On Characterization of Molecular Structures

Most physical and chemical properties of molecules are expressed as numbers, but structures are not numbers Sequences are ordered collections of numbers, not 

More than 65 years ago, J. R. Platt [46] suggested the count of paths of different lengths in molecules as a tool for numerical characterization of molecules. The suggestion by Platt is that the sequences of path numbers are the language of interest in comparative study of chemical structures. For some, such a proposition may appear to be a chemically futile mathematical exercise that may entertain some. In the central column of Table 7.1, we show the result of such a mathematical exercise, which offers a numerical representation of octane isomers. For example, 2,3-dimethyhexane 

FIGURE 7.1 Skeletal forms of octane isomers and their boiling points in °C. 

Men (Committee) Made Names and the God (Nature) Given Names for the 18 Isomers of Octane 

Partial ordering is an important tool of discrete mathematics, which has found visible application in chemistry [68-75]. The beginning started in 1903 with Scottish mathematician Muirhead [76], who considered ordering of sequences of the same length, such as A (a a2, aj,. .. a ) and B (bj, bj, bj,. .. bj. To do this, he first constructed the corresponding sequences of partial sums, the elements of which involve an increasing number of sequence terms  

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A number of reviews can be consulted for an introduction to the fundamentals both theoretical and practical covering XPS. These include Riggs and Parker (2) and the book by Carlson (3). Electron spectroscopy is reviewed in alternate years in the Fundamental Reviews issue of Analytical Chemistry. The last literature review was published in 1980 (4) and this and previous reviews can be consulted for a coverage of all aspects of the literature of XPS. A number of recent symposia have been held on applications of surface analytical methods in various aspects of materials science such as the symposium on characterization of molecular structures of polymers by photon, electron, and ion probes at the March 1980 American Chemical Society meetings in Houston ( 5) and the International Symposium on Physiochemical Aspects of Polymer Surfaces at this meeting as well as the symposium on industrial applications of surface analysis of which this article is a part. Review articles on various applications of XPS in materials science are listed in Table I. 

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