N.M.R. lineshapes from quadrupolar nuclei in biaxial lyotropic structures

The appearance of the N.M.R. spectrum of a quadrupolar nucleus in a lyotropic liquid crystal reflects the molecular organization in the surfactant aggregates. In particular, the spectral lineshape is a sensitive probe of deviations from circular cross-section in rod-like aggregates. This circumstance has been exploited by Chidichimo, Doane et al. to characterize the so-called ribbon phase, using a model based on the assumption that the aggregates are built from lamellar and hemi-cylindrical sections. In this work, we present an alternative model based on an elliptic-rod geometry. Using this model, we relate the N.M.R. observables to the eccentricity of the cross-section and to the inhomogeneity in the local orientational order and the molecular distribution. The two models differ mainly in two respects: (i) the elliptic geometry does not have the unphysical curvature discontinuity of the ribbon geometry, and (ii) unlike the ribbon model, the elliptic model can always distinguish between effects of aggregate shape and molecular segregation.