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BackgroundLiquid crystal (LC) mesophases have an orientational and positional order that can be found in both synthetic and biological materials. These orders are maintained until some parameter, mainly the temperature or concentration, is changed, inducing a phase transition. Among these transitions, a special sequence of mesophases has been observed, in which priority is given to the direct smectic liquid crystal transition. The description of these transitions is carried out using the Landau–de Gennes (LdG) model, which correlates the free energy of the system with the orientational and positional order.MethodologyThis work explored the direct isotropic-to-smectic A transition studying the free energy landscape constructed with the LdG model and its relation to three curve families: (I) level-set curves, steepest descent, and critical points; (II) lines of curvature (LOC) and geodesics, which are directly connected to the principal curvatures; and (III) the Casorati curvature and shape coefficient that describe the local surface geometries resemblance (sphere, cylinder, and saddle).ResultsThe experimental data on 12-cyanobiphenyl were used to study the three curve families. The presence of unstable nematic and metastable plastic crystal information was found to add information to the already developed smectic A phase diagram. The lines of curvature and geodesics were calculated and laid out on the energy landscape, which highlighted the energetic pathways connecting critical points. The Casorati curvature and shape coefficient were computed, and in addition to the previous family, they framed a geometric region that describes the phase transition zone.Conclusion and significanceA direct link between the energy landscape’s topological geometry, phase transitions, and relevant critical points was established. The shape coefficient delineates a stability zone in which the phase transition develops. The methodology significantly reduces the impact of unknown parametric data. Symmetry breaking with two order parameters (OPs) may lead to novel phase transformation kinetics and droplets with partially ordered surface structures.

Abstract Gas hydrates are crystalline inclusion compounds formed by trapping gas molecules inside water cages at high pressures and low temperatures. Hydrates are promising materials for hydrogen storage, but their potential depends on understanding their mechanical properties. This work integrates density functional theory (DFT) simulations with a geometry-inspired composite material model to explore the bulk moduli of structure II hydrogen hydrates subjected to pressure loads of − 0.2 to 3 GPa, representative of the hydrogen hydrate formation conditions. Our findings reveal that structure II hydrate comprises a bi-continuous composite of small and large cages with nearly equal volume fractions. The bulk modulus increases with rising pressure but decreases with increasing composition. Notably, these results align closely with the ideal laws of mixtures, especially at low pressures and compositions, where cage interactions are minimal. This integrated DFT-laws of mixtures methodology provides a key database for fast estimation of hydrate mechanical properties without costly computations.

Abstract Gas hydrate mechanical stability under pressure is critically important in energy supply, global warming, and carbon-neutral technologies. The stability of these polyhedral guest–host crystals under increasing pressure is affected by host cage type and face connectivity as well as guest gas occupancy. The geometry-imposed cage connectivity generates crystal lattices that include inclusion-matrix material composite structures. In this paper, we integrate Density Functional Theory simulations with a polyhedral-inspired composite material model that quantifies stability limits, failure modes, and the impact of the type of cage occupancy. DFT reveals the existence of two failure mechanisms under increasing pressure: (i) a multistep lattice breakdown under total occupancy and under only large cage occupancy and (ii) a single-step breakdown under zero occupancy as well as with only small cage occupancy. The DFT-composite model predicts optimal occupancy pathways to generate strength and critical occupancy pathways to promote decomposition.

Tactoids, consisting of micro-confined liquid crystalline colloids with self-selected shape, bear both fundamental and technological significance. The authors show that the shape relaxation of tactoids follows an exponential decay and develop a model to predict this out-of-the-equilibrium process.

This review presents an integrated theoretical and computational characterization and analysis of surface pattern formation in chiral and achiral liquid crystal self-assembly and the mechanical/optical/tribological/tissue engineering surface functionalities that emerge from various wrinkling processes. Strategies to target surface patterns include linear, non-linear, multidirectional and multiscale wrinkling phenomena. The focus of the review is to show the unique surface structure-functionalities that emerge from anisotropic liquid crystal soft matter, eliminating or reducing the need of aggressive solvents, extreme pressure/temperature conditions, erosion and other surface morphing approaches. The surface pattern formation theoretical-modelling- computational results are then connected and validated with actual biological surfaces that are considered solid liquid crystal analogues, such as exocuticles of insects, fish scales, and flowers. A unique feature of the in silico surface pattern formation platform used throughout this review is the generalized liquid crystal shape equation that includes surface anchoring elasticity, membrane elasticity, and stress loads from liquid crystals orientation gradients. Clear characterization of surface shapes, curvatures, roughness, that are behind surface functionalities are introduced and applied to strengthen validation of predictions with actual nature’s surfaces. Wrinkling scaling laws, and the dependence of material properties on morphing mechanisms are elucidated. The predictions capture very well the two-scale wrinkling patterns in tulips, wrinkling gradients that display water sensor capabilities, egg carton shapes in rose petals and their potential for cell alignment, and the ability to create surface roughness with targeted kurtosis and skewness to control and optimize friction and tribological functionalities. The results are summarized in terms of surface geometry (open or closed) mechanisms and phenomena (anchoring, membrane elasticity), material properties (anchoring coefficients, membrane bending modulus, Frank elasticity), wrinkling scales and scaling laws (amplitude, wave-lengths, skewness, kurtosis) and functionalities (optical iridescence, friction, wettability, structural color, curvature-driven cell alignment and differentiation). Taken together, the range of surface geometries and surface functionalities captured by the liquid crystal biomimetic in silico platform provides a foundation for future experimental green manufacturing pathways based on anisotropic soft matter.

Flexoelectric liquid crystalline membranes immersed in asymmetric viscoelastic media is a material system model with physiological applications such as outer hair cells (OHCs), where membrane oscillations generate bulk flow. Motivated by this physiological process, here we extend our previous work by characterizing the force transmission output of our model in addition to viscoelastic fluid flow, since solid–fluid interactions are an essential feature of confined physiological flow and flow in immersed elastic structures. In this work, the rigidity of the confinement results in a passive force reception, while more complete solid–fluid interactions will be considered in the future. A significant contribution of this work is a new asymmetry linear viscoelastic electro-rheological model and the obtained implicit relation between force transmission and flow generation and how this relation is modulated by electric field frequency and the material properties of the device. Maximal force and flow are found at resonant frequencies of asymmetry viscoelastic bulk phases, flexoelectric and dispersion mechanisms through the elastic and Womersley numbers.

Relaxation of liquid crystals is crucial in a broad area, e.g. biomimicry and stimuli-responsive material design. Here Khadem et al explore distinct relaxations, reveal the corresponding physics and propose a novel method for estimating viscoelastic properties without applying external fields.

(1) Background: New technologies involving gas hydrates under pre-nucleation conditions such as gas separations and storage have become more prominent. This has necessitated the characterization and modeling of the transport properties of such systems. (2) Methodology: This work explored methane hydrate systems under pre-nucleation conditions. All-atom molecular dynamics simulations were used to quantify the performance of the TIP4P/2005 and TIP4P/Ice water models to predict the viscosity, diffusivity, and thermal conductivity using various formulations. (3) Results: Molecular simulation equilibrium was robustly demonstrated using various measures. The Green–Kubo estimation of viscosity outperformed other formulations when combined with TIP4P/Ice, and the same combination outperformed all TIP4P/2005 formulations. The Green–Kubo TIP4P/Ice estimation of viscosity overestimates (by 84% on average) the viscosity of methane hydrate systems under pre-nucleation conditions across all pressures considered (0–5 MPag). The presence of methane was found to increase the average number of hydrogen bonds over time (6.7–7.8%). TIP4P/Ice methane systems were also found to have 16–19% longer hydrogen bond lifetimes over pure water systems. (4) Conclusion: An inherent limitation in the current water force field for its application in the context of transport properties estimations for methane gas hydrate systems. A re-parametrization of the current force field is suggested as a starting point. Until then, this work may serve as a characterization of the deviance in viscosity prediction.

(1) Background: Gas hydrates are historically notable due to their prevalence and influence on operational difficulties in the oil and gas industry. Recently, new technologies involving the formation of gas hydrates to accomplish various applications have been proposed. This has created new motivation for the characterization of rheological and mechanical properties and the study of molecular phenomena in gas hydrates systems, particularly in the absence of oil and under pre-nucleation conditions. (2) Methodology: This work reviews advances in research on the promotion, inhibition, rheology, and mechanical properties of gas hydrates obtained through an integrated material synthesis-property characterization-multi-scale theoretical and computational platform at McGill University. (3) Discussion: This work highlights the findings from previous experimental work by our group and identifies some of their inherent physical limitations. The role of computational research methods in extending experimental results and observations in the context of mechanical properties of gas hydrates is presented. (4) Summary and Future perspective: Experimental limitations due to the length and time scales of physical phenomena associated with gas hydrates were identified, and future steps implementing the integrated experimental-computational platform to address the limitations presented here were outlined.

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.

The collagen triple helix is a ubiquitous biomacromolecule used in acidic aqueous solutions as precursor in the fabrication of artificial compact bone and cornea and in tissue engineering. The primary architecture of these highly structured solid tissues is formed during the cholesteric liquid-crystalline stage of their morphogenesis. The theoretical platform that describes the coupled dynamics of phase-ordering and mass transfer developed, implemented and validated here can be used for optimal material design and plays a significant complementary role to future experimental studies. Based on uniaxiality assumption, we have recently developed and validated a theory for the free energy tailored for acidic collagenous dispersions. Here we significantly expand and generalize our previous study, by including biaxiality since cholesteric phases must have a degree of biaxiality. In this work, we first modify the proposed interchain interaction and excluded-volume contribution by use of the addition theorem for spherical harmonics. Then, the Euler-Lagrange minimization followed by expansion around I/N* transition allows us to construct the free energy of ordering in terms of the phenomenological Landau–de Gennes formulation. Finally, we use the time-dependent Ginzburg-Landau equations to study the non-Fickian evolution of a single two dimensional cholesteric tactoid through a shallow quench from the isotropic to biphasic region of the phase diagram. Although equilibrium biaxiality is considerably low for these long-pitch cholesterics, we found that during self-assembly the biaxial order parameter achieves significant larger values than the equilibrium value. Additionally, the relaxed director field becomes both onion-like and defect-less, which is consistent with the twisted bipolar structure observed experimentally. The self-assembly simulations demonstrate that the formulated theoretical platform is not only consistent with previous theoretical and experimental studies but also able to be used to explore new routes for non-equilibrium collagen self-assembly. Taken together, this study deepens our understanding of cholesteric (chiral nematic N*) mesophase in acidic solutions of tropocollagen, and suggests a systematic spatio-temporal model that is capable of being used to extract the engineering principles for processing of these sought-after biomaterials.

Evaluating gas hydrates properties contributes valuably to their large-scale management and utilization in fundamental science and applications. Noteworthy, structure-H (sH) gas hydrate lacks a comprehensive characterization of its structural, mechanical, and anisotropic properties. Anisotropic and pressure dependent properties are crucial for gas hydrates’ detection and recovery studies. The objective of this work is the determination of pressure-dependent elastic constants and mechanical properties and the direction-dependent moduli of sH gas hydrates as a function of guest composition. First-principles DFT computations are used to evaluate the mechanical properties, anisotropy, and angular moduli of different sH gas hydrates under pressure. Some elastic constants and moduli increase more significantly with pressure than others. This introduces variations in sH gas hydrate’s incompressibility, elastic and shear resistance, and moduli anisotropy. Young’s modulus of sH gas hydrate is more anisotropic than its shear modulus. The anisotropy of sH gas hydrates is characterized using the unit cell elastic constants, anisotropy factors, and the angular dependent moduli. Structure-properties composition correlations are established as a function of pressure. It is found that compressing filled sH gas hydrates increases their moduli anisotropy. Differences in atomic bonding across a crystal’s planes can be expected in anisotropic structures. Taken together the DFT-based structure–properties–composition relations for sH gas hydrates provide novel and significant material physics results for technological applications.

The vibrational characteristics of gas hydrates are key identifying molecular features of their structure and chemical composition. Density functional theory (DFT)-based IR spectra are one of the efficient tools that can be used to distinguish the vibrational signatures of gas hydrates. In this work, ab initio DFT-based IR technique is applied to analyze the vibrational and mechanical features of structure-H (sH) gas hydrate. IR spectra of different sH hydrates are obtained at 0 K at equilibrium and under applied pressure. Information about the main vibrational modes of sH hydrates and the factors that affect them such as guest type and pressure are revealed. The obtained IR spectra of sH gas hydrates agree with experimental/computational literature values. Hydrogen bond’s vibrational frequencies are used to determine the hydrate’s Young’s modulus which confirms the role of these bonds in defining sH hydrate’s elasticity. Vibrational frequencies depend on pressure and hydrate’s O···O interatomic distance. OH vibrational frequency shifts are related to the OH covalent bond length and present an indication of sH hydrate’s hydrogen bond strength. This work presents a new route to determine mechanical properties for sH hydrate based on IR spectra and contributes to the relatively small database of gas hydrates’ physical and vibrational properties.

This paper presents theory and simulation of viscous dissipation in evolving interfaces and membranes under kinematic conditions, known as astigmatic flow, ubiquitous during growth processes in nature. The essential aim is to characterize and explain the underlying connections between curvedness and shape evolution and the rate of entropy production due to viscous bending and torsion rates. The membrane dissipation model used here is known as the Boussinesq-Scriven fluid model. Since the standard approaches in morphological evolution are based on the average, Gaussian and deviatoric curvatures, which comingle shape with curvedness, this paper introduces a novel decoupled approach whereby shape is independent of curvedness. In this curvedness-shape landscape, the entropy production surface under constant homogeneous normal velocity decays with growth but oscillates with shape changes. Saddles and spheres are minima while cylindrical patches are maxima. The astigmatic flow trajectories on the entropy production surface, show that only cylinders and spheres grow under the constant shape. Small deviations from cylindrical shapes evolve towards spheres or saddles depending on the initial condition, where dissipation rates decrease. Taken together the results and analysis provide novel and significant relations between shape evolution and viscous dissipation in deforming viscous membrane and surfaces.

We present a theoretical analysis and linear scaling of two-wavelength surface nanostructures formed at the free surface of cholesteric liquid crystals (CLC). An anchoring model based on the capillary shape equation with the high order interaction of anisotropic interfacial tension is derived to elucidate the formation of the surface wrinkling. We showed that the main pattern-formation mechanism is originated due to the interaction between lower and higher order anchoring modes. A general phase diagram of the surface morphologies is presented in a parametric space of anchoring coefficients, and a set of anchoring modes and critical lines are defined to categorize the different types of surface patterns. To analyze the origin of surface reliefs, the correlation between surface energy and surface nano-wrinkles is investigated, and the symmetry and similarity between the energy and surface profile are identified. It is found that the surface wrinkling is driven by the director pressure and is annihilated by two induced capillary pressures. Linear approximation for the cases with sufficient small values of anchoring coefficients is used to realize the intrinsic properties and relations between the surface curvature and the capillary pressures. The contributions of capillary pressures on surface nano-wrinkling and the relations between the capillary vectors are also systematically investigated. These new findings establish a new approach for characterizing two-length scale surface wrinkling in CLCs, and can inspire the design of novel functional surface structures with the potential optical, friction, and thermal applications.

Plant petioles and stems are hierarchical cellular structures, displaying structuralfeatures defined at multiple length scales. The current work focuses on the multi-scalemodelling of plant tissue, considering two orders of structural hierarchy, cell wall and tissue.The stiffness of plant tissue is largely governed by the geometry of the tissue cells, thecomposition of the cell wall and the structural properties of its constituents. The cell wallis analogous to a fiber reinforced composite, where the cellulose microfibril (CMF) is theload bearing component. For multilayered cell wall, the microfibril angle (MFA) in themiddle layer of the secondary cell wall (S2 layer) largely affects the longitudinal stiffnessfor values up to 40o. The MFA in turn influences the overall wall stiffness. In this work,the effective stiffness of a model system based on collenchyma cell wall of a dicotyledonousplant, the Rheum rhabarbarum, is computed considering generic MFA and volume fractions.At the cellular level, a 2-D Finite Edge Centroidal Voronoi tessellation (FECVT) has beendeveloped and implemented to generate the non-periodic microstructure of the plant tissue.The effective elastic properties of the cellular tissue are obtained through finite elementanalysis (FEA) of the Voronoi model coupled with the cell wall properties. The stiffness ofthe hierarchically modeled tissue is critically important in determining the overall structuralproperties of plant petioles and stems.

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 significant implications for the widely used van der Waals and Platteeuw thermodynamic model for gas hydrates. Also, hydrogen bonds prove to be the most likely factor contributing to the resistance of gas hydrates to compression; bulk modulus was found to increase linearly with hydrogen bond density, resulting in a relationship that could be used predictively to determine the bulk modulus of various structure II gas hydrates. Taken together, these results fill a long existing gap in the material chemical physics of these important clathrates.

Biological liquid crystalline polymers are found in cellulosic, chitin, and DNA based natural materials. Chiral nematic liquid crystalline orientational order is observed frozen-in in the solid state in plant cell walls and is known as a liquid crystal analogue characterized by a helicoidal plywood architecture. The emergence of the plywood architecture by directed chiral nematic liquid crystalline self assembly has been postulated as the mechanism that leads to optimal cellulose fibril organization. In natural systems, tissue growth and development takes place in the presence of inclusions and secondary phases leaving behind characteristic defects and textures, which provide a unique testing ground for the validity of the liquid crystal self-assembly postulate. In this work, a mathematical model, based on the Landau-de Gennes theory of liquid crystals, is used to simulate defect textures arising in the domain of self assembly, due to presence of secondary phases representing plant cells, lumens and pit canals. It is shown that the obtained defect patterns observed in some plant cell walls are those expected from a truly liquid crystalline phase. The analysis reveals the nature and magnitude of the viscoelastic material parameters that lead to observed patterns in plant-based helicoids through directed self-assembly. In addition, the results provide new guidance to develop biomimetic plywoods for structural and functional applications.

Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending, this phenomenon is found in outer hair cells (OHC) located in the inner ear, whose role is to amplify sound through the 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 rheological 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 membrane attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting viscoelastic phases, which are characterized by the Jeffreys constitutive equation with different material conditions. The membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equations and assuming small Mach numbers, analytical equations for the transfer function, associated to the average curvature, and for the volumetric rate flow as a function of the electrical field were found, and these equations can be expressed as a third-order differential equation which depends on the material properties of the system. When the inertial mechanisms are considered, the power spectrum shows several resonance peaks in the average membrane curvature and volumetric flow rate. When the inertia is neglected, the system follows a non-monotonic behavior in the power spectrum. This behavior is associated with the solvent contributions related to the retardation-Jeffreys mechanisms. The specific membrane-viscoelastic fluid properties that control the power response spectrum are identified. The present theory, model, and computations contribute to the evolving fundamental understanding of biological shape actuation through electromechanical couplings.

The Maier-Saupe model for binary mixtures of uniaxial discotic nematogens, formulated in a previous study [1], is used to compute and characterize orientational entropy [2] and orientational specific heat. These thermodynamic quantities are used to determine mixture type (ideal or non-ideal) which arise due to their different intrinsic properties, determined by the molecular weight asymmetry ΔMw and the molecular interaction parameter β. These molecular properties are also used to characterize the critical concentration where the mixture behaves like a single component system and exhibits the minimum nematic to isotropic (NI) transition temperature (pseudo-pure mixture). A transition within the nematic phase takes place at this specific concentration. According to the Maier-Saupe model, in a single mesogen, entropy at NI transition is a universal value; in this work we quantify the mixing effect on this universal property. The results and analysis provide a new tool to characterize molecular interaction and molecular weight differences in mesogenic mixtures using standard calorimetric measurements.

La relajación de dos defectos lineales de magnitud opuesta dentro de un cristal líquido confinado, es investigada solucionando acopladamente la ecuación de evolución del parámetro de orden y las ecuaciones de momentum en tres dimensiones. Las interacciones hidrodinámicas hacen que los defectos se muevan con velocidades diferentes incrementado el tiempo de relajación, sin embargo este efecto desaparece al incrementar el grado de confinamiento. Las características del flujo mas notables en el sistema son grandes vórtices que rodean los defectos a medida que estos se aproximan uno a otro.