Effective Interface Potential Research Articles

Wetting transitions on soft substrates

Within mean-field theory we study wetting of elastic substrates. Our analysis is based on a grand canonical free energy functional of the fluid number density and of the substrate displacement field. The substrate is described in terms of the linear theory of elasticity, parametrized by two Lamé coefficients. The fluid contribution is of the van der Waals type. Two potentials characterize the interparticle interactions in the system. The long-ranged attraction between the fluid particles is described by a potential , and characterizes the substrate-fluid interaction. By integrating out the elastic degrees of freedom we obtain an effective theory for the fluid number density alone. Its structure is similar to the one for the wetting of an inert substrate. However, the potential is replaced by an effective potential which, in addition to , contains a term bilinear in . We discuss the corresponding wetting transitions in terms of an effective interface potential , where ℓ denotes the thickness of the wetting layer. We show that in the case of algebraically decaying interactions the elasticity of the substrate may suppress critical wetting transitions, and may even turn them first order.

Wedge wetting by electrolyte solutions.

The wetting of a charged wedgelike wall by an electrolyte solution is investigated by means of classical density functional theory. As in other studies on wedge wetting, this geometry is considered as the most simple deviation from a planar substrate, and it serves as a first step toward more complex confinements of fluids. By focusing on fluids containing ions and surface charges, features of real systems are covered that are not accessible within the vast majority of previous theoretical studies concentrating on simple fluids in contact with uncharged wedges. In particular, the filling transition of charged wedges is necessarily of first order, because wetting transitions of charged substrates are of first order and the barrier in the effective interface potential persists below the wetting transition of a planar wall; hence, critical filling transitions are not expected to occur for ionic systems. The dependence of the critical opening angle on the surface charge, as well as the dependence of the filling height, of the wedge adsorption, and of the line tension on the opening angle and on the surface charge are analyzed 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.

Order of wetting transitions in electrolyte solutions.

For wetting films in dilute electrolyte solutions close to charged walls we present analytic expressions for their effective interface potentials. The analysis of these expressions renders the conditions under which corresponding wetting transitions can be first- or second-order. Within mean field theory we consider two models, one with short- and one with long-ranged solvent-solvent and solvent-wall interactions. The analytic results reveal in a transparent way that wetting transitions in electrolyte solutions, which occur far away from their critical point (i.e., the bulk correlation length is less than half of the Debye length) are always first-order if the solvent-solvent and solvent-wall interactions are short-ranged. In contrast, wetting transitions close to the bulk critical point of the solvent (i.e., the bulk correlation length is larger than the Debye length) exhibit the same wetting behavior as the pure, i.e., salt-free, solvent. If the salt-free solvent is governed by long-ranged solvent-solvent as well as long-ranged solvent-wall interactions and exhibits critical wetting, adding salt can cause the occurrence of an ion-induced first-order thin-thick transition which precedes the subsequent continuous wetting as for the salt-free solvent.

Density functional theory of electrowetting.

The phenomenon of electrowetting, i.e., the dependence of the macroscopic contact angle of a fluid on the electrostatic potential of the substrate, is analyzed in terms of the density functional theory of wetting. It is shown that electrowetting is not an electrocapillarity effect, i.e., it cannot be consistently understood in terms of the variation of the substrate-fluid interfacial tension with the electrostatic substrate potential, but it is related to the depth of the effective interface potential. The key feature, which has been overlooked so far and which occurs naturally in the density functional approach, is the structural change of a fluid if it is brought into contact with another fluid. These structural changes occur in the present context as the formation of finite films of one fluid phase in between the substrate and the bulk of the other fluid phase. The nonvanishing Donnan potentials (Galvani potential differences) across such film-bulk fluid interfaces, which generically occur due to an unequal partitioning of ions as a result of differences of solubility contrasts, lead to correction terms in the electrowetting equation, which become relevant for sufficiently small substrate potentials. Whereas the present density functional approach confirms the commonly used electrocapillarity-based electrowetting equation as a good approximation for the cases of metallic electrodes or electrodes coated with a hydrophobic dielectric in contact with an electrolyte solution and an ion-free oil, a significantly reduced tendency for electrowetting is predicted for electrodes coated with a dielectric which is hydrophilic or which is in contact with two immiscible electrolyte solutions.

Neither Lippmann nor Young: Enabling Electrowetting Modeling on Structured Dielectric Surfaces

Aiming to illuminate mechanisms of wetting transitions on geometrically patterned surfaces induced by the electrowetting phenomenon, we present a novel modeling approach that goes beyond the limitations of the Lippmann equation and is even relieved from the implementation of the Young contact angle boundary condition. We employ the equations of the capillary electrohydrostatics augmented by a disjoining pressure term derived from an effective interface potential accounting for solid/liquid interactions. Proper parametrization of the liquid surface profile enables efficient simulation of multiple and reconfigurable three-phase contact lines (TPL) appearing when entire droplets undergo wetting transitions on patterned surfaces. The liquid/ambient and the liquid/solid interfaces are treated in a unified context tackling the assumption that the liquid profile is wedge-shaped at any three-phase contact line. In this way, electric field singularities are bypassed, allowing for accurate electric field and liquid surface profile computation, especially in the vicinity of TPLs. We found that the invariance of the microscopic contact angle in electrowetting systems is valid only for thick dielectrics, supporting published experiments. By applying our methodology to patterned dielectrics, we computed all admissible droplet equilibrium profiles, including Cassie-Baxter, Wenzel, and mixed wetting states. Mixed wetting states are computed for the first time in electrowetting systems, and their relative stability is presented in a clear and instructive way.

Quantized Contact Angles in the Dewetting of a Structured Liquid

We investigate the dewetting of a disordered melt of diblock copolymer from an ordered residual wetting layer. In contrast to simple liquids where the wetting layer has a fixed thickness and the droplets exhibit a single unique contact angle with the substrate, we find that structured liquids of diblock copolymer exhibit a discrete series of wetting layer thicknesses each producing a different contact angle. These quantized contact angles arise because the substrate and air surfaces each induce a gradient of lamellar order in the wetting layer. The interaction between the two surface profiles creates an effective interface potential that oscillates with film thickness, thus, producing a sequence of local minimums. The wetting layer thicknesses and corresponding contact angles are a direct measure of the positions and depths of these minimums. Self-consistent field theory is shown to provide qualitative agreement with the experiment.

Wetting of Macromolecules: From Linear Chain to Soft Colloid-Like Behavior

The ability to control the wetting properties of a polymeric liquid on a given surface is important for several emerging technological applications including protective coatings, lubricants and sensors. Here we show that star-shaped polystyrene (PS) molecules exhibit notably different wetting properties than their linear analogues of the same chemical structure and their wetting properties can be controlled through changes of their functionality f (number of arms per molecule). Unlike linear chains, the wetting of star-shaped macromolecules is determined by the competition between entropic forces. Wetting is enhanced due to reductions in the loss of entropy upon adsorption of the stars with increasing f; soft colloidal-like entropic repulsion effects suppress the ability of the stars to exhibit a high degree of surface adsorption and to efficiently pack, for sufficiently large values of f. This phenomenon is manifested in the existence of a minimum in the macroscopic contact angle and other related microscopic parameters embodied in the effective interface potential as a function of f.

The influence of van der Waals forces on droplet morphological transitions and solvation forces in nanochannels

The morphological phase transition between sessile and lenticular shapes of a droplet placed in a nanochannel is observed upon increasing the droplet volume. The phase diagram for this system is discussed within both macroscopic and mesoscopic approaches. On the mesoscopic level, the van der Waals forces are taken into account via the effective interface potential acting between the channel walls and the droplet. We discuss the contact angle dependence on the droplet volume and the distance between the walls; this angle turns out to be smaller than the macroscopic Young’s angle. The droplet’s presence induces the solvation force acting between the channel walls. It can be either attractive or repulsive, depending on the width of the channel.

Interface-induced states at the boundary between a 3D topological insulator and a normal insulator

We show that, when a three-dimensional (3D) narrow-gap semiconductor with inverted band gap (“topological insulator,” TI) is attached to a 3D wide-gap semiconductor with non-inverted band gap (“normal insulator,” NI), two types of bound electron states having different spatial distributions and spin textures arise at the TI/NI interface. Namely, the gapless (“topological”) bound state can be accompanied by the emergence of the gapped (“ordinary”) bound state. We describe these states in the framework of the envelope function method using a variational approach for the energy functional; their existence hinges on the ambivalent character of the constraint for the envelope functions that correspond to the “open” or “natural” boundary conditions at the interface. The properties of the ordinary state strongly depend on the effective interface potential, while the topological state is insensitive to the interface potential variation.

Slippage and nanorheology of thin liquid polymer films

Thin liquid films on surfaces are part of our everyday life; they serve, e.g., as coatings or lubricants. The stability of a thin layer is governed by interfacial forces, described by the effective interface potential, and has been subject of many studies in recent decades. In recent years, the dynamics of thin liquid films has come into focus since results on the reduction of the glass transition temperature raised new questions on the behavior of especially polymeric liquids in confined geometries. The new focus was fired by theoretical models that proposed significant implication of the boundary condition at the solid/liquid interface on the dynamics of dewetting and the form of a liquid front. Our study reflects these recent developments and adds new experimental data to corroborate the theoretical models. To probe the solid/liquid boundary condition experimentally, different methods are possible, each bearing advantages and disadvantages, which will be discussed. Studying liquid flow on a variety of different substrates entails a view on the direct implications of the substrate. The experimental focus of this study is the variation of the polymer chain length; the results demonstrate that inter-chain entanglements and in particular their density close to the interface, originating from non-bulk conformations, govern the liquid slip of a polymer.

Semi-infinite boundary conditions for the simulation of interfaces: The Ar/CO2(s) model revisited

We propose a method to account for the long tail corrections of dispersive forces in inhomogeneous systems. This method deals separately with the two interfaces that are usually present in a simulation setup, effectively establishing semi-infinite boundary conditions that are appropriate for the study of the interface between two infinite bulk phases. Using the wandering interface method, we calculate surface free energies of vapor-liquid, wall-liquid, and wall-vapor interfaces for a model of Lennard-Jones argon adsorbed on solid carbon dioxide. The results are employed as input to Young's equation, and the wetting temperature located. This estimate is compared with predictions from the method of effective interface potentials and good agreement is found. Our results show that truncating Ar-Ar interactions at two and a half molecular diameters results in a dramatic decrease of the wetting temperature of about 40%.

Can liquids slide? Linking stability and dynamics of thin liquid films to microscopic material properties

Whether a lubricant or a coating wets a surface or not is of great technical importance. Theoretically, it is possible to predict the stability of a thin liquid film on a surface, since it is governed by the effective interface potential. In practice, however, a prediction can be quite cumbersome, since liquids as well as surfaces often consist of numerous components which all influence the effective interface potential. A molecular layer on a substrate's surface like a self-assembled monolayer mainly changes the short-range potential whereas the composition of the substrate below the surface determines the long-range interactions such as the van der Waals potential. The interplay of short- and long-range interactions, including the dielectric properties of all layers in the case of van der Waals interactions, governs the stability of a liquid film. If the film is not stable, distinct rupture mechanisms can be observed causing characteristic film morphologies: spinodal dewetting and dewetting by nucleation of holes, which both entail liquid flow and reveal new routes to study microscopic parameters such as the hydrodynamic boundary condition at the solid/liquid interface. A rather old question turns out to become very important again: Can liquids slide? The article links stability and dynamics of thin liquid films to microscopic material properties and, moreover, describes their experimental access.

Critical wetting transitions in two-dimensional systems subject to long-ranged boundary fields

Using the quasiexact density-matrix renormalization-group method and ground-state analysis we study interface delocalization transitions in wide two-dimensional Ising strips subject to long-ranged boundary fields with opposite signs at the two surfaces. Based on this approach, our explicit calculations demonstrate that critical wetting transitions do exist for semi-infinite two-dimensional systems even if the corresponding effective interface potentials decay asymptotically for large l as slow as l(-delta) with delta<2, where l is the distance of the mean interface position from the one-dimensional surface. This supersedes opposite claims by Kroll and Lipowsky [Phys. Rev. B 28, 5273 (1983)] and by Privman and Svrakić [Phys. Rev. B 37, 5974 (1988)] obtained within effective interface models. The corresponding wetting phase diagram is determined, including the cases delta=2 and delta=49 with the latter mimicking short-ranged surface fields. Our analysis highlights the limits of reliability of effective interface models.

Nano-droplets on structured substrates

The dynamics of nano-droplets on structured substrates differs qualitatively from the macroscopically expected behavior. The long-range van der Waals interactions acting in such systems induce lateral forces on nano-droplets in the vicinity of chemical and topographical steps even if the three-phase contact line of the droplets does not touch the step. Moreover, macroscopic considerations based on differences or gradients of local equilibrium contact angles are invalid because nano-droplets do not sample the long-range tails of the effective interface potential. As one of the consequences, nano-droplets spanning chemical steps can move towards the less wettable side.

Size dependent motion of nanodroplets on chemical steps

Nanodroplets on chemically structured substrates move under the action of disjoining pressure induced forces. A detailed analysis of them shows that, even in the absence of long-ranged lateral variations of the effective interface potential, already the fact that due to their small size nanodroplets do not sample the disjoining pressure at all distances from the substrate can lead to droplet motion toward the less wettable part of the substrate, i.e., in the direction opposite to the one expected on the basis of macroscopic wettability considerations.

Control of Interfacial Instabilities in Thin Polymer Films with the Addition of a Miscible Component

We show that while polystyrene (PS) thin films are structurally unstable on oxidized silicon wafers, the addition of as little as a few weight percent tetramethylbisphenol A polycarbonate (TMPC) has a stabilizing effect on the topographical structure of the films. The stabilization is evident from the existence of a threshold TMPC concentration, φt, and a threshold thickness, ht, beyond which films do not dewet. The concentration threshold occurs for φTMPC ≤ 0.10. An examination of the effective interface potential, which accounts for short- and long-range intermolecular interactions, indicates that this dewetting inhibition is metastable.

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.

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.

Adsorption of polymers on a brush: Tuning the order of the wetting phase transition

We develop a computational methodology for the direct measurement of a wetting transition and its order via the effective interface potential. The method also allows to estimate contact angles in the nonwet state and to study adsorption isotherms. The proposed methodology is employed in order to study the wetting behavior of polymers on top of a brush consisting of identical polymers. In the absence of long-range forces, the system shows a sequence of nonwet, wet, and nonwet states as the brush density is increased. Including attractive long-range interactions we can make the polymer liquid wet the bush at all grafting densities, and both first- and second-order wetting transitions are observed. The latter case is limited to a small interval of grafting densities where the melt wets the brush in the absence of long-range interactions. Second-order wetting transitions are preceded by a first-order surface transition from a thin to a thick adsorbed layer. The interval of second-order wetting transitions is limited at low grafting densities by a surface critical end point and at high grafting densities by a tricritical wetting point. Our study highlights the rich wetting behavior that results when competing adsorbent-substrate interactions of different scales are tuned over a broad range.