Elasticity of polydomain liquid crystal elastomers

Abstract

We model polydomain liquid-crystal elastomers by extending the neo-classical soft and semi-soft free energies used successfully to describe monodomain samples. We show that there is a significant difference between polydomains cross-linked in homogeneous high symmetry states then cooled to low symmetry polydomain states and those cross-linked directly in the low symmetry polydomain state. For example, elastomers cross-linked in the isotropic state then cooled to a nematic polydomain will, in the ideal limit, be perfectly soft, and with the introduction of non-ideality, will deform at very low stress until they are macroscopically aligned. The director patterns observed in them will be disordered, characteristic of combinations of random deformations, and not disclination patterns. We expect these samples to exhibit elasticity significantly softer than monodomain samples. Polydomains cross-linked in the nematic polydomain state will be mechanically harder and contain characteristic schlieren director patterns. The models we use for polydomain elastomers are spatially heterogeneous, so rather than solving them exactly we elucidate this behavior by bounding the energies using Taylor-like (compatible test strain fields) and Sachs (constant stress) limits extended to non-linear elasticity. Good agreement is found with experiments that reveal the supersoft response of some polydomains. We also analyze smectic polydomain elastomers and propose that polydomain SmC* elastomers cross-linked in the SmA monodomain state are promising candidates for low field electrical actuation.

An electro‐elastic phase‐field model for nematic liquid crystal elastomers based on Landau‐de‐Gennes theory

“…This assumption is in line with the formulations of, for example, UCHIDA & ONUKI [60], KÖPF & PISMEN [31] and DESIMONE, DICARLO & TERESI [19], see DESI-MONE & TERESI [20] and AGOSTINIANI & DESIMONE [1] for theoretical background 4 .…”

“…The underlying unity constraint poses a severe challenge on the numerical treatment of the time integration ofṅ; we refer the interested reader to the works [24,35] as well as to related literature on the theory and numerics of micro-magnetics [73,72,38,53]. 4 We however note that usually nematic elastomers experience large deformations so that a geometrically nonlinear approach will be more appropriate. Ongoing research is devoted to an extension of the present model to large deformations.…”

Soft Elasticity in Main Chain Liquid Crystal Elastomers

“…The elastomers do not quite follow an entirely reverse path while the initial polydomain state is recovered by heating from the mechanically induced monodomain state. The experimental results discussed here should help in advancing the theoretical understanding [82,83] of soft elasticity exhibited by these polydomain SmC MCLCEs.…”

Dynamic Theory of Polydomain Liquid Crystal Elastomers

“…Effects of quenched disorder have further been modeled and visualized through numerical simulations [18][19][20][21]. More macroscopic theories have shown that the resulting polydomain structure has profound consequences for the material's effective elasticity [22,23].The purpose of this paper is to suggest a different mechanism for the origin of the polydomain state, not related to quenched disorder. We develop a theory for the dynamics of the isotropic-nematic transition in liquidcrystal elastomers, in which growing nematic order is coupled to elastic strain.…”

“…Effects of quenched disorder have further been modeled and visualized through numerical simulations [18][19][20][21]. More macroscopic theories have shown that the resulting polydomain structure has profound consequences for the material's effective elasticity [22,23].…”