Last updated on September 4, 2001


R.J. ATKIN
(University of Sheffield)
Static domain wall solutions for smectic C liquid crystals
In this paper the continuum theory for smectic C liquid crystals proposed by Leslie et al [Mol. Cryst. Liq. Cryst. 198, 443-454, (1991)] is used to discuss static domain wall solutions in infinite samples. Following a review of the Cartesian case, attention is restricted to an infinite sample of concentric, cylindrical layers arranged with a fixed inner radius. In the absence of an applied field, a solution similar to the one given by Schiller et al [Liq. Crystals, 2, 21-30, (1987)] is found. Various estimates on the relative magnitudes of the smectic elastic constants lead to physically meaningful stability results. When an azimuthal magnetic field is applied the situation is more complex. Various critical fields are obtained. The application of the results to the possible experimental determination of some of the elastic constants is discussed.



F. BISI
(Politecnico di Milano)
Curvature effects on membrane-mediated interactions of proteins
We study the interactions of lipid-membrane-embedded proteins pictured as rigid inclusions. We determine the exact shape of the membrane by means of a two-dimensional model and compute the mediated forces on proteins as a function of their distance along the membrane. When two proteins are embedded in a membrane, the mediated force exhibits features depending on the relative orientations of the inclusions and the membrane, as well as on the size of the inclusion and other parameters; in configurations with asymmetric orientations, non-trivial optimal distances between the proteins can be found. In some other cases, too, a critical value of such a distance is found, although unstable. The force does not vanish even if each protein is positioned symmetrically across the membrane. Moreover, the shape of the system appears to be strongly affected by the type of configuration, and the other variables, which shows that a closed-geometry model is useful in order to give a complete picture of these systems, being able to show features that might escape the classic approach based on the analysis of linearized models in three dimensions.



H.R. BRAND, P.E. CLADIS, and H. PLEINER
(University of Bayreuth)
Physical properties of fluid biaxial smectic phases: selected recent developments
In this survey, we review the symmetry-based macroscopic classification, hydrodynamics and phase transitions of smectic as well as biaxial nematic banana (and dolphin) phases. Banana-shaped molecules can order spontaneously in smectic superstructures such that the geometrically preferred molecular axes give rise to a macroscopic polarization. Depending on the orientation relative to the smectic layers (untilted, tilted about a non-polar or about the polar axis, tilted about two axes) various phases are possible. The polarization can be 1-,2-, or 3-dimensional with components in, or across, the layers. Some of the phases possess a handedness (spontaneous twist) that is geometrical in nature and does not result from molecular shapes, thus allowing both types of handedness to occur (ambidextrous phases). These low symmetry smectic phases still bear a lot of interesting scientific questions, e.g. regarding defect structures and phase transitions. Quite recently, dolphin phases came into consideration. There, two polar axes give rise to low symmetry phases even without tilt or with only one tilt. In principle, biaxial nematic phases made of banana and dolphin molecules are a possibility, although up to date, no such phase has been identified experimentally with certainty. The low symmetry phases shown above come in several modifications (e.g. eight for CG), differing by the orientation of the polarization and/or by the handedness. Stacking such different modifications one can get a host of globally ferro- and antiferroelectric phases with and without a helix. Thus the global symmetry of those heterogeneously stacked phases can be different from the local one. Helix-free ferroelectric phases seem to be very interesting for fast-switching devices, especially when the rotation of the polarization occurs within a layer plane with only minimal changes of the smectic layer spacing.



B. FOURCADE
(Université J. Fourier, Grenoble)
Membrane coated with polymers: from soft condensed matter to bio-adhesion



J.-B. FOURNIER
(ESPCI, Paris)
Coarse-graining of soft-matter interfaces
I shall discuss how large-scale effective elastic theories can be inferred from more microscopic descriptions through a coarse-graining procedure. This line of analysis reveals: (i) universal features of the anchoring of nematic liquid crystals close to their isotropic bulk transition; (ii) applied to surfactant bilayers, it yields a clear and operational definition of the somewhat obscure concept of "effective membrane tension".



P. GALATOLA
(Université Paris 7)
Elastically-mediated anisotropic interactions in colloids
Colloidal suspensions are dispersions of small particles or liquid droplets in a host fluid. They are long-lived metastable states of considerable technological importance and of fundamental interest from the point of view of collective interactions in complex matter. We will discuss two novel non-trivial examples of anisotropic interactions mediated by the elasticity of the host fluid: colloidal particles embedded in the isotropic phase of a nematogenic liquid, that interact because of a wetting nematic layer induced by their surface, and particles trapped at a liquid-fluid interface, that interact because of the pinning of their contact lines.



E.C. GARTLAND, A.M. SONNET, and E.G. VIRGA
(Kent State University)
Elastic forces on nematic point defects
We present a general method to compute the elastic forces on nematic defects. It is derived from a dissipation principle and relies only on the director field in a neighborhood of a defect. It is valid in both equilibrium and non-equilibrium settings. We have applied it to study the force of attraction between a hedgehog/anti-hedgehog defect pair in a capillary. Our results validate other works and provide extensions and new aspects. We will discuss these as well as present details of the numerical modeling.



S. HESS
(Technische Universität Berlin)
Modelling plastic flow of soft solids
The methods of Non-Equilibrium Molecular Dynamics (NEMD) computer simulations previously used to study the flow properties of liquids and liquid crystals are adopted to the treatment of plastic flow in solids. The modelling of the materials, including colloidal crystals and metals, by simple potentials and by the embedded atom method are discussed. The response of the soft solid to shear deformations, in particular the transition from elastic behavior to plastic flow, as inferred from the NEMD simulations, is analyzed. An analytical model describing this transition is proposed. Furthermore, the yielding under a compressional load is studied. Shear-induced structural changes are observed and presented graphically. The importance of these phenomena for the friction between solids is indicated.



S. KRALJ, Z. BRADAC, S. ZUMER, and E.G. VIRGA
(University of Maribor)
Kinetics of defects in confined nematic liquid crystals
We study statics and dynamics of nematic defects in confined geometries. Using the Landau de Gennes approach we first investigate the field influence on the detail biaxial structure of a nematic point defect of a topological charge M=1. The cylindrically symmetric field used in the study is either caused by a global external electric field or a localised surface anchoring field. The field induced hysteresis of the uniaxial ring characterizing the point defect structure is calculated. Then we proceed to a biaxial annihilation scenario of a pair nematic monopole-antimonopole within a cylindrical tube. We distinguish between the precollisional and postcollisional regime. In the later regime, which we study in detail, the biaxial structure of interacting defects strongly overlap and gradually decays in to the defectless uniaxial state. In the second part we study the evolution of a nematic texture after a sudden quench from the isotropic phase. The semi-microscopic induced dipol-induced dipole type model is used. The dynamic evolution is monitored using molecular Brownian dynamics. We focus to the scaling growth of an average domain size and explore analogy with similar phenomena in cosmology.



M. KLÉMAN
(Université Paris 6)
Defects in a TGBA liquid crystal phase: optical observations, theory
We report on optical observations of nontrivial pretransition phenomena evidenced by defects transformations at the cholesteric (N*) ´ smectic A (SmA) transition in cholesteryl nonanoate (CN), in two geometries: films with degenerate anchoring conditions, free suspended droplets with tangential director conditions on their surface. The defects observed in CN are akin into all the details to those of a tolane compound, T10, a material known to have a helical SmA phase (also termedTGBA). TGBA's, which are frustrated chiral phases and in fact liquid crystalline analogs of Abrikosov phases, have been already under study for 10 years,but yet little investigated for the nature of their defects. Our purpose is precisely, on the basis of a comparison between the defects textures in CN, T10, CM (cholesteryl myristate), and chiralized 8CB, a)-to conclude to the similar nature of the phase transitions in CN and T10, different from those in the two other materials., b)- to characterize novel defects, proper to the TGBA phase. They certainly bear a resemblance to defects in N*, but carry definite differences, which will be discussed in the light of the topological theory of defects.



P.L. MAFFETTONE
(Politecnico di Torino)
Complex dynamics in sheared liquid crystalline polymers
A rheological model for rodlike polymers in the nematic liquid crystalline phase is analysed to characterise irregular dynamical response under shear flows. The model is studied with a continuation approach, and a period doubling scenario is detected. Time series generated via simulation are studied with nonlinear analysis tools to prove the existence of chaotic regime. Similar irregular dynamics have been found experimentally in the same parameter region.



G. IANNIRUBERTO and G. MARRUCCI
(Università Federico II, Napoli)
Molecular models for the rheology of polymer melts
In recent times the well known Doi-Edwards theory for entangled polymers has been augmented by including the mechanism of convective constraint release(CCR),which improves on the problem of excessive shear thinning at moderate to high shear rates predicted by the classical theory. Mead et al. have proposed a model that also accounts for chain stretching, which takes place at even higher shear rates, i.e., in flows faster than the reciprocal Rouse time. Here we present a different way of accounting for chain stretching, based on considerations previously developed for a simple dumb bell model. Without adding further parameters to the basicCCR model, the constitutive equation proposed here seems to predict correctly the nonlinear rheological response in a variety of situations, ranging from step strains to transient and steady shear and elongational flows.



T. BIBEN and C. MISBAH
(Université J. Fourier, Grenoble)
Nonequilibrium vesicle dynamics
We discuss some nonequilibrium phenomena of vesicles under shear flow. We first present the boundary integral formulation, and analyze some general features:
(i) We show that a vesicle moving on an adhering wall in an external force obeys a nontrivial migration law as function of its size.
(ii) We show numerically and analytically that a vesicle which is initially adhering to a substrate experiences a hydrodynamical lift force of viscous nature, in contrast to the well known lift force of Magnus which is responsible for balls deviation. We provide a universal form of the lift force.
(iii) In the presence of a viscosity contrast between inside and outside, the vesicle undergoes tumbling in a similar fashion as for red blood cells. For a swelling factor of the order of that of a red blood cell, the tumbling occurs when the viscosity inside is of about 7 times that of the fluid outside. Surprisingly this ratio is close to that of a red cell viscosity over the blood plasma one. We introduce a new method, the advected field approach, is much superior to the usual boundary integral formulation. This method allows to handle various problems such as the one where a vesicle is filled with complex fluids and where the determination of a Green function is the exception rather than the rule. We discuss various far-reaching consequences offered by the advected-field approach in many biological and rheological problems.



N. MOTTRAM
(University of Strathclyde)
Flexoelectric switching in bistable nematic cells



M. OSIPOV
(University of Strathclyde)
Orientational ordering, chiral structures and formation of superlattices in organic monolayers



R. ROSSO
(Università di Pavia)
Stability of lipid membranes: handle with care



T. SLUCKIN and R.J. ATKIN
(University of Southampton, University of Sheffield)
The life and work of Frank Leslie (1935-2000)
The Ericksen-Leslie equations generalise the Navier-Stokes equations to describe nematic liquid crystals. They represent a landmark in the application of continuum theory to complex fluids, and immortalise Frank Leslie, who died on June 15, 2000. In this talk we shall combine a brief history of continuum approaches to liquid crystal problems with an overview of the life and work of Frank Leslie.



E. VICENTE ALONSO, A.A. WHELLER, D.R.J. CHILLINGWORTH, and T. SLUCKIN
(University of Southampton)
Non-linear dynamics of nematic liquid crystals in the presence of a shear flow
We examine the behaviour of the Olmsted-Goldbart generalisation of dynamic Landau-de Gennes theory in the control space of shear rate and temperature, using computational and analytic methods. If the space of solutions is restricted to the set which are symmetric under reflection in the shear plane, we find a stable in-plane nematic state at higher temperatures, which gives way to the so-called log-rolling state at low temperatures. A Takens-Bogdanov bifurcation in the underlying bifurcation diagram organises the steady-state and periodic solutions in the state diagram. The periodic solutions latter may be of the tumbling type (for low shear rates) or of the wagging type (at higher shear rates), and these types are seen to be qualitatively similar. We also allow symmetry-breaking states (so-called kayaking orbits) and undersome circumstances a period-doubling bifurcation is found. The model appears however to be structurally unstable because the only out-of plane steady solution is an anomalous continuum of equilibria.



A.M. SONNET
(Università di Pavia)
Balance of angular momentum in the presence of microstructure



H. STARK
(Universität Konstanz)
A Poisson-bracket approach to the dynamics of liquid crystals
The Ericksen-Leslie (EL) equations for the velocity and director field of a nematic liquid crystal are derived from the respective balance equations of the momentum and angular momentum based on methods of rational thermodynamics. There seemed to bea debate how the angular momentum balance is applicable as a dynamic equation for the director. Using rigorous ideas of hydrodynamics, which regards the director as a broken-symmetry variable, the Harvard group formulated a set of equations which is identical to the linearized EL equations.
In this talk I present the Poisson-Bracket formalism as a method to address the dynamics of both hydrodynamic and quasi-hydrodynamic fields. It is demonstrated that the EL equations are exactly reproduced. Furthermore, the Poisson-Bracket formalism naturally leads to a set of dynamic equations involving the symmetric and traceless alignment tensor field Q which is important for all cases where the liquid crystalline order becomes biaxial or possesses a non-uniform degree of ordering. I show first results of a numerical problem involving the Q-tensor dynamics.



I. STEWART
(University of Strathclyde)
Backflow in planar layers of ferroelectric smectic C: switch-on times and relaxation effects
Analytical and numerical results are presented for the switch-on and relaxation of a ferroelectric smectic C* liquid crystal cell under the application or removal of an electric field. For the equilibrium states for high and low DC applied field strengths the director relaxation to the zero field equilibrium state is seen to induce flow of the liquid crystal which incorporates backflow and kickback effects.



S. SVETINA, B. BOZIC, and B. ZEKS
(University of Ljubljana)
Shapes of membranes constrained by cellular walls
Some unicellular organisms such as fission yeast grow in either one or two directions in a way that their cell walls attain the shape approximately described by a tube with rounded ends. We follow the hypothesis that the requirement for the cell wall growth is its contact with the plasma membrane. We are therefore interested in the shape of a membrane constrained in a solid cage formed by the cellular wall, whereby the plasma volume is smaller than the volume of the cage, and the membrane can contact the wall only partially. In general, the shape of a closed membrane depends on the membrane elastic energy and on the forces acting on the membrane.Membrane shapes are theoretically determined by assuming that they correspond to the minimum of the energy functional comprising the corresponding elastic energy and potential energy terms. The formulation of the problem consists in the derivation of the corresponding Euler-Lagrange equations and the boundary conditions that apply for the boundaries between membrane domains which are and which are not in contact with the wall. For the shape of the cell wall we choose a simple axisymmetrical body exhibiting the equatorial mirror symmetry. We are limiting our studies to membrane shapes in which the membrane is in contact with the wall at least at its poles. For the membrane elastic energy it is assumed that it consists of an area expansivity energy, the local and non-local bending energies, and the surface tension energy contribution.It is also taken into consideration that the membrane and the wall interact at their contact areas, and that the osmotic equilibrium is established between the external and internal solutions giving rise to the pressure difference across the membrane. The consequent shapes are predicted for cells of different volumes, and for different values of the membrane lateral tension and relevant elastic constants. Membrane shapes are analyzed with the particular emphasis on their symmetry properties.



E. TERENTJEV
(University of Cambridge)
Nematohydrodynamics and anomalous viscoelasticity of liquid crystalline elastomers and gels
Recent theoretical and experimental studies of linear viscoelastic response in oriented monodomain nematic elastomers show a dramatic decrease in the dynamic modulus in certain deformation geometries. The results,also showing very substantial mechanical loss factors,are associated with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics coupled to anelastic medium. We shall examine how the Leslie-Ericksen linear nematodynamics and classical polymer viscoelasticity combine in these unique systems to produce unusual dynamic-mechanical properties.



B. ZEKS, B. BOZIC, and S. SVETINA
(University of Ljubljana)
The stability of long, nearly cylindrical phospholipid vesicles
Shapes of nearly-cylindrical axisymmetric sections of phospholipid vesicles are studied theoretically. Describing the shape of such sections by their deviation from a reference cylinder, the well-established shape equation for axisymmetric bilayer membranes is expanded in terms of this deviation, and it is then solved analytically. The phase diagram shows the resulting stationary shapes in dependence of system parameters and external conditions, i.e. the pressure difference across the membrane, the membrane tension and the difference between the tensions of the two monolayers. Shapes of central parts of long vesicles can be the cylinder without any modulation, the cylinder with sinusoidal modulation or the cylinder with two sinusoidal modulations. At boundaries the section can adjust to the rest of the vesicle exponentially or by damped sinusoidal functions. The method is then extended to non-axisymmetric sections of vesicles and the results are compared with the results of the stability analysis of a cylinder. The accuracy of the approximate analytical solutions is demonstrated by comparison with numerical results. The obtained modulated nearly-cylindrical shapes represent the basis for the numerical iterative evaluation of cylinders with larger deviations that eventually leads to soliton-lattice-like periodically deformed cylinders.



S. ZUMER
(University of Ljubljana)
Disjoining pressure in very thin nematogenic film
Disjoining pressure in a thin liquid crystal film originates from effective forces between bodies constraining the fluidic material. In nematogenic systems the main contributions are van der Waals, structure mediated, and pseudo Casimir interactions. They crucially depend on details of liquid crystalline ordering. Here we discuss some peculiarities of the relevant effective forces in very thin nematic and pre-nematic liquid crystalline layers. These effective interactions depend on elastic and dielectric properties of the constrained medium, and on the anchoring, ordering, wetting, and dielectric properties of the confining matrix. Stability of liquid crystalline structures and their behavior near the vicinity of structural or phase transitions are examined. Recent experimental results on capillary condensation are briefly discussed.



Round Table on Liquid Crystals
Chairman: I. Stewart

P. GALATOLA
(Université Paris 7)
Reversible creation of pairs of defects of opposite charge
By means of a simplified 2D model, we address the possibility of reversible creating pairs of defects of opposite charge.

E.G. VIRGA, A.M. SONNET
(Università di Pavia)
Dynamics of dissipative systems
The equations of motion for dissipative systems are derived from a variational principle. The only constitutive ingredients are the densities for the free energy and the dissipation, both subject to appropriate invariance requirements. As an illustration, one can derive within this setting the classical equations of the hydrodynamic theory of Ericksen and Leslie.



Round Table on Membranes
Chairman: J.-B. Fournier

E. CANETTA, A. LEYRAT, and C. VERDIER
(Université J. Fourier, Grenoble)
New developments in the biophysics of cellular adhesion
In recent years, biophysical studies of cellular adhesion have been extensively developed both from a theoretical and experimental point of view. In particular, in the '90s three main theoretical physical models have been proposed: Stochastic model, Dynamic model and Statistical physical model. The RICM (Reflection Interference Contrast Microscopy) experimental technique, based on the statistical physical model, has been successfully used in order to analyse the thermal fluctuations of membranes adhering to a substrate. To investigate the cell-substrate interactions further, we have designed an experimental apparatus which allows us to study the behaviour of a cell adhering to a bead subjected to a displacement. Three different techniques have been coupled to the experiment: RICM, Fluorescence and JKR technique. The experimental results obtained will be compared with models of cellular systems.

A. NICOLAS
(Université J. Fourier, Grenoble)
Polymers grafted onto a membrane: frustration effects

C. TORDEUX
(ESPCI, Paris)
Adhesion of vesicles to curved substrates

P. BISCARI
(Politecnico di Milano)
Mediated forces between proteins