Mean-field density-functional model of a second-order wetting transition

First- and second-order wetting transitions are contrasted. A mean-field density-functional model that leads to a second-order transition is introduced. The way in which it differs from an earlier, otherwise similar model in which the transition is first order is noted. The interfacial and line tensions in the model are obtained numerically and their behavior on approach to the transition is determined. The spatial variation of the model's densities in the neighborhood of the contact line near the wetting transition is also found and seen to be characteristically different at a second-order transition from what it is at a first-order transition. The results for the line tension and for the spatial variation of the densities are in accord with those from an earlier interface-displacement model of the same phenomena.     

When tethered chains meet free ones; the stability of polymer wetting films on polymer brushes

We present a combined experimental and theoretical self-consistent field (SCF) investigation of the wetting behavior of a polystyrene melt (composed of chains with degree of polymerization P) on top of a polystyrene brush (composed of chains with length N) grafted onto a silica surface. The control variables are the grafting density σ of the brush chains and the length of mobile chains P. Experiments show in agreement with the theory that there is a window of complete wetting. Both at very low and at high grafting densities the system remains partial wet. At large degree of polymerization P, there is a difference between the experimental and theoretical results. Theory predicts partial wetting only, whereas the window of complete wetting persists in the experiments even when P >> N. This difference is attributed to the double-well structure of the disjoining pressure as revealed by the SCF theory. With this type of disjoining pressure it is conceivable that a metastable zero contact angle remains present for very long times.     

Combinatorial study of the mushroom-to-brush crossover in surface anchored polyacrylamide

We present a method for fabricating anchored polymers with a gradual variation of grafting densities on solid substrates. The technique for generating such structures comprises (i) formation of a molecular gradient of polymerization initiator on the solid substrate and (ii) polymerization from the substrate-bound initiator centers ("grafting from"). We measure the mushroom-to-brush transition in grafted polyacrylamides and show that the mushroom and brush behavior can be described using existing scaling theories.     

The effect of shear flow on the conformation of polyelectrolyte brushes

The behavior of flat polyelectrolyte brushes under the action of a lateral force or flow was studied. Special attention was focused on the case when a lateral force acts on a brush that occurs near the point of phase transition from the swollen state to the collapsed state. The difference between phase transitions in a brush induced by isotropic and anisotropic interactions is analyzed. As examples of such transitions, the collapse of a polyelectrolyte brush upon cooling and the nematic collapse of an anisotropic brush are considered. It was shown that lateral force (flow), exerting a marked effect on the nematic collapse of an anisotropic brush, has no practical effect on the collapse of a brush with isotropic interactions.     

Hydrogen-bonded layer-by-layer films of block copolymer micelles with pH-responsive cores

The structure of grafted adsorbing polymers on surfaces is described as a statistical ensemble of loops generated by an one-dimensional random walk perpendicular to the surface. The configuration of each chain is considered as a succession of closed loops ended by an open loop (a tail). The probability of formation of each individual loop is the product between the probability of first return to the surface and a Boltzmann factor containing the free energy of the Flory-Huggins kind, which is approximated by the minimum free energy of all possible configurations of that loop. At high grafting densities, the attractive interactions between monomers and surface control the fraction of polymer belonging to either closed loops or tails, hence the formation of a stretched grafted brush. At low grafting densities, the increase of that interaction above a critical value generates an abrupt collapse of the brush on the surface. Whereas for long polymers (with more than about 100 Kuhn segments), the structure of the brush can be determined, in general, only via Monte-Carlo sampling, it is argued that the two structural transitions indicated above can be well predicted by simple approximations.     

Theoretical description of the adsorption and the wetting behavior of alkanes on water

The wetting behavior of alkanes of medium chain length (e.g., pentane, hexane, and heptane) on water is more complex than the usually observed first-order wetting transition from partial to complete wetting by showing a sequence of two transitions. In this sequential-wetting scenario, a first-order transition from a microscopically thin to a mesoscopically thick layer of liquid on the substrate surface is followed by a continuous divergence of the film thickness upon increase of the temperature. This critical transition to complete wetting at T(w,c) is solely determined by long-range interactions between substrate and adsorbate, which are well-described by Dzyaloshinskii-Lifshitz-Pitaevskii [Adv. Phys. 10, 165 (1961)] theory in terms of the static dielectric constants and the refractive indices of the media involved. The first-order thin-thick transition, however, which occurs at a lower temperature T(w,1), results from an interplay of short-range and long-range forces and is notoriously more difficult to describe because a satisfactory theory of the short-range interactions between substrate and adsorbate is still missing. The approach presented in this paper attempts to account for the short-range interactions in an effective way: Within a Cahn-type [J. Chem. Phys. 66, 3667 (1977)] theory that has been augmented for long-range interactions and modified to treat the first layer of adsorbed molecules in a lattice-gas approach, the contact energy is deduced from the surface pressure, which in turn is calculated using a two-dimensional van der Waals equation of state and an expression for the Henry's law constant that was derived by Hirasaki [J. Adhes. Sci. Technol. 7, 285 (1993)]. The method uses only the dielectric properties of the isolated bulk media and simple assumptions on the size and the shape of the adsorbed alkane molecules and leads to satisfactory results for the transition temperatures T(w,1) and T(w,c).     

Attractive bridging interactions in dense polymer brushes in good solvent measured by atomic force microscopy

Using an atomic force microscope (AFM), we have investigated the interaction forces exerted by latex particles bearing densely grafted polymer brushes consisting of poly(N,N-dimethylacrylamide) (PDMA), poly(methoxyethylacrylamide) (PMEA), poly(N-isopropylacrylamide) (PNIPAM), and PMEA-b-PNIPAM in aqueous media (good solvent). The brushes were prepared by controlled surface-initiated atom transfer radical polymerization, and the hydrodynamic thicknesses were measured by dynamic light scattering. The molecular weight (Mn), grafting density (sigma), and polydispersity (PDI) of the brushes were determined by gel permeation chromatography and multiangle laser light scattering after cleaving the polymer from the latex surface by hydrolysis. Force profiles of PDMA (0.017 nm(-2) < or = sigma < or = 0.17 nm-2) and PMEA (sigma = 0.054 nm-2) brushes were purely repulsive upon compression, with forces increasing with Mn and a, as expected, due to excluded volume interactions. At a sufficiently low grafting density (sigma = 0.012 nm-2), PDMA exhibited a long-range exponentially increasing attractive force followed by repulsion upon further compression. The long-range attractive force is believed to be due to bridging between the free chain ends and the AFM tip. The PNIPAM brush exhibited a bridging force at a grafting density of 0.037 nm(-2), a value lower than the sigma needed to induce bridging in the PDMA brush. Bridging was therefore found to depend on grafting density as well as on the nature of the monomer. The grafting densities of these polymers were larger than those typically associated with bridging. Bridging interactions were used to confirm the presence of PNIPAM in a block copolymer PMEA-b-PNIPAMA brush given that the original PMEA homopolymer brush produced a purely repulsive force. The attractive force was first detected in the block copolymer brush at a separation that increased with the length of the PNIPAM block.     

Connecting the wetting and rheological behaviors of poly(dimethylsiloxane)-grafted silica spheres in poly(dimethylsiloxane) melts

Using dynamic light scattering, mechanical rheometry, and visual observation, the static wetting behavior of PDMS-grafted silica spheres (PDMS-g-silica) in PDMS melts is related to their rheology. A phase diagram is mapped out for a constant grafted chain length as a function of grafting density and free polymer chain length. The transition between stable and aggregated regions is determined optically and with dynamic light scattering. It is associated with a first-order wetting transition. In the stable region Newtonian behavior is observed for semidilute suspensions. The hydrodynamic brush thicknesses, deduced from viscosity measurements, correspond closely to values obtained from self-consistent field calculations for the various parameter values. At the transition, the brush collapses suddenly and shear-thinning and thixotropy appear. The rheology indicates a degree of aggregation that increases with increasing length of the free polymer, as suggested by the theory.     

Density functional theory study of the nematic-isotropic transition in an hybrid cell

We have employed the density functional theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyze the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropiclike to nematiclike states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition the system presents interfacelike states which allow us to continuously transform the nematiclike phase to the isotropiclike phase without undergoing a sharp phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematiclike state is homogeneously planar-anchored with respect to the substrates, the capillary transition ends up in a critical point. This scenario is analogous to the observed in Ising models when confined in slit pores with opposing surface fields which have critical wetting transitions. When the nematiclike state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematiclike states.     

Statics of polymer droplets on deformable surfaces

The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation of an AFM experiment, we measure the shear modulus of the brush surface and compare the results to theoretical predictions. Then, we study the wetting behavior of polymer droplets with different surface/drop compatibility and on substrates that differ in softness. Density profiles reveal, under certain conditions, the formation of a wetting ridge beneath the three-phase contact line. Cap-shaped droplets and cylindrical droplets are also compared to estimate the effect of the line tension with respect to the droplet size. Finally, the results of the simulations are compared to a phenomenological free-energy calculation that accounts for the surface tensions and the compliance of the soft substrate. Depending on the surface/drop compatibility, surface softness, and drop size, a transition between two regimes is observed: from one where the drop surface energy balances the adhesion with the surface, which is the classical Young-Dupre? wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies.     

Microphase segregation in bridging polymeric brushes: Regular and singular phase diagrams

A mean-field theory of deformation-induced microphase segregation in bridging polymeric brushes anchored to two parallel surfaces is presented. Models with isotropic and orientation-dependent liquid-crystalline interactions between segments are considered. For the first model, the problem is similar to that of classical liquid-vapor phase separation, and the phase diagram in the P-T plane has a line of first-order transitions terminating at the critical point. We show that the critical pressure is negative implying that a free brush tethered only to one surface always exists at supercritical conditions and hence cannot undergo the collapse phase transition. In the second model, the free energy density depends on two coupled order parameters, one related to segment density and the other to the orientational order, which strongly modifies the phase behavior. Depending on the grafting density the system is described by a phase diagram of a regular or a singular type. In the regular phase diagram the first-order transition line terminates at the critical point. In a singular diagram, the first-order transition line extends to infinity; the critical point corresponds to infinite pressure so that the system undergoes the phase transition at arbitrary external pressures. Regular phase diagrams correspond to dense grafting, and singular ones to sparse grafting. The change from a regular phase behavior to another occurs at a certain marginal value of the grafting density. On approaching this value the critical point on the regular diagram moves to infinity, logarithmically with the deviation from the critical grafting density. We relate the analytical properties of the free energy density as a function of the segment concentration to the type of the phase diagram and the shape of the coexistence curve in the temperature- concentration plane.     

Molecular dynamics studies of anchored polyelectrolytes

We study polyelectrolytes end-grafted to a surface in a model which includes counterions explicitly and treats the full long-range Coulomb interaction. For strongly charged polyelectrolytes the counterions are localized inside the brush and electroneutrality is satisfied locally. Under these conditions, we find that the brush thickness is linearly proportional to the chain length and the grafting density. The counterion distribution is strongly inhomogeneous, and counterion condensation can be observed although the Bjerrum length is smaller than the average bond length. Varying the Bjerrum length we find a non-monotonic behaviour of the brush height. Counterion diffusion is anisotropic, and is enhanced at higher grafting densities. For partially charged polyelectrolytes we obtain a crossover from quasi-neutral behaviour to the strongly charged behaviour reported above.     

Transition from Incomplete to Complete Wetting of Solid Surface in Polymer–Solvent System: 2. The Regime of Strong Adsorption

The transition from incomplete to complete wetting of the solid surface by a semidilute polymer solution coexisting at equilibrium with the very-dilute polymer solution was studied using the Canh–de Gennes theory under the conditions corresponding to the tricritical state of semidilute solution and strong adsorption of the chain units on a substrate. It was established that the wetting transition can occur as the first- or second-order phase transition or as the transition of tricritical wetting depending on the repulsion energy of segments that are on the substrate surface. Near the temperatures of these transitions, the character of the variations in the differences of surface concentrations that are established at the boundaries of the substrate with semidilute and dilute polymer solutions, as well as in the differences of interfacial tensions and the cosine of contact angle were determined. It was shown that the temperature of each of these phase transitions varies in proportion to the surface potential of the substrate and does not depend on the polymer molecular mass. The observed behavior differs essentially from that established near the critical point of a polymer–solvent system.     

Molecular dynamics simulations of grafted layers of bottle-brush polyelectrolytes

Using molecular dynamics simulations, we study the effect of the brush grafting density and degree of polymerization of the side chains on conformations of brush layers made of charged bottle-brush macromolecules. The thickness of the brush layer first decreases with increasing brush grafting density; then, it saturates and remains constant in the wide interval of the brush grafting densities. The brush layers consisting of the bottle-brush macromolecules with longer side chains have a larger layer thickness. The elongation of the side chains of the bottle-brush macromolecules decreases with increasing brush grafting density. This contraction of the side chains is due to counterion condensation inside the volume occupied by bottle-brushes. Our simulations showed that counterion condensation is a multiscale process reflecting different symmetries of the bottle-brush layer.     

Solvent quality effects on scaling behavior of poly(methyl methacrylate) brushes in the moderate- and high-density regimes

Herein, we give a detailed experimental analysis for scaling law behavior in the "moderately dense" and "high-density" brush regimes for poly(methyl methacrylate) brushes swollen in a range of solvent conditions. This expansive experimental analysis aims to validate decades of mean field theory predictions on power law scaling behavior of grafted polymer chains. Brushes with grafting densities (σ) ranging from 0.1 to 0.8 nm(-2) are prepared by atom-transfer radical polymerization. The swollen thickness (h) is characterized using liquid cell ellipsometry, and the solvent quality is varied using mixtures of acetone and methanol. In a good solvent, the exponential scaling behavior (h ∝ σ(n)) has the typical n = 1/3 dependency for grafting densities of σ ≤ 0.4 nm(-2). For grafting densities of >0.4 nm(-2), n increases, indicating the transition from the moderately dense to the high-density brush regime. However, in a poor solvent, the scaling behavior is independent of σ and scales as h ∝ σ(0.80), approaching the theoretical expectations of h ∝ σ(1). An abrupt transition between these scaling law behaviors occurs at the Θ-solvent condition of ～45% (v/v) methanol in acetone. While our experimental results parallel trends predicted by mean field theory, differences are observed and appear to be attributed to self-solvation of the polymer, polydispersity in the molecular weight, and chain termination.     

Line and boundary tensions on approach to the wetting transition

A mean-field density-functional model often used in the past in the study of line and boundary tensions at wetting and prewetting transitions is reanalyzed by extensive numerical calculations, approaching the wetting transition much more closely than had previously been possible. The results are what are now believed to be definitive for the model. They include strong numerical evidence for the presence of the logarithmic factors predicted by theory both in the mode of approach of the prewetting line to the triple-point line at the point of the first-order wetting transition and in the line tension itself on approach to that point. It is also demonstrated with convincing numerical precision that the boundary tension on the prewetting line and the line tension on the triple-point line have a common limiting value at the wetting transition, again as predicted by theory. As a by product of the calculations, in the model's symmetric three-phase state, far from wetting, it is found that certain properties of the model's line tension and densities are almost surely given by simple numbers arising from the symmetries, but proving that these are exact for the model remains a challenge to analytical theory.     

Lattice model for the wetting transition of alkanes on aqueous surfactant solutions

Droplets of alkanes on aqueous solutions of the cationic surfactants C(n)TAB (CH3(CH2)(n-1)N+ (CH3)3Br-) exhibit a first-order wetting transition as the concentration of the surfactant is increased. A theoretical model is presented in which the surface free energy is broken down into a long-range dispersion interaction and a short-range interaction described by a 2D lattice gas, taking into account the interaction between oil and surfactant molecules. The model provides quantitative agreement with the observed wetting transitions and the variation in composition of the wetting film with bulk surfactant concentration. The behavior of oil drops on large reservoirs of dilute surfactant is discussed.     

Polymer brushes in solvents of variable quality: molecular dynamics simulations using explicit solvent

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.     

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular-dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model, which includes excluded volume and backbone connectivity of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and nonequilibrium molecular-dynamics simulations at constant temperature and volume using the dissipative particle dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The obtained boundary conditions and slip length show a rich behavior as a function of grafting density and shear velocity.