SPECTROSCOPIC DISPERSION VS ABSORPTION - NEW METHOD FOR DISTINGUISHING A DISTRIBUTION IN PEAK POSITION FROM A DISTRIBUTION IN LINE-WIDTH

For a single Lorentzian spectral line, a plot of dispersion vs. absorption (DISPA) gives a semicircle passing through the origin and centered on the abscissa. For an arbitrary superposition of Lorentzians of common peak position and different line width (and for any symmetrical distribution of Lorentzians of common width and different peak position), the DISPA plot will still pass through the origin, but the radius of curvature (measured from a point on the abscissa at half the maximum absorption peak height) will no longer be constant. Particular examples are given in earlier papers. In this paper, it is shown that the superposition of two or more Lorentzians of the same peak position but different line width always gives a DISPA curve lying below the reference semicircle (i.e., a circle whose diameter is the maximum absorption peak height, centered on the abscissa at half the maximum absorption peak height), while the superposition of two or more symmetrically displaced Lorentzians of the same line width but different peak position will in general give a DISPA curve lying above the reference semicircle. It is therefore proposed that an experimental DISPA plot should readily distinguish between these two general mechanisms for inhomogeneous line broadening in various forms of spectroscopy. Experimental examples of each mechanism are given. © 1979 American Chemical Society.