Least-squares analysis chromatogram

A statistical analysis of the peak counts obtained from the simulated chromatograms was made as follows. We changed the random number sequence, by means of the seed change previously described, to generate random changes In component retention times and amplitudes while holding constant component number, zone width, and peak capacity. This procedure. In essence, mimicked the Injection of different samples with the same component number and zone width onto a column. A mean peak count and standard deviation at each of the different peak capacities were calculated. The means and standard deviations of the peak counts were fit by a least squares analysis to Equation 11 with a proper transformation of the standard deviations from an exponential to a linear function (5). From the value of the least squares slope and Intercept, an estimated component number was calculated. 

In some cases, many different spectra (or chromatograms) of the same object are available. For inhomogenous objects, for example, several samples of different constitution can be taken. This allows to apply multivariate data processing techniques. When the signals of the compounds in the sample are specific and linearly additive, the number of compounds which contribute to the signal, can be determined by a Principal Components Analysis (PCA) " (see Sect. 3.2.1). Without knowing the identity of all compounds, which are present and without knowing their spectra, a calibration by partical least squares (PLC) allows to quantify the compounds of interest. 

The resulting spectro-chromatograms (SCG) are 3D-representations of the tar matrices with the UV-absorbances as function of the retention time in the gel column and the wavelength of absorption, respectively fig. 3). Sections of the SCG parallel to the retention time axis at 215 nm UV-absorption ("tar profiles" in the following) enable quick qualitative tar characterization. For the quantitative evaluation of the SCG, chemometric methods such as factor analysis and the classical least squares method are applied. This requires the set-up of a spectral library which contains the SCG of the quantitative important tar compounds. 

Figure 12.16 Adsorption isotherms and displacement chromatogram for 3,4-dihydroxyphenyl, 2-hydroxyphenyl, and 4-hydroxyphenyl acetic acids. (Left) Adsorption isotherms measured by frontal analysis on a 250 x4.6 mm column packed with 10 tm Partisil ODS-2 from 0.1 M phosphate buffer, pH 2.12 at 25°C. The soUd Unes are a least-squares fit of the data points to the Langmuir isotherm. (Right) Displacement chromatogram, carrier 0.1 M phosphate buffer, pH 2.12 displacer n-butanol at 0.97 M. Flow rate 0.05 mL/min at 25°C. Feed 1.5 mL of 30, 35, and 45 mg of 3,4 dihydroxy-, 4-, and 2-hydroxyphenylacetic acids, respectively. Fraction size, 0.15 mL. Fraction 40 marks 12 mL of eluent volume. Reproduced with permission from Cs. Horvath, A. Nahum and J.H. Frenz, J. Chroniatogr. 218 (1981) 365 (Figs. 6 and 7).

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