Buckyballs, Diamond, and Graphite

1.0 Introduction

1.1 Why are old materials catching current attention?

The cutting edge of new materials technology is represented by surprisingly mundane and old forms of matter. Consider diamond (the gem) and graphite (the main component of pencil leads). Although both have been known for many years, recent newspaper and magazine headlines (see Figure 1.1) demonstrate tremendous current interest in these materials. For example, diamond was named "molecule of the year" by Science magazine in 1990. Also, a material closely related to graphite, carbon fiber, recently has entered our everyday lives in the form of reinforcing material in bicycle frames, tennis racquets, and even the B-2 Stealth bomber.

Figure 1.1 Headlines from magazines and newspapers

Since 1985, a new compound called buckyball has received much publicity in both the scientific and popular press. Buckyball, which has the full name buckminsterfullerene in honor of the architect of the geodesic dome, Buckminster Fuller, was added to the group of fascinating materials that included diamond and carbon fiber. Following the footsteps of diamond, buckminsterfullerene was named "molecule of the year" by Science magazine in 1991.

1.2 What's the connection?

The properties of these new materials are so different that it seems illogical to group them together. Diamond is the hardest known substance (however, this designation is under challenge by yet another new material, carbon nitride). In contrast, graphite is flaky and so slippery that it is often used as a lubricant. Pure diamonds are clear and colorless (some diamonds are colored, but this is due to impurities). Graphite, on the other hand, is a black, lustrous solid that is completely opaque. Buckyball, too, is deeply colored, so much so that the solid looks black. However, solid buckyball dissolves readily in organic solvents such as gasoline whereas diamond and graphite do not dissolve in common solvents. In solution buckyball's deep red color is revealed. Although practical uses for buckyball have not yet been discovered, researchers believe that it may find applications in medicine, new types of polymers, and other areas. Figure 1.2 shows real diamond, graphite, and buckyball samples.

Figure 1.2 Samples of Buckyball, diamond and graphite

Why do chemists group together materials with such different properties? What's the connection? Carbon! Despite their widely varying appearances, diamond, buckyball, and graphite are closely related because each is a form of carbon. In the language of chemistry, carbon is an element. Formally, this means it is a substance that cannot be decomposed into simpler substances by ordinary chemical or physical means. Another useful definition of an element is to say that all of the atoms of an element are the same (soon we will discover that atoms of the same element do have variants called isotopes). The chemistry viewpoint emphasizes the role of the atom as the building block of matter, even though it recognizes that atoms themselves are made of smaller particles.

Is this confusing? Consider an analogy with language. A word in a sentence is comparable to an atom. Each word contributes characterstic meaning, meter, and sound to the sentence. However, a word can be isolated from a sentence, yet retain its characteristics. Analogously, a carbon atom can be removed from a substance and isolated, but still retains recognizable characteristics. A word can be further broken down into letters, but this action causes the characteristic meaning, meter, and sound to be lost. Similarly, an atom can be broken into its component subatomic particles but its unique character is lost in the process. At the risk of over-extending our analogy, we can say that an element in language would be a sentence in which all of the words were the same. The atoms for diamond, buckyball, and graphite are all the same (they are all carbon), but the way these building blocks are assembled is not the same. Different forms of matter made of a single type of atom are called allotropes. Diamonds, buckyballs, and graphite are allotropes of carbon. It is the difference in the assembly of carbon atoms that gives the three different compounds such different properties.

1.3 Atoms--What are they?

If an element could be cut up into tiny pieces, then the atom is the smallest piece that would still have the essential properties of that element. Regardless of whether you started with a diamond, a buckyball, or graphite, when you finished cutting you would have carbon atoms only. Chemists organize all the different elements using the periodic table (Figure 1.3). The periodic table gives many different levels of information about the elements. The columns on the periodic table organize elements according to similar properties. Thus, because bromine (Br) and chlorine (Cl) are in the same column, it is easy to remember that they have many properties in common. Each box on the periodic table contains a wealth of information about the element it is describing. The symbol in the center of the box ("C" for carbon) is the accepted symbol for the element. The integer found above the symbol describes the number of a particular subatomic particle contained within each atom of that element.

Figure 1.3 A periodic table

An atom, even though it is the smallest piece that makes up every element, is made up of even smaller (i.e., subatomic) particles. Think of an atom as a large indoor football stadium. In the middle of the stadium, there is a small but very heavy marble. This marble is the nucleus of the atom and contains protons and neutrons. Protons have a positive charge while neutrons are electrically neutral, but protons and neutrons have almost exactly the same mass. In fact, protons and neutrons each weigh one atomic mass unit(amu). These particles are very light; an atomic mass unit equals just 1.66 x 10^-24 grams. This number is written in scientific notation and is equivalent to grams. The rest of the stadium is where an atom's electrons are found. Each electron has a mass equal to only about 1/2000th the mass of a proton or neutron, but the electron has a negative charge equal in magnitude to the positive charge of the proton (Table 1.1).

Table 1.1 Subatomic particles

1.4 What makes a carbon atom uniquely carbon?

But what makes the carbon atom different from all other atoms? The number of protons in the nucleus. In the box on the periodic table, the number above the element's symbol is the number of protons in an atom of that element. Each element has a unique number of protons, or atomic number. For carbon, this number is 6, so there are 6 protons in one atom of carbon. Most carbon atoms have 6 neutrons as well. In order to neutralize the charge of the 6 protons there must be 6 electrons. Therefore, the most common carbon atom has 6 protons, 6 neutrons, and 6 electrons. However, variants of carbon atoms exist. These are called isotopes. Different isotopes of the carbon atom have different numbers of neutrons. Three different isotopes of the carbon atom are found commonly (Table 2). Carbon-12 is the most abundant isotope and is represented as ¹²C (12 is the sum of the protons and neutrons); the mass of one atom of ¹²C is approximately 12 amu. Carbon-13 (or ¹³C) has 7 neutrons and 6 protons; approximately 1.1% of all carbon atoms are made of this isotope which has an approximate mass of 13 amu. Carbon-14 (¹⁴C) has 8 neutrons and 6 protons, hence, a mass of around 14 amu; less than 0.0000000001% of all carbon atoms found on earth are the radioactive ¹⁴C isotope.

Table2. Carbon Isotopes

The number below the element's symbol is the average mass of the atom; this number is called the atomic mass. Notice that this number is an average . Because there are three different isotopes of carbon, not all carbon atoms have the same mass. A similar situation exists for many coins. Dimes that were minted in 1940 do not have the same mass as today's dime. We cannot give a single, definitive mass for either atoms or for coins because each has a distribution of defined masses. However, we can talk about average masses. About 98.9% of all carbon atoms are ¹²C atoms with a mass of about 12 amu. The remaining 1.1% of carbon atoms are essentially all ¹³C isotopes. If you were to randomly pick out 1000 atoms from a pile of carbon, on average 989 of the atoms would be of the ¹²C isotope and 11 would be of the ¹²C isotope. You can guess that the mass of the average carbon atom will be very close to 12 amu but let's calculate the result more exactly.

Many elements have one dominant isotope, like carbon. Because electrons weigh so little compared to protons and neutrons, for these elements the number of neutrons can be estimated from the atomic mass. Thus for carbon, 12.01 - 6 = 6.01, and we estimate the number of neutrons to be 6.

To make a neutral carbon atom, 6 electrons must be present to neutralize the 6 protons in the nucleus. The way in which the electrons are arranged in an atom is called the electronic structure of the atom. Figure 1.4 depicts the electronic structure of a carbon atom. Notice that the electrons are arranged in shells around the nucleus. The shells correspond to rows of the periodic table. For example, H and He (hydrogen and helium) have electrons only in the first shell. Carbon, in the second row in the periodic table, has 2 shells of electrons around its nucleus. The first shell contains 2 electrons and the second shell, or valence shell, contains 4 electrons. The valence shell is the outermost occupied shell of an atom. Let's focus now on the number of electrons in each valence shell. Carbon has 4 valence electrons in its valence shell as does Silicon (Si). Elements in the same column of the periodic table not only have similar properties, they have the same number of valence electrons (with the exception of H and He). Note that the valence shell of He is filled. Atoms with filled valence shells are particularly reluctant to undergo chemical reactions. Other examples of filled valence shells occur for Ne and Ar. The elements in the last column of the periodic table frequently are called the inert or noble gases due to their low chemical reactivity.

Lewis dot representations of the atoms of the first three periods are shown in Figure 1.5. A Lewis dot structure depicts the valence electrons. The first four dots are arranged singly on the four sides of the elemental symbol; if there are more than four electrons the remaining dots are arranged pairwise with those that are already present. We will see later that a simple examination of the Lewis dot structure reveals much about the ways in which an element arranges itself with other atoms.

Figure 1.4 Shell structures of H, He, C, Ne, and Si

Figure 1.5 Lewis dot structures of first three periods

1.5 So how are the carbon building blocks assembled?

Recall the samples of carbon in various forms shown in Figure 1.3. Now examine Figure 1.6. In this figure, buckyball, diamond, and graphite are all shown using a frequently used representation called the ball-and-bond model. In these models each "ball" represents a Carbon atom. Each stick represents a chemical bond, i.e., a strong force that holds two atoms close in space. Before we delve into the details of what is meant by a chemical bond, let's see what we can understand about differences between diamond, graphite and buckyball based only on the ways in which the atoms are arranged.

Figure 1.6. Buckyballs, diamond, and graphite in a ball-and-bond representation.

Understanding how carbon is oriented in each of the three types of material allows for a better understanding of why these compounds have different properties. Notice that graphite, for example, has large sheets of hexagonal rings. The sheets do interact, but they are so far apart that the interactions are weak and broken easily. Because the layers of carbon rings can rub over each other, graphite is a good lubricant. Diamond, however, has each carbon bonded to four other carbons in a tetrahedral arrangement. Diamond can be cleaved along its planes, but it cannot flake apart into layers because of this tetrahedral arrangement of carbons. Buckyball has a structure very different from the structure of either diamond or graphite. Buckyball is shaped like a soccer ball, and a soccer ball is another symbol that is often used to represent a buckyball.

Perhaps the biggest difference in the structure of buckyball compared to diamond and graphite is that every buckyball has an exact number of carbon atoms (60) but diamond and graphite do not. Buckyball is a discrete structure or a molecule; diamond and graphite are extended lattices. Just as the soccer ball is an object used to represent buckyball, C60 symbolically represents buckyball. Because diamond and graphite are not composed of a discrete number of atoms (they are not molecules, the number of atoms in a piece of diamond depend on the size of the piece), their symbols are Cdiamond and Cgraphite.

1.6 More on bonding

The carbon atoms in buckyball, diamond, and graphite are held together by bonds. As we have seen it is the arrangement of atoms and bonds that differentiate these forms of elemental carbon. Every carbon atom in these materials has four bonds or connections between itself and neighboring atoms. However the connections between pairs of carbon atoms are not all identical. Whereas diamond only has single bonds (represented by one stick) between atoms, both buckyball and graphite have two bonds (represented by two sticks) to one neighboring carbon and two single bonds to two other neighboring carbons. The two bonds that span a pair of carbon atoms commonly is called a double bond. Refer to Figure 1.6, where the picture of both buckyball and graphite shows the network of single and double bonds that are present in these compounds. Note how each carbon atom atom has two single bonds and one double bond.

Why are all the bonds in diamond represented as single bonds whereas graphite and buckyball have mixtures of single and double bonds? Although you will later learn theoretical models for rationalizing these bonding patterns, ultimately the answer derives from experiment. The lengths of the carbon-carbon bonds in diamond, graphite, and buckyball have been measured by a technique called x-ray diffraction. In diamond the bond lengths are 1.54 Å (1.54 x 10^-10 m, the Å unit represents 1 x 10^-10m). Although these absolute distances between adjacent carbon atoms are very small, just meters long, the distances in buckyball and graphite are even shorter. Bond distances in buckyballs and graphite are about 1.4 Å. We can rationalize the shorter bond lengths as arising from greater forces of attraction between atoms sharing bonds. Thus we expect that double bonds should be stronger and shorter than single bonds. In other words the shorter bonds observed in buckyballs and graphite relative to diamond are consistent with the presence of more than a single bond between the carbon atoms.

The number of bonds formed by atoms of various elements is correlated with the position of the atoms in the periodic table. For example, we have seen that carbon atoms generally make four bonds. Similarly, the elements in the same column of the periodic table as carbon (Si, Ge, Sn, Pb) all are observed to make stable forms of matter in which each atom has a total of four bonds to other atoms. This column of periodic table is called Group 14. As one proceeds to the right of carbon on the periodic table, the number of bonds commonly formed by the element decreases by one for each column moved. Thus the elements in the nitrogen column (or Group 15) form three bonds, elements in the same column as oxygen (Group 16) form two bonds, and the elements from the same column as fluorine (Group 17) usually form one bond. Neon and the other elements in the last row of the periodic table (helium, argon, krypton, xenon, and radon, Group 18) resist the formation of bonds unless special conditions are used. Hydrogen is a special case. Hydrogen tends to form just one bond. This feature makes it similar to Group 17 elements. However, many of the other properties of hydrogen are not like those of fluorine, chlorine, and bromine so that H usually is not placed in the column adjacent to He. Figure 1.7 shows several examples of molecules that illustrate these bonding patterns.

Figure 1.7 Simple molecules and bonding patterns

How can we make sense of these bonding patterns? Early in this century, Gilbert N. Lewis at the University of California, Berkeley proposed that atoms form bonds such that each atom in the molecule experiences a complete valence shell. For example, the formation of methane (CH4) involves four bonds between carbon and hydrogen. Each of these bonds involves sharing a pair of electrons between C and H. The Lewis dot structure of CH4 is shown in Figure 1.8.

Figure 1.8 Lewis Dot Structures of CH4, C2H4, and C2H2.