Long-Range Ordering in the Lyotropic Lamellar Phase Studied by High-Resolution Magnetic Resonance Diffusion-Weighted Imaging Kosma Szutkowski* and Stefan Jurga Department of Macromolecular Physics, Faculty of Physics, Adam Mickiewicz UniVersity, ul. Umultowska 85, PL61614 Poznan, Poland ReceiVed: July 28, 2009; ReVised Manuscript ReceiVed: NoVember 24, 2009 Diffusion-weighted magnetic resonance imaging (DW MRI) was applied to the lyotropic lamellar phase of the dodecylammonium chloride/water system (DDACl/H 2 O). In the course of employing a well-known medical imaging method, namely, diffusion tensor imaging (DTI), the system morphology was assessed accurately in the most straightforward way by two-dimensional visualization of eigenvectors associated with planar distribution of effective diffusion tensors throughout the whole slice with 40 μm in-plane resolution. Long- range order was observed in the studied lamellar phase, and morphology was best described by a combination of three- and one-dimensional diffusion. 1. Introduction The matter of sampling morphologies over several orders of magnitude, e.g., from nano- to microscale, is important as long as desired properties of a complex lyotropic system are under consideration. 1-4 Nowadays, a variety of “nano”applications have emerged due to numerous studies on diverse properties of amphiphile systems on a nanoscale. At the same time, a behavior on a microscale, such as long-range ordering, seems to attract less attention. Despite that, there are some interesting and appealing applications of such behavior. For example, optical properties are determined by a long-range orientational correla- tion, or simply long-range order, which renders them useful for novel applications such as optical display systems based on lyotropic chromonic liquid crystals (LCLCs). 5 A quantitative characterization and monitoring of amphiphilic morphologies in a wide range of scales and various conditions are essential and central though. If we consider the morphology on a nanoscale, we think of methods like small-angle X-ray scattering (SAXS), transmission electron microscopy (TEM), or atomic force microscopy (AFM). However, considering structures on elevated scales, the so-called diffusion tensor imaging (DTI) coupled with high-resolution NMR microimaging can be exploited to assess long-correlation features of a diversity of amphiphilic systems. 6-8 Long-range ordering and structural defects are in fact unambiguously analyzed by DTI, and in comparison with some classical “structural” methods, much more quantitative information is derived. One gets a precise spatial distribution of solvent diffusion anisotropy, related in a straightforward way to topological barriers such as smectic structures, double layers, platelates, micelles, and lamellas, thus affecting translational self-diffusion. Hence, DTI may fill a gap in the micro- and millimeter scale methods, especially when one is interested in the quantitative characterization of macroscopically ordered morphologies. As a model system for DTI investigation, a favorable sample was chosen. The sample was characterized by a relatively high water content, which assured sufficiently long transverse relaxation time T 2 of water. 2. Theory Calculation of Diffusion Tensors from Diffusion Maps. The chosen DTI scheme is based on prior calculation of apparent diffusion maps (ADC). Each diffusion map is calculated for a specific set of gradient vector directions. For the following directions, related to the principal axis system of the spectrom- eter, x, y, z, xy, xz, and yz, the elements of the diffusion tensor, D xx , D yy , D zz , D xy , D xz , and D yz , relate to ADCs as ADC xx ) D xx (1) ADC yy ) D yy (2) ADC zz ) D zz (3) ADC xy ) 1 2 D xx + 1 2 D yy + D xy (4) ADC xz ) 1 2 D xx + 1 2 D zz + D xz (5) ADC yz ) 1 2 D yy + 1 2 D zz + D yz (6) By using eqs 1-6, the diffusion tensors are calculated in a much more convenient way than in typical medical applications, where tensors due to time limitations are often estimated from the minimum possible number of scans. The other advantageous feature of this approach is the possibility of analysis of multicomponent diffusion, for example, due to two or more diffusion coefficients. Characterization of Diffusion Tensors. One of the possible ways of representation of diffusion tensors is an ellipsoidal approximation. A diffusion ellipsoid shows a distance in three dimensions which is likely to be covered by diffusing molecules. 9-11 The shape and orientation of the ellipsoid are thus crucial, especially for medical applications such as white matter tractography used for the early stage diagnosis of neurological diseases. 11 On the other hand, in nonmedical applications, it is not always necessary to visualize ellipsoids. Instead, ellipsoids are characterized by specific shape measures, and directional anisotropy can be determined through eigen- vectors e. The linear, planar, and spherical measures C l , C p , and C s are calculated from resorted eigenvalues such that λ 1 > λ 2 > λ 3 . 12 * Corresponding author. E-mail: kosma_sz@amu.edu.pl. J. Phys. Chem. B 2010, 114, 165–173 165 10.1021/jp9072087  2010 American Chemical Society Published on Web 12/17/2009