Carbon Nanostructures

5.1. INTRODUCTION

This chapter is concerned with various nanostructures of carbon. A separate chapter is devoted to carbon because of the important role of carbon bonding in the organic molecules of life (see Chapter 12), and the unique nature of the carbon bond itself. It is the diverse nature of this bond that allows carbon to form some of the more interesting nanostructures, particularly carbon nanotubes. Possibly more than any of die other nanostructares, these carbon nanotubes have enormous applications potential which we will discuss in this chapter,

5.2. CARBON MOLECULES 5.2.1. Nature of the Carbon Bond

In order to understand the nature of the carbon bond it is necessary to examine the electronic structure of the carbon atom. Carbon contains six electrons, which are distributed over the lowest energy levels of the carbon atom. The structure is designated as follows (Is)2, (2s), (2px), (2py), (2p2) when bonded to atoms in molecules. The lowest energy level Is with the quantum number N= 1 contains two

Introduction to Nartotechhology, by Charles P. Poole Jr. and Frank J. Owens. ISBN 0-471-07935-9. Copyright © 2003 John Wiley & Sons, Inc.

electrons with oppositely paired electron spins. The electron charge distribution in an s state is spherically symmetric about die nucleus. These li electrons do not participate in the chemical bonding. The next four electrons are in the N=2 energy state, one in a spherically symmetric s orbital, and three in px, py, and pz orbitals, which have the very directed charge distributions shown in Fig. 5.1a, oriented perpendicular to each other. This outer s orbital together with die three p orbitals form the chemical bonds of carbon with other atoms. The charge distribution associated with these orbitals mixes (or overlaps) with the charge distribution of each other atom being bonded to carbon. In effect, one can view the electron charge between the two atoms of a bond as the glue that holds the atoms together. On the basis of this simple picture the methane molecule, CH4, might have the structure shown in Fig. 5.1b, where the H—C bonds are at right angles to each other. However, z z z z z z

(a)
(c)

Figure 5.1. (a) Illustration of p„ Py, and pz orbitals of the carbon atom; (b) structure of methane CH« assuming that the valence orbitals of carbon are pure p„ Py, and p, orbitals; (c) actual structure of CH4, which is explained by sp3 hybridization.

methane does not have this configuration; rather, it has the tetrahedral structure shown in Fig. 5.1c, where the carbon bonds make angles of 109°28' with each other. The explanation lies in the concept of hybridization. In the carbon atom the energy separation between the 2s level and the 2p levels is very small, and this allows an admixture of the 2s wavefiinction with one or more of the 2p, wavefunctions. The un-normalized wavefunction *F in a valence state can be designated by the expression va = s+xP (5.i)

where p indicates an admixture of p\ orbitals. With this hybridization the directions of the p lobes and the angles between them changes. The angles will depend on the relative admixture X of the p states with the s state. Three kinds of hybridization are identified in Table 5.1, which shows the bond angles for the various possibilities, which are 180°, 120°, and 109°28' for the linear compound acetylene (H-C=C-H), the planar compound ethylene (H2C=CH2), and tetrahedral methane (CH4), respectively. In general, most of die bond angles for carbon in organic molecules have these values. For example, the carbon bond angle in diamond is 109°, and in graphite and benzene it is 120°.

Solid carbon has two main structures called allotropie forms that are stable at room temperature: diamond and graphite. Diamond consists of carbon atoms that are tetrahedrally bonded to each other through sp3 hybrid bonds that form a three-dimensional network. Each carbon atom has four nearest-neighbor carbons. Graphite has a layered structure with each layer, called a graphitic sheet, formed from hexagons of carbon atoms bound together by sp2 hybrid bonds that make 120° angles with each other. Each carbon atom has three nearest-neighbor carbons in the planar layer. The hexagonal sheets are held together by weaker van der Waals forces, discussed in the previous chapter.

5.2.2. New Carbon Structures

Until 1964 it was generally believed that no other carbon bond angles were possible in hydrocarbons, that is, compounds containing only carbon and hydrogen atoms. In that year Phil Eaton of the University of Chicago synthesized a square carbon molecule, CgHg, called cubane, shown in Fig. 5.2a. In 1983 L. Paquette of Ohio State University synthesized a C2oH20 molecule having a dodecahedron shape,

Table 5.1. Types ot sp" hybridization, the resulting bond angles, and examples of molecules

Type of Hybridization

Digonal sp

Trigonal sp2

Tetrahedral sp3

Orbitals used for bond

S,Px

S, Px, Py

s, Px, Py, Pz

Example

Acetylene C2H2

Ethylene C2H,

Methane CH4

Value of X

0 0

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