Phase diagram for morphological transitions of wetting films on chemically structured substrates

Height of a liquid drop on a wetting stripe

Adsorption of liquid on a planar wall decorated by a hydrophilic stripe of width L is considered. Under the condition that the wall is only partially wet (or dry) while the stripe tends to be wet completely, a liquid drop is formed above the stripe. The maximum height ℓ_{m}(δμ) of the drop depends on the stripe width L and the chemical potential departure from saturation δμ where it adopts the value ℓ_{0}=ℓ_{m}(0). Assuming a long-range potential of van der Waals type exerted by the stripe, the interfacial Hamiltonian model is used to show that ℓ_{0} is approached linearly with δμ with a slope which scales as L^{2} over the region satisfying L≲ξ_{∥}, where ξ_{∥} is the parallel correlation function pertinent to the stripe. This suggests that near the saturation there exists a universal curve ℓ_{m}(δμ) to which the adsorption isotherms corresponding to different values of L all collapse when appropriately rescaled. Although the series expansion based on the interfacial Hamiltonian model can be formed by considering higher order terms, a more appropriate approximation in the form of a rational function based on scaling arguments is proposed. The approximation is based on exact asymptotic results, namely, that ℓ_{m}∼δμ^{-1/3} for L→∞ and that ℓ_{m} obeys the correct δμ→0 behavior in line with the results of the interfacial Hamiltonian model. All the predictions are verified by the comparison with a microscopic density functional theory (DFT) and, in particular, the rational function approximation-even in its simplest form-is shown to be in a very reasonable agreement with DFT for a broad range of both δμ and L.

Symmetry-breaking morphological transitions at chemically nanopatterned walls

We study the structure and morphological changes of fluids that are in contact with solid composites formed by alternating and microscopically wide stripes of two different materials. One type of the stripes interacts with the fluid via long-ranged Lennard-Jones-like potential and tends to be completely wet, while the other type is purely repulsive and thus tends to be completely dry. We consider closed systems with a fixed number of particles that allows for stabilization of fluid configurations breaking the lateral symmetry of the wall potential. These include liquid morphologies corresponding to a sessile drop that is formed by a sequence of bridging transitions that connect neighboring wet regions adsorbed at the attractive stripes. We study the character of the transitions depending on the wall composition, stripes width, and system size. Using a (classical) nonlocal density functional theory (DFT), we show that the transitions between different liquid morphologies are typically weakly first-order but become rounded if the wavelength of the system is lower than a certain critical value L_{c}. We also argue that in the thermodynamic limit, i.e., for macroscopically large systems, the wall becomes wet via an infinite sequence of first-order bridging transitions that are, however, getting rapidly weaker and weaker and eventually become indistinguishable from a continuous process as the size of the bridging drop increases. Finally, we construct the global phase diagram and study the density dependence of the contact angle of the bridging drops using DFT density profiles and a simple macroscopic theory.

Microscopic aspects of wetting using classical density functional theory

Wetting is a rather efficient mechanism for nucleation of a phase (typically liquid) on the interface between two other phases (typically solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid-fluid and fluid-substrate intermolecular interactions brings about an entire 'zoo' of possible fluid configurations, such as liquid films with a thickness of a few nanometers, liquid nanodrops and liquid bridges. These fluid configurations are often associated with phase transitions occurring at the solid-gas interface and at lengths of just several molecular diameters away from the substrate. In this special issue article, we demonstrate how a fully microscopic classical density-functional framework can be applied to the efficient, rational and systematic exploration of the rich phase space of wetting phenomena. We consider a number of model prototype systems such as wetting on a planar wall, a chemically patterned wall and a wedge. Through density-functional computations we demonstrate that for these simply structured substrates the behaviour of the solid-gas interface is already highly complex and non-trivial.

Scaling behavior of thin films on chemically heterogeneous walls

We study the adsorption of a fluid in the grand canonical ensemble occurring at a planar heterogeneous wall which is decorated with a chemical stripe of width L. We suppose that the material of the stripe strongly preferentially adsorbs the liquid in contrast to the outer material which is only partially wet. This competition leads to the nucleation of a droplet of liquid on the stripe, the height h_{m} and shape of which (at bulk two-phase coexistence) has been predicted previously using mesoscopic interfacial Hamiltonian theory. We test these predictions using a microscopic Fundamental Measure Density Functional Theory which incorporates short-ranged fluid-fluid and fully long-ranged wall-fluid interactions. Our model functional accurately describes packing effects not captured by the interfacial Hamiltonian but still we show that there is excellent agreement with the predictions h_{m}≈L^{1/2} and for the scaled circular shape of the drop even for L as small as 50 molecular diameters. For smaller stripes the droplet height is considerably lower than that predicted by the mesoscopic interfacial theory. Phase transitions for droplet configurations occurring on substrates with multiple stripes are also discussed.

Classical density functional study of wetting transitions on nanopatterned surfaces

Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.

Nematic films at chemically structured surfaces

We investigate theoretically the morphology of a thin nematic film adsorbed at flat substrate patterned by stripes with alternating aligning properties, normal and tangential respectively. We construct a simple 'exactly-solvable' effective interfacial model where the liquid crystal distortions are accounted for via an effective interface potential. We find that chemically patterned substrates can strongly deform the nematic-air interface. The amplitude of this substrate-induced undulations increases with decreasing average film thickness and with increasing surface pattern pitch. We find a regime where the interfacial deformation may be described in terms of a material-independent universal scaling function. Surprisingly, the predictions of the effective interfacial model agree semi-quantitatively with the results of the numerical solution of a full model based on the Landau-de Gennes theory coupled to a square-gradient phase field free energy functional for a two phase system.

Instabilities of Layers of Deposited Molecules on Chemically Stripe Patterned Substrates: Ridges versus Drops

A mesoscopic continuum model is employed to analyze the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic stripe-like wettability patterns. Transversally invariant ridges located on the more wettable stripes are identified as very important transient states and their linear stability is analyzed accompanied by direct numerical simulations of the fully nonlinear evolution equation for two-dimensional substrates. It is found that there exist two different instability modes that lead to different nonlinear evolutions that result (i) at large ridge volume in the formation of bulges that spill from the more wettable stripes onto the less wettable bare substrate and (ii) at small ridge volume in the formation of small droplets located on the more wettable stripes. In addition, the influence of different transport mechanisms during redistribution is investigated focusing on the cases of convective transport with no-slip at the substrate, transport via diffusion in the film bulk and via diffusion at the film surface. In particular, it is shown that the transport process does neither influence the linear stability thresholds nor the sequence of morphologies observed in the time simulation, but only the ratio of the time scales of the different process phases.

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

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

Density functional study of complete, first-order and critical wedge filling transitions

We present numerical studies of complete, first-order and critical wedge filling transitions, at a right angle corner, using a microscopic fundamental measure density functional theory. We consider systems with short-ranged, cut-off Lennard-Jones, fluid-fluid forces and two types of wall-fluid potential: a purely repulsive hard wall and also a long-ranged potential with three different strengths. For each of these systems we first determine the wetting properties occurring at a planar wall, including any wetting transition and the dependence of the contact angle on temperature. The hard wall corner is completely filled by vapour on approaching bulk coexistence and the numerical results for the growth of the meniscus thickness are in excellent agreement with effective Hamiltonian predictions for the critical exponents and amplitudes, at leading and next-to-leading order. In the presence of the attractive wall-fluid interaction, the corresponding planar wall-fluid interface exhibits a first-order wetting transition for each of the interaction strengths considered. In the right angle wedge geometry the two strongest interactions produce first-order filling transitions while for the weakest interaction strength, for which wetting and filling occur closest to the bulk critical point, the filling transition is second-order. For this continuous transition the critical exponent describing the divergence of the meniscus thickness is found to be in good agreement with effective Hamiltonian predictions.

Stability of thin wetting films on chemically nanostructured surfaces

The morphology and stability of thin volatile wetting films on model chemically patterned surfaces composed of periodic arrays of alternating completely and partially wettable nanostripes are investigated. The equilibrium film morphology is recorded as a function of undersaturation using noncontact atomic force microscopy. Films spanning the entire pattern are found to be stable only for thicknesses in excess of a critical value, h(c), whereas thinner films spontaneously dewet the partially wettable regions of the substrate. The critical thickness h(c) increases linearly with the width of the partially wettable stripes in good agreement with an interface displacement model derived from microscopic density functional theory. These results provide detailed insights into the dewetting of thin films driven by competing intermolecular forces.

Morphology and self-arraying of SDS and DTAB dried on mica surface

Dewetting phenomena produce interesting patterns that may impart new properties to solid surfaces. Sodium dodecyl sulfate (SDS) and dodecyltrimethylammonium bromide (DTAB) aqueous solutions, dried on mica surfaces under different drying conditions, undergo dewetting events forming structured deposits that were imaged by scanning electron microscopy (SEM), atomic force (AFM) and Kelvin force microscopy (KFM). Dry SDS, in most situations, displays long branched stripes formed due to fingering instability, while DTAB undergoes stick-slip motion forming patterns of parallel continuous or split stripes. In both systems, independently of drying conditions, surfactants pack forming lamellar structures, but with different orientations: SDS lamellae are aligned parallel to the substrate whereas DTAB lamellae are normal to the mica plane. Electric potential maps of SDS obtained by KFM show well-defined electrostatic patterns: surfactant layers deposited on mica are overall negative with a larger excess of negative charge in the interlamellar space than in the lamellar faces.

Scaling of anisotropic droplet shapes on chemically stripe-patterned surfaces

We present an experimental study of the tunable anisotropic wetting behavior of chemically patterned anisotropic surfaces. Asymmetric glycerol droplet shapes, arising from patterns of alternating hydrophilic (pristine SiO2) and hydrophobic (fluoroalkylsilane self-assembled monolayers) stripes with dimensions in the low-micrometer range, are investigated in relation to stripe widths. Owing to the well-defined small droplet volume, the equilibrium shape as well as the observed contact angles exhibit unique scaling behavior. Only the relative width of hydrophilic and hydrophobic stripes proves to be a relevant parameter. Our results on morphologically flat, chemically patterned surfaces show similarities with those of experiments on topographically corrugated substrates. They are discussed in terms of the energetics at the liquid-solid interface.

Motion of nanodroplets near chemical heterogeneities

We investigate the dynamics of nanoscale droplets in the vicinity of chemical steps which separate parts of a substrate with different wettabilities. Due to long-ranged dispersion forces, nanodroplets positioned on one side of the step perceive the different character of the other side even at a finite distance from the step, leading to a dynamic response. The direction of the ensuing motion of such droplets depends not only on the difference between the equilibrium contact angles on these two parts but in particular on the difference between the corresponding Hamaker constants. Therefore, the motion is not necessarily directed toward the more wettable side and can also be different from that of droplets which span the step.

Liquid templating for nanoparticle organization into complex patterns

Dewetting of thin films of charged polymer solutions produces complex patterns that can be applied to direct nanoparticle organization on solid substrates. The morphology produced by dewetting can be controlled by the solution properties, temperature, and substrate wetting. In this work, new results on this liquid-template self-assembly system are presented, with special emphasis on producing large arrays of organized nanoparticles. On a hydrophilic substrate with complete wetting, the patterns include polygonal networks and parallel-track arrays that extend over several hundreds of microns. These large structures are formed under well-controlled drying conditions and characterized by scanning electron microscopy, which is better suited for the examination of large as well as small areas than atomic force microscopy. On partial wetting substrates, new patterns are observed, including a complex set of parallel curved bands with variable particle number densities.

High resolution non-contact AFM imaging of liquids condensed onto chemically nanopatterned surfaces

The wetting of ethanol and octane on chemically nanopatterned surfaces has been investigated using Atomic Force Microscopy (AFM) under controlled environmental conditions. The patterns were generated on a methyl-terminated, organic monolayer using an AFM electro-oxidation process. The subsequent wetting of the organic liquids was studied using non-contact mode AFM under equilibrium conditions with the vapor. This study of condensed nanoliquids provides the first reliable measurements of sub 100 nm liquid profile shapes. The derived contact angles give an estimate of the line tension.

Ellipsometric study of adsorption on nanopatterned block copolymer substrates

We report ellipsometrically obtained adsorption isotherms for a carefully chosen test liquid on block copolymer films of Kraton G1650, compared with adsorption isotherms on homogeneous films of the constituent polymers. Standard atomic force microscopy images imply the outer surface of Kraton G1650 is chemically patterned on the nanoscale, but this could instead be a reflection of structure buried beneath a 10 nm layer of the lower energy component. Our test liquid was chosen on the basis that it did not dissolve in either component and in addition that it was nonwetting on the lower energy polymer while forming thick adsorbed films on pure substrates of the higher energy component. Our ellipsometry data for Kraton G1650 rule out the presence of segregation by the lower energy constituent to the outer surface, implying a mixed surface consistent with Cassie's law. We discuss implications of our findings and related work for the outer surface structures of block copolymer films.

Wetting, drying, and layering of colloid-polymer mixtures at porous interfaces

The influence of interface porosity on the wetting properties of colloid-polymer mixtures is studied within density functional theory for the Asakura-Oosawa-Vrij model at the surface of a quenched hard-sphere matrix. While the porosity hardly changes the location of the transition from partial to complete wetting at colloidal bulk gas-liquid coexistence, the onset of wetting, as signaled by the first discontinuous layering transition, can be efficiently controlled by tailoring the porosity. We furthermore find that the penetrability of the porous interface induces complete drying into the matrix upon approaching capillary coexistence.

Dewetting of conducting polymer inkjet droplets on patterned surfaces

The manufacture of high-performance electronic devices with micrometre or even submicrometre dimensions by solution processing and direct printing, requires the ability to control accurately the flow and spread of functional liquid inks on surfaces. This can be achieved with the help of surface-energy patterns causing inks to be repelled and dewetted from pre-defined regions of the substrate. To exploit this principle for the fabrication of submicrometre device structures, a detailed understanding of the factors causing ink droplets to dewet on patterned surfaces is required. Here, we use hydrophobic surface-energy barriers of different geometries to study the influence of solution viscosity, ink volume, and contact angle on the process of dewetting of inkjet-printed droplets of a water-based conducting polymer. We demonstrate polymer field-effect transistor devices with channel length of 500 nm fabricated by surface-energy-assisted inkjet printing.

Wetting of nanopatterned surfaces: The hexagonal disk surface

Metropolis Monte Carlo simulations are used to investigate the wetting of chemically nanopatterned surfaces, for the case of hexagonal disk patterns where liquid wishes to wet high-energy circular patches but not wet the background surface. We calculate the density profiles of saturated liquid adsorbed on a variety of such substrates, spanning the nanoscale to atomic scale patterns. In addition, statistical mechanical sum rules are used to obtain interfacial order parameters and interfacial free energies. We observe that Cassie's law is typically obeyed, together with an associated breakdown of the mechanical interpretation of Young's equation, for pattern wavelengths greater than 15 molecular diameters. Here, the adsorbed fluid exists as an array of hemi-drops. At about half this wavelength, the breakdown of Cassie's law lies within realistic energy scales and is associated with the unbending of the outer surface of adsorbed films. For atomic scale patterns, the usual interpretation of Young's equation is restored for films thicker than one monolayer. At high chemical contrast, when the monolayer in contact with high-energy regions would prefer to be crystalline, we observe a variety of exotic interfacial phenomena that may have technological significance.

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.

Adsorption in a nonsymmetric wedge

We study adsorption in a nonsymmetric wedge consisting of two chemically different, homogeneous planes. First, we macroscopically analyze configurations of nonvolatile liquid drop placed in such a two-dimensional wedge and construct phase diagrams describing transitions between various interfacial shapes. Then adsorption is discussed within MFT based on the effective interfacial Hamiltonian. Two regimes for the system parameters--the wedge opening angle (2phi) and the critical wetting temperatures of each of the planar walls (T(W1) and T(W2), T(W2)<T(W1))--are identified. In one of them we find the critical filling transition at T(F)<T(W2) and the corresponding critical indices which are equal to those found for a symmetric wedge. In the other regime (T(W2)<T(F)<T(W1)) interfacial configurations are similar to those exhibited in the case of a planar substrate consisting of two chemically different parts. In the borderline case (T(F)=T(W2)), the interface profile above the wall with the lower wetting temperature becomes parallel to it. The line tensions corresponding to T(F)<T(W2) and T(F)=T(W2) cases are evaluated and the critical exponents - different in each case - are identified. An effective one-dimensional Hamiltonian describing fluctuations along the wedge is constructed for the T(F)<T(W2) case.

Dewetting of thin films on heterogeneous substrates: pinning versus coarsening

We study a model for a thin liquid film dewetting from a periodic heterogeneous substrate (template). The amplitude and periodicity of a striped template heterogeneity necessary to obtain a stable periodic stripe pattern, i.e., pinning, are computed. This requires a stabilization of the longitudinal and transversal modes driving the typical coarsening dynamics during dewetting of a thin film on a homogeneous substrate. If the heterogeneity has a larger spatial period than that of the critical dewetting mode, weak heterogeneities are sufficient for pinning. Our results imply a large region of coexistence between coarsening dynamics and pinning.