces. These forces arise from the interaction between two permanent dipoles that are continuously rotating. On average, these rotating dipoles have no net charge, but there is still a weak attractive force between them because the movement of one dipole induces some correlation in the movement of a neighboring dipole. When the interaction between the two dipoles is strong enough to cause them to be permanently aligned, this contribution is replaced by the electrostatic dipole-dipole interaction described in the previous section.

As will be seen in the next chapter, an understanding of the origin of these three contributions to the van der Waals interaction has important consequences for predicting the stability of emulsion droplets to aggregation.

The overall intermolecular pair potential due to van der Waals interactions is given by:

where Cdisp, Cind, and Corient are constants which depend on the dispersion, induction, and orientation contributions, respectively (Hiemenz 1986). Their magnitude depends on the dipole moment (for permanent dipoles) and the polarizability (for induced dipoles) of the molecules involved in the interaction (Table 2.2). The polarizability is a measure of the strength of the dipole induced in a molecule when it is in the presence of an electrical field: the larger the polarizability, the easier it is to induce a dipole in a molecule. For most biological molecules, the dominant contribution to the van der Waals interaction is the dispersion force, with the important exception of water, where the major contribution is from the orientation force (Israelachvili 1992). Examination of Equation 2.2 and Figure 2.3b provides some useful physical insights into the factors that influence the van der Waals interactions between molecules:

1. The value of Cdisp, Cind, and Corient is always positive, which means that the overall interaction potential between two molecules is always negative (attractive).

2. The interaction is relatively short range, decreasing rapidly with intermolecular separation (1/s6).

3. The attraction between molecules decreases as the dielectric constant of the intervening medium increases, which highlights the electromagnetic origin of van der Waals interactions.

4. The magnitude of the interaction increases as the polarizability and dipole moment of the molecules involved increase.

Although van der Waals interactions act between all types of molecular species, they are considerably weaker than electrostatic interactions (Figure 2.3 and Table 2.3). For this reason, they are most important in determining interactions between nonpolar molecules, where electrostatic interactions do not make a significant contribution. Indeed, the structure and physicochemical properties of organic liquids are largely governed by the van der Waals interactions between the molecules (Israelachvili 1992).

All types of van der Waals interaction involve either the electronic or orientational polarization of molecules and have a 1/s6 dependence on intermolecular separation (Hiemenz 1986). Another type of interaction that depends on molecular polarization but which does not have a 1/s6 dependence on intermolecular separation is ion polarization (Israelachvili 1992). Although this type of interaction is not strictly a van der Waals interaction, it is convenient to consider it in this section because it also involves polarization. A positively charged ion causes the electrons in a neighboring molecule to be pulled toward it, thus inducing a dipole whose 5- pole faces toward the ion. Similarly, a negatively charged ion causes the electrons in a neighboring molecule to be repelled away from it, thus inducing a dipole whose 5+ pole faces toward the ion. Thus there is an attractive force between the ion and the induced dipole because of electronic polarization. For polar molecules, there may be an additional contribution due to orientational polarization. When the interaction between an ion and a dipole is not strong enough to cause the dipole to become permanently aligned, the dipole continuously rotates because of its thermal energy (Section 2.5). On average, there is no net charge on a rotating dipole because of its continuous rotation, but in the presence of an ion there is a net attraction between the ion and the dipole because the low-energy orientations are preferred (Israelachvili 1992). When the interaction between the ion and the dipole is strong enough to cause the dipole to be permanently aligned, this contribution should be replaced by the electrostatic ion-dipole interaction described in the previous section.

The intermolecular pair potential for ion polarization is given by:

where the a0 term is the contribution from the electronic polarizability of the molecule and the |j,2/3kTterm is the contribution from the orientational polarizability. For nonpolar molecules, only the electronic polarization term contributes to this interaction, but for polar molecules, both electronic and orientational polarization contribute. This type of interaction is significantly stronger than the van der Waals interactions mentioned above and should therefore be included in any calculation of the interaction energy between molecules involving ions.

2.3.4. Steric Overlap Interactions

When two atoms or molecules come so close together that their electron clouds overlap, there is an extremely large repulsive force generated between them (Figure 2.3c). This steric overlap force is very short range and increases rapidly when the separation between the two molecules becomes less than the sum of their radii (o = rx + r2). A number of empirical equations have been derived to describe the dependence of the steric overlap intermolecular pair potential, wsteric(s), on molecular separation (Israelachvili 1992). The "hard-shell" model assumes that the repulsive interaction is zero when the separation is greater than o but infinitely large when it is less than o:

In reality, molecules are slightly compressible, and so the increase in the steric overlap repulsion is not as dramatic as indicated by Equation 2.4. The slight compressibility of molecules is accounted for by a "soft-shell" model, such as the power-law model:

At separations greater than o, the steric overlap repulsion is negligible, but at separations less than this value, there is a steep increase in the interaction pair potential, which means that the molecules strongly repel one another. The strong repulsion that arises from steric overlap determines the effective size of atoms and molecules and how closely they can come together. It therefore has a strong influence on the packing of molecules in liquids and solids.

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