Scaling Law for Cracking in Shrinkable Granular Packings

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.

Scaling laws to predict humidity-induced swelling and stiffness in hydrogels

From pasta to biological tissues to contact lenses, gel and gel-like materials inherently soften as they swell with water. In dry, low-relative-humidity environments, these materials stiffen as they de-swell with water. Here, we use semi-dilute polymer theory to develop a simple power-law relationship between hydrogel elastic modulus and swelling. From this relationship, we predict hydrogel stiffness or swelling at arbitrary relative humidities. Our close predictions of properties of hydrogels across three different polymer mesh families at varying crosslinking densities and relative humidities demonstrate the validity and generality of our understanding. This predictive capability enables more rapid material discovery and selection for hydrogel applications in varying humidity environments.

Time Evolution and Spatial Hierarchy of Crack Patterns

Cracks generated due to desiccation of wet colloidal systems are ubiquitous, examples being nanomaterial films, painted walls, cemented floors, mud fields, river beds, and even giant rocks. In all such cases, crack patterns are often appreciably similar but for the length and time scales, which can be widely differing. In this work, we have examined the crack formation more closely to see if there exists some generality with regard to the length scale of parameters and the formation time. Specifically, using a commonly used colloidal dispersion and optimized conditions to form polygonal network patterns rather than isolated cracks (films of subcritical thickness), we have studied the time evolution of the pattern parameters, the area occupied by the cracks, their lengths, and the widths. As is well known, initially, a network of cracks forms, which we term as the primary generation, followed by interconnecting cracks inside the polygonal regions (secondary) and, later, cracks spreading in local regions (tertiary). We find that the area and the width increase nearly linearly with time with the change in the slope corresponding to the change in the generation. When normalized with respect to the final values, the trends obtained for different film thicknesses overlap, the only exception being the pattern containing unconnected cracks. Thus, the time evolution of cracks is shown to be predictable based on width filtering. Including the angle between cracks as further input into the recursive model, the possibility of identifying the hierarchy of crack segments is also shown. The approach may be useful in determining the age, authenticity, and details of old paintings, understanding the stress profile of geological rocks, and analyzing various natural and manmade hierarchical structures.

Under pressure: Hydrogel swelling in a granular medium

Hydrogels hold promise in agriculture as reservoirs of water in dry soil, potentially alleviating the burden of irrigation. However, confinement in soil can markedly reduce the ability of hydrogels to absorb water and swell, limiting their widespread adoption. Unfortunately, the underlying reason remains unknown. By directly visualizing the swelling of hydrogels confined in three-dimensional granular media, we demonstrate that the extent of hydrogel swelling is determined by the competition between the force exerted by the hydrogel due to osmotic swelling and the confining force transmitted by the surrounding grains. Furthermore, the medium can itself be restructured by hydrogel swelling, as set by the balance between the osmotic swelling force, the confining force, and intergrain friction. Together, our results provide quantitative principles to predict how hydrogels behave in confinement, potentially improving their use in agriculture as well as informing other applications such as oil recovery, construction, mechanobiology, and filtration.