Materials for Biomedical Engineering. Mohamed N. Rahaman

      Relationship of Interatomic Force and Bonding Energy to Properties of Materials

      As we go from two atoms to solid materials composed of a large number of atoms, the bond length, interatomic force, and bonding energy will be modified by the way the atoms arrange themselves and by their nearest atomic neighbors. Nevertheless, the representations of the interaction between two atoms in Figure 2.3 in terms of interatomic force and bonding energy provide a useful way to understand how many of the intrinsic properties of a material arise. The shape and depth of the potential energy curve, in particular, define various properties.

Molecules with large bonding energy typically exist as solids. Furthermore, the melting point of these solids typically increase as the depth of the potential well increases. This is because a larger amount of energy, in the form of heat, is required to break the interatomic bonds and convert the material from a solid to a liquid (Table 2.2). The elastic modulus is a measure of a material’s stiffness, that is, its ability to initially deform when subjected to a mechanical load. It is proportional to the slope of the F versus x curve at x = x_o (Figure 2.4). A steep slope represents a strongly bonded material with high elastic modulus whereas a gradual slope represents a weakly bonded material with low elastic modulus (Table 2.3).

Table 2.2 Bonding energy and melting temperature of various substances.

Type of bond	Substance	Bonding energy	Melting temperature (°C)
kJ/mol	eV per atom, ion or molecule
Ionic	NaCl	640	3.3	801
	MgO	1000	5.2	2800
Covalent	Si	450	4.7	1410
	C (diamond)	713	7.4	>3550
Metallic	Hg	68	0.7	−39
	Al	324	3.4	660
	Fe	406	4.2	1538
	W	849	8.8	3410
Van der Waals	Ar	7.7	0.08	−189
	Cl2	31	0.32	−101
Hydrogen	NH3	35	0.36	−78
	H2O	51	0.52	0

Figure 2.4 Relationship between interatomic force versus displacement curve and the Young’s modulus of a solid.

Table 2.3 Calculated stiffness and Young’s modulus (the elastic modulus in tension or compression) for various types of bonds.

Type of bond	Stiffness (N/m)	Young’s modulus (GPa)
Covalent	50−180	200−1000
Ionic	8−24	30−90
Metallic	15−75	60−300
Hydrogen	2−3	8−12
Van der Waals	0.5−1	2−4

As F and U are related through Eq. (2.2), an alternative view is that a deeper potential energy well (that is, a larger bonding energy), represents a higher elastic modulus. Another property that can be understood from the potential energy curve is the coefficient of thermal expansion. The shape of the potential energy well provides a measure of the relative expansion coefficient of materials. A symmetrical potential energy well, for example, means that there is no change in the average interatomic separation and, thus, no expansion of the material when it is heated. On the other hand, the more asymmetric potential energy well, the larger the thermal expansion coefficient.

2.3 Types of Bonds between Atoms and Molecules

The types of bonds in materials can be classified broadly into two main types: primary bonds and secondary bonds. Primary bonds are interatomic bonds, that is, chemical bonds between atoms. They are strong bonds characterized by a high bond strength and a high bonding energy in the range of ~20–250 kJ/mol (Table 2.2). Primary bonds are formed by transfer of one electron or more from one atom to another which leads to the formation of ions with discrete charges, or by sharing of electrons between atoms. There are three types of primary bonds: ionic, covalent, and metallic bonds.

      Secondary bonds are intermolecular bonds. They are physical bonds formed by attraction of molecules that are nonpolar or that have a permanent dipole moment and, thus, they do not involve chemical transfer or sharing of electrons. Secondary bonds are weak, with a low bonding energy of ~2–12 kJ/mol (Table 2.2). Common types of secondary bonds are the van der Waals bond and the hydrogen bond.

2.4