Generic morphologies of viscoelastic dewetting fronts

Instability and rupture of ultrathin freestanding viscoelastic solid films

We analyze the instability of viscoelastic solid freestanding thin films under the influence of van der Waals forces using linear stability analysis and nonlinear simulations. Linear stability analysis shows that the zero-frequency elastic modulus governs the onset of instability and stabilizes the film beyond a critical value analogous to thin supported viscoelastic solid films. However, for freestanding solid films, the critical shear modulus is found to be independent of surface tension, unlike that of thin supported viscoelastic solid films. It is further shown that freestanding viscoelastic solid films with higher moduli can be destabilized for a given film thickness and Hamaker constant compared to supported solid films. In contrast to thin viscoelastic liquid films where the growth rate is enhanced due to elastic effects but length scale is unaltered, freestanding films with solidlike viscoelasticity show a retarded growth rate and enhanced length scale. The presence of solidlike viscoelasticity has a stabilizing effect and affects all the key aspects of instability such as critical wave number, dominant wave number, and maximum growth rate. We numerically solve the set of coupled nonlinear evolution equations for film thickness and tangential displacement in order to elucidate the dynamics of film rupture. Our simulations show that, consistent with the linear stability predictions, an increase in the elastic modulus delays film rupture. The dynamics exhibits self-similarity in the vicinity of film rupture and the film thins as (t_{r}-t)^{3/4}, where t_{r} is the rupture time and t_{r}-t is the time remaining until film rupture. The scaling exponent 3/4 obtained for a thin freestanding viscoelastic solid film is significantly greater than the scaling exponent (1/3) for a thin freestanding viscous film.

Liquid dewetting under a thin elastic film

We study the dewetting of liquid films capped by a thin elastomeric layer. When the tension in the elastomer is isotropic, circular holes grow at a rate which decreases with increasing tension. The morphology of holes and rim stability can be controlled by changing the boundary conditions and tension in the capping film. When the capping film is prepared with a biaxial tension, holes form with a non-circular shape elongated along the high tension axis. With suitable choice of elastic boundary conditions, samples can even be designed such that square holes appear.

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.

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems

The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.

Asymptotic analysis of the dewetting rim

Consider a film of viscous liquid covering a solid surface, which it does not wet. If there is an initial hole in the film, the film will retract further, forming a rim of fluid at the receding front. We calculate the shape of the rim as well as the speed of the front using lubrication theory. We employ asymptotic matching between the contact line region, the rim, and the film. Our results are consistent with simple ideas involving dynamic contact angles and permit us to calculate all free parameters of this description, previously unknown.

Reduced interfacial entanglement density affects the boundary conditions of polymer flow

Hydrodynamic boundary conditions play a crucial role in the flow dynamics of thin films and can be probed by the analysis of liquid front profiles. For long-chained polymer films it was reported that a deviation from a symmetric profile is a result of viscoelastic effects. In this Letter, however, evidence is given that merely a slip-boundary condition at the solid-liquid interface can lead to an asymmetric profile. Variation of molecular weight shows that slippage is directly linked to chain entanglements. We find a reduced entanglement density at the solid-liquid interface (factors 3 to 4), which stresses the importance of considering nonbulk polymer properties in the vicinity of an interface.

Dewetting dynamics of stressed viscoelastic thin polymer films

Ultrathin polymer films that are produced, e.g., by spin coating are believed to be stressed since polymers are "frozen in" into out-of-equilibrium configurations during this process. In the framework of a viscoelastic thin-film model, we study the effects of lateral residual stresses on the dewetting dynamics of the film. The temporal evolution of the height profiles and the velocity profiles inside the film as well as the dissipation mechanisms are investigated in detail. Both the shape of the profiles and the importance of frictional dissipation vs viscous dissipation inside the film are found to change in the course of dewetting. The interplay of the nonstationary profiles, the relaxing initial stress, and the changes in the dominance of the two dissipation mechanisms caused by nonlinear friction with the substrate is responsible for the rich behavior of the system. In particular, our analysis sheds a different light on the occurrence of the unexpected maximum in the rim width obtained recently in experiments on polystyrene-polydimethylsiloxane systems.

Ripples in a wetting film formed by a moving meniscus

We carry out a theoretical investigation of the evolution of a wetting film formed by pressing a bubble against a solid substrate. Our model incorporates the effects of capillarity and Derjaguin-Landau-Verwey-Overbeek (DLVO) (van der Waals and electrostatic) components of the disjoining pressure. Rapid changes in the relative position of the bubble and the substrate are shown to result in surprisingly rich dynamics of wetting film deformations. Even for stable films, we find transient rippled deformations with several points of local maximum of wetting film thickness and discuss how their evolution depends on changes in the meniscus position relative to the substrate and the disjoining pressure parameters. A connection is made to the recently reported experimental observations of one such rippled deformation, the so-called wimple, characterized by a local minimum of the thickness in the center, surrounded by a ring of greater film thickness and bounded at the outer edge by the barrier rim. Guidelines are provided for experimental detection of more complex rippled deformations in stable wetting films. Development of instability is studied in a situation when the electrostatic component of disjoining pressure is destabilizing, with particular emphasis on the nonlinear evolution and rupture of the film. Potential applications of our findings to small-scale mixing and deposition of nanoparticles are discussed.

Dewetting dynamics in miscible polymer-polymer thin film mixtures

Thin polystyrene films supported by oxidized silicon (SiOx/Si) substrates may be unstable or metastable, depending on the film thickness, h, and can ultimately dewet the substrate when heated above their glass transition. In the metastable regime, holes nucleate throughout the film and subsequently grow due to capillary driving forces. Recent studies have shown that the addition of a second component, such as a copolymer or miscible polymer, can suppress the dewetting process and stabilize the film. We examined the hole growth dynamics and the hole morphology in thin film mixtures composed of polystyrene and tetramethyl bisphenol-A polycarbonate (TMPC) supported by SiOx/Si substrates. The hole growth velocity decreased with increasing TMPC content beyond that expected from changes in the bulk viscosity. The authors show that the suppression of the dewetting velocity is primarily due to reductions in the capillary driving force for dewetting and to increased friction at the substrate-polymer interface. The viscosity, as determined from the hole growth dynamics, decreases with decreasing film thickness, and is connected to a depression of the glass transition of the film.

Dewetting of thin polymer films

We study the dewetting of thin polymer films deposited on slippery substrate. Recent experiments on these systems have revealed many unexpected features. We develop here a model that takes into account the rheological properties of polymer melts, focussing on two dewetting geometries (the receding of a straight edge, and the opening of a hole). We show that the friction law associated with the slippage between the film and the substrate has a direct influence on the dewetting dynamic. In addition, we demonstrate that residual stresses, which can be stored in the films due to their viscoelasticity, are a source of destabilization for polymer films, and accelerate the dewetting process.

Slip vs. viscoelasticity in dewetting thin films

Ultrathin polymer films on non-wettable substrates display dynamic features which have been attributed to either viscoelastic or slip effects. Here we show that in the weak- and strong-slip regime, effects of viscoelastic relaxation are either absent or essentially indistinguishable from slip effects. Strong slip modifies the fastest unstable mode in a rupturing thin film, which questions the standard approach to reconstruct the effective interface potential from dewetting experiments.

Instability and dynamics of thin viscoelastic liquid films

The instability, rupture, and subsequent growth of holes in a thin Jeffreys-type viscoelastic film under the influence of long-range van der Waals force are investigated using both linear stability analysis and nonlinear numerical solutions. The linear stability analysis of full governing equations valid for arbitrary wave numbers shows that although fluid rheology does not influence the dominant length scale of the instability, it significantly affects the growth rate. It is shown that neglect of inertia and solvent dynamics results in a nonphysical singularity in the growth rate beyond a critical value of relaxation time. We further carry out numerical simulations of a set of long-wave, nonlinear differential equations (also derived in Rauscher et al., Eur. Phys. J. E 17, 373 (2005)) governing the evolution of the free surface. The nonlinear simulations, in their domain of validity, confirm the results of the linear analysis. Interestingly, results from nonlinear simulations further show that both for Newtonian and viscoelastic liquids, the shape and the dewetting dynamics of a hole are identical when examined in terms of a rescaled time which depends on rheological parameters. Thus, viscoelasticity of Jeffreys type merely accelerates the growth rate, without however affecting the important morphological characteristics.

Viscoelastic dewetting of a polymer film on a liquid substrate

The Dewetting of thin polymer films (60-300 nm) on a non-wettable liquid substrate has been studied in the vicinity of their glass transition temperature. In our experiment, we observe a global contraction of the film while its thickness remains uniform. We show that, in this case, the strain corresponds to simple extension, and we verify that it is linear with the stress applied by the surface tension. This allows direct measurement of the stress/strain response as a function of time, and thus permits the measurement of an effective compliance of the thin films. It is, however, difficult to obtain a complete viscoelastic characterization, as the short time response is highly dependant on the physical age of the sample. Experimental results underline the effects of residual stress and friction when dewetting is analyzed on rigid substrates.

New slip regimes and the shape of dewetting thin liquid films

We compare the flow behavior of liquid polymer films on silicon wafers coated with either octadecyl-(OTS) or dodecyltrichlorosilane (DTS). Our experiments show that dewetting on DTS is significantly faster than on OTS. We argue that this is tied to the difference in the solid/liquid friction. As the film dewets, the profile of the rim advancing into the undisturbed film is monotonically decaying on DTS but has an oscillatory structure on OTS. For the first time we can describe this transition in terms of a lubrication model with a Navier-slip condition for the flow of a viscous Newtonian liquid.

Hole growth in freely standing polystyrene films probed using a differential pressure experiment

We have probed the whole chain mobility of polymer molecules confined to freely standing films by measuring the flow of gas through holes growing in the films at elevated temperatures using a differential pressure experiment. Freely standing polystyrene films were measured for the temperature range 92 degrees C<T<105 degrees C for films with two different molecular weights Mw=717 x 10(3) and 2240 x 10(3) , with thicknesses 51 nm<h<97 nm . This range of film thicknesses is of particular interest because large reductions in the glass transition temperature Tg have been measured previously for freely standing PS films in this thickness range. We find that hole formation and growth, and therefore substantial chain mobility, does not occur until temperatures close to the bulk value of the glass transition temperature T(bulk)g. The characteristic growth times tau for the thinnest films, which have reduced values of Tg, are not substantially less than those for thicker films, and we find that these small differences in tau can be understood in terms of the bulk phenomenon of shear thinning. We also show that the viscosity at the edge of the hole inferred from the characteristic growth times obtained in this and previous studies exhibit shear thinning with reduced shear strain rates beta that span twelve orders of magnitude.

A thin-film equation for viscoelastic liquids of Jeffreys type

We derive a novel thin-film equation for linear viscoelastic media describable by generalized Maxwell or Jeffreys models. As a first application of this equation we discuss the shape of a liquid rim near a dewetting front. Although the dynamics of the liquid is equivalent to that of a phenomenological model recently proposed by Herminghaus et al. (S. Herminghaus, R. Seemann, K. Jacobs, Phys. Rev. Lett. 89, 056101 (2002)), the liquid rim profile in our model always shows oscillatory behaviour, contrary to that obtained in the former. This difference in behaviour is attributed to a different treatment of slip in both models.

Moving fronts in entangled polymeric films

Thin liquid films can become structurally unstable and dewet, forming holes which subsequently grow on the substrate. Considerable research has been conducted on the structural evolution and growth of holes, which invariably are shown to be circular. We show that morphologies characterized by circular holes comprise one of three possible morphological regimes. In polystyrene films, supported by silicon oxide substrates, two other regimes are observed with decreasing film thickness. In the second regime, the moving boundary of the growing hole may become unstable and form fingers. The spacing between the fingers is characterized by a well-defined wavelength lambda proportional to h(7/6) M(-1/2) , where h is the film thickness and M is the molecular weight. A dense branchlike morphology characterizes the peripheral regions of the holes in the third regime and is found only in the thinnest films.

Solvent-driven dewetting and rim instability

An experimental method suitable for reproducible results has been used to investigate dewetting behavior of thin films of solvent-laden polymer. This solvent-driven dewetting enables one to change spreading coefficient by an order of magnitude that is not readily realizable in thermal dewetting and to study polar interactions that have not been fully exploited experimentally. While the film instability is similar to that found in thermal dewetting, the rim instability is quite different. Two different types of the rim instability have been found. With a polar solvent, the rim instability changes from one type to another with increasing film thickness whereas the unstable rim becomes stable for an apolar solvent.

Dewetting of thin polymer films at temperatures close to the glass transition

We present detailed studies on dewetting of thin polystyrene (PS) films which were deposited onto silicon wafers coated with a polydimethylsiloxane (PDMS) monolayer. Experiments were performed at temperatures close to the glass transition temperature of PS. Several significant deviations from the dewetting behaviour of Newtonian liquids were observed. The length of the PS molecules, and thus the viscosity, turned out to be of minor importance in determining the dewetting velocity, in particular for the later regimes. In stark contrast, the geometry of the drying spot had a striking influence on the dewetting velocity. Initially, dewetting from straight contact lines proceeded faster than the opening of circular holes. At later stages, the process slowed down significantly in both cases. Under the conditions at which our experiments were performed, PS cannot flow like a simple liquid. Thus, the observed dewetting has to be the consequence of plastic deformation induced by capillary forces. Our results indicate that under such conditions the energy dissipation process is strongly affected by geometry, which is not the case for viscous liquids.

Complex dewetting scenarios captured by thin-film models

In the course of miniaturization of electronic and microfluidic devices, reliable predictions of the stability of ultrathin films have a strategic role for design purposes. Consequently, efficient computational techniques that allow for a direct comparison with experiment become increasingly important. Here we demonstrate, for the first time, that the full complex spatial and temporal evolution of the rupture of ultrathin films can be modelled in quantitative agreement with experiment. We accomplish this by combining highly controlled experiments on different film-rupture patterns with computer simulations using novel numerical schemes for thin-film equations. For the quantitative comparison of the pattern evolution in both experiment and simulation we introduce a novel pattern analysis method based on Minkowski measures. Our results are fundamental for the development of efficient tools capable of describing essential aspects of thin-film flow in technical systems.

Dewetting of thin-film polymers

In this paper we present a theoretical model for the dewetting of ultrathin polymer films. Assuming that the shear-thinning properties of these films can be described by a Cross-type constitutive equation, we analyze the front morphology of the dewetting film, and characterize the time evolution of the dry region radius, and of the rim height. Different regimes of growth are expected, depending on the initial film thickness, and on the power-law index involved in the constitutive equation. In the thin-films regime, the dry radius and the rim height obey power-law time dependences. We then compare our predictions with the experimental results obtained by Debrégeas et al. [Phys. Rev. Lett. 75, 3886 (1995)] and by Reiter [Phys. Rev. Lett. 87, 186101 (2001)].