Adhesion and Wetting of Nanoparticles on Soft Surfaces

Flexible hydrogels connecting adhesion and wetting

Raindrops falling on window-panes spread upon contact, whereas hail can cause dents or scratches on the same glass window upon contact. While the former phenomenon resembles classical wetting, the latter is dictated by contact and adhesion theories. The classical Young-Dupre law applies to the wetting of pure liquids on rigid solids, whereas conventional contact mechanics theories account for rigid-on-soft or soft-on-rigid contacts with small deformations in the elastic limit. However, the crossover between adhesion and wetting is yet to be fully resolved. The key lies in the study of soft-on-soft interactions with material properties intermediate between liquids and solids. In this work, we translate adhesion to wetting by experimentally probing the static signature of hydrogels in contact with soft PDMS of varying elasticity of both the components. Consequently, we probe this transition across six orders of magnitude in terms of the characteristic elasto-adhesive parameter of the system. In doing so, we reveal previously unknown phenomenology and a theoretical model which smoothly bridges adhesion of glass spheres with total wetting of pure liquids on any given substrate.

The interaction between particles and vascular endothelium in blood flow

Particle-based drug delivery systems have shown promising application potential to treat human diseases; however, an incomplete understanding of their interactions with vascular endothelium in blood flow prevents their inclusion into mainstream clinical applications. The flow performance of nano/micro-sized particles in the blood are disturbed by many external/internal factors, including blood constituents, particle properties, and endothelium bioactivities, affecting the fate of particles in vivo and therapeutic effects for diseases. This review highlights how the blood constituents, hemodynamic environment and particle properties influence the interactions and particle activities in vivo. Moreover, we briefly summarized the structure and functions of endothelium and simulated devices for studying particle performance under blood flow conditions. Finally, based on particle-endothelium interactions, we propose future opportunities for novel therapeutic strategies and provide solutions to challenges in particle delivery systems for accelerating their clinical translation. This review helps provoke an increasing in-depth understanding of particle-endothelium interactions and inspires more strategies that may benefit the development of particle medicine.

Wetting dynamics of viscoelastic solid films

We study the wetting phenomena of a soft viscoelastic solid film on a smooth and flat substrate. A poly-dimethylsiloxane (PDMS) rubber film is suspended from a stage at both ends, and the wetting behavior of the film against a glass substrate is observed while lowering the stage at a constant velocity. We find that the dynamics of the rubber-glass-air contact lines vary with the lowering velocity of the stage. When the stage velocity is sufficiently low, the film wets the substrate smoothly and the contact lines are straight throughout. Consequently, the contact line velocity is proportional to the lowering velocity. As the stage velocity is increased, the contact line velocity reaches a maximum at the critical stage velocity and then subsequently decreases. The contact lines are wavy and sensitive to the defects above the critical velocity, resulting in the trapping of air bubbles at the interface. We reproduce the wetting behavior using a simple numerical model, assuming an upper limit for the contact line velocity. The wetting behavior observed in our experiments is attributed to the transition in the in-plane stress state from tensile to compressive along the film, leading to buckling of the film above the critical stage velocity. Our results suggest the existence and importance of the maximum wetting velocity for viscoelastic solids.

Polydopamine nanoparticles and hyaluronic acid hydrogels for mussel-inspired tissue adhesive nanocomposites

Bioadhesives are intended to facilitate the fast and efficient reconnection of tissues to restore their functionality after surgery or injury. The use of mussel-inspired hydrogel systems containing pendant catechol moieties is promising for tissue attachment under wet conditions. However, the adhesion strength is not yet ideal. One way to overcome these limitations is to add polymeric nanoparticles to create nanocomposites with improved adhesion characteristics. To further enhance adhesiveness, polydopamine nanoparticles with controlled size prepared using an optimized process, were combined with a mussel-inspired hyaluronic acid (HA) hydrogel to form a nanocomposite. The effects of sizes and concentrations of polydopamine nanoparticles on the adhesive profiles of mussel-inspired HA hydrogels were investigated. Results show that the inclusion of polydopamine nanoparticles in nanocomposites increased adhesion strength, as compared to the addition of poly (lactic-co-glycolic acid) (PLGA), and PLGA-(N-hydroxysuccinimide) (PLGA-NHS) nanoparticles. A nanocomposite with demonstrated cytocompatibility and an optimal lap shear strength (47 ± 3 kPa) was achieved by combining polydopamine nanoparticles of 200 nm (12.5% w/v) with a HA hydrogel (40% w/v). This nanocomposite adhesive shows its potential as a tissue glue for biomedical applications.

On Demand Sequential Release of (Sub)Micron Particles Controlled by Size and Temperature

Polymeric devices capable of releasing submicron particles (subMP) on demand are highly desirable for controlled release systems, sensors, and smart surfaces. Here, a temperature-memory polymer sheet with a programmable smooth surface served as matrix to embed and release polystyrene subMP controlled by particle size and temperature. subMPs embedding at 80 °C can be released sequentially according to their size (diameter D of 200 nm, 500 nm, 1 µm) when heated. The differences in their embedding extent are determined by the various subMPs sizes and result in their distinct release temperatures. Microparticles of the same size (D ≈ 1 µm) incorporated in films at different programming temperatures T_p (50, 65, and 80 °C) lead to a sequential release based on the temperature-memory effect. The change of apparent height over the film surface is quantified using atomic force microscopy and the realization of sequential release is proven by confocal laser scanning microscopy. The demonstration and quantification of on demand subMP release are of technological impact for assembly, particle sorting, and release technologies in microtechnology, catalysis, and controlled release.

A surface flattening method for characterizing the surface stress, drained Poisson's ratio and diffusivity of poroelastic gels

When a poroelastic gel is released from a patterned mold, surface stress drives deformation and solvent migration in the gel and flattens its surface profile in a time-dependent manner. Specifically, the gel behaves like an incompressible solid immediately after removal from the mold, and becomes compressible as the solvent is able to squeeze out of the polymer network. In this work, we use the finite element method (FEM) to simulate this transient surface flattening process. We assume that the surface stress is isotropic and constant, the polymer network is linearly elastic and isotropic, and that solvent flow obeys Darcy's law. The short-time and long-time surface profiles can be used to determine the surface stress and drained Poisson's ratio of the gel. Our analysis shows that the drained Poisson's ratio and the diffusivity of the gel can be obtained using interferometry and high-speed video microscopy, without mechanical measurement.

Desorption energy of soft particles from a fluid interface

The efficiency of soft particles to stabilize emulsions is examined by measuring their desorption free energy, i.e., the mechanical work required to detach the particle from a fluid interface. Here, we consider rubber-like elastic as well as microgel particles, using coarse-grained molecular dynamics simulations. The energy of desorption is computed for two and three-dimensional configurations by means of the mean thermodynamic integration method. It is shown that the softness affects the particle-interface binding in two opposing directions as compared to rigid particles. On the one hand, a soft particle spreads at the interface and thereby removes a larger unfavorable liquid-liquid contact area compared to rigid particles. On the other hand, softness provides the particle with an additional degree of freedom to get reshaped instead of deforming the interface, resulting in a smaller restoring force during the detachment. It is shown that the first effect prevails so that a soft spherical particle attaches to the fluid interface more strongly than rigid spheres. Finally, we consider microgel particles both in the swollen and in the collapsed state. Surprisingly, we find that the latter has a larger binding energy. All results are rationalised using thermodynamic arguments and thereby offer detailed insights into the desorption energy of soft particles from fluid interfaces.

Modeling of surface mechanical behaviors of soft elastic solids: theory and examples

Surfaces of soft solids can have significant surface stress, extensional modulus and bending stiffness. Previous theoretical studies have usually examined cases in which both the surface stress and bending stiffness are constant, assuming small deformation. In this work we consider a general formulation in which the surface can support large deformation and carry both surface stresses and surface bending moments. We demonstrate that the large deformation theory can be reduced to the classical linear theory (Shuttleworth equation). We obtain exact solutions for problems of an inflated cylindrical shell and bending of a plate with a finite thickness. Our analysis illustrates the different manners in which surface stiffening and surface bending stabilize these structures. We discuss how the complex surface constitutive behaviors affect the stress field of the bulk. Our calculation provides insights into effects of strain-dependent surface stress and surface bending in the large deformation regime, and can be used as a model to implement surface finite elements to study large deformation of complex structures.

Elastocapillarity and rolling dynamics of solid nanoparticles on soft elastic substrates

The motion of nanoparticles on soft surfaces is the result of interplay between capillary, elastic and friction forces. To elucidate the importance of the different contributions controlling nanoparticle rolling dynamics on soft surfaces, we performed molecular dynamics simulations of solid nanoparticles in contact with soft elastic substrates. The nanoparticle motion is initiated by applying a constant force resulting in stationary, steady rolling, and accelerating states, depending on the nanoparticle-substrate work of adhesion, W, the magnitude of the net applied force, F, and the substrate shear modulus G. In the stationary state, the restoring torque produced in the contact area balances the torque due to the external force. The rolling force Fr, determining the crossover to the rolling state, is proportional to the product of the work of adhesion W and nanoparticle size Rp, Fr ∼ WRp. In the steady rolling state, F > Fr, the nanoparticle maintains a constant rolling velocity which is a manifestation of the balance between the rolling friction force and the applied force. The observed scaling relationships between the applied force and nanoparticle velocity reflect a viscoelastic nature of the substrate deformation dynamics. A nanoparticle begins to accelerate when the energy supplied to the nanoparticle exceeds the energy dissipated in the contact area due to viscoelastic substrate deformation. Using these simulation results, we have constructed a diagram of states in terms of the dimensionless parameters F/WRp and W/GRp.

Coupled flow and deformation fields due to a line load on a poroelastic half space: effect of surface stress and surface bending

In the past decade, many experiments have indicated that the surfaces of soft elastic solids can resist deformation by surface stresses. A common soft elastic solid is a hydrogel which consists of a polymer network swollen in water. Although experiments suggest that solvent flow in gels can be affected by surface stress, there is no theoretical analysis on this subject. Here we study the solvent flow near a line load acting on a linear poroelastic half space. The surface of this half space resists deformation by a constant, isotropic surface stress. It can also resist deformation by surface bending. The time-dependent displacement, stress and flow fields are determined using transform methods. Our solution indicates that the stress field underneath the line load is completely regularized by surface bending-it is bounded and continuous. For small surface bending stiffness, the line force is balanced by surface stresses; these forces form what is commonly known as 'Neumann's triangle'. We show that surface stress reduces local pore pressure and inhibits solvent flow. We use our line load solution to simulate the relaxation of the peak which is formed by applying and then removing a line force on the poroelastic half space.

Mechanisms of Adhesive Micropatterning of Functional Colloid Thin Layers

Thin-film layers of nanoparticles exhibit mechanical fragility that depends on their interactions. Balancing the cohesive force of particles with their interfacial adhesion to a substrate enables the selective transfer of micrometer-scale layer features. Here, the versatility of this adhesion-based transfer approach from poly(dimethylsiloxane) (PDMS) is presented by demonstrating micropatterns of various functional nanoparticulate materials, including Ag, Cu, indium tin oxide, poly(3,4-ethylenedioxythiophene) polystyrene sulfonate, and dielectric silica. With the attachment of the Johnson-Kendall-Roberts interaction to a simple strain model of particle layers during the patterning process, the patterning criteria for successful printing at both macroscale and nanoscale levels are deduced. Discrete element modeling analysis was used to validate the scaling laws and to highlight the fracture modes of particle layers during the patterning process. In particular, the balance among cohesive forces in the tensile direction and in the shear direction and the adhesion force at the layer-PDMS interface mainly regulates the patterning quality of adhesion patterning.

Effects of strain-dependent surface stress on the adhesive contact of a rigid sphere to a compliant substrate

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.

Evaluation of Material Properties for Practical Microstructured Adhesives: Low Dust Adhesion and High Shear Strength

The development of microstructure (gecko-like) adhesives has focused almost solely on their adhesive strength. However, for practical applications, especially in real-world environments, the adhesive's long-term performance is arguably equally important. One impediment to long-term viability is the adhesive's susceptibility to contamination. It is a challenge to develop an adhesive that can both adhere to a substrate while not becoming contaminated with dust and debris. In response, this paper experimentally explores the effect of modulus of elasticity, work of separation, and work of adhesion (adhesion energy) on the shear stress and particle detachment capabilities of wedge-shaped, directional microstructured adhesives. Particle removal is evaluated using both noncontact cleaning methods (centripetal force and electrostatic particle repulsion) and a dry contact cleaning method (load-drag-unload test). Results show that for a material with a high work of separation, high elastic modulus, and low work of adhesion, it is possible to create a microstructured adhesive with both high shear stress strength and low adhesion to dust particles. Results also show that, for dry contact cleaning, shear stress recovery mostly stems from particle rolling and not particle sliding. Moreover, shear test results show that augmenting the microstructured adhesive with electrostatic adhesion can reduce the negative effects on adhesion of a high elastic modulus materials' conformability to a substrate by providing a preload to the microstructured elements. Last, this paper is the first to report on a electrostatic/gecko-like adhesive that uses its electrostatic elements for both adhesion and dust repulsion; they were reported separately before.

Colloidal particles at fluid interfaces: behaviour of isolated particles

The adsorption of colloidal particles to fluid interfaces is a phenomenon that is of interest to multiple disciplines across the physical and biological sciences. In this review we provide an entry level discussion of our current understanding on the physical principles involved and experimental observations of the adsorption of a single isolated particle to a liquid-liquid interface. We explore the effects that a variation of the morphology and surface chemistry of a particle can have on its ability to adhere to a liquid interface, from a thermodynamic as well as a kinetic perspective, and the impact of adsorption behaviour on potential applications. Finally, we discuss recent developments in the measurement of the interfacial behaviour of nanoparticles and highlight open questions for future research.

Rolling Dynamics of Nanoscale Elastic Shells Driven by Active Particles

Self-propelled elastic shells capable of transducing energy to rolling motion could have potential applications as drug delivery vehicles. To understand the dynamics of the nanoscale size elastic shells, we performed molecular dynamics simulations of shells filled with a mixture of active and passive beads placed in contact with an elastic substrate. The shell skin is made of cross-linked polymer chains. The energy transduction from active beads to elastic shell results in stationary, steady rolling, and accelerating states depending on the strength of the shell-substrate adhesion and the magnitude of a force applied to the active beads. In the stationary state, the torque produced by a friction (rolling resistance) force in the contact area balances that due to the external force generated by the active beads, and the shell sticks to the substrate. In the steady rolling state, a rolling friction force balances the driving force, and the shell maintains a constant rolling velocity. The scaling relationship between the magnitude of the driving force and the shell velocity reflects a viscoelastic nature of the shell skin deformation dynamics. In the accelerating state, the energy supplied to a system by active beads exceeds the energy dissipation due to viscoelastic shell deformation in the contact area. Furthermore, the contact area of the shell with a substrate decreases with increasing shell instantaneous velocity.

Effect of ZrO₂ Nanomaterials on Wettability and Interfacial Characteristics of Al-19Cu-11Si-2Sn Filler Metal for Low Temperature Al to Cu Dissimilar Brazing

Dissimilar Al 3003 and Cu tubular components were successfully brazed without interface cracking using ZrO₂ nanomaterials reinforced with Al-19Cu-11Si-2Sn filler. The filler was initially cast using an induction furnace and processed into ring form for brazing. Al-19Cu-11Si-2Sn filler with coarse CuAl₂ and Si phases (43 and 20 μm) were refined to 8 and 4 μm, respectively, after the addition of 0.1 wt. % ZrO₂ and shows significant improvement in the mechanical properties. ZrO₂ nanomaterials' induced diffusion controlled growth mechanism is found be the responsible for the refinement of CuAl₂ intermetallic and Si particles. The wettability of Al-19Cu-11Si-2Sn-0.1ZrO₂ increased to 78.17% on Cu side and 93.19% on the Al side compared from 74.8% and 89.9%, respectively. Increase in the yield strength, ultimate tensile strength, and percentage elongation were noted for the brazed joints. Microstructure of induction brazed joint with 40 kW for 6 seconds using Al-19Cu-11Si-2Sn-0.1ZrO₂ filler shows thin interfacial CuAl₂ intermetallic compound along the copper side and inter-diffusion region along the aluminum side and their respective mechanism is discussed. The tensile strength of the joints increased with increasing the nanomaterials addition and shows a base metal fracture. Analysis of fractured samples shows the effectiveness of ZrO₂ reinforced filler in crack propagation through the filler.

Effect of surface bending and stress on the transmission of line force to an elastic substrate

For a broad class of soft materials their surface stress can strongly influence mechanical behaviour. For example, a line force applied to the surface of an elastic substrate is locally supported by surface stress over an elasto-capillary length l c (surface stress/elastic modulus). Surface stress regularizes the otherwise highly singular stress and strain fields. However, surface such as lipid bilayer interfaces can also resist deformation by bending. This has not been studied either by experiments or theories. We analyse a theoretical model of the response of a half-space to a line force when the surface carries both a stress and resistance to bending. We find that surface bending further regularizes the singular fields. The local stress field near the line load can be separated into three regions. Region 1 occupies distances from the line load smaller than an elasto-capillary bending length l b (bending stiffness/elastic modulus to the 1/3 power) where surface bending dominates and the elastic stress and strains are continuous. Region 2 occupies intermediate distances between l b and l c   ( > l b ) where surface stress dominates. At distances larger than l c we retrieve the classical elasticity solution. The size of region 2 depends on κ = l c / l b and vanishes for small l c .

Surface Stresses and a Force Balance at a Contact Line

Results of the coarse-grained molecular dynamics simulations are used to show that the force balance analysis at the triple-phase contact line formed at an elastic substrate has to include a quartet of forces: three surface tensions (surface free energies) and an elastic force per unit length. In the case of the contact line formed by a droplet on an elastic substrate an elastic force is due to substrate deformation generated by formation of the wetting ridge. The magnitude of this force f_el is proportional to the product of the ridge height h and substrate shear modulus G. Similar elastic line force should be included in the force analysis at the triple-phase contact line of a solid particle in contact with an elastic substrate. For this contact problem elastic force obtained from contact angles and surface tensions is a sum of the elastic forces acting from the side of a solid particle and an elastic substrate. By considering only three line forces acting at the triple-phase contact line, one implicitly accounts the bulk stress contribution as a part of the resultant surface stresses. This "contamination" of the surface properties by a bulk contribution could lead to unphysically large values of the surface stresses in soft materials.

Size-Dependent Submerging of Nanoparticles in Polymer Melts: Effect of Line Tension

Adhesion of nanoparticles to polymer films plays a key role in various polymer technologies. Here we report experiments that reveal how silica nanoparticles adhere to a viscoelastic PMMA film above the glass transition temperature. The polymer was swollen with CO₂, closely matching the conditions of nanoparticle-nucleated polymer foaming. It is found that the degree by which the particles sink into the viscoelastic substrate is strongly size dependent and can even lead to complete engulfment for particles of diameter below 12 nm. These findings are explained quantitatively by a thermodynamic analysis, combining elasticity, capillary adhesion, and line tension. We argue that line tension, here proposed for the first time in elastic media, is responsible for the nanoparticle engulfment.

Surface Stress and Surface Tension in Polymeric Networks

Understanding of how surface properties could change upon deformation is of paramount importance for controlling adhesion, friction, and lubrication of soft polymeric materials (i.e., networks and gels). Here, we use a combination of the theoretical calculations and coarse-grained molecular dynamics simulations to study surface stress dependence on deformation in films made of soft and rigid polymeric networks. Simulations have shown that films of polymeric networks could demonstrate surface properties of both polymer melts and elastic solids depending on their deformation. In particular, at small film deformations the film surface stress ϒ is equal to the surface tension obtained at zero film strains, γ₀, and surface properties of networks are similar to those of polymer melts. The surface stress begins to show a strain dependence when the film deformation ratio λ approaches its maximum possible value λ_max corresponding to fully stretched network strands without bond deformations. In the entire film deformation range the normalized surface stress ϒ(λ)/γ₀ is a universal function of the ratio λ/λ_max. Analysis of the simulation data at large film deformations points out that the significant increase in the surface stress can be ascribed to the onset of the bond deformation. In this deformation regime network films behave as elastic solids.

A closed form large deformation solution of plate bending with surface effects

We study the effect of surface stress on the pure bending of a finite thickness plate under large deformation. The surface is assumed to be isotropic and its stress consists of a part that can be interpreted as a residual stress and a part that stiffens as the surface increases its area. Our results show that residual surface stress and surface stiffness can both increase the overall bending stiffness but through different mechanisms. For sufficiently large residual surface tension, we discover a new type of instability - the bending moment reaches a maximum at a critical curvature. Effects of surface stress on different stress components in the bulk of the plate are discussed and the possibility of self-bending due to asymmetry of the surface properties is also explored. The results of our calculations provide insights into surface stress effects in the large deformation regime and can be used as a test for implementation of finite element methods for surface elasticity.

Droplet impact on soft viscoelastic surfaces

In this work, we experimentally investigate the impact of water droplets onto soft viscoelastic surfaces with a wide range of impact velocities. Several impact phenomena, which depend on the dynamic interaction between the droplets and viscoelastic surfaces, have been identified and analyzed. At low We, complete rebound is observed when the impact velocity is between a lower and an upper threshold, beyond which droplets are deposited on the surface after impact. At intermediate We, entrapment of an air bubble inside the impinging droplets is found on soft surfaces, while a bubble entrapment on the surface is observed on rigid surfaces. At high We, partial rebound is only identified on the most rigid surface at We≳92. Rebounding droplets behave similarly to elastic drops rebounding on superhydrophobic surfaces and the impact process is independent of surface viscoelasticity. Further, surface viscoelasticity does not influence drop spreading after impact-as the surfaces behave like rigid surfaces-but it does affect drop recoiling. Also, the postimpact drop oscillation on soft viscoelastic surfaces is influenced by dynamic wettability of these surfaces. Comparing sessile drop oscillation with a damped harmonic oscillator allows us to conclude that surface viscoelasticity affects the damping coefficient and liquid surface tension sets the spring constant of the system.

Surface tension regularizes the crack singularity of adhesion

The elastic and adhesive properties of a solid surface can be quantified by indenting it with a rigid sphere. Indentation tests are classically described by the JKR-law when the solid is very stiff, while recent work highlights the importance of surface tension for exceedingly soft materials. Here we show that surface tension plays a crucial role even in stiff solids: Young's wetting angle emerges as a boundary condition and this regularizes the crack-like singularity at the edge of adhesive contacts. We find that the edge region exhibits a universal, self-similar structure that emerges from the balance of surface tension and elasticity. The similarity theory is solved analytically and provides a complete description of adhesive contacts, by which we reconcile global adhesion laws and local contact mechanics.

Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids

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≡γ/E. 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 particles at a fluid interface

Particles added to a fluid interface can be used as a surface stabilizer in the food, oil and cosmetic industries. As an alternative to rigid particles, it is promising to consider highly deformable particles that can adapt their conformation at the interface. In this study we compute the shapes of soft elastic particles using molecular dynamics simulations of a cross-linked polymer gel, complemented by continuum calculations based on linear elasticity. It is shown that the particle shape is not only affected by the Young's modulus of the particle, but also strongly depends on whether the gel is partially or completely wetting the fluid interface. We find that the molecular simulations for the partially wetting case are very accurately described by the continuum theory. By contrast, when the gel is completely wetting the fluid interface the linear theory breaks down and we reveal that molecular details have a strong influence on the equilibrium shape.

Robust Design of a Particle-Free Silver-Organo-Complex Ink with High Conductivity and Inkjet Stability for Flexible Electronics

Currently, silver-nanoparticle-based inkjet ink is commercially available. This type of ink has several serious problems such as a complex synthesis protocol, high cost, high sintering temperatures (∼200 °C), particle aggregation, nozzle clogging, poor shelf life, and jetting instability. For the emerging field of printed electronics, these shortcomings in conductive inks are barriers for their widespread use in practical applications. Formulating particle-free silver inks has potential to solve these issues and requires careful design of the silver complexation. The ink complex must meet various requirements, such as in situ reduction, optimum viscosity, storage and jetting stability, smooth uniform sintered films, excellent adhesion, and high conductivity. This study presents a robust formulation of silver-organo-complex (SOC) ink, where complexing molecules act as reducing agents. The 17 wt % silver loaded ink was printed and sintered on a wide range of substrates with uniform surface morphology and excellent adhesion. The jetting stability was monitored for 5 months to confirm that the ink was robust and highly stable with consistent jetting performance. Radio frequency inductors, which are highly sensitive to metal quality, were demonstrated as a proof of concept on flexible PEN substrate. This is a major step toward producing high-quality electronic components with a robust inkjet printing process.

Contact Mechanics of Nanoparticles: Pulling Rigid Nanoparticles from Soft, Polymeric Surfaces

Detachment of rigid nanoparticles from soft, gel-like polymeric surfaces is studied by using a combination of the molecular dynamics simulations and theoretical calculations. Simulations show that detachment of nanoparticles from soft surfaces proceeds through a neck formation. Analysis of the simulation results demonstrates that the magnitude of the detachment force f* depends on the nanoparticle radius R(p), shear modulus of substrate G(s), surface tension of substrate γ(s), and work of adhesion W. It is controlled by the balance of the elastic energy, surface energy of the neck, and nanoparticle adhesion energy to a substrate and depends on the dimensionless parameter δ ∝ γ(s)(G(s)R(p))(-1/3)W(-2/3). In the case of small values of the parameter δ ≪ 1, the critical detachment force approaches a critical detachment force calculated by Johnson, Kendall, and Roberts for adhesive contact, f* = 1.5πWR(p). However, in the opposite limit, corresponding to soft substrates, for which δ ≫ 1, the critical detachment force f* ∝ γ(s)(3/2)R(p)(1/2)G(s)(-1/2). All simulation data can be described by a scaling function f* ∝ γ(s)(3/2)R(p)(1/2)G(s)(-1/2)δ(-1.89).

Wetting and phase separation in soft adhesion

In the classic theory of solid adhesion, surface energy drives deformation to increase contact area whereas 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 phase 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. Whereas 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 nonzero surface stress between the gel and its solvent.

Elasticity of polymeric nanocolloidal particles

Softness is an essential mechanical feature of macromolecular particles such as polymer-grafted nanocolloids, polyelectrolyte networks, cross-linked microgels as well as block copolymer and dendrimer micelles. Elasticity of individual particles directly controls their swelling, wetting, and adsorption behaviour, their aggregation and self-assembly as well as structural and rheological properties of suspensions. Here we use numerical simulations and self-consistent field theory to study the deformation behaviour of a single spherical polymer brush upon diametral compression. We observe a universal response, which is rationalised using scaling arguments and interpreted in terms of two coarse-grained models. At small and intermediate compressions the deformation can be accurately reproduced by modelling the brush as a liquid drop, whereas at large compressions the brush behaves as a soft ball. Applicable far beyond the pairwise-additive small-strain regime, the models may be used to describe microelasticity of nanocolloids in severe confinement including dense disordered and crystalline phases.

Adsorption of soft particles at fluid interfaces

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≪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, σp. 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.

Adhesive contact of a rigid circular cylinder to a soft elastic substrate--the role of surface tension

This article studies the effects of surface tension on the adhesive contact mechanics of a long rigid cylinder on an infinite half space comprising an incompressible elastic material. We present an exact solution based on small strain theory. The relationship between the indentation force and contact width was found to depend on a single dimensionless parameter ω = σ/[4(μR)(2/3)(W(ad)/2π)(1/3'), where R is the cylinder radius, Wad is the interfacial work of adhesion, and σ and μ are the surface tension and shear modulus of the half space, respectively. For small ω the solution reduces to the classical Johnson-Kendall-Roberts (JKR) theory, whereas for large ω the solution reduces to the small slope version of the Young-Dupre equation. The pull-off phenomenon was carefully examined and it was found that the contact width at pull-off reduces to zero when surface tension is larger than a critical value.

Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion

The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that owing to elasticity. This paper studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter: ω=σ(μR)^-2/3((9π/4)W_ad)^-1/3, where σ and μ are the surface tension and shear modulus of the substrate, R is the sphere radius and W_ad is the interfacial work of adhesion. Our theory reduces to the Johnson-Kendall-Roberts (JKR) theory and Young-Dupre equation in the limits of small and large ω, respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by one-third compared with the JKR limit and the pull-off behaviour is completely determined by ω.

Adhesion and wetting of soft nanoparticles on textured surfaces: transition between Wenzel and Cassie-Baxter states

We use a combination of the molecular dynamics simulations and scaling analysis to study interactions between gel-like nanoparticles and substrates covered with rectangular shape posts. Our simulations have shown that nanoparticles in contact with substrate undergo a first-order transition between the Cassie–Baxter and Wenzel states, which depends on nanoparticle shear modulus, the strength of nanoparticle–substrate interactions, height of the substrate posts, and nanoparticle size, Rp. There is a range of system parameters where these two states coexist such that the average indentation δ produced by substrate posts changes with nanoparticle shear modulus, Gp. We have developed a scaling model that describes deformation of nanoparticle in contact with patterned substrate. In the framework of this model, the effect of the patterned substrate can be taken into account by introducing an effective work of adhesion, Weff, which describes the first-order transition between Wenzel and Cassie–Baxter states. There are two different shape deformation regimes for nanoparticles with shear modulus Gp and surface tension γp. The shape of small nanoparticles with size Rp < γp(3/2)Gp(-1)Weff(-1/2) is controlled by capillary forces, while deformation of large nanoparticles, Rp > γp(3/2)Gp(-1)Weff(-1/2), is determined by nanoparticle elastic and contact free energies. The model predictions are in good agreement with simulation results.

Surface tension and the mechanics of liquid inclusions in compliant solids

Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which has recently been shown to control many processes in soft materials such as gels, elastomers and biological tissue. To extend Eshelby's theory of inclusions to soft materials, we consider liquid inclusions within an isotropic, compressible, linear-elastic solid. We solve for the displacement and stress fields around individual stretched inclusions, accounting for the bulk elasticity of the solid and the surface tension (i.e. isotropic strain-independent surface stress) of the solid-liquid interface. Surface tension significantly alters the inclusion's shape and stiffness as well as its near- and far-field stress fields. These phenomena depend strongly on the ratio of the inclusion radius, R, to an elastocapillary length, L. Surface tension is significant whenever inclusions are smaller than 100L. While Eshelby theory predicts that liquid inclusions generically reduce the stiffness of an elastic solid, our results show that liquid inclusions can actually stiffen a solid when R<3L/2. Intriguingly, surface tension cloaks the far-field signature of liquid inclusions when R=3L/2. These results are have far-reaching applications from measuring local stresses in biological tissue, to determining the failure strength of soft composites.