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

Designing antiviral surfaces to suppress the spread of COVID-19

Surface engineering is an emerging technology to design antiviral surfaces, especially in the wake of COVID-19 pandemic. However, there is yet no general understanding of the rules and optimized conditions governing the virucidal properties of engineered surfaces. The understanding is crucial for designing antiviral surfaces. Previous studies reported that the drying time of a residual thin-film after the evaporation of a bulk respiratory droplet on a smooth surface correlates with the coronavirus survival time. Recently, we [Chatterjee et al., Phys. Fluids. 33, 021701 (2021)] showed that the evaporation is much faster on porous than impermeable surfaces, making the porous surfaces lesser susceptible to virus survival. The faster evaporation on porous surfaces was attributed to an enhanced disjoining pressure within the thin-film due the presence of horizontally oriented fibers and void spaces. Motivated by this, we explore herein the disjoining pressure-driven thin-film evaporation mechanism and thereby the virucidal properties of engineered surfaces with varied wettability and texture. A generic model is developed which agrees qualitatively well with the previous virus titer measurements on nanostructured surfaces. Thereafter, we design model surfaces and report the optimized conditions for roughness and wettability to achieve the most prominent virucidal effect. We have deciphered that the optimized thin-film lifetime can be gained by tailoring wettability and roughness, irrespective of the nature of texture geometry. The present study expands the applicability of the process and demonstrates ways to design antiviral surfaces, thereby aiding to mitigate the spread of COVID-19.

Coarsening and pattern formation during true morphological phase separation in unstable thin films under gravity

We address in detail the problem of true morphological phase separation (MPS) in three-dimensional or (2+1)-dimensional unstable thin liquid films (>100nm) under the influence of gravity. The free-energy functionals of these films are asymmetric and show two points of common tangency, which facilitates the formation of two equilibrium phases. Three distinct patterns formed by relative preponderance of these phases are clearly identified in "true MPS". Asymmetricity induces two different pathways of pattern formation, viz., defect and direct pathway for true MPS. The pattern formation and phase-ordering dynamics have been studied using statistical measures such as structure factor, correlation function, and growth laws. In the late stage of coarsening, the system reaches into a scaling regime for both pathways, and the characteristic domain size follows the Lifshitz-Slyozov growth law [L(t)∼t^{1/3}]. However, for the defect pathway, there is a crossover of domain growth behavior from L(t)∼t^{1/4}→t^{1/3} in the dynamical scaling regime. We also underline the analogies and differences behind the mechanisms of MPS and true MPS in thin liquid films and generic spinodal phase separation in binary mixtures.

Analytical solutions for the profile of two-dimensional droplets with finite-length precursor films

By means of the lubrication approximation we obtain the full family of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by a disjoining-conjoining pressure. We show that for a set of quite general disjoining-conjoining pressure potentials, the free surface can adopt only five nontrivial static patterns; in particular, we find solutions when the height goes to zero which describe satisfactorily the complete free surface for a finite amount of fluid deposited on a substrate. To test the extension of the applicability of our solutions, we compare them with those obtained when the lubrication approximations are not employed and under conditions where the lubrication hypothesis are not strictly valid, and also with axisymmetric solutions. For a given disjoining-conjoining potential, we report a new analytical solution that accounts for all the five possible solutions.

Coarsening Dynamics of True Morphological Phase Separation in Unstable Thin Films

Unstable thin films can spontaneously phase separate into two equilibrium flat-film morphologies of different thicknesses under the influence of gravity or favorable combinations of apolar and polar excess intermolecular forces. Two distinct pathways and associated dynamics of this morphological phase separation are presented based on numerical simulations of the 2-D thin film equation. The two pathways are (1) the "direct pathway" whereby the thicker phase forms directly and concurrently with the thinner phase and (2) the "defect pathway" whereby the thicker phase forms by the coarsening of defects of intermediate thickness and appears much later than the thinner phase. The defect pathway is favored by films whose initial thickness lies closer to the thickness of the thinner phase. Both pathways show an initial power law decay with exponent -1/4 in time followed by a plateau in the number density of domains/defects. Thereafter, the defect pathway shows another universal power law decay with exponent -1/3 and ends with a logarithmic decay, which is specific to the d = 2 case as there is no interfacial curvature in d = 2. The direct pathway skips the second power law decay and goes directly to the logarithmic decay.

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.

Final state of a perturbed liquid film inside a container under the effect of solid-liquid molecular forces and gravity

We investigate theoretically the possible final stationary configurations that can be reached by a laterally confined uniform liquid film inside a container. The liquid is under the action of gravity, surface tension, and the molecular interaction with the solid substrate. We study the case when the container is in an upright position as well as when it is turned upside down. The governing parameters of the problem are the initial thickness of the film, the size of the recipient that contains the liquid, and a dimensionless number that quantifies the relative strength of gravity with respect to the molecular interaction. The uniform film is always a possible final state and depending on the value of the parameters, up to three different additional final states may exist, each one consisting in a droplet surrounded by a thin film. We derive analytical expressions for the energy of these possible final configurations and from these we analyze which state is indeed reached. A uniform thin film may show three different behaviors after a perturbation: The system recovers its initial shape after any perturbation, the fluid evolves towards a drop (if more than one is possible, it tends toward that with the thinnest precursor film) for any perturbation, or the system ends as a uniform film or a drop depending on the details of the perturbation.

Stability of thin liquid films and sessile droplets under confinement

The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. This instability of a nonvolatile sessile droplet turns out to be equivalent to the instability of a volatile drop which can attain chemical equilibrium with its vapor.

Formation of precise 2D Au particle arrays via thermally induced dewetting on pre-patterned substrates

The fabrication of precise 2D Au nanoparticle arrays over a large area is presented. The technique was based on pre-patterning of the substrate before the deposition of a thin Au film, and the creation of periodic particle arrays by subsequent dewetting induced by annealing. Two types of pre-patterned substrates were used: The first comprised an array of pyramidal pits and the second an array of circular holes. For the dewetting of Au films on the pyramidal pit substrate, the structural curvature-driven diffusion cooperates with capillarity-driven diffusion, resulting in the formation of precise 2D particle arrays for films within a structure dependent thickness-window. For the dewetting of Au films on the circular hole substrate, the periodic discontinuities in the films, induced by the deposition, can limit the diffusion paths and lead to the formation of one particle per individual separated region (holes or mesas between holes), and thus, result in the evolution of precise 2D particle arrays. The influence of the pre-patterned structures and the film thickness is analyzed and discussed. For both types of pre-patterned substrate, the Au film thickness had to be adjusted in a certain thickness-window in order to achieve the precise 2D particle arrays.

Strands, networks, and continents from polystyrene dewetting at the air-water interface: implications for amphiphilic block copolymer self-assembly

We demonstrate that nanoscale aggregates similar to those formed via amphiphilic block copolymer self-assembly at the air-water interface, including strands, networks, and continents, can be generated by the simple spreading of PS homopolymer solutions on water. Two different PS homopolymers of different molecular weight (PS-405k, M(n) = 405 000 g mol(-1) and PS-33k, M(n) = 33 000 g mol(-1)) are spread at the air-water interface at various spreading concentrations ranging from 0.25 to 3.0 mg/mL. Aggregate formation is driven by PS dewetting from water as the spreading solvent evaporates. We propose that a high spreading concentration or a high molecular weight lead to chain entanglements that restrict macromolecular mobility in the solution, enabling the kinetic trapping of nanostructures associated with early and intermediate stages of PS dewetting. Comparison of PS-405k with a mainly hydrophobic PS-b-PEO block copolymer of similar molecular weight (PSEO-392k, M(n) = 392 000 g mol(-1), 2.0 wt % PEO) allows the effect of a relatively short surface active block on aggregate formation to be investigated. We show that whereas the PEO block is not a required component for the formation of strands and other nonglobular aggregates, it does increase the number of these aggregates at a given spreading concentration and decreases the minimum spreading concentration at which these aggregates are observed, along with decreasing the dimensions and polydispersity of specific surface features. The results provide supporting evidence for the role of PS dewetting in the generation of multiple PS-b-PEO aggregate morphologies at the air-water interface, as originally described in earlier paper from our group.

Coarsening in the electrohydrodynamic patterning of thin polymer films

Periodic pillarlike microstructures can be created from initially flat polymer films via the electrohydrodynamic instabilities. Those patterns, however, are metastable. Our experimental observations show that the average pillar size increases slowly after linear growth. Major coarsening events then take place over times several orders of magnitude longer than the linear growth time. For all fill ratios, a logarithmic time dependence of the average pillar size can be identified, i.e., <S> proportional to ln t. Thicker films, however, have faster coarsening rates than thinner films. Linear stability analysis of the pseudosteady states reveals two major coarsening mechanisms, collision and Ostwald ripening, which can also be identified from experimental images. We then reduce the original partial differential equation (PDE) into a pair of ODEs, which govern the interaction between pillars due to the above two coarsening mechanisms. From this, a logarithm scaling law is obtained for both low and high fill ratios and the coarsening rate is slower for lower fill ratios, consistent with experimental observations. We also find that arrays with more uniform sizes tend to start coarsening later, but they coarsen faster than more "disperse" arrays, which could be possibly utilized in experiments for controlling the onset and speed of coarsening. The logarithm scaling in the electrohydrodynamic coarsening phenomenon, which differs from coarsening in spinodal decomposition and dewetting of thin liquid films, is due to the significant nonlinear effect of Maxwell stresses and geometric confinement on the disjoining pressure at both top and bottom electrodes.

Solvent-assisted dewetting during chemical vapor deposition

This study examines the use of a nonreactive solvent vapor, tert-butanol, during initiated chemical vapor deposition (iCVD) to promote polymer film dewetting. iCVD is a solventless technique to grow polymer thin films directly from gas phase feeds. Using a custom-built axisymmetric hot-zone reactor, smooth poly(methyl methacrylate) films are grown from methyl methacrylate (MMA) and tert-butyl peroxide (TBPO). When solvent vapor is used, nonequilibrium dewetted structures comprising of randomly distributed polymer droplets are observed. The length scale of observed topographies, determined using power spectral density (PSD) analysis, ranges from 5 to 100 microm and is influenced by deposition conditions, especially the carrier gas and solvent vapor flow rates. The use of a carrier gas leads to faster deposition rates and suppresses thin film dewetting. The use of solvent vapor promotes dewetting and leads to larger length scales of the dewetted features. Control over lateral length scale is demonstrated by preparation of hierarchal "bump on bump" topographies. Vapor-induced dewetting is demonstrated on silicon wafer substrate with a native oxide layer and also on hydrophobically modified substrate prepared using silane coupling. Autophobic dewetting of PMMA from SiOx/Si during iCVD is attributed to a thin film instability driven by both long-range van der Waals forces and short-range polar interactions.

Nanoparticle formation in Au thin films by electron-beam-induced dewetting

We carried out investigations on electron-beam-induced nanoparticle formation in thin (5-30 nm) Au films on smooth SiO(2)/Si substrates. When the Au films were irradiated with an electron beam, the Au films broke up into nanoparticles through the dewetting process. The dominant wavelengths of the surface (corresponding to the pitch between nanoparticles) were closely related with the thickness of the Au. We then developed a new technique for the formation of periodically arranged Au nanoparticles using a holed substrate. The nanoholes induced heterogeneous nucleation and helped to form ordered nanoparticles between the holes. Two-dimensionally, periodically arranged Au nanoparticles with a pitch of 100 nm were obtained.

Coarsening of unstable thin films subject to gravity

Thin films of viscous fluids coating hydrophobic substrates are unstable to dewetting instabilities, and long-time evolution leads to the formation of an array of near-equilibrium droplets connected by ultrathin fluid layers. In the absence of gravity, previous use of lubrication theory has shown that coarsening dynamics will ensue-the system will evolve by successively eliminating small drops to yield fewer larger drops. While gravity has only a weak influence on the initial thin film, we show that it has a significant influence on the later stages of the coarsening dynamics, dramatically slowing the rate of coarsening for large drops. Small drops are relatively unaffected, but as coarsening progresses, these aggregate into larger drops whose shape and dynamics are dominated by gravity. The change in the mean drop shape causes a corresponding gradual transition from power-law coarsening to a logarithmic behavior.

Theory of slope-dependent disjoining pressure with application to Lennard–Jones liquid films

A liquid film of thickness h<100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure Pi. Since Pi dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives Pi=Pi(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h-->0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of Pi that depends on the slope h(x) as well as the height h of the film. When this theory is implemented for Lennard-Jones liquid films, the new Pi=Pi(h,h(x)) is bounded near a contact line as h-->0. Thus, the singularity in Pi(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new Pi can capture all three regimes of drop behavior (complete wetting, partial wetting, and pseudo-partial wetting) without altering the signs of the long and short-range interactions. We find that a drop with a precursor film is linearly stable.

Free-surface thin-film flows over uniformly heated topography

The long-wave (lubrication) approximation governing the evolution of a thin film over a uniformly heated topographical substrate is solved numerically. We study the initial-value problem for a variety of governing dimensionless parameters and topographical substrates. We demonstrate that the dynamics is characterized by a slow relaxation process with continuous coarsening of drops up to a large time where coarsening is terminated and the interface organizes into a series of drops each of which is located in a trough in topography.

Self-assembly of polystyrene-block-poly(ethylene oxide) copolymers at the air-water interface: is dewetting the genesis of surface aggregate formation?

Block copolymer self-assembly at the air-water interface is commonly regarded as a two-dimensional counterpart of equilibrium block copolymer self-assembly in solution and in the bulk; however, the present analysis of atomic force microscopy (AFM) and isotherm data at different spreading concentrations suggests a nonequilibrium mechanism for the formation of various polystyrene-b-poly(ethylene oxide) (PS-b-PEO) aggregates (spaghetti, dots, rings, and chainlike aggregates) at the air-water interface starting with an initial dewetting of the copolymer spreading solution from the water surface. We show that different spreading concentrations provide kinetic snapshots of various stages of self-assembly at the air-water interface as a result of different degrees of PS chain entanglements in the spreading solution. Two block copolymers are investigated: MW = 141k (11.4 wt % PEO) and MW = 185k (18.9 wt % PEO). Langmuir compression isotherms for the 185k sample deposited from a range of spreading concentrations (0.1-2.0 mg/mL) indicate less dense packing of copolymer chains within aggregate cores formed at lower spreading concentrations due to a competition between the interfacial adsorption of PEO blocks and the kinetic restrictions of PS chain entanglements. From AFM analysis of the transferred Langmuir-Blodgett films, it is clear that PS chain entanglements in the spreading solution also affect the morphological evolution of surface aggregates for both samples, with earlier structures being trapped at higher concentrations. At the highest spreading concentration for the 141k copolymer, the coexistence of long spaghetti aggregates with cellular arrays of holes, along with various transition structures, indicates that various surface aggregates evolve from networks of rims formed as a result of dewetting of the evaporating spreading solution from the water surface.

Ultrathin film deposition by liquid CO2 free meniscus coating-uniformity and morphology

Ultrathin organic films of sucrose octaacetate (SOA) were deposited on 12.5 cm diameter silicon wafer substrates using high-pressure free meniscus coating (hFMC) with liquid CO2 (l-CO2) as a coating solvent. The dry film thickness across the wafer and the morphology of deposited films were characterized as a function of coating conditions-withdrawal velocity, solution concentration, and evaporation driving force (deltaP). When no evaporation driving force was applied (deltaP = 0), highly uniform films were deposited with thickness in the range of 8-105 angstroms over the entire concentration range (3-11 wt%). Uniform films were also obtained at low concentrations (3-5 wt%) with a low evaporation driving force (deltaP = 0.0138 MPa). However, films deposited at medium to high concentrations (7-11 wt%) were thicker (110-570 angstroms) and less uniform, with larger nonuniformities at higher applied evaporation driving forces. Optical microscopy and atomic force microscopy (AFM) were used to characterize film morphology including drying defects and film roughness. Films deposited without evaporation had no apparent drying defects and very low root-mean-square (RMS) roughness (1.4-3.8 angstroms). Spinodal-like dewetting morphologies including holes with diameters in the range of 100-300 nm, and surface undulations were observed in films deposited at medium concentration (7 wt%) and low deltaP (0.0138-0.0276 MPa). At higher concentrations and higher evaporative driving forces, spinodal-like dewetting morphologies disappeared but concentric ring defect structures were observed with diameters in the range 20-125 microm. The film thickness and morphology of SOA films deposited from 1-CO2 hFMC were compared to those deposited from toluene and acetone under normal dip coating. Films deposited from l-CO2 hFMC were much thinner, more uniform, and exhibited much fewer drying defects and lower RMS roughness.

Nonlinear stability analysis of a two-layer thin liquid film: Dewetting and autophobic behavior

The nonlinear stability analysis of a liquid film composed of two superposed thin layers of immiscible liquids resting on a solid substrate is performed. It is shown that the coupling of van der Waals interactions in the two layers can lead to an autophobic behavior in the form of spinodal decomposition of two planar liquid layers into a system of localized drops divided by almost planar wetting layers. The results of the weakly nonlinear analysis near the instability threshold are confirmed by the numerical solution of a system of two strongly nonlinear evolution equations for the liquid-liquid and liquid-gas interfaces. The kinetics of the drop coarsening at late stages is studied and is found to be close to that reported for a one-layer film. It is also shown that gravity effects can become significant even for very thin two-layer films.