Spontaneous surface roughening induced by surface interactions between two compressible elastic films

Modeling Adhesive Hysteresis

When an elastomer approaches or retracts from an adhesive indenter, the elastomer’s surface can suddenly become unstable and reshape itself quasi-discontinuously, e.g., when small-scale asperities jump into or snap out of contact. Such dynamics lead to a hysteresis between approach and retraction. In this study, we quantify numerically and analytically the ensuing unavoidable energy loss for rigid indenters with flat, Hertzian and randomly rough profiles. The range of adhesion turns out to be central, in particular during the rarely modeled approach to contact. For example, negligible traction on approach but quite noticeable adhesion for nominal plane contacts hinges on the use of short-range adhesion. Central attention is paid to the design of cohesive-zone models for the efficient simulation of dynamical processes. Our study includes a Griffith’s type analysis for the energy lost during fracture and regeneration of a flat interface. It reveals that the leading-order corrections of the energy loss are due to the finite-range adhesion scale at best, with the third root of the linear mesh size, while leading-order errors in the pull-off force disappear linearly.

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.

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.

Miniaturized pattern formation in elastic films cast on sinusoidally patterned substrates

The various morphologies that are formed when van der Waals forces or electric field is induced between film cast on a sinusoidal substrate and in contact proximity with a contactor or electrode are studied. Remarkably smaller length scales are achieved (λc < 2.96h) than those obtained with films cast on flat substrates. With van der Waals interactions, the patterns are uniformly formed throughout the film but are not regularly ordered. When electric field is used at critical voltage, more ordered, localized patterns are formed at the zones of large local interaction strengths. When these patterns are evolved by increasing the applied voltage, coexistence of all three phases-cavities, stripes, and columns-is observed throughout the film. The localized patterns that are initially formed vary with the voltage applied and strongly dictate the phases of evolution. A patterned substrate/patterned contactor assembly can be made to operate like its unpatterned counterpart by making the interaction strength same everywhere and yet yield uniform, regularly ordered, highly miniaturized patterns. Such patterns are very useful in various applications like microfluidics; they are formed with great ease and can be morphologically tuned by tuning the externally applied electric field.

Direct measurement of the surface tension of a soft elastic hydrogel: exploration of elastocapillary instability in adhesion

An adhesively stressed thin film of a soft hydrogel confined between two rigid flat substrates autoroughens with its dominant wavelength (λ) exhibiting pronounced dependence on the film thickness (H). A linear stability analysis confirmed that this long wavelength instability (λ ~ 7H) is due to an elastocapillary effect, the implementation of which required direct measurements of the surface tension and the elasticity of the gel. The surface tension of the gel was estimated from the fundamental spherical harmonic of a hemispherical cap of the gel that was excited by an external noise. The shear modulus (μ) of the gel was determined from its resonant shear mode in a confined geometry. During the course of this study, it was found that a high density steel ball submerges itself inside the gel by balancing its excess weight with the accumulated strain induced elastic force that allows another estimation of its elastic modulus. The large ratio (1.8 mm) of the surface tension to its elasticity ascertains the role of elastocapillarity in the adhesion-induced pattern formation with such gels. Experimental results are in accord with a linear stability analysis that predicts that the rescaled wavelength λ(μH/γ)(0.27) is linear with H, which also modifies the conventional stress to pull a flat rigid object out of a very soft film by a multiplicative factor: (γ/μH)(1/4). The analysis also suggests some new results related to the role of the finite dilation of a material in interfacial pattern formation that may have nontrivial consequences in the adhesive delamination of very thin and/or soft elastic films via self-generated cracks.

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.

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.

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.

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.

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.

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

When two thin soft elastomeric films are separated from each other, an elastic instability develops at the interface. Although similar instability develops for the case of a soft film separating from a rigid adherent, there are important differences in the two cases. For the single-film case, the wavelength of instability is independent of any material properties of the system, and it scales only with thickness of the film. For the two-film case, a co-operative instability mode develops, which is a non-linear function of the thicknesses and the elastic moduli of both films. We investigate the development of such instability by energy minimization procedures. Understanding the nature of this instability is important, as it affects the adhesive compliance of the system and thus the energy release rate in the debonding of soft interfaces.

Adhesion and debonding of soft elastic films: crack patterns, metastable pathways, and forces

We study the phenomenon of debonding in a thin soft elastic film sandwiched between two rigid plates as one of the plates is brought into intimate contact and then pulled away from contact proximity by application of a normal force. Nonlinear simulations based on minimization of total energy (composed of stabilizing elastic strain energy and destabilizing adhesive interaction energy) are employed to address the problems of contact hysteresis, cavitation, crack morphology, variation of contact area, snap-off distance, pull-off force, work done, and energy loss. Below a critical distance (d(c)) upon approach, simulations show the formation of columnar structures and nonrandom, regularly arranged nanocavities at the soft interface at a length scale of approximately 3h (h being the thickness of the film). The persistence of such instability upon withdrawal (distance >>d(c)) indicates a contact hysteresis, which is caused by an energy barrier that separates the metastable states of the patterned configuration and the global minimum state of the flat film. The energy and the pull-off force are found to be nonequilibrium and nonunique properties depending on the initial contact, defects, noise, etc. Three broad pathways of debonding leading to adhesive failure of the interface, depending on the stiffness of the film, step size of withdrawal, and the imposed noise, are identified: a catastrophic column collapse mode, a peeling mode involving a continuous decrease in the contact area, and a column splitting mode. The first two modes are caused by a very high stress concentration near the cavity edges. These metastable patterned configurations engender pull-off forces that are orders of magnitude smaller than that required to separate two flat surfaces from contact.