Surface Stresses and a Force Balance at a Contact Line

Pinning Forces on the Omniphobic Dry, Liquid-Infused, and Liquid-Attached Surfaces

Omniphobic coatings effectively repelling water, oils, and other liquids are of great interest and have a broad number of applications including self-cleaning, anti-icing surfaces, biofouling protection, selective filtration, etc. To create such coatings, one should minimize the pinning force that resists droplet motion and causes contact angle hysteresis. The minimization of the free surface energy by means of the chemical modification of the solid surface is not enough to obtain a nonsticky slippery omniphobic surface. One should minimize the contact between the solid and the droplet. Besides coating the surface with flat polymer films, among the major approaches to create omniphobic coatings, one can reveal "lotus effect" textured coatings, slippery liquid-infused porous surfaces (SLIPS), and slippery omniphobic covalently attached liquid (SOCAL) coatings. It is possible to turn one surface type into other by texturizing, impregnating with liquids, or grafting flexible liquid-like polymer chains. There are a number of models describing the pinning force on surfaces, but the transitions between states with different wetting regimes remain poorly understood. At the same time, such studies can significantly broaden existing ideas about the physics of wetting, help to design coatings, and also contribute to the development of generalized models of the pinning force. Here we review the existing pinning force (contact angle hysteresis) models on various omniphobic substrates. Also, we discuss the current studies of the pinning force in the transitions between different wetting regimes.

Comparative Molecular Dynamics Simulation of Wetting on Liquid-like Surfaces

We utilize molecular dynamics simulations to comparably investigate the wetting and motion behavior of droplets on liquid-like surfaces (LLS) with varying grafting conditions. Polydimethylsiloxane (PDMS) and perfluoropolyether (PFPE) have been considered to be flexible molecules versus rigid molecules of trichloro(octadecyl) silane (OTS) and trichloro(1H,1H,2H,2H-perfluorooctyl) silane (PFOS), respectively. Our findings reveal that droplets on surfaces tethered with either PDMS or PFPE brushes can generate indentations and wetting ridges, providing microscopic evidence of their liquid-like nature. The grafting density of mobile chains exerts a dominant influence on the wetting properties compared to the molecular weight. A parameter map is created to pinpoint the precise range of grafting densities essential for the optimal construction of LLS at predetermined molecular weights. Furthermore, the investigation of droplet motion dynamics on LLS demonstrates that droplets consistently exhibit a rolling state, regardless of the intensity of the applied lateral force. The movement pattern of the droplet shifts only under conditions where the grafting density is significantly reduced and the substrate exhibits hydrophilic tendencies. These findings and the developed model are anticipated to offer valuable guidelines for optimal designs of LLS.

Nanoscale Elasto-Capillarity in the Graphene-Water System under Tension: Revisiting the Assumption of a Constant Wetting Angle

Wetting highly compliant surfaces can cause them to deform. Atomically thin materials, such as graphene, can have exceptionally small bending rigidities, leading to elasto-capillary lengths of a few nanometers. Using large-scale molecular dynamics (MD), we have studied the wetting and deformation of graphene due to nanometer-sized water droplets, focusing on the wetting angle near the vesicle transition. Recent continuum theories for wetting of flexible membranes reproduce our MD results qualitatively well. However, we find that when the curvature is large at the triple-phase contact line, the wetting angle increases with decreasing tension. This is in contrast to existing macroscopic theories but can be amended by allowing for a variable wetting angle.

Dependence of Slippery and Elastic Properties of Thin Polymer Films on the Grafted Flexible Sidechain Amount

In modern life, people face a wide number of sticky problems when adhesion is highly undesirable: water and dirt stick to clothes, useful materials stick to the walls of their containers and cannot be fully used, water sticking and freezing on airplane wings affects handling and can be dangerous, biological liquids can stick and form clots inside medical devices threatening patients' lives, etc. Slippery liquid-infused porous surfaces (SLIPSs) with pressure stable omniphobicity could help to solve these issues. Lubricant depletion from porous surface and subsequent degradation of omniphobic properties is the major problem for SLIPS. It could be resolved by attaching flexible, liquid-like sidechains to the polymer matrix. Understanding the relationship between the structure of such polymer films and wetting effects is therefore of great importance. The present work is devoted to the study of droplet pinning on crosslinked polydimethylsiloxane (PDMS) polymer films with varied amounts of attached flexible PDMS sidechains and clarification of the relationship between slippery and viscoelastic properties of the films. An one-stage approach to the synthesis of such slippery coatings on smooth and porous substrates in "eco-friendly" pressurized CO₂ solutions is proposed. Pinning force and Young's modulus (E) of the films on silicon substrates with variation of the grafted sidechains amount (x) are measured. The non-monotonic dependence of the pinning force on the amount of sidechains is obtained: the pinning force decreases at small x values (region I) and starts to increase at higher x (region II). The effects of the grafted sidechains amount, as well as matrix softening, are discussed for each case. It is demonstrated that the proposed method of film synthesis allows one to obtain thin, uniform coatings on fabrics without gluing the fibers. Such coatings with an optimal amount of PDMS sidechains demonstrate decreased sliding angles for droplets of water and aqueous alcohol solutions, as compared to PDMS coatings without grafted sidechains. The proposed technique may be of interest for deposition of coatings on porous surfaces having a complex morphology, such as textiles, aerogels, porous electrodes, etc.

Soft wetting with (a)symmetric Shuttleworth effect

The wetting of soft polymer substrates brings in multiple complexities when compared with the wetting on rigid substrates. The contact angle of the liquid is no longer governed by Young's Law, but is affected by the substrate's bulk and surface deformations. On top of that, elastic interfaces exhibit a surface energy that depends on how much they are stretched-a feature known as the Shuttleworth effect (or as surface-elasticity). Here, we present two models through which we explore the wetting of drops in the presence of a strong Shuttleworth effect. The first model is macroscopic in character and consistently accounts for large deformations via a neo-Hookean elasticity. The second model is based on a mesoscopic description of wetting, using a reduced description of the substrate's elasticity. While the second model is more empirical in terms of the elasticity, it enables a gradient dynamics formulation for soft wetting dynamics. We provide a detailed comparison between the equilibrium states predicted by the two models, from which we deduce robust features of soft wetting in the presence of a strong Shuttleworth effect. Specifically, we show that the (a)symmetry of the Shuttleworth effect between the 'dry' and 'wet' states governs horizontal deformations in the substrate. Our results are discussed in the light of recent experiments on the wettability of stretched substrates.

The role of crosslinking density in surface stress and surface energy of soft solids

Surface stress and surface energy are two fundamental parameters that determine the surface properties of any material. While it is commonly believed that the surface stress and surface energy of liquids are identical, the relationship between the two parameters in soft polymeric gels remains debatable. In this work, we measured the surface stress and surface energy of soft silicone gels with varying weight ratios of crosslinkers in soft wetting experiments. Above a critical density, k₀, the surface stress was found to increase significantly with crosslinking density while the surface energy remained unchanged. In this regime, we can estimate a non-zero surface elastic modulus that also increases with the ratio of crosslinkers. By comparing the surface mechanics of the soft gels with their bulk rheology, the surface properties near the critical density k₀ were found to be closely related to the underlying percolation transition of the polymer networks.

Elasticity-to-Capillarity Transition in Soft Substrate Deformation

Whereas capillarity controls fluid dynamics at submillimeter scale and elasticity determines the mechanics of rigid solids, their coupling governs elastocapillary deformations on soft solids. Here, we directly probed the deformations on soft substrates induced by sessile nanodroplets. The wetting ridge created around the contact line and the dimple formed underneath the nanodroplet were imaged with a high spatial resolution using atomic force microscopy. The ridge height nonmonotonically depends on the substrate stiffness, and the dimple depth nonlinearly depends on the droplet size. The capillarity of the substrate overcomes the elasticity of the substrate in dominating the deformations when the elastocapillary length is approximately larger than the droplet contact radius, showing an experimental observation of the elasticity-to-capillarity transition. This study provides an experimental approach to investigate nanoscale elastocapillarity, and the insights have the potential to kick-off future work on the fundamentals of solid mechanics.

Gradient-dynamics model for liquid drops on elastic substrates

The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.

Droplets Sit and Slide Anisotropically on Soft, Stretched Substrates

Anisotropically wetting substrates enable useful control of droplet behavior across a range of applications. Usually, these involve chemically or physically patterning the substrate surface, or applying gradients in properties like temperature or electrical field. Here, we show that a flat, stretched, uniform soft substrate also exhibits asymmetric wetting, both in terms of how droplets slide and in their static shape. Droplet dynamics are strongly affected by stretch: glycerol droplets on silicone substrates with a 23% stretch slide 67% faster in the direction parallel to the applied stretch than in the perpendicular direction. Contrary to classical wetting theory, static droplets in equilibrium appear elongated, oriented parallel to the stretch direction. Both effects arise from droplet-induced deformations of the substrate near the contact line.

Nonlinear theory of wetting on deformable substrates

The spreading of a liquid over a solid material is a key process in a wide range of applications. While this phenomenon is well understood when the solid is undeformable, its "soft" counterpart is still misunderstood and no consensus has been reached with regard to the physical mechanisms ruling the spreading of liquid drops over soft deformable materials. In this work we provide a theoretical framework, based on the nonlinear theory of discontinuities, to describe the behavior of a triple line on a soft material. We show that the contact line motion is opposed both by nonlinear localized capillary and visco-elastic forces. We give an explicit analytic formula relating the dynamic contact angle of a moving drop to its velocity for arbitrary rheology. We then specialize this formula to the experimentally relevant case of elastomers with the Chasset-Thirion (power-law) type of rheologies. The theoretical prediction is in very good agreement with experimental data, without any adjustable parameters. We then show that the nonlinear force balance presented in this work can also be used to recover classical models of wetting. Finally we provide predictions for the dynamic behavior of the yet largely unexplored case of a viscous drop spreading over a soft visco-elastic material and predict the emergence of a new form of apparent hysteresis.

Adaptive Liquid Interfacially Assembled Protein Nanosheets for Guiding Mesenchymal Stem Cell Fate

There is a growing interest in the development of dynamic adaptive biomaterials for regulation of cellular functions. However, existing materials are limited to two-state switching of the presentation and removal of cell-adhesive bioactive motifs that cannot emulate the native extracellular matrix (ECM) in vivo with continuously adjustable characteristics. Here, tunable adaptive materials composed of a protein monolayer assembled at a liquid-liquid interface are demonstrated, which adapt dynamically to cell traction forces. An ultrastructure transition from protein monolayer to hierarchical fiber occurs through interfacial jamming. Elongated fibronectin fibers promote formation of elongated focal adhesion structures, increase focal adhesion kinase activation, and enhance neuronal differentiation of stem cells. Cell traction force results in spatial rearrangement of ECM proteins, which feeds back to alter stem cell fate. The reported biomimetic adaptive liquid interface enables dynamic control of stem cell behavior and has potential translational applications.

Distinguishing deformation mechanisms in elastocapillary experiments

Soft materials are known to deform due to a variety of mechanisms, including capillarity, buoyancy, and swelling. In this paper, we present experiments on polyvinylsiloxane gel threads partially-immersed in three liquids with different solubility, wettability, and swellability. Our results demonstrate that deformations due to capillarity, buoyancy, and swelling can be of similar magnitude as such threads come to static equilibrium. To account for all three effects being present in a single system, we derive a model capable of explaining the observed data and use it to determine the force law at the three-phase contact line. The results show that the measured forces are consistent with the expected Young-Dupré equation, and do not require the inclusion of a tangential contact line force.

Elastocapillary Ridge as a Noninteger Disclination

Understanding the interfacial properties of solids with their environment is a crucial problem in fundamental science and applications. Elastomers have challenged the scientific community in this respect, and a satisfying description is still missing. Here, we argue that the interfacial properties of elastomers, such as their wettability, can be understood with a nonlinear elastic model with the assumption of a strain-independent surface energy. We show that our model captures accurately available data on elastomer wettability and discuss its implications.

Wetting of Polymer Brushes by Polymeric Nanodroplets

End-anchoring polymers to a solid surface to form so-called polymer brushes is a versatile method to prepare robust functional coatings. We show, using molecular dynamics simulations, that these coatings display rich wetting behavior. Depending on the interaction between the brushes and the polymeric droplets as well as on the self-affinity of the brush, we can distinguish between three wetting states: mixing, complete wetting, and partial wetting. We find that transitions between these states are largely captured by enthalpic arguments, while deviations to these can be attributed to the negative excess interfacial entropy for the brush droplet system. Interestingly, we observe that the contact angle strongly increases when the softness of the brush is increased, which is opposite to the case of drops on soft elastomers. Hence, the Young to Neumann transition owing to softness is not universal but depends on the nature of the substrate.