Elastomers are artificial polymeric materials created for industrial and commercial applications. Depending on their purpose, they are performing in different species and structure modifications. Our studies focus on the systems of elastomers randomly standing-distributed in a smectic $A$ (Sm$A$) liquid crystal. Basing on the suggestion following from the experiment, that at a phase transition from Sm$A$ to nematic phase caused by an increase of a crosslink concentration, such a system survives a percolation transition at low crossilink concentrations, we propose a modeling explaining this phenomena. We approve the three-dimensional Villain spin glass model and apply lattice Monte Carlo (MC) techniques on differential forms on a dual lattice, that is an alternative of a replica trick, developed for nematic elastomers in the 3D XY universality. In the results of that we have confirmed a concentration phase transition of percolation nature at a small crosslink concentration ($\sim$ 10 weight %).
Smectic-C elastomers can be prepared by crosslinking, e.g., liquid crystal polymers, in the smectic-A phase followed by a cooling through the smectic-A to smectic-C phase transition. This transition from $D_{\infty h}$ to $C_{2h}$ symmetry spontaneously breaks rotational symmetry in the smectic plane as does the transition from a smectic-A to a biaxial smectic phase with $D_{2h}$ symmetry. We study these transitions and the emergent elasticity of the smectic-C and biaxial phases in three related models and show that these phases exhibit soft elasticity analogous to that of nematic elastomers.
We present a model for smectic elastomer membranes which includes elastic and liquid crystalline degrees of freedom. Based on our model, we determined the qualitative phase diagram of a smectic elastomer membrane using mean-field theory. This phase diagram is found to comprise five phases, viz. smectic-A--flat, smectic-A--crumpled, smectic-C--flat, smectic-C--crumpled and smectic-C--tubule, where in the latter phase, the membrane is flat in the direction of mesogenic tilt and crumpled in the perpendicular direction. The transitions between adjacent phases are second order phase transitions. We…
Stenull and Lubensky [Phys. Rev. E {\bf 76}, 011706 (2007)] have argued that shear strain and tilt of the director relative to the layer normal are coupled in smectic elastomers and that the imposition of one necessarily leads to the development of the other. This means, in particular, that a Smectic-A elastomer subjected to a simple shear will develop Smectic-C-like tilt of the director. Recently, Kramer and Finkelmann [arXiv:0708.2024, Phys. Rev. E {\bf 78}, 021704 (2008)] performed shear experiments on Smectic-A elastomers using two different shear geometries. One of the experiments, which …
We study two aspects of the elasticity of smectic-$A$ elastomers that make these materials genuinely and qualitatively different from conventional uniaxial rubbers. Under strain applied parallel to the layer normal, monodomain smectic-$A$ elastomers exhibit a drastic change in Young's modulus above a threshold strain value of about 3%, as has been measured in experiments by Nishikawa and Finkelmann [Macromol. Chem. Phys. {\bf 200}, 312 (1999)]. Our theory predicts that such strains induce a transition to a smectic-$C$-like state and that it is this transition that causes the change in elastic …
We present a detailed analysis of the molecular packing of a strained liquid crystal elastomer composed of chiral mesogens in the smectic A phase. X-ray diffraction patterns of the elastomer collected over a range of orientations with respect to the X-ray beam were used to reconstruct the three-dimensional scattering intensity as a function of tensile strain. For the first time, we show that the smectic domain order is preserved in these strained elastomers. Changes in the intensity within a given scattering plane are due to reorientation, and not loss, of the molecular order in directions ort…
Models of smectic-C liquid crystal elastomers predict that it can display soft elasticity, in which the shape of the elastomer changes at no energy cost. The amplitude of the soft mode and the accompanying shears are dependent on the orientation of the layer normal and the director with respect to the stretch axis. We demonstrate that in some geometries the director is forced to rotate perpendicular to the stretch axis, causing lateral expansion of the sample; a negative Poisson's ratio. Current models do not include the effect of imperfections that must be present in the physical sample. We i…
We study anomalous elasticity in the tubule phases of nematic and smectic elastomer membranes, which are flat in one direction and crumpled in another. These phases share the same macroscopic symmetry properties including spontaneously-broken in-plane isotropy and hence belong to the same universality class. Below an upper critical value $D_c =3$ of the membranes' intrinsic dimension D, thermal fluctuations renormalize the elasticity with respect to elastic displacements along the tubule axis so that elastic moduli for compression along the tubule axis and for bending the tubule axis become le…
We present a numerical study of stretching monodomain smectic-A elastomer sheets, computed using the finite element method. When stretched parallel to the layer normal the microscopic layers in smectic elastomers are unstable to a transition to a buckled state. We account for the layer buckling by replacing the microscopic energy with a coarse grained effective free energy that accounts for the fine scale deformation of the layers. We augment this model with a term to describe the energy of deforming buckled layers, which is necessary to reproduce the experimentally observed Poisson's ratios p…
We present a theory for the low-frequency, long-wavelength dynamics of soft smectic-C elastomers with locked-in smectic layers. Our theory, which goes beyond pure hydrodynamics, predicts a dynamic soft elasticity of these elastomers and allows us to calculate the storage and loss moduli relevant for rheology experiments as well as the mode structure.
We study the low-frequency, long-wavelength dynamics of liquid crystal elastomers, crosslinked in the smectic-$A$ phase, in their smectic-$A$, biaxial smectic and smectic-$C$ phases. Two different yet related formulations are employed. One formulation describes the pure hydrodynamics and does not explicitly involve the Frank director, which relaxes to its local equilibrium value in a non-hydrodynamic time. The other formulation explicitly treats the director and applies beyond the hydrodynamic limit. We compare the low-frequency, long-wavelength dynamics of smectic-$A$ elastomers to that of ne…
The reorientation behaviour of a smectic-A (SmA) elastomer deformed parallel to the smectic layer normal has been interpreted as a Sm-C like transition by Stenull and Lubensky. Experiments, however, prove that such a transition does not occur.
Ideal (monodomain) smectic-$A$ elastomers crosslinked in the smectic-$A$ phase are simply uniaxial rubbers, provided deformations are small. From these materials smectic-$C$ elastomers are produced by a cooling through the smectic-$A$ to smectic-$C$ phase transition. At least in principle, biaxial smectic elastomers could also be produced via cooling from the smectic-$A$ to a biaxial smectic phase. These phase transitions, respectively from $D_{\infty h}$ to $C_{2h}$ and from $D_{\infty h}$ to $D_{2h}$ symmetry, spontaneously break the rotational symmetry in the smectic planes. We study the ab…
We address the physics of nematic liquid crystalline elastomers randomly crosslinked in the isotropic state. To do this, we construct a phenomenological effective replica Hamiltonian in terms of two order-parameter fields: one for the vulcanization, the other for nematic alignment. Using a Gaussian variational approach, we analyze both thermal and quenched fluctuations of the local nematic order, and find that, even for low temperatures, the macroscopically isotropic polydomain state is stabilized by the network heterogeneity. For sufficiently strong disorder and low enough temperature, our th…
Experimentally it is possible to manipulate the director in a (chiral) smectic-$A$ elastomer using an electric field. This suggests that the director is not necessarily locked to the layer normal, as described in earlier papers that extended rubber elasticity theory to smectics. Here, we consider the case that the director is weakly anchored to the layer normal assuming that there is a free energy penalty associated with relative tilt between the two. We use a recently developed weak-anchoring generalization of rubber elastic approaches to smectic elastomers and study shearing in the plane of …
Structural studies by synchrotron x-ray diffraction on two main-chain smectic-C elastomers reveal the presence of two different relaxation mechanisms in these systems at low and high strains. At low strains, the smectic layers are reoriented with layer-normals distributed in a plane perpendicular to the stretch direction. The system relaxes relatively slowly (time-constant ~ 45 minutes) which is attributed to the flow properties of the LC layers embedded in the elastomer network. At high strains, the equilibration time (~ 4 - 8 minutes) conforms to a faster relaxation and appears to have its o…
We once more specify an universality of a phase transition from smectic-A to nematic phase in the crosslinked polymer network with a smectic liquid crystal, basing on the X-ray and $^1H$-NMR spectroscopy experiments. Comparing the superconducting 3D XY gauge theory and typical spin-glass models for such systems, it is possible to clarify a type of a phase transition, which might be the reason of percolation.
Self-healing polymers crosslinked by solely reversible bonds are intrinsically weaker than common covalently crosslinked networks. Introducing covalent crosslinks into a reversible network would improve mechanical strength. It is challenging, however, to apply this design concept to dry elastomers, largely because reversible crosslinks such as hydrogen bonds are often polar motifs, whereas covalent crosslinks are non-polar motifs, and these two types of bonds are intrinsically immiscible without co-solvents. Here we design and fabricate a hybrid polymer network by crosslinking randomly branche…
In liquid-crystalline elastomers, the nematic order parameter and the induced strain vary smoothly across the isotropic-nematic transition, without the expected first-order discontinuity. To investigate this smooth variation, we measure the strain as a function of temperature over a range of applied stress, for elastomers crosslinked in the nematic and isotropic phases, and analyze the results using a variation on Landau theory. This analysis shows that the smooth variation arises from quenched disorder in the elastomer, combined with the effects of applied stress and internal stress.
Liquid crystalline elastomers (LCE) undergo reversible shape changes in response to stimuli, which may enable a wide range of smart applications, such as soft robot, adhesive systems or implantable medical devices. Here we introduce new dynamic covalent chemistry based on siloxane equilibrium exchange into the LCE to enable processing (director alignment, remolding, and welding). Unlike, the traditional siloxane-based LCE, which are produced by a other reaction schemes with irreversible bonds (e.g. hydrosilylation), here we use a much more robust reaction (thiol-acrylate/thiol-ene 'double-clic…
In this article, we construct and analyze models of anisotropic crosslinked polymers employing tools from the theory of liquid crystal elastomers. The anisotropy of these systems stems from the presence of rigid-rod molecular units in the network. We study minimization of the energy for incompressible as well as compressible materials, combining methods of isotropic nonlinear elasticity with the theory of lyotropic liquid crystals. We apply our results to the study of phase transitions in networks of rigid rods, in order to model the behavior of actin filament systems found in the cytoskeleton…
A range of monodomain nematic liquid crystal elastomers containing differing proportions of photo-isomerisable mesogenic moieties, which turn from a rod-like to a kinked shape upon ultraviolet (UV) irradiation, was studied. Depending on the proportion and positional role of the photo-sensitive groups in the crosslinked polymer network, different types and magnitudes of response were found. The principle consequence of such photo-isomerisation is the destabilisation of the nematic phase, whose order parameter depends on temperature in a near-critical fashion. Accordingly, the effect of UV-irrad…
The blue phases are observed in highly chiral liquid crystalline compositions that nascently organize into a three-dimensional, crystalline nanostructure. The periodicity of the unit cell lattice parameters is on the order of the wavelength of visible light and accordingly, the blue phases exhibit a selective reflection as a photonic crystal. Here, we detail the synthesis of liquid crystalline elastomers (LCEs) that retain blue phase I, blue phase II, and blue phase III. The mechanical properties and deformation of LCEs retaining the blue phases are contrasted to the cholesteric phase in fully…
Elastic effects in a model of disordered nematic elastomers are numerically investigated in two dimensions. Networks crosslinked in the isotropic phase exhibit unusual soft mechanical response against stretching. It arises from gradual alignment of orientationally correlated regions that are elongated along the director. A sharp crossover to a macroscopically aligned state is obtained on further stretching. The effect of random internal stress is also discussed.
Liquid crystal elastomers realize a fascinating new form of soft matter that is a composite of a conventional crosslinked polymer gel (rubber) and a liquid crystal. These {\em solid} liquid crystal amalgams, quite similarly to their (conventional, fluid) liquid crystal counterparts, can spontaneously partially break translational and/or orientational symmetries, accompanied by novel soft Goldstone modes. As a consequence, these materials can exhibit unconventional elasticity characterized by symmetry-enforced vanishing of some elastic moduli. Thus, a proper description of such solids requires …
Properties of disordered nematic elastomers and gels are theoretically investigated with emphasis on the roles of non-local elastic interactions and crosslinking conditions. Networks originally crosslinked in the isotropic phase lose their long-range orientational order by the action of quenched random stresses, which we incorporate into the affine-deformation model of nematic rubber elasticity. We present a detailed picture of mechanical quasi-Goldstone modes, which accounts for an almost completely soft polydomain-monodomain (P-M) transition under strain as well as a ``four-leaf clover'' pat…
