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Measurement of structural distribution functions in disordered systems: a general approach for sensitivity estimation

Measurement of structural distribution functions in disordered systems: a general approach for sensitivity estimation
Measurement of structural distribution functions in disordered systems: a general approach for sensitivity estimation
A novel approach is proposed that allows the evaluation of distribution functions of structural parameters, such as dihedral angles and orientations of molecular segments, from suitable NMR spectra in disordered solids. The relationship between the distribution function and the observable spectrum is represented by a linear integral operator G. The distribution function corresponding to a measured spectrum is expanded into the eigenfunctions of G, the expansion coefficients being found by projecting the measured data onto the basis spectra associated with the eigenfunctions. The accuracy of the expansion coefficients, thus obtained, is related to the eigenvalues of G. Unlike other sets of orthogonal functions, the eigenfunctions of G have the interesting property that also their associated basis spectra (“eigenspectra”) are orthogonal. Therefore, we refer to this novel scheme as the “conjugate orthogonal functions” (COF) approach. Beyond the utility of the COF approach for data evaluation and sensitivity analysis, it also represents a means for comparing systematically the analytic power of spectroscopic techniques. The nature of the information delivered by a particular technique (e.g., its symmetry), is reflected in the eigenfunctions of G, whereas the eigenvalues are related to the “amount” of information that can be extracted from spectra with a given signal-to-noise ratio. By way of example, the approach is applied to the determination of the distribution of dihedral angles in doubly 13C-labeled bisphenol-A poly(carbonate) by solid-state NMR spectroscopy, and experimental data from heteronuclear separated-local-field and double quantum two-dimensional (2-D) correlation experiments are compared.
0021-9606
6110
Utz, Marcel
c84ed64c-9e89-4051-af39-d401e423891b
Utz, Marcel
c84ed64c-9e89-4051-af39-d401e423891b

Utz, Marcel (1998) Measurement of structural distribution functions in disordered systems: a general approach for sensitivity estimation. The Journal of Chemical Physics, 109 (14), 6110. (doi:10.1063/1.477238).

Record type: Article

Abstract

A novel approach is proposed that allows the evaluation of distribution functions of structural parameters, such as dihedral angles and orientations of molecular segments, from suitable NMR spectra in disordered solids. The relationship between the distribution function and the observable spectrum is represented by a linear integral operator G. The distribution function corresponding to a measured spectrum is expanded into the eigenfunctions of G, the expansion coefficients being found by projecting the measured data onto the basis spectra associated with the eigenfunctions. The accuracy of the expansion coefficients, thus obtained, is related to the eigenvalues of G. Unlike other sets of orthogonal functions, the eigenfunctions of G have the interesting property that also their associated basis spectra (“eigenspectra”) are orthogonal. Therefore, we refer to this novel scheme as the “conjugate orthogonal functions” (COF) approach. Beyond the utility of the COF approach for data evaluation and sensitivity analysis, it also represents a means for comparing systematically the analytic power of spectroscopic techniques. The nature of the information delivered by a particular technique (e.g., its symmetry), is reflected in the eigenfunctions of G, whereas the eigenvalues are related to the “amount” of information that can be extracted from spectra with a given signal-to-noise ratio. By way of example, the approach is applied to the determination of the distribution of dihedral angles in doubly 13C-labeled bisphenol-A poly(carbonate) by solid-state NMR spectroscopy, and experimental data from heteronuclear separated-local-field and double quantum two-dimensional (2-D) correlation experiments are compared.

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More information

Published date: 8 July 1998
Organisations: Chemistry, Faculty of Natural and Environmental Sciences, Magnetic Resonance

Identifiers

Local EPrints ID: 355589
URI: http://eprints.soton.ac.uk/id/eprint/355589
ISSN: 0021-9606
PURE UUID: f891a0c9-8c74-4b0a-8477-60d8ebadd891
ORCID for Marcel Utz: ORCID iD orcid.org/0000-0003-2274-9672

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Date deposited: 21 Nov 2013 14:33
Last modified: 17 Dec 2019 01:37

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