Near-critical series development

A Near-Critical Series Development for A(x). It is interesting to compare Equations 18 and 19 with the forms which would be required to satisfy a Guggenheim-type power law,... 

Another effect of the mobile phase/sample solvent mismatch is a change in the sensitiviy (AR/AC) of the method for an analyte. As an example, Perlman and Kirschbaum [889] prepared a series of solutes (e.g., captopril, nadolol, o-nitroani-line, triamcinolone acetate, methylparaben) in neat solvents acetonitrile, methanol, DMSO, and dichloromethane. These solutions were then injected onto a C,g or I enyl column (2 = 214 run or 270 run) and eluted with 50/50 methanol/water or 38.8/1.1/960 ethanol/water/dichloromethane mobile phases. Significant differences in the peak areas resulted for some but not all analytes. Deterioration of peak shapes was also common. Prediction of these changes was nearly impossible. For example, o-nitoaniline (in methanol) exhibited an increased peak area in methanol/water, whereas p-nitroaniline was unaffected. An awareness of the unexpected and unpredictable effects the sample solvent has on both the quantitative results and the overall separation is critical when developing a method. 

The PKS model has been criticized (27-29) for the assumption of a single frequency and its unsatisfactory description of the magnetic circular dichroism (MCD) found for the intervalence band of the Creutz-Taube ion (30). In a series of papers (31), Ondrechen and coworkers developed a more realistic three-site model for delocalized (class III) bridged mixed-valence complexes. This model incorporates many features of the PKS model but differs in that it explicitly includes the bridge, it uses a molecular orbital basis of one-electron functions, and the choice of important vibrational modes is not the same. The near-IR band line shape of the Creutz-Taube ion has been reasonably... 

Near a critical point, or if large particles are involved, the elements of may have important or R dependence. Suppose, however, that we ignore such complexities for the moment. The inverse of may be developed in a perturbation series about the inverse of the block diagonal (i.e., no Bk k -Sk,k elements, kVk"). In this way, we find that the corrections to the block diagonal inverse are Bk k - k.k. kVk", terms that are 0(1/N) with respect to the diagonal terms. 

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