Nano- and Microscopic Surface Wrinkles of Linearly Increasing Heights Prepared by Periodic Precipitation

Periodic Stratification of Colloids in a Liquid Phase Produced by a Precipitation Reaction and Gel Swelling

Pattern formation is a frequent phenomenon occurring in animate and inanimate systems. The interplay between the mass transport of the chemical species and the underlying chemical reaction networks generates most patterns in chemical systems. Periodic precipitation is an emblematic example of reaction-diffusion patterns, in which the process generates a spatial periodic structure in porous media. Here, we use the dormant reagent method to produce colloidal particles of Prussian blue (PB) and PB analogues at the liquid-gel interface. The generated particles produced a stable periodic stratification pattern in time in the liquid phase placed on top of the solid hydrogel. The phenomenon is governed by periodic swelling of the gel driven by the osmotic stress and stability of the formed particles. To illustrate the phenomenon, we developed an extended reaction-diffusion model, which incorporated the gel swelling and sedimentation effect of the formed colloids and could qualitatively reproduce the pattern formation in the liquid phase.

Non-equilibrium-Growing Aesthetic Ionic Skin for Fingertip-Like Strain-Undisturbed Tactile Sensation and Texture Recognition

Humans use periodically ridged fingertips to precisely perceive the characteristics of objects via ion-based fast- and slow-adaptive mechanotransduction. However, designing artificial ionic skins with fingertip-like tactile capabilities remains challenging because of the contradiction between structural compliance and pressure sensing accuracy (e.g., anti-interference from stretch and texture recognition). Inspired by the formation and modulus-contrast hierarchical structure of fingertips, an aesthetic ionic skin grown from a non-equilibrium Liesegang patterning process is introduced. This ionic skin with periodic stiff ridges embedded in a soft hydrogel matrix enables strain-undisturbed triboelectric dynamic pressure sensing as well as vibrotactile texture recognition. By coupling with another piezoresistive ionogel, an artificial tactile sensory system is further fabricated as a soft robotic skin to mimic the simultaneous fast- and slow-adaptive multimodal sensations of fingers in grasping actions. This approach may inspire the future design of high-performance ionic tactile sensors for intelligent applications in soft robotics and prosthetics.

Wrinkled Interfaces: Taking Advantage of Anisotropic Wrinkling to Periodically Pattern Polymer Surfaces

Periodically patterned surfaces can cause special surface properties and are employed as functional building blocks in many devices, yet remaining challenges in fabrication. Advancements in fabricating structured polymer surfaces for obtaining periodic patterns are accomplished by adopting "top-down" strategies based on self-assembly or physico-chemical growth of atoms, molecules, or particles or "bottom-up" strategies ranging from traditional micromolding (embossing) or micro/nanoimprinting to novel laser-induced periodic surface structure, soft lithography, or direct laser interference patterning among others. Thus, technological advances directly promote higher resolution capabilities. Contrasted with the above techniques requiring highly sophisticated tools, surface instabilities taking advantage of the intrinsic properties of polymers induce surface wrinkling in order to fabricate periodically oriented wrinkled patterns. Such abundant and elaborate patterns are obtained as a result of self-organizing processes that are rather difficult if not impossible to fabricate through conventional patterning techniques. Focusing on oriented wrinkles, this review thoroughly describes the formation mechanisms and fabrication approaches for oriented wrinkles, as well as their fine-tuning in the wavelength, amplitude, and orientation control. Finally, the major applications in which oriented wrinkled interfaces are already in use or may be prospective in the near future are overviewed.

Effect of the Polarity of Solvents on Periodic Precipitation: Formation of Hierarchical Revert Liesegang Patterns

Liesegang pattern (LP) is one example of self-organized periodic precipitation patterns in nonequilibrium systems. Several studies have demonstrated that the LP morphology can track physicochemical environmental conditions (e.g., temperature); however, the polarity effect has not been explored to date. In this study, a copper chromate system is used to reveal the impact of solvent polarity on the evolving LP structure using water/organic solvent mixtures. In the typical case of using water/dimethyl sulfoxide (DMSO) mixtures, two drastic changes in LP morphology with increasing DMSO contents were found: (i) increasing frequency of the original structure and (ii) formation of a hierarchical pattern with the appearance of another, lower-frequency structure. Furthermore, the simulation model operating with a bimodal size distribution, allowing both homogeneous and heterogeneous precipitations showed good agreement with the experimental results. Therefore, this study demonstrated that LP can be tailored by solvent polarity and can be used for designing hierarchical precipitation patterns in a straightforward manner.

Rapid formation of uniformly layered materials by coupling reaction-diffusion processes with mechanical responsiveness

Straightforward manufacturing pathways toward large-scale, uniformly layered composites may enable the next generation of materials with advanced optical, thermal, and mechanical properties. Reaction-diffusion systems are attractive candidates to this aim, but while layered composites theoretically could spontaneously arise from reaction-diffusion, in practice randomly oriented patches separated by defects form, yielding nonuniformly patterned materials. A propagating reaction front can prevent such nonuniform patterning, as is the case for Liesegang processes, in which diffusion drives a reaction front to produce layered precipitation patterns. However, while diffusion is crucial to control patterning, it slows down transport of reactants to the front and results in a steady increase of the band spacing as the front advances. Here, we circumvent these diffusive limitations by embedding the Liesegang process in mechanically responsive hydrogels. The coupling between a moving reaction front and hydrogel contraction induces the formation of a self-regulated transport channel that ballistically carries reactants toward the area where patterning occurs. This ensures rapid and uniform patterning. Specifically, large-scale ([Formula: see text]5-cm) uniform banding patterns are produced with tunable band distance (d = 60 to 160 µm) of silver dichromate crystals inside responsive gelatin-alginate hydrogels. The generality and applicability of our mechanoreaction-diffusion strategy are demonstrated by forming patterns of precipitates in significantly smaller microscopic banding patterns (d = 10 to 30 µm) that act as self-organized diffraction gratings. By circumventing the inherent limitations of diffusion, our strategy unlocks the potential of reaction-diffusion processes for the manufacturing of uniformly layered materials.

Phase separation mechanism for a unified understanding of dissipative pattern formation in a Liesegang system

Dissipative patterns with solid-phase transitions are ubiquitous in nature. Despite their ubiquitous nature, there is no unified understanding of the non-equilibrium self-assembly mechanisms of such pattern formation. The Liesegang pattern (LP) is a typical model that has the potential to describe dissipative pattern formation arising from the nonlinear coupling of directional mass transport of water-soluble substances into a porous media with their solid-phase transition processes. However, the conventional mechanism in a Liesegang system lacks practicality because most of the existing studies have focused only on the transition mechanism of nucleation from the molecular to the solid state. In this study, we demonstrate a novel experimental system based on a phase transition and separation mechanism that does not require nucleation, namely, the pH-induced aggregation of gold nanoparticles modified with 11-mercaptoundecanoic acid (MUA-Au NPs) by H⁺ diffusion in a solid hydrogel. Combined experiments and numerical simulations reveal that pattern formation is driven by the macroscopic phase-separation mechanism. Furthermore, the pattern periodicity obtained from both experiments and simulations follows the classical spacing law of LP, namely, the LP morphology is determined without the need for nucleation. Therefore, we can show that the formation of LPs can be described in a unified mechanism, regardless of whether nucleation occurs. This finding opens the possibility that the chemical Liesegang system can be applied as a practical model for proving the mechanisms of similar dissipative pattern formation.

Evolution of Micron-Spaced Patterns within Precipitating Patterns of In Situ Synthesized Silver Nanoparticles in a Nanodot-Embedded PVA/PVP Film

Periodic pattern formation beyond conventional precipitation reactions of electrolytes is of greater importance for gaining insights into the driving forces behind spontaneous spatiotemporal pattern formation in living matter. The Liesegang phenomenon is considered to be one of the important models for understanding well-defined periodic patterns. In this study, we have used biomolecule-derived photoluminescent carbon nanodots as reducing agents that were embedded in thin polymer films. The poor water content of polyvinyl alcohol/polyvinyl pyrrolidone films has been found to dictate the temporal scale of reaction-diffusion kinetics. Moreover, the precursors for the synthesis of nanodots have been varied to decipher the role of thiol groups present in glutathione in micron-spaced pattern formation of silver nanoparticles. A method to develop periodic patterns of plasmonic silver nanoparticles is of significant interest from technological aspects. Moreover, the formation of a micron-spaced pattern has been rationed by invoking a lowered nucleation threshold in terms of slow reaction-controlled aggregation. We expect that such an understanding of the chemical reaction-based pattern formation will help in resolving the formation of artistic spatiotemporal patterns in nature.

Self-organization of nanoparticles and molecules in periodic Liesegang-type structures

Chemical organization in reaction-diffusion systems offers a strategy for the generation of materials with ordered morphologies and structural hierarchy. Periodic structures are formed by either molecules or nanoparticles. On the premise of new directing factors and materials, an emerging frontier is the design of systems in which the precipitation partners are nanoparticles and molecules. We show that solvent evaporation from a suspension of cellulose nanocrystals (CNCs) and l-(+)-tartaric acid [l-(+)-TA] causes phase separation and precipitation, which, being coupled with a reaction/diffusion, results in rhythmic alternation of CNC-rich and l-(+)-TA-rich rings. The CNC-rich regions have a cholesteric structure, while the l-(+)-TA-rich bands are formed by radially aligned elongated bundles. The moving edge of the pattern propagates with a finite constant velocity, which enables control of periodicity by varying film preparation conditions. This work expands knowledge about self-organizing reaction-diffusion systems and offers a strategy for the design of self-organizing materials.

Mechanical Control of Periodic Precipitation in Stretchable Gels to Retrieve Information on Elastic Deformation and for the Complex Patterning of Matter

Material design using nonequilibrium systems provides straightforward access to complexity levels that are possible through dynamic processes. Pattern formation through nonequilibrium processes and reaction-diffusion can be used to achieve this goal. Liesegang patterns (LPs) are a kind of periodic precipitation patterns formed through reaction-diffusion. So far, it has been shown that the periodic band structure of LPs and the geometry of the pattern can be controlled by experimental conditions and external fields (e.g., electrical or magnetic). However, there are no examples of these systems being used to retrieve information about the changes in the environment as they form, and there are no studies making use of these patterns for complex material preparation. This work shows the formation of LPs by a diffusion-precipitation reaction in a stretchable hydrogel and the control of the obtained patterns by the unprecedented and uncommon method of mechanical input. Additionally, how to use this protocol and how deviations from "LP behavior" of the patterns can be used to "write and store" information about the time, duration, extent, and direction of gel deformation are presented. Finally, an example of using complex patterning to deposit polypyrrole by using precipitation patterns is shown as a template.

Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon

Pattern formation is a frequent phenomenon in physics, chemistry, biology, and materials science. Bottom-up pattern formation usually occurs in the interaction of the transport phenomena of chemical species with their chemical reaction. The oldest pattern formation is the Liesegang phenomenon (or periodic precipitation), which was discovered and described in 1896 by Raphael Edward Liesegang, who was a German chemist and photographer who was born 150 years ago. The purpose of this feature article is to provide a comprehensive overview of this type of pattern formation. Liesegang banding occurs because of the coupling of the diffusion process of the reagents with their chemical reactions in solid hydrogels. We will discuss several phenomena observed and discovered in the past century, including reverse patterns, precipitation patterns with dissolution (due to complex formation), helicoidal patterns, and precipitation waves. Additionally, we will review all existing models of the Liesegang phenomenon including pre- and postnucleation scenarios. Finally, we will highlight several applications of periodic precipitation.

Periodic Surface-Ring Pattern Formation for Hydroxyapatite Thin Films Formed by Biomineralization-Inspired Processes

Surface morphology is a key factor that might significantly influence the properties of biomaterials. In this study, periodic surface-ring structures have been constructed for calcium phosphate thin films via biomineralization-inspired crystallization process. The patterned octacalcium phosphate crystals have been obtained on poly(2-hydroxyethyl methacrylate) (PHEMA) matrix in the presence of poly(acrylic acid) (PAA). The patterned surface morphologies of the crystal thin films could be tuned by the amount of PAA additives. In addition, the rapid and topotactic transformation to hydroxyapatite (HAP) thin films with surface-ring structures has also been achieved. This study may provide new strategy toward the design of functional calcium phosphate-based thin-film hybrids.

Probing the mystery of Liesegang band formation: revealing the origin of self-organized dual-frequency micro and nanoparticle arrays

Periodic precipitation processes in gels can result in impressive micro- and nanostructured patterns known as periodic precipitation (or Liesegang bands). Under certain conditions, the silver nitrate-chromium(vi) system exhibits the coexistence of two kinds of Liesegang bands with different frequencies. We now present that the two kinds of bands form independently on different time scales and the pH-dependent chromate(vi)-dichromate(vi) equilibrium controls the formation of the precipitates. We determined the spatial distribution and constitution of the particles in the bands using focused ion beam-scanning electron microscopy (FIB-SEM) and scanning transmission X-ray spectromicroscopy (STXM) measurements. This provided the necessary empirical input data to formulate a model for the pattern formation; a model that quantitatively reproduces the experimental observations. Understanding the pattern-forming process at the molecular level enables us to tailor the size and the shape of the bands, which, in turn, can lead to new functional architectures for a range of applications.

Formation of Ultrathin Liesegang Patterns

For many years, it has been believed that self-organized periodic ring structures known by the name of Liesegang patterns (LPs) are formed only in quite thick media, typically thicker than at least several micrometers. Actually growing LPs in ultrathin films is extremely difficult because of the drying of film and susceptibility to rapid capillary wetting. The present work reports how we obtain successful LPs in ultrathin films of 65 nm thick. The key parameters are temperature control and the introduction of equilibrium water vapor in the sample environment. Atomic force microscope images clearly showed that the LPs are composed of 300-600 nm laterally coagulated particles. We have also evaluated the densities and thicknesses of the ultrathin films by X-ray reflectivity. During the present research, new patterns, which are different from ordinary LPs, have been discovered for the first time in the outermost part of the whole pattern. Studying LPs in ultrathin films may help to forge a better understanding of the mechanism underlying the intriguing phenomenon. Because of nanoscale scale thicknesses, self-organized periodic structures including so-called LPs will open up new opportunities in nanotechnologies.

Self-organization in precipitation reactions far from the equilibrium

Far from the thermodynamic equilibrium, many precipitation reactions create complex product structures with fascinating features caused by their unusual origins. Unlike the dissipative patterns in other self-organizing reactions, these features can be permanent, suggesting potential applications in materials science and engineering. We review four distinct classes of precipitation reactions, describe similarities and differences, and discuss related challenges for theoretical studies. These classes are hollow micro- and macrotubes in chemical gardens, polycrystalline silica carbonate aggregates (biomorphs), Liesegang bands, and propagating precipitation-dissolution fronts. In many cases, these systems show intricate structural hierarchies that span from the nanometer scale into the macroscopic world. We summarize recent experimental progress that often involves growth under tightly regulated conditions by means of wet stamping, holographic heating, and controlled electric, magnetic, or pH perturbations. In this research field, progress requires mechanistic insights that cannot be derived from experiments alone. We discuss how mesoscopic aspects of the product structures can be modeled by reaction-transport equations and suggest important targets for future studies that should also include materials features at the nanoscale.

Chemical gardens without silica: the formation of pure metal hydroxide tubes

Contrary to common belief, hollow precipitation tubes form in the absence of silicate if sodium hydroxide solution is injected into solutions of various metal ions. In many cases, the growth speed has a power law dependence on the flow rate. For vanadyl, we observe damped oscillations in the tube height.

Self-Alignment of Beads and Cell Trapping in Precipitate Tubes

Propagating reaction fronts allow the formation of materials in self-sustained, steep concentration gradients, which would otherwise rapidly decay. These conditions can result in macroscopic, noncrystallographic structures, such as tubes with large aspect ratios. For hollow silica/Zn(OH)2 tubes, we report the inclusion of diverse mesoscopic building blocks ranging from polymer beads to biological cells. For agarose beads, we observe spontaneous alignment along vertical tracks; the nearly periodic spacing of the beads along these tracks follows a log-normal distribution. We interpret this patterning in terms of hydrodynamic recruitment and discuss similarities to the adhesion dynamics of leukocytes in blood vessels. For diatoms and other cells, we observe novel surface textures, and yeast tagged with a green fluorescent protein shows strong fluorescence activity after trapping. The inclusion of these guest units should improve the possibilities for the application of these tubes in microfluidics and biotechnology.

From hydrodynamic plumes to chemical gardens: the concentration-dependent onset of tube formation

Many inorganic precipitation reactions self-organize macroscopic tubes known as chemical gardens. We study the nonequilibrium formation of these structures by injecting aqueous sodium sulfide solution into a reservoir of iron(II) chloride solution. Our experiments reveal a distinct, concentration-dependent transition from convective plumes of reaction-induced, colloidal particles to mechanically connected, hollow tubes. The transition concentration (0.1 mol/L) is widely independent of the injection rate and causes a discontinuous change from the radius of the plume stalk to the radius of the tube. In addition, tubes have lower growth speeds than plumes. At the transition concentration, one observes the initial formation of a plume followed by the growth of a mechanically weak tube around a jet of upward-moving precipitation particles. We find that the plumes' morphology and geometric scaling are similar to that of laminar starting plumes in nonreactive systems. The characterization of dried tubes by X-ray diffraction indicates the presence of greigite and lepidocrocite.

Vesicle-to-micelle oscillations and spatial patterns

A pH oscillator is coupled to and controls rhythmic interconversion of nanoscopic vesicles and micelles made of fatty acids. When changes in pH are combined with diffusion, self-assembly produces spatially extended patterns of vesicle/micelle "stripes" or concentric "shells".

Nanostructure formation via print diffusion etching through block copolymer templates

The present work demonstrates nanoscale etching of silicon with standard aqueous fluoride etchants running through the hydrophilic domains of a vertically aligned copolymer template. The delivery of etchants was unprecedentedly achieved by an etchant-solution-saturated agarose gel stamp, a technique we call print diffusion etching. Three-dimensional nanoprotrusion features with controllable shapes and sizes (about 20 nm) were formed. To prove that the block copolymers serve to direct the silicon surface morphology by controlling the spatial location of the reaction as well as concentration of reagents, the same etching steps both on silicon and PS-b-PEO (polystyrene-block-polyethyleneoxide) templates were carried out for comparison. The mechanism of the nanoprotrusion formation was elucidated, and the morphology evolution vs. etching time studied.

Multilevel surface nano- and microstructuring via sequential photoswelling of dichromated gelatin

Photoswelling of thin films of dichromated gelatin provides a basis for fabrication of multilevel surface reliefs via sequential UV illumination through different photomasks. The remarkable feature of this simple, benchtop technique is that by adjusting irradiation times, film thickness, or its hydration state the heights of the developed features can be varied from few nanometers to tens of microns. After UV exposure, the surface structures can be replicated faithfully into either soft or hard PDMS stamps.

Highly oriented tunable wrinkling in polymer bilayer films confined with a soft mold induced by water vapor

The authors report the formation of highly oriented wrinkling on the surface of the bilayer [polystyrene (PS)/poly(vinyl pyrrolidone) (PVP)] confined by a polydimethylsiloxane (PDMS) mold in a water vapor environment. When PVP is subjected to water vapor, the polymer loses its mechanical rigidity and changes to a viscous state, which leads to a dramatic change in Young's modulus. This change generates the amount of strain in the bilayer to induce the wrinkling. With a shape-controlled mold, they can get the ordered wrinkles perfectly perpendicular or leaned 45 degrees to the channel orientation of the mold because the orientation of the resultant force changes with the process of water diffusion which drives the surface to form the wrinkling. Additionally, they can get much smaller wrinkles than the stripe spacing of PDMS mold about one order. The wrinkle period changes with the power index of about 0.5 for various values of the multiplication product of the film thicknesses of the two layers, namely, lambda approximately (h(PS)h(PVP))(1/2).

Microchameleons: nonlinear chemical microsystems for amplification and sensing

In biological systems, the coupling of nonlinear biochemical kinetics and molecular transport enables functional sensing and "signal" amplification across many length scales. Drawing on biological inspiration, we describe how artificial reaction-diffusion (RD) microsystems can provide a basis for sensing applications, capable of amplifying micro- and nanoscopic events into macroscopic visual readouts. The RD applications reviewed here are based on a novel experimental technique, WETS for Wet Stamping, which offers unprecedented control over RD processes in microscopic and complex geometries. It is discussed how RD can be used to sense subtle differences in the thickness and/or absorptivity of thin absorptive films, amplify macromolecular phase transitions, detect the presence and quality of self-assembled monolayers, and provide dynamic spatiotemporal readouts of chemical "metabolites."

Systematic Front Distortion and Presence of Consecutive Fronts in a Precipitation System

A new simple reaction-diffusion system is presented focusing on pattern formation phenomena as consecutive precipitation fronts and distortion of the precipitation front. The chemical system investigated here is based on the amphoteric property of aluminum hydroxide and exhibits two unique phenomena. Both the existence of consecutive precipitation fronts and distortion are reported for the first time. The precipitation patterns could be controlled by the pH field, and the distortion of the precipitation front can be practical for microtechnological applications of reaction-diffusion systems.