Alejandro D. Rey

Structure and dynamics of biological liquid crystals

A review of thermodynamic and flow liquid crystal models is presented and applied to a wide range of biological liquid crystals (BLCs), including helicoidal plywoods, biopolymer solutions and in vivo liquid crystals. The key characteristics of liquid crystals (self-assembly, packing, defects, functionalities, processability) are discussed in relation to biological materials and the strong correspondence between different synthetic and biological materials is discussed. Viscoelastic models for nematic and chiral nematics are reviewed and discussed in terms of key parameters that facilitate understanding and quantitative information from experimental measurements. The range and consistency of the predictions demonstrates that the use of mesoscopic liquid crystal models is an efficient tool to develop the science and biomimetic applications of mesogenic biological materials.

Ab initio DFT study of structural and mechanical properties of methane and carbon dioxide hydrates

The structural and mechanical properties of methane and carbon dioxide hydrates were investigated using density functional theory simulations. Well-established equations of state of solids and exchange-correlation functionals were used for fitting the unit lattice total energy as a function of volume, and the full second-order elastic constants of these two gas hydrates were determined by energy–strain analyses. The polycrystalline elastic properties were also calculated from the unit lattice results. The final results for methane hydrate agree well with available experimental data and with other theoretical results. The two gas hydrates were found to be highly elastically isotropic, but they differed significantly in shear properties. The presented results for carbon dioxide hydrates are the first complete set reported so far. The results are a significant contribution to the ab initio material characterisation of gas hydrates required for ongoing fundamental studies and technological applications.

Computational study of the elastic properties of Rheum rhabarbarum tissues via surrogate models of tissue geometry

Plant petioles and stems are hierarchical cellular structures, displaying geometrical features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues in which the cellular distribution is quasi-random, a factor that affects the elastic properties of the tissues. The current work focuses on the finite element analysis (FEA) of the constituent tissues of the plant Rheum rhabarbarum (rhubarb). The geometric model is generated via a recently introduced method: the finite edge centroidal Voronoi tessellation (FECVT), which is capable to capture the gradients of cellularity and diversified pattern of cellular materials, as opposed to current approaches in literature. The effective stiffness of the tissues is obtained by using an accurate numerical homogenization technique via detailed finite element analysis of the models of sub-regions of the tissues. As opposed to a large-scale representative volume element (RVE), statistical volume elements (SVE) are considered in this work to model tissue microstructures that are highly random. 2D finite element analyses demonstrate that the distribution of cells in collenchyma and parenchyma tissue make them stiffer in two different directions, while the overall effect of the combined tissues results in approximately equal stiffness in both directions. The rhubarb tissues, on the other hand, are more compliant than periodic and quasi-uniform random cellular materials by a factor of up to 47% and 44%, respectively. The variations of the stiffness shows the stiffening role that cell shape, size, and graded cellular distribution play in the mechanics of the rhubarb tissue.

Defect textures in polygonal arrangements of cylindrical inclusions in cholesteric liquid crystal matrices

A systematic, computational and scaling analysis of defect textures in polygonal arrangement of cylindrical particles embedded in a cholesteric (Ch) liquid crystal matrix is performed using the Landau–de Gennes model for chiral self-assembly, with strong anchoring at the particles surface. The defect textures and LC phases observed are investigated as a function of chirality, elastic anisotropy (monomeric and polymeric mesogens), and polygonal arrangement and size of particles. The presence of a polygonal network made of N circular inclusions results in defect textures of a net charge of −(N − 2)/2 per unit polygonal cell, in accordance with Zimmers rule. As the chirality increases, the LC matrix shows the following transition sequence: weakly twisted cholesterics, 2D blue phases with non-singular/singular defect lattices, cholesteric phases with only disclinations, and finally fingerprint cholesteric textures with disclinations and dislocations. For monomeric mesogens at concentrations far from the I–Ch phase transition and low chirality, for a given symmetry of the LC phase, the particle with weaker (stronger) confinement results in a phase with lower (higher) elastic energy, while at high chirality the elastic energy of the LC phase is proportional to the number of particles that form the polygonal network. Thus, hexagonal (triangular) particle arrangement results in low elastic energy at low (high) chirality. For semiflexible polymeric mesogens (high elastic anisotropy), defect textures with fewer disclinations/dislocations arise but due to lamellar distortions we find a higher elastic energy than monomeric mesogens. The defects arising in the simulations and the texture rules established are in agreement with experimental observations in cellulosic liquid crystal analogues such as plant cell walls and helical biological polymeric mesophases made of DNA, PBLG and xanthan. A semi-quantitative phase diagram that shows different LC phases and defect textures as a function of chirality and elastic anisotropy is obtained. The inclusion of particles has a stabilizing effect on the LC phases, as they occupy λ+1 disclination cores, thereby reducing the free energy cost associated with these disclinations. These findings provide a comprehensive set of trends and mechanisms that contribute to the evolving understanding of biological plywoods and serve as a platform for future biomimetic applications.

First-principles density functional theory (DFT) study of gold nanorod and its interaction with alkanethiol ligands.

The structure and mechanical properties of gold nanorods and their interactions with alkenthiolate self-assembled monolayers have been determined using a novel first-principle density functional theory simulation approach. The multifaceted, 1-dimensional, octagonal nanorod has alternate Au100 and Au110 surfaces. The structural optimization of the gold nanorods was performed with a mixed basis: the outermost layer of gold atoms used double-ζ plus polarization (DZP), the layer below used double-ζ (DZ), and the inner layers used single-ζ (SZ). The final structure compares favorably with simulations using DZP for all atoms. Phonon dispersion calculations and ab initio molecular dynamics (AIMD) were used to establish the dynamic and thermal stability of the system. From the AIMD simulations it was found that the nanorod system will undergo significant surface reconstruction at 300 K. In addition, when subjected to mechanical stress in the axial direction, the nanorod responds as an orthotropic material, with uniform expansion along the radial direction. The Youngs moduli are 207 kbar in the axial direction and 631 kbar in the radial direction. The binding of alkanethiolates, ranging from methanethiol to pentanethiol, caused formation of surface point defects on the Au110 surfaces. On the Au100 surfaces, the defects occurred in the inner layer, creating a small surface island. These defects make positive and negative concavities on the gold nanorod surface, which helps the ligand to achieve a more stable state. The simulation results narrowed significant knowledge gaps on the alkanethiolate adsorption process and on their mutual interactions on gold nanorods. The mechanical characterization offers a new dimension to understand the physical chemistry of these complex nanoparticles.

Tunable nano-wrinkling of chiral surfaces: Structure and diffraction optics

Periodic surface nano-wrinkling is found throughout biological liquid crystalline materials, such as collagen films, spider silk gland ducts, exoskeleton of beetles, and flower petals. These surface ultrastructures are responsible for structural colors observed in some beetles and plants that can dynamically respond to external conditions, such as humidity and temperature. In this paper, the formation of the surface undulations is investigated through the interaction of anisotropic interfacial tension, swelling through hydration, and capillarity at free surfaces. Focusing on the cellulosic cholesteric liquid crystal (CCLC) material model, the generalized shape equation for anisotropic interfaces using the Cahn-Hoffman capillarity vector and the Rapini-Papoular anchoring energy are applied to analyze periodic nano-wrinkling in plant-based plywood free surfaces with water-induced cholesteric pitch gradients. Scaling is used to derive the explicit relations between the undulations amplitude expressed as a function of the anchoring strength and the spatially varying pitch. The optical responses of the periodic nano-structured surfaces are studied through finite difference time domain simulations indicating that CCLC surfaces with spatially varying pitch reflect light in a wavelength higher than that of a CCLCs surface with constant pitch. This structural color change is controlled by the pitch gradient through hydration. All these findings provide a foundation to understand structural color phenomena in nature and for the design of optical sensor devices.

Stress-Sensor Device Based on Flexoelectric Liquid Crystalline Membranes

Membrane flexoelectricity is an electromechanical coupling process that describes membrane bending and membrane electrical polarization caused by bending under electric fields. In this paper we propose, formulate, and characterize a stress-sensor device for mechanically loaded solids, consisting of a soft flexoelectric thin membrane attached to the loaded deformed solid. Because the curvature of the deformed solid is transferred to the attached flexoelectric membrane, the electromechanical transduction of the latter produces a charge that is proportional to the stress of the solid. The model of the stress-sensor device is based on the integration of the thermodynamics of polarizable membranes with isotropic solid elasticity, leading to a transfer function that identifies the elastic, electromechanical, and geometrical parameters involved in electrical-signal generation. The model is applied to representative normal bending and then to more complex off-axis bending of elastic bars. In all cases, a common transfer function shows the generic material and its geometric contributions. The sensor sensitivity increases linearly with flexoelectricity and the membrane-solid interface, and the sensitivity decreases with increasing membrane thickness and Youngs modulus of the solid. The theoretical results contribute to ongoing experimental efforts towards the development of anisotropic soft-matter-based stress-sensor devices through solid-membrane interactions and electromechanical transduction.

Generalized Boussinesq-Scriven surface fluid model with curvature dissipation for liquid surfaces and membranes

Curvature dissipation is relevant in synthetic and biological processes, from fluctuations in semi-flexible polymer solutions, to buckling of liquid columns, tomembrane cell wall functioning. We present a micromechanical model of curvature dissipation relevant to fluid membranes and liquid surfaces based on a parallel surface parameterization and a stress constitutive equation appropriate for anisotropic fluids and fluid membranes.The derived model, aimed at high curvature and high rate of change of curvature in liquid surfaces and membranes, introduces additional viscous modes not included in the widely used 2D Boussinesq-Scriven rheological constitutive equation for surface fluids.The kinematic tensors that emerge from theparallel surface parameterization are the interfacial rate of deformation and the surface co-rotational Zaremba-Jaumann derivative of the curvature, which are used to classify all possibledissipative planar and non-planar modes. The curvature dissipation function that accounts for bending, torsion and twist rates is derived and analyzed under several constraints, including the important inextensional bending mode.A representative application of the curvature dissipation model to the periodic oscillation in nano-wrinkled outer hair cells show how and why curvature dissipation decreases with frequency, and why the 100kHz frequency range is selected. These results contribute to characterize curvature dissipation in membranes and liquid surfaces.

Atomistic modeling of structure II gas hydrate mechanics: Compressibility and equations of state

This work uses density functional theory (DFT) to investigate the poorly characterized structure II gas hydrates, for various guests (empty, propane, butane, ethane-methane, propane-methane), at the atomistic scale to determine key structure and mechanical properties such as equilibrium lattice volume and bulk modulus. Several equations of state (EOS) for solids (Murnaghan, Birch-Murnaghan, Vinet, Liu) were fitted to energy-volume curves resulting from structure optimization simulations. These EOS, which can be used to characterize the compressional behaviour of gas hydrates, were evaluated in terms of their robustness. The three-parameter Vinet EOS was found to perform just as well if not better than the four-parameter Liu EOS, over the pressure range in this study. As expected, the Murnaghan EOS proved to be the least robust. Furthermore, the equilibrium lattice volumes were found to increase with guest size, with double-guest hydrates showing a larger increase than single-guest hydrates, which has sign...

Theory and simulation of ovoidal disclination loops in nematic liquid crystals under conical confinement

We present analysis, scaling and modelling based on a previously presented nonlinear nonlocal nematic elastica equation of disclination loop growth in nematic liquid crystals confined to conical geometries with homeotropic anchoring conditions. The +1/2 disclination loops arise during the well-known planar radial to planar polar texture transformation and are attached to +1 singular core disclination at two branch points. The shape of the +1/2 loops is controlled by the axial speed of the branch points and the bending stiffness of the disclination both of which being affected by the confinement gradients (reduction in cross-sectional area) of a conical geometry. Motion towards the cone apex results in faster branch point motions and weaker curvature changes, but motion away from the apex results in slower branch point motion and stronger curvature changes. The simultaneous action of these effects results in novel ovoidal disclination loops. The numerical results are condensed into useful power laws and integrated into a shape/energy analysis that reveals the effects of confinement and its gradient on ovoidal disclination loops. These new findings are useful to characterise the Frank elasticity of new nematic mesophases and to predict novel defect structures under complex confinement.