Curvature induced hierarchical wrinkling patterns in soft bilayers

Swelling-induced patterning in soft microchannels

We study the effect of inflation on the swelling-induced wrinkling of thin elastic membranes in a set-up that is commonly used to create microchannels in lab-on-chip applications. Using a combination of experiments and associated numerical simulations, we demonstrate that the out-of-plane deformation of the inflated membrane and the resulting anisotropic stress lead to two distinct instabilities as the swelling progresses. The membrane first develops small-amplitude wrinkles that retain the cross-channel symmetry. Their wavelength depends on the pressure and is set in a process similar to the axisymmetric buckling of pressurised, uni-axially compressed cylindrical shells. As swelling increases, the membrane undergoes a secondary instability during which the wrinkles coarsen into large-amplitude folds whose morphology can be controlled by the degree of pre-inflation. We elucidate the fundamental mechanisms responsible for this behaviour and explain how inflation can be used as a control mechanism in the manufacture of microchannels.

Wrinkles, Folds, Creases, Buckles: Small-Scale Surface Deformations as Periodic Functions on 3D Meshes

We propose a method for adding small-scale details to surfaces of 3D geometries in the context of interactive deformation computation of elastic objects. This is relevant in real-time applications, for instance, in surgical simulation or interactive animation. The key idea is the procedural generation of surface details via a weighted sum of periodic functions, applied as an on-surface displacement field. We first calculate local deformation strains of a low-resolution 3D input mesh, which are then employed to estimate amplitudes, orientations, and positions of high-resolution details. The shapes and spatial frequencies of the periodic details are obtained from mechanical parameters, assuming the physical model of a film-substrate aggregate. Finally, our approach creates the highly-detailed output mesh fully on the GPU. The performance is independent of the spatial frequency of the inserted details as well as, within certain limits, of the resolution of the output mesh. We can reproduce numerous commonly observed, characteristic surface deformation patterns, such as wrinkles or buckles, allowing for the representation of a wide variety of simulated materials and interaction processes. We highlight the performance of our method with several examples.

Biomechanical Aspects of Actin Bundle Dynamics

Lamellipodial and filopodial protrusions are two of the main aggregate types of filamentous actin in living cells. Even though filopodia are essential to a range of vital cell functions, the mechanisms leading to their formation are still debated. Filopodia are relatively stiff and rod-like structures that are embedded in the highly dynamic framework of the backward flowing meshwork of the lamellipodium. Phenomena such as lateral filopodia drift and collision events suggest that mechanical aspects play a significant role in filopodia dynamics. In this paper, we systematically analyze the interplay between the backward flow of actin in the lamellipodium and the drift velocity of actin bundles, that we identify to be filopodia, in a quantitative manner in cells of given morphology and controlled myosin activity. Moreover, we study mechanical aspects of fusion of actin bundles drifting laterally in the lamellipodium. We find that the dynamics of actin bundles drift and fusion can be captured in a mechanical framework, which leads to a model of actin bundles orientation.

Bioinspired Multiscale Wrinkling Patterns on Curved Substrates: An Overview

The surface wrinkling of biological tissues is ubiquitous in nature. Accumulating evidence suggests that the mechanical force plays a significant role in shaping the biological morphologies. Controlled wrinkling has been demonstrated to be able to spontaneously form rich multiscale patterns, on either planar or curved surfaces. The surface wrinkling on planar substrates has been investigated thoroughly during the past decades. However, most wrinkling morphologies in nature are based on the curved biological surfaces and the research of controllable patterning on curved substrates still remains weak. The study of wrinkling on curved substrates is critical for understanding the biological growth, developing three-dimensional (3D) or four-dimensional (4D) fabrication techniques, and creating novel topographic patterns. In this review, fundamental wrinkling mechanics and recent advances in both fabrications and applications of the wrinkling patterns on curved substrates are summarized. The mechanics behind the wrinkles is compared between the planar and the curved cases. Beyond the film thickness, modulus ratio, and mismatch strain, the substrate curvature is one more significant parameter controlling the surface wrinkling. Curved substrates can be both solid and hollow with various 3D geometries across multiple length scales. Up to date, the wrinkling morphologies on solid/hollow core-shell spheres and cylinders have been simulated and selectively produced. Emerging applications of the curved topographic patterns have been found in smart wetting surfaces, cell culture interfaces, healthcare materials, and actuators, which may accelerate the development of artificial organs, stimuli-responsive devices, and micro/nano fabrications with higher dimensions.

Strain-Dependent Nanowrinkle Confinement of Block Copolymers

This paper describes an all-soft, templated assembly of block copolymers (BCPs) with programmable alignment. Using polymeric nanowrinkles as a confining scaffold, poly(styrene)-block-poly(dimethylsiloxane) (PS-b-PDMS) BCPs were assembled to be parallel or perpendicular to the wrinkle orientation by manipulating the substrate strain. Self-consistent field theory modeling revealed that wrinkle curvature and surface affinity govern the BCP structural formation. Furthermore, control of BCP alignment was demonstrated for complex wrinkle geometries, various copolymer molecular weights, and functional wrinkle skin layers. This integration of BCP patterning with flexible 3D architectures offers a promising nanolithography approach for next-generation soft electronics.

Graphene Wrinkles Enable Spatially Defined Chemistry

This paper reports a scalable approach to achieve spatially selective graphene functionalization using multiscale wrinkles. Graphene wrinkles were formed by relieving the strain in thermoplastic polystyrene substrates conformally coated with fluoropolymer and graphene skin layers. Chemical reactivity of a fluorination process could be tuned by changing the local curvature of the graphene nanostructures. Patterned areas of graphene nanowrinkles and crumples followed by a single-process plasma reaction resulted in substrates with regions having different fluorination levels. Notably, conductivity of the functionalized graphene nanostructures could be locally tuned as a function of feature size without affecting the mechanical properties.

Non-uniform curvature and anisotropic deformation control wrinkling patterns on tori

We investigate wrinkling patterns in a tri-layer torus consisting of an expanding thin outer layer, an intermediate soft layer and an inner core with a tunable shear modulus, inspired by pattern formation in developmental biology, such as follicle pattern formation during the development of chicken embryos. We show from large-scale finite element simulations that hexagonal wrinkling patterns form for stiff cores whereas stripe wrinkling patterns develop for soft cores. Hexagons and stripes co-exist to form hybrid patterns for cores with intermediate stiffness. The governing mechanism for the pattern transition is that the stiffness of the inner core controls the degree to which the major radius of the torus expands - this has a greater effect on deformation in the long direction as compared to the short direction of the torus. This anisotropic deformation alters stress states in the outer layer which change from biaxial (preferred hexagons) to uniaxial (preferred stripes) compression as the core stiffness is reduced. As the outer layer continues to expand, stripe and hexagon patterns will evolve into zigzags and segmented labyrinths, respectively. Stripe wrinkles are observed to initiate at the inner surface of the torus while hexagon wrinkles start from the outer surface as a result of curvature-dependent stresses in the torus. We further discuss the effects of elasticities and geometries of the torus on the wrinkling patterns.

2.5D Hierarchical Structuring of Nanocomposite Hydrogel Films Containing Cellulose Nanocrystals

Although two-dimensional hydrogel thin films have been applied across many biomedical applications, creating higher dimensionality structured hydrogel interfaces would enable potentially improved and more biomimetic hydrogel performance in biosensing, bioseparations, tissue engineering, drug delivery, and wound healing applications. Herein, we present a new and simple approach to control the structure of hydrogel thin films in 2.5D. Hybrid suspensions containing cellulose nanocrystals (CNCs) and aldehyde- or hydrazide-functionalized poly(oligoethylene glycol methacrylate) (POEGMA) were spin-coated onto prestressed polystyrene substrates to form cross-linked hydrogel thin films. The films were then structured via thermal shrinking, with control over the direction of shrinking leading to the formation of biaxial, uniaxial, or hierarchical wrinkles. Notably, POEGMA-only hydrogel thin films (without CNCs) did not form uniform wrinkles due to partial dewetting from the substrate during shrinking. Topographical feature sizes of CNC-POEGMA films could be tuned across 2 orders of magnitude (from ∼300 nm to 20 μm) by varying the POEGMA concentration, the length of poly(ethylene glycol) side chains in the polymer, and/or the overall film thickness. Furthermore, by employing adhesive masks during the spin-coating process, structured films with gradient wrinkle sizes can be fabricated. This precise control over both wrinkle size and wrinkle topography adds a level of functionality that to date has been lacking in conventional hydrogel networks.

Shell buckling: from morphogenesis of soft matter to prospective applications

Being one of the commonest deformation modes for soft matter, shell buckling is the primary reason for the growth and nastic movement of many plants, as well as the formation of complex natural morphology. On-demand regulation of buckling-induced deformation associated with wrinkling, ruffling, folding, creasing and delaminating has profound implications for diverse scopes, which can be seen in its broad applications in microfabrication, 4D printing, actuator and drug delivery. This paper reviews the recent remarkable developments in the shell buckling of soft matter to explain the most representative natural morphogenesis from the perspectives of theoretical analysis in continuum mechanics, finite element analysis, and experimental validations. Imitation of buckling-induced shape transformation and its applications are also discussed for the innovations of sophisticated materials and devices in future.

Surface Instability of Bilayer Hydrogel Subjected to Both Compression and Solvent Absorption

The bilayered structure of hard thin film on soft substrate can lose stability and form specific patterns, such as wrinkles or creases, on the surface, induced by external stimuli. For bilayer hydrogels, the surface morphology caused by the instability is usually controlled by the solvent-induced swelling/shrinking and mechanical force. Here, two important issues on the instability of bilayer hydrogels, which were not considered in the previous studies, are focused on in this study. First, the upper layer of a hydrogel is not necessarily too thin. Thus we investigated how the thickness of the upper layer can affect the surface morphology of bilayer hydrogels under compression through both finite element (FE) simulation and theoretical analysis. Second, a hydrogel can absorb water molecules before the mechanical compression. The effect of the pre-absorption of water before the mechanical compression was studied through FE simulations and theoretical analysis. Our results show that when the thickness of the upper layer is very large, surface wrinkles can exist without transforming into period doublings. The pre-absorption of the water can result in folds or unexpected hierarchical wrinkles, which can be realized in experiments through further efforts.

Mechanoresponsive Tuning of Anisotropic Wetting on Hierarchically Structured Patterns

Here, we propose a simple mechanoresponsive system on patterned soft surfaces to manipulate both anisotropy and orientation of liquid wetting. On the poly(dimethylsiloxane) embedding line patterned structures, additional topographies, such as wrinkles and cracks, can be provided by applying compressive and tensile stress, respectively. This tunable hierarchy of structures with the different scales and directions of lines, wrinkles, and cracks allow the mechanoresponsive control of anisotropic wetting in a single platform. In addition, the wetting behavior on those surfaces is precisely investigated based on the concept of critical contact angle to overcome the ridges in a step flow.

Small degree of anisotropic wetting on self-similar hierarchical wrinkled surfaces

We studied the wetting behavior of multiscale self-similar hierarchical wrinkled surfaces. The hierarchical surface was fabricated on poly(dimethylsiloxane) (PDMS) substrates by manipulating the sequential strain release and combined plasma/ultraviolet ozone (UVO) treatment. The generated structured surface shows an independently controlled dual-scale roughness with level-1 small-wavelength wrinkles (wavelength of 700-1500 nm and amplitude of 50-500 nm) resting on level-2 large-wavelength wrinkles (wavelength of 15-35 μm and amplitude of 3.5-5 μm), as well as accompanying orthogonal cracks. By tuning the aspect ratio of hierarchical wrinkles, the degree of wetting anisotropy in hierarchical wrinkled surfaces, defined as the contact angle difference between the parallel and perpendicular directions to the wrinkle grooves, is found to change between 3° and 9°. Through both experimental characterization (confocal fluorescence imaging) and theoretical analyses, we showed that the wetting state in the hierarchical wrinkled surface is in the Wenzel wetting state. We found that the measured apparent contact angle is larger than the theoretically predicted Wenzel contact angle, which is found to be attributed to the three-phase contact line pinning effect of both wrinkles and cracks that generates energetic barriers during the contact line motion. This is evidenced by the observed sudden drop of over 20° in the static contact angles along both perpendicular and parallel directions after slight vibration perturbation. Finally, we concluded that the observed small degree of wetting anisotropy in the hierarchical wrinkled surfaces mainly arises from the competition between orthogonal wrinkles and cracks in the contact line pinning.

Swelling-induced wrinkling in layered gel beams

Gels are widely employed in smart mechanical devices and biomedical applications. Swelling-induced bending actuation can be obtained by means of a simple bilayer gel beam. We show that this system can also exhibit wrinkling patterns of potential interest for structural morphing and sensing. We study swelling-induced wrinkling at the extrados of a bilayer gel beam with the softer layer on top. The bent configuration at finite strain is recovered first and, starting from it, a linear perturbation analysis is performed. We delimit the zone corresponding to wrinkling modes in a parameter plane encompassing a mechanical stiffness ratio and a geometric top layer to total height ratio. Interestingly, we observe that surface instability precedes and envelopes wrinkling modes of finite wavelength. Finally, we discuss the effect of changes in stiffness and of the Flory-Huggins parameters χ on the size of the wrinkling domain.

Elucidating "screw dislocation"-driven film formation of sodium thiosulphate with complex hierarchical molecular assembly

Sodium thiosulphate (Na₂S₂O₃) films were synthesized on carbon steel substrates through solution deposition, and a film formation growth mechanism is delineated in detail herein. Dislocation-driven film formation took place at the lower concentration of Na₂S₂O₃ (0.1 M) studied, where screw dislocation loops were identified. Interestingly, we observed the co-existence of screw dislocation spiral loops and hierarchically-ordered molecular assembly in the film, and showed the importance of hierarchical morphology in the origin of screw dislocation. The screw dislocation loops were, however, distorted at the higher studied concentration of Na₂S₂O₃ (0.5 M), and no hierarchical structures were formed. The mechanisms of film formation are discussed in detail and provide new insights into our understanding regarding morphology of the hierarchical molecular assembly, screw dislocation loop formation, and the role of chemical elements for their development. The main crystalline and amorphous phases in the surface films were identified as pyrite/mackinawite and magnetite. As sodium thiosulphate is widely used for energy, corrosion inhibition, nanoparticle synthesis and catalysis applications, the knowledge generated in this study is applicable to the fields of corrosion, materials science, materials chemistry and metallurgy.