Formation Of Wrinkle Patterns Research Articles

Wrinkling pattern formation with periodic nematic orientation: From egg cartons to corrugated surfaces.

Egg cartons, known as doubly sinusoidal surfaces, display a rich variety of saddles-cylinder-spherical patches organized with different spatial symmetries and connectivities. Egg carton surfaces, rich in functionalities, are observed in synthetic and biological materials, as well as across atomic and macroscopic scales. In this work we use the liquid crystal shape equationin the absence of elastic effects and normal stress jumps to predict and classify a family of uniaxial, equibiaxial, and biaxial egg cartons, according to the periodicities of the surface director field in nematic (N) and cholesteric (N*) liquid crystals under the presence of anisotropic surface tension (anchoring). Egg carton surface shape periodic solutions to the nonlinear and linearized liquid crystal shape equationspredict that the mean curvature is a linear function of the orthogonal (along the surface normal) splay and bend contributions. Mixtures of egg carton surfaces (uniaxial, equibiaxial, and biaxial) emerge according to the symmetries of the nonsingular director field, and the spatial distributions of the director escape into the third dimension; pure uniaxial egg cartons emerge when the director escape has linelike geometries and mixtures of egg cartons arise under source or sink orientation lattices. Orientation symmetry and permutation analysis are incorporated into a full curvature (Casorati, shape parameter, mean curvature, and Gaussian curvature) characterization. Under a fixed anchoring parameter, conditions for maximal nanoscale curvedness and microscale maximal shape gradient diversity are identified. The present results contribute to various pathways to surface pattern formation using intrinsic anisotropic interfacial tension.

Transient structures in rupturing thin films: Marangoni-induced symmetry-breaking pattern formation in viscous fluids.

In the minutes immediately preceding the rupture of a soap bubble, distinctive and repeatable patterns can be observed. These quasistable transient structures are associated with the instabilities of the complex Marangoni flows on the curved thin film in the presence of a surfactant solution. Here, we report a generalized Cahn-Hilliard-Swift-Hohenberg model derived using asymptotic theory that describes the quasielastic wrinkling pattern formation and the consequent coarsening dynamics in a curved surfactant-laden thin film. By testing the theory against experiments on soap bubbles, we find quantitative agreement with the analytical predictions of the nucleation and the early coarsening phases associated with the patterns. Our findings provide fundamental physical understanding that can be used to (de-)stabilize thin films in the presence of surfactants and have important implications for both natural and industrial contexts, such as the production of thin coating films, foams, emulsions, and sprays.

Thermal wrinkling of liquid crystal polymer shell/core spheres

Smart soft materials that can flexibly respond to external multi-physics stimuli, have shown intriguing applications in shape-morphing and morphology control. Here, we present tunable wrinkling patterns in core–shell spheres under thermal load via controlling the orientation of director in nematic liquid crystal polymer (LCP). To analyze nonlinear instability and morphological evolution of LCP shell/core spheres, we develop a shallow core–shell model that accounts for director-induced anisotropic spontaneous strains. By tuning the alignment of liquid crystal director, we explore effects of anisotropy of spontaneous strains on wrinkling pattern formation and evolution. When the director is along the out-of-plane direction, the surface shell undergoes equi-biaxial expansion, resulting in hexagonal, checkerboard, herringbone or labyrinth pattern, determined by a single dimensionless parameter Cs which characterizes the stiffness ratio and curvature of the system. Moreover, stability analysis yields an analytical solution of the critical wrinkling strain and wavelength for equi-biaxially stressed shell/core spheres. When the director is in-plane aligned, leading to primary uniaxial expansion upon heating, the core–shell usually buckles into stripes. For general spatial director alignment, the ultimate wrinkling patterns depending on the anisotropy state of spontaneous strains, can be hexagonal, parallel bead-chain, stripe, herringbone, labyrinth or hybrid. Lastly, we provide director-affected phase diagrams on pattern selection, which could be used to quantitatively guide the effective design of morphology-related smart surfaces such as anticounterfeiting system.

Hyperthermal hydrogen induced cross-linking and fabrication of nano-wrinkle patterns in ultrathin polymer films

This paper presents an efficient and simple processing method for the fabrication and regulation of nano-scale wrinkle patterns. The stiff film is created through cross-linking the surface of ultrathin polymer film within twenty nanometers by using the hyperthermal hydrogen induced cross-linking (HHIC) method, and then the bilayer is heated above the glass transition temperature of the polymer before quenched to room temperature. In this way, wrinkle patterns with wavelength ranging from 150 to 300nm are prepared. And a morphology transition between the pattern of single points (convex bumps) and the pattern of ridges (labyrinth) is observed. The formation of wrinkle patterns is systematically investigated as functions of the thickness of original ultrathin film, the time of HHIC treatment, the annealing temperature and the chemical structure of polymers. Furthermore, nano-patterned silicon wafer is used as a template to create multiscale, anisotropic wrinkle patterns.

Mechanical properties investigation of monolayer h-BN sheet under in-plane shear displacement using molecular dynamics simulations

The mechanical properties, including wrinkling patterns and fracture behavior, of monolayer h-BN sheets have been investigated using classic molecular dynamics simulations and continuum model. The wrinkling pattern formation and evolution have been first explored. The dependences of the wrinkling shape, amplitude, and wavelength, as well as wrinkling number on shear displacement are extensively elucidated. The influences of geometry and shear load direction, as well as temperature, on the fracture behavior have also been studied to obtain further insights into the properties of the monolayer h-BN sheets.

Spontaneous wrinkle branching by gradient stiffness

The concept of coherency loss is proposed to understand wrinkle branching as a pathway toward hierarchical wrinkling pattern formation in a compressed film-substrate system with gradient stiffness of the film or substrate. A simple model indicates that the wrinkle branching arises when the characteristic length of the stiffness inhomogeneity zone is larger than the coherency persistent length, which depends on the amplitude of the stiffness inhomogeneity. Numerical simulations of nonlinear wrinkles based on the model of the Föppl-von Kármán plate on compliant substrates show how regulating the size and amplitude of the stiffness inhomogeneities results in branched wrinkles in striking agreement with the existing observations. The paper reveals the origin of such kinds of branched wrinkles and may provide a guideline for controllable hierarchical wrinkles by patterning the stiffness gradient.

Kinetic study of swelling-induced surface pattern formation and ordering in hydrogel films with depth-wise crosslinking gradient

Hydrogels undergo extensive three-dimensional volume changes when immersed in water, the degree of which is determined by the network chemical composition and degree of crosslinking. When the hydrogel is attached to a rigid substrate, it swells preferentially perpendicular to the substrate. This anisotropic swelling generates a compressive stress, which drives the formation of surface patterns when exceeding a critical stress value (σ ≥ σc). In order to develop an indepth understanding of the mechanism of surface pattern formation in hydrogels, we investigated the dynamic evolution of surface patterns in photocured hydrogel films from poly(2-hydroxyethyl methacrylate) (PHEMA) crosslinked with different concentrations of ethylene glycol dimethacrylate (EGDMA, 0–3 wt%). During curing in the presence of oxygen, a modulus gradient along the film depth was generated due to oxygen inhibition of the radical polymerization near the film surface. The swelling-induced wrinkling pattern formation followed Fickian-type kinetics (λ ∼ t1/2) at early stages, which was independent of the final pattern morphology. The onset of wrinkling was found at a linear expansion of αc ≈ 1.12, which remained constant with increasing EGDMA concentration but decreased with increasing film thickness, indicating an increase in critical stress with crosslinker concentration. In contrast, the equilibrium linear expansion value, αe, decreased significantly (from 2.55 to 1.20) with increasing crosslinker concentration (from 0 to 3 wt%), resulting in transition from random patterns to highly ordered hexagonal structures.

A numerical study of the wrinkling evolution of an elastic film on a viscous layer

The wrinkling phenomenon of a compressed elastic thin film bonded to a viscous layer is studied. Linear stability analysis (LSA) shows that, for materials with cubic crystalline symmetry, the sign of the degree of elastic anisotropy ζ = ((C12 + 2C44)/C11) − 1 plays an important role in the anisotropy of the buckling instability of the thin film system. More precisely, the growth rate of the fastest growing wave number, taken as a function of directions, reaches a peak in the ⟨1 0 0⟩ directions for ζ > 0 and in the ⟨1 1 0⟩ directions for ζ < 0. A highly efficient semi-implicit spectral method is established. The numerical experiments of long time wrinkling evolution processes of a 1 + 2-dimensional system verified the LSA results, successfully simulated anisotropic wrinkling pattern formation and coarsening, produced a power law scaling and reproduced certain featured phenomena observed in physical experiments.

Sol-Gel-derived ZnO Coating with Nanopatterns Fabricated by Nanoimprinting

The influence of an applied pressure on the relaxation of stress for sol–gel-derived zinc oxide (ZnO) thin film and the formation of nanopatterns during nanoimprinting has been carried out. Wrinkling pattern formation in thin films caused by the relaxation of stress is a phenomenon frequently encountered. In this study, a route for sol–gel-derived ZnO film imprinted with poly(dimethylsiloxane) mold was used to attain pattern transfer with excellent uniformity and smooth profile. The ZnO nanoscale rib patterns are obtained by altering the processing parameters, such as baking conditions, applied pressure, and content of solvent within the gel films. The surface roughness that caused by the relaxation of stress, and the wrinkles generated to relieve the stress can self-assemble into the contour of the mold during the imprinting process with an applied pressure. By altering the pretreatment parameters to render some residual solvent in the film can enhance the fluidity of the film, which in turn leads to a faster and deeper penetration of the mold into the film. In conclusion, the effect of processing conditions for eliminating wrinkling pattern of sol–gel-derived ZnO, and to prepare nanopatterns with good uniformity and smooth surface has been demonstrated.

Formation of Wrinkle Patterns on Porous Elastomeric Membrane and Their Fabrication of Hierarchical Architectures

AbstractWe report the formation of wrinkle patterns on porous elastomeric membrane and their fabrication of hierarchical architectures through mechanical stretching and replica molding. The technique builds upon a buckling instability of a stiff layer supported by a porous elastomeric membrane which was induced by surface plasma oxidation of the pre-stretched porous elastomer followed by removal of the applied mechanical strain to form wrinkle patterns, and replica molding of the deformed features on the porous membrane into epoxy to form hierarchical architectures through casting the UV-curable epoxy prepolymer and UV curing. We find that due to the existence of micropores on the membrane, the formation of wrinkle patterns is different from that formed on a continuous elastomeric film, and by varying the applied mechanical stretching strain condition and plasma oxidation condition, the wrinkle patterns could be either confined by the micropores on the membrane to exhibit a wavelength equal to its pitch or form wrinkles with much large wavelength compared with that formed on a continuous elastomeric film. Therefore, the micropillar arrays fabricated by replica molding could stand on different types of wrinkle patterns to form different hierarchical architectures. The method we illustrate here offers a simple and cost-effective approach to fabricate various hierarchical structures, and provides possibilities for potential applications in various fields, such as microfluidics, micro- and nanofabrication of complex structures, crystal formation, cell attachment, superhydrophobicity and dry adhesion.