J Phys. Chem. 1996,
100, 8180-8189
Global Least-Squares Analysis of Large, Correlated
Spectral Data Sets: Application to Component-Resolved FT-PGSE
NMR Spectroscopy
P.Stilbs*, K. Paulsen, and P.C. Griffiths
Physical Chemistry, Royal Institute of Technology,
S-10044 Stockholm, Sweden
Received: November 30, 1995; in Final Form: February
7, 1996
A new data processing mode for Fourier Transform
Pulsed-Gradient Spin-Echo (FT-POSE) data sets is described. Unlike
conventional analysis methods, it uses all of the significant
spectral information of a data set of typically 16 or 32 different
magnetic field gradient settings for 10-1000 significant frequency
channels out of a 1 - 16K FT-PGSE data set. The procedure is based
on a global least-squares minimization approach at two levels:
an upper level that optimizes the actual global
self-diffusion coefficient data
and a lower one that optimizes the amplitude(s) of the component(s)
for a particular frequency channel. This approach relies on the
intrinsic property of FT-PGSE data sets in that the whole bandshape
of a particular component attenuates by exactly the same relative
amount upon incrementing the field gradient pulse parameters (Stilbs,
P. AnaL Chem. 1981,
53, 2135)
which was also shown to provide a pathway for separating the spin-echo
bandshapes of the constituents of multicomponent systems. As a
consequence of the coupled, global minimization approach of the
method, the signal-to-noise ratio (S/N) of the FT-POSE 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 present (global)
optimization procedure (named CORE-NMR, COmponentREsolved NMR
spectroscopy) fundamentally differs from the diffusion-ordered
spectroscopy procedure(s) introduced by Johnson et
al., but the two approaches can
be regarded as complementary. CORE-NMR is expected to find particular
use in current studies on aggregation and binding in polymer and
surfactant solutions, solving evaluation problems originating
from the poor S/N, overlapping bandshapes, and high dynamic range
with regard to relative constituent spectral intensities. Typically
these difficulties are all present at the same time in such studies.
CORE-NMR is equally well applicable to electrophoretic FT-NMR,
where the signals 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 applicable to any other type of spectroscopic
data, where individual intensities of separated or overlapping
component spectral bandshapes decay/evolve in a sirnilarly correlated
manner as in, e.g., FT-PGSE
NMR.