A NEW TECHNIQUE FOR STUDYING MICROSTRUCTURES : 2H NMR BANDSHAPES OF POLYMERIZED SURFACTANTS AND COUNTERIONS IN MICROSTRUCTURES DESCRIBED BY MINIMAL SURFACES

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Abstract
The polymerization of bicontinuous cubic and, in particular, aligned intermediate phases provides a new way to use NMR to study and characterize these microstructures. The computation of the 2H NMR bandshape for a polymerized, deuterated surfactant or counterion in an aligned cubic or intermediate phase is given here for many model microstructures. The calculation applies over the whole volume fraction range defined by the family of parallel surfaces. The polymerization of the surfactant (which has been performed in a cubic phase without inducing change in the SAXS pattern or optical isotropy) prevents the self-diffusion of the surfactant and, since the distribution of normal directions over a surface parallel to a minimal surface does not cover the sphere uniformly, the NMR bandshape will not be a delta function nor a Pake pattern. Instead, this bandshape will be a distinctive signature of the structure. Using the expressions for the Gauss map and Gaussian curvature of the underlying minimal surface in the isothermal coordinates of the usual Weierstraß representation, the expected bandshape can be computed in terms of elliptic integrals. The computation of this bandshape is demonstrated in the case of the family of minimal surfaces which includes the CLP, Scherk, G, D, and P minimal surfaces, and for rhombohedral and tetragonal relatives of the P and D surfaces. The latter surfaces would seem to provide particularly good models for the intermediate phases of rhombohedral and tetragonal symmetry

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