NONLINEAR CURVE-FITTING OF BILINEAR DATA USING ORTHOGONAL PROJECTIONSFOR RANK ANALYSIS - APPLICATIONS TO GAS-CHROMATOGRAPHY INFRARED SPECTROMETRY AND VARIABLE-TEMPERATURE INFRARED STUDIES

Non-linear curve fitting of bilinear data structures is demonstrated a nd used on one simulated and two real analytical infrared (IR) systems . Information regarding the number of peaks and their relative positio ns is revealed by orthogonal projection techniques. The systems have b een studied without using any a priori information. The bilinearities of the analytical model systems are used to resolve corresponding IR s pectra from fitted elution profiles based upon Gaussian curves in a ga s chromatography/infrared spectrometry (GC/IR) study, and similarly to resolve concentration profiles from Gaussian and Lorentzian curves fi tted to IR bands in a variable-temperature IR study. A GC/IR system (m - and p-xylene) was investigated revealing both the elution profiles, the IR spectra (887-702 cm-1, aromatic =C-H deformation) and the relat ive concentrations of the analytes. The 0-H deformation band (approxim ately 1640 cm-1) from a temperature study of water was resolved into a broad and a narrow peak, the narrow peak being located within the bro ad one. This indicates that water can be regarded as a two-structure s ystem composed of a fully hydrogen-bonded and a partially hydrogen-bon ded structure. The result from Gaussian and Lorentzian curve fitting l eads to different interpretations regarding relative peak positions an d widths of the two structures. Results obtained using latent projecti ve graphs suggest that the 0-H deformation band consists of two Gaussi an peaks.