Gaussian bandshape

A Gaussian bandshape results when the partition coefficient, K (= Cs/Cm), is independent of the concentration of solute on the column. In real columns, K changes as the concentration of solute increases, and bandshapes are skewed.10 A graph of Cs versus Cm (at a given temperature) is called an isotherm. Three common isotherms and their resulting bandshapes are shown in Figure 23-20. The center isotherm is the ideal one, leading to a symmetric peak. 

Describe how nonlinear partition isotherms lead to non-Gaussian bandshapes. Draw the bandshape produced by an overloaded column and a column with tailing. 

Figure 24 Transient spectra (anisotropic signal) for to = 0 ps and excitation at the peak position of the OH band at three temperature values 273 K (a), 298 K (b), and 343 K (c). Experimental points the calculated thin lines indicate the analysis of the transient bandshapes (thin full line) in terms of the major spectral components I—III (dash-dotted, broken, long-dashed) with Gaussian shape and a Lorentzian spectral hole contribution (dotted line, b,c) the pump frequencies are indicated in the figure by vertical arrows. 

Investigation of methanol-pyridine complexes, on the other hand, produced a relatively narrow (75 cm 1 FWHM) bleached hole that is burned into the 260 cm 1 FWHM OH-stretch (v = 0 -> 1) absorption band. The methanofpyridinc complex OH-stretch absorption band was better fit by a Gaussian function than with a Lorentzian bandshape, indicating this system is inhomogeneously broadened on the >1 ps timescale. 

Apart from the obvious variables of peak height and width, the type of bandshape needs to be considered. Ilie class of bandshape of an infrared spectrum depends on the type of sample. A choice of Gaussian, Lorentzian or a combination of these bandshapes, is usually considered. Figure 5.2f illustrates a typical. curve-fitting process. 

Figure 9. Spectra of two molecules, D and E, exhibiting different intensities in the vibronic band, and of one, C, having a broadened spectrum. The fit to the spectrum of molecule C is the convolution of D with a 15-nm gaussian (FWHM), shifted to shorter wavelength by 5 nm. Although molecule C photobleached after a single 1-min. integration, photostability and spectral width were generally uncorrelated. E was shifted 5.5nm to longer wavelength to facilitate bandshape comparison, and D and E were displaced vertically for clarity. Adapted from Ref. 17.

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