Linear hydrodynamics and viscoelasticity of nematic elastomers

We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors.Comment: Latex 2e or PDFlatex (4 EPS or JPG figures) - to appear in Euro.Phys.J.

Dynamic Soft Elasticity in Monodomain Nematic Elastomers

We study the linear dynamic mechanical response of monodomain nematic liquid crystalline elastomers under shear in the geometry that allows the director rotation. The aspects of time-temperature superposition are discussed at some length and Master Curves are obtained between the glassy state and the nematic transition temperature Tni. However, the time-temperature superposition did not work through the clearing point Tni, due to change from the ``soft-elasticity'' nematic regime to the ordinary isotropic rubber response. We focus on the low-frequency region of the Master Curves and establish the power-law dependence of the modulus G' ~ omega^a. This law agrees very well with the results of static stress relaxation, where each relaxation curve obeys the analogous power law G' ~ t^{-a} in the corresponding region of long times and temperatures.Comment: Latex, [epj]{svjour} style, 9 pages 11 figures submitted to Euro. Phys. J.

Tube Model for the Elasticity of Entangled Nematic Rubbers

Dense rubbery networks are highly entangled polymer systems, with significant topological restrictions for the mobility of neighbouring chains and crosslinks preventing the reptation constraint release. In a mean field approach, entanglements are treated within the famous reptation approach, since they effectively confine each individual chain in a tube-like geometry. We apply the classical ideas of reptation dynamics to calculate the effective rubber-elastic free energy of anisotropic networks, nematic liquid crystal elastomers, and present the first theory of entanglements for such a material.Comment: amended version (typos corrected, appendix extended

Cellular solid behaviour of liquid crystal colloids. 2. Mechanical properties

This paper presents the results of a rheological study of thermotropic nematic colloids aggregated into cellular structures. Small sterically stabilised PMMA particles dispersed in a liquid crystal matrix densely pack on cell interfaces, but reversibly mix with the matrix when the system is heated above Tni. We obtain a remarkably high elastic modulus, G'~10^5 Pa, which is a nearly linear function of particle concentration. A characteristic yield stress is required to disrupt the continuity of cellular structure and liquify the response. The colloid aggregation in a ``poor nematic'' MBBA has the same cellular morphology as in the ``good nematic'' 5CB, but the elastic strength is at least an order of magnitude lower. These findings are supported by theoretical arguments based on the high surface tension interfaces of a foam-like cellular system, taking into account the local melting of nematic liquid and the depletion locking of packed particles on interfaces.Comment: Latex 2e (EPJ style) EPS figures included (poor quality to comply with space limitations

Spontaneous thermal expansion of nematic elastomers

We study the monodomain (single-crystal) nematic elastomer materials, all side-chain siloxane polymers with the same mesogenic groups and crosslinking density, but differing in the type of crosslinking. Increasing the proportion of long di-functional segments of main-chain nematic polymer, acting as network crosslinking, results in dramatic changes in the uniaxial equilibrium thermal expansion on cooling from isotropic phase. At higher concentration of main chains their behaviour dominates the elastomer properties. At low concentration of main-chain material, we detect two distinct transitions at different temperatures, one attributed to the main-chain, the other to the side-chain component. The effective uniaxial anisotropy of nematic rubber, r(T) proportional to the effective nematic order parameter Q(T), is given by the average of the two components and thus reflects the two-transition nature of thermal expansion. The experimental data is compared with the theoretical model of ideal nematic elastomers; applications in high-amplitude thermal actuators are discussed in the end

Ageing of Natural Rubber under Stress

We report a dynamical-mechanical study of stress relaxation at small deformation in a natural (polyisoprene) rubber well above its glass transition temperature Tg. We find that an almost complete relaxation of stress takes place over very long periods of time, even though the elastic network integrity is fully retained. The relaxation rate and the long-time equilibrium modulus are sensitive functions of temperature which do not follow time-temperature superposition. Many characteristic features of non-ergodic ageing response are apparent at both short and very long times. We interpret the observed behaviour in terms of the properties of rubber crosslinks, capable of isomerisation under stress, and relate the results to recent models of soft glassy rheology.Comment: Latex 2e (EPJ style), 5 EPS figure

Microscopic origin of nonlinear non-affine deformation and stress overshoot in bulk metallic glasses

The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented in compact analytical form using a qualitative method for the many-body Smoluchowski equation. The resulting nonlinear stress-strain (constitutive) relation is very simple, with few fitting parameters, yet contains all the microscopic physics. The theory is successfully tested against experimental data on metallic glasses, and it is able to reproduce the ubiquitous feature of stress-strain overshoot upon varying temperature and shear rate. A clear atomic-level interpretation is provided for the stress overshoot, in terms of the competition between the elastic instability caused by nonaffine deformation of the glassy cage and the stress buildup due to viscous dissipation.Comment: Physical Review B Rapid Comm., in pres