Four data pairs method

Another method for determining n and a/R from (a,T) data makes use of four data pairs. In this method, it is assumed that four values, i, a2, and tt4, are known at four temperatures, Ti, T2, T3, and T4, respectively. Further, for simpHcity, we will assume that aj < a2 < 3 < 4. The method makes use of the two-point form of the Coats and Redfem equation, written as... 

Several studies have employed chemometric designs in CZE method development. In most cases, central composite designs were selected with background electrolyte pH and concentration as well as buffer additives such as methanol as experimental factors and separation selectivity or peak resolution of one or more critical analyte pairs as responses. For example, method development and optimization employing a three-factor central composite design was performed for the analysis of related compounds of the tetracychne antibiotics doxycycline (17) and metacychne (18). The separation selectivity between three critical pairs of analytes were selected as responses in the case of doxycycline while four critical pairs served as responses in the case of metacychne. In both studies, the data were htted to a partial least square (PLS) model. The factors buffer pH and methanol concentration proved to affect the separation selectivity of the respective critical pairs differently so that the overall optimized methods represented a compromise for each individual response. Both methods were subsequently validated and applied to commercial samples. 

The Hanawalt method is relatively straightforward for unknowns which are nearly single phase. For multiphase mixtures the identification becomes tedious. Consider the data for a white powder given in Table 4 (7). Again the search is begun with the two most intense lines, 2.41 A and 3.04 A, but no match is found for this line-pair. Now a new line-pair must be chosen and the first and third most intense lines seem likely. Searching the Hanawalt manual with the pair 2.41 A and 1.70 A yields the possibilities 7-TaH, CaO, and NaYOa. Only the four lines of the CaO standard pattern lines match the lines in the unknown pattern. 

A simple and classical method is Wold s criterion [39], which resembles the well-known F-test, defined as the ratio between two successive values of PRESS (obtained by cross-validation). The optimum dimensionality is set as the number of factors for which the ratio does not exceeds unity (at that moment the residual error for a model containing A components becomes larger than that for a model with only A - 1 components). The adjusted Wold s criterion limits the upper ratio to 0.90 or 0.95 [35]. Figure 4.17 depicts how this criterion behaves when applied to the calibration data set of the working example developed to determine Sb in natural waters. This plot shows that the third pair (formed by the third and fourth factors) yields a PRESS ratio that is slightly lower than one, so probably the best number of factors to be included in the model would be three or four. 

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