Dewetting patterns and molecular forces: a reconciliation

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.

Morphology changes in the evolution of liquid two-layer films

We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100-nm thickness, or due to temperature-gradient-caused Marangoni flows in the heated case. Using a long-wave approximation, we derive coupled evolution equations for the interface profiles for the general nonisothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers, taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag, or mixed type. However, in the nonlinear stage of the evolution the mode type, and therefore the pattern morphology, can change via switching between two different branches of stationary solutions or via coarsening along a single branch.

Dynamics of ultrathin films in the glassy state

We report hole growth experiments in free-standing polystyrene (PS) films at temperatures up to 10 degrees C below the bulk glass transition. The data show an unexpected result: the growth rate of nucleated holes increases with increasing molecular weight, up to a limiting value beyond which the rate is approximately constant. Film thicknesses of 45, 80, and 100 nm were studied, using PS molecular weights ranging from 65K to 11.4 Mg/mol. Hole diameters grew linearly with time, and no growing rims were observed to form around the developing holes. Possible explanations in terms of elasticity, yield, and influence of sample preparation and confinement effects are discussed.

Electric field induced instability and pattern formation in thin liquid films

Electrostatic field induced instability, morphology, and patterning of a thin liquid film confined between two electrodes with an air gap are studied on the basis of nonlinear 3D simulations, both for spatially homogeneous and heterogeneous fields. In addition to the spinodal flow resulting from the variation of field because of local thickness changes, a heterogeneous imposed field also moves the liquid from the regions of low field to high field, thus allowing a more precise control of pattern. Hexagonal packing of liquid columns is observed for a spatially homogeneous electric field, which is in accord with the e-field experiments on thin polymer films (Schaffer et al. Nature 2000, 403, 874). For a large liquid volume fraction in the gap, varphi > or = 0.75, the coalescence of columns causes a phase inversion, leading to the formation of air columns or cylindrical holes trapped in the liquid matrix (air-in-liquid dispersion). Locally ordered aligned patterns are formed by imposing a spatial variation of the electrostatic field by using a topographically patterned electrode. For example, multiple rows/lines of liquid columns are formed near the edge of a step-like heterogeneity of the electrode and annular rings of ordered columns or concentric ripples are formed around a heterogeneous circular patch. Simulations predict that the electrode pattern is replicated in the film only when the pattern periodicity, L(p), exceeds the instability length scale on the basis of the minimum interelectrode separation distance, L(p) > or = lambda(m)-d(min). Thus, the formation of secondary structures can be suppressed by employing an electrode with deep grooves and stronger field gradients, which produces almost ideal templating. The number density of the electric field induced patterns can be altered by tuning the mean film thickness (or the volume fraction of liquid in the gap), periodicity and depth (amplitude) of the grooves on the top electrode, and the applied voltage. The implications are in electrostatic lithography, pattern replication in soft materials, and the design and interpretation of thin film experiments involving electric fields.

Nonlinear rupture of thin liquid films on solid surfaces

In this letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the relevant dimensionless groups is in striking agreement with the results of the numerical simulations of the original nonlinear evolution equations. This suggests that the weakly nonlinear theory adequately captures the underlying physics of the instability. When antagonistic (attractive/repulsive) molecular forces are considered, nonlinear saturation of the instability becomes possible. We show that the stability boundaries are determined by the van der Waals potential alone.

Self-organization of Mn12 single-molecule magnets into ring structures induced by breath-figures as templates

Cooling evaporation of a CH2Cl2 solution of Mn12 clusters on highly oriented pyrolitic graphite (HOPG) initiates the formation of water droplets that act as templates for the formation of self-assembled molecular magnetic rings.

Pattern formation and dewetting in thin films of liquids showing complete macroscale wetting: from "pancakes"to "swiss cheese"

Based on the complete 3D numerical solutions of the nonlinear thin film equation, we address the problems of surface instability, dynamics, morphological diversity and evolution in unstable thin films of the liquids that display complete macroscale wetting. The twin constraints of complete macroscale wettability and nanoscale instability produce a variety of microscopic morphological phases approximating sharp crystal surfaces with flat tops resembling a mesa or a micro "pancake" or a slice of Swiss cheese. While the maximum thickness of flat regions is found to be independent of the initial film thickness, the precise lateral morphology of microdomains formed depends on the film thickness. As the film thickness is increased, the initial pathway of evolution changes from the formation of small spherical droplets, to long mesas (parapets) and islands, to circular holes, all of which eventually resolve by ripening into a collection of round pancakes at equilibrium. However, beyond a certain transition thickness, a novel metastable honeycombed morphology, resembling a membrane or a slice of Swiss cheese, is uncovered, which is produced by an abrupt "freezing" of the evolution during hole growth. In contrast, the spinodal dewetting in thin films of partially wettable systems always engenders spherical droplets at equilibrium. The equilibrium dewetted area from simulations, as well as from simple mass balance, is shown to decline linearly with the initial film thickness.

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.

Disjoining pressure measurements using a microfabricated groove for a molecularly thin polymer liquid film on a solid surface

A method for measuring disjoining pressure of a molecularly thin liquid film on a solid surface by using a microfabricated groove has been developed. The shape of the meniscus of a thin film in the microgroove was measured with an atomic force microscope, and the disjoining pressure was obtained from the capillary pressure obtained from the measured curvature of the meniscus. Our method is applicable to a film with a thickness greater than the diameter of gyration in the polymer molecule. Moreover, the method can detect the changes in the disjoining pressure caused by ultraviolet light irradiation, and it is effective in investigating the intermolecular interaction between a thin film and a solid surface.

Dynamic domain formation in membranes: thickness-modulation-induced phase separation

A simple model investigates the amplification of fluctuations on membranes constituted of two lipids having different lengths. Van der Waals and electrostatic interactions across the lipid bilayer result in a destabilization favoring thickness variations of the membrane. Close to spontaneous demixing of the two components, the additional gain in free energy due to thickness undulations shifts the stability boundary which promotes phase separation into domains. Interestingly, this effect can be induced by an applied electric field or membrane potential. In biological systems, the dynamic model presented here indicates that electric fields might be important for controlling phase separation and the formation of domains called "rafts".

Controlled nanoparticle assembly by dewetting of charged polymer solutions

In this paper, we present an alternative approach for controlled nanoparticle organization on a solid substrate by applying dewetting patterns of charged polymer solutions as a templating system. Thin films of charged polymer solutions dewet a solid substrate to form complex dewetting patterns that depend on the polymer charge density. These patterns, ranging from polygonal networks to elongated structures that are stabilized by viscous forces during dewetting, serve as potential templates for two-dimensional nanoparticle organization on a solid substrate. Thus, while nanoparticles dried in pure water undergo self-assembly to form close-packed arrays, addition of charged polymer in the dispersion leads to the formation of open structures that are directed by the dewetting patterns of the polymer solution. In this study, we focus on the application of elongated structures resulting from dewetting of high-charge-density polymer solutions to align nanoparticles of silica and gold into long chains that are several micrometers in length. The particle ordering process is a two-step mechanism: an initial confinement of the nanoparticles in the dewetting structures and self-assembly of the particles within these structures upon further drying by lateral capillary attractions.

Polystyrene thin films in CO(2)

In air, or vacuum environments, liquid polystyrene (PS) thin films (thickness, h<100 nm ) supported by SiOx /Si substrates are structurally metastable or unstable, depending on film thickness. They rupture and eventually form droplets on the SiOx /Si substrates (dewet) due to the influence of destabilizing long-ranged van der Waals dispersion forces. We used scanning force microscopy to examine the structural stability of liquid PS films in the thickness range 5 nm<h<100 nm in liquid and in supercritical carbon dioxide ( CO2 ) environments. All films in this thickness range were metastable; holes developed throughout the films and over time these holes grew, impinged, and eventually formed droplets. The rate of destabilization is controlled by three factors: film thickness, temperature, and CO2 pressure (which dictates CO2 volume fraction in the films). Calculations of the effective interface potentials suggest that the energy barrier for nucleation and growth of holes in CO2 is larger than that in air, and in the limit of vanishingly low PS volume fraction the films should be stable.

Molecular forces caused by the confinement of thermal noise

We have investigated spontaneous surface instabilities of very thin polymer films. Film stability and the wavelength of the dominating unstable mode were found to depend sensitively on the media adjacent to the film. Our experimental results cannot be explained by van der Waals interactions alone. To account for the presence of an additional destabilizing force, we propose that the geometrical confinement of thermally excited acoustic waves gives rise to a force that is strong enough to destabilize thin films. This thermoacoustic effect is of similar magnitude as van der Waals forces.

Ordered droplet formation by thin polymer film dewetting on a stripe-patterned substrate

The dewetting process of thin polystyrene (PS) film on flat and stripe-patterned substrates is presented. Different dewetting processes were observed when the thin PS films annealed at above the glass transition temperature on these different kinds of substrates. The final dewetting on the flat substrate led to formation of polygonal liquid droplets, while on the stripe-patterned substrate, the droplets were observed to align at the centers of the stripes. A possible explanation for the dewetting process on the stripe-patterned substrate is proposed.

The spreading of surfactant solutions on thin liquid films

The spreading of a surfactant solution on a water film at first glance seems a trivial problem. However, in the last 30 years or so this has been shown to be anything like the case. There have been numerous studies which show that Marongoni driven fingering of the spreading surfactant front exists. In this paper this work has been reviewed and an attempt has been made to rationalise the results. The paper concludes with some recent observations of ours concerning the spreading of sodium dodecyl sulfate over relatively thick water films, 200 microm or less.

Capillary instabilities by fluctuation induced forces

The spontaneous break-up of thin films is commonly attributed to the destabilizing effect of van der Waals forces. Dispersion forces can be considered in terms of the confinement of the electromagnetic fluctuation spectrum. The principle of confinement is more general than the usual argument of interacting dipole fluctuations. It includes also disjoining pressures that are caused by thermal fluctuations. In this context, we review recent publications on the dewetting of thin polymer films, and argue that the presence of an acoustic disjoining pressure is necessary to adequately describe some of these experimental results.

Influence of surface cleaning on dewetting of thin polystyrene films

Thin polystyrene (PS) films on top of silicon substrates are a frequently investigated model system in the framework of unstable films. However, with respect to stability the various experiments yielded contradictory results. Focussing on the influence of preparation conditions such as the surface cleaning solves these contradictions. By applying different surface cleans the PS film can be changed from a stable homogeneous one into a completely dewetted one. In addition to the type of clean applied, the time between cleaning the surface and spin-coating the polymeric layer on top turned out to be an important experimental parameter.

Spinodal-like dewetting of thermodynamically-stable thin polymer films

Energetic considerations indicate that long-range Van der Waals forces stabilize thin polystyrene (PS) films against height fluctuations on silicon substrates. Nevertheless, we report here on the amplification of capillary waves of specific wavelengths for 15 nm thick PS films on silicon, ultimately leading to dewetting in a "spinodal-like" process. However, the temporal dependence of the wavelength of the growing instability does not agree with the "classical" spinodal dewetting mechanism. Therefore, this phenomenon is ascribed to the existence of "structural" forces resulting either from the restructuring of the films or from density variations within the films during annealing, in accordance with recent theoretical treatments. The process is shown not to be limited to polystyrene films, which indicates the generality of our findings.

Structural relaxation of spin-cast glassy polymer thin films as a possible factor in dewetting

Reiter has recently reported a situation in which the dewetting of quasi-solid films is linked to plastic deformation--rather than viscous flow--resulting from capillary forces. Herein we propose that, in thin films of some glassy polymers--especially poly(methyl methacrylate) (PMMA)--prepared by spin-casting from solvent, structural relaxation might impart sufficient stress to cause plastic deformation. We find that PMMA films decrease in thickness by several percent, which is sufficient to create significant stress in those cases in which the film is attached to a rigid substrate. The floating technique, which can take tens of minutes, might allow most of the structural relaxation to occur prior to dewetting experiments.

Viscoelastic dynamics of polymer thin films and surfaces

The strain relaxation behavior in a viscoelastic material, such as a polymer melt, may be strongly affected by the proximity of a free surface or mobile interface. In this paper, the viscoelastic surface modes of the material are discussed with respect to their possible influence on the freezing temperature and dewetting morphology of thin polymer films. In particular, the mode spectrum is connected with mode coupling theory assuming memory effects in the melt. Based on the idea that the polymer freezes due to these memory effects, surface melting is predicted. As a consequence, the substantial shift of the glass transition temperature of thin polymer films with respect to the bulk is naturally explanied. The experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. Finally, a simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid polymer films. It demonstrates that by taking into account the viscoelastic properties of the film, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.

Modelling thin-film dewetting on structured substrates and templates: bifurcation analysis and numerical simulations

We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.

Surface dynamics of polymer films

The dynamics of supported polymer films were studied by probing the surface height fluctuations as a function of lateral length scale using x-ray photon correlation spectroscopy. Measurements were performed on polystyrene (PS) films of thicknesses varying from 84 to 333 nm at temperatures above the PS glass transition temperature. Within a range of wave vectors spanning 10(-3) to 10(-2) nm(-1), good agreement is found between the measured surface dynamics and the theory of overdamped thermal capillary waves on thin films. Quantitatively, the data can be accounted for using the viscosity of bulk PS.

Coarsening dynamics of dewetting films

Lubrication theory for unstable thin liquid films on solid substrates is used to model the coarsening dynamics in the long-time behavior of dewetting films. The dominant physical effects that drive the fluid dynamics in dewetting films are surface tension and intermolecular interactions with the solid substrate. Instabilities in these films lead to rupture and other morphological changes that promote nonuniformity in the films. Following the initial instabilities, the films break up into near-equilibrium droplets connected by an ultrathin film. For longer times, the fluid will undergo a coarsening process in which droplets both move and exchange mass on slow time scales. The dynamics of this coarsening process will be obtained through the asymptotic reduction of the long-wave PDE governing the thin film to a set of ODEs for the evolution of the droplets. From this, a scaling law that governs the coarsening rate is derived.

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.

Instability of thin liquid films by density variations: a new mechanism that mimics spinodal dewetting

Based on the linear stability analysis and nonlinear simulations, conditions are established under which instability and dewetting of a thin liquid film can be engendered solely by the density variations (for example, due to confinement, layering, defects, and restructuring) related to changes in the local film thickness. An increase in the density with the increasing film thickness can stabilize a thermodynamically unstable film, and, equally interesting, a decrease in the density with increasing film thickness can render a thermodynamically stable film unstable. Morphological characteristics of this novel density variation induced instability closely resemble the well-known spinodal dewetting.

Line tension behavior of a first-order wetting system

Line tension of hexaethylene glycol on a silicon wafer is measured with positive values up to +2.5x10(-11) N below a contact angle of 6 degrees and negative values down to -2x10(-10) N above 6 degrees, as expected for a first-order wetting system. From the measured interface potentials, a semiquantitative model function for the overall interface potential is derived as a superposition of a constant nonretarded van der Waals interaction with a Hamaker constant of -2.6x10(-19) J and an exponentially decaying term, allowing the prediction of a finite positive line tension at the wetting transition.

Generic morphologies of viscoelastic dewetting fronts

A simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid coatings. It demonstrates that, by taking into account the elastic properties of the coating, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.

Hole formation in thin polymer films: a two-stage process

Thin, supported liquid films are known to rupture, creating holes throughout the film, due to defects or to van der Waals interactions. We show that the hole formation process before rupturing occurs in two stages, each characterized by distinct dynamical and morphological features. The time scale for the formation process is orders of magnitude slower than the translational (reptation) relaxation time of the individual chains. This has implications regarding the transition from the formation regime to subsequent hole growth regime on the underlying substrate.

Viscosity of entangled polystyrene thin film melts: Film thickness dependence

We determined the low-shear effective viscosity of entangled polystyrene thin film melts, in the thickness range of 27<h<100 nm, on SiO(x)/Si substrates. This was accomplished using a method based on the notion that thin liquid films can become unstable and rupture due to defects or to destabilizing, long-range van der Waals interactions (dewetting). The holes that are created in the film subsequently grow at a rate determined by a balance between the capillary driving forces and the viscous resistive forces. Based on the velocity of growth of holes on the substrate, we show that the viscosity decreases appreciably with decreasing thickness for 25<h<50 nm. These results are consistent with studies which suggest that the glass transition of entangled polystyrene thin film melts on SiO(x)/Si substrates exhibit an apparent decrease with decreasing film thickness over the same range of h.

Shape of a liquid front upon dewetting

The profile of a liquid front of a polymer film dewetting a solid substrate is examined by atomic force microscopy. The material removed from the substrate is accumulated in a rim next to the three-phase contact line. Theory predicts the leading edge of the rim profile to be a damped harmonic oscillation for a large class of systems. This is investigated experimentally for the first time, and we show that a non-Newtonian liquid behaves qualitatively different due to viscoelastic effects. It is pointed out that analysis of the rim shapes allows one to study quantitatively the rheological properties of complex fluids on a nanometer scale.