&Cartridge; physics 14, 110

A mechanism created by liquid wetting can cause a pleated area in a soft microscale solid to adhere to itself, creating scars on the surface of the material that can control its morphological evolution.

In everyday life we ​​are surrounded by soft materials. Most biological tissues are made of soft materials, which means that they deform easily under typical mechanical loads. Large deformations of soft solids lead to complex morphologies that arise when the free surface succumbs to a compressive force like an accordion. With sufficient pressure, a free interface bends into a fold, creating deep, folded valleys and ultimately regions with self-contacting surfaces. Wrinkles formed by compression in biological tissue permeate nature and include the sulci of the brain and the folds of a flexed elbow. Such wrinkles often remain in the form of a permanent “scar” on the surface of the soft material. However, despite the ubiquity of such features, it is not clear why scars remain when the stress subsides. It is also not clear why a homogeneous, evenly compressed material wrinkles in a particular place. Michiel van Limbeek from the Max Planck Institute for Dynamics and Self-Organization in Germany and his colleagues [1] found that soft materials exposed to repeated deformation cycles develop scars from a fold-unfold asymmetry due to liquid wetting (Fig. 1).

One way previously suggested to explain the appearance and persistence of scars on soft solids is a mechanism observed in other systems such as folded or wrinkled paper [2, 3] . In these cases, permanent weakening or damage changes the mechanical properties of the material locally and makes certain areas susceptible to subsequent wrinkling. Alternatively, the adhesion between the two sides of a fold can cause the surfaces in the fold to stick together, creating a configuration that will persist even when the tension is removed. But neither plastic deformation nor adhesion can explain the sensitivity to liquid-solid surface tension.

To understand the phenomenon of wrinkling in soft materials, van Limbeek and his colleagues carried out an experiment in which a layer of soft polymer gel was applied to a pre-stretched rubber sheet. The soft polymer gel was then immersed in liquids with more or less surface tension. By gradually releasing the tension on the rubber sheet, they compressed the gel layer evenly, one micrometer each time. Eventually the gel surface began to bend and eventually formed a crease when the two sides of the bend came into contact. Then the researchers gradually released the compression, watching how the surface wrinkled – and how it didn’t – when the gel was immersed in various liquids.

Observations of the gel’s surface morphology with confocal microscopy allowed researchers to directly measure the extent and angle of deformation of the gel at the crease. Fluorescently labeled nanoparticles attached to the surface of the gel highlighted the gel-liquid interface, making it possible to continuously monitor the fold when the two sides of the fold were in contact and otherwise inaccessible for direct measurement.

The experiments showed a hysteresis in the response of the fold to compression and relaxation. In particular, the depth of the fold at a given load depended on whether the gel was in the compression or relaxation phase of the cycle. Such a result would be expected if the dynamics of the system were controlled by the adhesion between the two sides. However, adhesion alone cannot explain how the surface profile changed while the entire compression area was applied and removed when the gel was immersed in various liquids. Under compression, the fold resembled the letter Y in cross-section, with the “stem” of the Y representing the self-contacting region and the “arms” representing the folded surface of the gel. When the compression was relaxed, the crease looked more like the letter T, with the surface flexing sharply into the area of ​​self-contact (Fig. 2). The different shapes suggest that the unfolding process required more energy than was actually necessary for the formation of the fold with increasing surface tension. This difference in energy could be explained by the need to overcome surface tension forces in addition to adhesion between the two sides.

The researchers suggest that the role of surface tension in this system corresponds to a phenomenon known in interfacial fluid mechanics as contact line pinning. When a liquid-air interface meets a solid surface – for example a droplet of liquid resting on a table top – the three-phase connection forms what is known as a line of contact. The angle between the tabletop and the tangent to the liquid-air interface can be used to measure the surface tension when the droplet is in equilibrium. When out of balance, this tension drives the line of contact in motion; However, due to tiny surface heterogeneities, the movement of the contact line is often not smooth. Experiments show that on the smallest scales contact lines in fits and beginnings shift because they get stuck locally or stay in place [4] . Van Limbeek’s result shows that the same fixation of a contact line is responsible for the persistence of wrinkles on soft solids.

As systems that exhibit highly nonlinear behavior and large deformation, creases and interfacial creases have become useful tools for investigating such mundane questions as “Why does dried fruit wrinkle?” and as rich as “Why does the brain have wrinkles?” [5] . By identifying another non-linear phenomenon caused by pinning contact lines, van Limbeek and his colleagues have expanded this research toolbox.

The discovery of an alternative mechanism for surface scarring in a manner similar (though not mechanically identical) to how paper wrinkles when it is repeatedly wrinkled [6] could also have practical applications – for example in soft robotic devices that fold [7] or in surface technology for liquid transport [8] . Indeed, one could envision manipulating the surface tension of soft solids in order to “program” their fold pattern to control the transport of liquids over such surfaces. Manipulating the local surface tension of a soft material that can expand through swelling could also provide a way to control its morphological development and thus guide a swelling surface to take on a desired shape [9] . By identifying the key role of the contact line pen in the formation of such wrinkles, van Limbeek and colleagues opened the door to such uses.

## References

1. MA J. van Limbeek et al., “Pinning-induced folding-unfolding asymmetry in adhesive folds”, Phys. Rev. Lett.127, 028001 (2021).
2. T. Tallinen et al., “The effect of plasticity when crumpling thin sheets”, Nat. Mater.8th, 25 (2008).
3. O. Gottesman et al., “Furrows after the expansion of D-cones”, Nat. Come over.6th, 7232 (2015).
4. DM Kaz et al., “Physical aging of the contact line on colloidal particles at liquid interfaces”, Nat. Mater.11, 138 (2011).
5. E. Hohlfeld and L. Mahadevan, “Development of the Sulcus”, Phys. Rev. Lett.106, 105702 (2011).
6. J. Andrejevic et al., “A model for the fragmentation kinetics of crumpled thin sheets”, Nat. Come over.12, 1470 (2021).
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8. M. Coux and JM Kolinski, “Surface textures suppress viscoelastic braking on soft surfaces”, Proc. Natl. Academic Science USA117, 32285 (2020).
9. Y. Klein et al., “Forming elastic plates by specifying non-Euclidean metrics”, science315, 1116 (2007).