Page 34 - Materials Chemistry, Second Edition

21
2.2. Types of Bonding in Solids

the polarizability of the nonpolar component. Once again, this relation does not
include the interactions between the polar molecule and solvent molecules.
2
m a 2
ð4Þ 2 1 6
r
4pe o
Hydrogen bonding may be considered a special case of dipole–dipole forces, where
there exist relatively strong interactions between extremely polar molecules. This
interaction is often designated by A – H ... B, where the hydrogen bond is formed
between a Lewis basic group (B) and the hydrogen covalently bonded to an
electronegative group (A). In general, the magnitudes of these interactions (ca.
1
12–30 kJ mol ) are much less than a covalent bond. However, the linear

[F-H—F] anion present in concentrated hydrofluoric acid has a bond energy of
1
ca. 50 kJ mol , representing the strongest hydrogen bond ever discovered. The
degree of hydrogen bonding has an influence on many physical properties of a
compound such as melting and boiling points, dielectric constants, vapor pressure,
thermal conductivity, index of refraction, viscosity, and solubility behavior.
The potential energy between pairs of non-bonded neutral atoms or molecules as a
function of internuclear/intermolecular separation may be described as a combination
of attraction and repulsion terms – referred to as the Lennard-Jones potential (Eq. 5).

s 12 s 6

ð5Þ VðrÞ¼ 4e
r r
where V(r) is the potential energy as a function of atomic separation, r; s is the Lennard-
Jones size parameter, the intermolecular separation for which the energy is zero
(s ¼ 2 1=6 r o , where r o is the intermolecular separation at minimum energy); and e is
the Lennard-Jones energy constant, the minimum energy of the potential energy well.
At farther atomic separations, electron-nuclei attractive forces will dominate;
however, as the atoms closely approach one another, there will be increasing mutual
repulsion among negatively-charged electrons and positively-charged nuclei, result-
ing in an exponential increase in the total potential energy (Figure 2.3). However, at
an intermediate atomic separation distance, a potential energy well will be gener-
ated, corresponding to bond formation between the two atoms. The atomic separa-
tion, r o , at which the force is zero, is referred to as the equilibrium bond length.
As one would expect, the value of r o will increase concomitantly with temperature,
as atomic motions become greater with increasing thermal energy. The value of the
potential energy, V(r o ), at the equilibrium bond length is termed the binding energy.
For two polar molecules, the long-range electrostatic interactions between molecu-
lar dipoles must be accounted for. Hence, another term referred to as the Stockmayer
potential must be added to Eq. 5. The d term in Eq. 6 is the polarity correction term,
based on the magnitude and directions of the polar dipoles.
s 12 s 6 s 3

ð6Þ VðrÞ¼ 4e þ d
r r r