Liquid-crystalline elastomers (original) (raw)

Liquid crystalline elastomers: dynamics and relaxation of microstructure

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2003

The equilibrium mechanical response of nematic elastomers can be soft or hard depending on the relation between the imposed strains and the nematic director, in particular, if the local nematic director is able to respond by rotating. The dynamical response proves to be equally unusual. We examine the linear dynamic mechanical response of monodomain nematic elastomers under shear and the aspects of time{ temperature superposition of the dynamical data across phase-transition regions. In the low-frequency region of the master curves, one nds a dramatic reduction of rubber plateau modulus and the rise in internal dissipation: in the shear geometries compatible with dynamic soft elasticity. Power-law variation of the storage modulus with frequency G 0 / ! a agrees very well with the results of static stress relaxation, where each relaxation curve obeys the analogous power law G 0 / t ¡a in the corresponding region of long times and temperatures.

Soft elasticity and mechanical damping in liquid crystalline elastomers

Journal of Applied Physics, 2001

The dynamic soft response of polydomain liquid crystalline elastomers to simple shear is reported. Significantly, these materials also show extremely large loss behavior with tan ␦ exceeding 1 or even 1.5 over very wide temperature ranges, with clear implications for damping applications. By comparing materials that exhibit different types of liquid crystalline phases, we identify the nematic state as a better damping phase than that in materials with smectic phases. Additionally, we provide experimental evidence for directions which should be explored for further improvements in the damping behavior of liquid crystalline elastomers.

Anomalous Viscoelastic Response of Nematic Elastomers

Physical Review Letters, 2001

We report a combined theoretical and experimental study of linear viscoelastic response in oriented monodomain nematic elastomers. The model predicts a dramatic decrease in the dynamic modulus in certain deformation geometries in an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics. Dynamic mechanical measurements on monodomain nematic elastomers confirm our predictions of dependence on shear geometry and on nematic order, and also show a very substantial mechanical loss clearly associated with director relaxation.

Order and Disorder in Liquid-Crystalline Elastomers

2011

Order and frustration play an important role in liquid-crystalline polymer networks (elastomers). The first part of this review is concerned with elastomers in the nematic state and starts with a discussion of nematic polymers, the properties of which are strongly determined by the anisotropy of the polymer backbone. Neutron scattering and X-ray measurements provide the basis for a description of their conformation and chain anisotropy. In nematic elastomers, the macroscopic shape is determined by the anisotropy of the polymer backbone in combination with the elastic response of elastomer network. The second part of the review concentrates on smectic liquid-crystalline systems that show quasi-long-range order of the smectic layers (positional correlations that decay algebraically). In smectic elastomers, the smectic layers cannot move easily across the crosslinking points where the polymer backbone is attached. Consequently, layer displacement fluctuations are suppressed, which effectively stabilizes the one-dimensional periodic layer structure and under certain circumstances can reinstate true long-range order. On the other hand, the crosslinks provide a random network of defects that could destroy the smectic order. Thus, in smectic elastomers there exist two opposing tendencies: the suppression of layer displacement fluctuations that enhances translational order, and the effect of random disorder that leads to a highly frustrated equilibrium state. These effects can be investigated with high-resolution X-ray diffraction and are discussed in some detail for smectic elastomers of different topology.

Nonlinear elasticity, fluctuations and heterogeneity of nematic elastomers

Annals of Physics, 2008

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 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 an essential modification of the classical elasticity theory. In this work, we develop a rotationally invariant, nonlinear theory of elasticity for the nematic phase of ideal liquid crystal elastomers. We show that it is characterized by soft modes, corresponding to a combination of long wavelength shear deformations of the solid network and rotations of the nematic director field. We study thermal fluctuations of these soft modes in the presence of network heterogeneities and show that they lead to a large variety of anomalous elastic properties, such as singular length-scale dependent shear elastic moduli, a divergent elastic constant for splay distortion of the nematic director, long-scale incompressibility, universal Poisson ratios and a nonlinear stress-strain relation for arbitrary small strains. These long-scale elastic properties are universal, controlled by a nontrivial zero-temperature fixed point and constitute a qualitative breakdown of the classical elasticity theory in nematic elastomers. Thus, nematic elastomers realize a stable "critical phase", characterized by universal power-law correlations, akin to a critical point of a continuous phase transition, but extending over an entire phase.

Nematic elastomers: From a microscopic model to macroscopic elasticity theory

Physical Review E, 2008

A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media.

Symmetries and elasticity of nematic gels

Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our descriptio...

Structure and elastic properties of smectic liquid crystalline elastomer films

Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

Mechanical measurements, x-ray investigations, and optical microscopy are employed to characterize the interplay of chemical composition, network topology, and elastic response of smectic liquid crystalline elastomers (LCEs) in various mesophases. Macroscopically ordered elastomer films of submicrometer thicknesses were prepared by cross linking freely suspended smectic polymer films. The cross-linked material preserves the mesomorphism and phase transitions of the precursor polymer. The elastic response of the smectic LCE is entropic, and the corresponding elastic moduli are of the order of MPa. In the tilted ferroelectric smectic-C* phase, the network structure plays an important role. Due to the coupling of elastic network deformations to the orientation of the mesogenic groups in interlayer cross-linked materials (mesogenic cross-linker units), the stress-strain characteristics is found to differ qualitatively from that in the other phases.

Thermal Characterisation of Thermotropic Nematic Liquid-Crystalline Elastomers

Liquid Cryst., 2016

Nematic liquid-crystalline elastomers (LCEs) are weakly cross-linked polymeric networks that exhibit rubber elasticity and liquid-crystalline orientational order due to the presence of mesogenic groups. Three end-on side-chain nematic LCEs were investigated using real-time synchrotron wide-angle X-ray scattering (WAXS), differential scanning calorimetry (DSC), and thermogravimetry (TG) to correlate the thermal behaviour with structural and chemical differences among them. The elastomers differed in cross-linking density and mesogen composition. Thermally reversible glass transition temperature, Tg, and nematic-to-isotropic transition temperature, Tni, were observed upon heating and cooling. By varying the heating rate, Tg 0 and Tni 0 were determined at zero heating rate. The temperature dependence of the orientational order parameter was determined from the anisotropic azimuthal angular distribution of equatorial reflections seen during real-time WAXS. Results show that the choice of cross-linking unit, its shape, density, and structure of co-monomers, all influence the temperature range over which the thermal transitions take place. Including multi-ring aromatic groups as cross-linkers increased the effective stiffness of the cross-linking, resulting in a higher glass transition temperature. The nematic-to-isotropic transition temperature increased in the presence of multi-ring aromatic structures, as either cross-linkers or mesogens, particularly when the multi-ring structures were larger than the low-molar-mass mesogen common to all three samples.