Electric-field-induced crack patterns: experiments and simulation

Crack control in dried ferro-colloidal droplets: effect of particle aspect-ratio and magnetic field orientations

Crack formation in dried colloidal films is a common phenomenon encountered in diverse fields, from coatings and materials science to biological and environmental applications. Understanding the mechanisms behind crack patterns and their dependency on external factors is crucial for tailoring deposit structures. In this study, we investigate the impact of an externally directed magnetic field on the crack morphology and self-assembly in dried deposits composed of anisotropically shaped ferro-colloidal particles of varying sizes. Employing a sessile drop configuration, distinct crack patterns are observed in ring-like deposits as the magnetic field is applied in parallel, perpendicular, and oblique orientations. Notably, crack propagation in the oblique field direction transitions from wavy to helical-shaped patterns depending on the size of the nanoparticles, in contrast to the patterns seen in parallel and perpendicular fields. Our findings demonstrate that ferro-colloids align with the magnetic moment along the tensile stress direction, particularly at the edges of the deposits where cracks propagate. The particle orientation and self-assembly in the deposits were controlled by the interaction of hydrodynamic and magnetic forces, with force calculations revealing that this interaction strongly depends on particle size and field angle. This interaction leads to crack alignment along the particle's long axes, emphasizing the influence of the magnetic field on the deposit's structural integrity. Additionally, ferro-colloid concentration significantly impacts crack density, with higher concentrations promoting the development of prominent cracks at the rim edges of the deposits. By leveraging the interplay between magnetic interactions and evaporation dynamics, we can develop novel strategies for manipulating nanoscale structures for advanced technology.

Colloidal droplet desiccation on a electrowetting-on-dielectric (EWOD) platform

The physics of the effects of electric field on the desiccation of colloidal droplets, comprising of dispersed negatively charged nanoparticles [2 μl, 1(w/w. %)], are studied in a standard electrowetting-on-a-dielectric configuration. The extent of contact line pinning during evaporation is found to be a function of the magnitude of the applied voltage and quantified in terms of the dimensionless electrowetting number (η). The pinned contact line led to higher particle compaction as evidenced by the characterization of dried colloidal film thicknesses. Crack formation and their dynamics have been analyzed in detail to elicit the interplay of forces near the contact line region and on the compaction front. These aspects of crack formation are elucidated in the light of magnitude and polarity of the applied electric field. It is found to influence the crack front initiation velocity, the geometry, the number of cracks, and an attempt is made to explain the same via first principle-based approaches. Therefore, this study indicates the possibility of using electrowetting as a technique to fine-tune the crack formation behavior in thin colloidal films.

Three-Dimensional Modeling of Polygonal Ridges in Salt Playas

In this work, we investigate the formation of the curious polygonal salt ridges that tessellate salt playas worldwide using suitable three-dimensional modeling and simulation of the dynamical processes that are responsible for their formation. We employ the principles of fracture mechanics under cyclic wetting and drying, fluid and mass transport in fracture channels, and processes of crystallization and self-organization to finally replicate the almost Voronoidal pattern of salt ridge mosaics observed in playas. The model is generic and applicable to playas having different salt compositions, as the effect of the salt diffusion coefficient and critical salinity for crystallization are factored in. The final pattern of polygonal salt ridges obtained by simulation visually resembles the geometry of the salt ridges reported in the literature. A single equation describing the time of first crystallization of salt in terms of evaporation suction pressure P, diffusion coefficient D of salt, and relative salinity Δc with respect to critical salinity at saturation, has been proposed. The saturation of crystal growth rate is shown to be a dynamic equilibrium between advection and diffusion processes. We show that the stable polygonal geometry of the salt playas is an effort toward the total minimization of system energy.

Morphologies of electric-field-driven cracks in dried dispersions of ellipsoids

We report an experimental and theoretical study of the morphology of desiccation cracks formed in deposits of hematite ellipsoids dried in an externally applied alternating current (ac) electric field. A series of transitions in the crack morphology is observed by modulating the frequency and the strength of the applied field. We also found a clear transition in the morphology of cracks as a function of the aspect ratio of the ellipsoid. We show that these transitions in the crack morphology can be explained by a linear stability analysis of the equation describing the effective dynamics of an ellipsoid placed in an externally applied ac electric field.

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.

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.

Ordered ring-shaped cracks induced by indentation in metal films on soft elastic substrates

Ordered crack patterns contain plentiful physical mechanisms and are useful for technological applications such as lithography, template, and biomimicry. Here we report on ordered multiple ring-shaped cracks induced by indentation in metal films on soft elastic polydimethylsiloxane (PDMS) substrates. It is shown that the indentation triggers the deformation of PDMS substrate and generates a radial tensile stress in the film, leading to the formation of ring-shaped cracks with a nearly uniform spacing. The morphological characteristics and evolution behaviors of the multiple ring-shaped cracks are revealed by optical microscopy, atomic force microscopy, and scanning electron microscopy. Their formation mechanisms are discussed by theoretical analysis based on the fracture mechanics. The report in this work can promote better understanding of the indentation-induced stress anisotropy and mode competition in rigid-film-soft-substrate systems and provide a facile strategy to control the crack patterns by simple mechanical loading.

Branched crack patterns in layers of Laponite® dried under electric fields: Evidence of power-laws and fractal scalin>

In the present work we report crack patterns formed in aqueous Laponite^® gel in a rectangular box, while exposed to a uniform static electric field. The crack pattern shows a very interesting tree-like geometry extending from the positive to the negative electrode. At the positive electrode a large number of cracks appear at first and merge with each other in stages thus forming tree-like fractal structures. These structures are reminiscent of the Bethe lattice or Cayley tree. The "trees" divide the system into peds of varying size, with numerous smaller ones on the positively charged end, gradually increasing in size, and decreasing in number towards the negative end. If the cumulative distribution of the number of peds exceeding a certain area in size, is plotted against that area, a power-law relation is obtained. This implies a scale-invariant fractal character of the pattern. For a given system size, the exponent of the power-law has a nearly constant value for different applied voltages. We present an experimental study demonstrating this behaviour and discuss how it compares with similar distributions of river-basin areas and viscous fingers in a Hele-Shaw cell.

Narrowing Desiccating Crack Patterns by an Azeotropic Solvent for the Fabrication of Nanomesh Electrodes

Desiccation of a colloidal layer produces crack patterns because of stress arising out of solvent evaporation. Associated with it is the rearrangement of particles, while adhesion to the substrate resists such movements. The nature of solvent, which is often overlooked, plays a key role in the process as it dictates evaporation and wetting properties of the colloidal film. Herein, we study the crack formation process by using a mixture of solvents, water, and isopropyl alcohol (IPA). Among the various ratios, a water/IPA mixture (15:85 by volume) close to the azeotropic composition possesses unusual evaporation and wetting properties, leading to narrower cracks with widths down to ∼162 nm, uncommon among the known crackle patterns. The dense and narrow crack patterns have been used as sacrificial templates to obtain metal meshes on transparent substrates for optoelectronic applications.

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.

Formation of desiccation crack patterns in electric fields: a review

Desiccation crack formation is an important and interesting part of the broad area of fracture mechanics. Generation of cracks due to drying depends on ambient conditions, which may include externally applied fields. In this review, we discuss the effect of both direct and alternating electrical fields on desiccation crack formation. After a brief introduction to materials which crack on drying, e.g. colloids, clay and ceramics we discuss how they respond to an electric field. Following that, we present an account of experiments and modelling studies performed on granular pastes or clays drying while exposed to an electric field. Specific patterns formed under different geometries, strengths and frequencies of the electric field are described and explained. The review includes work on cracks formed in clay droplets, where a memory effect has been observed and analysed using a generalized calculus formalism.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Electric field induced gelation in aqueous nanoclay suspensions

Aqueous colloidal LAPONITE® clay suspensions transform spontaneously to a soft solid-like arrested state as its aging or waiting time increases. This article reports the rapid transformation of aqueous LAPONITE® suspensions into soft solids due to the application of a DC electric field. A substantial increase in the speed of solidification at higher electric field strengths is also observed. The electric field is applied across two parallel brass plates immersed in the LAPONITE® suspension. The subsequent solidification that takes place on the surface of the positive electrode is attributed to the dominant negative surface charges on the LAPONITE® particles and the associated electrokinetic phenomena. With increasing electric field strength, a dramatic increase is recorded in the elastic moduli of the samples. These electric field induced LAPONITE® soft solids demonstrate all the typical rheological characteristics of soft glassy materials. They also exhibit a two-step shear melting process similar to that observed in attractive soft glasses. The microstructures of the samples, studied using cryo-scanning electron microscopy (SEM), are seen to consist of percolated network gel-like structures, with the connectivity of the gel network increasing with increasing electric field strengths. In comparison with salt induced gels, the electric field induced gels studied here are mechanically stronger and more stable over longer periods of time.

Crack Patterns in Drying Laponite-NaCl Suspension: Role of the Substrate and a Static Electric Field

We report the formation of crack patterns in drying films of Laponite-NaCl solution. Crack patterns that develop upon drying aqueous Laponite-NaCl solution change drastically as the amount of NaCl is varied in the solution. In this work, we have investigated the effect of NaCl on drying films of aqueous solution of Laponite under two conditions: (i) when the film is bounded by a wall, as in Petri dish experiments and (ii) when the film does not have any boundary, as in experiments with droplets. In order to obtain insights into the effect of the substrate, the experiments have been done with two different substrates of different hydrophobicities, polypropylene and glass. The formation of crack patterns has been explained on the basis of the wetting and spreading properties of the solution on these substrates and the effect of salt on colloidal aggregation. In this work, we have shown that the presence of salt in aqueous Laponite solution can induce crack patterns depending on the nature of the substrate. Another important aspect of this work is the role of NaCl in crack inhibition in desiccating films of aqueous Laponite, in the presence of static electric field. This effect can be utilized to suppress undesirable crack formation in many applications.

Memory effect and anisotropy of particle arrangements in granular paste

It is known that pastes of fine powder, for example those of clay, retain memory of shaking applied early in a drying process. This memory results in the appearance of anisotropic patterns of desiccation cracks after drying. In this work, we find a similar behavior in pastes consisting of large granular particles, specifically cornstarch and Lycopodium spores. Because of the large particle size, we were able to observe particle arrangements in Lycopodium paste with micro-focus X-ray computerized tomography ( μ CT). We prepared pastes consisting of Lycopodium particles and water. Agar was added to the paste in order to allow for solidification during a drying process. In these samples, we found statistical anisotropy induced by shaking applied early in the drying process. This anisotropy possesses a feature that was predicted on the basis of results obtained in previous experimental and theoretical studies.

Magnetic-field-driven crack formation in an evaporated anisotropic colloidal assembly

We report the effect of applied magnetic field on the morphology of cracks formed after evaporation of a colloidal suspension consisting of shape-anisotropic ellipsoidal particles on a glass substrate. The evaporation experiments are performed in sessile drop configuration, which usually leads to accumulation of particles at the drop boundaries, commonly known as the "coffee-ring effect." The coffee-ring-like deposits that accompany cracks are formed in the presence as well as in the absence of magnetic field. However, the crack patterns formed in both cases are found to differ markedly. The direction of cracks in the presence of the magnetic field is found to be governed by the orientation of particles and not solely by the magnetic field direction. Our experimental results show that at the vicinity of cracks the particles are ordered and oriented with their long-axis parallel to crack direction. In addition, we observe that the crack spacing in general increases with the height of the particulate film.

Unstable crack propagation in LAPONITE® gels: selection of a sinusoidal mode in an electric field

We report observation of wavy cracks and naturally patterned fracture surfaces in drying LAPONITE® paste.

Topology of desiccation crack patterns in clay and invariance of crack interface area with thickness

We study the crack patterns developed on desiccating films of suspensions of three different clays-bentonite, halloysite nanoclay and laponite on a glass substrate. Varying the thickness of the layer, h gives the following new and interesting results: i) We can identify a critical thickness h c for bentonite and halloysite, above which isolated cracks join each other to form a fully connected network. ii) A topological analysis involving the Euler number is shown to be useful for characterising the patterns. iii) We find, further, that the total vertical surface area of the clay A v, which has opened up due to cracking, and the total area of the glass substrate A s, exposed by the hierarchical sequence of cracks are constant, independent of the layer thickness for a certain range of h. These results are shown to be consistent with a simple energy conservation argument, neglecting dissipative losses. Finally we show that if the crack pattern is viewed at successively finer resolution, the total cumulative area of cracks visible at a certain resolution scales with the layer thickness.

Effect of Surface Wettability on Crack Dynamics and Morphology of Colloidal Films

The effect of surface wettability on the dynamics of crack formation and their characteristics are examined during the drying of aqueous colloidal droplets (1 μL volume) containing nanoparticles (53 nm mean particle diameter, 1 w/w %). Thin colloidal films, formed during drying, rupture as a result of the evaporation-induced capillary pressure and exhibit microscopic cracks. The crack initiation and propagation velocity as well as the number of cracks are experimentally evaluated for substrates of varying wettability and correlated to their wetting nature. Atomic force and scanning electron microscopy are used to examine the region in the proximity of the crack including the particle arrangements near the fracture zone. The altered substrate-particle Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions, as a consequence of the changed wettability, are theoretically evaluated and found to be consistent with the experimental observations. The resistance of the film to cracking is found to depend significantly on the substrate surface energy and quantified by the critical stress intensity factor, evaluated by analyzing images obtained from confocal microscopy. The results indicate the possibility of controlling crack dynamics and morphology by tuning the substrate wettability.

Dynamical scaling of fragment distribution in drying paste

Crack patterns of drying paste and their statistical properties are investigated through smoothed particle hydrodynamics, which is one method for solving continuum equations in the Lagrangian description. In addition to reproducing a realistic crack pattern, we also find that the average area of a fragment decays inversely with time in the case of linearly increasing desiccation stress. We find that the distribution can be scaled with the average area of the fragment over the corresponding time, even though the distribution function of the fragment area changes the functional form during evolution.

Crack formation under an electric field in droplets of laponite gel: memory effect and scaling relations

When a colloidal gel dries through evaporation, cracks are usually formed, which often reveal underlying processes at work during desiccation. Desiccating colloid droplets of a few hundred microliters size show interesting effects of pattern formation and cracking which makes this an active subject of current research. Because aqueous gels of clay are known to be strongly affected by an electric field, one may expect crack patterns to exhibit a field effect. In the present study we allow droplets of laponite gel to dry under a radial electric field. This gives rise to highly reproducible patterns of cracks, which depend on the strength, direction, and time of exposure to the electric field. For a continuously applied DC voltage, cracks always appear on dissipation of a certain constant amount of energy. If the field is switched off before cracks appear, the observed results are shown to obey a number of empirical scaling relations, which enable us to predict the time of appearance and the number of cracks under specified conditions. Scanning electron microscopy (SEM) images of the surface between the macroscopic cracks show the presence of microcracks, which are wider and more numerous when no electric field is applied. The microcracks are reduced in the presence of stronger fields.