Chasing the Critical Wetting Transition. An Effective Interface Potential Method.

Wettablity is one of the important characteristics defining a given surface. Here we show that the effective interface potential method of determining the wetting temperature, originally proposed by MacDowell and Müller for the surfaces exhibiting the first order wetting transition, can also be used to estimate the wetting temperature of the second order (continuous) wetting transition. Some selected other methods of determination of the wetting temperature are also discussed.

Revisiting Wetting, Freezing, and Evaporation Mechanisms of Water on Copper.

Wetting of metal surfaces plays an important role in fuel cells, corrosion science, and heat-transfer devices. It has been recently stipulated that Cu surface is hydrophobic. In order to address this issue we use high purity (1 1 1) Cu prepared without oxygen, and resistant to oxidation. Using the modern Fringe Projection Phase-Shifting method of surface roughness determination, together with a new cell allowing the vacuum and thermal desorption of samples, we define the relation between the copper surface roughness and water contact angle (WCA). Next by a simple extrapolation, we determine the WCA for the perfectly smooth copper surface (WCA = 34°). Additionally, the kinetics of airborne hydrocarbons adsorption on copper was measured. It is shown for the first time that the presence of surface hydrocarbons strongly affects not only WCA, but also water droplet evaporation and the temperature of water droplet freezing. The different behavior and features of the surfaces were observed once the atmosphere of the experiment was changed from argon to air. The evaporation results are well described by the theoretical framework proposed by Semenov, and the freezing process by the dynamic growth angle model.

What Is the Value of Water Contact Angle on Silicon?

Silicon is a widely applied material and the wetting of silicon surface is an important phenomenon. However, contradictions in the literature appear considering the value of the water contact angle (WCA). The purpose of this study is to present a holistic experimental and theoretical approach to the WCA determination. To do this, we checked the chemical composition of the silicon (1,0,0) surface by using the X-ray photoelectron spectroscopy (XPS) method, and next this surface was purified using different cleaning methods. As it was proved that airborne hydrocarbons change a solid wetting properties the WCA values were measured in hydrocarbons atmosphere. Next, molecular dynamics (MD) simulations were performed to determine the mechanism of wetting in this atmosphere and to propose the force field parameters for silica wetting simulation. It is concluded that the best method of surface cleaning is the solvent-reinforced de Gennes method, and the WCA value of silicon covered by SiO2 layer is equal to 20.7° (at room temperature). MD simulation results show that the mechanism of pure silicon wetting is similar to that reported for graphene, and the mechanism of silicon covered by SiO2 layer wetting is similar to this observed recently for a MOF.

Water Nanodroplet on a Hydrocarbon "Carpet"-The Mechanism of Water Contact Angle Stabilization by Airborne Contaminations on Graphene, Au, and PTFE Surfaces.

Wetting is very common phenomenon, and it is well documented that the wettability of a solid depends on the surface density of adsorbed airborne hydrocarbons. This "hydrocarbon hypothesis" has been experimentally confirmed for different surfaces, for example, graphene, TiO2, and SiO2; however, there are no scientific reports describing the influence of airborne contaminants on the water contact angle (WCA) value measured on the polytetrafluoroethylene (PTFE) surface. Using experimental data showing the influence of airborne hydrocarbons on the wettability of graphene, gold and PTFE by water, together with Molecular Dynamics simulation results we prove that the relation between the WCA and the surface concentration of hydrocarbons ( n-decane, n-tridecane, and n-tetracosane) is more complex than has been assumed up until now. We show, in contrast to commonly approved opinion, that adsorbed hydrocarbons can increase (graphene, Au) or decrease (PTFE) the WCA of a nanodroplet sitting on a surface. Using classical thermodynamics, a simple theoretical approach is developed. It is based on two adsorbed hydrocarbon states, namely, "carpet" and "dimple". In the "carpet" state a uniform layer of alkane molecules covers the entire substrate. In contrast, in the "dimple" state, the preadsorbed layer of alkane molecules covers only the open surface. Simple thermodynamic balance between the two states explains observed experimental and simulation results, forming a good starting point for future studies.

Microscopic density functional theory for monolayers of diblock copolymers.

We propose density functional theory for diblock copolymers in two dimensions. Our theoretical framework is based on Wertheim's first order thermodynamic perturbation theory. Using the proposed approach, we investigate the structure and phase behavior of monolayers of symmetric diblock copolymers. We find that the phase behavior of symmetric diblock copolymer monolayers is similar to that in 3D. This includes the scaling of the equilibrium lamellar width with chain length. We find that the topology of the resulting phase diagrams depends on the chain length and the unlike segment interaction incompatibility and involves either one, two, or three triple points (one of them being the peritectic point). We expect that a similar phase behavior could be obtained for monolayers of colloidal suspensions with carefully tuned interparticle interactions.

Two-dimensional binary mixtures of patchy particles and spherical colloids.

Using Monte Carlo simulation we study two dimensional mixtures of patchy and spherically symmetric particles. Such mixtures can be synthesized experimentally by covering colloids with appropriate types of DNA strands [L. Feng, et al., Adv. Mater., 2013, 25, 2779]. We focus on finding out the ordered structures that can be formed in such systems. The type of ordered phase strongly depends on the valency, size and binding energy of the patchy particles. If the patch size is small enough, i.e. it allows only one spherically symmetric particle to be bound, the ordered structure follows either a hexagonal or a tetragonal pattern depending on the valency of the patchy particles. Moreover, we find stable quasicrystals of dodecagonal symmetry. Additional structures can be obtained if the patches are larger and the binding energy is higher. Depending on the valency of the patchy particles we find either lanes or branched structures forming polygons of the spherically symmetric particles with few patchy particles inside. For pentavalent patchy particles we find stable quasicrystals of decagonal symmetry.

Density functional theory for polymeric systems in 2D.

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.

Structure and phase behaviour of diblock copolymer monolayers investigated by means of Monte Carlo simulation.

We use grand canonical Monte Carlo simulation paired with multiple histogram reweighting, hyperparallel tempering and finite size scaling to investigate the structure and phase behaviour of monolayers of diblock copolymers. The chain molecules are arranged on the square lattice and we consider both fully flexible and rod-coil polymer models. In contrast to the majority of previous studies we assume that the interactions between the segments belonging to one of the two subunits are weaker than the remaining segment-segment interactions. We find that when the diblock copolymer is fully flexible, this choice of the interactions leads to a suppression of the ordered phase, and the phase behaviour is analogous to that of the fully flexible homopolymer model. However, when one of the subunits is rigid, we observe the formation of a novel hairpin chessboard ordered structure with fully stretched chains bent in the middle. The topology of the phase diagram depends on the chain length. For shorter chains the global phase diagram features a critical point and a triple point. For longer chains the gas-disordered liquid phase transition is suppressed and only the order-disorder transition remains stable. The resulting phase diagram is of the swan neck type.

Adsorption of block copolymers on solid surfaces: A Monte Carlo study.

Using hyper-parallel tempering Monte Carlo simulation, multiple histogram reweighting method, and finite size scaling, we investigate the adsorption of fully flexible and rod-coil chains on the square lattice. We find that the phase behaviour changes with the chain length and flexibility. For homonuclear rod-coil chains, the phase diagram consists of only gas-disorder liquid critical point. Weakening of the interaction energy between the segments belonging to two different subunits gives rise to an order-disorder transition. The topology of the resulting phase diagram depends on the chain length and flexibility. For short chains, both fully flexible and rod-coil diblock copolymers form lamellar ordered phase with fully stretched chains, and the order-disorder transition is of the first order. The phase diagrams are similar for both chain architectures and consist of two binodals meeting in the triple point. When the chain length increases the order-disorder transition becomes second-order and the difference in the phase behaviour between the fully flexible and the rod-coil diblock copolymers becomes more pronounced. While for the former chain architecture the topology of the phase diagram involves a λ-line which meets the gas-disordered liquid binodal in the critical end-point, in the latter case the λ-line meets the gas-disordered liquid critical point and forms the tricritical point. We trace back these changes to the change in the morphology of the ordered phase. The mechanism of the order-disorder transition involves the formation of domains resembling those observed during the spinodal decomposition process. The domains subsequently merge and arrange into lamellae. These observations are supported by integral geometry analysis.

Non-mean-field behavior of critical wetting transition for short-range forces.

Critical wetting transition for short-range forces in three dimensions (d=3) is reinvestigated by means of Monte Carlo simulation. Using an anisotropic finite size scaling approach, as well as approaches that do not rely on finite size scaling, we show that the critical wetting transition shows clear deviation from mean-field behavior. We estimate that the effective critical exponent ν_{∥}^{eff}=1.76 ± 0.08 for J/kT=0.35 and ν_{∥}^{eff}=1.85 ± 0.07 for J/kT=0.25. These values are in accord with predictions of Parry et al. [Phys. Rev. Lett. 100, 136105 (2008)]. We also point out that the anisotropic finite size scaling approach in d=3 requires additional modification in order to reach full consistency of simulational results.

Solvation effects for polymers at an interface: a hybrid self-consistent field-density functional theory approach.

Using polyatomic density functional theory of Kierlik and Rosinberg, we show that Wertheim's thermodynamic perturbation theory (TPT) incorporates solvation effects in a systematic, although simplified form. We derive two approximate solvation potentials, which require the knowledge of the correlation function in the reference unbonded fluid only. The theoretical predictions are tested against many-chain Monte Carlo simulations for moderate chain lengths. The predictions of the end-to-end distance in the bulk are in a reasonable agreement with simulations for the TPT(M-1) approximation, while the simpler TPT2_e approximation leads to the solvation potential that is shorter ranged and considerably less accurate. The resulting conformations are used in the subsequent self-consistent field theory calculations of hard-sphere polymers at a hard wall. While the incorporation of the solvation effects has little impact on the density profiles, the predictions of the components of the end-to-end distance vector as a function of the distance to the wall are much improved.

Self-consistent field/density functional study of conformational properties of polymers at interfaces: role of intramolecular interactions.

We study the properties of athermal polymers at hard walls using two different versions of self-consistent field theory (SCFT). We calculate the segment density profiles, center of mass profiles, bond orientation vector profiles, and end-to-end vector distributions and compare with grand canonical Monte Carlo simulations. Using the same excess free energy prescription for both theories, we investigate the role of the excluded volume intramolecular interactions on these properties, show the relation between SCFT and density functional theory, and discuss several numerical implementations of the SCFT method. The phantom chain model gives Gaussian chain statistics independent of the conditions. Including the full intramolecular potential leads to an improved description of the low density regime but it does not produce any significant improvement in the semidiluted and concentrated regimes. We show that a viable compromise is achieved by using the effective field resulting from the phantom chain model and by calculating single chain properties using the full intramolecular potential.

Direct calculation of interfacial tensions from computer simulation: results for freely jointed tangent hard sphere chains.

We develop a methodology for the calculation of surface free energies based on the probability distribution of a wandering interface. Using a simple extension of the NpT sampling, we allow the interface area to randomly probe the available space and evaluate the surface free energy from histogram analysis and the corresponding average. The method is suitable for studying systems with either continuous or discontinuous potentials, as it does not require explicit evaluation of the virial. The proposed algorithm is compared with known results for the surface tension of Lennard-Jones and square well fluids, as well as for the interface tension of a bead-spring polymer model, and good agreement is found. We also calculate the interfacial tensions of freely jointed tangent hard sphere chains on athermal walls for a wide range of chain lengths and densities. The results are compared with three different theoretical approaches: scaled particle theory (SPT), Yu-Wu density functional theory, and an analytical approximation based on the latter approach. Whereas SPT only yields qualitative results, the last two approaches are found to yield very good agreement with simulations.

Surface phase transitions in athermal mixtures of hard rods and excluded volume polymers investigated using a density functional approach.

Using fundamental measures' density functional framework based on Wertheim's first order perturbation theory [J. Chem. Phys. 87, 7323 (1987)] we study the surface phase transitions in athermal polymer-needle mixtures, which demix in bulk into the isotropic polymer-rich (rod-poor) and polymer-poor (rod-rich) phases. We find that the polymer-rich (rod-poor) phase wets the hard wall at coexistence and the wetting transition is of first order. In the partial wetting regime we find a sequence of layerings but these transitions are gradually suppressed as the chain length increases. For long enough chains we detect the prewetting line. Rods exhibit pronounced ordering at the wall in the polymer-rich phases. Our results imply that experiments on the (isotropic) wetting transition for colloidal rod-polymer mixtures should be easier to carry out than those for the colloidal rod-sphere mixtures because the wetting transition occurs at lower rod densities. On the other hand, layerings in sphere-needle mixtures may turn out to be difficult to observe experimentally because some of them will be metastable with respect to the freezing transition, whereas the remaining ones are located very close to the binodal.

Effective interactions in colloid-semipermeable membrane systems.

We investigate effective interactions between a colloidal particle, immersed in a binary mixture of smaller spheres, and a semipermeable membrane. The colloid is modeled as a big hard sphere, and the membrane is represented as an infinitely thin surface, which is fully permeable to one of the smaller spheres and impermeable to the other one. Within the framework of the density functional theory, we evaluate depletion potentials and we consider two different approximate theories: the simple Asakura-Oosawa approximation and the accurate White-Bear version of the fundamental measure theory. The effective potentials are compared with the corresponding potentials for the hard, nonpermeable wall. Using statistical-mechanical sum rules, we argue that the contact value of the depletion potential between a colloid and a semipermeable membrane is smaller in magnitude than the potential between a colloid and a hard wall. A heuristic argument is provided that the colloid-semipermeable membrane effective interactions are generally weaker than these near a hard nonpermeable wall. These predictions are confirmed by explicit calculations, and the effect is more pronounced for smaller osmotic pressures. The depletion potential for a colloidal particle inside a semipermeable vesicle is stronger than the potential for the colloidal particle located outside of a vesicle. We find that the asymptotic decay of the depletion potential for the semipermeable membrane is similar to that for the nonpermeable wall and reflects the asymptotics of the total correlation function of the corresponding binary mixture of smaller spheres. Our results demonstrate that the ability of the membrane to change its shape as well as specific interactions constitute an important factor in determining the effective interactions between the semipermeable membrane and the colloidal macroparticle.

Capillary condensation of short-chain molecules.

A density-functional study of capillary condensation of fluids of short-chain molecules confined to slitlike pores is presented. The molecules are modeled as freely jointed tangent spherical segments with a hard core and with short-range attractive interaction between all the segments. We investigate how the critical parameters of capillary condensation of the fluid change when the pore width decreases and eventually becomes smaller than the nominal linear dimension of the single-chain molecule. We find that the dependence of critical parameters for a fluid of dimers and of tetramers on pore width is similar to that of the monomer fluid. On the other hand, for a fluid of chains consisting of a larger number of segments we observe an inversion effect. Namely, the critical temperature of capillary condensation decreases with increasing pore width for a certain interval of values of the pore width. This anomalous behavior is also influenced by the interaction between molecules and pore walls. We attribute this behavior to the effect of conformational changes of molecules upon confinement.

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory.

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.

Bulk and inhomogeneous mixtures of hard rods and excluded-volume polymer: a density functional approach.

We present a density functional theory for a mixture of hard rods and polymer modeled as chains of hard tangent spheres which refines the theory proposed in the paper by Phys. Rev. E 68, 062501 (2003)]. The improvement involves a semiempirical formula for the contact value of the sphere-sphere radial distribution function of the sphere and needle reference system, which includes the important depletion effect induced by the needles. The new functional yields slightly broader phase coexistence envelopes but the changes affect mainly the polymer-rich binodal branches. After analyzing the bulk phase behavior the structure of hard-rod-polymer mixture close to a hard wall is examined. An increase of the chain length leads to an increase of the average polymer segment contact value. This behavior may lead to a qualitative difference of the polymer segment profiles: from an effective repulsion of the polymer segments to an effective attraction, which can be observed by a change of sign of the excess adsorption. By analyzing the orientational order parameter profiles we have found that the polymer coils decrease the tendency of needles to adopt anisotropic configurations.

Wetting in mixtures of colloids and excluded-volume polymers from density-functional theory.

We use a microscopic density-functional theory based on Wertheim's [J. Chem. Phys. 87, 7323 (1987)] first-order thermodynamic perturbation theory to study the wetting behavior of athermal mixtures of colloids and excluded-volume polymers. In opposition to the wetting behavior of the Asakura-Oosawa-Vrij [J. Chem. Phys. 22, 1255 (1954); Pure Appl. Chem. 48, 471 (1976)] model we find the polymer-rich phase to wet a hard wall. The wetting transition is of the first order and is accompanied by the prewetting transition. We do not find any hints for the layering transitions in the partial wetting regime. Our results resemble the wetting behavior in athermal polymer solutions. We point out that an accurate, monomer-resolved theory for colloid-polymer mixtures should incorporate the correct scaling behavior in the dilute polymer regime and an accurate description of the reference system.