Hygroscopic study of hydroxypropylcellulose : Structure and strain-induced birefringence of capillary bridges.

The hygroscopic method developed previously for studies of lyotropic liquid crystals is used for the first time in experiments with millimetric capillary bridges made of a hydroxypropylcellulose/water mixture. Composition of such very small samples is controlled via humidity of the surrounding air. By a slow and well-controlled drying of initially isotropic samples, the isotropic/anisotropic phase transition is crossed and polydomain pseudo-isotropic capillary bridges are prepared. Kept in an atmosphere of constant humidity, these bridges are stretched and the strain-induced birefringence [Formula: see text] n is measured as a function of the draw ratio [Formula: see text] . The variation of [Formula: see text] n with [Formula: see text] is interpreted in terms of an affine uniaxial deformation of the initial pseudo-isotropic texture.

Generation of umbilics by Poiseuille flows.

The Fredericks transition in homeotropic nematic layers submitted to an electric field can be described in terms of a 2D vectorial order parameter [Formula: see text]. We have shown previously that umbilics which are point defects of the field [Formula: see text] can be generated in a controlled manner by magnetic fields. Here we report on a serendipitous discovery of generation of umbilics during cleaning of a sample and on a series of experiments which were performed with the aim to unveil conditions necessary for a controlled reproduction of this phenomenon. From the analysis of all circumstances in which umbilics were generated we conclude that umbilics are generated by Poiseuille flows and appear in π-walls in points where these walls are orthogonal to the flow direction. We discuss theoretical aspects of the action of Poiseuille flows on the field [Formula: see text] and unveil the relationship [Formula: see text]→ system π-walls. Finally we explain why and where umbilics are generated in π-walls.

Facets of lyotropic liquid crystals.

The bicontinuous lyotropic liquid phases surrounded by the isotropic phase form monocrystals with well-developed facets. We investigate the structure and stability of the facets formed by the bicontinuous phase of Pn3̅m symmetry, at three preferred directions, which are developed on a spherical droplet of Pn3̅m phase surrounded by the isotropic phase. The structure of the facets is obtained by minimization of the Landau-Brazovskii functional with one scalar order parameter.

Symmetry, topology and faceting in bicontinuous lyotropic crystals.

Phase diagrams of phytantriol/ethanol/water and phytantriol/DSPG/ethanol/water systems are explored and experiments on facetings of Pn3m-in-L1 and Im3m-in-L1 crystals are performed. Observed crystal habits do not agree with the Friedel-Donnay-Harker rules. We argue that this paradox can be explained in terms of constraints imposed on Pn3m/L1 and Im3m/L1 interfaces by the bicontinuous topology of the cubic phases. We point out that when free edges of the surfactant bilayer are prohibited at these interfaces, the two labyrinthes separated by the bilayer cannot anymore be equivalent. The corresponding [Formula: see text] and [Formula: see text] symmetry breakings are unveiled by the abnormal facetings.

Anisotropic surface melting in lyotropic cubic crystals: part 2: facet-by-facet melting at Ia3d/vapor interfaces.

From experiments with metal crystals, in the vicinity of their crystal/liquid/vapor triple points, it is known that melting of crystals starts on their surfaces and is anisotropic. Recently, we have shown that anisotropic surface melting occurs also in lyotropic systems. In our previous paper (Eur. Phys. J. E 19, 223 (2006)), we have focused on the case of poor faceting at the Pn3m/L1 interface in C12EO2/water binary mixtures. There anisotropic melting occurs in the vicinity of a Pn3m/L3/L1 triple point. In the present paper, we focus on the opposite case of a rich devil's-staircase-type faceting at Ia3d/vapor interfaces in monoolein/water and phytantriol/water mixtures. We show that anisotropic surface melting takes place in these systems in a narrow humidity range close to the Ia3d-L2 transition. As whole (hkl) sets of facets disappear one after another when the transition is approached, surface melting occurs in a facet-by-facet type.

Exploring the facets of "soft crystals" using an Atomic Force Microscope.

We obtained monocrystalline droplets in a thermotropic cubic phase, of approximate size 100 microm, deposited on a flat surface. The facets of these soft crystals are explored using both an optical microscope and an AFM. The height of individual steps on the principal facets and the lateral distance between steps in vicinal facets are measured using AFM in imaging (tapping) mode. Moreover, the elastic modulus is measured locally, using the AFM tip (in contact mode) as a local rheological probe.

Anisotropic surface melting in lyotropic cubic crystals. Part 1: Pn3m/L1 interface, poor faceting.

From experiments with ice or metal crystals, in the vicinity of their crystal/liquid/vapor triple points, it is known that melting of crystals starts on their surfaces and is anisotropic. It is shown here by direct observations under an optical microscope that this anisotropic surface melting phenomenon occurs also in lyotropic systems. In the case of C12EO2/water mixture, it takes place in the vicinity of the peritectic Pn3m/L3/L1 triple point. Above the peritectic triple point, where the Pn3m and L1 phases coexist in the bulk, the surface of a Pn3m-in-L1 crystal is composed of (111)-type facets surrounded by rough surfaces. The angular junction suggests that rough surfaces are wet by a L3-like layer while facets stay "dry". This is analogous to the pre-melting at rough surfaces in solid crystals. Upon cooling below the peritectic triple point, where L3 and L1 phases coexist in the bulk, a thick layer of the L3 phase grows from the pre-melted, rough Pn3m/L1 interface. Simultaneously, facets stay dry and their radius decreases. In this tri-phasic configuration, stable in a narrow temperature range, the L3/L1 and L3/Pn3m interfaces have shapes of constant mean curvature surfaces having common borders: edges of facets.

Steps and dislocations in cubic lyotropic crystals.

It has been shown recently that lyotropic systems are convenient for studies of faceting, growth or anisotropic surface melting of crystals. All these phenomena imply the active contribution of surface steps and bulk dislocations. We show here that steps can be observed in situ and in real time by means of a new method combining hygroscopy with phase contrast. First results raise interesting issues about the consequences of bicontinuous topology on the structure and dynamical behaviour of steps and dislocations.

Ratchet effect in faceting: a growth of perfect lyotropic crystals by temperature cycles.

The paper deals with a new phenomenon, named ratchet effect, envisioned theoretically as a likely consequence of metastability of crystal facets and expected to occur upon a temperature cycling. In experiments, Pn3m lyotropic crystals surrounded by the isotropic L1 phase in the mixture C(12)EO(2)/water are used. At equilibrium, the Pn3m/L1 interface contains small (111)-type facets in coexistence with rough surfaces. In agreement with theoretical expectations, it is shown that upon a saw-tooth-shaped temperature cycling, facets are growing until the rough surfaces are completely eliminated. A model of the ratchet effect is proposed.

Concave and convex shapes of the Pn3m/L1 interface.

Shapes of the interface between the L1 and cubic Pn3 m phases in the mixture C(12)EO(2)/water are studied. The concave and convex variants of the interface are realised using Pn3 m crystals surrounded by the L1 phase and L1 inclusions on surfaces and in the bulk of the Pn3 m phase. It is shown that both variants of the Pn3 m/L1 interface contain the (111)-type facets in coexistence with everywhere else rough surfaces. The matching between facets and curved parts of the interface is angular. In the vicinity of the upper limit of the L1 + Pn3 m coexistence domain, additional (200)-type facets appear on the interface. The influence of the contact angle at glass walls on shapes of crystals and of inclusions is discussed.

Ideal trefoil knot.

A set of self-contact points of the most tight, parametrically tied trefoil knot is determined. The knot is subjected to further tightening procedure based on the shrink-on-no-overlaps algorithm. Changes in the structure of the set of the self-contact points are monitored and the final form of the set is determined.

Devil's staircase-type faceting of a cubic lyotropic liquid crystal

The faceting of monocrystals of the lyotropic cubic liquid crystals in equilibrium with a humid atmosphere is observed. Experiments reveal the presence of more than 60 different types of facets on the surface of a spherical crystal of radius R = 1 mm. The devil's staircase type of faceting has been predicted theoretically when the interaction between steps on the crystal surface is repulsive.

Sedimentation and electrophoretic migration of DNA knots and catenanes.

Various site-specific recombination enzymes produce different types of knots or catenanes while acting on circular DNA in vitro and in vivo. By analysing the types of knots or links produced, it is possible to reconstruct the order of events during the reaction and to deduce the molecular "architecture" of the complexes that different enzymes form with DNA. Until recently it was necessary to use laborious electron microscopy methods to identify the types of knots or catenanes that migrate in different bands on the agarose gels used to analyse the products of the reaction. We reported recently that electrophoretic migration of different knots and catenanes formed on the same size DNA molecules is simply related to the average crossing number of the ideal representations of the corresponding knots and catenanes. Here we explain this relation by demonstrating that the expected sedimentation coefficient of randomly fluctuating knotted or catenated DNA molecules in solution shows approximately linear correlation with the average crossing number of ideal configurations of the corresponding knots or catenanes.

Properties of ideal composite knots.

The shortest tube of constant diameter that can form a given knot represents the 'ideal' form of the knot. Ideal knots provide an irreducible representation of the knot, and they have some intriguing mathematical and physical features, including a direct correspondence with the time-averaged shapes of knotted DNA molecules in solution. Here we describe the properties of ideal forms of composite knots-knots obtained by the sequential tying of two or more independent knots (called factor knots) on the same string. We find that the writhe (related to the handedness of crossing points) of composite knots is the sum of that of the ideal forms of the factor knots. By comparing ideal composite knots with simulated configurations of knotted, thermally fluctuating DNA, we conclude that the additivity of writhe applies also to randomly distorted configurations of composite knots and their corresponding factor knots. We show that composite knots with several factor knots may possess distinct structural isomers that can be interconverted only by loosening the knot.