Structure characterisation method for ideal and non-ideal twisted plywoods

Complex Nanowrinkling in Chiral Liquid Crystal Surfaces: From Shaping Mechanisms to Geometric Statistics

Surface wrinkling is closely linked to a significant number of surface functionalities such as wetting, structural colour, tribology, frictions, biological growth and more. Given its ubiquity in nature’s surfaces and that most material formation processes are driven by self-assembly and self-organization and many are formed by fibrous composites or analogues of liquid crystals, in this work, we extend our previous theory and modeling work on in silico biomimicking nanowrinkling using chiral liquid crystal surface physics by including higher-order anisotropic surface tension nonlinearities. The modeling is based on a compact liquid crystal shape equation containing anisotropic capillary pressures, whose solution predicts a superposition of uniaxial, equibiaxial and biaxial egg carton surfaces with amplitudes dictated by material anchoring energy parameters and by the symmetry of the liquid crystal orientation field. The numerical solutions are validated by analytical solutions. The blending and interaction of egg carton surfaces create surface reliefs whose amplitudes depend on the highest nonlinearity and whose morphology depends on the anchoring coefficient ratio. Targeting specific wrinkling patterns is realized by selecting trajectories on an appropriate parametric space. Finally, given its importance in surface functionalities and applications, the geometric statistics of the patterns up to the fourth order are characterized and connected to the parametric anchoring energy space. We show how to minimize and/or maximize skewness and kurtosis by specific changes in the surface energy anisotropy. Taken together, this paper presents a theory and simulation platform for the design of nano-wrinkled surfaces with targeted surface roughness metrics generated by internal capillary pressures, of interest in the development of biomimetic multifunctional surfaces.

Band structure of a rotating helical phononic crystal

We consider an elastic helical medium whose tensor stiffness twirls uniformly along the helix axis. We are interested in analyzing the band structure when the whole material is externally forced to rotate around the helix axis to a fixed constant frequency. Departing from a general dynamic description of the elastic phenomena, we establish a set of equations for the displacement vector and the stress tensor. These equations allow us to calculate the band structure parametrized by the externally imposed rotating frequency. We find that the band structure strongly depends on the rotation frequency, and we show that backward and forward modes propagate differently, particularly for the longitudinal and right-polarized modes.

Dependence of the elastic band structure of a helical medium on thermal dilatation

We consider an elastic helical medium formed by uniformly rotating a triclinic crystal around a given axis to constitute a helical medium giving rise to a material whose tensor stiffness rotates uniformly and varies along the helix axis. A detailed analysis of its elastic properties has been done previously. Here, we are concerned in analyzing the role of thermal coupling with heat flow through the dilatation tensor. Starting from a general dynamic description of the thermoelastic phenomena which takes into account the finite speed of propagation of thermal waves, we establish a set of equations for the strains, stresses, temperature and heat flow. These equations allow to calculate the band structure and the logarithmic ratio between longitudinal and transverse strains. We express our results for different values of the thermoelastic coupling and period of the helix which show remarkable modifications when compared with the case in which no thermoelastic coupling is present.

Thermodynamic modelling of acidic collagenous solutions: from free energy contributions to phase diagrams

Tropocollagen is considered one of the main precursors in the fabrication of collagen-based biomaterials. Triple helix acidic solutions of collagen I have been shown experimentally to lead to chiral plywood architectures found in bone and "cornea" like tissues. As these plywoods are solid analogues of liquid crystal architectures, bio-inspired processing and fabrication platforms based on liquid crystal physics and thermodynamics will continue to play an essential role. For tissue engineering applications, it has been shown that dilute isotropic collagen solutions need to be flow processed first and then dehydrated. Thus, a complete fundamental understanding of the thermodynamics and free energy contributions in acidic collagen aqueous solutions is necessary to avoid expensive trial-and-error fabrication. To achieve this goal, we analyze the microscopic mechanisms of ordering and interactions in solutions of triple helix collagen, namely mixing, attraction, excluded-volume and chirality. To capture the mentioned physics, we then incorporate and integrate the Flory-Huggins, Maier-Saupe, Onsager and Frank theories. Nonetheless, they together are incapable of providing an acceptable mesophasic description in acidic collagenous solutions because tropocollagen biomacromolecules are positively charged. We then explore a simple and accurate electrostatic mean-field potential. Our results on collagen are in good agreement with experiments and include phase diagrams, phase transition thresholds, and critical isotropic/cholesteric order parameters. The present extended theory is shown to properly converge to classical liquid crystal models and is used to express the phenomenological Landau-de Gennes parameters with more fundamental quantities. This study provides a platform to derive accurate process models for the fabrication of collagen-based materials, considering and benefitting from the full range of underlying interactions.

Two-wavelength wrinkling patterns in helicoidal plywood surfaces: imprinting energy landscapes onto geometric landscapes

We present a model to investigate the formation of two-length scale surface patterns in biological and synthetic anisotropic soft matter materials through the high order interaction of anisotropic interfacial tension and capillarity at their free surfaces. The unique pattern-formation mechanism emerging from the presented model is based on the interaction between lower and higher order anchoring modes. Analytical and numerical solutions are used to shed light on why and how simple anisotropic anchoring generates two-lengthscale wrinkles whose amplitudes are given in terms of anchoring coefficients. The novel finding is that the surface energy landscape with its maxima and minima can be imprinted onto the surface geometric landscape. Symmetry relations and scaling laws are used to provide the explicit relations between the anchoring constants and surface profile of the two length scale wrinkles. These new findings establish a new paradigm for characterizing surface wrinkling in biological liquid crystals, and inspire the design of novel functional surface structures.

Cholesteric liquid crystals in living matter

Liquid crystals play an important role in biology because the combination of order and mobility is a basic requirement for self-organisation and structure formation in living systems. Cholesteric liquid crystals are omnipresent in living matter under both in vivo and in vitro conditions and address the major types of molecules essential to life. In the animal and plant kingdoms, the cholesteric structure is a recurring design, suggesting a convergent evolution to an optimised left-handed helix. Herein, we review the recent advances in the cholesteric organisation of DNA, chromatin, chitin, cellulose, collagen, viruses, silk and cholesterol ester deposition in atherosclerosis. Cholesteric structures can be found in bacteriophages, archaea, eukaryotes, bacterial nucleoids, chromosomes of unicellular algae, sperm nuclei of many vertebrates, cuticles of crustaceans and insects, bone, tendon, cornea, fish scales and scutes, cuttlebone and squid pens, plant cell walls, virus suspensions, silk produced by spiders and silkworms, and arterial wall lesions. This article specifically aims at describing the consequences of the cholesteric geometry in living matter, which are far from being fully defined and understood, and discusses various perspectives. The roles and functions of biological cholesteric liquid crystals include maximisation of packing efficiency, morphogenesis, mechanical stability, optical information, radiation protection and evolution pressure.

Multiwavelength micromirrors in the cuticle of scarab beetle Chrysina gloriosa

Beetles from the genus Chrysina show vivid reflections from bright green to metallic silver-gold as a consequence of the cholesteric liquid crystal organization of chitin molecules. Particularly, the cuticle of Chrysina gloriosa exhibits green and silver stripes. By combining confocal microscopy and spectrophotometry, scanning electron microscopy and numerical simulations, the relationship between the reflectance and the structural parameters for both stripes at the micro- and nanoscales are established. Over the visible and near IR spectra, polygonal cells in tessellated green stripes behave as multiwavelength selective micro-mirrors and the silver stripes as specular broadband mirrors. Thermoregulation, conspecifics or intra-species communication, or camouflage against predators are discussed as possible functions. As a prerequisite to bio-inspired artificial replicas, the physical characteristics of the polygonal texture in Chrysina gloriosa cuticle are compared to their equivalents in synthetic cholesteric oligomers and their fundamental differences are ascertained. It is shown that the cuticle has concave cells whereas the artificial films have convex cells, contrary to expectation and assumption in the literature. The present results may provide inspiration for fabricating multiwavelength selective micromirrors or spatial wavelength-specific light modulators.

STATEMENT OF SIGNIFICANCE

Many insects own a tessellated carapace with bumps, pits or indentations. Little is known on the physical properties of these geometric variations and biological functions are unknown or still debated. We show that the polygonal cells in scarab beetle Chrysina gloriosa behave as multiwavelength selective micromirrors over the visible and infrared spectra, with a variety of spatial patterns. In the context of biomimetic materials, we demonstrate that the carapace has concave cells whereas the artificial films have convex cells, contrary to expectation in the literature. Thermoregulation, communication or camouflage are discussed as advanced functions. Results may provide inspiration for fabricating spatial wavelength-specific light modulators and optical packet switching in routing technologies.

Geometric reconstruction of biological orthogonal plywoods

In this paper we focus on the structural determination of biological orthogonal plywoods, fiber-like composite analogues of liquid crystalline phases, where the fibrils of the building blocks show sharp 90° orientation jumps between fibers in adjacent domains. We present an original geometric and computational modelling that allows us to determine the fibrillary orientation in biological plywoods from periodic herringbone patterns commonly observed in cross-sections. Although herringbone patterns were long reported, the specific and quantitative relationships between herringbones and the orthogonal plywoods were absent or at best incomplete. Here we provide an efficient and new procedure to perform an inverse problem that connects two specific features of the herringbone patterns (aperture angle and wavelength) with the 3D morphology of the structure, whose accuracy and validity were ascertained through in silico simulations and also with real specimens ("Eremosphaera viridis"). This contribution extends significantly the better known characterization methods of 2D cross sections, such as the arced patterns observed in biological helicoidal plywoods, and with the present proposed methodology it adds another characterization tool for a variety of biological fibrous composites that form cornea-like tissues.