Wetting of a chemically heterogeneous surface

Three-Phase Fluid Coexistence in Heterogenous Slits

We study the competition between local (bridging) and global condensation of fluid in a chemically heterogeneous capillary slit made from two parallel adjacent walls each patterned with a single stripe. Using a mesoscopic modified Kelvin equation, which determines the shape of the menisci pinned at the stripe edges in the bridge phase, we determine the conditions under which the local bridging transition precedes capillary condensation as the pressure (or chemical potential) is increased. Provided the contact angle of the stripe is less than that of the outer wall we show that triple points, where evaporated, locally condensed, and globally condensed states all coexist are possible depending on the value of the aspect ratio a=L/H, where H is the stripe width and L the wall separation. In particular, for a capillary made from completely dry walls patterned with completely wet stripes the condition for the triple point occurs when the aspect ratio takes its maximum possible value 8/π. These predictions are tested using a fully microscopic classical density functional theory and shown to be remarkably accurate even for molecularly narrow slits. The qualitative differences with local and global condensation in heterogeneous cylindrical pores are also highlighted.

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.

Fluid bridges confined between chemically nanopatterned solid substrates

We discuss equilibrium properties of classical fluids confined to nanoscopic volumes by solid substrates. The substrates themselves are endowed with wettable chemical patterns of variable symmetry. We develop a thermodynamic description suitable for these highly anisotropic systems. Based upon a combination of Monte Carlo simulations in the grand canonical ensemble and lattice density functional theory at mean-field level we analyze the structure and phase behaviour of the confined fluid. Under suitable thermodynamic conditions the fluid may condense partially in regions controlled by the wettable nanopatterns. The resulting fluid bridges are established as thermodynamic phases and exhibit unique rheological features.

Hard-sphere fluid adsorbed in an annular wedge: the depletion force of hard-body colloidal physics

Many important issues of colloidal physics can be expressed in the context of inhomogeneous fluid phenomena. When two large colloids approach one another in solvent, they interact at least partly by the response of the solvent to finding itself adsorbed in the annular wedge formed between the two colloids. At shortest range, this fluid mediated interaction is known as the depletion force/interaction because solvent is squeezed out of the wedge when the colloids approach closer than the diameter of a solvent molecule. An equivalent situation arises when a single colloid approaches a substrate/wall. Accurate treatment of this interaction is essential for any theory developed to model the phase diagrams of homogeneous and inhomogeneous colloidal systems. The aim of our paper is a test of whether or not we possess sufficient knowledge of statistical mechanics that can be trusted when applied to systems of large size asymmetry and the depletion force in particular. When the colloid particles are much larger than a solvent diameter, the depletion force is dominated by the effective two-body interaction experienced by a pair of solvated colloids. This low concentration limit of the depletion force has therefore received considerable attention. One route, which can be rigorously based on statistical mechanical sum rules, leads to an analytic result for the depletion force when evaluated by a key theoretical tool of colloidal science known as the Derjaguin approximation. A rival approach has been based on the assumption that modern density functional theories (DFT) can be trusted for systems of large size asymmetry. Unfortunately, these two theoretical predictions differ qualitatively for hard sphere models, as soon as the solvent density is higher than about 23 that at freezing. Recent theoretical attempts to understand this dramatic disagreement have led to the proposal that the Derjaguin and DFT routes represent opposite limiting behavior, for very large size asymmetry and molecular sized mixtures, respectively. This proposal implies that nanocolloidal systems lie in between the two limits, so that the depletion force no longer scales linearly with the colloid radius. That is, by decreasing the size ratio from mesoscopic to molecular sized solutes, one moves smoothly between the Derjaguin and the DFT predictions for the depletion force scaled by the colloid radius. We describe the results of a simulation study designed specifically as a test of compatibility with this complex scenario. Grand canonical simulation procedures applied to hard-sphere fluid adsorbed in a series of annular wedges, representing the depletion regime of hard-body colloidal physics, confirm that neither the Derjaguin approximation, nor advanced formulations of DFT, apply at moderate to high solvent density when the geometry is appropriate to nanosized colloids. Our simulations also allow us to report structural characteristics of hard-body solvent adsorbed in hard annular wedges. Both these aspects are key ingredients in the proposal that unifies the disparate predictions, via the introduction of new physics. Our data are consistent with this proposed physics, although as yet limited to a single colloidal size asymmetry.

Wetting of rings on a nanopatterned surface: a lattice model study

We perform mean-field density functional theory calculations on a lattice model to study the wetting of a solid substrate decorated with a ring pattern of nanoscale dimensions. We have found three different liquid morphologies on the substrate: a ring morphology where the liquid covers the pattern, a bulge morphology where a droplet is forming on one side of the ring, and a morphology where the liquid forms a cap spanning the nonwetting disk inside the pattern. We investigate the relative stability of these morphologies as a function of the ring size, wall-fluid interaction, and temperature. The results found are in very good agreement with experiments and calculations performed on similar systems at a micrometer length scale. The bulge morphology has also been observed in Monte Carlo simulations of the lattice model. Our results show that (i) morphologies of wetting patterns previously observed on a much larger (microm) scale can also form on a nm length scale, (ii) whether or not this happens depends crucially on the size of the wettable pattern, and (iii) the wettable ring may only be partially wet by the bulge morphology of the fluid. This morphology is a result of a spontaneously broken symmetry in the system.

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.

Decoration lattices of colloids adsorbed on stripe-patterned substrates

The equilibrium structure of decoration lattices composed of colloidal particles adsorbed on periodic stripe-patterned substrates is calculated as a function of the stripe width and separation and for different interparticle interactions. Due to a competition of length scales, a wealth of different stable decoration lattices occurs such as triangular, quadratic, rhombic, kitelike, and sheared honeycomb lattices, triangular slices as well as triangle superlattices. This is of relevance for constructing templates that enforce crystal growth of unusual solid structures.

Density functional theories and molecular simulations of adsorption and phase transitions in nanopores

The nonlocal density functional theory (NLDFT) of confined fluids is tested against Monte Carlo simulations by using the example of Lennard-Jones (LJ) fluid sorption in slit-shaped and cylindrical nanopores ranging from 0.3 to 10 nm in width. The fluid-fluid and solid-fluid parameters of the LJ potentials were chosen to represent several experimentally important adsorption systems: nitrogen and carbon dioxide in activated carbons, zeolites, and mesoporous molecular sieves of the MCM-41 type. Freezing in nanopores is discussed using the example of methane sorption in carbon at 111 K. Comparison with reference experiments is given when available. Two versions of NLDFT, the smoothed density approximation and the fundamental measure theory, are considered. It is shown that NLDFT approaches with properly chosen parameters provide quantitative agreement with the results of Monte Carlo simulations and reference experiments. Appreciable deviations are found in extremely narrow pores of less than two molecular diameters in width. In wider pores, NLDFT models can be used for quantitative predictions of reversible and hysteretic adsorption isotherms and analyses of the specifics of phase transformations, including the equilibrium and spinodal phase transitions.

Correlation of stress and structure in a simple fluid confined to a pore with furrowed walls

A Lennard-Jones (12,6) film confined between two furrowed walls was simulated by the grand canonical ensemble Monte Carlo method. The walls are constructed by gouging triangular grooves in planar substrates that are structureless on the molecular scale. The furrows are infinitely long in one transverse direction (y) and of nanoscopic width (s(x)) and depth (D). The furrows in the two walls are maintained parallel and in register. The diagonal components of the stress tensor (T(alphaalpha), alpha=x,y,z) are computed as functions of D and the separation between the substrates (s(z)) at fixed temperature, chemical potential, and s(x). The T(alphaalpha) for the film between the furrowed walls are strongly shifted from their counterparts for the film between flat (i.e., planar) walls. The shifts are rationalized in terms of the structure of the film, which becomes more ordered as the furrows deepen and the packing of film molecules becomes more restricted in the two dimensions normal to the y direction. The results demonstrate the profound impact of the coupling between molecular and nanoscopic scales on the properties of geometrically constrained fluids.

Surface freezing on patterned substrates

We show that the structure of a substrate pattern drastically influences the nature of surface freezing. By using phenomenological theory and computer simulations of a hard sphere fluid next to a substrate formed by a periodic array of fixed spheres, we find that a pattern which is commensurate with the bulk crystal induces complete surface freezing through a cascade of layering transitions. A rhombic pattern, on the other hand, either generates a crystalline sheet which is unstable as a bulk phase or prohibits surface freezing completely.

Rapid prototyping of patterned functional nanostructures

Living systems exhibit form and function on multiple length scales and at multiple locations. In order to mimic such natural structures, it is necessary to develop efficient strategies for assembling hierarchical materials. Conventional photolithography, although ubiquitous in the fabrication of microelectronics and microelectromechanical systems, is impractical for defining feature sizes below 0.1 micrometres and poorly suited to pattern chemical functionality. Recently, so-called 'soft' lithographic approaches have been combined with surfactant and particulate templating procedures to create materials with multiple levels of structural order. But the materials thus formed have been limited primarily to oxides with no specific functionality, and the associated processing times have ranged from hours to days. Here, using a self-assembling 'ink' we combine silica-surfactant self-assembly with three rapid printing procedures--pen lithography, ink-jet printing, and dip-coating of patterned self-assembled monolayers--to form functional, hierarchically organized structures in seconds. The rapid-prototyping procedures we describe are simple, employ readily available equipment, and provide a link between computer-aided design and self-assembled nanostructures. We expect that the ability to form arbitrary functional designs on arbitrary surfaces will be of practical importance for directly writing sensor arrays and fluidic or photonic systems.

Wetting films on chemically heterogeneous substrates

Based on a microscopic density functional theory, we investigate the morphology of thin liquid-like wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical step and on a single stripe. In view of applications in microfluidics, the accuracy of guiding liquids by chemical microchannels is discussed. Finally we give a general prescription of how to investigate theoretically the wetting properties of substrates with arbitrary chemical structures.