Schedule for: 16w5021 - Mathematical Problems of Orientationally Ordered Soft Solids

A welcome drink will be served at the hotel.

Light-matter interactions that involve photoisomerization of azobenzene molecules with polymer network evolution have limited our understanding of complex photo-induced deformation in cantilever films and surface relief grating structures. A unified modeling framework is presented to advance the understanding of different deformation states con- trolled by linear or circularly polarized light or optical vortex beams. Prior research that uses higher order field gradients to model surface relief grating deformation is found to be unnecessary. The proposed model, which couples time-dependent Maxwell equations with nonlinear mechanics and internal dipole electronic structure evolution, is found to compare well with a broad range of photomechanical data including both surface relief gratings and deformation of free standing films. These simulation have led to the develop- ment of new constitutive relations that include viscoelastic and viscoplastic deformation as a function of light and heat. The unified modeling approach is validated against photomechanical experiments using Bayesian uncertainty analysis to provide insight on model predictability.

Liquid crystal elastomers and gels are an intriguing material that has a feature that the macroscopic shape is strongly correlated with molecular orientational order and vice versa. Among the LCEs with several types of orientational order, we focus on cholesteric LCEs (CLCEs) with helical director configuration. We have fabricated the two types of CLCE films with the helical axis parallel and normal to the film surface (designated as P-CLCE and N-CLCE, respectively). N-CLCEs under temperature variation exhibit uniaxial deformation along the helical axis accompanying a shift of selective reflection band. P-CLCEs have the periodic surface undulation with a period corresponding to a half of helical pitch, and it varies like as stationary wave with temperature. The N- CLCE swollen by liquid crystal solvent exhibit the simultaneous electromechanical and electrooptical effects under the electric field parallel to the helical axis: The gels are elongated along the helical axis, and a shift of selective reflection band toward the longer wavelengths occurs.

Liquid crystal flexoelectric actuation uses an imposed electric field to create mem- brane bending and it is used by the Outer Hair Cells (OHC) located in the inner ear, whose role is to amplify sound through generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHC is to find the relations and impact of the electro-mechanical properties of the membrane, the rheolog- ical properties of the viscoelastic media, and the frequency response of the generated mechanical power output. The model developed and used in this work is based on the integration of: (i) the flexoelectric membrane shape equation applied to a circular mem- brane attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting viscoelastic phases, such that the membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equation an analytical expression for the transfer function, associated to the curvature and electrical field, power dissipation elastic storage were found. The integrated flexoelectric/viscoelastic model and the novel findings contribute to the ongoing quest for a fundamental understanding of the functioning of outer hair cells (OHC), especially on the role of membrane deformation in delivering mechanical power through electromotility and its frequency-dependent power conversion efficiency.

Minimal models of active Brownian colloids consisting of self-propelled spherical par- ticles with purely repulsive interactions have recently been identified as excellent quanti- tative testing grounds for theories of active matter and have been the subject of extensive numerical and analytical investigation. These systems have a rich phase diagram, forming active gases, liquids and solids with novel mechanical properties and exhibiting behaviour such as motility induced phase separation. A particularly interesting phenomenon can be found if we introduce noisy aligning interactions. By varying the density of the sys- tem or the intensity of the noise one can switch between a disordered phase where the particles move randomly and independently and a flocking state where the velocities of the particles are aligned. In this work we study the effect that disorder has on this flock. In particular, we consider what happens if a fraction p of the particles does not expe- rience the aligning interaction or if the particles have to flock through a medium with obstacles. By carrying out extensive molecular dynamics simulations we show that even a very small fraction of such ”dissenters” can have a dramatic effect on the whole system and, indeed, that the flocking can be destroyed for a very low value of p.

We will discuss some recent case studies in which we address the problem of how some unicellular organisms control their shape, and how we can try to replicate some of these mechanisms in synthetic, soft structures.

Among soft active materials, i.e. systems that respond to a non-mechanical stimulus (electric field, exposure to a solvent, pH change, temperature field) with a mechanical deformation, polymer gels play a major role in the current research on innovative materi- als. Applications where gels are employed in the form of thin structures have stimulated the interest in developing dimensionally reduced theories. Hence, a number of plate and shell models have been proposed in the recent years, mainly based on the framework of incompatible elasticity. Despite their success in reproducing experimental results, these models are restricted to equilibrium problems. In general, while dimensionally reduced theories are well established in the study of equilibrium problems in elasticity and struc- tural mechanics, the development of the same theories in a multiphysics, non-equilibrium context such that of swelling thin gels poses challenging theoretical questions. In this talk, we present a survey of our contribution to the derivation of reduced theories for swelling gels. Specifically, we present a theory of swelling material surfaces to model poly- mer gel membranes and demonstrate its features by numerically studying applications in the contexts of biomedicine, micro-motility, and coating technology. Furthermore, we introduce a transient large-strain plate theory for polymer gels obtained by a thermo- dynamically consistent dimensional reduction of a coupled three-dimensional model. We apply the model to the shape programming of composite gel plates, where the spatial modulation of the gel stiffness can be designed so that the composite realizes a target, three-dimensional shape upon swelling. Fracture is another challenging aspect of the mechanics of polymer gels that provides, in the context of these materials, a new angle of a classical, well-studied issue. Indeed, fracture in hydrogels is often accompanied by vari- ous instabilities and dissipation mechanisms that may significantly affect the macroscopic toughness of the system. In synthetic chemical gels, fracture is typically brittle. However, here we show that the unstable character that is characteristic of brittle fracture may be radically altered when a brittle, impermeable hydrogel is hydraulically coupled with a tougher, poroelastic solid. Moreover we revisit the classical problem of Mode I fracture in the context of gels. Specifically, we show the existence of a velocity-independent toughen- ing, which is innate in the poroelastic nature of polymer gels. These fundamental studies on the flaw-tolerance of hydrogels may both shed light on the fracture of soft biological tissues and suggest toughening strategies to improve their mechanical performance.

Liquid crystal elastomers (LCEs) are rubber-like solids that spontaneously deform under stimuli such as a temperature change, light and electric field. The nature of the spontaneous deformation can be controlled in nematic genesis LCEs by controlling the nematic director while forming the elastomer. Recent studies have shown that non- uniform spontaneous deformation can be exploited in thin sheets to deform them out of plane. Importantly, they can do so while lifting significant loads. This talk discusses strategies to design LCEs to act like machines that can form complex shapes and lift substantial loads.

Throughout the science of soft matter, there are many examples of thin films that form complex curved structures. Examples range from liquid-crystal elastomers on the cen- timeter length scale, to self-assembled aggregates of lipid molecules or lyotropic liquid crystals on the micron or submicron scale. Theorists have often addressed these struc- tures through separate approaches that are applicable to each case. In recent years, there has been extensive theoretical and experimental work on elastic sheets, which has led to a unified approach to describe shape selection problems. This approach is based on a target metric tensor for 3D bodies, which implies target metric and curvature tensors for thin (effectively 2D) sheets. The purpose of this talk is to apply that unified approach to liquid crystals. In particular, we consider: (1) Nematic elastomer films with director gradients in the 2D plane, (2) Nematic elastomer films with director gradients across the thickness, (3) Lyotropic liquid crystals with spontaneous curvature (splay), (4) Lyotropic liquid crystals with intrinsic chiral twist, (5) Lyotropic liquid crystals with bend flexo- electricity. In all of these cases, we discuss how the observed shapes can be understood in terms of the target metric and target curvature.

This talk will explore elastic and mechanical properties and mode structures of model periodic lattices, such as the square, kagome, pyrochlore, and jammed packings with central-force springs, that are at or near the Maxwell limit mechanical stability with coordination number z equal to twice the spatial dimension d. It will discuss the origin and nature of zero modes and elasticity of these structures under both periodic (PBC) and free boundary conditions (FBC), and it will investigate lattices (a) whose zero modes under the two boundary conditions are essentially identical, (b) whose phonon modes in the bulk are gapped with no zero modes in the periodic spectrum (except at zero wavenumber) but include zero-frequency surface in the free spectrum, and (c) whose bulk phonon modes include isolated points or lines where their frequency is zero. In case (a), lattices are generally in a type of critical state that admits states of self-stress in which there can be tension in bars with zero force on any node. Distortions away from that state gap the spectrum and give rise to surface modes under free boundary conditions whose degree of penetration into the bulk diverges at the critical state. The gapped states have a topological characterization, similar to those of polyacetylene and topological insulators, that define the nature of zero-modes at the boundary between systems with different topology. Case (c) is closely analogous to Weyl semi-metals with isolated points in the Brillouin zone where valence and conduction bands meet. These critical lattices generally have macroscopic elastic distortions, called Guest Modes, that cost no energy.

Active liquid crystals are a new class of soft materials that have recently raised a huge interest. In particular, reconstituted suspensions of cytoskeletal filaments and associated motor proteins have proven ideal for quantitative studies of the origin of subcellular or- ganization. Here we refer to the system initially engineered by the group of Z. Dogic, consisting of bundled microtubules powered by ATP-fueled kinesin motors. We concen- trate on two-dimensional preparations showing nematic textures and streaming flows, from largely-organized to seemingly chaotic. We will present results on different scenar- ios where this active nematics system is conditioned with interfacial fluids. The simplest situation corresponds to prepare them in contact with isotropic oils of different viscosities. From this we can extract a prediction for the as of now unknown shear viscosity of the nematic film. More striking is the situation when the contacting passive fluid is a liquid crystal in its smectic phase. In this latter situation a totally unprecedented strategy of control of the active flows has been recently demonstrated. Other scenarios correspond- ing to encapsulated active nematics, both in contact with isotropic and anisotropic oils will be briefly presented.

Liquid crystal flexoelectric actuation uses an imposed electric field to create mem- brane bending and it is used by the Outer Hair Cells (OHC) located in the inner ear, whose role is to amplify sound through generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHC is to find the relations and impact of the electro-mechanical properties of the membrane, the rheolog- ical properties of the viscoelastic media, and the frequency response of the generated mechanical power output. The model developed and used in this work is based on the integration of: (i) the flexoelectric membrane shape equation applied to a circular mem- brane attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting viscoelastic phases, such that the membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equation an analytical expression for the transfer function, associated to the curvature and electrical field, power dissipation elastic storage were found. The integrated flexoelectric/viscoelastic model and the novel findings contribute to the ongoing quest for a fundamental understanding of the functioning of outer hair cells (OHC), especially on the role of membrane deformation in delivering mechanical power through electromotility and its frequency-dependent power conversion efficiency.

Liquid crystal elastomers (LCE) — polymer networks with embedded liquid crystal units — are functional materials characterized by a pronounced coupling between elastic strain and liquid crystalline orientational ordering. When prepared by polymerization and cross-linking in the isotropic phase, and then cooled, the resulting polydomain ma- terials exhibit an extraordinary soft elastic behavior under unidirectional pulling, with a plateau-like region in the stress-strain curve, before turning into a monodomain LCE where a standard elastic resistance is recovered. Here we investigate the microscopic origin of this behavior by performing large-scale molecular iso-stress Monte Carlo simula- tions of swollen polydomain main-chain LCE. Our simulations are based on the soft-core Gay-Berne interaction potential and reproduce the stress-strain experiment featuring the plateau-like behavior. Deeper insight into the molecular organization of our sim- ulated samples reveals that the underlying mechanisms are local domain rotation and growth, excluding orientational order destruction-reconstruction. It also suggests that these mechanisms may be assisted by a dissipation of elastic free energy stored in topo- logical defects created during the synthesis, which is compatible with the stress-strain irreversibility observed in some main-chain LCE

Studying the mechanics of Bauhinia seeds pod opening we quantified the twisted to helical transition in ribbons with spontaneous negative curvature. Such ribbons appear in pre-stressed materials, nematic ellastomer sheets and various fibrous plants tissues. The intrinsic negative curvature results from active deformation, oriented at different directions on opposite faces of the ribbon. We show that the same geometry governs shape selection in nano-scale self assembled ribbons, made of lipids and peptides with chiral head groups. We find that the ribbon’s configurations are well described by the elastic theory and suggest how the parameters in the theory are determined from the molecular interactions. Finally, developing a one-dimensional effective description of the ribbons, we combine elasticity with statistical mechanics to derive predictions for various statistical properties of ribbon shapes at finite temperature. Some of the predictions are quantitatively verified by analyzing experimental data.

Nematic elastomers are rubbery solids which have liquid crystals incorporated into their polymer chains. These materials display many unusual mechanical properties, one such being the ability to from fine-scale microstructure. In this talk, we explore the response of thin membranes made of nematic elastomer under loading which takes these membranes beyond the regime of soft elasticity. Such membranes feature two potential instabilities – the formation of fine-scale material microstructure and the formation of fine-scale wrinkles. We develop a theoretical framework to study these membranes that accounts for both instabilities, and we implement this framework numerically. Using both analytical and numerical studies, we show that nematic elastomer membranes can suppress wrinkling due to the complex stress states introduced by fine-scale microstructure.