Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 65

Van der Waals bonding is the weakest type of intermolecular bonding. It exists between all atoms and molecules regardless of what other interactions might be present. There are three types of van der Waals bonds, classified in terms of the type of attractive force between the molecules.

 Dispersion forces, sometimes referred to as London forces, are the type of force that exists between nonpolar atoms such as argon, or between nonpolar molecules such as nitrogen. To see how this type of attractive force arises, we will consider the argon atom (Figure 2.12a). Although the argon atom (Atom 1) has a symmetrical distribution of electrons surrounding its nucleus so that is has no dipole, this situation is only true as an average over time. At any instant, the electron cloud undergoes local fluctuations in charge density, making the argon atom an instantaneous dipole. This instantaneous dipole produces an electric field that polarizes the electron distribution in a neighboring argon atom (Atom 2), so that the neighboring atom itself acquires a dipole. The electrostatic interaction between these two dipoles leads to an attractive force.

 Debye forces, sometimes described as dipole‐induced dipole forces: In this type of force, a polar molecule such as hydrogen chloride (HCl), for example, can induce a dipole in a neighboring nonpolar atom or molecule, such as an argon atom, for example, which results in an attractive electrostatic force between them (Figure 2.12b).

 Keesom forces, sometimes described as dipole–dipole forces: A polar molecule such as HCl, for example, can interact electrostatically with another polar molecule, such as HCl, to produce an attractive force (Figure 2.12c).

Figure 2.12 Illustration of the interactions in van der Waals bonding: (a) dispersion force between nonpolar atoms or molecules; (b) Debye force between a polar molecule with a permanent dipole moment and a nonpolar atom or molecule; (c) Keesom force between two polar molecules, each having a permanent dipole moment.

The attractive force between two dipoles can be calculated from Coulomb’s law of electrostatics. A simple case is the force between two parallel dipoles, that is, when their dipole moment is in the same direction, as illustrated in Figure 2.12. A dipole of charge magnitude δq and distance of separation r between its ends has a dipole moment given by

(2.6)

The attractive force between two parallel dipoles of moment p₁ and p₂, respectively, separated by a distance x that is much larger than r, is

(2.7)

where, ε_o is the permittivity of free space. According to Eq. (2.7), the attractive force is equal to the product of the two dipole moments and inversely proportional to the fourth power of their separation distance. The larger the dipole moments, the larger the attractive force.

Keesom forces between permanent dipoles typically provide the strongest van der Waals attraction whereas dispersion forces provide the weakest. Figure 2.13 shows an illustration of the structure of trichloromethane (CHCl₃), a molecule with a permanent dipole due to the difference in electronegativity of the atoms in the molecule. In comparison, the tetrachloromethane molecule (CCl₄), where the H in CHCl₃ is replaced with Cl, is nonpolar because there is no net dipole moment.

Figure 2.13 Illustration of (a) polarity of each covalent bond in the trichloromethane molecule (CHCl₃), and (b) overall net dipole of the molecule.