Crack patterns over uneven substrates

Crack densification in drying colloidal suspensions

As sessile drops of aqueous colloidal suspensions dry, a close-packed particle deposit forms that grows from the edge of the drop toward the center. To compensate for evaporation over the solid's surface, water flows radially through the deposit, generating a negative pore pressure in the deposit associated with tensile drying stresses that induce the formation of cracks. As these stresses increase during drying, existing cracks propagate and additional cracks form, until the crack density eventually saturates. We rationalize the dynamics of crack propagation and crack densification with a local energy balance between the elastic energy released by the crack, the energetic cost of fracture, and the elastic energy released by previously formed cracks. We show that the final spacing between radial cracks is proportional to the local thickness of the deposit, while the aspect ratio of the crack segments depends on the shape of the deposit.

Assisting and eliminating memory effects of paste by adding polysaccharides

A densely packed colloidal suspension, called a paste, is known to remember the direction of its motion because of its plasticity. Because the memory in the paste determines the preferential direction for crack propagation, the desiccation crack pattern morphology depends on memory of its motions (memory effect of paste). Two types of memory effects are memory of vibration and memory of flow. When a paste is dried, it usually shows an "isotropic and random cellular" desiccation crack pattern. However, when a paste is vibrated before drying and it remembers the direction of its vibrational motion, primary desiccation cracks propagate in a direction perpendicular to its vibrational motion before drying (memory of vibration). Once it flows and remembers the direction of its flow motion, primary desiccation cracks propagate in the direction parallel to its flow motion (memory of flow). Anisotropic network formation via interparticle attraction among colloidal particles in a suspension is the dominant factor affecting a paste's memory of its motion. Calcium carbonate (CaCO_{3}) paste remembers the direction of its vibrational motion, but not its own flow direction because Coulombic repulsion among charged CaCO_{3} colloidal particles prevents the formation of a network structure in a flow. For this study, we strove to assist and eliminate CaCO_{3} paste memory effects by adding polysaccharides. First, to characterize memory in paste, we propose a method of image analysis to quantify the strength and the direction of the anisotropy of desiccation crack patterns using Shannon's information entropy. Next, we conduct experiments to add polysaccharide to CaCO_{3} paste, revealing that the addition of a small amount of polysaccharide to CaCO_{3} paste assists the paste in remembering its own flow motion. Findings also indicate that the addition of a large amount of polysaccharide prevents the formation of both memories of its flow and vibrational motion and eliminates the memory effects of paste. We then perform "flocculation and sedimentation" experiments to investigate the interaction among CaCO_{3} colloidal particles in a solution. Results show that, in an aqueous solution with low polysaccharide concentration, CaCO_{3} colloidal particles flocculate each other and quickly form a sediment in a short time, whereas, in an aqueous solution with high polysaccharide concentration, a longer time is necessary for flocculation and sedimentation. Because the addition of small amounts of polysaccharides to CaCO_{3} paste induces polymer bridging between colloidal particles as interparticle attraction, it helps to produce a macroscopic network structure which retains memory of its flow motion and thereby assists the formation of memory of flow, whereas the addition of large amounts of polysaccharides induces interparticle repulsion, which prevents the formation of memory effects of all types.

Self-organized mud cracking amplifies the resilience of an iconic "Red Beach" salt marsh

Self-organized patterning, resulting from the interplay of biological and physical processes, is widespread in nature. Studies have suggested that biologically triggered self-organization can amplify ecosystem resilience. However, if purely physical forms of self-organization play a similar role remains unknown. Desiccation soil cracking is a typical physical form of self-organization in coastal salt marshes and other ecosystems. Here, we show that physically self-organized mud cracking was an important facilitating process for the establishment of seepweeds in a "Red Beach" salt marsh in China. Transient mud cracks can promote plant survivorship by trapping seeds, and enhance germination and growth by increasing water infiltration in the soil, thus facilitating the formation of a persistent salt marsh landscape. Cracks can help the salt marsh withstand more intense droughts, leading to postponed collapse and faster recovery. These are indications of enhanced resilience. Our work highlights that self-organized landscapes sculpted by physical agents can play a critical role in ecosystem dynamics and resilience to climate change.

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.

Crack morphologies in drying suspension drops

A drop of an aqueous suspension of nanoparticles placed on a substrate forms a solid deposit as it dries. For dilute suspensions, particles accumulate within a narrow ring at the drop edge, whereas a uniform coating covering the entire wetted area forms for concentrated suspensions. In between these extremes, we report two additional regimes characterized by non-uniform deposit thicknesses and by distinct crack morphologies. We show that both the deposit shape and the number of cracks are controlled exclusively by the initial particle volume fraction. The different regimes share a common avalanche-like crack propagation dynamics, as a result of the delamination of the deposit from the substrate.

From Chaos to Control: Programmable Crack Patterning with Molecular Order in Polymer Substrates

Cracks are typically associated with the failure of materials. However, cracks can also be used to create periodic patterns on the surfaces of materials, as observed in the skin of crocodiles and elephants. In synthetic materials, surface patterns are critical to micro- and nanoscale fabrication processes. Here, a strategy is presented that enables freely programmable patterns of cracks on the surface of a polymer and then uses these cracks to pattern other materials. Cracks form during deposition of a thin film metal on a liquid crystal polymer network (LCN) and follow the spatially patterned molecular order of the polymer. These patterned sub-micrometer scale cracks have an order parameter of 0.98 ± 0.02 and form readily over centimeter-scale areas on the flexible substrates. The patterning of the LCN enables cracks that turn corners, spiral azimuthally, or radiate from a point. Conductive inks can be filled into these oriented cracks, resulting in flexible, anisotropic, and transparent conductors. This materials-based processing approach to patterning cracks enables unprecedented control of the orientation, length, width, and depth of the cracks without costly lithography methods. This approach promises new architectures of electronics, sensors, fluidics, optics, and other devices with micro- and nanoscale features.

Universal scaling of polygonal desiccation crack patterns

Polygonal desiccation crack patterns are commonly observed in natural systems. Despite their quotidian nature, it is unclear whether similar crack patterns which span orders of magnitude in length scales share the same underlying physics. In thin films, the characteristic length of polygonal cracks is known to monotonically increase with the film thickness; however, existing theories that consider the mechanical, thermodynamic, hydrodynamic, and statistical properties of cracking often lead to contradictory predictions. Here we experimentally investigate polygonal cracks in drying suspensions of micron-sized particles by varying film thickness, boundary adhesion, packing fraction, and solvent. Although polygonal cracks were observed in most systems above a critical film thickness, in cornstarch-water mixtures, multiscale crack patterns were observed due to two distinct desiccation mechanisms. Large-scale, primary polygons initially form due to capillary-induced film shrinkage, whereas small-scale, secondary polygons appear later due to the deswelling of the hygroscopic particles. In addition, we find that the characteristic area of the polygonal cracks, A_{p}, obeys a universal power law, A_{p}=αh^{4/3}, where h is the film thickness. By quantitatively linking α with the material properties during crack formation, we provide a robust framework for understanding multiscale polygonal crack patterns from microscopic to geologic scales.

Entropy Signature for Crack Networks in Old Paintings: Saturation Prospectus

In desiccated films, particularly with old paintings, molecular bonds may break to create intricate patterns of macroscopic cracks. The resulting directions of the cracks quantifiably enable an evaluation of the entropy and degree of disorder in the network. Experimental tests on prepared samples and a two-interacting-variables model allow the evolution of entropy to be tracked. Calculations were performed, primarily using data from the painting Girl with a Pearl Earring by Vermeer, revealing that the left side of the girl's face features a crack structure with higher entropy (or less order) than the right side. Other old paintings were considered. The extrapolation of experiments to these old paintings confirms that saturation still is not reached.

Drying colloidal systems: Laboratory models for a wide range of applications

The drying of complex fluids provides a powerful insight into phenomena that take place on time and length scales not normally accessible. An important feature of complex fluids, colloidal dispersions and polymer solutions is their high sensitivity to weak external actions. Thus, the drying of complex fluids involves a large number of physical and chemical processes. The scope of this review is the capacity to tune such systems to reproduce and explore specific properties in a physics laboratory. A wide variety of systems are presented, ranging from functional coatings, food science, cosmetology, medical diagnostics and forensics to geophysics and art.

Cracking pattern of tissue slices induced by external extension provides useful diagnostic information

Although biopsy is one of the most important methods for diagnosis in diseases, there is ambiguity based on the information obtained from the visual inspection of tissue slices. Here, we studied the effect of external extension on tissue slices from mouse liver with different stages of disease: Healthy normal state, Simple steatosis, Non-alcoholic steatohepatitis and Hepatocellular carcinoma. We found that the cracking pattern of a tissue slice caused by extension can provide useful information for distinguishing among the disease states. Interestingly, slices with Hepatocellular carcinoma showed a fine roughening on the cracking pattern with a characteristic length of the size of cells, which is much different than the cracking pattern for slices with non-cancerous steatosis, for which the cracks were relatively straight. The significant difference in the cracking pattern depending on the disease state is attributable to a difference in the strength of cell-cell adhesion, which would be very weak under carcinosis. As it is well known that the manner of cell-cell adhesion neatly concerns with the symptoms in many diseases, it may be promising to apply the proposed methodology to the diagnosis of other diseases.

Arcuate wrinkling on stiff film/compliant substrate induced by thrust force with a controllable micro-probe

Wrinkling patterns are widely observed in nature and can be used in many high-tech applications such as microfluidic channel, self-assembly ordered microstructures and improved adhesives. In order to use the wrinkling patterns for these applications, it is necessary to precisely control the formation and geometry of the wrinkles. In this paper, we investigate the localized wrinkling of a stiff film/compliant substrate system subjected to a thrust force with a controllable micro-probe. A thin Au film is deposited onto a thick PDMS substrate attached to a glass to form the stiff film/compliant substrate system. And a micro-probe is controlled by a piezoelectric microrobotic system to exert a point force onto the stiff film/compliant substrate to demonstrate the evolution of the localized wrinkles. The experiments show that the film will wrinkle into orthoradial morphology spontaneously when it is deformed in the vertical direction, and then it will wrinkle into arcuate morphology with deformation in the horizontal direction. Since the compressive stress and tensile stress of the film are generated simultaneously, the evolution of the arcuate wrinkles is always accompanied by some radial cracks. The morphological characteristic, formation mechanism and dynamic evolution of the arcuate wrinkles are demonstrated and discussed in detail.

Morphometric analysis of polygonal cracking patterns in desiccated starch slurries

We investigate the geometry of two-dimensional polygonal cracking that forms on the air-exposed surface of dried starch slurries. Two different kinds of starches, made from potato and corn, exhibited distinguished crack evolution, and there were contrasting effects of slurry thickness on the probability distribution of the polygonal cell area. The experimental findings are believed to result from the difference in the shape and size of starch grains, which strongly influence the capillary transport of water and tensile stress field that drives the polygonal cracking.

Stress-induced surface instabilities and defects in thin films sputter deposited on compliant substrates

Existing analyses predict that thin metal films deposited on compliant substrates are subject to a variety of surface instabilities, such as wrinkles, folds, creases, etc., that become more prominent with increased compressive residual stress. Under compressive stress, cracks have been assumed to form only when the interfacial strength is weak, allowing the film to detach from the substrate. In this work, we demonstrate that cracks also form on surfaces under compressive mismatch strain when the interface is strong. In particular, we consider metal alloy films sputter deposited under bias on elastomers with different thicknesses, curing temperatures or surface treatments. The deposition parameters created residual compressive strains and strong adhesion in the bilayers. Samples without surface treatment formed wrinkles and through-thickness cracks at 0.25-0.4% mismatch strains. Only through-thickness cracks were observed in UV treated samples. The crack spacing was found to decrease by a factor of 4 when the surface was UV treated and by a factor of 3 as the elastomer thickness decreased from 30 to 6 μm. Cracks penetrated through the elastomer, 15-30 times deeper than the film thickness, and formed in all samples with a brittle coating. A numerical model was developed to explain the formation of through-thickness cracks and wrinkles under applied compressive mismatch strains. The model suggests that cracks can initiate from the peak of wrinkles when the critical fracture strength of the coating is exceeded. For the UV treated samples, through-thickness cracks are possibly impacted by the formation of an embrittled near surface PDMS layer.

Drying paint: from micro-scale dynamics to mechanical instabilities

Charged colloidal dispersions make up the basis of a broad range of industrial and commercial products, from paints to coatings and additives in cosmetics. During drying, an initially liquid dispersion of such particles is slowly concentrated into a solid, displaying a range of mechanical instabilities in response to highly variable internal pressures. Here we summarize the current appreciation of this process by pairing an advection-diffusion model of particle motion with a Poisson-Boltzmann cell model of inter-particle interactions, to predict the concentration gradients in a drying colloidal film. We then test these predictions with osmotic compression experiments on colloidal silica, and small-angle X-ray scattering experiments on silica dispersions drying in Hele-Shaw cells. Finally, we use the details of the microscopic physics at play in these dispersions to explore how two macroscopic mechanical instabilities-shear-banding and fracture-can be controlled.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Mean-field crack networks on desiccated films and their applications: Girl with a Pearl Earring

Usual requirements for bulk and fissure energies are considered in obtaining the interdependence among external stress, thickness and area of crack polygons in desiccated films. The average area of crack polygons increases with thickness as a power-law of 4/3. The sequential fragmentation process is characterized by a topological factor related to a scaling finite procedure. Non-sequential overly tensioned (prompt) fragmentation is briefly discussed. Vermeer's painting, Girl with a Pearl Earring, is considered explicitly by using computational image tools and simple experiments and applying the proposed theoretical analysis. In particular, concerning the source of lightened effects on the girl's face, the left/right thickness layer ratio (≈1.34) and the stress ratio (≈1.102) are evaluated. Other master paintings are briefly considered.

NET: a new framework for the vectorization and examination of network data

Background

The analysis of complex networks both in general and in particular as pertaining to real biological systems has been the focus of intense scientific attention in the past and present. In this paper we introduce two tools that provide fast and efficient means for the processing and quantification of biological networks like Drosophila tracheoles or leaf venation patterns: the Network Extraction Tool (NET) to extract data and the Graph-edit-GUI (GeGUI) to visualize and modify networks.

Results

NET is especially designed for high-throughput semi-automated analysis of biological datasets containing digital images of networks. The framework starts with the segmentation of the image and then proceeds to vectorization using methodologies from optical character recognition. After a series of steps to clean and improve the quality of the extracted data the framework produces a graph in which the network is represented only by its nodes and neighborhood-relations. The final output contains information about the adjacency matrix of the graph, the width of the edges and the positions of the nodes in space. NET also provides tools for statistical analysis of the network properties, such as the number of nodes or total network length. Other, more complex metrics can be calculated by importing the vectorized network to specialized network analysis packages.

GeGUI is designed to facilitate manual correction of non-planar networks as these may contain artifacts or spurious junctions due to branches crossing each other. It is tailored for but not limited to the processing of networks from microscopy images of Drosophila tracheoles.

Conclusion

The networks extracted by NET closely approximate the network depicted in the original image. NET is fast, yields reproducible results and is able to capture the full geometry of the network, including curved branches. Additionally GeGUI allows easy handling and visualization of the networks.

Electronic supplementary material

The online version of this article (doi:10.1186/s13029-017-0064-3) contains supplementary material, which is available to authorized users.