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Structural colors are produced by wavelength-dependent scattering of light from nanostructures. While living organisms often exploit phase separation to directly assemble structurally colored materials from macromolecules, synthetic structural colors are typically produced in a two-step process involving the sequential synthesis and assembly of building blocks. Phase separation is attractive for its simplicity, but applications are limited due to a lack of robust methods for its control. A central challenge is to arrest phase separation at the desired length scale. Here, we show that solid-state polymerization-induced phase separation can produce stable structures at optical length scales. In this process, a polymeric solid is swollen and softened with a second monomer. During its polymerization, the two polymers become immiscible and phase separate. As free monomer is depleted, the host matrix resolidifies and arrests coarsening. The resulting polymeric composites have a blue or white appearance. We compare these biomimetic nanostructures to those in structurally-colored feather barbs, and demonstrate the flexibility of this approach by producing structural color in filaments and large sheets., Soft Matter, 17 (23), ISSN:1744-683X, ISSN:1744-6848

We characterize the mechanical recovery of compliant silicone gels following adhesive contact failure. We establish broad, stable adhesive contacts between rigid microspheres and soft gels, then stretch the gels to large deformations by pulling quasi-statically on the contact. Eventually, the adhesive contact begins to fail, and ultimately slides to a final contact point on the bottom of the sphere. Immediately after detachment, the gel recoils quickly with a self-similar surface profile that evolves as a power law in time, suggesting that the adhesive detachment point is singular. The singular dynamics we observe are consistent with a relaxation process driven by surface stress and slowed by viscous flow through the porous, elastic network of the gel. Our results emphasize the importance of accounting for both the liquid and solid phases of gels in understanding their mechanics, especially under extreme deformation.

Single particle tracking has found broad applications in the life and physical sciences, enabling the observation and characterization of nano- and microscopic motion. Fluorescence-based approaches are ideally suited for high-background environments, such as tracking lipids or proteins in or on cells, due to superior background rejection. Scattering-based detection is preferable when localization precision and imaging speed are paramount due to the in principle infinite photon budget. Here, we show that micromirror-based total internal reflection dark field microscopy enables background suppression previously only reported for interferometric scattering microscopy, resulting in nanometer localization precision at 6 μs exposure time for 20 nm gold nanoparticles with a 25 × 25 μm2 field of view. We demonstrate the capabilities of our implementation by characterizing sub-nanometer deterministic flows of 20 nm gold nanoparticles at liquid–liquid interfaces. Our results approach the optimal combination of background suppression, localization precision, and temporal resolution achievable with pure scattering-based imaging and tracking of nanoparticles at interfaces., ACS Photonics, 8 (10), ISSN:2330-4022

We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu et al. 2018 Soft Matter 14, 916–920 (doi:10.1039/C7SM02431B)). Following a Green’s function approach, we extend the surface-stress regularized Flamant–Cerruti problem to account for uniaxial pre-strains of the substrate. Surface profiles, including the heights and opening angles of wetting ridges, are provided for linearized and finite kinematics. We fit experimental wetting ridge shapes as a function of applied strain using two free parameters, the surface Lamé coefficients. In comparison with experiments, we find that observed opening angles are more accurately captured using finite kinematics, especially with increasing levels of applied pre-strain. These fits qualitatively agree with the results of Xu et al ., but revise values of the surface elastic constants.

The surface of soft solids carries a surface stress that tends to flatten surface profiles. For example, surface features on a soft solid, fabricated by moulding against a stiff-patterned substrate, tend to flatten upon removal from the mould. In this work, we derive a transfer function in an explicit form that, given any initial surface profile, shows how to compute the shape of the corresponding flattened profile. We provide analytical results for several applications including flattening of one-dimensional and two-dimensional periodic structures, qualitative changes to the surface roughness spectrum, and how that strongly influences adhesion.

Switchable adhesives have the potential to improve the manufacturing and recycling of parts, and to enable new modes of motility for soft robots. Here, we demonstrate magnetically-switchable adhesion of a two-phase composite to non-magnetic objects. The composite's continuous phase is a silicone elastomer, and the dispersed phase is a magneto-rheological fluid. The composite is simple to prepare, and to mold into different shapes. When a magnetic field is applied, the magneto-rheological fluid develops a yield stress, which dramatically enhances the composite's adhesive properties. We demonstrate up to a nine-fold increase of the pull-off force of non-magnetic objects in the presence of a 250 mT field., Soft Matter, 16 (25), ISSN:1744-683X, ISSN:1744-6848

Phase separated macromolecules play essential roles in many biological and synthetic systems. Physical characterization of these systems can be challenging because of limited sample volumes, particularly for phase-separated proteins. Here, we demonstrate that a classic method for measuring the surface tension of liquid droplets, based on the analysis of the shape of a sessile droplet, can be effectively scaled down to measure the interfacial tension between a macromolecule-rich droplet phase and its co-existing macromolecule-poor continuous phase. The connection between droplet shape and surface tension relies on the density difference between the droplet and its surroundings. This can be determined with small sample volumes in the same setup by measuring the droplet sedimentation velocity. An interactive MATLAB script for extracting the capillary length from a droplet image is included in the ESI.

Michael Bartlett and Robert Style introduce the Soft Matter themed collection on liquid composites.

Recent experiments have reported that the surface stress of soft elastic solids can increase rapidly with surface strain. For example, when a small hard sphere in adhesive contact with a soft silicone gel is slowly retracted from its rest position, it was found that the retraction force versus displacement relation cannot be explained either by the Johnson-Kendall-Roberts (JKR) theory or a recent indentation theory based on an isotropic surface stress that is independent of surface strain. In this paper, we address this problem using a finite element method to simulate the retraction process. Our numerical model does not have the restrictions of the aforementioned theories; that is, it can handle large nonlinear elastic deformation as well as a surface-strain-dependent surface stress. Our simulation is in good agreement with experimental force versus displacement data with no fitting parameters. Therefore, our results lend further support to the claim that significant strain-dependent surface stresses can occur in simple soft elastic gels. However, significant challenges remain in the reconciliation of theory and experiments, particularly regarding the geometry of the contact and substrate deformation.

With a specific stimulus, shape-memory materials can assume a temporary shape and subsequently recover their original shape, a functionality that renders them relevant for applications in fields such as biomedicine, aerospace, and wearable electronics. Shape-memory in polymers and composites is usually achieved by exploiting a thermal transition to program a temporary shape and subsequently recover the original shape. This may be problematic for heat-sensitive environments, and when rapid and uniform heating is required. In this work, a soft magnetic shape-memory composite is produced by encasing liquid droplets of magneto-rheological fluid into a poly(dimethylsiloxane) matrix. Under the influence of a magnetic field, this material undergoes an exceptional stiffening transition, with an almost 30-fold increase in shear modulus. Exploiting this transition, fast and fully reversible magnetic shape-memory is demonstrated in three ways, by embossing, by simple shear, and by unconstrained 3D deformation. Using advanced synchrotron X-ray tomography techniques, the internal structure of the material is revealed, which can be correlated with the composite stiffening and shape-memory mechanism. This material concept, based on a simple emulsion process, can be extended to different fluids and elastomers, and can be manufactured with a wide range of methods.

In the dilute limit Eshelby's inclusion theory captures the behavior of a wide range of systems and properties. However, because Eshelby's approach neglects interfacial stress, it breaks down in soft materials as the inclusion size approaches the elastocapillarity length $L$. Here, we use a three-phase generalized self-consistent method to calculate the elastic moduli of composites comprised of an isotropic, linear-elastic compliant solid hosting a spatially random monodisperse distribution of spherical liquid droplets. As opposed to similar approaches, we explicitly capture the liquid-solid interfacial stress when it is treated as an isotropic, strain-independent surface tension. Within this framework, the composite stiffness depends solely on the ratio of the elastocapillarity length $L$ to the inclusion radius $R$. Independent of inclusion volume fraction, we find that the composite is stiffened by the inclusions whenever $R < 3L/2$. Over the same range of parameters, we compare our results with alternative approaches (dilute and Mori-Tanaka theories that include surface tension). Our framework can be easily extended to calculate the composite properties of more general soft materials where surface tension plays a role.

Soft materials with a liquid component are an emerging paradigm in materials design. The incorporation of a liquid phase, such as water, liquid metals, or complex fluids, into solid materials imparts unique properties and characteristics that emerge as a result of the dramatically different properties of the liquid and solid. Especially in recent years, this has led to the development and study of a range of novel materials with new functional responses, with applications in topics including soft electronics, soft robotics, 3D printing, wet granular systems and even in cell biology. Here a review of solid–liquid composites, broadly defined as a material system with at least one, phase-separated liquid component, is provided and discussed their morphology and fabrication approaches, their emergent mechanical properties and functional response, and the broad range of their applications. © 2020 Wiley-VCH GmbH ISSN:1616-3028 ISSN:1616-301X

In the fall of 2015, Martin Muser suggested a Contact Mechanics Challenge for the Tribology community. The challenge was an ambitious effort to compare a wide variety of theoretical and computational contact-mechanics approaches, and involved researchers voluntarily tackling the same hypothetical contact problem. The result is an impressive collection of innovative approaches – including a surprise experimental effort – that highlight the continuing importance of surface contact mechanics and the challenges of solving these large-scale problems. Here, we describe how the Contact Mechanics Challenge also reveals exciting opportunities for the Soft Matter community to engage intensely with classical and emerging problems in tribology, surface science, and contact mechanics.

Recent experiments have shown that surface stresses in soft materials can have a significant strain-dependence. Here we explore the implications of this surface elasticity to show how, and when, we expect it to arise. We develop the appropriate boundary condition, showing that it simplifies significantly in certain cases. We show that surface elasticity's main role is to stiffen a solid surface's response to in-plane tractions, in particular at length-scales smaller than a characteristic elastocapillary length. We also investigate how surface elasticity affects the Green's-function problem of a line force on a flat, incompressible, linear-elastic substrate. There are significant changes to this solution, especially in that the well-known displacement singularity is regularised. This raises interesting implications for soft phenomena like wetting contact lines, adhesion and friction. Finally, we discuss open questions, future directions, and close ties with existing fields of research.

Soft particles can be better emulsifiers than hard particles because they stretch at fluid interfaces. This deformation can increase adsorption energies by orders of magnitude relative to rigid particles. The deformation of a particle at an interface is governed by a competition of bulk elasticity and surface tension. When particles are partially wet by the two liquids{} deformation is localized within a material dependent distance L from the contact line. At the contact line{} the particle morphology is given by a balance of surface tensions. When the particle radius R [double less than] L{} the particle adopts a lenticular shape identical to that of an adsorbed fluid droplet. Particle deformations can be elastic or plastic{} depending on the relative values of the Young modulus{} E{} and yield stress{} [sigma]p. When surface tensions favour complete spreading of the particles at the interface{} plastic deformation can lead to unusual fried egg morphologies. When deformable particles have surface properties that are very similar to one liquid phase{} adsorption can be extremely sensitive to small changes of their affinity for the other liquid phase. These findings have implications for the adsorption of microgel particles at fluid interfaces and the performance of stimuli responsive Pickering emulsions.

Solid interfaces have intrinsic elasticity. However, in most experiments, this is obscured by bulk stresses. Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched substrate, we measure two surface-elastic constants that quantify the linear dependence of the surface stress of a soft polymer gel on its strain. With these two parameters, one can predict surface stresses for general deformations of the material in the linear-elastic limit., 5 pages, 4 figures

We study the freezing of a dispersion of colloidal silica particles in water, focusing on the formation of segregated ice in the form of ice lenses. Local temperature measurements in combination with video microscopy give insight into the rich variety of factors that control ice lens formation. We observe the initiation of the lenses, their growth morphology and their final thickness and spacing, over a range of conditions, in particular the effect of the particle packing and the cooling rate. We find that increasing the particle density drastically reduces the thickness of lenses, but has little effect on the lens spacing. Therefore, the fraction of segregated ice formed reduces. The effect of the cooling rate, which is the product of the temperature gradient and the pulling speed across the temperature gradient, depends on which parameter is varied. A larger temperature gradient causes ice lenses to be initiated more frequently, while a lower pulling speed allows for more time for ice lenses to grow: both increase the fraction of segregated ice. Surprisingly, we find that the growth rate of a lens does not depend on its undercooling. Finally, we have indications of pore ice in front of the warmest ice lens, which has important consequences for the interpretation of the measured trends. Our findings have important consequences for ice segregation occurring in a wide range of situations, ranging from model lab experiments and theories, to geological and industrial processes, like frost heave and frozen food production.

Surface stress, also known as surface tension, is a fundamental material property of any interface. However, measurements of solid surface stress in traditional engineering materials, such as metals and oxides, have proven to be very challenging. Consequently, our understanding relies heavily on untested theories, especially regarding the strain dependence of this property. Here, we take advantage of the high compliance and large elastic deformability of a soft polymer gel to directly measure solid surface stress as a function of strain. As anticipated by theoretical work for metals, we find that the surface stress depends on the strain via a surface modulus. Remarkably, the surface modulus of our soft gels is many times larger than the zero-strain surface tension. This suggests that surface stresses can play a dominant role in solid mechanics at larger length scales than previously anticipated., Nature Communications, 8, ISSN:2041-1723

Surface stresses have recently emerged as a key player in the mechanics of highly compliant solids. The classic theories of contact mechanics describe adhesion with a compliant substrate as a competition between surface energies driving deformation to establish contact and bulk elasticity resisting this. However, it has recently been shown that surface stresses provide an additional restoring force that can compete with and even dominate over elasticity in highly compliant materials, especially when length scales are small compared to the ratio of the surface stress to the elastic modulus, Υ/E. Here, we investigate experimentally the contribution of surface stresses to the total force of adhesion. We find that the elastic and capillary contributions to the adhesive force are of similar magnitude and that both are required to account for measured adhesive forces between rigid silica spheres and compliant, silicone gels. Notably, the strain dependence of the solid surface stress contributes to the stiffness of soft solid contacts at leading order., Physical Review X, 7 (4), ISSN:2160-3308

We investigate the mechanical behavior of particle-stabilized droplets using micropipette aspiration. We observe that droplets stabilized with amphiphilic dumbbell-shaped particles exhibit a two-stage response to increasing suction pressure. Droplets first drip, then wrinkle and buckle like an elastic shell. While particles have a dramatic impact on the mechanism of failure, the mechanical strength of the droplets is only modestly increased. On the other hand, droplets coated with the molecular surfactant Sodium Dodecyl Sulfate are even weaker than bare droplets. In all cases, the magnitude of the critical pressure for the onset of instabilities is set by the fluid surface tension.

It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play a central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresses play an important role. We highlight how surface stresses cause dramatic departures from classic theories for wetting (Young–Dupré), adhesion (Johnson–Kendall–Roberts), and composites (Eshelby). A common thread is the importance of the ratio of surface stress to an elastic modulus, which defines a length scale below which surface stresses can dominate.

Soft solids differ from stiff solids in an important way: their surface stresses can drive large deformations. Based on a topical workshop held in the Lorentz Center in Leiden, this Opinion highlights some recent advances in the growing field of solid capillarity and poses key questions for its advancement., Comment: 5 pages, 1 figure

In the classic theory of solid adhesion, surface energy drives deformation to increase contact area while bulk elasticity opposes it. Recently, solid surface stress has been shown also to play an important role in opposing deformation of soft materials. This suggests that the contact line in soft adhesion should mimic that of a liquid droplet, with a contact angle determined by surface tensions. Consistent with this hypothesis, we observe a contact angle of a soft silicone substrate on rigid silica spheres that depends on the surface functionalization but not the sphere size. However, to satisfy this wetting condition without a divergent elastic stress, the gel separates from its solvent near the contact line. This creates a four-phase contact zone with two additional contact lines hidden below the surface of the substrate. While the geometries of these contact lines are independent of the size of the sphere, the volume of the phase-separated region is not, but rather depends on the indentation volume. These results indicate that theories of adhesion of soft gels need to account for both the compressibility of the gel network and a non-zero surface stress between the gel and its solvent., Comment: 6 pages, 3 figures

Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites—i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori–Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, R , to an elastocapillary lengthscale, L . Interfacial tension substantially impacts the effective elastic moduli of the composite when R / L ≲ 100 . When R L /2 ( R =3 L /2) liquid inclusions stiffen (cloak the far-field signature of) the solid.

Johnson-Kendall-Robert (JKR) theory is the basis of modern contact mechanics. It describes how two deformable objects adhere together, driven by adhesion energy and opposed by elasticity. However, it does not include solid surface tension, which also opposes adhesion by acting to flatten the surface of soft solids. We tested JKR theory to see if solid surface tension affects indentation behaviour. Using confocal microscopy, we characterised the indentation of glass particles into soft, silicone substrates. While JKR theory held for particles larger than a critical, elastocapillary lengthscale, it failed for smaller particles. Instead, adhesion of small particles mimicked the adsorption of particles at a fluid interface, with a size-independent contact angle between the undeformed surface and the particle given by a generalised version of Young's law. A simple theory quantitatively captures this behaviour, and explains how solid surface tension dominates elasticity for small-scale indentation of soft materials., 6 pages, 5 figures

Numerous cell types have shown a remarkable ability to detect and move along gradients in stiffness of an underlying substrate—a process known as durotaxis. The mechanisms underlying durotaxis are still unresolved, but generally believed to involve active sensing and locomotion. Here, we show that simple liquid droplets also undergo durotaxis. By modulating substrate stiffness, we obtain fine control of droplet position on soft, flat substrates. Unlike other control mechanisms, droplet durotaxis works without imposing chemical, thermal, electrical, or topographical gradients. We show that droplet durotaxis can be used to create large-scale droplet patterns and is potentially useful for many applications, such as microfluidics, thermal control, and microfabrication.

Droplets deform soft substrates near their contact lines. Using confocal microscopy, we measure the deformation of silicone gel substrates due to glycerol and fluorinated-oil droplets for a range of droplet radii and substrate thicknesses. For all droplets, the substrate deformation takes a universal shape close to the contact line that depends on liquid composition, but is independent of droplet size and substrate thickness. This shape is determined by a balance of interfacial tensions at the contact line and provides a novel method for direct determination of the surface stresses of soft substrates. Moreover, we measure the change in contact angle with droplet radius and show that Young's law fails for small droplets when their radii approach an elastocapillary length scale. For larger droplets the macroscopic contact angle is constant, consistent with Young's law., Comment: 5 pages, 4 figures