Clusters of atoms

Type of physical science: Chemistry

Field of study: Chemistry of molecules: types of molecules

A "cluster" is a group of three or more like atoms bound to one another in a geometrical array. Clusters have properties that are similar to, but distinct from, discrete molecules and bulk phases and are of interest in understanding properties of bulk phases and in catalysis.

Overview

There are probably as many different definitions for clusters as there are cluster chemists. Clusters may contain anywhere from three to thousands of atoms with each atom chemically bound to several other identical atoms in a precise three-dimensional array.

Atoms in a cluster may all be of the same element, which results in a homonuclear cluster, or may incorporate varying numbers of additional types of atoms, yielding a heteronuclear cluster. As a result, clusters display diverse chemical and physical properties, which are dependent on both the type of elements in the cluster as well as the three-dimensional geometry and size of the cluster. Clusters containing only a few atoms may behave similarly to ordinary discrete molecules, while large clusters often display properties reminiscent of those in bulk phases, such as a metal surface. Clusters, then, occupy a transitional niche between small molecules and bulk phases.

A widely publicized example of a cluster of atoms is buckminsterfullerene, which was first detected in 1985 by Richard Smalley and coworkers. This substance is composed of sixty carbon atoms covalently bonded together and is of interest to chemists for a variety of reasons, not the least of which is the structure of the cluster in which the carbon atoms may be viewed as occupying sites on the surface of a sphere. The actual placement of atoms and chemical bonds in the cluster is geometrically identical to the pattern on a soccer ball or geodesic dome.

Incidentally, this is the reason for the name given to the compound.

There are several types of clusters, and the definition of a cluster is somewhat variable depending on the conditions under which the cluster is made and studied. The carbon cluster was produced via one major technique of cluster synthesis in which a rod of some pure element, such as graphite in the case of carbon, is made the target of a laser beam, which vaporizes the surface of the rod to form a plasma. This plasma is carried away by an inert gas, typically helium, which allows the plasma to cool and condense to form clusters. These clusters may then be channeled directly into some sort of analyzing device such as a mass spectrometer, or they may first be made to flow through an area in which other reactants are added so that the chemical reactivity of the clusters may be examined. These reaction products are then typically carried into some sort of analyzer to elucidate information about the reaction products. Laser vaporization synthesis allows for formation of clusters whose properties and composition can be precisely determined.

Other methods of generating gas phase atom clusters differ from the laser vaporization method mainly in the technique utilized to form the vapor. Rather than firing a laser at the target to form the plasma, the solid element may be vaporized thermally and allowed to condense into clusters in a stream of cooling gas. This method works very well with metals.

A disadvantage of these vapor condensation techniques is that it is difficult to isolate the substances produced in any appreciable quantity. This is partly intrinsic to the nature of the syntheses, and partly resulting from the fact that naked clusters of atoms tend to be highly reactive substances. This extreme reactivity is observed because the exposed surface atoms of clusters typically have the capacity to form additional bonds with other substances. Clusters of this type are called bare or unligated clusters. Ligated clusters, or cluster complexes, are a related class of compounds in which a core of like atoms is bonded together in a cluster geometry, with other substances, called ligands, bound to the remaining bonding sites of the surface cluster atoms via coordinate covalent bonds in which the ligand donates the shared electron pair to the chemical bond. Cluster complexes are, typically, much easier to isolate in large quantities for subsequent study than bare clusters, as they are not as reactive and are of interest for many of the same reasons as unligated clusters.

Rather than attempt to isolate the highly reactive bare clusters produced from vapor condensation, these species are usually left in the gas phase after synthesis and during study without subsequent isolation. Alternatively, the clusters may be trapped on a cold surface with an inert element such as argon. This technique, called matrix isolation, allows isolation of the clusters so that a broader range of analytical methods can be utilized to study them.

As mentioned previously, only small amounts of clusters are typically produced in vapor condensation synthesis. Experimentally, clusters can often be isolated in larger quantities by generating them in a solution and allowing them to precipitate from the solution, or by trapping them in the spaces present in a porous polymer of some type. While these methods may produce clusters in a weighable amount, typically, the product size and structure are not well defined. In other words, the products isolated display a variety of sizes, and the actual range of sizes isolated is somewhat difficult to control. In addition, these materials are extremely reactive, and to isolate unligated clusters from a solution, they must be coated or encapsulated by some inert material so that, once formed, they do not immediately react with other substances in the solution.

Not all clusters are highly reactive. As early as 1891, clusters of unligated main group elements were generated in solution, although at the time it was not known that they were clusters. These materials were produced by the reaction of bulk metals with metallic sodium in liquid ammonia, resulting in deeply colored solutions. Evaporation of the ammonia from these mixtures produced metallic phases with very precise compositions, called Zintl phases. It was not until 1970 that the first isolation of a discrete cluster from one of these solutions was accomplished. These clusters are typically electrically charged, or ionic, and are easily isolated by encapsulating them in another chemical substance. Atoms occupy the vertices of a polyhedral shape in these clusters, as is typically the case for clusters isolated from the vapor phase.

With a fairly detailed body of experimental knowledge about clusters, it is possible to develop theories for describing and predicting their structure and bonding. Nevertheless, the difficulty arises from determining the approach to use with any such theory. As clusters are too small to be bulk phases, models for bulk phases may not work adequately. In addition, clusters are too large to be considered discrete molecules, so the approach used to describe bonding in molecules is not quite right either. Some theoreticians have had success working from both directions. A description of the electronic structure of a species will yield information about its geometry as well. Beginning from the small perspective, electronic motion for individual atoms can be described very accurately through quantum mechanics. To describe molecules, which may be viewed as small groups of atoms bound together, a similar method may be used. The electronic structure is much more complicated than that of an individual atom, and exact calculations of electronic structure become impossible. It is possible, however, to do semiempirical calculations based on further approximations such as the effect of electron-electron repulsions to get a good description of the molecular electronic structure.

Further approximations relevant to clusters allow determination of a reasonable picture of the structure and bonding in clusters.

In bulk phases, the individual electron motions are impossible to describe, but the collective motion, or plasmon, can be accurately described. This is the basis of the jellium model utilized in solid-state physics. With suitable approximations, this model can be applied to clusters to generate a description of the electronic structure. The jellium model and the molecular model yield similar results for clusters.

These models allow insight into the transition from discrete molecular behavior to extended bulk phase properties that is typical of clusters. As a rule of thumb, clusters with more than twelve atoms will display hybrid characteristics. This is the case because typically the geometries of clusters with twelve or more atoms are such that they contain internal atoms, or atoms that are not on the surface of the cluster. Yet another way to define clusters is in terms of the fraction of atoms on the surface of the aggregate. Clusters have a large fraction of atoms on their surface, whereas in the bulk phase most atoms are internal. Not surprisingly, then, as the number of internal atoms increases and the fraction of surface atoms in the species decreases, the properties of the cluster become more and more like those of the bulk phase.

Applications

With their unique properties as a hybrid state of matter lying between bulk phases and discrete molecules, clusters are a valuable tool in the study to understand further the nature of chemical bonding. Because of their high reactivity and unusual chemical and physical properties, clusters are of importance in many potential commercial applications as well.

By studying clusters, it is possible to gain insight into the bonding and arrangement of atoms in bulk phases. Large clusters often adopt a three-dimensional geometry that is the same as that of bulk phases, so that a cluster may be viewed as a chunk of metal. Since the cluster is of a discrete size, its conductivity will be greater than that of a molecule, but less than that of a bulk phase. Miniaturization is of great interest in many technological applications, and with their unusual electrical properties, clusters offer a means to produce innovative devices such as semiconducting thin films for microelectronics applications. This is a very real possibility, as indium phosphide clusters have been synthesized which display properties of classical semiconductors. Once the problems of large-scale synthesis and isolation of suitable materials have been solved, clusters may find widespread applicability in this industry.

Of greater historical and practical interest to chemists is the use of clusters as catalysts or catalyst models. Many chemical reactions are catalyzed by the presence of a metal surface. An example is the production of polyethylene via a Ziegler-Natta catalyst. As the reaction mixture and catalyst are in different phases, the metal surface is called a heterogeneous catalyst. A catalyst in the same phase as the reaction mixture is called a homogeneous catalyst, and as a rule, they are more selective and efficient than heterogeneous catalysts. This is partly a result of the large surface area of the catalyst in contact with the reaction mixture. A bulk metal has only a tiny fraction of its atoms on the surface where they can actually contact the solution and catalyze a chemical process. A large fraction of the atoms in a cluster occupy surface positions in the structure, making clusters desirable candidates for homogeneous catalysis. They have the potential to be far more efficient than bulk phase materials because of the high fraction of surface atoms.

As clusters often have a structure similar to that of the bulk phase, they are often useful as models of the processes taking place on the surface of the metal. Ligated clusters are much more useful in this respect as they are easily isolated and their structures may be readily determined through X-ray diffraction analysis. The bonding modes of ligands in these clusters may mimic the bonding modes of the species in a catalysis process. Understanding these bonding modes may allow for refinements in the catalyst design to improve selectivity and efficiency of the catalyst.

The relationship of cluster structure to that of the bulk phase is important in refining the theoretical models for structure and bonding in the bulk phase. In addition, clusters provide a means for theoreticians to relate the properties of the individual atoms of an element to the behavior of the element in the bulk phase. As clusters containing varying numbers of atoms of a given element are produced and studied, trends in relative stability may be noted. For example, in the synthesis of buckminsterfullerene, several other clusters, which are not as stable, are also observed. Typically, the clusters containing an even number of carbon atoms are, relatively speaking, more stable than those with an odd number of atoms. These stability trends in clusters indicate that, just as the electrons of atoms occupy certain energy levels, or shells, in which certain configurations are more stable than others, so may clusters display this shell-like electronic structure in which certain cluster compositions are more stable than others, with the stable configurations dependent on the element in the cluster. A clearer understanding of the electronic structure in clusters will foster further understanding of the electronic structure of solids.

One property of clusters that is particularly interesting is that their freezing and melting points may not be quite the same. In other words, rather than freezing or melting at a single temperature, as does water, the phase change may take place over a small, finite temperature range. Such properties of clusters are shedding new insight onto the true nature of solids and liquids.

Finally, clusters, especially carbon clusters, are of interest to astronomers, as they may represent some of the major constituents of interstellar gas and dust and isolation of such species allows detailed study of their light-absorbing properties, facilitating understanding of processes taking place in these clouds in space.

Context

Modern interest in clusters may be traced back to the first isolation of Zintl phases in the nineteenth century, while work on vapor phase clusters has its origins in the 1950's. With the advent in the twentieth century of modern instrumental methods of analysis, scientists now have the tools both to synthesize these novel species and to characterize their chemical compositions and reactivities. Isolation of buckminsterfullerene gave the field of cluster chemistry quite a boost, attracting the interest of both the scientific community and the popular press. The novelty of a soccer ball-shaped molecule seemed to strike a common cord of interest in both groups, with scientists intrigued by the stability and properties of the substance and the general public fascinated by the shape. The surge of publicity generated a flood of related research on all types of clusters, not merely carbon clusters.

As more understanding of the structure and reactivity of clusters is gleaned from this ongoing research, they will come to occupy an important niche in several areas of chemistry.

Theoreticians will continue to develop theories to explain the properties and structure of clusters, while the development of new synthetic techniques will certainly produce clusters with novel properties.

As has occurred in past research and development, the prime focus of cluster chemistry will remain on their use in the chemical industry as catalysts in industrial processes. As the methods of producing and isolating bare clusters of controlled composition are continually refined, they will become increasingly important in the industry.

Of greater long-term significance may be the unusual electronic properties of these substances. With the possibility of molecular semiconductors in electronics applications, the capability of microelectronic devices may potentially be tremendously increased. There is a good chance that clusters may open new areas in the exploration of high-temperature superconductors.

In early 1991, it was reported that a doped buckminsterfullerene displayed superconductivity at a higher temperature than any previously produced organic molecular substance.

While superficially a simple thing, a cluster occupies a unique role in modern chemistry and physics by providing the stepping-stone from discrete molecular behavior to the extensive delocalized behavior of the bulk phase. Further research with clusters is certain to have a dramatic impact on accepted theories in materials science.

Principal terms

BULK PHASE: a very large, extended array of atoms in which the properties of individual atoms are not discernible, but the collective behavior of the phase may be accurately described

CATALYSIS: a process in which a reaction rate is increased because of the addition of a chemical substance which is not itself changed by the reaction

COVALENT BOND: a chemical bond in which two electrons are shared between two atoms

MASS SPECTROMETER: an analytical device in which the precise mass and, to some extent, composition of a compound may be determined

METALLIC BOND: a type of bonding in which loosely held electrons in the metal are free to move throughout the volume of the solid

Bibliography

Baum, Rudy. "American Chemical Society Fullerene Symposium." CHEMICAL AND ENGINEERING NEWS 69 (April 22, 1991): 8. A brief but very readable account of a special symposium held at the spring, 1991, American Chemical Society meeting in Atlanta. Includes a brief summary of the latest developments in carbon cluster chemistry.

Baum, Rudy. "Physical Chemistry." In YEARBOOK OF SCIENCE AND THE FUTURE: 1987, edited by David Calhoun. Chicago: Encyclopedia Britannica, 1986. Written shortly after the initial buckminsterfullerene synthesis, this easy-to-read review presents an excellent overview of the history of carbon clusters. Of special significance is an easy-to-interpret diagram of the apparatus used to generate the cluster.

Berry, Stephen R. "When the Melting and Freezing Points Are Not the Same." SCIENTIFIC AMERICAN 263 (August, 1990): 68. Written for a general audience, this informative and fascinating article describes the way clusters can be used to gain a fuller understanding of the solid-liquid or liquid-solid transition. This is described in terms of the energy levels accessible in the liquid and solid state and is a reasonable explanation of why clusters may display distinct melting and freezing points.

Cohen, Marvin L., and Walter D. Knight. "The Physics of Metal Clusters." PHYSICS TODAY 43 (December, 1990): 42-50. Written from the perspective of physicists, this article presents excellent summaries of cluster types, various reasons for studying metal clusters, and a good discussion of the different methods used to describe bonding in clusters, including the jellium model. This reference also includes a good description of the components of a cluster synthesis apparatus.

Duncan, Michael A., and Dennis H. Rouvray. "Microclusters." SCIENTIFIC AMERICAN 261 (December, 1989): 110-115. A good description of structural characteristics of clusters, including an overview of historical developments in cluster synthesis. Includes an excellent description of cluster generation methods.

Jelski, Daniel A., and Thomas F. George. "Clusters: Link Between Molecules and Solids." JOURNAL OF CHEMICAL EDUCATION 65 (October, 1988): 879-883. Although geared to educators, this article presents an excellent overview of the unique properties of clusters. Includes general discussion of the approximation methods applicable to molecular orbital calculations for clusters and discusses factors dictating cluster geometries. Contains a summary of carbon cluster chemistry and buckminsterfullerene.

Moskovits, Martin, ed. METAL CLUSTERS. New York: John Wiley & Sons, 1986. A technical work, this reference nevertheless is a good source of detailed information about cluster chemistry. Includes chapters by various contributors on topics such as structure, supported cluster catalysts, and matrix isolation applications. Includes good illustrations of cluster structure and rules governing the stability and structure of clusters.

Pool, Robert. "Clusters: Strange Morsels of Matter." SCIENCE 248 (June 8, 1990): 1186-1188. Another good, but brief, description of interesting cluster properties, especially optical properties and color. Describes possible techniques for preparative scale generation and isolation of reactive clusters. In addition, there is discussion of some fairly exotic potential applications.

Buckminsterfullerene molecule

The Formation of Aggregates

Calculations of Molecular Structure