Pattern formation, structure and functionalities of wrinkled liquid crystal surfaces: A soft matter biomimicry platform

Abstract

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.

Geometry-structure models for liquid crystal interfaces, drops and membranes: wrinkling, shape selection and dissipative shape evolution

“…Numerical methods and computational techniques used to solve the various viscoelastic shape equations identify challenges and solutions due to constraints, multiple scales, and self-assembly, including novel nanoparticle crystal-liquid crystal phases, and nematic drops with complex disclinations networks. Essentially all presented results were validated with experimental data 316 and the connections with the soft matter theory/simulation literature were also established so as to build a strong future platform for computational soft matter science. Finally, the outlook section summarizes important future challenges and opportunities in the area of surface pattern formation and dissipative shape evolution.…”

Fluctuating Flexoelectric Membranes in Asymmetric Viscoelastic Media: Power Spectrum through Mechanical Network and Transfer Function Models

“…This turning point coincides with the dominant resonance peaks (green color of the FTF and STF), which is associated with the mean Maxwell relaxation time. In the range of small and ω ∈ [1,10], there is frequency (green point) where the starts to oscillate and the coupled transfer functions show a multivalued function in the dynamical response. From a mathematical point of view, a plausible explanation of these oscillations deals with the ratio of the Bessel modified function of the first and second it is possible that the system undergoes transitions from real to imaginary roots (See Appendix F for the mathematical details of the complex roots).…”

“…Liquid crystalline organization, structure, and properties are found in a variety of biological systems, whose behavior is specified by complex processes [1,2]. The science of liquid crystal has been used in biological systems such as: (i) plants, (ii) insects, and (iii) membranes and living matter physics [3].…”

Geometric modeling of phase ordering for the isotropic–smectic A phase transition

“…Importantly, possible LC mesogens include rod-, board-, disk-, and screw-like molecules with flexibilities ranging from semi-flexible to rigid, involving monomers or main/side-chain polymers and colloids (Donald et al, 2006;Demus et al, 2008b;Demus et al, 2011). The synthesis and formation of these mesophase materials follow equilibrium self-assembly processes driven by temperature (thermotropic), concentration (lyotropic), or both (Bowick et al, 2017;Wang et al, 2023b). The presence of multiple components, as in nanoparticle-loaded mesophases, gives rise to couplings between self-assembly and phase separation with states that can combine the crystallinity (positional order) of one component with the liquid crystallinity (various degrees of positional and orientational order) of the other (Soulé et al, 2012a;Soulé et al, 2012b;Soulé et al, 2012c;Soule and Rey, 2012;Milette et al, 2013;Gurevich et al, 2014).…”

“…Describing the shape using the dimensionless normalized shape coefficient (S) avoids co-mingling properties associated with shape with those associated with curvedness, such as when using the classical differential geometry descriptions based on Gaussian (K), mean (H), and deviatoric (D) curvatures. The shape coefficient-Casorati curvedness (S, C) method has been successfully applied to several soft-matter materials and equilibrium and dissipative processes (Wang et al, 2020;Wang et al, 2022b;Wang et al, 2022a;Wang et al, 2023b). For example, for a saddle point, the classical approach yields K −D 2 .…”