June 9-11, 2011
Room 601, Pao Yue-Kong Library
The International workshop on Physics of Poly-Domain Liquid Crystalline Elastomers will be held on June 9-11, 2011, at 601, Pao Yue-Kong Library(North Gate Entrance) Shanghai Jiao Tong University, Shanghai, P.R. China.
The physics of the poly-domain phase of liquid crystalline elastomers (LCE) has attracted strong interest from many of us for quite some time. In addition to their potential for technological applications, these systems pose fascinating fundamental questions about the statistical mechanics of amorphous solids that possess internal orientational order. In contrast to conventional (i.e., fluid) liquid crystals, within a nelastomer deformations of the LC order necessarily induce elastic strains in the solid itself. These would impose a large elastic energy cost on the system as a whole — as we would naively expect from our intuition about elastic solids. Regardless of our intuition, the LC order within a liquid crystalline elastomer, when cross-linked under isotropic conditions, tends to form fine-grained patterns, characteristically at the micron lengthscale. This surely reflects the properties of low-energy states, simply because it is what is observed in experiments. But how is nematic order reconciled with network elasticity at such short distances? What is the mechanism of the extremely soft response to elastic strain in poly-domain nematic elastomers? Are there liquid crystalline defects within poly-domain nematic elastomers and, if so, how do they couple to elastic strains? By contrast, nematic elastomers cross-linked at temperatures below the isotropic-nematic transition exhibit no soft elasticity at all. What fundamental differences are there between these two types of poy-domain nematic elastomers? And, finally, what is the appropriate theoretical formalism that is capable of describing these phenomena? Answers to these highly intriguing questions may only be obtainable via in-depth collaborative efforts involving chemists, physicists, and mathematicians.
We (i.e., Xiangjun Xing, and Hongru Ma of Shanghai Jiao Tong University, Paul Goldbart of Georgia Institute of Technology, and Kenji Urayama of Kyoto University) are organizing a three-day workshop to focus on this topic, entitled: The Physics of Poly-domain Liquid Crystalline Elastomers. The purpose of this workshop is to bringing together a number of scientists who are active in the field of LCEs, with the aims of exchanging ideas and results, and developing and nurturing interdisciplinary collaborations. The workshop will be held at Shanghai Jiao Tong University during the week of June 9-11, 2011. It will consist of a series of informal talks, along with ample time for discussions.
In addition, there will be a public lecture delivered by Prof. Mark Warner, tailored to suit a more general audience, for the purposes of advertising our research fields.
Mark Warner, Cambridge University
Mark Warner Cavendish Laboratory,Cambridge University, UK
Rubber is only a solid from its quenched topology. Locally it is still mobile as a liquid. On cooling to a nematic phase, it lengthens to mirror the extension of its molecular distribution - the spectacular spontaneous distortions that are observed. Subsequently, it can rotate its director and hence the long axis of its molecular distribution to achieve shape changes at low energy cost. It is simply putting its naturally long dimension towards directions that are being extended. Such rotations and large extensions at low stress are well observed in monodomain nematic elastomers. But in polydomains, neighbouring regions in principle need different distortions from each other to respond at low cost. We expect these to be incompatible, and therefore the detailed mechanism of low energy response by complex shears to thereby fail. We explain, first by reference to monodomains deforming under constraints, just how domains can resolve these elastic incompatibilities with their neighbours and deform at even lower cost than the corresponding monodomains. Both randomness and elastic coherence are required. It seems clear that polydomains offer perhaps the best route to applications of liquid crystal elastomers – they are easier to prepare, more subtly responsive, and couple 7
I present numerical simulation results on the director texture and stress-strain properties of polydomain nematic elastomers (PDNEs). By use of the neo-classical affine-deformation model with quenched random stress, it is demonstrated that PDNEs crosslinked in the isotropic phase exhibit extremely soft response to stretching . The softness is closely linked to anisotropic director correlation in the polydomain state, as suggested by analysis of effective elastic interactions between domains . A generic elastic free energy of isotropic-genesis PDNEs in 2D and 3D is formulated using rotational invariants of the deformation tensor [3,4]. Simulations based on the generic model confirm that the softness is a universal feature, and that topological defects in both 2D and 3D are of disclination type.Properties of PDNEs crosslinked in the nematic polydomain state are also studied . It is shown that the mechanical stress under polydomain-monodomain transition sharply increases with the correlation length of the director field at the moment of crosslinking.  NU, PRE 60, R13 (1999); PRE 62, 5119 (2000).  NU and A. Onuki, Europhys. Lett. 45, 341 (1999).  NU, PRL 89, 025702 (2002).  NU, in preparation.more sensitively to stimuli than monodomains do.
Cold-drawing is a well-known phenomenon observed in both glassy amorphous and semicrystalline polymers, but it is rarely noted in rubber-like networks above their glass transition temperatures (Tg). Cold-drawing and neck formation have recently been reported in polydomain smectic main-chain liquid crystalline elastomers (LCE) above Tg,under certain conditions of temperature and elongation rate. Cold-drawing and necking in LC elastomers, glassy amorphous polymers, and semicrystalline polymers cannot be attributed to common morphological features, but may have common origins in conformational transitions at the chain level. Our work is aimed at understanding the underlying molecular basis for mechanical instability in polydomain smectic LCE. The necking instability is proposed to arise from strong energetic contributions to the elastic free-energy upon elongation, in contrast to classical entropy-driven rubber elasticity. Mechanical experiments indicate that neck formation is favored at high elongation rates and at temperatures « Tsi, the smectic-isotropic clearing temperature. A pressing fundamental issue underlying all of the proposed work is the concept of hairpins, or folds in the polymer backbone. The number of hairpins per elastic chain affects the domain size along the layer normal, which can be probed by X-ray lineshape analysis. X-ray measurements of domain size indicate that annealing at a temperature near Tsi increases the average domain size. As a result, thermal history plays an important role in the mechanical response under tension. Elastomers containing larger, more stable domains exhibit a larger yield stress (and are therefore more prone to necking) due to an increased energetic penalty for disrupting smectic ordering during elongation. Quickcooled smectic LCE have smaller domain size, so the observed yield stress is lower, but the extensibility is increased. The combined results of mechanical characterization and X-ray lineshape analysis can provide new insights regarding the role of hairpin defects in mechanical behavior of smectic LCE.
Mark Warner , Cavendish Laboratory ,Cambridge University, UK
I describe what happens when two unusual materials, rubbers (elastomers) and liquid crystals, combine to make remarkable new materials – liquid crystal elastomers. Rubbers are capable of huge distortions. Though notionally solids, their shear moduli are close to the compression modulus of air, and they have the molecular mobility of liquids, and will be demonstrated during the lecture. Liquid crystals have long range orientational order, but are liquid-like in their mobility and lack of positional order. They suffer first order phase transitions, essentially without volume change, which will also be shown in the lecture. Combining elastomers with liquid crystals gives solids with even stranger properties than conventional rubber. I will show what these properties are and why they arise. They include: (i) Huge spontaneous distortions on changing nematic order by cooling, heating, illumination and darkness. Such responses have potential usage in actuation, microfluidics, and micromechanics. (ii) Mechanical response involving rotation of the liquid crystalline order. The usual rules of Hooke classifying solid, liquid and gas by elastic and mechanical response appear to be blurred. We are interested to find new applications for new types of behaviour. (iii) Selective response of polydomain nematic elastomers to light and mechanical stress. (iv) Exotic responses of cholesterics and smectics include changes in colour on stretching, deformable rubber lasers, and soft ferro-electric rubbers.
A rubber laser – Palffy & Finkelmann
Tom Lubensky, Department of Physics and Astronomy University of Pennsylvania, Philadelphia, PA 19014
The mechanical stability of bridges, buildings, and other architectural wonders is of critical importance to us all. In 1864, James Clerk Maxwell formulated a theory for the stability of frames composed of straight struts, capable of supporting tension and compression, connected at points of contact. Of particular interest are isostatic systems that have just enough struts to ensure mechanical stability. Maxwellʼs ideas have found applications in many fields from civil engineering to biophysics. This talk will present an overview of condensed-matter systems, including network glasses, jammed solids, and networks of semi-flexible polymers for which Maxwellʼs ideas have provided fruitful insight. It will then consider the properties of the square and kagome lattices with nearest- and next-nearest neighbor springs, which are examples of periodic lattices whose continuous approach to the isostatic limit can be controlled with analytic precision. It will conclude with a discussion of auxetic or negative Poisson-ratio lattices, endowed with the unusual property that they expand rather than contract in directions perpendicular to applied uniaxial tension, that can be constructed from the isostatic kagome and related lattices. These lattices have zero-frequency surface Rayleigh waves that can be described by a conformal field theory in the long-wavelength limit.
Elasticity of Networks of Semi-Flexible Polymers (30 minute talk)
Tom Lubensky, Department of Physics and Astronomy University of Pennsylvania, Philadelphia, PA 19014 Networks of crosslinked semi-flexible polymers, including actin, neuronal intermediate filaments, and fibrin protofibrils, play an important role in controlling mechanical response of biological tissue. The elastic response of these networks is controlled by both bending and stretching energy of their constituent filaments as well as by their network architecture. Since each crosslink typically binds two filaments together at one point, the average coordination number of each crosslink is generally less than four. Arguments due to Maxwell establish that networks of nodes with coordination number z < z_c = 2d in dimension d are unstable if only central stretching forces between nodes are active. Thus, bending rigidity is critical to the stability of biopolymer networks in both two and three dimension. This talk will explore various models for biopolymer networks based largely on variations of the kagome lattice, including a new three-dimensional 4-coordinated lattice. Undiluted these lattices consist of sample spanning filaments; when diluted they consist of finite-length filaments. The undiluted lattice can support shear and compression if the filaments are straight, but not compression and sometimes not shear if they are bent. Thus, the latter lattices require bending for stability even when undiluted. The diluted lattices exhibit a rigidity percolation threshold and strongly nonaffine, bending-dominated response upon dilution.
Fangfu Ye, Bing Lu
Tetsuya Okamoto, Kenji Urayama, Toshikazu Takigawa Department of Material Chemistry, Kyoto University
The cross-linking history markedly influences the mechanical response of polydomain nematic elastomers (PNEs): The PNEs originally made in the high-temperature isotropic state (I-PNEs) requires much smaller mechanical work for the strain-induced polydomain-to-monodomain transition than those prepared in the low-temperature nematic state (N-PNEs)[1-3]. We have also observed the similar effect of cross-linking history on the response of PNEs to electric fields: The I-PNEs exhibit a finite electrical deformation reaching 20% whereas the N-PNEs show no appreciable deformation. It should be noted that the material is paraelectric (not ferroelectric) and the deformation is observed in the dry and nematic state. To our knowledge, a finite electrical deformation of LCEs has been reported so far only for some ferroelectric LCEs in the dry state or paraelectric LCEs swollen by low molecular weight LCs. We have also examined the mesogen reorientation under electric fields by FT-IR. We elucidate the relation between the macroscopic strain and mesogen reorientation under electric fields.  Uchida, N., Phys. Rev. E., 62, 5119 (2000).  Urayama, K., Kohmon, E., Kojima, M., Takigawa, T., Macromolecules, 42, 4084 (2009).  Biggins, J. S., Warner, M., Bhattacharya, K., Phys. Rev. Lett., 103, 037802 (2009).
Yang Ho Na, Yuki Aburaya,Kazuyuki Hiraoka,and Hiroshi Orihara
The mechanical response to electrical stimulation was investigated in a chiral smectic elastomer. The displacement in an elastomer film was precisely measured by tracking fluorescent beads dispersed on the film with accuracy of 20 nm (Fig.1). From the displacements of 10 beads, all the components of the two-dimensional strain tensor were calculated. Shear deformation in the film was clearly observed when an electric field was applied perpendicular to the film surface. This shear deformation depended on the polarity of the applied electric field. The temperature dependence of the strain tensor was also investigated (Fig.2), and it was also concluded that the contribution of the phase mode, that is, the coupling of the azimuthal rotation to the applied electric field, primarily caused the electrically induced deformation whose magnitude increased with decreasing temperature. It indicates that the origin of the electric-field-induced shear strain in the chiral smectic C phase was mainly attributed to the Nambu-Goldstone mode.
*Y. H. Na, Y. Aburaya, K. Hiraoka, and H. Orihara, Phys. Rev. E, submitted
Antoni Sánchez-Ferrer Food & Soft Materials Science, Institute of Food, Nutrition & Health, ETH Zurich, Schmelzbergstrasse 9, CH-8092 Zurich, Switzerland. e-mail: firstname.lastname@example.org
Liquid-crystalline elastomers (LCEs) are materials with a huge potential for the use as actuators,sensors and switchers, and for integration in nanotechnology and microsystems . Their chemical and physical characterization is of high interest for chemists, physicists and engineers, especially regarding the inusual collection of properties: solid materials which behave as fluids (crosslinked polymer melt networks showing entropy elasticity) with local orientational order (enthalpy elasticity resulting from the liquid-crystalline mesophase). The stress-induced transformation of a polydomain (Figure 1) with a statistical orientation of the mesogens into a monodomain with a macroscopically uniform director orientation in a SmC mainchain LCE has been studied in detail by means of mechanical and X-Ray experiments . The results are compared to the deformation applied to its corresponding monodomain , and detailed explanations are provided to the following questions: How do the molecules reorient when a uniaxial deformation is applied? What happens to the smectic layers? Is this process similar to the nematics?
*Figure 1. Polydomain to monodomain stress-induced transformation in a SmC LCE.
References  A. Sánchez-Ferrer, T. Fischl, M. Stubenrauch, H. Wurmus, M. Hoffmann, H. Finkelmann, Macromol. Chem. Phys. 210, 1671 (2009).  A. Sánchez-Ferrer, H. Finkelmann, Macromol. Rapid Commun. 32, 309 (2011)  A. Sánchez-Ferrer, H. Finkelmann, Macromolecules 41, 970 (2008).
Jonathan Selinger (Liquid Crystal Institute, Kent State University)
In most technological applications of liquid crystals, it is necessary to eliminate dust and other quenched disorder from the liquid-crystal cells. In this talk, we discuss whether quenched disorder can ever have positive benefits for liquid-crystal applications. In the Kerr effect, an electric field applied to an optically isotropic material induces orientational order and hence induces optical birefringence. Recently, many investigators have used the Kerr effect to develop liquid-crystal displays and other electro-optic devices that can operate at high speed and with no need for aligning substrates. This application requires a large and fairly temperature-independent Kerr coefficient. One approach to achieve this goal is by using liquidcrystal blue phases, perhaps with polymer stabilization. As an alternative approach, D.-K. Yang has suggested using a nematic phase within a disordered polymer network, which is a structure with the same symmetry as a polydomain liquid-crystal elastomer. This structure would be disordered and optically isotropic in the absence of a field, but it would develop order and birefringence under an applied field. To assess this approach, we perform Monte Carlo simulations of a nematic liquid crystal in a disordered polymer network, and calculate the response to an applied field. We compare the results with analytic studies of liquid crystals under quenched disorder and with experiments. This work was done in collaboration with graduate student Lena Lopatina, and was supported by NSF Grant DMR-0605889.
Kazuyuki HIRAOKA, Kouta ONOZUKA, Yui KONDO, and Tohru TASHIRO
<Thermomechnical deformation of l-c elastomers cross-linked at Iso, SmA, and SmC* phases>
While there have been several investigations on the structures and properties of the uniformly aligned SmC* elastomers with the unwound state, much less work has been carried out on those concerned with the helicoidal structure, which is the ground state of the SmC* phase. To investigate the effect of the molecular alignment at cross-linking on thermomechanical properties of a SmC* elastomer, we analyze three samples: an elastomer cross-linked at the isotropic phase (Iso-crosslinked-elastomer), an elastomer cross-linked at the SmA phase (A-crosslinked-elastomer), and an elastomer cross-linked at the SmC* phase (C-crosslinked-elastomer). A main-chain liquid-crystalline elastomer, which is prepared by UV-cross-linking a main-chain liquid-crystalline polymer ((S)-BB-4(2Me)/6) with photo-cross-linkable p-phenylenediacrylate (PDA) units, is used for investigation. Its non-crosslinked system exhibits the SmA phase and the SmC* phase, as shown in the following phase sequence: g - (35°C) - SmC* - (145°C) - SmA - (220°C) - Iso. Circular dichroism measurements of the (S)-BB-4(2Me)/6 polymer indicated a right-handed helix emerges in the SmC phase.
The thermotropic SmC-SmA-Iso transformations take place in the C-crosslinked-elastomer,
in which spontaneous twist deformation is observed during the SmC*-SmA transformation. As for the A-crosslinked-elastomer, however, only an orthogonal alignment due to the SmA phase is recognized in X-ray measurement between RT and 250°C. While no twist deformation is observed in the A-crosslinked-elastomer, elongation and shrinkage along to the layer normal occurs in the SmA-Iso transformation. In addition, no anisotropic deformation is recognized in the Iso-crosslinked-elastomer. These results indicate that theromomechanical properties of the liquid-crystalline elastomer are dominated by the molecular alignment memorized at cross-linking reaction.
Ref.: Kondo,Y.; Master Thesis, Tokyo Polytech. Univ., Atsugi, Japan, 2011.
俞燕蕾 , Yanlei Yu, Department of Materials Science Fudan University
In this work, a good method was developed to incorporate widely-used photodeformable trigger molecules, azobenzenes, into side chains of polymer networks, in which the azobenzene units are able to act as mesogens. Then the cooperative motion of liquid crystals was utilized to magnify the microscopic structural change of azobenzene units to a significant macroscopic deformation (such as bending, rotation, inchworm-like walk, and arm-mimic motion) of the whole material upon irradiation of UV light. Recently, azotolane-containing liquid crystal polymer networks have been developed whose deformations can be induced by visible light and even directly by sunlight. Furthermore, full-light-driven microrobots, microvalves and micropumps have also been fabricated.