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We deal with the genesis and decay of knots and links made of dislocations in a cholesteric layer confined in the gap between orthogonal cylindrical mica sheets. The genesis starts by nucleation of folded unknots driven by a compressive strain. The nucleation process of the trivial and folded unknots is studied and discussed in detail. We show that the expansion of the folded unknots leads to their lateral collisions followed by the coalescence into the torus knots, such as the trefoil knot, or into the links, such as the Hopf and Solomon links. The viscoelastic decays of knots and links follow well-defined paths involving topological and geometrical transformations. In particular, the symmetric configuration of the Hopf link is unstable with respect to the shrinking of one of its interlaced loops. The final asymmetric configuration, made of a minimal loop tethered on a large cargo loop, is called the Hopf necklace. Similarly, the double Hopf necklace is obtained by the elastic decay of the Solomon link. We emphasise that Hopf necklaces of various orders are quite ubiquitous. [ABSTRACT FROM AUTHOR]

We deal here with three metastable systems: 1° – the dowser texture, 2° – supertwisted cholesterics and 3° – hypotwisted cholesterics. We outline remarkable properties of the tropisms of the dowser texture stemming from its low symmetry, and we show that, using setups called Dowsons Colliders, nematic monopoles can be nucleated, set into motion and brought into collisions in the dowser texture. Subsequently, we point out that nucleation of dislocation loops occurs in cholesteric layers compressed or dilated between cylindrical mica sheets. Under compression, three modes of nucleation of dislocation loops have been identified: individual, serial and continuous. The serial mode generates dislocation nets made of L circular loops connected by C radial crossing into superloops. Similar superloops can also be generated under dilation. We analyse the topology of superloops in terms of the theory of knots and point out that they can be reduced to the unknot by Reidemeister moves. In other words, superloops are multiply folded loops that can be continuously unfolded. [ABSTRACT FROM AUTHOR]

Abstract.: 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 $ \Delta$ n is measured as a function of the draw ratio $ \lambda$ . The variation of $ \Delta$ n with $ \lambda$ is interpreted in terms of an affine uniaxial deformation of the initial pseudo-isotropic texture. Graphical abstract: [ABSTRACT FROM AUTHOR]

Abstract.: The Fredericks transition in homeotropic nematic layers submitted to an electric field can be described in terms of a 2D vectorial order parameter $\vec c$ . We have shown previously that umbilics which are point defects of the field $\vec c$ 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 $\vec c$ and unveil the relationship $\vec c$ → system π-walls. Finally we explain why and where umbilics are generated in π-walls. Graphical abstract: [ABSTRACT FROM AUTHOR]

Umbilics in a nematic layer can be seen as topological defects of a complex order parameter. Being analogous to vortex lines in superfluids or superconductors, they are much easier to handle. We describe classroom experiments on controlled generation of umbilics in a nematic layer with homeotropic anchoring conditions submitted to an electric field. For this purpose we submit nematic samples to magnetic fields created by small NdFeB magnets. Umbilics induced by applied fields are unveiled by observation between crossed polarisers in monochromatic or white light. We report also on the winding action of rotating localised magnetic fields and on the winding reversal induced by Poiseuille flows. [ABSTRACT FROM PUBLISHER]

In 1982, P. G. de Gennes wrote two articles on two apparently disjoined subjects: (1) the Ludwig-Soret effect in porous media filled with pure liquids and (2) bicontinuous structures in microemulsions. In the study of bicontinuous cubic lyotropic crystals subjected to temperature gradients which we present here, these two subjects are now intimately related. Our experiments consist of the observation, by means of an optical microscope, of crystal shapes in three types of phase coexistence: Ia3d-in-vapour, Pn3m-in-L1 and Im3m-in-L1. In all three cases, we infer from changes in the crystal shapes that the surfactant is transferred, along the unique periodic bilayer, from the warm to the cold extremities of crystals. In order to explain this phenomenon of 'thermopermeation' of the surfactant, inspired by de Gennes we assume that: (1) the periodic bilayer acts as a viscoelastic matrix and (2) a slip occurs at the surfactant/water interface. [ABSTRACT FROM AUTHOR]

The dynamics of the tip of a falling chain is analyzed. The results of laboratory experiments are presented and compared with the results of numerical simulations. The time dependence of the velocity and the acceleration of the chain tip for several initial conformations of the chain are determined. A simple analytical model of the system is also considered. [ABSTRACT FROM AUTHOR]

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 C12EO2/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. [ABSTRACT FROM AUTHOR]

Shapes of the interface between the L1 and cubic Pn3m phases in the mixture C12EO2/water are studied. The concave and convex variants of the interface are realised using Pn3m crystals surrounded by the L1 phase and L1 inclusions on surfaces and in the bulk of the Pn3m phase. It is shown that both variants of the Pn3m/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 + Pn3m 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. [ABSTRACT FROM AUTHOR]

The discovery of a cholesteric liquid crystalline phase in concentrated aqueous solutions of (hydroxypropyl)cellulose (HPC) dates back to the 1970s. Due to its biocompatibility, low cost and ease of conversion to fibres and films, HPC is still the target of numerous studies. In this article, some of the properties of the HPC/water lyotropic system are reviewed, and original results describing a humidity-generated instability on HPC fibres are presented. The use of HPC films which respond to external stimuli is highlighted. In particular, novel applications include the manufacture of soft motors driven by a difference of humidity, and the production of electro-optical cells when the solid films are used in conjunction with low molecular mass thermotropic mesogens. [ABSTRACT FROM AUTHOR]

In lyotropic systems, four different isotropic phases may coexist with several cubic phases having different topologies and/or symmetries. We review here faceting phenomena, rising new conceptual issues, that have been recently found to occur at different cubic/isotropic interfaces: 1°- depending on their tension, these interfaces can be either rich or poor in facets or even completely rough, 2°- when facets coexist with rough surfaces, facets can grow due to the redistribution of the surfactant in the crystal, 3°- upon a temperature cycling, ratchet-like growth of facets, until an elimination of rough surfaces takes place, 4°- asymmetric crystal shapes are induced by temperature gradients, 5°-rough surfaces “melt” prior to facets that stay “dry”. [ABSTRACT FROM AUTHOR]

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 $ {\rm Pn3m}\rightarrow {\rm Fd3m}$ and $ {\rm Im3m}\rightarrow {\rm Pm3m}$ symmetry breakings are unveiled by the abnormal facetings. Graphical abstract: [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

The curvature and torsion profiles of the tight trefoil knot found with the SONO algorithm are analysed. Their characteristics are discussed. Comparison of curvature and torsion profiles with the tightest parametrically defined knot is performed. [ABSTRACT FROM AUTHOR]

We obtained monocrystalline droplets in a thermotropic cubic phase, of approximate size 100μm, 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. [ABSTRACT FROM AUTHOR]

The production of fibres and films with enhanced mechanical properties, from liquid crystalline cellulose-based systems, has always been a challenge. Previous works indicate that the use of spinning and electrospinning allows the fabrication of non-woven membranes with optical and mechanical characteristics distinct from casting films. The subsequent interactions of the micro/nanofibres inside membranes can modify their topology and geometry so they are found crucial for tuning the membranes' properties. In this work, we deal with the evolution of networks made of highly stretched liquid filaments. Three main mechanisms were identified: the thinning of filaments feeding growing nodes, breaking of the thinner filaments before the thicker ones and the zipping of pairs of filaments crossing at small angles. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We examine the vibration spectrum of smectic films both experimentally and theoretically. We show that the main energies involved in the dynamics are the capillarity, the stretching energy, when the films are curved, and the viscous dissipation between layers. We propose a theoretical treatment of the resonance spectrum for the family of the catenoid. When the capillarity plays the dominant role (smectic A or smectic C phase), there exists a continuous family of isospectral surfaces. When the film has some elasticity (smectic B phase), we predict a deviation of the resonances governed by the Gaussian curvature. [ABSTRACT FROM AUTHOR]