Mohamed N. Rahaman - Materials for Biomedical Engineering

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

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.

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.

The type of primary bond formed between two atoms depends on their position in the periodic table of elements. Ionic bonding involves transfer of electrons from one atom to the other, resulting in the formation of a positive ion (cation) and a negative ion (anion) as, for example, the creation of sodium (Na +) and chlorine (Cl −) ions to form a sodium chloride molecule (NaCl) ( Figure 2.1a). The transferred electrons reside in the outermost shell of the anion and, thus, are almost bound to that ion. Covalent bonding, on the other hand, involves sharing of electrons between two atoms but the shared electrons are bound between the atoms as, for example, in the chlorine molecule (Cl 2) ( Figure 2.1b). In the metallic bond, electrons tend to leave the parent atoms, making them cations, and combine to form a sea of highly mobile electrons, as illustrated in Figure 2.1c for sodium (Na). In contrast to the ionic bond, the electrons that leave the metal atoms are not transferred to any one ion. The electrons involved in the formation of primary bonds are typically those in the outermost orbital of the atoms, referred to as valence electrons.

Guidelines have been proposed to predict the type of primary bond that two atoms will form. We provide a description of a few of these guidelines.

A useful guideline is the octet rule. The basis of this rule is that the unreactive nature of the inert gases in Group VIII of the periodic table is related to their outermost electron shell composed of eight electrons, except for helium that has two electrons in its outer shell. The electron configuration of argon (Ar), for example, written as 1s 22s 22p 63s 23p 6, has two electrons in the 3s subshell and six in the 3p subshell, making eight electrons in the outermost shell. According to the octet rule, when two atoms combine to form a molecule, they do so in a manner to form a complete octet in their outermost shell as far as possible. Then the electron configuration of each atom will correspond to that of its closest inert gas in the periodic table. The octet rule is illustrated for the sodium chloride (NaCl) and methane (CH 4) molecules.

The sodium (Na) and chlorine (Cl) atoms have the following electronic configurations:

Na: 1s22s22p63s1 which can be written [Ne]3s1, where [Ne] represents the electronic configuration of the inert gas neon (Ne)

Cl: 1s22s22p63s23p5 which can be written [Ne]3s23p5

According to the octet rule, in combining to form an NaCl molecule, the sodium atom can lose an electron (the 3s 1electron) to from a stable octet in the outermost shell while the chlorine atom can gain an electron in its outermost shell ( Figure 2.1). This results in the formation of Na +and Cl −ions with an electronic configuration corresponding to Ne and Ar, respectively. Electrostatic attraction between the cations and anions leads to the formation of an ionic bond.

The carbon (C) and hydrogen (H) atoms have the following electronic configurations:

C: 1s22s22p2

H: 1s1

The formation of a CH 4molecule can be achieved by the carbon atom sharing each of its four electrons in the outermost shell with an H atom. As described later ( Section 2.7), the 2s orbital and three 2p orbitals in the carbon atom combine to form four hybrid orbitals (called sp 3orbitals), each occupied by one valence electron. By sharing one electron in each orbital with an electron from the hydrogen atom, the carbon atom achieves an outer shell of eight electrons, corresponding to the neon configuration, while the hydrogen atom has two electrons in its shell, corresponding to the helium configuration.

The octet rule is a useful guideline but there are exceptions to it. Furthermore, it does not consider electrons in the d and f shells of atoms. As only s and p electrons are considered, the octet rule is a useful rule for predicting the type bonding in the main group elements in the periodic table, that is, elements not in the transition metal blocks.

Another guiding principle in interatomic bonding is that when atoms lose, gain, or share electrons to form an octet in their outermost shell, they do so in a manner to minimize the number of charges that have to be transferred or shared. An alternative way to form an ionic bond between sodium and chlorine atoms, for example, is by the transfer of seven electrons from the outer shell of the chlorine atom to the sodium atom, forming Cl 7+and Na 7−ions, respectively. However, this does not occur because the energy required to create the Cl 7+and Na 7−ions with these many charges in the first place is exorbitant.

The ability of an atom to lose, gain, or share electrons is crucial to the type of bond that it forms with other atoms. This has been quantified in terms of a measureable property called the electronegativity, defined as the ability of an atom in a particular molecule to attract electrons to itself. Linus Pauling originally developed an electronegativity scale for atoms in the 1930s, referred to as the Pauling electronegativity scale, based on measurements of the strengths of covalent bonds between different elements. In this scale, atoms have an electronegativity value between 0 and 4, a range selected arbitrarily by Pauling. A limitation of Pauling’s method is that many elements do not form stable covalent compounds with other elements and, thus, their electronegativity cannot be measured. Other methods have since been developed which address this problem but the Pauling electronegativity scale is still widely used. For the main group elements, that is, elements not in the transition metal blocks, the electronegativity values increase as the atomic number decreases in a particular column of the periodic table and increase with atomic number along a particular row.