Pattern formation. Spiral cracks without twisting

Recent progress on crack pattern formation in thin films

Fascinating pattern formation by quasi-static crack growth in thin films has received increasing interest in both interdisciplinary science and engineering applications. The paper mainly reviews recent experimental and theoretical progress on the morphogenesis and propagation of various quasi-static crack patterns in thin films. Several key factors due to changes in loading types and substrate confinement for choosing crack paths toward different patterns are summarized. Moreover, the effect of crack propagation coupled to other competing or coexisting stress-relaxation processes in thin films, such as interface debonding/delamination and buckling instability, on the formation and transition of crack patterns is discussed. Discussions on the sources and changes in the driving force that determine crack pattern evolution may provide guidelines for the reliability and failure mechanism of thin film structures by cracking and for controllable fabrication of various crack patterns in thin films.

Cracking of Colloidal Films to Generate Rectangular Fragments

Cracks are common in nature. Cracking is known as an irreversible and uncontrollable process. To control the cracking patterns, many researchers have proposed methods to prepare notches for stress localization on films. In this work, we investigate a method of controlling cracks by making microscale pyramid patterns that have notches between the pyramids. After preparing pyramid patterns consisting of colloidal particles with organic residue, we annealed them to induce volume shrinkage and cracking between the pyramids. We studied the effect of film thickness on cracking and the generation of rectangular fragments consisting of multiple pyramids. The area of rectangular fragments was in good agreement with the results of scaling analysis. The concept of controlling cracks by imprinting notches on a film and the relationship with the film thickness can guide the study of cracking phenomena.

Programming fracture patterns of thin films

Controlled fracture presents opportunities for the advanced fabrication of thin films. However, programmability analogous to that of Chinese paper cutting is still challenging, where fracture patterns can be created as required without preformed cracks for guidance. Here, we establish a design framework for tearing adhesive thin films from foldable substrates with such programmability. Our analytical model captures the observed crack behavior, demonstrating that the deflection of crack paths can exceed 90^{∘}. Besides, for thick foldable substrates with multiple ridges, we additionally propose a robust method of directional fracture where the cracks are forced to extend along the ridges.

Synergy between the crack pattern and substrate elasticity in colloidal deposits

Desiccation cracks in colloidal deposits occur to release the excess strain energy arising from the competition between the drying induced shrinkage of the deposit and its adhesion to the substrate. Here we report remarkably different morphology of desiccation cracks in the dried patterns formed by the evaporation of sessile drops containing colloids on elastomer (soft) or glass (stiff) substrates. The change in the crack pattern, i.e., from radial cracks on stiff substrates to circular cracks on soft substrates, is shown to arise solely due to the variation in elasticity of the underlying substrates. Our experiments and calculations reveal an intricate correlation between the desiccation crack patterns and the substrate's elasticity. The mismatch in modulus of elasticity between the substrate and that of the particulate deposit significantly alters the energy release rate during the nucleation and propagation of cracks. The stark variation in crack morphology is attributed to the tensile or compressive nature of the drying-induced in-plane stresses.

Griffith Criterion for Nanoscale Stress Singularity in Brittle Silicon

Brittle materials such as silicon fail via the crack nucleation and propagation, which is characterized by the singular stress field formed near the crack tip according to Griffith or fracture mechanics theory. The applicability of these continuum-based theories is, however, uncertain and questionable in a nanoscale system due to its extremely small singular stress field of only a few nanometers. Here, we directly characterize the mechanical behavior of a nanocrack via the development of in situ nanomechanical testing using a transmission electron microscope and demonstrate that Griffith or fracture mechanics theory can be applied to even 4 nm stress singularity despite their continuum-based concept. We show that the fracture toughness in silicon nanocomponents is 0.95 ± 0.07 MPa√m and is independent of the dimension of materials and therefore inherent. Quantum mechanics/atomistic modeling explains and provides insight into these experimental results. This work therefore provides a fundamental understanding of fracture criterion and fracture properties in brittle nanomaterials.

Drying kinetics of deformable and cracking nano-porous gels

The desiccation of porous materials encompasses a wide range of technological and industrial processes and is acutely sensitive to the hierarchical structure of the porous materials resulting in complex dynamics which are challenging to unravel. Macroscopic observations of the surface and geometry of model colloidal gels during desiccation under controlled air flow highlight the role of crack formation in drying. The density of cracks and their rate of appearance depend on the initial solid fraction of the gels and their adherence to the substrate. While under certain conditions cracking leads to an increase of the drying rate, in other cases cracking allows for its conservation over an extended period of the drying process. Nevertheless, as long as the sample is saturated with water, each piece within the sample shrinks isotropically as if it were an independent drying system. By simulating the airflow around the sample and inside the crack cavities, we show the existence of a perturbation in the air velocity in the vicinity of the crack cavity whose scale depends on the aspect ratio (depth/width) of the latter. On this basis, we propose a simple model which predicts the observed drying rate variations encountered while the sample cracks; and further enables to simulate the desiccation for a designated crack density.

Golden Spirals and Scalp Whorls: Nature's Own Design for Rapid Expansion

This paper documents what began as an exercise in curiosity—logarithmic spiral designs abound in nature—in galaxies, flowers, even pinecones, and on human scalps as whorls. Why are humans the only primates to have whorls on the scalp? Is the formation of scalp whorls mechanical or genetic? A mechanical theory has long been postulated– the mechanical theory suggests that hair whorl patterning is determined by the tension on the epidermis during rapid expansion of the cranium while the hair follicle is growing downwards—however, this has never before, to the author's knowledge, been experimentally proven conclusively. We found, that under certain conditions, we were able to experimentally recreate spirals on the scalp to demonstrate that the basis of scalp whorls is indeed mechanical—and that logarithmic spirals may be nature’s own design for rapid expansion of organic tissues. Given our experiments only created whorls when certain conditions were satisfied (and not in others), they have given us great insight into the mechanical formation of skin whorls and the physiology of skin stretch. We believe that these findings will lead to many more advances in understanding skin dynamics and indeed the changes that occur in tissue when confronted by stretch.

Cracking-assisted fabrication of nanoscale patterns for micro/nanotechnological applications

Cracks are frequently observed in daily life, but they are rarely welcome and are considered as a material failure mode. Interestingly, cracks cause critical problems in various micro/nanofabrication processes such as colloidal assembly, thin film deposition, and even standard photolithography because they are hard to avoid or control. However, increasing attention has been given recently to control and use cracks as a facile, low-cost strategy for producing highly ordered nanopatterns. Specifically, cracking is the breakage of molecular bonds and occurs simultaneously over a large area, enabling fabrication of nanoscale patterns at both high resolution and high throughput, which are difficult to obtain simultaneously using conventional nanofabrication techniques. In this review, we discuss various cracking-assisted nanofabrication techniques, referred to as crack lithography, and summarize the fabrication principles, procedures, and characteristics of the crack patterns such as their position, direction, and dimensions. First, we categorize crack lithography techniques into three technical development levels according to the directional freedom of the crack patterns: randomly oriented, unidirectional, or multidirectional. Then, we describe a wide range of novel practical devices fabricated by crack lithography, including bioassay platforms, nanofluidic devices, nanowire sensors, and even biomimetic mechanosensors.

Growing a Chemical Garden at the Air-Fluid Interface

Here we grow chemical gardens using a novel, quasi two-dimensional, experimental configuration. Buoyant calcium chloride solution is pumped onto the surface of sodium silicate solution. The solutions react to form a precipitation structure on the surface. Initially, an open channel forms that grows in a spiral. This transitions to radially spreading and branching fingers, which typically oscillate in transparency as they grow. The depth of the radial spreading, and the fractal dimension of the finger growth, are surprisingly robust, being insensitive to the pumping rate. The curvature of the channel membrane and the depth of the radially spreading solution can be explained in terms of the solution densities and the interfacial tension across the semipermeable membrane. These unusually beautiful structures provide new insights into the dynamics of precipitation structures and may lead to new technologies where structures are grown instead of assembled.

Cracking-assisted photolithography for mixed-scale patterning and nanofluidic applications

Cracks are observed in many environments, including walls, dried wood and even the Earth's crust, and are often thought of as an unavoidable, unwanted phenomenon. Recent research advances have demonstrated the the ability to use cracks to produce various micro and nanoscale patterns. However, patterns are usually limited by the chosen substrate material and the applied tensile stresses. Here we describe an innovative cracking-assisted nanofabrication technique that relies only on a standard photolithography process. This novel technique produces well-controlled nanopatterns in any desired shape and in a variety of geometric dimensions, over large areas and with a high throughput. In addition, we show that mixed-scale patterns fabricated using the 'crack-photolithography' technique can be used as master moulds for replicating numerous nanofluidic devices via soft lithography, which to the best of our knowledge is a technique that has not been reported in previous studies on materials' mechanical failure, including cracking.

Self-replicating cracks: a collaborative fracture mode in thin films

Straight cracks are observed in thin coatings under residual tensile stress, resulting into the classical network pattern observed in china crockery, old paintings, or dry mud. Here, we present a novel fracture mechanism where delamination and propagation occur simultaneously, leading to the spontaneous self-replication of an initial template. Surprisingly, this mechanism is active below the standard critical tensile load for channel cracks and selects a robust interaction length scale on the order of 30 times the film thickness. Depending on triggering mechanisms, crescent alleys, spirals, or long bands are generated over a wide range of experimental parameters. We describe with a simple physical model, the selection of the fracture path and provide a configuration diagram displaying the different failure modes.

Guided fracture of films on soft substrates to create micro/nano-feature arrays with controlled periodicity

While the formation of cracks is often stochastic and considered undesirable, controlled fracture would enable rapid and low cost manufacture of micro/nanostructures. Here, we report a propagation-controlled technique to guide fracture of thin films supported on soft substrates to create crack arrays with highly controlled periodicity. Precision crack patterns are obtained by the use of strategically positioned stress-focusing V-notch features under conditions of slow application of strain to a degree where the notch features and intrinsic crack spacing match. This simple but robust approach provides a variety of precisely spaced crack arrays on both flat and curved surfaces. The general principles are applicable to a wide variety of multi-layered materials systems because the method does not require the careful control of defects associated with initiation-controlled approaches. There are also no intrinsic limitations on the area over which such patterning can be performed opening the way for large area micro/nano-manufacturing.

Patterning by controlled cracking

Crack formation drives material failure and is often regarded as a process to be avoided. However, closer examination of cracking phenomena has revealed exquisitely intricate patterns such as spirals, oscillating and branched fracture paths and fractal geometries. Here we demonstrate the controlled initiation, propagation and termination of a variety of channelled crack patterns in a film/substrate system comprising a silicon nitride thin film deposited on a silicon substrate using low-pressure chemical vapour deposition. Micro-notches etched into the silicon substrate concentrated stress for crack initiation, which occurred spontaneously during deposition of the silicon nitride layer. We reproducibly created three distinct crack morphologies--straight, oscillatory and orderly bifurcated (stitchlike)--through careful selection of processing conditions and parameters. We induced direction changes by changing the system parameters, and we terminated propagation at pre-formed multi-step crack stops. We believe that our patterning technique presents new opportunities in nanofabrication and offers a starting point for atomic-scale pattern formation, which would be difficult even with current state-of-the-art nanofabrication methodologies.

Cracks in magnetic nanocrystal films: do directional and isotropic crack patterns follow the same scaling law?

In this letter, we show that the use of nanocrystals enables new insights into the scaling law of crack patterns. Directional and isotropic crack patterns made of gamma-Fe2O3 nanocrystals follow the same scaling law, with the film height varying by 3 orders of magnitude. A simple two-dimensional computer model for elastic fracture also leads to the same scaling behavior for directional and isotropic cracks, in good agreement with the experiments.

Silver halide colloid precursors for the synthesis of monolayer-protected clusters

A new method for the synthesis of monolayer-protected silver clusters (MPCs) based on the two-phase reduction of a stable negatively charged silver bromide sol is described. Phase transfer of the colloid to toluene is accomplished using tetra-n-octylammonium bromide as the phase transfer reagent. The advantage of this synthesis is to uncouple the formation of the silver halide colloid from its transfer and reduction in the organic phase, thus allowing control over each reaction step. The silver colloid in toluene was reduced with aqueous borohydride in the presence of 4-bromobenzenethiol as the passivating agent. The UV-visible absorption spectra indicate the intermediate formation of Ag(core)AgBr(shell) clusters during reduction. The resulting MPCs have been characterized by optical and transmission electron microscopy, energy-dispersive X-ray analysis, thermogravimetry, and UV-vis absorption spectroscopy. The formation of spiral cracks in the nanoparticulate agglomerates on solvent evaporation was observed. The spectra of thin films obtained by solvent evaporation have been analyzed using an effective medium theory.

Capillarity-driven assembly of two-dimensional cellular carbon nanotube foams

Capillary forces arising during the evaporation of liquids from dense carbon nanotube arrays are used to reassemble the nanotubes into two-dimensional contiguous cellular foams. The stable nanotube foams can be elastically deformed, transferred to other substrates, or floated out to produce free-standing macroscopic fabrics. The lightweight cellular foams made of condensed nanotubes could have applications as shock-absorbent structural reinforcements and elastic membranes. The ability to control the length scale, orientation, and shape of the cellular structures and the simplicity of the assembly process make this a particularly attractive system for studying pattern formation in ordered media.

Regular patterns generated by self-organization of ammonium-modified polymer nanospheres

Macroscopic regular stripe-crack patterns have been observed in the course of drying the aqueous suspensions of ammonium-modified polymer nanospheres. These forms emerged because the evaporation of dispersed water and self-assembly of nanospheres originates shrinkage during drying the aqueous suspensions. The drying condition plays an important role as well as the nature of the ammonium-modified polymer nanospheres for the stripe-crack pattern formation. By means of the vertical deposition method, directional stripe-crack patterns have been achieved in the macroscopic scale. Surprisingly, we have still noted an interesting secondary stripe pattern occurred spontaneously on the stripes.

Spiral cracks in drying precipitates

We investigate the formation of spiral crack patterns during the desiccation of thin layers of precipitates in contact with a substrate. This symmetry-breaking fracturing mode is found to arise naturally not from torsion forces but from a propagating stress front induced by the foldup of the fragments. We model their formation mechanism using a coarse-grain model for fragmentation and successfully reproduce the spiral cracks. Fittings of experimental and simulation data show that the spirals are logarithmic. Theoretical aspects of the logarithmic spirals are discussed. In particular we show that this occurs generally when the crack speed is proportional to the propagating speed of stress front.

Inwardly rotating spiral waves in a reaction-diffusion system

Almost 30 years have passed since the discovery of concentric (target) and spiral waves in the spatially extended Belousov-Zhabotinsky (BZ) reaction. Since then, rotating spirals and target waves have been observed in a variety of physical, chemical, and biological reaction-diffusion systems. All of these waves propagate out from the spiral center or pacemaker. We report observations of inwardly rotating spirals found in the BZ system dispersed in water droplets of a water-in-oil microemulsion. These "antispirals" were also generated in computer simulations.