Confinement-induced instability and adhesive failure between dissimilar thin elastic films

Geometry-controlled instabilities for soft-soft adhesive interfaces

Soft materials interfaces can develop complex morphologies, such as cavities or finger-like features, during separation as a result of a mechanical instability. While the onset and growth of these instabilities have been investigated previously for interfaces between rigid and soft materials, no existing predictive model provides insight for controlling the separation morphology associated with these instabilities when both "sides" of the interface are soft. Here, we expand previous models to account for the geometry and materials properties of two soft materials that form an interface. The total compliance of the system, which depends nonlinearly on the thickness of each contacting soft material, plays a primary role in governing the morphology of the separating interface. We validate this model with experimental measurements using a series of soft elastomers with varying layer thicknesses and fixed materials properties, in order to emphasize the geometry alone can give rise to the observed differences in the interface separation process. This model also demonstrates that the degree of geometric asymmetry, or the ratio of the layer thicknesses that form an interface, influences the stress experienced in either layer, thus providing a rich means of controlling how unstable interface separations develop and propagate. This framework is a powerful tool to understand and control adhesion mechanisms in fields ranging from biology to soft robotics, and provides intuition for engineering a separation mode for a desired end result.

Fingering instability during fracture of a gel block subjected to shear loading

We report here an alternative kind of fingering instability observed during fracture of an unconfined gel consisting of two cuboids joined by a thin gel disk, and all prepared monolithically. When the blocks are sheared across the joint, fracture ensues with the appearance of fingers at the fracture front. The spacing between the fingers remains independent of the shearing speed, planar shape of the joint, and the shear modulus of gel. Importantly this instability appears without any effect of confinement of the gel block, and its wavelength remains dependent on the lateral size of the disk, in contrast to all known instances of fingering phenomena in confined viscous, elastic, and viscoelastic systems.

Fringe instability in constrained soft elastic layers

Soft elastic layers with top and bottom surfaces adhered to rigid bodies are abundant in biological organisms and engineering applications. As the rigid bodies are pulled apart, the stressed layer can exhibit various modes of mechanical instabilities. In cases where the layer's thickness is much smaller than its length and width, the dominant modes that have been studied are the cavitation, interfacial and fingering instabilities. Here we report a new mode of instability which emerges if the thickness of the constrained elastic layer is comparable to or smaller than its width. In this case, the middle portion along the layer's thickness elongates nearly uniformly while the constrained fringe portions of the layer deform nonuniformly. When the applied stretch reaches a critical value, the exposed free surfaces of the fringe portions begin to undulate periodically without debonding from the rigid bodies, giving the fringe instability. We use experiments, theory and numerical simulations to quantitatively explain the fringe instability and derive scaling laws for its critical stress, critical strain and wavelength. We show that in a force controlled setting the elastic fingering instability is associated with a snap-through buckling that does not exist for the fringe instability. The discovery of the fringe instability will not only advance the understanding of mechanical instabilities in soft materials but also have implications for biological and engineered adhesives and joints.

Adhesion in hydrogel contacts

A generalized thermomechanical model for adhesion was developed to elucidate the mechanisms of dissipation within the viscoelastic bulk of a hyperelastic hydrogel. Results show that in addition to the expected energy release rate of interface formation, as well as the viscous flow dissipation, the bulk composition exhibits dissipation due to phase inhomogeneity morphological changes. The mixing thermodynamics of the matrix and solvent determines the dynamics of the phase inhomogeneities, which can enhance or disrupt adhesion. The model also accounts for the time-dependent behaviour. A parameter is proposed to discern the dominant dissipation mechanism in hydrogel contact detachment.

Instability, self-organization and pattern formation in thin soft films

The free surface of a thin soft polymer film is often found to become unstable and self-organizes into various meso-scale structures. In this article we classify the instability of a thin polymer film into three broad categories, which are: category 1: instability of an ultra-thin (<100 nm) viscous film engendered by amplification of thermally excited surface capillary waves due to interfacial dispersive van der Waals forces; category 2: instability arising from the attractive inter-surface interactions between the free surface of a soft film exhibiting room temperature elasticity and another rigid surface in its contact proximity; and category 3: instability caused by an externally applied field such as an electric field or a thermal gradient, observed in both viscous and elastic films. We review the salient features of each instability class and highlight how characteristic length scales, feature morphologies, evolution pathways, etc. depend on initial properties such as film thickness, visco-elasticity (rheology), residual stress, and film preparation conditions. We emphasize various possible strategies for aligning and ordering of the otherwise isotropic structures by combining the essential concepts of bottom-up and top-down approaches. A perspective, including a possible future direction of research, novelty and limitations of the methods, particularly in comparison to the existing patterning techniques, is also presented for each setting.

Adhesion-induced instabilities and pattern formation in thin films of elastomers and gels

A hydrostatically stressed soft elastic film circumvents the imposed constraint by undergoing a morphological instability, the wavelength of which is dictated by the minimization of the surface and the elastic strain energies of the film. While for a single film, the wavelength is entirely dependent on its thickness, a co-operative energy minimization dictates that the wavelength depends on both the elastic moduli and thicknesses of two contacting films. The wavelength can also depend on the material properties of a film if its surface tension has a pronounced effect in comparison to its elasticity. When such a confined film is subjected to a continually increasing normal displacement, the morphological patterns evolve into cracks, which, in turn, govern the adhesive fracture behavior of the interface. While, in general, the thickness provides the relevant length scale underlying the well-known Griffith-Kendall criterion of debonding of a rigid disc from a confined film, it is modified non-trivially by the elasto-capillary number for an ultra-soft film. Depending upon the degree of confinement and the spatial distribution of external stress, various analogs of the canonical instability patterns in liquid systems can also be reproduced with thin confined elastic films.

Squeezing instabilities and delamination in elastic bilayers: a linear stability analysis

A linear stability analysis is presented to understand the instabilities that arise in an elastic bilayer, consisting of a very thin bottom layer (thickness < 100 nm) that acts as a wetting film and a top layer that acts as an adhesive film, when placed in contact proximity with an external rigid contactor. Depending on whichever layer is more compliant, "squeezing modes" of instability with a variety of length scales ranging from <<3h to <<3h (h: bilayer thickness) are found to be possible. The least length scales obtained are 0.1h. The squeezing instabilities are, however, accompanied by delamination of the film-film interface. The instability length scales, the strength of interactions required, and the delamination decrease as the compliance of the top film increases. Surface tension effects are found to have a stabilizing influence which increases the instability length scales and decreases the degree of delamination at the cost of high interaction penalty.

Electric-field-induced interfacial instabilities of a soft elastic membrane confined between viscous layers

We explore the electric-field-induced interfacial instabilities of a trilayer composed of a thin elastic film confined between two viscous layers. A linear stability analysis (LSA) is performed to uncover the growth rate and length scale of the different unstable modes. Application of a normal external electric field on such a configuration can deform the two coupled elastic-viscous interfaces either by an in-phase bending or an antiphase squeezing mode. The bending mode has a long-wave nature, and is present even at a vanishingly small destabilizing field. In contrast, the squeezing mode has finite wave-number characteristics and originates only beyond a threshold strength of the electric field. This is in contrast to the instabilities of the viscous films with multiple interfaces where both modes are found to possess long-wave characteristics. The elastic film is unstable by bending mode when the stabilizing forces due to the in-plane curvature and the elastic stiffness are strong and the destabilizing electric field is relatively weak. In comparison, as the electric field increases, a subdominant squeezing mode can also appear beyond a threshold destabilizing field. A dominant squeezing mode is observed when the destabilizing field is significantly strong and the elastic films are relatively softer with lower elastic modulus. In the absence of liquid layers, a free elastic film is also found to be unstable by long-wave bending and finite wave-number squeezing modes. The LSA asymptotically recovers the results obtained by the previous formulations where the membrane bending elasticity is approximately incorporated as a correction term in the normal stress boundary condition. Interestingly, the presence of a very weak stabilizing influence due to a smaller interfacial tension at the elastic-viscous interfaces opens up the possibility of fabricating submicron patterns exploiting the instabilities of a trilayer.

Structure and macroscopic tackiness of ultrathin pressure sensitive adhesive films

Ultrathin layers of the statistical copolymer P(nBA-stat-MA) with a majority of n-butyl acrylate (nBA) and a minority of methyl acrylate (MA) are characterized with respect to the film morphology and the mechanical response in a probe tack test. The probed copolymer can be regarded as a model system of a pressure sensitive adhesive (PSA). The films are prepared by spin-coating which enables an easy thickness control via the polymer concentration of the solution. The film thickness is determined with x-ray reflectivity (XRR) and white light interferometry (WLI). Grazing incidence small angle x-ray scattering (GISAXS) provides detailed and statistically significant information about the film morphology. Two types of lateral structures are identified and no strong correlation of these structures with the PSA film thickness is observed. In contrast, prominent parameters of the probe tack test, such as the stress maximum and the tack energy, exhibit an exponential dependence on the film thickness.

Creating self-organized submicrometer contact instability patterns in soft elastic bilayers with a topographically patterned stamp

The surface of a thin elastic bilayer becomes spontaneously unstable when it is brought in proximity to another rigid contactor. The instability patterns, which are random and isotropic, exhibit a dominant lateral length scale of instability λ, which linearly scales with the bilayer thickness (h) as: λ = R(F)h. It is known that for an elastic bilayer, R(F) exhibits a nonlinear dependence on the ratios of individual film thicknesses (H) and shear moduli (M) of the two constituent layers, and can have values as low as 0.5 under specific conditions. This is in contrast to a near constant value of R(F) ≈ 3 for a single layer elastic film. (1) These isotropic contact instability patterns in a bilayer can be ordered, aligned and modulated using a topographically patterned stamp. The precise morphology of the aligned structures depends on commensuration between λ and the stamp periodicity (λ(P)), and on the intersurface separation distance. A variety of patterns, like an array of circular holes, double periodic channels, etc., in addition to a positive and a negative replica of the stamp pattern, can be engineered with a simple stamp having 1D grating structure. A lower value of R(F) in a bilayer allows generating patterns with sub 500 nm lateral resolution, which is impossible to create by elastic contact lithography (ECL) of a single layer film due to strong surface tension effects in ultrathin films. Thus, control of elastic instability in a bilayer with a patterned stamp represents a flexible soft lithography tool allowing modulation of length scales, morphology, and order.

Instabilities of soft elastic microtubes filled with viscous fluids: pearls, wrinkles, and sausage strings

A linear stability analysis is presented to study the self-organized instabilities of a highly compliant elastic cylindrical shell filled with a viscous liquid and submerged in another viscous medium. The prototype closely mimics many components of micro- or nanofluidic devices and biological processes such as the budding of a string of pearls inside cells and sausage-string formation of blood vessels. The cylindrical shell is considered to be a soft linear elastic solid with small storage modulus. When the destabilizing capillary force derived from the cross-sectional curvature overcomes the stabilizing elastic and in-plane capillary forces, the microtube can spontaneously self-organize into one of several possible configurations; namely, pearling, in which the viscous fluid in the core of the elastic shell breaks up into droplets; sausage strings, in which the outer interface of the mircrotube deforms more than the inner interface; and wrinkles, in which both interfaces of the thin-walled mircrotube deform in phase with small amplitudes. This study identifies the conditions for the existence of these modes and demonstrates that the ratios of the interfacial tensions at the interfaces, the viscosities, and the thickness of the microtube play crucial roles in the mode selection and the relative amplitudes of deformations at the two interfaces. The analysis also shows asymptotically that an elastic fiber submerged in a viscous liquid is unstable for Y=γ/(G(e)R)>6 and an elastic microchannel filled with a viscous liquid should rupture to form spherical cavities (pearling) for Y>2, where γ, G(e), and R are the surface tension, elastic shear modulus, and radius, respectively, of the fiber or microchannel.

Surface wrinkling: a versatile platform for measuring thin-film properties

Surface instabilities in soft matter have been the subject of increasingly innovative research aimed at better understanding the physics of their formation and their utility in patterning, organizing, and measuring materials properties on the micro and nanoscale. The focus of this Review is on a type of instability pattern known as surface wrinkling, covering the general concepts of this phenomenon and several recent applications involving the measurement of thin-film properties. The ability of surface wrinkling to yield new insights into particularly challenging materials systems such as ultrathin films, polymer brushes, polyelectrolyte multilayer assemblies, ultrasoft materials, and nanoscale structured materials is highlighted. A perspective on the future directions of this maturing field, including the prospects for advanced thin-film metrology methods, facile surface patterning, and the control of topology-sensitive phenomena, such as wetting and adhesion, is also presented.

Embedded microstructures by electric-field-induced pattern formation in interacting thin layers

Electric-field-induced interfacial instabilities and pattern formation in a pair of interacting thin films are analyzed on the basis of linear stability analysis and long-wave nonlinear simulations. The films are coated onto two parallel plate electrodes and separated by an air gap between them. A linear stability analysis (LSA) is carried out for viscoelastic films to show that the ratios of material properties to films thickness control the length scale and timescale significantly and the presence of the second layer increases the overall capacitance and thus can lead to a smaller length scale as compared to the instability in a single film. Long-wave nonlinear analysis for interacting viscous layers indicates that the instabilities are always initiated by the antiphase squeezing rather than the in-phase bending mode of deformation at the interfaces. Nonlinear simulations on patterned electrodes show that this novel geometry for electric field patterning can be employed to generate intricate, embedded 3-D periodic patterns and to miniaturize patterns. Simulations are presented for e-molding of a number of periodic self-organized patterns such as pincushion structures, straight/corrugated embedded microchannels, and microbubbles. A few interesting examples are also shown where (1) the pathway of evolution changes without altering the equilibrium morphology when kinetic parameters such as viscous forces are changed and (2) the self-organized equilibrium morphology does not reproduce the underlying patterns on the electrodes.

A unified theory of instabilities in viscoelastic thin films: from wetting to confined films, from viscous to elastic films, and from short to long waves

A general unified theory of field (van der Waals, electric, etc.)-induced surface instabilities in thin viscoelastic films that accounts for a destabilizing field and stabilizing effects of elastic strain and surface energy is presented. The present theory seamlessly covers the instability and its different regimes in films ranging from elastic to viscous, from adhesive (confined) to wetting (free surface), and from short- to long-wave instabilities. The critical conditions for the onset of instability are found to be strongly dependent on elastic properties such as the shear modulus of the film, but the dominant wavelength is strikingly independent of the film rheology. Different regimes based on a nondimensional parameter (gamma/mu h) are uncovered, where gamma is the surface energy, mu is the elastic shear modulus, and h is the film thickness. A short-wave, elasticlike response with wavelength lambda approximately = 2.96 h is obtained for gamma/mu h < 0.1, whereas long waves that depend nonlinearly on the field strength and surface energy are obtained for gamma/mu h > 1. Owing to their small critical thickness, wetting films destabilized by intermolecular forces always display long-wave instability regardless of their viscoelasticity. Furthermore, our numerical simulations based on energy minimization for unstable wetting elastic films show the formation of islands for ultrathin films and a morphological phase transition to holes embedded in the film for relatively thicker films. Unlike viscous films, however, unstable elastic films do not display a unique dominant wavelength but a bimodal distribution of wavelengths.

Using electrocapillarity to measure the zeta potential of a planar hydrophobic surface in contact with water and nonionic surfactant solutions

A method is introduced for determining the zeta potential of planar surfaces by combining electroosmosis and capillarity. In this method, an electric field is applied across the channel, which is filled with aqueous solution seeded with fluorescent tracer particles. Some excess liquid is applied on both ends of the channel, which bulges out and modulates the capillary force across the channel by adjusting its curvature. While the velocity profile in the channel approaches steady state, a balance of the electroosmotic stress and Laplace pressure difference is achieved across the channel. However, as soon as the electric field is turned off, a Poiseuille flow develops in the channel due to the difference in the curvatures of the liquid bulges. We show that the measurement of the centerline velocity of the liquid inside the channel is enough to deduce the zeta potential of the surface. Utilizing this technique, the zeta potential of a hydrophobic glass surface (silanized by n-hexadecyltrichlorosilane, HC-16) has been measured to be -52.2 +/- 7.7 mV in distilled deionized water, which is in close agreement with the literature values. This technique has also been used to estimate the zeta potential of the HC-16 surface (zeta w(HC-16)), in the presence of the aqueous solutions of polyoxyethylene (23) lauryl ether (Brij 35). The zeta potential here at first becomes more negative than that in pure water, it stays flat for a while, and then it continues to become less negative as the concentration of the surfactant increases above the critical micelle concentration (CMC). This effect, where changes take place beyond the CMC but not below it, leads to a complementary Gibbs plot, where all the changes occur below the CMC but not above it. It is conjectured that the scavenging of hydroxyl ions by the Brij 35 micelles may be responsible for the observed effect.

Contact instability of thin elastic films on patterned substrates

The free surface of a soft elastic film becomes unstable and forms an isotropic labyrinth pattern when a rigid flat plate is brought into adhesive contact with the film. These patterns have a characteristic wavelength, lambda approximately 3H, where H is the film thickness. We show that these random structures can be ordered, modulated, and aligned by depositing the elastic film (cross-linked polydimethylsiloxane) on a patterned substrate and by bringing the free surface of the film in increasing adhesive contact with a flat stamp. Interestingly, the influence of the substrate "bleeds" through the film to its free surface. It becomes possible to generate complex two-dimensional ordered structures such as an array of femtoliter beakers even by using a simple one-dimensional stripe patterned substrate when the instability wavelength, lambda approximately 3H, nearly matches the substrate pattern periodicity. The free surface morphology is modulated in situ by merely varying the stamp-surface separation distance. The free surface structures originating from the elastic contact instability can also be made permanent by the UV-ozone induced oxidation and stiffening.

Studying friction and shear fracture in thin confined films using a rotational shear apparatus

This paper describes the effects of the elastic modulus and sliding velocity on the friction and shear fracture of smooth silanized rigid disks rotating against thin confined films of poly(dimethylsiloxane) (PDMS) elastomers. A rigid glass disk is rotated against thin PDMS films of different thicknesses and moduli bonded to a glass plate at various speeds. While the disk rotates on the PDMS coated glass plate, a load cell measures the resulting force with a cantilever beam. One end of the cantilever beam is glued to the glass plate, while its other end presses against a load cell. From the balance of forces and torques, the friction force at a given slip velocity is determined. The friction force increases with the slip velocity sublinearly, which is consistent with the results reported previously by Vorvolakos and Chaudhury (Langmuir 2003, 19, 6778). During rotation, however, the glass disk comes off the PDMS film when the shear stress reaches a critical value. This critical shear stress increases with the modulus of the film, but it decreases with its thickness, following a square root relationship, which is similar to the adhesive fracture behavior in thin films under pull-off conditions. A simple model is presented that captures the essential physics of the fracture behavior under shear mode.

Surface instability of confined elastic bilayers: Theory and simulations

The surface of a soft elastic film becomes unstable and forms a self-organized undulating pattern because of adhesive interactions when it comes in contact proximity with a rigid surface. For a single film, the pattern length scale lambda , which is governed by the minimization of the elastic stored energy, gives lambda approximately 3h , where h is the film thickness. Based on a linear stability analysis and simulations of adhesion and debonding, we consider the contact instability of an elastic bilayer, which provides greater flexibility in the morphological control of interfacial instability. Unlike the case of a single film, the morphology of the contact instability patterns, debonding distance, and debonding force in a bilayer can be controlled in a nonlinear way by varying the thicknesses and shear moduli of the films. Interestingly, the pattern wavelength in a bilayer can be greatly increased or decreased compared to a single film when the adhesive contact is formed by the stiffer or the softer of the two films, respectively. In particular, lambda as small as 0.5h can be obtained. This indicates a new strategy for pattern miniaturization in elastic contact lithography.

Shear-induced adhesive failure of a rigid slab in contact with a thin confined film

A rigid-glass prism (square or rectangular base, rectangular cross-section) is sheared off a thin film of silicone elastomer bonded to a glass plate by applying a tangential force at various distances above the prism/elastomer interface. At a given tangential force, the prism starts to slide on the elastomeric film. As the sliding velocity, thus the frictional force, is progressively increased, an elastic instability develops at the interface that results in the formation of numerous bubbles. These bubbles, the lateral dimension of which is comparable to the thickness of the film, move across the interface with speeds 1000 times faster than the overall sliding speed of the glass prism against the PDMS film. It is found that the glass prism continues to slide on the elastomeric film as long as the applied shear stress is less than a critical value. During sliding, however, a normal stress is developed at the interface that decays from the front (i.e. where the force is applied) to the rear end of the prism. When the normal stress reaches a critical value, the prism comes off the film. The critical shear stress of fracture increases with the modulus of the film, but decreases with the thickness following a square root relationship, as is the case with the removal of rigid punches from thin elastomeric films by normal pull-off forces.

Contact instability in adhesion and debonding of thin elastic films

Based on experiments and 3D simulations, we show that a soft elastic film during adhesion and debonding from a rigid flat surface undergoes morphological transitions to pillars, labyrinths, and cavities, all of which have the same lateral pattern length scale, lambda close to lambda/H approximately 3 for thick films, H > 1 microm . The linear stability analysis and experiments show a new thin film regime where lambda/H approximately equal to 3 + 2pi(lambda/3 muH)1/4 (gamma is surface tension, mu is shear modulus) because of a significant surface energy penalty (for example, lambda/H approximately equal to 6 for H = 200 nm; mu = 1 MPa).