Jean Charvolin

Structural fluctuations in the lamellar phase of sodium decyl sulphate/decanol/water

Abstract We present a neutron scattering study of oriented samples for the lamellar phase of the ternary mixture sodium decyl sulphate/1-decanol/water. Diffuse scatterings are observed, around the Bragg reflections and away from them, which show that the structure of this lamellar phase deviates from the periodic stacking of infinite homogeneous lamellae of water and amphiphilic molecules usually proposed for the structure of lamellar phases. The nature of this deviation evolves with the soap/decanol ratio, according to the location of the sample in the lamellar domain of the phase diagram. In the middle of the domain the deviation relates to the organization of the lamellar stacking, without apparent modification of the structure of the lamellae of amphiphiles. Moving away from the middle, for higher soap/decanol ratios, the structure of the lamellae appears to be randomly perturbed, eventually by the presence of a few water regions piercing them. When the boundary of the lamellar domain is approached, f...

Deformation of cylinders in the hexagonal phase of sodium decyl sulphate/decanol/water on the introduction of decanol

Abstract X-ray scattering studies show that aggregates of amphiphilic molecules in the hexagonal phase of the binary system sodium decyl sulphate/water are infinite cylinders whose radius is very close to that of the extended molecule. When sodium decyl sulphate molecules are progressively substituted by decanol molecules the phase remains hexagonal, up to a decanol/soap molar ratio of 0.15, but the radius of its cylinders becomes larger than the molecular length. We have developed specific experiments to investigate this growth and see if it is isotropic or anisotropic. We have focused our attention on the evolution of the configuration of soap and decanol molecules within the aggregates. Neutron scattering experiments show that the two molecules do not distribute themselves uniformly and D.M.R. measurements show that they stay anchored at the amphiphile/water interface by their polar heads. The distribution of the two molecules along the interface is not therefore uniform. This induces an inhomogeneity ...

An X-ray scattering study of the lamellar/nematic/isotropic sequence of phases in decylammonium chloride/H2O/NH4Cl

Abstract An X-ray scattering study is presented of the lamellar/nematic/isotropic sequence in the lyotropic system DACI/H2O/NH4Cl. The whole reciprocal space of monocrystalline samples oriented in magnetic fields are reconstructed from their two dimensional sections on photographic films. Intense diffuse scatterings are observed in the lamellar phase, around and away from the Bragg spots. Their evolution close to the lamellar/nematic transition reveals the presence of intense structural fluctuations. They take place over temperature ranges which are significantly greater than those associated with the smectic/nematic transitions in thermotropic liquid crystals. A similar situation is observed in the isotropic phase in the vicinity of the nematic/isotropic transition.

The Heterogeneity of Chain Lengths, A Factor in Lyotropic Polymorphism

Abstract The paraffinic medium of the lamellar phase. of a potassium soap is perturbed by introducing a soap with a different chain length, while the water content of the phase is kept constant. Structural changes are observed which depend upon the concentration and the length of the solute soap.

Structural phase transformations induced by the addition of decanol to the hexagonal phase of the binary sodium decyl sulphate/water system

Abstract The hexagonal phase of the sodium decyl sulphate/water system transforms into a lamellar phase on the introduction of decanol. This transformation occurs in several steps. We present here a study of the sequence of the corresponding phase transformations. The various phases are identified according to their textures by optical microscopy. It can be seen that, as the decanol/soap ratio increases the two dimensional hexagonal phase is followed by two dimensional rectangular phases before the one dimensional lamellar phase is reached. The symmetries of the structures of the phases and the shapes of their aggregates of amphiphilic molecules were determined by small angle X-ray and neutron scattering studies (SAXS and SANS). Two rectangular phases with cmm and pgg symmetries show up successively between the hexagonal and lamellar phases. The shape of the aggregates evolves along the sequence in an unexpected manner. In the two dimensional hexagonal phase, the aggregates are cylinders with an isotropic...

From Micelles to Liquid Crystals

Abstract Recent characterizations of aggregates of amphiphilic molecules in nematic phases of some amphiphiles/water phase diagrams gives new insight into the aggregation process. Thermo-dynamical models are being re-considered. We shall present some developments proposed to account for observations in the system sodium decyl sulfate/decanol/water.

Phyllotaxis on surfaces of constant Gaussian curvature

A close-packed organization with circular symmetry of a large number of small discs on a plane is obtained when the centres of the discs are distributed according to the algorithm of phyllotaxis. We study here the distributions obtained on surfaces of constant Gaussian curvatures, positive for the sphere or negative for the hyperbolic plane. We examine how the properties of homogeneity, isotropy and self-similarity, typical of the distribution on the plane and resulting from the presence of circular grain boundaries with quasicrystalline sequences, are affected by the curvature of the bearing surface. The quasicrystalline sequences of the grain boundaries appear indeed to be structural invariants, but the widths of the grains they separate vary differently with the curvature of the surface. The self-similarity of the whole organization observed on the plane is therefore lost on the hyperbolic plane and the sphere. The evolutions of the local order within the grains show no differences except on the equatorial belt of the sphere where the isotropy is decreased owing to the symmetry of this finite surface around its equator.

X-ray diffraction and deuterium N. M. R. of the lyomesophases of dipotassium hexadecanedioate–water mixtures

Abstract Mixtures of water and the dipotassium thapsate form hexagonal and lamellar lyomesophases with structures similar to those found for monosoaps. X-ray diffraction from a high intensity synchrotron radiation source exhibits the first four reflections of the hexagonal phase and the first two from the lamellar phase yielding lattice parameters of about 28 A and 22 A, respectively. Within the stability range of the mesophases these parameters do not vary significantly with the disoap concentration and the temperature. An intermediate phase, found previously at about 120°C between the hexagonal and the lamellar phase was shown to be an isotropic liquid rather than a cubic mesophase. Combined X-ray diffraction and N. M. R. experiments on magnetically aligned samples showed that the lamellar and hexagonal phases have respectively negative and positive anisotropic magnetic susceptibilities. Samples which are allowed to equilibrate in the isotropic-mesophase boundary region for several hours, in the absence...

Phyllotaxis: a non-conventional crystalline solution to packing efficiency in situations with radial symmetry

Phyllotaxis, the search for the most homogeneous and dense organizations of small disks inside a large circular domain, was first developed to analyze arrangements of leaves or florets in plants. Then it has become an object of study not only in botany, but also in mathematics, computer simulations and physics. Although the mathematical solution is now well known, an algorithm setting out the centers of the small disks on a Fermat spiral, the very nature of this organization and its properties of symmetry remain to be examined. The purpose of this paper is to describe a phyllotactic organization of points through its Voronoi cells and Delaunay triangulation and to refer to the concept of defects developed in condensed matter physics. The topological constraint of circular symmetry introduces an original inflation-deflation symmetry taking the place of the translational and rotational symmetries of classical crystallography.

A PHYLLOTACTIC APPROACH TO THE STRUCTURE OF COLLAGEN FIBRILS

Collagen fibrils, cable-like assemblies of long biological molecules, are dominant components of connective tissues. Their determinant morphological and functional roles motivated a large number of studies concerning their formation and structure. However, these two points are still open questions and, particularly, that of their organization which is certainly dense but not strictly that of a crystal. We examine here how the algorithm of phyllotaxis could contribute to the analysis of the structure of collagen fibrils. Such an algorithm indeed leads to organizations giving to each element of the assembly the most homogeneous and isotropic dense environment in a situation of cylindrical symmetry. The scattered intensity expected from a phyllotactic distribution of triple helices in collagen fibrils well agrees with the major features observed along the equatorial direction of their X ray patterns. Following this approach, the aggregation of triple helices in fibrils should be considered within the frame of soft condensed matter studies rather than that of molecular crystal studies.