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

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.

Memory of rotation in residual stress of paste

We numerically investigate the stress distribution in pastes after horizontal rotation by using an elastoplastic model. Residual stress remains as a memory of rotation. The stress in the circumferential direction increases after the rotation, whereas that in the radial direction decreases. The residual stress is analytically related to the plastic deformation induced by the rotation. Based on the time evolution of plastic deformation, we theoretically describe the mechanism of the changes in the stress distribution.

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.

Effect of Colloidal Surface Charge on Desiccation Cracks

We report the effect of polarity and surface charge density on the nucleation and growth kinetics of desiccation cracks in deposits of colloids formed by drying. We show that the average spacing between desiccation cracks and crack opening are higher for the deposit of positively charged colloids than that of negatively charged colloids. The temporal evolution of crack growth is found to be faster for positively charged particle deposits. The distinct crack patterns and their kinetics are understood by considering the spatial arrangement of particles in the deposit, which is strongly influenced by the substrate-particle and particle-particle interactions. Interestingly, the crack spacing, the crack opening, and the rate at which the crack widens are found to increase upon decreasing the surface charge of the colloids.

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.

Effect of the Shape of the Confining Boundary and Particle Shape Anisotropy on the Morphology of Desiccation Cracks

The control of the morphology of desiccation cracks is fascinating not only from the application point of view but also from the rich physics behind it. Here, we present a seemingly simple method to tailor the morphology of desiccation cracks by exploitation of the combined effect of particle shape anisotropy and the shape of the confining boundary. This allows us to make circular, square, and triangular-shaped desiccation cracks in the vicinity of the confining boundaries. As the colloidal dispersion dries in confined wells, a drying front appears at the center of the well. With further evaporation, the drying front recedes toward the boundary from the center of the well. We show that the temporal evolution of the drying front is strongly influenced by the shape of the well. Subsequently, desiccation cracks appear in the penultimate stage of drying, and the morphology of the cracks is governed by the shape of the drying front and hence by the shape of the wells. The spatial evolution of the crack pattern is quantified by estimation of the curvature of the cracks, which suggests that the influence of the confining boundary on crack formation is long-ranged. However, the cracks in the dried deposit consisting of spherical particles remain unaffected by the shape of the well, and the cracks are always radial. We establish a one-to-one correspondence between the shape of the drying front and the morphology of the crack pattern in the final dried deposit of ellipsoids.

Scaling mechanical instabilities in drying micellar droplets

Drying-induced mechanical instabilities in aqueous solution droplets occur primarily because, during evaporation, the central liquid minimizes the surface tension by pulling the packed gel-like region, leading to a stretching effect of the liquid region at the receding wet front. Under an appropriate scenario, it finally perturbs the gel-like zone at the droplet periphery, generating cracks, wrinkles, folds, cavities, buckles, etc. Here we report unique wrinkling patterns from evaporating sessile micellar aqueous droplets on rigid and soft substrates kept at temperatures well above the ambient. The wrinkling patterns remarkably vary depending on the material's elastic modulus and substrate, the concentration of the micellar solution (C_CTAB), and the substrate temperature (T_S). In the low concentration regime (C_CTAB ≤ 0.0364 wt%), coffee-ring-like morphologies are observed devoid of any wrinkling morphology irrespective of T_S and the substrate's elastic modulus. In the high initial concentration regime (C_CTAB ≥ 0.0364 wt%), for droplets deposited at T_S ≥ 85 °C, wrinkle formation starts at the droplet peripheral zone, radial on the stiff glass substrate, and annular on the soft cross-linked PDMS substrate. At C_CTAB ≥ 2.73 wt%, radial wrinkles on the glass substrate and annular wrinkles on the cross-linked PDMS substrate nucleate from the edges connecting to the central region of the deposit. The ratio between the width of the gel-like deposit (or wrinkle length) and the droplet's radius scales with the initial concentration of the surfactant and depends on the initial equilibrium contact angle of the micellar droplets. Our results support existing understandings of mechanical instabilities of dried deposits, which satisfies interdependent scaling relationships among their number, lengthscale (dried deposit radius, the wavelength of the wrinkles, and peripheral undulations from Rayleigh-Bénard instability), thickness, and elastic modulus. Interestingly, we found substrate-dependent antagonistic interdependence of the elastic modulus of the dried deposit with the initial surfactant concentration.

Memory effect of external oscillation on residual stress in a paste

We numerically investigate the stress distribution of a paste when an external oscillation is applied. The paste memorizes the oscillation through plastic deformation. Due to the plastic deformation, the residual stress remains after the oscillation, where the residual stress distribution depends on the number of cycles in the oscillation. As this number increases, the symmetry of the stress distribution is enhanced, which is consistent with the crack patterns observed in the experiments using a drying paste.

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.

Particle size and substrate wettability dependent patterns in dried pendant drops

The particle laden sessile drops when dried on solid surfaces under certain conditions leave a deposit pattern wherein all the particles are confined to a narrow region close to the edge of the deposit. Such patterns which often form when coffee drops dry are referred to as the coffee ring patterns or the coffee stains. Recent research points to the formation of intriguing patterns when colloidal particle laden drops are dried in configurations other than sessile mode. In this article, the combined effect of particle size and wettability of the substrate on the patterns formed by drying drops in sessile and pendant configurations is investigated via experiments. Our results demonstrate a transition from coffee ring to central dome-like deposit morphology with decrease in wettability of the substrates when drops containing 3 μm diameter particles are dried in pendent mode. A similar transition in the deposit morphology is observed with increase in the diameter of the particles in pendant drops dried on substrates of near neutral wettability (θ = 86 ± 3°). The influence of particles size, substrate wettability and drop configuration on the kinetics of deposition of particles at the three phase contact line will also be discussed. We compare our experimental observations with particle based simulations wherein the dried patterns are generated by accounting for three particle transport modes, namely, advective particle transport resulting from capillary flow, gravity driven settling of particles and particle capture by descending interface.

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.

Mechanism of memory effect of paste which dominates desiccation crack patterns

When a densely packed colloidal suspension, called a paste, behaves as plastic fluid, it can remember the direction of its motion it has experienced, such as vibrational motion and flow. These memories kept in paste can be visualized as the morphology of crack patterns that appear when the paste is dried. For example, when a paste remembers the direction of vibrational motion, all primary desiccation cracks propagate in the direction perpendicular to the direction of the vibrational motion that the paste has experienced. On the other hand, when a paste remembers the direction of flow motion, all primary cracks propagate along the flow direction. To find out the mechanism of memory effect of vibration, we perform experiments to rewrite memory in paste by applying additional vibration to the paste along a different direction before the paste is dried. By investigating the process of rewriting memory in paste, we find the competitive phenomena between quasi-linear effect and nonlinear effect, which were studied in each theoretical model based on residual tension theories. That is, at the initial stage of the memory-imprinting process of the vibrational motion, the mechanism predicted by the quasi-linear analysis based on residual tension theory holds, but, as the paste is vibrated repeatedly, the mechanism shown by the nonlinear analysis gradually come to play a dominant role in the memory effect.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Tailoring crack morphology in coffee-ring deposits via substrate heating

The drying of a sessile drop consisting of colloidal particles and the formation of particulate deposits with spatially periodic cracks were ubiquitous. The drying induced stress, which is generated during the evaporation of a colloidal drop, is released by the formation of cracks. We find that the morphology of cracks formed in particulate films dried at substrate temperature, T_sub = 25 °C is markedly different from that of cracks formed at T_sub > 45 °C. The cracks are disordered in the former case, but ordered and periodic in the latter. The disorderedness of cracks observed at T_sub = 25 °C is mainly due to the formation of a coffee-ring like particle deposit that exhibits a larger height gradient. The ultimate deposit pattern after complete drying is observed to be different for colloidal dispersion drops evaporated at different substrate temperatures. This is attributed to temperature-dependent solvent flow mechanisms and capillary-driven flow, which occur inside the colloidal drop during the course of drying. In addition, for the coffee-ring-like particulate deposit obtained at T_sub ≤ 45 °C, the ratio between the width of the deposit w and the radius of the ring R scales with the volume fraction of the colloids φ, w/R ∼ φ^0.5, in the range of volume fractions studied in this work. The deposited patterns obtained at temperature T_sub > 45 °C are largely dominated by the capture of particles by the receding liquid-vapor interface. This is due to the faster rate of decrease of the liquid-vapor interface position with an increase in substrate temperature.