GLOBAL LEAST-SQUARES ANALYSIS OF LARGE, CORRELATED SPECTRAL DATA SETS- APPLICATION TO COMPONENT-RESOLVED FT-PGSE NMR-SPECTROSCOPY

A new data processing mode for Fourier Transform Pulsed-Gradient Spin- Echo (FT-PGSE) data sets is described. Unlike conventional analysis me thods, it uses all of the significant spectral information of a data s et of typically 16 or 32 different magnetic field gradient settings fo r 10-1000 significant frequency channels out of a 1-16K FT-PGSE data s et. The procedure is based on a global least squares minimization appr oach at two levels: an upper level that optimizes the actual global se lf-diffusion coefficient data and a lower one that optimizes the ampli tude(s) of the component(s) for a particular frequency channel. This a pproach relies on the intrinsic property of FT-PGSE data sets in that the whole bandshape of a particular component attenuates by exactly th e same relative amount upon incrementing the field gradient pulse para meters (Stilbs, P. Anal. Chem. 1981, 53, 2135 which was also shown to provide a pathway for separating the spin-echo bandshapes of the const ituents of multicomponent systems. As a consequence of the coupled, gl obal minimization approach of the method, the signal-to-noise ratio (S /N) of the FT-PGSE experiment is enhanced by typically a factor of 10 or more, since all of the available spectral information is utilized ( effectively, a few 100 frequency channels/peak are combined). The pres ent (global) optimization procedure (named CORE-NMR, COmponent-REsolve d NMR spectroscopy) fundamentally differs from the diffusion-ordered s pectroscopy procedure(s) introduced by Johnson et al., but the two app roaches can be regarded as complementary. CORE-NMR is expected to find particular use in current studies on aggregation and binding in polym er and surfactant solutions, solving evaluation problems originating f rom the poor S/N, overlapping bandshapes, and high dynamic range with regard to relative constituent spectral intensities. Typically these d ifficulties are all present at the same time in such studies. CORE-NMR is equally well applicable to electrophoretic FT-NMR, where the signa ls of a particular component also vary coherently with an experimental parameter (the electrophoretic current) with regard to intensity and phase. As outlined, the generic CORE approach is of course also applic able to any other type of spectroscopic data, where individual intensi ties of separated or overlapping component spectral bandshapes decay/e volve in a similarly correlated manner as in, e.g., FT-PGSE NMR.