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Register a new userNonlinear smectic elasticity of a helical state in cholesterics and helimagnets
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General symmetry arguments, dating back to de Gennes dictate that at scales longer than the pitch, the low-energy elasticity of a chiral nematic liquid crystal (cholesteric) and of a Dzyaloshinskii-Morya (DM) spiral state in a helimagnet with negligible crystal symmetry fields (e.g., MnSi, FeGe) is identical to that of a smectic liquid crystal, thereby inheriting its rich phenomenology. Starting with a chiral Frank free-energy (exchange and DM interactions of a helimagnet) we present a transparent derivation of the fully nonlinear Goldstone mode elasticity, which involves an analog of the Anderson-Higgs mechanism that locks the spiral orthonormal (director/magnetic moment) frame to the cholesteric (helical) layers. This shows explicitly the reduction of three orientational modes of a cholesteric down to a single phonon Goldstone mode that emerges on scales longer than the pitch. At a harmonic level our result reduces to that derived many years ago by Lubensky and collaborators.
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In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this paper, we demonstrate that chirality qualitatively modifies the dynamics of layered liquid crystals in active systems in both two and three dimensions due to an active odder elasticity. In three dimensions, we demonstrate that the hydrodynamics of active cholesterics differs fundamentally from smectic-A liquid crystals, unlike their equilibrium counterpart. This distinction can be used to engineer a columnar array of vortices, with anti-ferromagnetic vorticity alignment, that can be switched on and off by external strain. A two-dimensional chiral layered state -- an array of lines on an incompressible, free-standing film of chiral active fluid with a preferred normal direction -- is generically unstable. However, this instability can be tuned in easily realisable experimental settings, when the film is either on a substrate or in an ambient fluid.
We report studies of the frequency dependent shear modulus, $G^*(omega)=G(omega)+iG(omega)$, of the liquid crystal octylcyanobiphenyl (8CB) confined in a colloidal aerosil gel. With the onset of smectic order, $G$ grows approximately linearly with decreasing temperature, reaching values that exceed by more than three orders of magnitude the values for pure 8CB. The modulus at low temperatures possesses a power-law component, $G^*(omega) sim omega^alpha$, with exponent $alpha$ that approaches zero with increasing gel density. The amplitude of $G$ and its variation with temperature and gel density indicate that the low temperature response is dominated by a dense population of defects in the smectic. In contrast, when the 8CB is isotropic or nematic, the modulus is controlled by the elastic behavior of the colloidal gel.
We study by simulation the physics of two colloidal particles in a cholesteric liquid crystal with tangential order parameter alignment at the particle surface. The effective force between the pair is attractive at short range and favors assembly of colloid dimers at specific orientations relative to the local director field. When pulled through the fluid by a constant force along the helical axis, we find that such a dimer rotates, either continuously or stepwise with phase-slip events. These cases are separated by a sharp dynamical transition and lead, respectively, to a constant or an ever-increasing phase lag between the dimer orientation and the local nematic director.
We present a Landau type theory for the non-linear elasticity of biopolymer gels with a part of the order parameter describing induced nematic order of fibers in the gel. We attribute the non-linear elastic behavior of these materials to fiber alignment induced by strain. We suggest an application to contact guidance of cell motility in tissue. We compare our theory to simulation of a disordered lattice model for biopolymers. We treat homogeneous deformations such as simple shear, hydrostatic expansion, and simple extension, and obtain good agreement between theory and simulation. We also consider a localized perturbation which is a simple model for a contracting cell in a medium.
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Nature Physics, 2011 7, 983]. In this work we generalize the scaling to the nonlinear regime with a two-parameter scaling law involving three critical exponents. We test the scaling law numerically for two disordered lattice models, and find a good scaling collapse for the shear modulus in both the linear and nonlinear regimes. We compute all the critical exponents for the two lattice models and discuss the applicability of our results to real systems.
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