We study numerically the rheological properties of a slab of active gel close o the isotropic-nematic transition. The flow behavior shows strong dependence on sample size, boundary conditions, and on the bulk constitutive curve, which, on entering the nematic phase, acquires an activity-induced discontinuity at the origin. The precursor of this within the metastable isotropic phase for contractile systems ({\em e.g.,} actomyosin gels) gives a viscosity divergence; its counterpart for extensile ({\em e.g.,} {\em B. subtilis}) suspensions admits instead a shear-banded flow with zero apparent viscosity.
In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transition. We also present phase diagrams that these systems may exhibit. In particular, we show that coexistence of two isotropic phases, of two nematic phases, or of an isotropic and a nematic phase can occur…
A spontaneous buckling transition in thin layers of monodomain nematic liquid crystalline gel was observed by polarized light microscopy. The coupling between the orientational ordering of liquid crystalline solvent and the translational ordering of crosslinked polymer backbones inside the nematic gel contributes to such buckling transition. As the nematic mesogens become more ordered when the gel is cooled down from a higher gelation temperature, the polymeric backbones tend to elongate along the direction parallel to the nematic director, which is perpendicular to the rigid glass surfaces in…
I put forward a continuum theory for active nematic gels, defined as fluids or suspensions of orientable rodlike objects endowed with active dynamics, that is based on symmetry arguments and compatibility with thermodynamics. The starting point is our recent theory that models (passive) nematic liquid crystals as relaxing nematic elastomers. The interplay between viscoelastic response and active dynamics of the microscopic constituents is naturally taken into account. By contrast with standard theories, activity is not introduced as an additional term of the stress tensor, but it is added as a…
We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infared fixed point. Namely, at long scales, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible and exhibit a universal negative Poisson ratio and a non-Hooke…
We derive a multiphysics model that accounts for network elasticity with spontaneous strains, swelling and nematic interactions in liquid crystal gels (LCGs). We discuss the coupling among the various physical mechanisms, with particular reference to the effects of nematic interactions on chemical equilibrium and that of swelling on the nematic-isotropic transition. Building upon this discussion and using numerical simulations, we explore the transient phenomena involving concurrent swelling and phase transition in LCGs subject to a temperature change. Specifically, we demonstrate separation i…
In a nematic gel, the appearance of nematic order is accompanied by a spontaneous elongation of the gel parallel to the nematic director. If such a gel is made chiral, it has a tendency to form a cholesteric helical texture, in which local elongation of the gel parallel to the nematic director is suppressed due to the requirement of elastic compatibility. We show that a conical helix in which the director makes an oblique angle with respect to the helix axis serves as an energy minimizing compromise between the competing tendencies for elongation and twisting. We find the dependence of the hel…
We have studied the effects of quenched random disorder created by dispersed aerosil nanoparticle gels on the nematic to smectic-A (N-SmA) and smectic-A to reentrant nematic (SmA- RN) phase transitions of thermotropic liquid crystal mixtures of 6OCB (hexyloxycyanobiphenyl) and 8OCB (octyloxycyanobiphenyl). These effects are probed using high-resolution synchrotron x-ray diffraction techniques. We find that the reentrant characteristics of the system are largely unchanged by the presence of the aerosil gel network. By comparing measurements of the smectic static structure amplitude for this 8OC…
The solid nematic equivalent of the Fredericks transition is found to depend on a critical field rather than a critical voltage as in the classical case. This arises because director anchoring is principally to the solid rubbery matrix of the nematic gel rather than to the sample surfaces. Moreover, above the threshold field, we find a competition between quartic (soft) and conventional harmonic elasticity which dictates the director response. By including a small degree of initial director misorientation, the calculated field variation of optical anisotropy agrees well with the conoscopy meas…
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 s…
We examine microstructural and mechanical changes which occur during oscillatory shear flow and reformation after flow cessation of an intermediate volume fraction colloidal gel using rheometry and Brownian Dynamics (BD) simulations. A model depletion colloid-polymer mixture is used, comprising of a hard sphere colloidal suspension with the addition of non-adsorbing linear polymer chains. Results reveal three distinct regimes depending on the strain amplitude of oscillatory shear. Large shear strain amplitudes fully break the structure which results into a more homogenous and stronger gel afte…
The effects of dispersed aerosil nanoparticles on two of the phase transitions of the thermotropic liquid crystal material 4-n-pentylphenylthiol-4'-n-octyloxybenzoate 8barS5 have been studied using high-resolution x-ray diffraction techniques. The aerosils hydrogen bond together to form a gel which imposes a weak quenched disorder on the liquid crystal. The smectic-A fluctuations are well characterized by a two-component line shape representing thermal and random-field contributions. An elaboration on this line shape is required to describe the fluctuations in the smectic-C phase; specifically…
We report numerical results for the hydrodynamics of inhomogeneous lyotropic and extensile active nematic gels. By simulating the coupled Cahn-Hilliard, Navier-Stokes, and Beris-Edwards equation for the evolution of the composition, flow and orientational order of an active nematic, we ask whether composition variations are important to determine its emergent physics. As in active gels of uniform composition, we find that increasing either activity or nematic tendency (e.g., overall active matter concentration) triggers a transition between an isotropic passive phase and an active nematic one.…
Randomly disordered (polydomain) liquid crystalline elastomers align under stress. We study the dynamics of stress relaxation before, during and after the Polydomain-Monodomain transition. The results for different materials show the universal ultra-slow logarithmic behaviour, especially pronounced in the region of the transition. The data is approximated very well by an equation Sigma(t) ~ Sigma_{eq} + A/(1+ Alpha Log[t]). We propose a theoretical model based on the concept of cooperative mechanical resistance for the re-orientation of each domain, attempting to follow the soft-deformation pa…
The effect on the nematic to smectic-A transition in octylcyanobiphenyl (8CB) due to dispersions of hydrogen-bonded silica (aerosil) particles is characterized with high-resolution x-ray scattering. The particles form weak gels in 8CB creating a quenched disorder that replaces the transition with the growth of short range smectic correlations. The correlations include thermal critical fluctuations that dominate at high temperatures and a second contribution that quantitatively matches the static fluctuations of a random field system and becomes important at low temperatures.
Based on a mesoscopic theory we investigate the non-equilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress $σ_{\mathrm{xy}}$ (rather than the usual shear rate, $\dotγ$). To this end we supplement the equations of motion for the orientational order parameters by an equation for $\dotγ$, which then becomes time-dependent. Shearing the system from an isotropic state, the stress- controlled flow properties turn out to be essentially identical to those at fixed $\dotγ$. Pronounced differences when the equilibrium state is nematic. Here, shearing at contr…
High-resolution X-ray scattering studies of the nonpolar thermotropic liquid crystal 4-n-pentylphenylthiol-4'-n-octyloxybenzoate (\bar{8}S5) in aerosil gel nano-networks reveal that the aerosil-induced disorder significantly alters both the nematic to Smectic-A and Smectic-A to Smectic-C phase transitions. The limiting Smectic-A correlation length follows a power-law dependence on the aerosil density in quantitative agreement with the limiting lengths measured previously in other Smectic-A liquid crystal gels. The Smectic-A to Smectic-C liquid crystalline phase transition is altered fundamenta…
Liquid crystalline polymers are materials of considerable scientific interest and technological value to society [1-3]. An important subset of such materials exhibit rubber-like elasticity; these can combine the remarkable optical properties of liquid crystals with the favourable mechanical properties of rubber and, further, exhibit behaviour not seen in either type of material independently [2]. Many of their properties depend crucially on the particular mesophase employed. Stretchable liquid crystalline polymers have previously been demonstrated in the nematic, chiral nematic, and smectic me…
We study pattern formation in gels undergoing simultaneous phase separation and orientational ordering. A 2D numerical simulation is performed using a minimal model of nonlinear elasticity with density-anisotropy coupling. For strong positive coupling, the collapsed phase elongates along the phase boundary and buckles, creating a folded structure with paired topological defects. For negative coupling, soft elasticity of the swollen phase causes a droplet morphology as in liquid-liquid phase separation. Their possible realizations in nematic liquid-crystalline gels are discussed.
The short-range order which remains when the isotropic to smectic-A transition is perturbed by a gel of silica nanoparticles (aerosils) has been studied using high-resolution synchrotron x-ray diffraction. The gels have been created \textit{in situ} in decylcyanobiphenyl (10CB), which has a strongly first-order isotropic to smectic-A transition. The effects are determined by detailed analysis of the temperature and gel density dependence of the smectic structure factor. In previous studies of the continuous nematic to smectic-A transition in a variety of thermotropic liquid crystals the aerosi…
Continuum hydrodynamic models of active liquid crystals have been used to describe dynamic self-organising systems such as bacterial swarms and cytoskeletal gels. A key prediction of such models is the existence of self-stabilising kink states that spontaneously generate fluid flow in quasi-one dimensional channels. Using simple stability arguments and numerical calculations we extend previous studies to give a complete characterisation of the phase space for both contractile and extensile particles (ie pullers and pushers) moving in a narrow channel as a function of their flow alignment prope…
We carry out numerical simulations to study the behavior of an athermal mixture of frictionless circular disks and elongated rods in two dimensions, under three different types of global linear deformation at a finite strain rate: (i) simple shearing, (ii) pure shearing, and (iii) isotropic compression. We find that the fluctuations induced by such deformations lead to depletion forces that cause rods to group in parallel oriented clusters for the cases of simple and pure shear, but not for isotropic compression. For simple shearing, we find that as the fraction of rods increases, this cluster…
Spinodal demixing of systems into two phases having very different viscosities leads to viscoelastic networks, i.e. gels. Here we consider demixing in a colloidal system where one phase is a nematic liquid crystal with a strongly anisotropic viscosity. We combine real space analysis of a sepiolite clay system with molecular dynamics computer simulation. We find a long-lived network with many of the characteristics of a colloidal gel. Remarkably the anisotropic viscosity means that flow is possible within the nematic network, but only along the network, which thus preserves its structure, leadi…
We report a high-resolution x-ray scattering study of the smectic liquid crystal octylcyanobiphenyl (8CB) confined to aligned colloidal aerosil gels. The aligned gels introduce orientational fields that promote long-range nematic order while imposing positional random fields that couple to the smectic density wave and disrupt the formation of an ordered smectic phase. At low densities of aerosil, the low-temperature scattering intensity is consistent with the presence of a topologically ordered XY Bragg glass phase that is predicted to form in response to such anisotropic quenched disorder. Th…
Living active collectives have evolved with remarkable self-patterning ability to meet the physical and biological constraints for growth and survival. However, how complex multicellular patterns emerge from a single founder cell remains elusive. Here, by recourse to an agent-based model, we track the three-dimensional (3D) morphodynamics and cell orientational order of growing bacterial biofilms encased by agarose gels. Confined growth causes spatiotemporally heterogeneous stress buildup in the biofilm. High hydrostatic and low shear stresses at the core of the biofilm promote viscous-to-elas…
Active matter locally converts chemical energy into mechanical work and, for this reason, it provides new mechanisms of pattern formation. In particular, active gels made of protein motors and filaments are far-from-equilibrium systems that exhibit spontaneous flow,[Kruse2004, Voituriez2005] leading to active turbulence in two and three dimensions[Sanchez2012, Kumar2018] and coherent flow in three dimensions[Wu2017] (3D). Although these dynamic flows reveal a characteristic length scale resulting from the interplay between active forcing and passive restoring forces, the observation of static …
With quenched disorder, we introduce two-dimensional active nematics suspended in an incompressible fluid. We write the coarse-grained hydrodynamic equations of motion for slow variables, viz. density, orientation and flow fields. The quenched disorder is introduced such that it interacts with the local orientation at every point with some strength. Disorder strength is tuned from zero to large values. We numerically study the defect dynamics and system's kinetics and find that the finite disorder slows the ordering. The presence of fluid induces large fluctuation in the orientation field, fur…
We use numerical simulations to study the flow of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. We study the resulting spatial structure of the sheared system, and compute correlation functions of the velocity, the particle density, the nematic order parameter, and the particle angular velocit…
We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate $\dotγ$. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions $ϕ$ and particle asphericities $α$ at small $\dotγ$, we study the angular rotation $\dotθ_i$ and the nematic orientational ordering $…
Properties of disordered nematic elastomers and gels are theoretically investigated with emphasis on the roles of non-local elastic interactions and crosslinking conditions. Networks originally crosslinked in the isotropic phase lose their long-range orientational order by the action of quenched random stresses, which we incorporate into the affine-deformation model of nematic rubber elasticity. We present a detailed picture of mechanical quasi-Goldstone modes, which accounts for an almost completely soft polydomain-monodomain (P-M) transition under strain as well as a ``four-leaf clover'' pat…
Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and topological defects. By contrast, little is known about positional coherence -- i.e., how a hidden dynamic skeleton organizes the underlying chaotic motion -- despite this being one of their most prominent and experimentally accessible features. Using a combination of dynamical systems theory, experiments on two-dimensional mixtures of microtubules and kinesin and hydrodynamic simulations, we characterize positional …
We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is uniform across the system, the Turing patterns dissociate when the flux from active advection balances that from the reaction-diffusion process. If the activity is coupled to the concentration of Turing morphogens, and neighbouring stripes have equal and opposite activity, the system self organises into a pattern of shearing flows, with stripes tending to fr…
With exquisite precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometer-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and replication. Besides their biological importance, such inherently non-equilibrium processes are an inspiration for developing biomimetic active materials from microscopic components that consume energy to generate continuous motion. Being actively driven, these materials are not constrained by the laws of equilibrium statistical mechanics and can thus exhibit highly…
