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Seminars (MLC)

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Event When Speaker Title Presentation Material
MLCW01 7th January 2013
10:00 to 11:00
Fluids with attitude
This talk includes: an account of the early development of liquid crystal science (c1888-1940), a history of key mathematical ideas, a discussion of devices in liquid crystals, and finally a personal view of future perspectives.

Friedrich Reinitzer (1888, Prague) found that cholesteryl benzoate exhibited two fluid phases, one of which was cloudy. Otto Lehmann (Karlsruhe) studied similar compounds, which seemed both liquid and crystal, hence the term “liquid crystal”. In France Georges Friedel (1922) realised that liquid crystals were instead orientationally ordered fluids, inventing the terms “nematic”, “smectic” and “cholesteric”. The first (“swarm”) theory was due to Emil Bose (Danzig, 1908). More successful was the distinguished Swedish theoretical physicist Carl Wilhelm Oseen, who constructed a hydrostatic theory of liquid crystals (1922-44). Oseen’s theory explained Frederiks’s results from the USSR on threshold fields, but his Ph.D. student Adolf Anzelius was not able to build a consistent dynamical theory.

The first statistical mechanical theory was a mean field picture based on Curie-Weiss magnetism, due to François Grandjean (France, 1917). His work was ignored. The later 1958 Maier-Saupe theory is essentially identical. The liquid crystal order parameter is due to the Russian physicist Victor Tsvetkov in 1941.

Liquid crystal devices emerged in the USA in the 1960s. The TN cell was patented in 1970. There remains dispute over its discovery. Device development was accompanied by enormous theoretical and mathematical activity. The current hydrodynamic theory due to Ericksen and Leslie in 1966, and the Landau theory due to de Gennes in 1970, have been immensely influential. The importance of lcd’s has focussed mathematical interest in liquid crystals in recent years, but in the future these ideas may be even more important in understanding processes in living cells.
MLCW01 7th January 2013
11:30 to 12:30
Liquid crystals, liquid crystal droplets and colloids: basic properties
The review presents basic physical properties of liquid crystals: orientational and translational elasticity (Oseen-Frank formalism), surface anchoring, and topological defects. A special emphasis is on liquid crystals in form of drops and on liquid crystals containing small particles in the bulk. The liquid crystal colloids enable new physical effects, such as nonlinear electrophoresis. The work presented is based on research sponsored by the National Science Foundation, USA.
MLCW01 7th January 2013
14:00 to 15:00
EG Virga Order tensors of equilibrium phases
Order in fluids is described by means of tensorial measures which have in general a statistical derivation, as appropriate moments of a molecular distribution function. Their very definition places order tensors at the crossroad between microscopic and macroscopic approaches, in that land of middle where "mesoscopic" theories flourish. We shall give specific examples of how different order tensors can describe the equilibrium phases of different ordered fluids. Both uniaxial and biaxial nematic liquid crystals will be covered, as well as smectic liquid crystals, thus showing how both orientational and spatial orderings can be represented in one and the same setting. Our presentation will not be limited to phases in bulk; ordering at interfaces will also be considered along with the ways it can be affected by the surface curvature. Similarly, ordering of fluids on two-dimensional curved manifolds will be described, and an "augmented" theory will be presente d for nematic shells, which to the in-plane orientational order adds information on the escape of molecules along the shell's normal.
MLCW01 7th January 2013
15:30 to 16:30
I Stewart Ericksen-Leslie theory for nematic liquid crystals and its developments
A review of the Ericksen-Leslie theory for the dynamics of nematic liquid crystals will be presented. Its developments related to smectic and other liquid crystals phases will also be discussed. Applications to 'switching phenomena' in liquid crystals will be mentioned.
MLCW01 7th January 2013
16:30 to 17:30
T.B.A.
MLCW01 8th January 2013
09:00 to 09:40
An Overview of the Oseen-Frank elastic model and some symmetry aspects of the Straley Mean-Field model for Biaxial Nematic liquid crystals
In this (mostly) expository talk, we will present a brief overview of two independent topics: (1) the Oseen-Frank model for the spatially varying orientational properties of confined uniaxial nematic liquid crystals and (2) the mean-field model of Straley for the bulk phase behavior of biaxial nematic liquid crystals. The Oseen-Frank elastic model is a phenomenological variational model for equilibrium orientational properties characterized by a unit-length vector field. It is a macroscopic continuum model that has been very successful in modeling liquid crystals at the typical scales of experiments and devices. We will discuss the development of the model, its range of applicability, its relation to other models, and its strengths and weaknesses. The mean-field model of Straley was put forward almost 40 years ago as an attempt to describe the bulk phases and transitions for molecules of an architecture that would promote the development of spontaneous biaxial order. The model has received an intensive re-examination in recent years. Some of the symmetry properties of the model arise in unconventional ways, such as through degeneracies in the representations of the states of the system. We will discuss the symmetries of this model and the multiple symmetry-breaking bifurcations encountered in the numerical exploration of its equilibrium phases.
MLCW01 8th January 2013
09:40 to 10:20
X Zheng On the Maier-Saupe theory of Nematic liquid crystals
Maier-Saupe theory, the first successful theoretical model of thermotropic nematic liquid crystals (LCs), is a mean field description of a system of cylindrically symmetric particles interacting via London dispersion forces. The theory predicts a uniaxial nematic phase at low temperatures, and a first order phase transition to an isotropic fluid phase as the temperature is increased. In this talk, I will first give a brief introduction of the canonical Maier-Saupe theory, then extend it to biaxial LC molecules, to inhomogeneous LCs, and to higher spatial dimensions, and discuss the relation between Maier-Saupe and other main theories of LCs.
MLCW01 8th January 2013
10:20 to 11:00
L Longa The Landau theory of liquid crystals and its molecular interpretation
A purpose of this review is to give a systematic exposition of the Landau theory of phase transitions (LTPT). The construction of the Landau free energy expansion and the methods to identify the equilibrium structures will be discussed and illustrated with examples of phase transitions involving nematic- and smectic phases. Then it will be demonstrated how the Landau theory can be derived in a systematic way from (molecular) density functional theories, like mean field. This connection is especially attractive for it allows to view the LTPT as a simple tool to study bifurcation mechanisms, leading to phase transitions at the level of molecular modeling.
MLCW01 8th January 2013
11:30 to 12:10
Onsager - type theorias, where to from here?
I will attempt to traverse the road from basic equations of molecular dynamics at the microscopic level to PDE dynamics at the level of coarse-grained order parameters, trying to clearly capture approximations and simplifications made along the way. My primary goal is to understand the relation of various mathematical frameworks to real liquid crystalline systems and to establish quantities most suitable for analysis of critical phenomena, defects, and symmetries in liquid crystalline systems.
MLCW01 8th January 2013
14:00 to 15:00
Solid liquid crystals
Liquid crystals can become solids when they form glasses or when liquid crystalline polymers are crosslinked to form rubber. They can show properties richer than solids and liquid crystals separately. Glasses have high moduli and their directors are not mobile with respect to the solid matrix. Rubber maintains the molecular mobility of a liquid; it can be deformed hugely, has a low modulus, and its director is mobile. Both can have their order reduced by heat, light and solvent, and then mechanically contract along the director by a few percent (glasses) and by 100s% (rubber). Topological defects in their director fields means that such mechanical response generates Gaussian curvature or topology changes.

Mobile directors respond to imposed strains by reapportioning natural length in directions required by distortions, rendering their energetic cost zero or very small. If necessary textures of such low cost deformations are required to comply with boundary conditions in much the same way as in Martensite. Indeed such techniques of quasi-convexification have been extended by DeSimone et al to complete and generalise the soft mechanics discovered theoretically and experimentally by physicists and chemists.

I shall sketch some of these phenomena and present recent results on the mechanical and topological effect of disclinations in nematic solids, and on how polydomain nematic solids can be super-soft.
MLCW01 8th January 2013
15:30 to 16:30
Molecular Origin of K13 Revisited
Expanding a distortion free energy in terms of spatial gradients of density is a standard approach to construct an elastic theory of condensed matter. When applied to nematic liquid crystals, this so-called gradient expansion leads to the celebrated Frank theory that serves as the sound basis on which to analyze the response of nematic liquid crystals to electric fields and boundary constraints. The success of the theory has been thoroughly proven except the anomalous surface contribution associated with K13 (splay-bend elasticity). The K13 term involves a gradient of the nematic director normal to the boundary, and hence the straightforward minimization of free energy under a given boundary condition becomes mathematically ill-posed, running into various unphysical behaviors.

More than a decade ago, I showed (at least I think I showed) that K13 is an artifact of gradient expansion as applied to a nonlocal interaction free energy by way of the density functional theory. When consistently done, the gradient expansion always results in K13=0 eliminating all the lingering problems that K13 has created.

The purpose of this talk is to revisit this issue. Close look at the K13 issue at the molecular level not only solves its own problem but also gives us a chance to shed new light on such fundamental structural characteristics of liquid crystals as chirality, flexoelectricity, and more.
MLCW01 8th January 2013
16:30 to 17:30
EG Virga What an old problem has still to say: the infamous K13-case
Since the introduction in the free-energy density of the K13-elastic term proposed by Nehring and Saupe at the beginning of the 70's on the basis of a molecular theory, objections have been raised as to both its variational compatibility and statistical consistency. Often, the misbehaviours introduced by this elastic term, which appears as a bulk energy but is indeed a surface energy, are also threateningly referred to as paradoxes. Famous among these are, in particular, Oldano-Barbero's and Somoza-Tarazona's. These paradoxes have been variously resolved, but the K13-problem is still intriguing. One reason is that yes, the K13 term is a surface energy, but by no means is it a null Lagrangian. Another reason is that its very motivation, being statistical in nature, is rooted in the molecular interaction thought of as responsible for liquid crystallinity in the first place. Combining these reasons, one readily identifies two interwoven themes of current research: co ntinuum limits and surface properties. The lecture will attempt to put the history of the K13-problem into the perspective of these avenues.
MLCW01 8th January 2013
17:30 to 18:30
A-M Sonnet Hard core effects in mean field theories
Classically, there have been two different ways to obtain mean field theories for liquid crystals. One is based on short range repulsive forces and the other on long range electrostatic forces. In the former approach, it is the anisotropic shape of the molecules that leads to the anisotropic interaction, and in the latter it is the anisotropy of the molecular charge distribution. In real molecules, both causes of anisotropy will be present and can be expected to contribute to the effective interaction. It is thus desirable to assess the combined effect of anisotropic long range attraction and short range repulsion.

Starting from a long range intermolecular interaction energy, a mean field pair potential can be obtained by averaging over all possible relative positions of two molecules in a fixed relative orientation. The effects of hard core repulsion can be taken into account by an appropriate choice of the domain of integration for the averaging. This involves determining an excluded region, the region that one molecule cannot penetrate due to the hard core repulsion exerted by the other.
MLCW01 9th January 2013
09:00 to 10:00
J Ball Function spaces and liquid crystals
Function spaces are an essential part of mathematical models of nature, specifying allowed singularities in solutions. The talk will discuss the definition and roles of function spaces appropriate for liquid crystals, how they influence the description of defects, and their interaction with boundary conditions and topology.
MLCW01 9th January 2013
10:00 to 10:40
On the cubic instability in the Q-tensor theory of nematics
Symmetry considerations, as well as compatibility with the Oseen-Frank theory, require the presence of a cubic term (involving spatial derivatives) in the Q-tensor energy functional used for describing variationally the nematics. However the presence of the cubic term makes the energy functional unbounded from below.

We propose a dynamical approach for addressing this issue, namely to consider the L^2 gradient flow generated by the energy functional and show that the energy is dynamically bounded, namely if one starts with a bounded, suitable, energy then the energy stays bounded in time. We discuss notions of suitability which are related to the preservation of a physical constraint on the eigenvalues of the Q-tensors (without using the Ball-Majumdar singular potential).

This is joint work with G. Iyer and X. Xu (Carnegie-Mellon).

MLCW01 9th January 2013
10:40 to 11:20
Problems related to defects in nematic liquid crystals
We describe several problems involving defects in liquid crystals and a mathematical framework in terms of tensors or directors that allows us to analyze the nature of defects in energy minimizing configurations.
MLCW01 9th January 2013
11:50 to 12:30
Defects in nematic polymer hydrodynamics: survey of our work over the past 10 years
The organizers, Peter and David, asked me to give a basic introduction to defects in nematic hydrodynamics and to cover whatever aspects of our group's work I felt appropriate for a kickoff workshop. The lecture touches on highlights of work with Qi Wang and Xiaofeng Yang at South Carolina and Ruhai Zhou at Old Dominion University. The first topic covered is the remarkable (to us) shear-induced dynamics of nematic polymers revealed by numerical solutions -- of various second-moment tensor approximations, and of the fully resolved Doi-Hess-Smoluchowski equation for the orientational PDF. Next we study nematic distortions arising due to physical boundary conditions at stationary and moving boundaries, in both 1D and 2D simulations, again revealing persistent non-stationary behavior in large regions of parameter space. Phase diagrams analogous to the monodomain problem show transitions between stationary and non-stationary attractors. What is the role of defects? We employ defect core detection and tracking diagnostics that apply independent of space dimension, and in dimensions 2 or higher we assess topology only after a positive test for defect cores. The fundamental role of oblate defect cores is illustrated in both 1D and 2D unsteady attractors. In each topic, open problems potentially of interest for rigorous mathematics are raised, with the hope of follow-up discussion during the program.
MLCW01 9th January 2013
13:30 to 14:30
Onsager's Variational Principle in Soft Matter Dynamics
In the celebrated paper on the reciprocal relation for the kinetic coefficients in irreversible processes, Onsager extended Rayleigh's principle of the least energy dissipation to general irreversible processes. In this presentation, I shall show that this variational principle is very convenient in considering the non-linear and non-equilibrium phenomena in soft matter. I will discuss this using the examples of (i) viscoelasticity of colloidal suspensions and polymer solutions, (ii)diffusion-mechanical coupling in polymer solutions and gels, and (iii) nemato-hydrodynamics etc.
MLCW01 9th January 2013
14:30 to 15:30
Describing and determining the order of liquid crystals in the bulk and close to interfaces
The definition and actual determination of orientational and positional order parameters plays a key role in describing the variety of molecular organizations of liquid crystals and in quantifying their changes, e.g. at phase transitions or when approaching an interface. The classical description of order in terms of a single parameter, which implicitly assumes a simple rigid and uniaxial molecular shape, has to be refined in a number of ways, e.g. to allow for biaxiality [1] or internal flexibility [2,3] or inhomogeneities in thin films [4] or nanodroplets [5]. This increased complication has become essential in view of progresses in experimental and simulation techniques, now offering an unprecedented level of detail and of possibilities of putting theories of liquid crystals and ultimately our understanding of anisotropic phases to the test. In the talk we present some examples of order and structure determinations from coarse grained [1,5] and atomistic simulations [2-4].
MLCW01 9th January 2013
16:00 to 17:00
Geometric theories of conservative liquid crystal dynamics
MLCW01 10th January 2013
09:00 to 10:00
When shapes collide: finding order in disorder
MLCW01 10th January 2013
10:00 to 11:00
Liquid crystals and what they have taught us
Broken symmetries and conservation laws lie at the very heart of our understanding of the physical world. They control the physical properties and phenomena ranging from the masses of elementary particles to the flow to the oceans. Liquid crystals provide an almost ideal laboratory for studying phenomena - low-energy elasticity and hydrodynamics, topological defects, and critical fluctuations - associated with broken symmetries. This talk will review some of the important things we have learned from liquid crystals including how to describe broken rotational symmetries, what crystals really are and how to describe their elasticity and dynamics, and how fluctuations and spatial dimension affect the existence of order.
MLCW01 10th January 2013
11:30 to 12:30
R Kamien Topological defects and the ground state manifold
Do homotopy groups completely characterize topological defects? In this presentation, I will describe the pitfalls to this notion and describe some progress in working around the ambiguities and puzzles that arise in such descriptions.
MLCW01 10th January 2013
14:00 to 15:00
P Chossat The mathematics of pattern formation: a modern view
After the seminal contributions of A. Turing, G.I. Taylor, L. Landau, L. Michel in the first half of the past century, new mathematical methods have emerged to study the phenomenon of spontaneous pattern formation. Decisive progress was made using geometrical methods (M. Golubitsky, I. Stewart) and analytical tools (G. Iooss, K. Kirchgässner). I shall show on examples how this theory, known as Equivariant Bifurcation Theory, applies to a variety of problems, including liquid crystals. I shall also quote some open questions which are still under investigation by mathematicians working in these topics.
MLCW01 10th January 2013
15:30 to 16:30
J Dawes Localised pattern formation
Pattern-forming (Turing) instabilities are observed sometimes to generate patches of periodic structure rather than domain-filling patterns. I will present physical examples and toy model PDEs, and outline the bifurcation theory that provides an explanation for this, at least in one spatial dimension.
MLCW01 11th January 2013
09:00 to 09:40
P Zhang From molecular symmetry to order parameters
We propose a systematic molecular modeling of liquid crystals, the models can be used to depict isotropic, nematic, smectic, columnar, cholesterics and blue phases. The tensor model can be reduced from molecular model using closure and Taylor expansion, the vector model can be reduced from tensor or molecular model using axial symmetry assumption. Using Newton mechanic and virial expansion, we build a generic molecular model to describe phase behaviors of rigid molecules of arbitrary shape. The system is characterized by a pairwise kernel function. The kernel function can be simplified by the molecular symmetry. Onsager potential is a leading order for rod-like molecular using hard core potential, and Maier-Saupe potential is a good second approximation using Lennard Jones potential. The new models including simplified kernel functions are proposed for bent-core molecules and other shape molecules. We also clarify the criteria of choosing order parameters, both from theoretical aspects and from results of experiments and simulations. According to these criteria, we explain why the eigenvalue of second moment is chosen to describe spatially homogeneous phases of rod-like molecules, and predict the choice of order parameters for bent-core molecules and other molecules of different symmetries. The rigorous analysis for choosing the order parameter will be given for Maier-Saupe model of rod-like molecular.
MLCW01 11th January 2013
09:40 to 10:20
Invariant theory: a useful tool for equivariant dynamics and the mathematics of liquid crystals
In this talk we will present some classical and modern results from invariant theory and and apply them to problems in equivariant dynamics and bifurcation and also to some problems in the theory of liquid crystals. We hope to identify and explain some problems where similar ideas are useful.
MLCW01 11th January 2013
10:20 to 11:00
Free energy according to Poincare' and Landau
In the Landau theory of phase transitions one considers an effective potential U whose symmetry group G and degree d depend on the system under consideration; generally speaking, U is the most general G-invariant polynomial of degree d. When such a U turns out to be too complicate for a direct analysis, it is essential to be able to drop unessential terms, i.e., to apply a simplifying criterion. Criteria based on singularity theory exist and have a rigorous foundation, but are often very difficult to apply in practice. Here we consider a simplifying criterion and rigorously justify it on the basis of classical Lie-Poincare theory; this builds on (and justifies) a proposal by Gufan.
MLCW01 11th January 2013
11:30 to 12:10
Three-wave interactions in problems with two length scales: Faraday waves and soft-matter quasicrystals
Three-wave interactions form the basis of our understanding of many pattern-forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the shorter wavelength to interact with one wave of the longer, as well as for two waves of the longer wavelength to interact with one wave of the shorter. Consideration of both types of three-wave interactions can generically explain the presence of complex patterns, such as quasipatterns, and spatiotemporal chaos. Two length scales arise naturally in some examples of polymer micelles and in the Faraday wave experiment, where a viscous fluid is subjected to vertical vibration. Our results enable some previously unexplained experimental observations of spatiotemporal chaos in the Faraday wave experiment to be interpreted in a new light; application to quasicrystals recently observed in self-assembled colloidal systems is more speculative.
MLCW01 11th January 2013
13:30 to 14:00
M Warner & M Osipov & J Ball Overviews of other MLC workshops
Liquid crystal (LC) phases were first identified and even named by their topological defects. The rich interplay between geometry, topology and optics is ubiquitous through all liquid crystals. Workshop 4 (WS4) addresses the characterisation of defects, their essential appearance in complex systems such as colloidal liquid crystals, how they template complex structures, and their special character in non-simple spaces (such as those with Gaussian curvature). WS4 is concerned with solid liquid crystals, both elastomers where the director remains mobile, and glasses where the director is pinned to the material frame. The unique mechanics of solid liquid crystals leads to new phenomena, some of which are described by techniques of quasi-convexification first exploited in Martensites. Their mechanics connects with the defects theme since topological defects in LC solids, on illumination or temperature change, cause changes in Gaussian curvature or topology. WS4 also pursues active nematics, their connections with solid nematics, and the role of defects in active systems.

I shall review the themes of the workshop, concentrating on those less familiar to liquid crystal specialists.
MLC 16th January 2013
14:10 to 17:00
Dynamics of bulk nematics in a uniform shear flow (informal workshop)
MLC 22nd January 2013
14:00 to 15:00
Polyelectrolyte gels: modeling chemo-mechanical interaction
MLC 23rd January 2013
15:30 to 17:00
Dynamics of bulk nematics in a uniform shear flow (informal workshop)
MLC 24th January 2013
11:00 to 12:00
N Mottram Modelling bistable displays using Q-tensor theory
MLC 29th January 2013
14:00 to 15:00
D Phillips Analysis of chevron patterns using gamma convergence
MLC 29th January 2013
16:00 to 17:00
J Dawes Informal workshop on groups, orbits and bifurcation I
MLC 1st February 2013
11:00 to 12:00
J Dawes Informal workshop on groups, orbits and bifurcation II
MLC 5th February 2013
14:00 to 15:00
Monte Carlo simulations and Onsager density functional theory of hard particle liquid crystal models
MLC 6th February 2013
16:00 to 17:00
Informal workshop on shear flow
MLC 7th February 2013
11:00 to 12:00
J Park Some mathematical analysis of molecules in Ferroelectric Liquid Crystals
MLC 7th February 2013
16:00 to 17:00
Informal workshop on Groups, Orbits and Bifurcation III
MLC 11th February 2013
15:00 to 17:00
L Longa Introduction to Density Functional Theory of Liquid Crystals
MLC 12th February 2013
14:00 to 15:00
S Kralj Stabilization of liquid crystalline structures exhibiting topological defects
MLC 14th February 2013
11:00 to 12:00
Informal workshop on groups, orbits and bifurcation
MLC 19th February 2013
14:00 to 15:00
Symmetry breaking and symmetry defects. Invariant theory applications
MLC 20th February 2013
14:00 to 15:00
Informal workshop on shear flow
MLC 20th February 2013
15:00 to 16:00
L Longa Introduction to Density Functional Theory of Liquid Crystals II
MLC 21st February 2013
11:00 to 12:00
Soft Bend Elastic Constant and Transition to a Modulated Nematic Phase
MLC 26th February 2013
14:00 to 15:00
Analysis and stability of bentcore liquid crystal fibers
MLC 28th February 2013
11:00 to 12:00
N Mottram Decoupling the Ericksen-Leslie equations
MLC 5th March 2013
14:00 to 15:00
Liquid crystals and general relativity
MLC 7th March 2013
11:00 to 12:00
Liquid crystals at patterned substrates
MLC 12th March 2013
14:00 to 15:00
Mathematical problems of the Q-tensor theory of nematics
MLC 13th March 2013
11:00 to 12:00
S Praetorius The (Liquid-Crystal) Phase-Field-Crystal model - Derivations and Applications
MLC 13th March 2013
14:00 to 15:00
Coarsening and Q-tensors for nematics (a mathematician's perspective)
MLC 14th March 2013
11:00 to 12:00
H Löwen Liquid crystals described within the phase-field crystal model
MLCW02 18th March 2013
09:00 to 09:50
J Ball Satisfaction of the eigenvalue constraints on the $Q$-tensor
We discuss how Onsager theory with the Maier-Saupe interaction leads naturally to a bulk free energy depending on the $Q$-tensor that blows up as the minimum eigenvalue $\lambda_{\rm min}(Q)\rightarrow -1/3$, using methods closely related to those of Katriel, Kventsel, Luckhurst and Sluckin (1986). With this bulk energy, and in the one constant approximation for the elastic energy, it is shown that for suitable boundary conditions, minimizers $Q$ of the total free energy for a nematic liquid crystal filling a region $\Omega$ satisfy the physical requirement that $\inf_{x\in\Omega}\lambda_{\rm min}(Q(x))>-1/3$.
MLCW02 18th March 2013
09:50 to 10:40
The physics of unphysical simulations
Simulations are patient. In particular, they can be used to model systems that are interesting but `unrealistic'. In fact, from the time of Onsager onwards, unphysical limits have played a key role in our understanding of lyotropic liquid crystals. Interestingly, simulations allow us to probe interesting limits that are inaccessible to experiments.
MLCW02 18th March 2013
11:00 to 11:50
Density Functional Theory for Hard-Body Models of Liquid Crystals
Hard-body models for lyotropic liquid crystalline phases date back to Onsager (1949) who showed that a fluid of hard rods can exhibit a transition from an isotropic to a nematic phase that is driven purely by entropy. Onsager’s treatment is based on a second-virial description of the free energy that is accurate in the (Onsager) limit of very long thin rods (spherocylinders). For shorter spherocylinders and for smectic and crystalline phases, as well as for treating inhomogeneous fluids, e.g. situations arising at interfaces between phases and in anchoring and wetting at substrates, it is necessary to develop theories in which the ensemble averaged one-body particle density depends on both the orientation and the position of the particles. Density Functional Theory (DFT), developed first for simple fluids with spherical particles, is one such theory and it has emerged as powerful means of tackling phase transitions and the structure and thermodynamics of inhomogeneous fl uids. This lecture will provide an overview of the basics of DFT before focusing on the successful geometry-based Fundamental Measure Theory (FMT) approach introduced originally by Rosenfeld (1989) for hard-sphere mixtures. FMT for spheres has as its starting point the incorporation of the exact second virial contribution into the free energy functional. Attempts to extend the ideas of FMT to hard bodies of arbitrary shape were made by Rosenfeld (1994, 1995). These failed to yield a stable nematic phase for spherocylinders, partly because they did not include the correct Onsager limit. In recent years there has been renewed effort to develop improved FMT that go towards capturing this limit. I shall describe progress for a variety of model colloidal liquid crystalline fluids including hard spherocylinders, mixtures of hard spheres and rods, and hard thin platelets. If time permits I shall mention some recent applications of Dynamical DFT to non-equilibrium properties.
MLCW02 18th March 2013
11:50 to 12:40
Coarse-grained modelling and computer simulations of liquid crystals
Coarse-grained models for liquid crystals are typically based on pair potentials where an entire mesogenic molecule is represented by one (or a few) anisotropic geometrical object (e.g. a spherocylinder, or an ellipsoid) with either purely repulsive or attractive-repulsive interactions. Computer simulations relying on these simple off-lattice models are able to reproduce the experimental phase sequences and order parameters of thermotropic mesogens and are useful for studying the relationship between specific molecular properties (e.g. shape or interaction anisotropies) and macroscopic liquid crystalline behaviour.

We will review the principal coarse-grained level models currently used in computer simulations of liquid crystals and discuss their advantages and shortcomings using the results for selected cases.

MLCW02 18th March 2013
14:00 to 14:50
Active liquid crystals and the origins of cellular locomotion
I will report theory and simulations of the continuum equations for a droplet of active polar liquid crystal. These equations offers a simple representation of a ``cell extract", such a droplet of actomyosin solution, in which myosin motors moving on actin filaments create internal stresses as a result of biological activity. (This system can in turn be viewed as a stripped-down representation of the cytoskeleton which causes locomotion of eukarotic cells.) Actomyosin is an active liquid crystal whose polarity describes the mean sense of alignment of actin fibres. In the absence of polymerization and depolymerization processes (`treadmilling') which arise respectively at the plus and minus ends of the filaments, the active dynamics should be unchanged when polarity is reversed. Our results suggest that, contrary to most literature opinion, locomotion can arise in the absence of treadmilling, by spontaneous symmetry breaking (SSB) of polarity inversion symmetry.
MLCW02 18th March 2013
14:50 to 15:40
A Vanakaras Biaxial Nematics: Symmetry and Hierarchical Domain Structure
We present theoretical and computer simulation studies on the structure of nematic liquid crystals formed by bent-core mesogens (BCM) and by board-like colloids (BLC). The presence of local orientational and/or positional ordering is a key feature for the interpretation of the biaxial nematic ordering observed in these systems.

In the first part we present the full phase diagram, calculated from MC molecular simulations, of sterically interacting BLC, for a range of experimentally accessible molecular dimensions/anisometries of colloids of this shape. New classes of phase transition sequences such as nematic-nematic and, for the first time, a direct transition from a discotic and a biaxial nematic to an orthogonal smectic-A phase have been identified. We demonstrate rigorously the formation of supramolecular entities and explain the observed phase transitions in terms of the "shape anisotropy" of these entropy driven supramolecular assemblies.

In the second part the structure of nematic liquid crystals formed by bent-core mesogens is studied in the context of MC simulations of a simple molecular model that captures the symmetry, shape, and flexibility of achiral BCMs. Our results indicate the formation of (i) clusters exhibiting local smectic order, orthogonal or tilted, with strong in-layer polar correlations and antiferroelectric juxtaposition of successive layers and (ii) large homochiral domains through the helical arrangement of the tilted smectic clusters, while the orthogonal clusters produce achiral (untwisted) nematic states.

The results of our work offers a deeper understanding of the nematic-nematic transitions and, ultimately, of the nematic phase and can serve as a comprehensive guide to experiment, towards the design of anisotropic liquids with the desired functionality, as well as to theory for testing and improving analytical molecular models using simple intermolecular potentials.

MLCW02 18th March 2013
16:00 to 16:50
S Belli Brick-by-brick stabilizing the Biaxial Nematic Phase
A fascinating way to improve the present-day liquid crystal technology consists of imagining to use new liquid crystal phases with "exotic" properties, like the biaxial nematic phase. However, as an essential step in this direction one has to establish the conditions under which such a phase is thermodynamically stable. Inspired by a recent experiment on a colloidal suspension of mineral goethite particles [1], we use a mean field theory to investigate the phase behavior of boardlike particles. By modelling these “nanoscopic bricks” as cuboids with a hard-body interaction, we analyze the conditions of stability of the long-searched biaxial-nematic phase. We show that under specific conditions size-polydispersity, a common property in most colloids, can increase appreciably the stability of this liquid crystal phase [2]. Moreover, we deduce that this effect can be interpreted in terms of an effective attraction, and therefore that a similar stability could be induced by a non-adsorbing depletant, like a polymeric solution [3]. [1] E. van den Pol et al., Phys. Rev. Lett. 103, 055901 (2009) [2] S. Belli, A. Patti, M. Dijkstra and R. van Roij, Phys. Rev. Lett. 107, 148303 (2011) [3] S. Belli, M. Dijkstra and R. van Roij, J. Phys.: Condens. Matter 24, 284128 (2012)
MLCW02 19th March 2013
09:00 to 09:50
Liquid Crystal Director Models with Coupled Electric Fields
Historically, many liquid-crystal devices and experiments have involved low-molecular-weight nematic liquid crystals, in supra-micron-size confinements, with coupled electric fields. In such settings, equilibrium orientational properties can be modeled most effectively using the Oseen-Frank elastic theory coupled with the equations of electrostatics. In this (mostly) expository talk, we will discuss some of the issues that arise in the mathematical and numerical treatment of such classical models. These issues include the intrinsic minimax nature of such models, which arises from the negative-definite way in which the electrostatic potential enters the free energy functional and which can also arise when Lagrange multipliers are used to enforce the pointwise unit-vector constraints on the liquid-crystal director field, as well as the complications this indefiniteness adds to the assessment of local stability of equilibria. We will also discuss the anomalous behavior that can be exhibited at the thresholds of certain electric-field-induced instabilities because of the nature of the coupling between the director field and the electric field. In addition, we will contrast the macroscopic Oseen-Frank model with the mesoscopic Landau-de Gennes model in such contexts.
MLCW02 19th March 2013
09:50 to 10:40
Modelling a planar bistable device on different scales
This talk focuses on the development, analysis and numerical implementation of mathematical models for a planar bistable nematic device reported in a paper by Tsakonas, Davidson, Brown and Mottram. We model this device within a continuum Landau-de Gennes framework and investigate the cases of strong and weak anchoring separately. In both cases, we find six distinct states and compute bifurcation diagrams as a function of the anchoring strength. We introduce the concept of an optimal boundary condition that prescribes the optimal interpolation between defects at the vertices. We develop a parallel lattice-based Landau-de Gennes interaction potential, by analogy with the Lebwohl-Lasher lattice-based model and study multistability within this discrete framework too by means of Monte Carlo methods. We also use the off-lattice based Gay Berne model to study the structure of the stable states. The different numerical approaches are compared and we discuss their relative strengths a nd shortcomings. We conclude by a brief discussion on a multiscale modelling approach wherein we can couple a lattice-based interaction potential to a conventional continuum model. This is joint work with Chong Luo and Radek Erban.
MLCW02 19th March 2013
11:00 to 11:50
N Mottram Modelling planar bistable devices: from Q-tensor to director models
In this talk we continue the theme of bistable devices from the previous presentation. Here we compare the Q-tensor model to a director based model, i.e. moving from a mesoscopic approach to a macroscopic approach, in a number of practical examples. We consider the polygonal confinement considered in the previous talk and extend to more general cases of bistability and multistability arising from the morphology of bounding substrates. Bifurcation diagrams of stable states, as parameters such as anchoring strength are varied, are computed. We review some of the advantages and disadvantages of the two modelling approaches and compare results to experimental measurements. Although a director based model is inherently restricted in its inability to model effects such as surface melting and disclination lines, we find that all stable states are in fact reproduced. Additionally we find that, rather surprisingly, the dynamics of switching in the bistable devices can be modelled accu rately using a director theory.
MLCW02 19th March 2013
11:50 to 12:40
SAFT force fields for coarse-grained MD simulations
A dangerous over-confidence now prevails in the assumption that detailed all-atom or united-atom models which are used to represent the properties of fluid molecules (e.g. the OPLS-type potentials) are sufficient to describe molecular systems with a precision that supplements experiments. More than 1% of all recent articles published in the open science and engineering community deal with molecular simulations at this level and in some cases the accuracy of the results is taken for granted. The fitting of parameter of the force fields is, however, still rather unsophisticated as compared to other aspects of computer modelling. Common practice is to hand fit a few parameters to a few experimental data points (e.g., a radial distribution function, solubility data and/or enthalpies at a given temperature or phase state). In this contribution we propose a new way of obtaining the required force field parameters. In our methodology one requires access to a physical-based equation of state that describes the complete Helmholtz free energy in closed algebraic form, i.e., an equation of state (EoS) that is based on a defined intermolecular potential. Such an equation can then be used to explore a very large parameter space to estimate the locally optimal parameter set that provides an optimal description of the available macroscopical experimental data. This parameter set represents not just a unique fit to a single temperature or density, but rather an over-arching average. If the equation of state is expressed in terms of the free energy of the system for a well defined intermolecular potential, it can be used to develop a “top-down averaged” intermolecular potential. Here we follow this line of thought and present a proof-of-concept of such methodology, employing a recently developed EoS of the Statistical Associating Fluid Theory (SAFT) family using the so-called Mie intermolecular potential.
MLCW02 20th March 2013
09:00 to 09:50
Glassy dynamics, spinodal fluctuations, and nucleation in suspensions of colloidal hard rods and plates
Using computer simulations we study nucleation in a colloidal supension of hard rods. We study the kinetic pathways for the isotropic-to-nematic transition in a fluid of long hard rods, and find spinodal decomposition as well as nucleation and growth depending on the supersaturation [1]. In supersaturated isotropic fluid states of short hard rods, we observe nucleation of multilayered crystalline clusters. At sufficiently high supersaturations, we find that the nucleation is hampered by glassy dynamics. For intermediat rods, we find that the formation of the (stable) smectic phase out of a supersaturated isotropic state is strongly suppressed by an isotropic-nematic spinodal instability that causes huge spinodal-like orientation fluctuations with nematic clusters diverging in size [2]. In suspensions of colloidal platelets, we find that the cubatic phase is metastable, and that perpendicularly oriented particle stacks in the isotropic fluid phase inhibits the formation of the columnar phase [3].

[1] A. Cuetos and M. Dijkstra, Physical Review Letters 98, 095701 (2007). [2] R. Ni, S. Belli, R. van Roij, and M. Dijkstra, Physical Review Letters 105, 088302 (2010). [3] M. Marechal, A. Patti, M. Dennison, and M. Dijkstra, Physical Review Letters 108, 206101 (2012).

MLCW02 20th March 2013
09:50 to 10:40
Simulations of model biaxial particles
The behaviour of axially symmetric particles has been well-investigated by both theory and computer simulation. Colloidal particles with such shapes have also been studied experimentally. For one component systems, nematic and smectic phases have been observed for rod-like particles, while discotic nematic and columnar phases have been noted for discs. If, however, one considers less symmetrical particles, then other phases become possible. Freiser (1970) showed theoretically that such a system might form a biaxial nematic phase, in which all particle axes are partially aligned, as opposed to a normal, uniaxial nematic where only one axis is ordered. Experimentally, a biaxial nematic phase has been reported for lyotropic systems (Yu & Saupe, 1980) and for suspensions of board-like goethite particles (van den Pol et al., 2009). There also exist reports of thermotropic biaxial nematic phases, though debate still continues as to whether these really exist for these systems. I would like to present simulation results (and hopefully some simple theory) on two types of model particle which might show biaxial behaviour. The first model is of V-shaped particles (also called boomerangs, bananas and bent-cores), while the second is closely related to the board-like shapes of goethite mentioned above. In both cases the particles interact via repulsive interactions only. Both models have received previous theoretical and simulation attention, but hopefully a little extra investigation will not come amiss.

In both cases we used constant pressure, and sometimes constant stress, molecular dynamics simulations, compressing the system from an initial isotropic phase. For relatively straight V-shped particles, the simulations are straightforward and result in uniaxial nematic and biaxial smectic phases. For a bond angle of less than ca. 130 degrees, however, the system tends to jam on compression and equilibration becomes problematic. We therefore investigated mixtures of V-shapes to see whether mixing suppressed the smectic phases, giving room for a biaxial nematic phase to form. While, at least to date, this hope was not fulfilled, we still observed some effects that we believe are of interest.

The other system studied is of fused hexagons – a model related to hard boards. The phase behaviour observed here was rather rich. Depending on geometry we found rod-like, discotic and biaxial nematic phases. Rod-like particles formed both uniaxial and biaxial smectic A and C phases. Disc-like particles formed not only columnar phases but also lamellar phases. Hopefully we will be able to rationalise the presence of at least some of these structures using simple-minded stability analysis.
MLCW02 20th March 2013
11:00 to 11:50
Phase behaviour in mixtures of unixial hard particles: biaxiality and confinement
The nematic biaxial phase has remained a key challenge in the science of liquid crystals since it was first proposed. Recently the first experimental evidence of stable biaxial nematic phases has been obtained in thermotropic liquid crystals of single component biaxial mesogens by Madsen et al., and others. Still elusive however is the possibility of stabilizing biaxial nematic phases in mixtures of uniaxial particles. This avenue has been explored in some detail using theory and computer simulation, but leads one to the conclusion that, at least in the case of mixtures of hard particles, the nematic biaxial phase is thermodynamically unstable with respect to demixing into two uniaxial phases. Theoretical calculations have, however, pointed out that with an appropriate attractive unlike interaction, a homogeneous biaxial nematic phase could be stabilized. Experimental work on mixtures of rod and disc-like molecules has tended to confirm the view that such a system would favou r phase separation, until the recent studies of Apreutesei and Mehl. In this contribution, we use canonical Monte Carlo molecular simulations to study model mixtures of rodlike and disklike molecules interacting through two intermolecular potential models: one incorporating spherically symmetric (isotropic) attractive interactions; another with anisotropic attractive interactions. These models exhibit nematic and smectic biaxial phases. In the final part of the talk, if time allows, I will briefly discuss the changes in the phase behavior that occur when uniaxial disc-like particles are placed in confinement between parallel walls and consider the surface ordering and capillary phenomena in this system.
MLCW02 20th March 2013
11:50 to 12:40
E Virga Different flavours of the mean-field theory
Since the proposal for a remarkably simple theory of ferromagnetism made by Weiss in 1906, under the assumption that each molecule suffered an effective magnetic field (le champ intérieur, in Weiss' words) mimicking the average action of all other molecules, the notion of mean field has grown and acquired a life of its own. The most striking application to liquid crystal science of the mean-field formalism is perhaps the Maier-Saupe theory for the nematic phase. Many other models and approximations are comprised under the general heading of mean-field theory, though often one may hardly find any trace of an average, collective field there, its place being taken instead by a generalized order field. Some theories in this ample catalogue are variational, while others are not. All feature a key self-consistency condition, which may involve a probability distribution density as well as an order field. The lecture will attempt to justify the key self-consistency equatio n in a rigorous way for the different flavours that theory has taken.
MLCW02 20th March 2013
14:00 to 14:50
L Longa Lebwohl-Lasher models of liquid crystals: from quadrupolar to spontaneously induced chiral order
In 1972 P. A. Lebwohl and Q. Lasher (LL) (PRA 6, 426 (1972)) have carried out standard Monte Carlo simulations on the lattice version of the Maier-Saupe (MS) model to test predictions of the MS mean-field calculations. Preserving uniaxial symmetry ($D_{\infty h}$)for nematics they assumed liquid crystalline molecules to occupy the sites of a three dimensional cubic lattice subjected to periodic boundary conditions. Pair interaction potential, limited to nearest-neighbor molecules, was given by the second Legendre polynomial of the relative angle between the molecular long axes. The simulations showed that the LL lattice model undergoes a weak first-order phase transition between isotropic and uniaxial nematic order, in qualitative agreement with MS predictions. Since the model has proved to correctly account for the essential symmetry of liquid crystalline orientational order a large amount of work has been and is currently devoted to generalizations of the LL model to more complex situations. They involve, without trying to be exhaustive, (a) investigation of the nematic ordering in confined geometries, subject to different surface anchoring fields, (b) effect of an external field on the isotropic - nematic phase transition(s), (c) simulations of electro-optical devices, (d) simulation of chiral liquid crystal phases, (e) orientational properties of elastomers and (f) physics of two-dimensional systems.

In this talk, after a brief review of properties and generalizations of the LL model, I will concentrate on simple versions of this model that can be useful in investigating spontaneous formation of macroscopic chiral domains of opposite handednesses observed in bent-core, dimer and ferrocene mesogens. More specifically, I will discuss properties of the LL model with quadrupolar and octupolar pair-interactions. The model will be shown to generate long-range biaxial order along with ambidextrous twist deformations. A possibility of generating nonzero splay and bent configurations will also be discussed. The class of LL models is generic in the sense that only symmetry allowed terms are retained in the interaction potential. Hence, orientational structures identified not only characterize nematic-like states but can also coexist with a long-range positional order, characteristic of smectic, columnar or crystalline phases.

MLCW02 20th March 2013
14:50 to 15:40
Atomistic molecular dynamics simulations of cyanobiphenyls: A test bench for liquid crystal theories
The recent increase in computer speed has determined unprecedented possibilities of modelling physical and chemical processes “in silico”. This is most true for liquid crystals, as the large system sizes and long time scales necessary for reliable predictions of their self-assembly are now becoming affordable, and where atomistic molecular dynamics simulations have proved that an accurate but classical description of intermolecular forces is adequate for obtaining a quantitative agreement with experiments for nematics and discotics. In this context, in Bologna we developed a force field for n-alkyl cyanobiphenyls (nCBs)able to reproduce their experimental phase transition temperatures within a few degrees. The choice of nCBs as prototypical liquid crystal systems opens the way to an informative cross comparison between experiments, simulations, and theory. In fact, the abundance of experimental studies provides a rich database of almost any possible physical property, which serves as a stringent test for simulation predictions, and is able to reveal weaknesses and strengths of the microscopic model. Once the model has been validated, simulations can be considered superior to theoretical predictions, because they rely on a much lower number of assumptions. It becomes then possible to “revisit” and validate existing and maybe even very successful theories, not only on the basis of their predictions (comparison with the experiment) but also on their physical foundations (comparison with simulation s). This presentation will cover all the stages of this “virtuous” exercise, including: the derivation of the force field; II) the calculation of macroscopic observables III) the comparison with mean field descriptions for the nematic and smectic phases; IV) new attempts of addressing continuum theories for liquid crystal alignment. To conclude, a personal perspective of where theory could help the simulation and of future applications will be given.
MLCW02 20th March 2013
16:00 to 16:50
Microphase separation driven transitions in macromolecular liquid crystals by computer simulations
We present the results of some recent simulations of macromolecular liquid crystal systems that undergo order-disorder transitions driven by a microphase separation. Molecular dynamics simulations are performed to study a liquid crystal elastomer of a side-chain architecture crosslinked in the SmA phase. Several effects have been observed: (i) the increase of the SmA-I transition temperature as the result of crosslinking; (ii) memory effects in liquid crystallinity and shape when the elastomer is driven through the Sm-I transition; (iii) both cases of homogeneous director reorientation and stripe formation when the load is applied along the nematic director [1]. In another set of results we consider bulk self-assembly of liquid crystal dendrimers studied by means of coarse-grained molecular dynamics simulations. We discuss the details of the modelling and its application to polymer-modified gold nanoparticles. The particular model dendrimer being studied demonstrates conforma tional bistability, with both rod-like and disc-like conformations stable at lower temperatures. Each conformation can be induced by the external field of appropriate symmetry, promoting further self-assembly of macromolecules into a bulk monodomain SmA or a columnar phase, respectively [2]. The domains of both phases are found to coexist and influence the system properties in a broad temperature interval including transition to the macroscopically isotropic phase. We also discuss the effect of surface anchoring on the self-assembly of these macromolecules [3].

[1] J.M.Ilnytskyi, M.Saphiannikova, D.Neher, M.P.Allen, Soft Matter (2012), DOI: 10.1039/c2sm26499d [2] J.M.Ilnytskyi, J.S.Lintuvuori, M.R.Wilson, Condens. Matter Phys. 13, 33001 (2010). [3] J.M.Ilnytskyi, M.Schoen, M.R.Wilson, in preparation.
MLCW02 21st March 2013
09:00 to 09:50
Design of liquid crystal superstructures: geometry, topology, flow, and mesophase
Structuring of liquid crystalline fluids allows for various exciting material mechanisms such as self-assembly [1], memory effects [2], entanglement [3], nonlinear electrophoresis [4], nonlinear rotary dynamics [5], and nanoscopic surface shape changing [6]. Here, we present strategies for creating colloidal and bulk liquid crystal superstructures, in 2D and 3D, using nematic, twisted nematic, and cholesteric blue phases. Our work is based on the numerical minimization of the phenomenological Landau-de Gennes free energy and solving hybrid Lattice Boltzmann algorithm for Beris-Edwards nematodynamics model, with full link to experiments. We show that 3D colloidal crystals can be assembled from elastic dipoles of spherical beads in nematic liquid crystals or via inherently inhomogeneous order profiles in cholesteric blue phases [7]. By using colloidal platelets, we show that crystalline [8] and quasi-crystalline symmetry can be imprinted into the structures. Topological defects are manipulated into structures of knots and links using various colloidal arrays [9]. Finally, passive and active material flow is used to produce distinct backflow generated complex nematic profiles in microfluidic channels.

[1] P. Poulin, H. Stark, T. C. Lubensky, D. A. Weitz, Science 275, 1770 (1997). [2] T. Araki, M. Buscaglia, T. Bellini, and H. Tanaka, Nature Materials 10, 303 (2011). [3] M. Ravnik, et al, Phys. Rev. Lett. 99, 247801 (2007). [4] O. D. Lavrentovich, I. Lazo and O. P. Pishnyak, Nature 467, 947 (2010). [5] J. S. Lintuvuori, K. Stratford, M. E. Cates, D. Marenduzzo, Phys. Rev. Lett. 107, 267802 (2012). [6] D. Vanzo, M. Ricci, R. Berardi and C. Zannoni, Soft Matter 8, 11790 (2012). [7] M. Ravnik, G. P. Alexander, J. M. Yeomans, and S. Zumer, Proc. Natl. Acad. Sci. USA 108, 5188 (2011). [8] J. Dontabhaktuni, M. Ravnik and S. Zumer, Soft Matter 8, 1657 (2012). [9] U. Tkalec, M. Ravnik, S. Copar, S. Zumer and I. Musevic, Science 333, 62 (2011).
MLCW02 21st March 2013
09:50 to 10:40
Isotropic-polar phase transition in an amphiphilic fluid
We present Monte Carlo simulations of the isotropic-polar (IP) phase transition in an am-phiphilic fluid carried out in the isothermal-isobaric ensemble. Our model consists of Lennard-Jones spheres where the attractive part of the potential is modified by an orientation-dependent function. This function gives rise to an angle dependence of the intermolecular attractions corresponding to that characteristic of point dipoles. Our data show a substantial system-size dependence of the dipolar order parameter. We analyze the system-size de-pendence in terms of the order-parameter distribution and a cumulant involving its first and second moments. The order parameter, its distribution, and susceptibility observe the scaling behavior characteristic of the classical 3D-Heisenberg universality class. Because of this scaling behavior and because all cumulants have a common intersection irrespective of sys-tem size we conclude that the IP phase transition is continuous. Considering pre ssures 1.3≤ P≤3.0 we demonstrate that a line of continuous phase transition exists which is analogous to the Curie line in systems exhibiting a ferroelectric transition. Our results are can be explained semi-quantitatively by a simple mean-field theory adapted from the theory of IP phase transi-tions in fluids in which molecules carry an electromagnetic point dipole.
MLCW02 21st March 2013
11:00 to 11:50
Modeling Multi-component Liquid Crystal Systems
Multicomponent thermotropic liquid crystal mixtures are widely used in the display industry to obtain desired material properties. Usually, the behavior of such mixtures differs little from that of pure materials. In other systems, such as lyotropic, chromonic, colloidal and elastomeric liquid crystals, the behavior can be dramatically different. Standard mean field theories assume a single component, and do not provide an adequate description for such systems. I will discuss strategies to incorporate both attractive and repulsive interactions of multicomponent systems into mean field models, and present some results.
MLCW02 21st March 2013
11:50 to 12:40
J de Pablo Directed assembly in liquid crystals. Nanoparticles and nanodroplets
Liquid crystals are remarkably sensitive to interfacial interactions. Small perturbations at a liquid crystal interface can in fact be amplified over relative long distances, thereby providing the basis for a wide range of applications. Our recent research efforts have focused on the reverse phenomenon; that is, we have sought to manipulate the interfacial assembly of nanoparticles or the organization of surface active molecules by controlling the structure of a liquid crystal. This presentation will consist of a review of the basic principles that are responsible for liquid crystal-mediated interactions, followed by demonstrations of those principles in the context of two types of systems. In the first, a liquid crystal is used to direct the assembly of nanoparticles; through a combination of molecular and continuum models, it is found that minute changes in interfacial energy and particle size lead to liquid-crystal induced attractions that can span multiple orders of magni tude. Theoretical predictions are confirmed by experimental observations, which also suggest that LC-mediated assembly provides an effective means for fabrication of plasmonic devices. In the second application, the structure of a liquid crystal is controlled by confinement. It is shown that when confined to submicron droplets, the morphology of the liquid crystal depends on a delicate balance between bulk and interfacial contributions to the free energy; that balance can be easily perturbed by adsorption of analytes at the interface, thereby providing the basis for development of chemical or biological sensors. Theoretical predictions also indicate that the three-dimensional order of a liquid crystal can be projected onto a two-dimensional interface, and give rise to novel nanostructures that are not found in simple isotropic fluids.
MLCW02 21st March 2013
14:00 to 14:50
Molecular modeling of liquid crystal elastomers
Liquid crystal elastomers (LCE) are functional materials consisting of weakly crosslinked polymer networks with embedded liquid crystalline (mesogenic) molecules. Consequently, LCE are characterized by a pronounced coupling between macroscopic strain and orientational mesogenic order. As the latter can be controlled by external stimuli such as temperature, electric field, or ultraviolet light, LCE have great potential for application as sensors and actuators.

Here large-scale molecular simulations of swollen main-chain LCE will be presented. The simulated experiments include temperature scans, stress-strain runs, and the application of an external electric field. Our isostress Monte Carlo simulations are capable of reproducing isotropic, nematic and smectic phases, as well as a stress-induced isotropic-to-nematic transition. Moreover, a transversal electric field is seen to induce nematic director rotation resulting in orientational stripe domains. The role of sample swelling has been explored as well.

The simulation output has also been used to connect to typical experimental observables, such as sample dimensions, specific heat, deuterium magnetic resonance spectra, and scattered X-ray patterns.
MLCW02 21st March 2013
14:50 to 15:40
The Round Table Discussion
MLCW02 22nd March 2013
09:00 to 09:50
Structure and Dynamics of Anisotropic Soft Matter
This paper presents theory and modeling of structure and dynamics of three representative anisotropic soft matter materials :(i) confined nematics ; (ii) membranes and surfactant-laden interfaces, and (iii) fiber-filled soft membranes, highlighting the interactions between geometry, order parameters, and material anisotropy. (i)Confined nematics are described using nematodynamics in the bulk, at surfaces and contact lines and used to analyze cholesteric collagen solutions under shear and in film casting processes and demonstrate how liquid crystalline polymer models are able to resolve experimentally observed flow-alignment, banded textures, and free surface undulations. (ii) Membranes are described using membrano-dynamics, which extends the Helfrich-Boussinesq-Scriven model by accounting for bending and torsion dissipation, and is used to establish direct connections between membrane shape and rheology. Lastly we describe (iii) fiber-filled membranes using the integration of nemato-dynamics and membrano-dynamics and apply the theory to plant cell walls, where the paranematic order of the cellulose semiflexible fibrils is coupled to the soft pectin-based membrane curvature, as reported experimentally.
MLCW02 22nd March 2013
09:50 to 10:40
Liquid crystals out of equilibrium: connecting molecular dynamics, kinetic and hydrodynamic equations
I will start from the microscopic Hamiltonian dynamics and use projection-operator formalism to derive a generalized Langevin equation for liquid crystalline systems. Using Markovian approximation this equation then may be tuned into a bona fide stochastic differential equation which may be used for molecular dynamics simulations. Further on, using ideas of propagation of chaos, we can derive kinetic Doi-Smoluchwski type equation, and finally, the hydrodynamic equations as equations for the moments.
MLCW22 22nd March 2013
11:00 to 11:50
Molecular and atomistic simulations of liquid crystals
Liquid crystals (LC) continue to offer a fascinating variety of fundamental physics problems related to molecular organizations in the bulk and their modifications close to interfaces [1]. Here we plan to show some recent results for the simulation of these organizations at molecular and atomistic resolution. At molecular resolution we employ Gay-Berne models and report results for the shape, internal order and chirality of freely suspended low molar mass nematic nanodroplets [2]. We also show that systems as complex as swollen LC elastomers and their deformation in response to the application of an electric field can be simulated [3]. At atomistic level molecular dynamics simulations [4] can now predict actual morphologies and properties in the bulk [4,5] from a specific molecular structure and they can also be useful to analyse NMR data [6,7]. Having validated simulations in the bulk, we also investigate LC close to selected interfaces like hydrogen terminated silicon [1] and crystalline and glassy silica with controlled roughness [8], trying to show how orientational anchoring can be introduced from the microscopic point of view probing the limits of continuum theory on the nanoscale [9].

1 A. Pizzirusso, R. Berardi, L. Muccioli, M. Ricci, C. Zannoni, Chemical Science,3,573(2012) 2 D. Vanzo, M.Ricci, R. Berardi, C.Zannoni, Soft Matter, 8, 11790(2012) 3 G. Skacej, C.Zannoni, PNAS,109,10193(2012) 4 G. Tiberio, L. Muccioli, R. Berardi, C. Zannoni, ChemPhysChem, 10, 125(2009) 5 M.F. Palermo, A. Pizzirusso, L. Muccioli, C. Zannoni, to be submitted (2013) 6 A.Pizzirusso, M.B. Di Cicco, G. Tiberio, L. Muccioli, R. Berardi, C. Zannoni, J.Phys.Chem.B 116,3760(2012) 7 A. C. J. Weber, A. Pizzirusso, L. Muccioli, C. Zannoni, W. L. Meerts, C. A. de Lange, E.E. Burnell, J. Chem. Phys. 136, 174506 (2012) 8 O. M. Roscioni, L. Muccioli, R. G. Della Valle, A. Pizzirusso, M. Ricci, C. Zannoni, to be submitted (2012) 9 M. Ruths, B. Zappone, Langmuir, 28, 8371 (2012).

MLCW22 22nd March 2013
11:50 to 12:40
M Wilson Self-assembly of liquid crystalline nanostructures in aqueous solution
Chromonic mesogens are non-conventional amphiphiles, which self-assemble in aqueous solution to form aggregate structures: rods, stacks or layers. At higher concentrations these aggregates can self-organise to form chromonic mesophases. Initial self-assembly is different to that seen in most conventional amphiphiles: it is enthalpically-driven and takes place in the absence of a critical micelle concentration. Subsequent mesophase formation is driven by entropic factors.

There is great interest in chromonic systems as materials for the fabrication of new thin films for biosensors and optical compensators; and also because a better fundamental understanding of chromonic self-assembly is required to control aggregate structure formation in certain classes of drug molecules.

This talk presents results from molecular simulation studies of chromonic self-assembly at different levels of detail. Atomistic molecular dynamics simulations of the dye molecule, sunset yellow, and the drug molecule, disodium cromoglycate, determine for the first time the structure and dynamical properties of chromonic aggregates in aqueous solution. Showing how subtle changes in intermolecular interactions can change the mode of self-assembly. Coarse-grained models, at the level of dissipative particle dynamics (DPD), demonstrate how simulation provides a tool to engineer new nanostructures by exploring the role of molecular shape and interactions in determining the structure of aggregates formed.

MLCW22 22nd March 2013
14:00 to 14:20
C Stokes Simulations of bent core molecules using molecular dynamics
The nematic phase is normally uniaxial – i.e. there is just one distinct optical axis. In such a phase one set of molecular axes are aligned but the other axes are orientationally disordered. In 1970, however, Freiser showed that a biaxial nematic phase was theoretically possible, in which all three molecular axes are aligned. This phase has since been observed experimentally, predicted to exist theoretically for various particle models and has been seen in simulation studies. Such a phase would have three distinct optical axis and there are possible applications to liquid crystal displays, should a suitable material be found. In this talk I would like to present the results of simulation studies on purely repulsive bent-core models (V-shaped particles). In the limit of very long, thin arms, such shapes have been predicted to exhibit a biaxial nematic phase for bend angles in the region of 110o. In order to test these predictions and also to explore the system’s pha se behaviour at pressures at which the nematic phase is unstable, we have run molecular dynamics simulations for one-component systems, binary mixtures and higher order mixtures (4 – 6 components). In all case the runs started from the isotopic phase and the system, was then slowly compressed, so any phase observed had formed spontaneously. We explored the effects of varying the arm lengths and bend angles of these particles on the phase behaviour. For a one-component system, only particles with bend angles greater than ca. 130o spontaneously formed ordered, equilibrated phases. Typically the phase sequence was isotropic →uniaxial nematic→biaxial smectic A (except for very straight particles in which the smectic phase was uniaxial). No biaxial nematic phase was observed for the arm-lengths simulated. It is possible that if the smectic phase could be destabilized, a biaxial nematic might form in its place. Such destabilization might occur in mixtures. Binary mixtures of bent cores, however, were found.
MLCW22 22nd March 2013
14:20 to 14:40
C Greco A molecular model for the electroclinic effect in nematic liquid crystals
The electroclinic effect (ECE) is an electro-optical effect that consists in a tilt of the optical dielectric tensor of a liquid crystal (LC) material upon application of an external electric field. The tilt is linear in the electric filed, and the proportionality coefficient, the electroclinic coefficient, is a property of the LC material. Originally observed in the orthogonal smectic-A phase made of chiral molecules (smectic-A* phase)[1], the ECE effect was subsequently also measured in the helix-unwound nematic N* phase [2], thus demonstrating that smectic layering is not essential for its appearance. Recently it was also measured in nematic LCs made of non-chiral molecules, upon imposition of an external mechanical twist [3]. The origin of the ECE in nematics is not obvious, and different molecular/environmental contributions have been proposed over the years. We have developed a molecular model for the ECE in nematics. Based on the molecular and phase symmetry, we hav e obtained expressions of the EC coefficient as a function of the relevant molecular properties (dipole moment, polarizability). The use of an atomistic representation of the molecular shape, charges and polarizability allows us to analyze the relationship between the ECE and the molecular structure. We will present some examples and discuss the role of the molecular and phase chirality.

[1] Garoff. S.; Meyer R. B. Phys. Rev. Lett. 1977, 38, 848-851. [2] Li, Z.; Petschek, R. G.; Rosenblatt, C. Phys. Rev. Lett. 1989, 62, 796-799. [3] Basu, R.; Pendery, J. S.; Petschek, R.G.; Lemieux, R. P.; Rosenblatt, C. Phys. Rev. Lett. 2011, 107, 237804: 1-4.

MLCW22 22nd March 2013
14:40 to 15:00
C Ferreiro Random packing of mixtures of hard rods and spheres
Random packing of mixtures of hard spherocylinders and hard spheres are studied for $d \approx L$, where $L$ is the length of the spherocylinder and $d$ the diameter of the spheres. Packing fractions of mixtures of hard spherocylindres with aspect ratios $ 4

References [1] Z. X. Zhang and J. S. van Duijneveldt, J. Chem. Phys., 124, 154910 (2006). [2] Henk N.W. Lekkerkerker and Remco Tuinier, Colloids and the Depletion Interaction, Springer, 2011. [3] N. Yasarawan and J.S. van Duijneveldt, Soft Matter, 6, 353-362 (2010).

MLCW22 22nd March 2013
15:40 to 16:00
P Teixeira The phase behaviour of shape-changing spheroids
Low-molecular-weight liquid crystals are typically modelled as collections of either hard rods or hard discs. However, small,flexible molecules known as tetrapodes also exhibit liquid crystalline phases, including the elusive biaxial nematic phase [1,2]. This is a consequence of the interplay between conformational and packing entropies: the molecules are able to adopt an anisometric stable conformation that allows then to pack more efficiently into orientationally ordered mesophases. Previous theoretical studies of such systems have been presented [3], but in order to capture the essential physics of the process, we introduce a minimal model which permits a clear detailed analysis. In our model a particle can exist in one of two states, corresponding to a prolate and an oblate spheroid. The energies of these two states differ by a prescriamount ε, and the two conformers are in chemical equilibrium. The interactions between the particles are described by the Gaussian Overlap Model [4] and we investigate the phase behaviour using a second-virial (Onsager) approach, which has been successfully applied to binary mixtures of plate-like and rod-like particles [5]. Depending on conditions these mixtures may exhibit biaxial nematic phases and N+--N– co-existence. We use both bifurcation analysis and a numerical minimisation of the free energy to show that, in the L2 approximation: (u) there is no stable biaxial phase even for ε=0 (although there is a metastable biaxial phase in the same density range as the stable uniaxial phase); (ii) the isotropic-to-nematic transition is into either one of two degenerate uniaxial phases, rod-rich or disc-rich.

References: [1] K. Merkel et al., Phys. Rev. Lett. 93, 237801 (2004). [2] J. L. Figueirinhas et al., Phys. Rev. Lett. 94, 107802 (2005). [3] A. G. Vanakaras et al., Mol. Cryst. Liq. Cryst. 362, 67 (2001). [4] B. J. Berne and P. Pechukas, J. Chem. Phys. 56, 4213 (1972). [5] P. J. Camp et al., J.

MLCW22 22nd March 2013
16:00 to 16:20
Simulation of armoured and swollen vesicles
Polymer vesicles, fluid filled polymer sacs, have attracted much attention for applications such as drug delivery vehicles, miniature chemical reactors, or as synthetic, minimal cells. In these applications the vehicles may undergo significant changes in osmotic pressure, pH, or concentration, which may lead to vesicle rupture or collapse. In order to avoid this a number of possible strategies may be used to stabilise vesicles against changes in external environment. In this talk I will discuss some recent simulation work studying two of these - armouring and swelling.

Recently it has been shown that polymer vesicles may be coated with a layer of colloidal particles that armour these, in a similar manner to some biological systems. Simple Monte Carlo simulations were used to reproduce the packing patterns seen in these experimental systems and to study the effect of surface charge density on the self-assembly [1]. Dissipative particle dynamics simulations were used to study the swelling of a polymer bilayer when exposed to small hydrophobic molecules. Above a critical density of hydrophobic molecules the bilayer undergoes a morphological transition characterised by the formation of a bud within the bilayer, consistent with experimental observations of polymer vesicles [2].

[1] R Chen, DJG Pearce, S Fortuna, DL Cheung, and SAF Bon, J Am Chem Soc, 133, 2151 (2011) [2] CDJ Parmenter, R Chen, DL Cheung, and SAF Bon, Soft Matter, in press

MLCW22 22nd March 2013
16:20 to 16:40
T Gibaud Reconfigurable self-assembly through chiral control of interfacial tension
The interfacial tension between molecular species in self-assembling systems plays a crucial role in determining the physical properties of the mesoscopic assemblages. The predominant method for controlling interfacial tension is the addition of surfactant molecules, which preferentially adsorb onto the interface and modify the interactions between the two phases. Using a model colloidal membrane (Fig.1) composed of chiral, rod-like fd-viruses, I will present a new method for controlling interfacial tension which does not require additional surfactant components, but instead utilizes the intrinsic chirality of the constituent rods. I will demonstrate that chirality can be used to continuously tune the interfacial tension of a membrane and to drive a dramatic phase transition from two-dimensional membranes to one-dimensional twisted ribbons. Using a wide variety of microscopic techniques, this transition is characterized over length-scales, ranging from nanometers to microns. Finally, using optical forces we demonstrate that malleable chiral assemblages can easily be moved, stretched, attached to each other, and transformed between multiple polymorphic states, thus enabling precise assembly and sculpting of highly adaptable materials with complex topologies
MLCW22 22nd March 2013
16:40 to 17:00
M Buzza Self-Assembly of Two Dimensional Colloidal Alloys
We study the self-assembly of mixed monolayers of hydrophobic and hydrophilic colloidal particles adsorbed at oil/water interfaces both experimentally and theoretically. Experimentally, we find that by tuning the interactions, composition and packing geometry of the mixed monolayer, a rich variety of two-dimensional super-lattice and cluster structures are formed which are stabilised by strong electrostatic interactions mediated through the oil phase [1,2]. The 2D structures obtained are in excellent agreement with zero temperature lattice sum calculations, indicating that the self-assembly process can be effectively controlled [1-3]. Monte Carlo simulations further reveal that the melting behaviour of these super-lattice structures proceeds via a multi-stage process, with melting temperatures that have a very strong and non-monotonic dependence on composition [3].

[1] A.D. Law, D.M.A. Buzza, T.S. Horozov, Phys. Rev. Lett., 106, 128302 (2011) [2] A.D. Law, M. Auriol, D. Smith, T.S. Horozov, D.M.A. Buzza, submitted [2] A.D. Law, T.S. Horozov, D.M.A. Buzza, Soft Matter, 7, 8923 (2011)

MLC 28th March 2013
11:00 to 12:00
Foundations and derivations of the popular molecular theories of nematics including Maier-Saupe, Onsager and Density functional ones
MLC 2nd April 2013
14:00 to 15:00
Disclinations & Biaxiality in Light
MLC 3rd April 2013
11:00 to 12:00
Projection-operator formalism, BBGKY hierarchy, and kinetic equations. Part I
MLC 4th April 2013
09:00 to 10:00
Orientational and hydrodynamic motions in chiral liquid crystalline films induced by transmembrane flow
Video Conference Seminar from Japan.
MLC 4th April 2013
14:00 to 15:00
D Liarte Elementary statistical models for nematic transitions in liquid-crystalline systems
MLC 5th April 2013
11:00 to 12:00
Projection-operator formalism, BBGKY hierarchy, and kinetic equations. Part 2
MLCW03 8th April 2013
10:00 to 11:00
D Kinderlehrer Remarks about the Janossy effect
Light can change the orientation of a liquid crystal. This is the optical Freedericksz transition, discovered by Saupe. In the Janossy effect, the threshold intensity of the Freedericksz transition is dramatically resuced by the addition of a small amount of dye to the sample. We investigate the theory for this effect derived by E, Kosa, and Palffy-Muhoray. Several themes come together, including molecular motors and Monge-Kantorovich mass transport. This is joint work with Michal Kowalczyk.
MLCW03 8th April 2013
11:30 to 12:30
Analysis of Disclination-Line Defects in Liquid Crytals
We describe mathematical results and techniques of analysis on the structure of defects in thin nematic liquid crystals described by minimizers of the Landau-de Gennes energy involving a tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the coefficient of the elasticity term tends to zero, a limiting uniaxial texture forms with a finite number of defects, all of degree 1/2 or -1/2. We also describe the location of defects and the limiting energy.
MLCW03 8th April 2013
14:00 to 15:00
Modeling the Dynamics of Liquid Crystalline Systems
A key characteristic of liquid crystals, exploited by many device applications, is their symmetry mandated responsivity. Describing the dynamics of the response of liquid crystalline systems to excitations is therefore of considerable interest and importance. Since orientational order is usually characterized in terms of an order parameter, the dynamic response of liquid crystals is often described in terms of the time evolution of the order parameter. A more general description, which gives more information yet is often simpler that the traditional approach, is the time evolution of the generalized density function. We describe a general procedure to obtain such a description, discuss its implementation and give several illustrative examples.
MLCW03 8th April 2013
15:30 to 16:00
Eigenvalue Constraints and Regularity of Q-tensor Navier-Stokes Dynamics
If the Q-tensor order parameter is interpreted as a normalised matrix of second moments of a probability measure on the unit sphere, its eigenvalues are bounded below by -1/3 and above by 2/3. This constraint raises questions regarding the physical predictions of theories which employ the Q-tensor; it also raises analytical issues in both static and dynamic Q-tensor theories of nematic liquid crystals. John Ball and Apala Majumdar recently constructed a singular map on traceless, symmetric matrices that penalises unphysical Q-tensors by giving them an infinite energy cost. In this talk, I shall discuss some mathematical results for a modified Beris-Edwards model of nematic dynamics into which this map is built, including the existence, regularity and so-called `strict physicality' of its weak solutions.
MLCW03 8th April 2013
16:00 to 16:30
Field instabilities of Smectic A liquid crystals in 2D and 3D
We study the de Gennes free energy to describe the undulations instability in smectic A liquid crystals subjected to magnetic fields. If a magnetic field is applied in the direction parallel to the smectic layers, an instability occurs above a threshold magnetic field. When the magnetic field reaches this critical threshold, periodic layer undulations are observed. We prove the existence and stability of the solution to the nonlinear system of de Gennes model using $\Gamma$-convergence method and bifurcation theory. Numerical simulations will be given near and well above the threshold. An efficient numerical scheme for some free energy containing the second order gradient will be presented. Undulation instabilities on three dimensional systems will be also discussed.

Co-author: Carlos J. Garcia-Cervera (UCSB)

MLCW03 9th April 2013
09:00 to 10:00
P Zhang The Small Deborah Number Limit of the Doi-Onsager Equation to the Ericksen-Leslie Equation
We present a rigorous derivation of the Ericksen-Leslie equation starting from the Doi-Onsager equation. As in the fluid dynamic limit of the Boltzmann equation, we first make the Hilbert expansion for the solution of the Doi-Onsager equation. The existence of the Hilbert expansion is connected to an open question whether the energy of the Ericksen-Leslie equation is dissipated. We show that the energy is dissipated for the Ericksen-Leslie equation derived from the Doi-Onsager equation. The most difficult step is to prove a uniform bound for the remainder in the Hilbert expansion. This question is connected to the spectral stability of the linearized Doi-Onsager operator around a critical point. By introducing two important auxiliary operators, the detailed spectral information is obtained for the linearized operator around all critical points. However, these are not enough to justify the small Deborah number limit for the inhomogeneous Doi-Onsager equation, since the elastic stress in the velocity equation is also strongly singular. For this, we need to establish a precise lower bound for a bilinear form associated with the linearized operator. In the bilinear form, the interactions between the part inside the kernel and the part outside the kernel of the linearized operator are very complicated. We find a coordinate transform and introduce a five dimensional space called the Maier-Saupe space such that the interactions between two parts can been seen explicitly by a delicate argument of completing the square. However, the lower bound is very weak for the part inside the Maier-Saupe space. In order to apply them to the error estimates, we have to analyze the structure of the singular terms and introduce a suitable energy functional. Furthermore, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg-Landau approximation, we construct an approximate system with the dissipated energy based on a new formulation of the system.
MLCW03 9th April 2013
10:00 to 11:00
Tangent unit-vector fields: nonabelian homotopy invariants, the Dirichlet energy and their applications in liquid crystal devices
We compute the infimum Dirichlet energy, E(H), of unit-vector fields defined on an octant of the unit sphere, subject to tangent boundary conditions on the octant edges and of arbitrary homotopy type denoted by H. The expression for E(H) involves a new topological invariant – the spelling length – associated with the (nonabelian) fundamental group of the n-times punctured two-sphere. These results are then used for the modelling of the Post Aligned Bistable Nematic (PABN) device, designed by Hewlett Packard Laboratories. We provide analytic approximations for the experimentally observed stable equilibria in the PABN device and propose novel topological and geometrical mechanisms for bistability or multistability in prototype liquid crystal device geometries. This is joint work with Jonathan Robbins, Maxim Zyskin and Chris Newton.
MLCW03 9th April 2013
11:30 to 12:30
On stability of radial hedgehog in Landau - de Gennes model
We investigate stability of radially symmetric solutions in the context of Landau - de Gennes theory. It is well known that radial hedgehog is an unstable solution for low enough temperatures. We show that radial hedgehog is locally stable solution for temperatures close to isotropic-nematic phase transition temperature.
MLCW03 9th April 2013
14:00 to 15:00
AD Zarnescu Eigenframe discontinuities, commutators and nematic defects
In the framework of De Gennes' Q-tensor theory of nematics one can interpret defects as eigenframe discontinuities. A significant analytical difficulty related to understanding these discontinuities is due to the rather complicated relation between the multiparameter dependent matrices and their parametrized eigenvectors. We present necessary and sufficient criteria for determining eigenframe discontinuities (criteria expressed in terms of suitable commutators) as well as some consequences. This is joint work with Jonathan Robbins and Valeriy Slastikov.
MLCW03 9th April 2013
15:30 to 16:00
Wellposedness of a Coupled Navier-Stokes/Q-tensor System
In this work, we show the existence and uniqueness of local strong solution for a coupled Navier-Stokes/Q-tensor system on a bounded domain $\Omega\subset\mathbb{R}^3$ with Dirichlet boundary condition. One of the novelties brought in with respect to the existing literature consists in the fact that we deal with Navier-Stokes equation with variable viscosity. Concerning the methodology, we use an approximation method to handle the linearized system and the existence of solution to the nonlinear system is proved via a Banach's fixed point argument, based on the estimates on the lower order terms.
MLCW03 9th April 2013
16:00 to 16:30
Radial symmetry and biaxiality in nematic liquid crystals
We study the model problem of a nematic liquid crystal confined to a spherical droplet subject to radial anchoring conditions, in the context of the Landau-de Gennes continuum theory. Based on the recent radial symmetry result by Millot & Pisante (J. Eur. Math. Soc. 2010) and Pisante (J. Funct. Anal. 2011) for the vector-valued Ginzburg-Landau equations in three-dimensional superconductivity theory, we prove that global Landau-de Gennes minimizers in the class of uniaxial Q-tensors converge, in the low-temperature limit, to the radial-hegdehog solution of the tensor-valued Ginzburg-Landau equations. Combining this with the result by Majumdar (Eur. J. App. Math. 2012) and by Gartland & Mkaddem (Phys. Rev. E. 1999) that the radial-hedgehog equilibrium is unstable under biaxial perturbations, we obtain the non-purely uniaxial character of global minimizers for sufficiently low temperatures.
MLCW03 10th April 2013
09:00 to 10:00
An inverse problem arising from polarimetric measurements of nematic liquid crystals
This work is motivated by a polarimetric experiment (performed in HP Labs) were a thin slab of nematic liquid crystal was placed on a cylindrical mount, and illuminated by a focused polarized laser beam. As the slab is rotated and the polarimetric measurement data (the so-called Stokes parameters) varies with the angle of incidence. The object of this work was to determine what information on the dielectric permittivity of the liquid crystal could be retrieved from this data.
MLCW03 10th April 2013
10:00 to 11:00
Spontaneous flows and defect proliferation in active nematic liquid crystals
Active liquid crystals are nonequilibrium fluids composed of internally driven elongated units. Examples include mixtures of cytoskeletal filaments and associated motor proteins, bacterial suspensions, the cell cytoskeleton and even non-living analogues, such as monolayers of vibrated granular rods. Due to the internal drive, these systems exhibit a host of nonequilibrium phenomena, including spontaneous laminar flow, large density fluctuations, unusual rheological properties, excitability, and low Reynolds number turbulence. In this talk I will review some of this phenomena and discuss new results on the dynamics and proliferation of topological defects in active liquid crystals. A simple analytical model for the defect dynamics will be shown to reproduce the key features of recent experiments in microtubule-kinesin assemblies.
MLCW03 10th April 2013
11:30 to 12:30
P Biscari Anisotropic elasticity and relaxation in nematic liquid crystals
As early as 1972, Mullen and coworkers showed experimentally that the director alignment of a nematic liquid crystal induces an anisotropic, frequency dependent sound speed in nematic liquid crystals. Similarly, Selinger and co-workers have studied a liquid crystal cell where the nematic molecules can be realigned by an ultrasonic wave, leading to a change in the optical transmission through the cell. The existing theoretical models for this acousto-optic effect propose a free energy that depends on the density gradient thus describing the nematic liquid crystal as a compressible second grade fluid. In this talk we will show that that the angular dependence of the sound speed can be easily reproduced by introducing a simple anisotropic term in the stress tensor, thus providing a simpler first-grade model for the acousto-optic effect. The simplest term is non-hyperelastic, but we show that it can be interpreted as the quasi-incompressible approximation of an elastic term which couples the director orientation with the strain. More interestingly, the frequency dependence of the anisotropic sound speed can be recovered by assuming an irreversible relaxation of the reference configuration with respect to which the strain is measured.
MLCW03 11th April 2013
09:00 to 10:00
Derivation of the Balance Laws for Liquid Crystals using Statistical Mechanics
I will outline how one can derive the continuum-level balances for liquid crystals using statistical mechanics. I will start by considering a discrete system of rigid rods, which motivates an appropriate state space. A probability function is then introduced that satisfies the Liouville equation. This equation serves as the starting point for the derivation of all of the continuum-level balances. The terms appearing in the derived balances, some being nonstandard, are interpreted as expected values.
MLCW03 11th April 2013
10:00 to 11:00
N Walkington Numerical Approximation of the Ericksen Leslie Equations
The Ericksen Leslie equations model the motion of nematic liquid crytaline fluids. The equations comprise the linear and angular momentum equations with non-convex constraints on the kinematic variables. These equations possess a Hamiltonian structure which reveals the subtle coupling of the two equations, and a delicate balance between inertia, transport, and dissipation. While a complete theory for the full nonlinear system is not yet available, many interesting sub-cases have been analyzed.

This talk will focus on the development and analysis of numerical schemes which inherit the Hamiltonian structure, and hence stability, of the continuous problem. In certain situations compactness properties of the discrete solutions can be established which guarantee convergence of schemes.

MLCW03 11th April 2013
11:30 to 12:30
Liquid crystal phases of biological networks: models and analysis
Cytoskeletal networks consist of rigid, rod-like actin protein units jointed by flexible crosslinks, presenting coupled orientational and deformation effects analogous to liquid crystal elastomers. The alignment properties of the rigid rods influence the mechanical response of the network to applied stress and deformation, affecting functionality of the systems. Parameters that characterize these networks include the aspect ratio of the rods and the average length of the crosslinks, with a large span of parameter values found across in-vivo networks. For instance, cytoskeletal networks of red blood cells have very large linkers and small rod aspect ratio, whereas those of cells of the outer hair of the ear have large aspect ratio and short linkers favoring well aligned nematic, in order to achieve optimal sound propagation. We propose a class of free energy densities consisting of the sum of polyconvex functions of the anisotropic deformation tensor and the Landau-de Gennes energy of lyotropic liquid crystals. The growth conditions of the latter, with respect to the rod density and the nematic order tensor at the limit of the minimum eigenvalue -1/3 are essential to recover the limiting deformation map from the minimizing sequences of the anisotropic deformation gradient. We consider a bulk free energy density encoding properties of the rod and the network based on the Lopatina-Selinger construction for the Maier-Saupe theory. We then analyze the phase transition behavior under uniform expansion, biaxial extension and shear deformation, showing that the nematic-isotropic transition may be accompanied by a change of volume, which manifests itself in the nonconvexity of the stress-strain relation. We also account for the fact that in-vivo networks are found in the gel state. We conclude with some remarks on the roles of active elements in the model.
MLCW03 11th April 2013
14:00 to 15:00
Some results on the existence of solutions to the Ericksen-Leslie system
The Ericksen-Leslie theory describes the dynamic flow of liquid crystals. In this talk, we will discuss global existence of solutions of the Ericksen-Leslie system for a general Oseen-Frank model in 2D. We also discuss some new results on the local existence, uniqueness and the blow up criterions of strong solutions to the Ericksen-Leslie system in 3D for the general Oseen-Frank model in 3D.
MLCW03 11th April 2013
15:30 to 16:30
C Wang Some recent results on analysis of nematic liquid crystal flows
In this talk, I will survey some recent works on the analysis of a simplified version of Ericksen-Leslie equation modeling the hydrodynamic motions of nematic liquid crystals.
MLCW03 12th April 2013
09:00 to 10:00
Mechanical response and microstructures in liquid crystal elastomers: small vs large strain theories
In this talk, we will present recent theoretical and numerical results for models of nematic elastomers within the small strain approach.

While strains exhibited by nematic elastomers are usually large, there are cases where this is not so, and the early modeling approaches were using this framework. In fact, the main reason for the developing small strain theories for nematic elastomers is the clear geometric structure of the resulting energy landscape.

We will exploit this structure to discuss material instabilities and stress-strain diagrams, and to suggest possible generalizations to more realistic models.

MLCW03 12th April 2013
10:00 to 11:00
Polar Active Liquid Crystals : microscopics, hydrodynamics and rheology
Colonies of swimming bacteria, mixtures of cytoskeletal protein filaments and motor proteins, and vibrated granular rods are examples of active systems composed of interacting units that consume energy and collectively generate motion and mechanical stresses. Due to their elongated shape, active particles can exhibit orientational order at high concentration and have been likened to ``living liquid crystals". Their rich collective behavior includes nonequilibrium phase transitions and pattern formation on mesoscopic scales. I will describe and summarise recent theoretical results characterising the behaviour of such soft active systems.
MLCW03 12th April 2013
11:30 to 12:30
D Phillips Analysis of defects in minimizers for a planar Frank energy
Smectic C* liquid crystal films are modeled with a relaxed Frank energy, \begin{equation*} \int_\Omega\Big( k_s(\text{div}\, u)^2 + k_b(\text{curl}\, u)^2 + \frac{1}{2\epsilon^2}(1 - |u|^2)^2 \Big)\, dx . \end{equation*} Here $k_s$ and $k_b$ represent the two dimensional splay and bend moduli for the film respectively with $k_s, k_b > 0$, $\Omega$ is a planar domain, and $u$ is an $\mathbb{R}^2$-valued vector field with fixed boundary data having degree $d>0$. We study the limiting pattern for a sequence of minimizers $\{u_\epsilon\}$ as $\epsilon\to 0$. We prove that the pattern contains $d$, degree one defects and that it has a either a radial or circular asymptotic form near each defect depending on the relative values of $k_s$ and $k_b$. We further characterize a renormalized energy for the problem and show that it is minimized by the limit. This is joint work with Sean Colbert-Kelly.
MLC 16th April 2013
14:00 to 15:00
Line defects in a variational model related to liquid crystals
We will analyze the asymptotic behavior of a two-dimensional Ginzburg-Landau model for gradient fields. The main feature of the model consists in the nucleation of line-defects on which the energy concentrates. We develop the concept of entropies coming from scalar conservation laws in order to carry on the asymptotic analysis and to characterize the limit line-energies. We will also discuss the structure of minimizing configurations.
MLC 16th April 2013
15:00 to 16:00
Landau Theory for ''Mendeleev's'' Tables of Polar Smectic Structures
Polar smectic liquid crystals exhibit a variety of phases with multilayer ordering. Recent progress in experimental technique and discovery of several ferrielectric and antiferroelectric phases has put forward a number of fundamental problems: whether the known set of structures is exhaustive or other polar smectic phases exist? Is there an interconnection between azimuthal ordering of molecules in smectic layers and other degrees of freedom such as polar orientation of molecules? We employed the discrete Landau model of phase transitions with two-component order parameter to calculate the structures and phase diagrams of polar smectic liquid crystals. Structures commensurate and incommensurate with layer spacing are formed due to frustrating next-nearest interlayer interaction. Sequences of phases on temperature and the dependence of the phase sequences on model parameters are studied. Influence of different interlayer interactions on the topology of the phase diagrams is analyzed. The calculated phase diagrams enable to describe formation of various polar phases and their temperature sequences, including the unusual reversed phase sequence and the polar phase with six-layer periodicity. Our calculations also predict the existence of a reentrant phase sequence with two incommensurate phases. The results of our calculations demonstrate that discrete Landau model of phase transitions can be successfully used to describe the manifold of polar smectic structures observed in experiment.

Co-authors: P.V.Dolganov (Institute of Solid State Physics, Chernogolvka, Russia), V.M.Zhilin (nstitute of Solid State Physics, Chernogolvka, Russia), V.K.Dolganov (nstitute of Solid State Physics, Chernogolvka, Russia)

MLC 17th April 2013
11:00 to 12:00
P Teixeira Liquid crystal foam
We investigate whether a liquid crystal foam, made by shearing an ionic mesogen, exhibits the same properties as an ordinary liquid foam. In particular, for a quiescent foam we find: (i) where three walls meet, they do so at approximately 120-degree angles, for all times studied; (ii) Lewis’s law of linear relation between cell area and number of sides is approximately satisfied at late times; (iii) the morphological patterns coarsen in time, both T1 and T2 processes are observed and, at late times, evolution is consistent with von Neumann’s law; and (iv) relatively large numbers of 5-sided cells survive up to fairly late times. Results (i) and (iii) suggest that surface tension may play a key role in determining the physics of this system, as it does in low-viscosity liquid foams. If our mesogen is subjected to controlled shear, there is a threshold shear rate below which no foam can form. Above this threshold, a steady-state foam pattern is obtained where the mean cell area generally decreases with increasing shear rate. Furthermore, the steady-state internal cell angles and distribution of cell number of sides deviate from their equilibrium (i.e. zero-shear) values.
MLC 17th April 2013
12:00 to 13:00
Using slow manifolds to model liquid crystals in Q-tensor theories
The $Q$-tensor description of the nematic director field is very powerful as it can cope with defects and complicated geometries. On the other hand, it is also computationally very expensive because the equations for the tensor components are stiff: the contain time scales that differ by six to eight orders of magnitude.

In this talk I will discuss how we can use the stiffness of the director equations to our advantage: we can separate the two time scales, eliminate the fast one and reduce the dynamics of interest to a slow manifold, where the equations are no longer stiff. The ensuing approximate model is both accurate and fast.

Of course, there is a price to be paid: the approximation is valid only away from defects. I will conclude the talk discussing how we are attempting to overcome this restriction.

Co-author Keith Daly (University of Southampton)

MLC 23rd April 2013
14:00 to 15:00
M Telo da Gama Nematics: how do they wet ?
MLC 23rd April 2013
15:00 to 16:00
Ferronematic and ferroelectric liquid crystal colloids
MLC 25th April 2013
11:00 to 12:00
Equivariant normal forms via the Moser trick
As is well known, phase transitions in Landau theory are described by bifurcations of critical points of the free energy. Phase transitions can be most easily analysed for certain normal forms, which contain a small number of essential terms. One would like to know when a given free energy can be brought into a normal form, locally at least, by a near-identity change of variables. If the free energy possesses some symmetries, then one would like this change of variables to preserve these symmetries.

Using as an example a free energy for biaxial nematic liquid crystals, I will discuss an approach to normal form transformations using Moser's trick. The Moser trick reduces the nonlinear problem to a linear one through the determination of the generator of a one-parameter family of transformations linking the identity to the required transformation.

MLC 25th April 2013
12:00 to 13:00
I Stewart Continuum model for smectic A liquid crystals
MLC 30th April 2013
14:00 to 15:00
Facets of Order in Liquid Crystalline Vesicles
The shape of liquid-crystalline vesicles, molecularly thin membrane sacs enclosing a finite volume, is determined by the competition between liquid-crystalline deformations on a surface to be determined and the bending energy of the surface in the ambient bulk. We analyze this problem in two limits: stiff (high bending rigidity compared to Frank modulus) and floppy (low bending energy compared to Frank modulus). The solution in the floppy limit is quite remarkable: it is the surface of a regular tetrahedron with topological defects at the vertices. Thus floppy liquid crystalline vesicles, which have no translational order, are sharp faceted structures more commonly found in hard crystalline materials.
MLC 30th April 2013
15:00 to 16:00
Two and half liquid crystal motors
I describe the theory for two LC-based motors for directly converting light and heat to electrical work. Underpinning these new photo-voltaic strategies is the reduction in LC order by light via photo-isomerisation of dye-rods.

The first motor rests on optically reducing the dielectric susceptibility, the second on reducing the ferro-electric polarisation. Non-linear absorption determines the dynamics by bleaching front propagation.

Motor 3 is an optical-to-mechanical converter, relying on a photo-mechanical force cycle or turbine. It is still work in progress and I only sketch the basic ideas.

In all cases the fundamental efficiency limits (Carnot?) still require evaluation, but it is possible to calculate the efficiencies of the motors as designed. They depend on material parameters, once geometry is optimised. In motors 1 and 2, they could range from about 2 - 7% for existing materials.

MLC 2nd May 2013
11:00 to 12:00
Molecular-statistical theory of surface anchoring of LCs. Fundamental problems
MLC 2nd May 2013
12:00 to 13:00
O Lavrentovich Statics and dynamics of colloidal particles in liquid crystals
MLC 7th May 2013
11:00 to 12:00
The Enigma of Optical Momentum
It is more than 100 years since the battle began to determine the correct form of the momentum of light inside a material medium. The two principal contenders for the momentum density are those attributed to Abraham

g$_Abr = $$ExH\over c$^2$

and to Minkowski

g$_Min = DxB

The work of Minkowski suggests that the momentum of each photon exceeds its value in free space by a factor of the refractive index. Abraham's approach, however, requires that the momentum is less than that in free space by the same factor.

Compelling arguments have been proposed for each of the two candidate momenta. A simple application of Newton's first law of motion to the combined system of a medium and a single photon, for example, leads unambiguously to the Abraham form. An equally simple analysis of single or double slit diffraction, however, leads equally powerfully to the Minkowski form. The problem has not been resolved by experiment, moreover, with experiments supporting both candidate momenta being reported.

The resolution, of course is that both are correct …

MLC 7th May 2013
12:00 to 13:00
Molecular organizations in the bulk and close to surfaces
Computer simulations (Monte Carlo and Molecular Dynamics) provide a powerful tool for obtaining molecular organizations starting from microscopic interactions. These interactions could be generic and very simple (based on arbitrarily chosen shapes and attraction laws) or realistic, atomistic, based on quantum mechanically generated representations of the constituent molecules. In all cases simulations provide the equivalent of computer experiments that offer terms of comparison for mathematical theories, with a level of detail and of possibilities for virtual experiments (e.g. the switching on and off of some of the interactions) not available in real life. A number of examples will be shown for liquid crystal systems in the bulk and close to interfaces, where recent results hint that the type of boundary conditions currently used in some mathematical theories may have to be extended.
MLC 7th May 2013
14:00 to 15:00
Topological defects in nematic liquid crystals dictated by topologically nontrivial confinement and colloids
Well known approaches for inducing topological defects in nematics include geometric confinement of the liquid crystalline material into spherical droplets and also the use of colloidal microspheres dispersed in the bulk of a uniformly aligned liquid crystal. In both cases, topological defects appear to assure the topological charge conservation while compensating for the topological charges due well-defined boundary conditions at the surfaces of droplets and particles. This lecture will discuss the topology-dictated generation of defects in liquid crystals confined into topologically nontrivial handlebody-shaped pores and droplets as well as when topologically nontrivial colloidal microparticles are introduced into an aligned liquid crystal. Furthermore, it will be shown that stable hierarchical arrays of defects in confined chiral nematic liquid crystals can be generated and controlled using optical vortex laser beams. Experimental studies will be compared with the results of numerical modeling.
MLC 9th May 2013
11:00 to 12:00
New numerical scheme and simulations for undulations in smectic A liquid crystals
MLC 9th May 2013
12:00 to 13:00
J Yeomans Active nematics: the role of defects
MLC 14th May 2013
14:00 to 15:00
Effect of flow on nematic fluctuations in a slab
MLC 16th May 2013
12:00 to 13:00
Soft active matter - liquid crystalline order, rheology and oscillations
MLCW05 21st May 2013
11:10 to 11:30
L Corson Liquid dielectrophoresis and wrinkling on the surface of a fluid layer
There is a growing technology-driven interest in using external forces to move or shape small quantities of liquids. One existing technique, electrowetting, involves the application of an electric field to a conducting liquid. A disadvantage of this technique is that the liquid must remain in contact with the electrodes. However, this is not the case in liquid dielectrophoresis, where a dielectric (i.e. non-conducting) liquid is used. A common aspect to both these techniques is that electrical surface stresses at liquid-air or liquid-liquid interfaces play an important role.

In this work we consider a layer of dielectric liquid of non-dimensional depth $h(x,t)$ wetting a horizontal electrode with a hydrodynamically passive dielectric fluid (e.g. air) above. A second electrode is located at a distance $d>h$ above the lower substrate. When the applied voltage is increased past a critical value, an instability occurs on the free surface of the liquid. We investigate how the material and cell geometry parameters affect the critical applied voltage and the form of the instability. Using linear stability analysis, we find that there exists a critical spacing $d_{c}$ above which the fastest growing unstable mode has a non-zero wave number, so that undulations (``wrinkles'') form on the free surface. Below this critical spacing, the fastest growing unstable mode has a zero wave number, so that wrinkles do not form. In general, we also find that higher values of the inverse Bond number $\tau$ (proportional to the surface tension) lead to a stab ilisation of the zero wave number mode, i.e. higher values of $d$ are required for wrinkling to occur. Furthermore, if the inverse Bond number is sufficiently low, a second critical spacing $\tilde{d}_c

MLCW05 21st May 2013
11:30 to 11:50
Hydrodynamic description of thin nematic films
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal. Firstly, we clarify how the elastic energy enters the evolution equation for the film thickness. We show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. Secondly, based on a gradient dynamics approach, we propose a film thickness evolution equation that describes a free surface thin film of nematic liquid crystals on a solid substrate under weak anchoring conditions at the free surface. We show that in the intermediate film thickness range anchoring and bulk energies compete what may result in a linear instability of the free surfa ce of the film.
MLCW05 21st May 2013
11:50 to 12:10
S Bedford Variational problems for cholesteric liquid crystals - Function spaces and competing theories
Generally chiral nematic liquid crystals have been seen as an aside to nematics, and have been studied less as a result. However they can exhibit many and varied patterns in the form of cholesteric fingers or filaments. If these behaviours were understood and controllable it could prove to be a valuable advance in industry devices. The notion of cholesteric frustration appears to be what drives the existence of the complicated minima, as a result boundary conditions, cell geometry and surface energies are all extremely important in the creation of a tractable problem, but so too is the function space in which we choose to minimise. More generally it might be possible, in some cases, to see different theories (Oseen-Frank, Ericksen, Q-Tensor) as merely minimisations in different function spaces.
MLCW05 21st May 2013
12:10 to 12:30
Open Problems Session
MLCW05 21st May 2013
13:30 to 13:50
Interfacial motion in flexo- and order-electric switching between nematic filled states
We consider a nematic liquid crystal, in coexistence with its isotropic phase, in contact with a substrate patterned with rectangular grooves. In such a system, the nematic phase may fill the grooves without the occurrence of complete wetting. There may exist multiple (meta)stable filled states, each characterised by the type of distortion (bend or splay) in each corner of the groove and by the shape of the nematic-isotropic interface, and additionally the plateaux that separate the grooves may be either dry or wet with a thin layer of nematic. Using numerical simulations, we analyse the dynamical response of the system to an externally-applied electric field, with the aim of identifying switching transitions between these filled states. We find that order-electric coupling between the fluid and the field provides a means of switching between states where the plateaux between grooves are dry and states where they are wet by a nematic layer, without affecting the configu ration of the nematic within the groove. We find that flexoelectric coupling may change the nematic texture in the groove, provided that the flexoelectric coupling differentiates between the types of distortion at the corners of the substrate. We identify intermediate stages of the transitions, and the role played by the motion of the nematic-isotropic interface. We determine quantitatively the field magnitudes and orientations required to effect each type of transition.
MLCW05 21st May 2013
13:50 to 14:10
M Nieuwenhuis A description of the smectic phase using statistical mechanics
Many different interaction potentials have been used in order to model phase transitions for liquid crystals. One of the most fundamental theories used for numerical simulations is the density functional theory. However, the main task in this theory is to find a suitable approximation for the energy functional which is in general very difficult. In this short presentation I would like to give a brief overview over the techniques that can be used in order to capture the mathematical characteristics of the smectic phase.
MLCW05 21st May 2013
14:10 to 14:30
R Lund Domain wall motion in magnetic nanowires: an asymptotic approach
We develop a systematic asymptotic description of domain wall motion in a magnetic nanowire. The Landau--Lifshitz--Gilbert equation is linearized about a static solution and the magnetization dynamics investigated via a perturbation expansion. We compute leading order behaviour, propagation velocities, and first order corrections of both travelling waves and oscillatory solutions, and find bifurcation points between these two types of solutions.
MLCW05 21st May 2013
16:00 to 16:20
Boundary-roughness effects in nematic liquid crystals
Paolo Biscari and Stefano Turzi considered a plate with an undulatory pattern. They replace the corrugation with sinusoidal boundary conditions, and use formal asymptotics for the analysis. I would like to use the method of gamma convergence to determine the effective energy and its minimizers for this problem.
MLCW05 21st May 2013
16:20 to 16:40
E Virga Open Problems Session
MLCW05 21st May 2013
16:40 to 17:00
Open Problems Session
MLCW05 22nd May 2013
09:00 to 09:20
Thermal effects in liquid crystal layers
In this talk I will give a brief overview of the work I have undertaken in the first few months of my PhD. Starting with a review of some classic thermally-driven instabilities in Newtonian liquids, including Rayleigh-Benard convection and the Marangoni effect, I then consider instabilities within liquid crystal systems. Using an extension of Ericksen-Leslie theory to include thermal effects, Rayleigh-Benard convection in a nematic is considered. Possible extensions of these previously known results are then discussed in the context of the microfluidics of liquid crystal materials.
MLCW05 22nd May 2013
09:20 to 09:40
Random packing of rods and spheres
Random packing of mixtures of hard spherocylinders and hard spheres are studied for spheres with a diameter similar to the length of the spherocylinders. Packing fractions of hard spherocylindres with aspect ratios 0
MLCW05 22nd May 2013
09:40 to 10:00
J Taylor A physical model to predict a ferroelectric nematic phase
A ferrroelectric nematic phase is desirable both from a practical and theoretical viewpoint, but experimentally it has yet to be observed. Mathematically, such a phase in polar mesogens could be described in a similar way to the Landau-De Gennes Q-tensor theory, but importantly disrespecting the typical head-to-tail symmetry, so that a second order parameter representing the polarisation of the state enters into the model. This talk is concerned with designing a model in terms of these moments that respects the physicality of order parameters.
MLCW05 22nd May 2013
10:00 to 10:20
T To Molecular field theory for biaxial smectic A liquid crystals
Stable biaxial nematics (Nb) have been reported in a few experimental systems and the phases are often difficult to prove conclusively; however, stable biaxial smectic A phases (SmAb) have been found in a larger number of systems in which the evident is conclusive. To understand the stability difference between Nb and SmAb, we use a molecular field theory that combines Straley's theory [1] for biaxial nematics and McMillan's theory [2] for uniaxial smectic A phases. To simplify the calculation, we use alternatively the geometric mean [3] and the Sonnet-Virga-Durand [4] approximation to reduce the number of biaxiality parameters to one; in addition, we use the Kventsel-Luckhurst-Zewdie [5] approximation to decouple the orientational and translational distribution functions. Thus our simple theory has one biaxiality parameter and one smecticity parameter; together with three order parameters. The resulting phase diagrams showed that, for a large region of the para meter space, the presence of the smectic A phases disallowed Nb to form. On the other hand, SmAb is always stable at ground state for positive smecticity parameter. Thus this may explain why SmAb has been found more abundant than Nb.

[1] J. P. Straley, Phys. Rev. A 10, 1881 (1974). [2] W. L. McMillan, Phys. Rev. A 4, 1238 (1971). [3] G. R. Luckhurst, C. Zannoni, P. L. Nordio, and U. Segre, Mol. Phys. 30, 1345 (1975). [4] A. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003). [5] G. F. Kventsel, G. R. Luckhurst, and H. B. Zewdie, Mol. Phys. 56, 589 (1985).

MLCW05 22nd May 2013
10:50 to 11:10
Modeling Sm-A LCEs with defects
Sm-A LCEs are known to exhibit very different responses to stretching parallel and perpendicular to the smectic layer normal.

Side-chain Sm-A LCE films in particular have been extensively studied both theoretically and experimentally since the work of Nishikawa and Finkelmann in 1999. Typically a drastic drop in the elastic modulus after a critical stress can be observed when stretching parallel to the layer normal. Adams and Warner (2005) derived a model for Sm-A LCEs that explains this softening behaviour by the onset of microstructure also theoretically. The simplest of these microstructures consists in a fine scale buckling of layers. However, more complex microstructures are possible, as was shown in (Adams, Conti, DeSimone, & Dolzmann, 2008).

Our aim is to adapt this theory to try to understand the recent experimental results of Komp and Finkelmann (2007), whose Sm-A LCE films show different optical behaviour and behaviour of the order parameter on stretching parallel to the director when compared with the response of the original Nishikawa and Finkelmann LCE. We believe that the difference may be related to the presence of defects in the sample, as suggested by Komp and Finkelmann: the difficulty lies in how to model this situation.

MLCW05 22nd May 2013
11:10 to 11:30
Designing a crawling cell using soft materials
Eukaryotic cells have been observed to be able to move in various media. One obvious example is provided by the keratocyte cells which are able to crawl on a 2D substrate (such as glass slides). In this talk, we aim to build a minimal hydrodynamic model of a crawling cell using ideas from soft matter physics such as binary liquid and liquid crystals. The simplest model of a cell is probably just a droplet sitting on a surface. However, a passive droplet will not be able to move on its own. To make it moves, we have to add some non-equilibrium physics into it. This is provided by actin polymerisation and actin-myosin contraction inside the cell cytoskeleton. These two active processes can then be coarse-grained into a set of hydrodynamic equations which are similar to that of active liquid crystals.
MLCW05 22nd May 2013
11:30 to 11:50
L Liu The approach to equilibrium for the Ericksen-Leslie system and related questions of Q-tensor theory
I will talk a bit about the approach to equilibrium in liquid crystal materials. And I shall talk about viscoelasticity equation and the connection of it to liquid crystal problems. The Ericksen-Leslie system plays an important row in describing the flow of nematic liquid crystal materials. Under Parodi's relation, we have the global well-posedness and Lyapunov stability for the system near local energy minimizers. There also exist some similar results in Q-tensor theory and I am interested to find the relation between the two theories. Further, there shares some common traits in the Ericksen-Leslie system with the problem of the approach to equilibrium in nonlinear quasistatic viscoelasticity system. I will try to compare the two systems and list the difficulties that need to be solved.
MLCW05 22nd May 2013
14:00 to 14:20
Open problems session
MLCW05 22nd May 2013
14:20 to 14:40
Open problems Session
MLCW05 22nd May 2013
14:40 to 15:00
Open Problems Session
MLC 23rd May 2013
11:00 to 12:00
Energies and Shear Moduli in Nematic Elastomers
MLC 23rd May 2013
12:00 to 13:00
Photorefractive effect and two beam energy exchange in hybrid liquid crystal cells
Hybrid organic-inorganic photorefractive cells possess many advantages among photorefractive systems. In such cells a liquid crystal (LC) is sandwiched between two photorefractive layers. The interfering incident light beams induce a periodic space-charge field in the photorefractive layers. Space-charge electric fields leak into the adjacent LC, causing director modulation, and hence the diffraction grating. Each light beam diffracts from the induced grating, leading to energy gain and loss within each beam.

We developed a theoretical model to describe two-beam energy exchange in a hybrid nematic cell and calculated the energy gain of the weak beam, as a result of its interaction with the pump beam. In the theory, the flexoelectric mechanism for electric field-director coupling is a more important than the LC static dielectric anisotropy coupling. Thus, flexoelectricity is the main physical mechanism governing the magnitude of the director grating and the two-beam coupling. The LC optics is described in the Bragg regime.

The theory has been compared with results of an experimental study on hybrid cells filled with the LC mixture TL 205. Experimentally the energy gain is maximal at much lower grating wave numbers than is predicted by naïve theory. However, if the director reorientation is cubic rather than linear in the space-charge field term, then good agreement between theory and experiment can be achieved using only a single fitting parameter. We provide a semiquantitative argument to justify this nonlinearity in terms of electric-field-induced local phase separation between different components of the liquid crystal.

Hybrid cholesteric systems exhibit extra features not observed in hybrid nematic cells. Specifically, the gain coefficient changes sign as a function of grating spacing. Following the paradigm used for hybrid nematic cells we developed a theory for the optical gain characteristics of hybrid cholesteric cells. Theoretical results for exponential gain coefficients have been compared with experimental results for hybrid cells filled with cholesteric mixtures TL205/CB15 and BL038/CB15. In order to reconcile theory and experiment, we require that near the cell surface, nematic ordering must dominate. Under this supposition, we are able to fit experimental data to theory for both cholesteric mixtures, subject to the use of some fitting parameters. This provides good evidence that the key physics of the system has been correctly identified.

*(joint work with Victor Reshetnyak, Tim Sluckin, Gary Cook, and Dean Evans)

MLC 28th May 2013
14:00 to 15:00
Landau weak crystallization theory of main phase transition in membranes
We demonstrate that experimental data concerning the main phase transition in membranes can be rationalized in the framework of a theoretical scheme constructed in the spirit of the so-called weak crystallization theory. The scheme enables to explain a combination of seemingly contradictory features of the main phase transition: its first order nature and a well pronounced pre-transitional critical behaviour of various physical quantities.
MLC 30th May 2013
11:00 to 12:00
J Ball Professor Jerry Ericksen interviewed by John Ball. A film of a recent interview of Jerry Ericksen will be shown.
MLC 4th June 2013
14:00 to 15:00
Photoinduced deformation of crosslinked liquid crystal polymers: from ultraviolet to near-infrared light
MLC 6th June 2013
11:00 to 12:00
The geometric elastic theory of fluid membrane vesicles with a liquid crystal model: the Helfrich model of lipid bilayers and its applications to soft matter
MLC 7th June 2013
14:00 to 17:00
Soviet Physics in 1920s-1950s and English- Russian Scientific Relations ( Cockroft, Dirac, Kapitsa, Peierls...)
MLC 11th June 2013
14:00 to 15:00
Existence and uniqueness of the radial hedgehog in Landau-de Gennes model
In the satellite meeting in Oxford in April, V. Slastikov reported on our joint work with R. Ignat and A. Zarnescu on the stability/instability of the radial hedgehog in the context of Landau-de Gennes theory. In this talk we discuss the existence and uniqueness of such solution. A comparison principle for (singular) nonlinear and radially symmetric elliptic equations will also be presented.
MLC 13th June 2013
11:00 to 12:00
B Pelcovits Self assembly of fd viruses
Self-assembled Smectic-A monolayers composed of chiral fd viruses in the presence of a polymer depletant have been shown by the Dogic group to exhibit a variety of novel structures as a function of temperature and polymer concentration. After reviewing some of the experimental findings I will discuss a phenomenological theoretical model of this system based on the Helfrich membrane energy and the de Gennes theory of smectics. I will show how this model can be used to understand some of the fascinating experimental observations of fd self-assembly.
MLC 13th June 2013
16:00 to 17:30
N Abbott Endotoxin-Induced Ordering Transitions in Liquid Crystalline Droplets
This is a remote lecture, from Wisconsin.
MLCW04 24th June 2013
09:45 to 10:30
Liquid crystal defects, a critical overview
Defects in liquid crystals present an extremely vast set of situations, depending on the nature of the order parameter, elasticity properties, boundary conditions. One distinguishes : defects characteristic of liquid crystalline media with one or two discrete repeat distances (smectic and columnar phases) which can be investigated by pure geometric methods ; defects characteristic of a director order parameter, which employ the Volterra process (for one dimensional defects) and topological methods, those latter providing scope for defects of various dimensionalities ; finally continuous defects whose consideration is essential for a description of defect physical properties. These topics will be confronted with an historical point of view and possible future developments.
MLCW04 24th June 2013
11:00 to 12:00
R Kamien Pure and Applied Focal Conics
The epitaxial assembly of toric focal conic domain (TFCD) arrays of smectic-A liquid crystals onto pillar arrays is studied. The 3D nature of the pillar array is crucial to confine and direct the formation of TFCDs on the top of each pillar and between neighboring pillars, leading to highly ordered square and hexagonal array TFCDs persisting deeply into the bulk.
MLCW04 24th June 2013
12:00 to 12:45
Exotic defect structures in a strongly confined chiral liquid crystal
We present our numerical results on the structures of a chiral nematic liquid crystal when it is confined in a thin planar cell with strong anchoring on its surfaces. We are interested in the cases where the liquid crystal exhibit a cholesteric blue phase under no confinement, and the cell thickness is of the order of or smaller than the cholesteric pitch. We show various stable exotic defect structures depending on temperature, cell thickness, and the type of anchoring. They include a hexagonal lattice of Skyrmion excitations, and a regular array of ring defects. These exotic defect structures can be regarded as a result of frustrations between bulk blue phase ordering and surface anchoring that does not allow it.
MLCW04 24th June 2013
14:00 to 14:45
Textures and Topology in Liquid Crystals
The textures of liquid crystals have always been central in identifying mesophases and understanding their properties. They are deeply connected with topology, both of the liquid crystal and of the environment that it lives in, so that controlling and describing topological properties provides a key tool in constructing and understanding complex three-dimensional textures. I will describe two applications of topological ideas to studying mesophases: the general characterisation of three-dimensional textures in nematics -- illustrated through the analysis of torons and the Hopf fibration in confined cholesterics -- and the formation of elegant knots and links around colloidal particles representing non-orientable surfaces.
MLCW04 24th June 2013
14:45 to 15:30
Nematic braids: Effects of chirality and confinement
Nematic disclinations can form stable braids when they are stabilized by a confining geometry, chirality, or by interplay of both effects. These are stable or metastable topologically diverse defect structures in the nematic ordering field. Based on the synergy of our theoretical and numerical, approaches we are able to characterize geometries and properties of disclination loops forming braids by winding numbers, lengths, knot or link types, and self-linking numbers. We focus our attention to selected nematic braids of the lowest complexity: knotted 2D colloidal crystals, opal structures permeated by nematics, and knots in cholesteic drops. With this overview I would like to show how topology and geometry enables the assembling of complex soft materials. [1] S. ?opar and S. Žumer, Nematic Braids: Topological Invariants and Rewiring of Disclinations, Phys. Rev. Lett. 106, 177801 (2011). [2] S. ?opar, and S. Žumer, Quaternions and hybrid nematic disclinations, Proc. R. Soc. A 469, 1471 (2013). [3] U. Tkalec, M. Ravnik, S. ?opar, S. Žumer and I. Muševi?, Reconfigurable Knots and Links in Chiral Nematic Colloids, Science 333, 62 (2011). [4] S. ?opar, N. A. Clark, M. Ravnik and S. Žumer, Elementary building blocks of nematic disclination networks in densely packed 3D colloidal lattices, Soft Matter, DOI: 10.1039/C3SM50475A (2013).
MLCW04 24th June 2013
16:00 to 17:00
T Lubensky Rigidity, Zero Modes, States of Self Stress, and Surface Phonons in Periodic and Diluted Periodic Networks near their Instability Limit
Frames consisting of nodes connected pairwise by rigid rods or central-force springs, possibly with preferred relative angles controlled by bending forces, are useful models for systems as diverse as architectural structures, crystalline and amorphous solids, sphere packings and granular matter, networks of semi-flexible polymers, and protein structure. The rigidity of these networks depends on the average coordination number z of the nodes: If z is small enough, the frames have internal zero-frequency modes, and they are "floppy"; if z is large enough, they have no internal zero modes and they are rigid. The critical point separating these two regimes occurs at a rigidity threshold, which corresponds closely to what is often referred to as the isostatic point, that for central forces in d-dimensions occurs at coordination number zc = 2d. At and near the rigidity threshold, elastic frames exhibit unique and interesting properties, including extreme sensitivity to boundary conditions, power-law scaling of elastic moduli with (z- zc), and diverging length and time scales.

This talk will explore elastic and mechanical properties and mode structures of model periodic and diluted periodic lattices, such as the square and kagome lattices with central-force springs, that are just on verge of mechanical instability, and 4-coordinated lattices in two and three dimensions that are stabilized by bending forces. It will discuss the origin and nature of zero modes of these structures under both periodic (PBC) and free boundary conditions (FBC), and it will derive general conditions under which (a) the zero modes under the two boundary conditions are essentially identical and (b) under which zero modes do not appear in the periodic spectrum but do appear as surface Rayleigh waves in the free spectrum. In the former situation, lattices are generally in a type of critical state that admits states of self-stress in which there can be tension in bars with zero force on any node, and distortions away from that state give rise to surface modes under free boundary conditions whose degree of penetration into the bulk diverges at the critical state. This general phenomenon also occurs in sub-isostatic lattices like the honeycomb lattice. The talk will also explore diluted 4-coordinated lattices as models for networks of semi-flexible polymers, discuss the special properties that result when constituent polymers adopt strictly straight configurations.

MLCW04 25th June 2013
09:00 to 09:45
Topological colloids and particle-induced defects in liquid crystals
We fabricate colloidal particles with nontrivial surface topology, including colloidal handlebodies, knots, links, Mobius strings, and Seifert surfaces. When introduced into a nematic liquid crystal with a uniform far-field director, these particles induce three-dimensional director fields and topological defects around them. We use director switching by electric fields, laser tweezing of defects, and local photothermal melting of the liquid crystal to promote transformations among many stable and metastable particle-induced director configurations and then explore them by means of a direct label-free three-dimensional nonlinear optical imaging. This reveals many peculiarities of the interplay between topologies of colloidal surfaces, director fields, and defects, which we find being in agreement with Gauss-Bonnet and Poincaré-Hopf index theorems. The lecture will conclude with a brief discussion of how these findings may lay the groundwork for new types of topology-di ctated elastic self-assembly in liquid crystals and experimental study of low-dimensional topology.
MLCW04 25th June 2013
09:45 to 10:30
Colloidal Doping of Cholesterics and Blue Phases
At the interface between a cholesteric phase and an isotropic fluid, an array of defects arises. This creates for embedded colloidal particles a free energy landscape that depends on the ratio of colloid size to cholesteric pitch and on the strength of anchoring at the colloid-cholesteric interface. I shall outline recent experiments and simulations that probe this landscape. A somewhat similar situation arises when colloids are added to blue phases, for which the defect array is not interfacial but permeates the bulk phase. Preliminary simulations suggest a variety of structures, many metastable, with interesting transitions inducible by external fields and/or flow.
MLCW04 25th June 2013
11:00 to 11:45
Modelling actomyosin droplets, and their consequences for cell motility
We present a lattice Boltzmann study of the dynamics of an actomyosin droplet, described in terms of a continuum model which follows the time evolution of actomyosin density, actin polarisation and flow. This analysis offers a simple representation of a “cell extract”, which is a highly simplified system used in vitro to understand cell dynamics, and which essentially only comprises the actin cytoskeleton and an enclosing cell membrane. In the absence of polymerization and depolymerization processes (‘treadmilling’), the dynamics of our actomyosin droplet arises solely from the contractile motion of myosin motors; this should be unchanged when polarity is inverted. Our results suggest that motility can arise in the absence of treadmilling, by spontaneous symmetry breaking (SSB) of polarity inversion symmetry. This motility mode driven by myosin contractility alone may be relevant to cell motion in three dimensions, where frictional forces, which are crucial to convert actin polymerisatino into motion, are likely to be modest. We also show of active droplets crawling on a substrate, when both treadmilling and contractility are taken into account. Our droplets can adopt a number of morphologies and motility modes found experimentally in cells, such as lamellipodia, pseudopodia and oscillatory cell motion.
MLCW04 25th June 2013
11:45 to 12:30
Polar Active LCs: Non-equilibrium steady states and fluctuations
MLCW04 25th June 2013
14:00 to 14:45
J Yeomans Active Nematics
Active systems, such as the cytoskeleton and bacterial suspensions, provide their own energy and hence operate out of thermodynamic equilibrium. Continuum models describing active systems are closely related to those describing liquid crystal hydrodynamics, together with an additional ‘active’ stress term. We discuss how the behaviour of the active continuum models depends on model parameters, such as the strength of the activity and the liquid crystal tumbling parameter, and we compare our results to recent experiments on cytoskeletal gels.
MLCW04 25th June 2013
14:45 to 15:30
Z Dogic Hierarchical active matter: from extensible bundles to active gels, streaming liquid crystals and motile emulsions
The emerging field of active matter promises an entirely new category of materials, with highly sought after properties such as autonomous motility and internally generated flows. In this vein, I will describe recent experiments that have focused on reconstituting dynamical structures from purified biochemical components. In particular I will describe recent advances that include: (1) assembly of a minimal model of synthetic cilia capable of generating periodic beating patterns, and conditions under which they exhibit metachronal traveling waves, (2) study of 2D active nematic liquid crystals whose streaming flows are determined by internal fractures and self-healing as well as spontaneous unbinding and recombination of oppositely charged disclination defects, (3) reconstitution of active gels characterized by highly tunable and controllable spontaneous internal flows, and (4) assembly of active emulsions in which aqueous droplets spontaneously crawl when in contact with a hard wall.
MLCW04 25th June 2013
16:00 to 16:45
J Toner Rice, Locusts and Chemical Waves: A Hydrodynamic Theory of Polar Active Smectics
We present a hydrodynamic theory of polar active smectics, by which we mean active striped systemsactive systems, both with and without number conservation. For the latter, we find quasi long-ranged smectic order in $d=2$ and long-ranged smectic order in $d=3$. In $d=2$ there is a Kosterlitz-Thouless type phase transition from the smectic phase to the ordered fluid phase driven by increasing the noise strength. For the number conserving case, we find that giant number fluctuations are greatly suppressed by the smectic order; that smectic order is long-ranged in $d=3$; and that nonlinear effects become important in $d=2$.
MLCW04 26th June 2013
09:00 to 09:45
V Vitelli Chiral symmetry breaking in confined nematics
We analyze the complex nematic textures and defect structures that result from the competition between topological constraints and the elasticity of nematic liquid crystals confined in droplets with handles stabilized against surface-tension-driven instabilities using a yield-stress material as outer fluid. We uncover a surprisingly persistent twisted configuration of the nematic director inside the droplets when tangential anchoring is established at their boundaries, which we explain after considering the influence of saddle-splay on the elastic free energy. For toroidal droplets, we find that the saddle-splay energy screens the twisting energy resulting in a spontaneous breaking of mirror symmetry; the chiral twisted state persists for aspect ratios as large as ~20. For droplets with additional handles, two additional -1 surface defects per handle are generated in regions with local saddle geometry.
MLCW04 26th June 2013
09:45 to 10:30
Hyperbolic geometry in liquid crystalline interfaces
Fluid interfaces, such as soap films, liquid droplets, or lipid membranes, are known to give rise to several special geometries, whose complexity and beauty continue to fascinate us, as observers of the natural world, and challenge us as scientists. Here I show that a special class of surfaces of constant negative Gaussian curvature can be obtained in fluid interfaces equipped with an orientational ordered phase. These arise in various soft and biological materials, such as nematic liquid crystals, cytoskeletal assemblies, or hexatic colloidal suspensions. The purely hyperbolic morphology originates from the competition between surface tension, that reduces the area of the interface at the expense of increasing its Gaussian curvature, and the orientational elasticity of the ordered phase, that in turn suffers for the distortion induced by the underlying curvature.
MLCW04 26th June 2013
11:00 to 11:45
CD Modes Avenues to Active Shape Control in Nematic Solid Sheets
Much recent progress has been made in the study of nematic solids, both glassy and elastomeric in connection with these materials' remarkable coupling of the nematic texture and liquid crystalline properties to bulk elasticity and deformations. This talk will present a survey of the mechanisms and machineries that have been recently developed to allow for active control of many aspects of the shape of a thin sheet or shell of nematic solid: extrinsic bending, the blueprinting of intrinsic curvature and shape, switchable pores, and more. These examples, in addition to providing a rich tool box for potential device design, will also elucidate the connection between the topology of the nematic director field and the geometry of elastic deformations in this model system.
MLCW04 26th June 2013
11:45 to 12:30
E Virga Curvature potentials for defects on nematic shells
Nematic shells are thin films of nematic liquid crystal deposited on rigid colloidal particles, which can be manufactured in different shapes and guises. The two-dimensional order tensor that describes the local organization of liquid crystal molecules, which tend to lie parallel to the colloids' surface, vanishes whenever no orientation is prevailing on average. The points where this takes place are called defect, as they lack order. The lectuer will review recent work concerned with the interaction between defects and the underlying surface. In particular, arguments will be offered that identify appropiate geometric potentials, depending on the shell's curvatures, which either promote or hamper defects, attract or repel them.
MLCW04 26th June 2013
14:00 to 14:45
Liquid Crystal elastomers: microstructures and active shape control
Liquid crystal elastomers are highly responsive materials thanks to their ability to switch between symmetry-related states of spontaneous distortion. We will review methods to predict their macroscopic response to applied loads and fields using the technique of quasi-convexification. In addition, we will discuss the possibilities of inducing prescribed shape changes through imprinted patterns of director orientations and/or localized actuation.
MLCW04 26th June 2013
14:45 to 15:30
K Urayama Stretching of Polydomain and Monodomain Nematic Elastomers: Experimental Study
We review our experimental studies on the stretching driven director-rotation of polydomain nematic elastomers (PNEs) and monodomain NEs (MNEs). The texture of PNEs primarily depends on the preparation state, i.e., whether the cross-links are introduced in the high-temperature isotropic or low-temperature nematic state. The director in the isotropic-genesis PNEs can be rotated at unusually low energy cost by external fields. As a result, the isotropic-genesis PNEs can be largely deformed at small tensile force and moderate electric field strength. In contrast, the nematic genesis PNEs do not show such soft response due to the memory of the initial random director configuration. We observe the remanent of the initial director configuration even in the highly stretched state. The formation of stripe patterns has been known as a typical phenomenon of mechanical instability for the MNEs stretched normally to the initial global director. We introduce a different type of mechanical instability observed in our recent experiments for monodomain NEs.
MLCW04 26th June 2013
16:00 to 16:15
M Warner & T Wilkinson I-CAMP Welcome
MLCW04 26th June 2013
16:15 to 16:45
I-CAMP Overview & Logistics
MLCW04 26th June 2013
16:45 to 17:30
Liquid Crystals History
MLCW04 26th June 2013
17:30 to 18:15
T Wilkinson & T Lubensky & J Ball & E Terentjev & T Sluckin PANEL Discussion - From history to future of liquid crystals
MLCW04 27th June 2013
09:00 to 09:45
Hard and soft elasticity of polydomain liquid crystal elastomers
Liquid crystal elastomers are solids that resist deformation with an elastic modulus appropriate for rubber. However, some special large deformations that induce the liquid-crystal order to rotate though the elastomer can be imposed at almost zero stress. These deformations are said to be soft. Soft elasticity is now well understood in monodomain liquid crystal elastomers (in which the liquid crystal order points in the same direction throughout the sample) but such samples are rather difficult to prepare, especially in anything but a thin film. If a liquid crystal polymer is simply crosslinked to make an elastomer, the results will be a polydomain. We model each domain of a polydomain as a small monodomain and ask whether such polydomains exhibit global soft elasticity. We show that the fabrication history of the sample is critical. Elstomers crosslinked in an isotropic state then cooled to a nematic state whilst a solid have global soft modes while those cooled to a nematic state then crosslinked do not. The addition of smectic phases allows more complicated fabrication histories with a variety of soft and hard behaviour. Finally, I will consider whether any of these polydomains can be used to build actuators.
MLCW04 27th June 2013
09:45 to 10:30
N Uchida Topological Defects in Nematic Elastomers, Gels and Membranes
We review the structure and mechanical properties of topological defects in nematic elastomers and membranes. Nematic elastomers crosslinked in the isotropic phase (isotropic-genesis polydomains) exhibit anomalously soft mechanical response, which is explained by anisotropic orientational correlation in the polydomain state. In contrast, nematic-genesis polydomains show large mechanical stress due to memory of initial defect distributions. Orientation-curvature coupling in nematic membranes causes a correlation pattern similar to that of isotropic-genesis polydomains, which results in low-energy defected states and anomalously slow ordering kinetics. The notion of relative orientational correlation function is introduced to characterize the multi-defect states in these and other materials.
MLCW04 27th June 2013
11:00 to 11:45
Fluctuations and nonlinear elasticity of nematic elastomers
In this talk, I will first discuss how to describe elastic deformations in systems with partial translational orders and orientational orders. I will then discuss how to incorporate the effects of thermal and quenched fluctuations into elasticity theory. Finally I will address the anomalous elasticity of ideal nematic elastomers in presence of thermal as well as quenched fluctuations.
MLCW04 27th June 2013
11:45 to 12:30
J Adams Modelling Smectic Liquid Crystal Elastomers
Liquid crystal elastomers (LCEs) are rubbery materials that composed of liquid crystalline polymers (LCPs) crosslinked into a network. The rod-like mesogens incorporated into the LCPs are have random orientations in the high temperature isotropic phase, but can adopt the canonical liquid crystalline phases as the temperature is lowered. In this talk I will describe some modelling work of the layered smectic phase of LCEs.

Smectic liquid crystal elastomers have highly anisotropic mechanical behaviour. This arises in side chain smectic-A systems because the smectic layers behave as if they are embedded in the rubber matrix [1] (the same cannot be said of main chain smectic systems). The macroscopic mechanical behaviour of these solids is sensitive to the buckling of the layers, so it is a multiscale problem. A coarse grained free energy that includes the fine-scale buckling of the layers has been developed [2], which enables continuum modelling of these systems. I will describe how this continuum model, when augmented with an additional energy term describing layer buckling and other effects such as finite chain extension, can be used to model deformation of smectic-A elastomers in different experimentally accessible geometries.

Modelling smectic-C elastomers, with their tilted director, present a bigger challenge to calculating their coarse grained energy. The constraint placed on the director by the layer normal results in some unusual properties of their soft modes such as negative Poisson ratio. I will describe the geometry of these deformation modes in smectic-C elastomers [3].

[1] C. M. Spillmann et al, Phys. Rev. E 82, 031705, (2010). [2] J. Adams, S. Conti and A. DeSimone, Mathematical Models and methods in Applied Sciences, 18, 1 (2008). [3] A. W. Brown and J. M. Adams, Phys. Rev. E, 85, 011703 (2012) .

MLCW04 27th June 2013
14:00 to 14:45
Joint Lecture with Dynamics of Suspensions, Gels, Cells and Tissues (CFMW01)
Growth and instabilities of healthy and cancerous tissues
Joanny, J-F (Institut Curie)
Thursday 27 June 2013, 14:00-14:45
http://www.newton.ac.uk/programmes/CFM/seminars/2013062714004.html
MLCW04 27th June 2013
14:45 to 15:30
Joint Lecture with Dynamics of Suspensions, Gels, Cells and Tissues (CFMW01)
Reconfigurable assemblies of active, auto-chemotactic gels
Balazs, A (University of Pittsburgh)
Thursday 27 June 2013, 14:45-15:30
http://www.newton.ac.uk/programmes/CFM/seminars/2013062714454.html
MLCW04 27th June 2013
16:00 to 16:45
Joint Lecture with Dynamics of Suspensions, Gels, Cells and Tissues (CFMW01)
Microscopic simulation of active gels: The controlling role of end detachment
Head, D (University of Leeds)
Thursday 27 June 2013, 16:45-17:15
http://www.newton.ac.uk/programmes/CFM/seminars/2013062716454.html

Phase transitions and solitons in self-propelled particles: kinetic theory and diagrammatic approach
Ihle, T (North Dakota State University)
Thursday 27 June 2013, 17:15-17:45
http://www.newton.ac.uk/programmes/CFM/seminars/2013062717154.html

MLCW04 28th June 2013
09:00 to 09:45
M Ravnik Three-dimensional liquid crystalline superstructures for photonics (** joint talk with I-CAMP)
Liquid crystalline materials allow for formation of complex optical and photonic patterns –the superstructures- within the bulk of the material or by adding colloidal inclusions. Memory [1], self-assembly [2], topology [3], and material flow [4] can serve as guiding and controlling mechanism of the structures, offering possible competitive advantages to be used in complex optics and photonics. Here, we present three dimensional colloidal and bulk liquid crystal superstructures, as recently achieved by numerical modelling and experiments. Central to the superstructures are complex conformations of topological defects, as they can bind, stabilise, or distort the structure. We show that 3D colloidal crystals can be assembled from elastic dipoles of spherical beads in nematic liquid crystals [5] or via inherently inhomogeneous order profiles in bulk and confined cholesteric blue phases [6]. Colloidal crystals are generalised to close-packed colloidal lattices, which we show can serve as natural templates for defect networks [7]. Finally, photonic bands are calculated for selected structures and possible defects in the structure are discussed [8].

[1] T. Araki, M. Buscaglia, T. Bellini, H. Tanaka, Nature Materials 10, 303 (2011). [2] P. Poulin, H. Stark, T. C. Lubensky, D. A. Weitz, Science 275, 1770 (1997). [3] U. Tkalec, M. Ravnik, S. Copar, S. Zumer I. Musevic, Science 333, 62 (2011). [4] A. Sengupta, U. Tkalec, M. Ravnik, J.M. Yeomans, C. Bahr, S. Herminghaus, Phys. Rev. Lett. 110, 048303 (2013). [5] A. Nych, U. Ognysta, M. Škarabot, M. Ravnik, S. Žumer, I. Muševič, Nature Comm. 4, 1489 (2013). [6] M. Ravnik, G. P. Alexander, J. M. Yeomans, S. Zumer, Proc. Natl. Acad. Sci. USA 108, 5188 (2011). [7] S. Copar, N.A. Clark, M. Ravnik, S. Zumer, Elementary building blocks of densely packed 3D colloidal lattice entangled by nematic disclinations, accepted in Soft Matter. [8] M. Stimulak and M. Ravnik, Photonic bands in blue phase colloidal crystals, to be submitted;

MLCW04 28th June 2013
09:45 to 10:30
C Modes Photo-Actuation in LC Glass (**joint talk with I-CAMP)
MLCW04 28th June 2013
11:00 to 11:30
Photo-elastomers (**joint talk with I-CAMP)
MLCW04 28th June 2013
11:30 to 11:45
Conclusions
Conclusions for Liquid Crystal Defects and their Geometry, Active and Solid Liquid Crystals, and Related Systems workshop.
MLCW04 28th June 2013
14:00 to 14:45
D Broer Responsive Liquid Crystal Polymer Networks & Hydogels (**joint talk with I-CAMP)
In-situ photopolymerization of liquid crystalline (LC) monomers has proven to be a valuable technique for the formation of well-ordered polymer networks. Their anisotropic properties led to a variety of applications in optics, electronics and mechanics. The use of light to initiate polymerization enables lithographic approaches for patterning. The LC behaviour enables formation of complex morphologies on molecular level. Controlling the director profile of an LC network film in transversal direction gives geometrical morphing upon minor changes in order parameter. Examples of suited profiles of molecular orientation are twisted or splayed director configurations tied up in the polymer network. Reversible order parameter changes can be induced by a variety of means. It can be simply induced by temperature changes resulting in gradients in thermal expansion over the cross-section of the film. But more sophisticated and of interest for applications is a light induced change as a result of the E-Z isomerization of a built-in azo group. When the LC polymer networks are confined in the x-y plane of the film, e.g. by strong adhesion to a high modulus substrate, deformation takes place into the third dimension forming surface topographies.

Rather than composing the netyworks of covalent bonds alone, one can chose to replace some bonds by secondary interactions such as hydrogen bridges, thus providing responsive molecularly organized hydrogels. We applied the H-bridge based dimerization of benzoic acid to form nematic LC acrylate monomers. By a controlled and reversible rupture of the H-bridges mechanical responses can be initiated. Photopolymerization of smectic LC monomers lock in structures of different length scales. The first length scale is the resolution of lithography, and goes down to a few micrometers. The second length scale is set by the spacing of smectic layers and is typically a few nanometers. The third length scale is the intermolecular distance in the layers, usually around 1 nm or below. By modifying smectic molecules with H-bridges the smectic periodicity can break-up into separated layers with a well-defined spacing, also in the nanometer range. The nanopores form by breaking the H-bridges at elevated temperatures or by contact with an alkaline solution. The integrity of the film is maintained by copolymerizing with fully covalent smectic crosslinkers. By making this crosslinker photosensitive the pore size can be regulated by UV light.

MLCW04 28th June 2013
14:45 to 15:30
Kinetics of Light-Induced Patterning in Liquid Crystal Elastomers (**joint talk with I-CAMP)
Liquid crystal elastomers doped with molecules that change conformation on absorption of a photon show very large changes photoelastic response. This can be investigated by recording a holographic grating in the material with the use of two crossed UV laser beams. Angular dependence of the diffraction efficiency in the vicinity of the Bragg peak can be analyzed using a numerical model that takes into account the propagation of writing beams and rate equations for the local concentration of the absorbing trans conformer, and spatial distribution of the trans and cis conformers can be obtained. Stress dependence on the irradiation time can be analyzed in a similar way. Strongly nonlinear relationship between the concentration of the cis isomers of the azomesogens and the refractive index modification of the material, which is characteristic for the phase transition region, results in non-monotonous time dependence of the diffraction efficiency of a probe beam. From this effect the sensitivity of the nematic transition temperature on the molar fraction of the cis isomers is determined. The relation between the cis isomer molar fraction and nematic order also provides a possibility for recording hidden holograms, which can be made visible by cooling the sample from the paranematic to the nematic phase.
MLCW04 28th June 2013
16:00 to 16:45
Liquid Crystal Elastomers and Light (**joint talk with I-CAMP)
Liquid crystal elastomers are solid liquid crystals; they combine elasticity with orientational order. Mechanical strain therefore changes liquid crystalline order and the optical properties of these materials. Conversely, light can change the orientational order, and give rise to mechanical forces and changes in shape. Light-matter interactions in LCEs therefore involve a broad range of unusual phenomena, which raise a number of intriguing questions. I will present the results of some experiments probing such phenomena, and discuss the underlying physics.
MLC 5th July 2013
09:00 to 09:45
The Excluded Volume of Convex Bodies
MLC 5th July 2013
09:45 to 10:00
Self-Assembled Nanoparticle-Ligand Optical Metasurfaces
MLC 5th July 2013
10:00 to 10:15
Towards an Optical Nano-Laboratory in a Liquid Crystal Defect
MLC 5th July 2013
10:15 to 10:30
NMR Studies of DNA Aligned in DMPC/DHPC/CS Bicelle Mixtures
MLC 5th July 2013
11:00 to 11:15
Probing Liquid Crystal Elastomer Structure with Polarized Light Scattering
MLC 5th July 2013
11:15 to 11:30
Modelling Light Propagation Through Radial-Director Liquid Crystal Waveguides
MLC 5th July 2013
11:30 to 11:45
Iridescent Films from Cellulose Nanocrystals
MLC 5th July 2013
11:45 to 12:00
Photonic Liquid Crystal Fiber Interferometer
MLC 5th July 2013
12:00 to 12:15
Visualizing Induced Fluid Flows around a Sphere in Isotropic and Nematic Liquids
MLC 5th July 2013
12:15 to 12:30
Flashing Flexodomains and Electroconvection Rolls in a Nematic Liquid Crystal
MLC 5th July 2013
14:00 to 15:15
Science Policy Forum
MLC 5th July 2013
15:15 to 17:00
Poster Session
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons