Incompatible strains associated with defects in nematic elastomers

Fried, Eliot; Sellers, Shaun

doi:10.1063/1.2149857

Cited by 10 publications

(9 citation statements)

References 27 publications

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“…Extension will not occur at zero stress, but extensions up to r 1=3 will occur at energies OðÞ ( 1. The deformation patterns and director patterns must still be very close to those in the ideal case, so the observed patterns will still be characterized as textured deformations driven by elastic compatibility-typically oscillations between regions of constant deformation separated by sharp boundaries [6,8,17]-not disclination textures which are not elastically compatible [18], although the choice of microstructure will change from point to point in the elastomer.…”

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Supersoft Elasticity in Polydomain Nematic Elastomers

2009

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We consider the equilibrium stress-strain behavior of polydomain liquid crystal elastomers (PLCEs). We show that there is a fundamental difference between PLCEs cross-linked in the high temperature isotropic and low temperature aligned states. PLCEs cross-linked in the isotropic state then cooled to an aligned state will exhibit extremely soft elasticity (confirmed by recent experiments) and ordered director patterns characteristic of textured deformations. PLCEs cross-linked in the aligned state will be mechanically much harder and characterized by disclination textures. DOI: 10.1103/PhysRevLett.103.037802 PACS numbers: 61.30.Vx, 81.40.Jj, 83.80.Va Liquid crystal elastomers are rubbery materials that possess liquid crystal order [1]. Their large spontaneous elongations at the symmetry-breaking isotropic-nematic transition have long made them ideal candidates for showing soft (zero energy) elastic modes [2,3] in the manner proposed by Golubovic and Lubensky [4]. Monodomain samples show qualitatively soft elasticity over a large range of deformations [5,6]. However, monodomains never show perfectly soft behavior because, to achieve their macroscopic alignment of the director, they require the imprinting of a direction on the network, breaking the isotropy of the high temperature state. A microscopic region extracted from a polydomain cross-linked in either the nematic or the isotropic state would have fairly soft elastic modes. As anticipated by Golubovic and Lubensky, in the isotropic cross-linking case these modes will be almost perfectly soft, while in the nematic cross-linking case they will only be qualitatively soft like those in monodomains. However, the macroscopic softness of the polydomain sample is not guaranteed because the soft modes of neighboring domains may not be elastically compatible, although there are experimental suggestions of softness [7]. Using textured deformations introduced by DeSimone and Dolzmann [8] we show that polydomains cross-linked in the isotropic state retain their extreme softness macroscopically, while polydomains cross-linked in the nematic state will not. This distinction has been confirmed by recent experiments [9].Polydomains cross-linked in the isotropic state can only deviate from perfect Golubovic-Lubensky soft elasticity because local fluctuations in, say, cross-link orientation, compromise the isotropy of the cross-linking state. Following [10] we model these fluctuations using a random field which drives the formation of the polydomain state and limits the softness of the macroscopic response.The distinctive behavior of monodomain samples has been well understood using a neoclassical model of Gaussian distributed chains [1,11]. The chain conformations are biased by the liquid crystal order so that the second moment of the conformation distribution of a free chain is hR i R j i / ' ¼ r À1=3 ð þ ðr À 1Þnn Þ, where R is the polymer span vector, is the identity matrix,n is the nematic director, and r is the anisotropy of the polymer conformation distribution which...

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Supersoft Elasticity in Polydomain Nematic Elastomers

2009

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“…Furthermore, the deformation patterns and director patterns in the non-ideal case must still be very close in energy to those in the ideal case, so the observed patterns will still be characterized as textured deformations driven by elastic compatibility -not disclination textures. Indeed, nematic disclinations never have zero-energy elastically compatible associated distortions [30], so cannot be observed in isotropic genesis systems.…”

Section: B Ideal Isotropic Genesis Polydomainsmentioning

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Elasticity of polydomain liquid crystal elastomers

Biggins

Warner

Bhattacharya

2012

Journal of the Mechanics and Physics of Solids

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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.

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“…Disclination defect textures are not extensively studied, experimentally or theoretically, in nematic solids. However it is known that the energy minimizing deformation associated locally with changes in their nematic order is not compatible in some 3-D disclinations [8]. We analyze the mechanical response and elastic ground state of the most experimentally accessible disclination defect in 2-D, that with topological charge +1.…”

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Disclination-mediated thermo-optical response in nematic glass sheets

2010

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Nematic solids respond strongly to changes in ambient heat or light, significantly differently parallel and perpendicular to the director. This phenomenon is well characterized for uniform director fields but not for defect textures. We analyze the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for some disclination defects with an eye toward reversibly inducing three-dimensional shapes from flat sheets of material, at the nanoscale all the way to macroscopic objects, including nondevelopable surfaces. The latter offers a paradigm to actuation via switchable stretch in thin systems. DOI: 10.1103/PhysRevE.81.060701 PACS number͑s͒: 61.30.Jf, 46.32.ϩx, 46.70.De, 46.70.Hg Nematic glasses ͑densely cross-linked networks͒ ͓1͔ are solids with a natural state of elongation along their director and contraction perpendicular that depends on their orientational order. Accordingly they suffer large, reversible length change with heating ͓2͔, illumination ͓3,4͔, solvent uptake, pH change and any other stimulus that causes order change. For glasses these strains can be 2 -3 % and of opposite sign ͑without conserving volume͒ along and perpendicular to the director. They can then exhibit spectacular effects such as large bend resulting from gradients of stimuli ͓5͔ ͑light, solvent͒ or from uniform stimuli ͑such as temperature or weakly absorbing light͒ but with a director gradient through, for instance, the section of a sheet or cantilever ͓2-4͔ ͑usually twist or splay-bend͒. Glasses are distinguished from elastomers by being so heavily cross-linked that the director field only changes as a result of convection due to material shape change from the elastic strain. Nematic glass directors do not rotate relative to the matrix as in nematic elastomers-they are ͓3͔ conventional uniaxial elastic solids, with moduli of about ϫ10 4 higher than those of elastomers. We are most concerned with the thermally or optically inspired length changes which we take to be by a factor along the director and by − perpendicular to the director ͑where fulfills the role of a thermal or optical Poisson ratio, were the deformations to be infinitesimal͒. Elastic energy cost would be associated with imposed changes away from these new natural shapes-we find deformation fields matching these thermo/ optical changes and thus of zero elastic energy in the membrane limit we take. Accordingly we do not need to explore the solid body elasticity specific to uniaxial materials.Director fields can be established in the nematic liquid progenitor phase before cross-linking and are permanently recorded in the solid state achieved after linkage. In fact complex, three-dimensional ͑3D͒ director fields for subtle mechanical response can be achieved in nematic glasses ͓6͔ via holography and surface preparation. From the point of view of device design, the ability to "write" an initial director field into a solid so that it distorts in a predictable ͑and reversible way͒ into a new shape with applied temperature or li...

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Incompatible strains associated with defects in nematic elastomers

Cited by 10 publications

References 27 publications

Supersoft Elasticity in Polydomain Nematic Elastomers

Supersoft Elasticity in Polydomain Nematic Elastomers

Elasticity of polydomain liquid crystal elastomers

Disclination-mediated thermo-optical response in nematic glass sheets

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