Accurate determination of frequency dependent cross-relaxation terms in homonuclear and heteronuclear two spin-1/2 systems

Abstract

One-dimensional N.M.R. methods are proposed for accurately determining homo- and heteronuclear longitudinal cross-relaxation terms. These sequences employ exclusively hard pulses and do not require critical adjustments of the instrument even in the case of selective perturbation (inversion) of one magnetization in a homonuclear two-spin system. Emphasis is put on the initial conditions which prevail at the beginning of the relaxation interval; they are determined by means of adequate experimental or numerical procedures. An algorithm, based on analytical solutions of Solomon equations, is described; it allows to analyse as many sets of data as desired for arbitrary initial conditions. These methods have been applied to the ¹H-¹H spin system of ortho protons in an aromatic ring, which bears in para positions the polar head and the aliphatic chain of benzene-sulphonate surfactants. Proton homonuclear cross-relaxation parameters are complemented by heteronuclear carbon-proton parameters and classical carbon-13 longitudinal relaxation rates. Measurements have been performed at several frequencies and allow to delineate dynamical features of two surfactants which differ by their alkyl chains. Results are discussed in terms of slow and fast local motions, and of order parameters relative to the benzenic ring.