Resolving complex mixtures by means of pulsed gradient spin-echo NMR experiments

We present a method to analyse pulsed gradient spin-echo (PGSE) NMR data from a mixture of compounds sharing the same NMR resonance (e.g. polymer solutions or mixtures of aliphatic compounds). If all the spin-bearing species undergo Brownian motion, their contribution to the experimental echo decay is exponential (i.e. e(-sD), with s a function of the parameters of the PGSE-NMR experiment and D the self-diffusion coefficient). For the case of more than one diffusing species at a given chemical shift, the (normalized) echo attenuation is the Laplace transform of the distribution function of the self-diffusion coefficients. The Laplace transform can be reduced to a Fredholm integral equation of the first kind in the variable z proportional to e(-sD) (in the interval [0,1]). Applying the algorithm previously developed by us (L. Ambrosone, A Ceglie, G. Colafemmina and G. Palazzo, J. Chem. Phys. 1999, 110, 797) we solve the integral equation, obtaining the distribution function of the diffusion coefficients. The method is tailored for small data sets (10-30 points) typical of PGSE-NMR measurements. Moreover, the relevant variable (z) being an exponential function of the self-diffusion coefficient, it allows insight on the ne structure of the diffusion spectrum. The method was successfully tested on a three-component solution and on an aqueous solution of seven PEG oligomers. In the latter case an estimate of the molecular mass distribution function was obtained. The reported results indicate that such an approach permits determination of self-diffusion coefficients differing by 15% with a high accuracy (6-3%).