The Structural Fingerprint in Lyotropic Mesophases by the Use of Inverse Laplace Transform Applied to PGSE NMR Data

Abstract

We present a theoretical study of the potentialities of the Inverse Laplace Transform when applied to Pulsed Gradient Spin Echo NMR data from water in lyotropic liquid crystalline mesophases. This mathematical application should be able to produce structural information about the studied systems by the determination of the self-diffusion coefficient distribution, giving in this way a significant fingerprint of the molecular organisation in lamellar and reverse hexagonal phases. The critical point of finding the best algorithm to treat the data has been faced: several numerical methods have been tested comparing the performances of the different algorithms with results predictable by theory.