Rupture of thin films with resonant substrate patterning

Physicochemical defect guided dewetting of ultrathin films to fabricate nanoscale patterns

Pathways to fabricate self-organized nanostructures have been identified exploiting the instabilities of ultrathin (<100 nm) polystyrene (PS) film on the polydimethylsiloxane (PDMS) substrates loaded with discrete and closely packed gold nanoparticles (AuNPs). The AuNPs were deposited on the PDMS substrates by chemical treatment, and the size and periodicity of the AuNPs were varied before coating the PS films. The study unveils that the physicochemical heterogeneity created by the AuNPs on the PDMS surface could guide the hole-formation, influence the average spacing between the holes formed at the initial dewetting stage, and affects the spacing and periodicity of the droplets formed at the end of the dewetting phase. The size and spacing of the holes and the droplets could be tuned by varying the nanoparticle loading on the PDMS substrate. Interestingly, as compared to the dewetting of PS films on the homogeneous PDMS surfaces, the AuNP guided dewetted patterns show ten-fold miniaturization, leading to the formation of the micro-holes and nanodroplets. The spacing between the droplets could also see a ten-fold reduction resulting in high-density random patterns on the PDMS substrate. Further, the use of a physicochemical substrate with varying density of physicochemical heterogeneities could impose a long-range order to the dewetted patterns to develop a gradient surface. The reported results can be of significance in the fabrication of high-density nanostructures exploiting the self-organized instabilities of thin polymers films.

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

The model problem examined here is the stability of a thin liquid film consisting of two miscible components, resting on a chemically patterned solid substrate and heated from below. In addition to surface tension gradients, the temperature variations also induce gradients in the concentration of the film by virtue of thermodiffusion/Soret effects. We study the stability and dewetting behaviour due to the coupled interplay between thermal gradients, Soret effects, long-range van der Waals forces, and wettability gradient-driven flows. Linear stability analysis is first employed to predict growth rates and the critical Marangoni number for chemically homogeneous surfaces. Then, nonlinear simulations are performed to unravel the interfacial dynamics and possible locations of the film rupture on chemically patterned substrates. Results suggest that appropriate tuning of the Soret parameter and its direction, in conjunction with either heating or cooling, can help manipulate the location and time scales of the film rupture. The Soret effect can either potentially aid or oppose film instability depending on whether the thermal and solutal contributions to flow are cooperative or opposed to each other.

Stability and break-up of thin liquid films on patterned and structured surfaces

Solid surfaces with chemical patterning or topographical structure have attracted attention due to many potential applications such as manufacture of flexible electronics, microfluidic devices, microscale cooling systems, as well as development of self-cleaning, antifogging, and antimicrobial surfaces. In many configurations involving patterned or structured surfaces, liquid films are in contact with such solid surfaces and the issue of film stability becomes important. Studies of stability in this context have been largely focused on specific applications and often not connected to each other. The purpose of the present review is to provide a unified view of the topic of stability and rupture of liquid films on patterned and structured surfaces, with particular focus on common mathematical methods, such as lubrication approximation for the liquid flow, bifurcation analysis, and Floquet theory, which can be used for a wide variety of problems. The physical mechanisms of the instability discussed include disjoining pressure, thermocapillarity, and classical hydrodynamic instability of gravity-driven flows. Motion of a contact line formed after the film rupture is also discussed, with emphasis on how the receding contact angle is expected to depend on the small-scale properties of the substrate.

Interaction of 3D dewetting nanodroplets on homogeneous and chemically heterogeneous substrates

Long-time interaction of dewetting nanodroplets is investigated using a long-wave approximation method. Although three-dimensional (3D) droplets evolution dynamics exhibits qualitative behavior analogous to two-dimensional (2D) dynamics, there is an extensive quantitative difference between them. 3D dynamics is substantially faster than 2D dynamics. This can be related to the larger curvature and, as a consequence, the larger Laplace pressure difference between the droplets in 3D systems. The influence of various chemical heterogeneities on the behavior of droplets has also been studied. In the case of gradient surfaces, it is shown how the gradient direction could change the dynamics. For a chemical step located between the droplets, the dynamics is enhanced or weakened depending on the initial configuration of the system.

Coarsening dynamics of nanodroplets on topographically structured substrates

Employing a biharmonic boundary integral method with linear elements, coarsening dynamics of nanodroplets on topographical step heterogeneity is investigated. It is shown that the step height and droplet configuration have an influential effect on the dynamics. Increasing the step height slows down the process while locating the droplets close to the step boosts the coarsening rate. Considering a slip boundary condition enhances the dynamics and reveals a transition in the droplet migration direction. Our results reveal that increasing the surface wettability weakens the dynamics. Various types of the disjoining pressure over the step are also considered and their effects on the coarsening are investigated.

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.

Rupture of thin liquid films on structured surfaces

We investigate stability and breakup of a thin liquid film on a solid surface under the action of disjoining pressure. The solid surface is structured by parallel grooves. Air is trapped in the grooves under the liquid film. Our mathematical model takes into account the effect of slip due to the presence of menisci separating the liquid film from the air inside the grooves, the deformation of these menisci due to local variations of pressure in the liquid film, and nonuniformities of the Hamaker constant which measures the strength of disjoining pressure. Both linear stability and strongly nonlinear evolution of the film are analyzed. Surface structuring results in decrease of the fastest growing instability wavelength and the rupture time. It is shown that a simplified description of film dynamics based on the standard formula for effective slip leads to significant deviations from the behavior seen in our simulations. Self-similar decay over several orders of magnitude of the film thickness near the rupture point is observed. We also show that the presence of the grooves can lead to instability in otherwise stable films if the relative groove width is above a critical value, found as a function of disjoining pressure parameters.

Rupture of thin liquid films: generalization of weakly nonlinear theory

In this paper, we investigate the rupture dynamics of thin liquid films driven by intermolecular forces via weakly nonlinear bifurcation analysis. The dynamic equations governing slow dynamics of the perturbation amplitude of the near-critical mode corresponding to several models describing the evolution of thin liquid films in different physical situations appear to have the same structure. When antagonistic (attractive and repulsive) molecular forces are considered, nonlinear saturation of the instability becomes possible, while the boundary of this supercritical bifurcation is determined solely by the form of the intermolecular potential. The rupture time estimate obtained in closed form shows an excellent agreement with the results of the previously reported numerical simulations of the strongly nonlinear coupled evolution equations upon fitting the amplitude of the small initial perturbation. We further extend the weakly nonlinear analysis of the film dynamics and apply the Galerkin approximation to derive the amplitude equation(s) governing the dynamics of the fastest growing linear mode far from the instability threshold. The comparison of the rupture time derived from this theory with the results of numerical simulations of the original nonlinear evolution equations shows a very good agreement without any adjustable parameters.

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.

Water-swelling-induced morphological instability of a supported polymethyl methacrylate thin film

The instability of supported poly(methyl methacrylate) (PMMA) thin films in water has been investigated. It is found that PMMA films partially detach from the solid substrate, resulting in the formation of bubbles under water. The process is reversible. Surface morphology analysis shows that the radius of curvature of the bubbles is dependent on the thickness of the PMMA films and is independent of the treatment of the films, such as the annealing temperature and the annealing time. Theoretical analysis based on a two-layer model (the swollen layer and the interior layer) shows that the partial swelling of PMMA in water is the physical origin of bubble formation.

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.

Electric-field-induced interfacial instabilities and morphologies of thin viscous and elastic bilayers

Electric-field-induced instabilities in thin bilayers composed of either purely viscous or purely elastic films resting on a solid substrate are studied. In contrast to the electric-field-induced instability in a single elastic film, the length scale of the instability for elastic bilayers can be tuned by changing the ratios of the shear moduli, thicknesses, and dielectric permittivities of the films. Linear stability analysis is employed to uncover the variations in the wavelength. The instabilities of the viscous bilayers follow different modes of interfacial evolution: either in-phase bending or antiphase squeezing. Linear and nonlinear analyses show that the mode type can be switched by changing the dielectric permittivities of the films. Nonlinear simulations find a number of intriguing interfacial morphologies: (a) an embedded upper layer in an array of lower layer columns, (b) upper layer columns encapsulated by lower layer beakers, (c) lower layer columns covered by the upper layer liquid resulting in concentric core-shell columns, (d) droplets of upper liquid on a largely undisturbed lower layer, and (f) evolution of two different wavelengths at the two interfaces of the bilayer. The simulated morphology types (a), (b) and (d) have been seen previously in experiments. The effect of the film viscosities on the evolution of the instability and final morphologies is also discussed.

Dewetting of the thin liquid bilayers on topographically patterned substrates: formation of microchannel and microdot arrays

A long-wave nonlinear analysis of the defect induced instabilities engendered by van der Waals forces in thin (<100 nm) viscous bilayers is presented. The major focus of this study is on generation of periodic patterns and its miniaturization by exploiting the self-organized instabilities of thin bilayers on topographically patterned substrates. A large variety of self-organized interfacial patterns such as periodic arrays of open and closed micro/nanochannels, isolated and encapsulated micro/nanodroplets, and membranes with ordered pores are obtained on different types of prepatterned substrates. In addition, we show that a bilayer can also be a suitable tool for (i) pattern transfer involving replication of the morphology of the lower layer interface to the free surface of the upper layer and (ii) generation of a mold by the upper layer material filling the periodic interstitial spaces formed by dewetting of the lower layer. Simulations suggest a profound influence of the substrate pattern directed lateral confinement, which governs the length scale of the dewetted structure when the substrate pattern periodicity is well below the spinodal length scale of the unstable bilayer. The influence of the initial configuration of the interfaces on the dewetting pathway and the dewetted structures are also shown.