Instability, dynamics, and morphology of thin slipping films

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.

Relaxation of Thermal Capillary Waves for Nanoscale Liquid Films on Anisotropic-Slip Substrates

The relaxation dynamics of thermal capillary waves for nanoscale liquid films on anisotropic-slip substrates are investigated using both molecular dynamics (MD) simulations and a Langevin model. The anisotropy of slip on substrates is achieved using a specific lattice plane of a face-centered cubic lattice. This surface's anisotropy breaks the simple scalar proportionality between slip velocity and wall shear stress and requires the introduction of a slip-coefficient tensor. The Langevin equation can describe both the growth of capillary wave spectra and the relaxation of capillary wave correlations, with the former providing a time scale for the surface to reach thermal equilibrium. Temporal correlations of interfacial Fourier modes, measured at thermal equilibrium in MD, demonstrate that (i) larger slip lengths lead to a faster decay in wave correlations and (ii) unlike isotropic-slip substrates, the time correlations of waves on anisotropic-slip substrates are wave-direction-dependent. These findings emerge naturally from the proposed Langevin equation, which becomes wave-direction-dependent, agrees well with MD results, and allows us to produce experimentally verifiable predictions.

Processing Induced Nonequilibrium Behavior of Polyvinylpyrrolidone Nanofilms Revealed by Dewetting

Polyvinylpyrrolidone (PVP) nanofilms prepared by spin-coating have vast applications in biological and microdevice fields. However, detailed knowledge of processing induced nonequilibrium behavior of PVP nanofilms and solutions for minimizing residual stresses toward high-quality films has still been lacking. In the present study, we first explored the rapid film formation process via statistics on nascent holes. Next, by employing dewetting as a major probe, we revealed that many processing conditions, particularly previously overlooked variables like the atmosphere, substrates, and immersion time, were correlated substantially with the degree of nonequilibrium of nanofilms. Proper aging temperature and time were demonstrated essential for releasing residual stresses and achieving more equilibrium nanofilms. This work offered abundant experimental evidence in the building relationship between the processing and nonequilibrium nature of polymer nanofilms, which were crucial for their preparation and application.

Signatures of slip in dewetting polymer films

Thin polymer films on hydrophobic substrates are susceptible to rupture and hole formation. This, in turn, initiates a complex dewetting process, which ultimately leads to characteristic droplet patterns. Experimental and theoretical studies suggest that the type of droplet pattern depends on the specific interfacial condition between the polymer and the substrate. Predicting the morphological evolution over long timescales and on the different length scales involved is a major computational challenge. In this study, a highly adaptive numerical scheme is presented, which allows for following the dewetting process deep into the nonlinear regime of the model equations and captures the complex dynamics, including the shedding of droplets. In addition, our numerical results predict the previously unknown shedding of satellite droplets during the destabilization of liquid ridges that form during the late stages of the dewetting process. While the formation of satellite droplets is well known in the context of elongating fluid filaments and jets, we show here that, for dewetting liquid ridges, this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip. This work shows how dissipative processes can be used to systematically tune the formation of patterns.

Thermal-induced slippage of soft solid films

The dynamics of interfacial slippage of entangled polystyrene (PS) films on an adsorbed layer of polydimethylsiloxane on silicon was studied from the surface capillary dynamics of the films. By using PS with different molecular weights, we observed slippage of the films in the viscoelastic liquid and rubbery solid state, respectively. Remarkably, all our data can be explained by the linear equation, J=-M∇P and a single friction coefficient, ξ, where J is the unit-width current, M is mobility, and P is Laplace pressure. For viscous films, M is accountable by using conventional formulism. For rubbery films, M takes on different expressions depending on whether the displacements associated with the slip velocity, v_{s}(∼∇P/ξ), dominate or elastic deformations induced by ∇P dominate. For viscoelastic liquid films, M is the sum of the mobility of the films in the viscous and rubbery states.

Giant Slip Induced Anomalous Dewetting of an Ultrathin Film on a Viscous Sublayer

A 'giant' slip dynamics was engineered to a highly confined interface of a dewetting polymethylmethacrylate (PMMA) ultrathin film by introducing a lubricating viscous polystyrene (PS) sublayer. The crossover of regimes from no-slip to giant-slip was engendered by tuning the viscosity and thickness of the sublayer. A long-range hole-rim interaction with increase in slippage on the PMMA-PS interface transformed the circular holes on the PMMA surface into the noncircular faceted ones. The extent of the slippage and the transition of the length scales from slip-dominated to no-slip regime were evaluated using a general linear stability analysis. The proposed formulation provided an analytical tool to evaluate the slippage effective at the soft and deformable liquid-liquid interfaces.

Kinetics of sub-spinodal dewetting of thin films of thickness dependent viscosity

An alternative explanation of the time varying and very low growth exponents in dewetting of polymer films like polystyrene films is presented based on non-linear simulations. The kinetics of these films is explored within the framework of experimentally observed thickness dependent viscosity. These films exhibit sub-spinodal dewetting via formation of satellite holes in between primary dewetted holes under favorable conditions of excess intermolecular forces and film thicknesses. We find that conditions responsible for sub-spinodal dewetting concurrently lead to remarkable changes in the kinetics of dewetting of even primary holes. For example, the radius of the hole grows in time with a power-law growth exponent sequence of [Formula: see text], in contrast to the usual  ∼4/5. This is due to the cumulative effect of reduced rim mobility due to thickness dependent viscosity and hindrance created by satellite holes.

Capillary Leveling of Freestanding Liquid Nanofilms

We report on the capillary-driven leveling of a topographical perturbation at the surface of a freestanding liquid nanofilm. The width of a stepped surface profile is found to evolve as the square root of time. The hydrodynamic model is in excellent agreement with the experimental data. In addition to exhibiting an analogy with diffusive processes, this novel system serves as a precise nanoprobe for the rheology of liquids at interfaces in a configuration that avoids substrate effects.

Short chains enhance slip of highly entangled polystyrenes during thin film dewetting

We investigate the effect of short chains on slip of highly entangled polystyrenes (PS) during thin film dewetting from non-wetting fluorinated surfaces.

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.

Unusual dewetting of thin polymer films in liquid media containing a poor solvent and a nonsolvent

We investigate the control of pattern size and kinetics in spontaneous dewetting of thin polymer films (polystyrene) that are stable to thermal annealing by annealing in a poor solvent (acetone)/nonsolvent (ethanol or n-hexane) liquid mixture. Dewetting occurs by the formation and growth of circular holes that coalesce to form droplets. The influence of the nature and the volume fraction of the nonsolvents on the contact angle of polymer droplets, number density of holes, and the kinetics of holes formation and growth is studied. Addition of ethanol greatly increases the hole density and slows down the kinetics substantially, while affecting only a small change in wettability. n-Hexane addition shows an interesting nonmonotonic response in decreasing the hole density and contact angle in the volume fraction range of 0-0.3 but an opposite effect beyond that. Although the two nonsolvents chosen cannot by themselves induce dewetting, their relative affinity for the solid substrate vis-à-vis acetone can strongly influence the observed dewetting scenarios that are not understood by the existing theoretical considerations. n-Hexane, for example, has great affinity for silicon substrate. In addition to the changes in wettability, viscosity, and film interfacial tension engendered by the nonsolvents, the possibility of the formation of adsorbed liquid layers at the substrate-polymer interface, which can modify the interfacial friction and slippage, needs to be considered.

Kinetically engendered subspinodal length scales in spontaneous dewetting of thin liquid films

Numerical simulations reveal emergence of subspinodal length scales in spontaneous dewetting of nonslipping unstable thin liquid films on homogeneous substrates if the liquid viscosity decreases with decrease in film thickness.

Continuous and discontinuous dynamic unbinding transitions in drawn film flow

When a plate is withdrawn from a liquid bath a coating layer is deposited whose thickness and homogeneity depend on the velocity and the wetting properties of the plate. Using a long-wave mesoscopic hydrodynamic description that incorporates wettability via a Derjaguin (disjoining) pressure we identify four qualitatively different dynamic transitions between microscopic and macroscopic coatings that are out-of-equilibrium equivalents of known equilibrium unbinding transitions. Namely, these are continuous and discontinuous dynamic wetting and emptying transitions. Several of their features have no equivalent at equilibrium.

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.

Stability and dewetting of metal nanoparticle filled thin polymer films: control of instability length scale and dynamics

We investigate the influence of gold nanoparticle addition on the stability, dewetting, and pattern formation in ultrathin polymer-nanoparticle (NP) composite films by examining the length and time scales of instability, morphology, and dynamics of dewetting. For these 10-50 nm thick (h) polystyrene (PS) thin films containing uncapped gold nanoparticles (diameter approximately 3-4 nm), transitions from complete dewetting to arrested dewetting to absolute stability were observed depending on the concentration of the particles. Experiments show the existence of three distinct stability regimes: regime 1, complete dewetting leading to droplet formation for nanoparticle concentration of 2% (w/w) or below; regime 2, partial dewetting leading to formation of arrested holes for NP concentrations in the range of 3-6%; and regime 3, complete inhibition of dewetting for NP concentrations of 7% and above. Major results are (a) length scale of instability, where lambdaH approximately hn remains unchanged with NP concentration in regime 1 (n approximately 2) but increases in regime 2 with a change in the scaling relation (n approximately 3-3.5); (b) dynamics of instability and dewetting becomes progressively sluggish with an increase in the NP concentration; (c) there are distinct regimes of dewetting velocity at low NP concentrations; (d) force modulation AFM, as well as micro-Raman analysis, shows phase separation and aggregation of the gold nanoparticles within each dewetted polymer droplet leading to the formation of a metal core-polymer shell morphology. The polymer shell could be removed by washing in a selective solvent, thus exposing an array of bare gold nanoparticle aggregates.

Slip effects in polymer thin films

Probing the fluid dynamics of thin films is an excellent tool for studying the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid, due to the fact that the dewetting process, an internal mechanism, acts as a driving force for liquid flow. Viscous dissipation, within the liquid, and slippage balance interfacial forces. Thus, friction at the solid/liquid interface plays a key role towards the flow dynamics of the liquid. Probing the temporal and spatial evolution of growing holes or retracting straight fronts gives, in combination with theoretical models, information on the liquid flow field and, especially, the boundary condition at the interface. We review the basic models and experimental results obtained during the last several years with exclusive regard to polymers as ideal model liquids for fluid flow. Moreover, concepts that aim to explain slippage on the molecular scale are summarized and discussed.

Spinodal dewetting of thin films with large interfacial slip: implications from the dispersion relation

We compare the dispersion relations for spinodally dewetting thin liquid films for increasing magnitude of interfacial slip length in the lubrication limit. While the shape of the dispersion relation, in particular the position of the maximum, are equal for no-slip up to moderate-slip lengths, the position of the maximum shifts to much larger wavelengths for large slip lengths. Here, we discuss the implications of this fact for recently developed methods to assess the disjoining pressure in spinodally unstable thin films by measuring the shape of the roughness power spectrum. For polystyrene (PS) films on octadecyltrichlorosilane (OTS) covered Si wafers (with slip length b approximately 1 microm), we predict a 20% shift of the position of the maximum of the power spectrum which should be detectable in experiments.

Adhesion and fingering in the lifting Hele-Shaw cell: role of the substrate

The lifting Hele-Shaw cell (LHSC) is used to study adhesion as well as viscous fingering. In the present paper we report a series of observations of development of the interface for different viscous fluids, both Newtonian and non-Newtonian, in a LHSC operated at a constant lifting force. Glass and perspex are used as the plates in two different sets of experiments. The objectives are 1) to measure the time required to separate the plates as a function of the lifting force and 2) to note the force above which viscous fingering appears. We find that for the Newtonian fluids, the plate separation time follows a universal power law with the lifting force, irrespective of fluid and substrate. The non-Newtonian fluids too, with proper scaling obey the same power law. The appearance of fingering, however, depends on the properties of the fluid as well as the substrate. We suggest a modified form of the capillary number which controls the onset of fingering; this new quantity, termed the "fingering parameter" involves the dielectric constants of the substrate and fluid in addition to the viscosity and surface tension.

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.

Capillary wave dynamics on supported viscoelastic films: single and double layers

We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu, Phys. Rev. E 74, 010602(R) (2006)].

Density variation-induced sign change of the effective hamaker constant in continuum theory

The density variation-induced dewetting model is reformulated in terms of the Dzyaloshinskii-Lifshitz-Pitaevskii continuum theory for van der Waals interactions. Though the density dependence is more complicated than in the London-Hamaker microscopic theory, numerical calculations for model polystyrene films show that the two theories yield qualitatively similar results. The physics of the dewetting model is thus not changed. Quantitatively, the differences between the two theories are notable. The calculations also show that a linear approximation suffices to take density variations into account, thus simplifying the density variation-induced dewetting models.

A thin-film model for corotational Jeffreys fluids under strong slip

We derive a thin-film model for viscoelastic liquids under strong slip which obey the stress tensor dynamics of corotational Jeffreys fluids.

Dynamic instability of thin viscoelastic films under lateral stress

We study the influence of lateral stress on the stability of thin viscoelastic films. The free surface of a deposited film under stress is shown to undergo an instability initiated by an anisotropic diffusion of the polymer molecules. This instability ultimately results in the formation of holes provided that the initial surface fluctuations are larger than a critical value. The latter is found to decrease when increasing the stress. An increase of the holes number density with the stress is therefore predicted. Most interestingly, the holes number density is also predicted to increase when increasing the molecular weight of the polymers. Additionally, we demonstrate that the friction of the substrate suppresses any spatial coherence between holes on large length scales. These predictions explain recent experimental observations made on thin spin-coated polystyrene films [G. Reiter, Nat. Mater. 4, 754 (2005)10.1038/nmat1484].

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.

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.

Dewetting induced by complete versus nonretarded van der Waals forces

Spontaneous rupture of some polymer films upon heating is commonplace. The very criterion for this instability is the system free energy, G(L), possessing a negative curvature. In films that are apolar with h < or = 100 nm van der Waals (vdW) interactions usually constitute a major contribution to G(L) for which the approximate form G(L) = -A/12piL(2) (where A is the Hamaker constant), ignoring retardation, has been widely used. In this work, we investigate the limits to this approximation by calculating the complete vdW interactions for popular polymer film systems in dewetting experiments including air-polystyrene-SiO2-Si, air-polystyrene-poly(methyl methacrylate)-Si, and air-poly(methyl methacrylate)-polystyrene-Si based on the theory of Dzyaloshinskii, Lifshitz, and Pitaevskii (DLP). We found that retardation effects could produce significant modifications to G(L) even when the thickness of the polymer and/or the interlayer is only 1-2 nm, contrary to conventional presumption.