Fluids density functional theory studies of supramolecular polymers at a hard surface.

We have applied a fluids density functional theory based on that of Yu and Wu [J. Chem. Phys. 116, 7094 (2002)] to treat reversible supramolecular polymers near a hard surface. This approach combines a hard-sphere fluids density functional theory with the first-order thermodynamic perturbation theory of Wertheim. The supramolecular polymers are represented in the theory by hard-spheres with two associating sites. We explore the effects of the bonding scheme, monomer concentration, and association energy upon the equilibrium chain sizes and the depletion lengths. This study is performed on simple systems containing two-site monomers and binary mixtures of two-site monomers combined with end stopper monomers which have only a single association site. Our model has correct behavior in the dilute and overlap regimes and the bulk results can be easily connected to simpler random-flight models. We find that there is a nonmonotonic behavior of the depletion length of the polymers as a function of concentration and that this depletion length can be controlled through the concentration of end stoppers. These results are applicable to the study of colloidal dispersions in supramolecular polymer solutions.

Phase behavior of flowerlike micelles in a SCF cell model.

We study the interactions between flowerlike micelles, self-assembled from telechelic associative polymers, using a molecular self-consistent field (SCF) theory and discuss the corresponding phase behavior. In these calculations we do not impose properties such as aggregation number, micellar structure and number of bridging chains. Adopting a SCF cell model, we calculate the free energy of interaction between a central micelle surrounded by others. Based on these results, we predict the binodal for coexistence of dilute and dense liquid phases, as a function of the length of the hydrophobic and hydrophilic blocks. In the same cell model we compute the number of bridges between micelles, allowing us to predict the network transition. Several quantitative trends obtained from the numerical results can be rationalized in terms of transparent scaling arguments.

Shear banding and rheochaos in associative polymer networks.

We present experimental evidence of an instability in the shear flow of transient networks formed by telechelic associative polymers. Velocimetry experiments show the formation of shear bands, following a complex pattern upon increasing the overall shear rate. The chaotic nature of the stress response in transient flow is indicative of spatiotemporal fluctuations of the banded structure. This is supported by time-resolved velocimetry measurements.

Equilibrium capillary forces with atomic force microscopy.

We present measurements of equilibrium forces resulting from capillary condensation. The results give access to the ultralow interfacial tensions between the capillary bridge and the coexisting bulk phase. We demonstrate this with solutions of associative polymers and an aqueous mixture of gelatin and dextran, with interfacial tensions around 10 microN/m. The equilibrium nature of the capillary forces is attributed to the combination of a low interfacial tension and a microscopic confinement geometry, based on nucleation and growth arguments.

Direct measurement of depletion and hydrodynamic forces in solutions of a reversible supramolecular polymer.

In this paper, the investigation of surface forces in semidilute solutions of a nonadsorbing hydrogen-bonded reversible supramolecular polymer is described. Colloidal probe atomic force microscopy was used for direct measurement of depletion forces. Hydrodynamic drag on the AFM cantilever with the colloidal probe was measured both far away from and close to the planar substrate surface. The results indicate that the presence of the depletion layer causes slip at the surfaces with a large apparent slip length. Our analysis explains how the presence of slip enables the measurement of (relatively weak) depletion forces in solutions with a high viscosity by significantly reducing the hydrodynamic forces. The range and magnitude of the measured depletion forces are qualitatively in agreement with previous experiments and theoretical predictions. Due to the relatively large experimental error, no quantitative conclusions can be drawn. Depletion-induced phase separation of suspensions of stearylated silica particles was also observed. Phase separation becomes more pronounced with increasing polymer concentration.

Micellization of telechelic associative polymers: self-consistent field modeling and comparison with scaling concepts.

We present numerical results from self-consistent field calculations on the micellization of telechelic associative polymers and their mono-functional analogues. These results are confronted with relatively simple scaling concepts. The proportionality of the critical micelle concentration (CMC) with the hydrophilic backbone length, as found in the calculations, shows good correspondence with a scaling argument based on the entropic penalty of loop formation. It is also shown that models for the conformation of spherical brushes can be applied to predict the structure of the flowerlike micelles formed by these telechelic polymers. Furthermore, we find good agreement between the numerical dependence of the aggregation number upon both backbone and terminal hydrophobe length and an analytical expression derived from the well-known Daoud-Cotton model by introducing a correction for the finite size of the micellar core.

Rheology of a reversible supramolecular polymer studied by comparison of the effects of temperature and chain stoppers.

The rheology of a reversible supramolecular polymer is studied by comparing the effects of an increase in temperature and the addition of chain stoppers. The dependence of the zero-shear viscosity and the terminal relaxation time on temperature is exponential, and the activation energy for viscous flow can be calculated. Above a critical stopper fraction, power laws describe the stopper dependence of the viscosity and relaxation time. A simple model for the effect of the addition of chain stoppers on the average degree of polymerization adequately describes the results. A comparison of flow curves at several temperatures and stopper fractions reveals considerable differences between solutions with the same zero-shear viscosity. These are mainly associated with differences in the terminal relaxation time. A mechanism of shear-induced alignment and subsequent elongation of chains is proposed, with which the experimental results are consistent.

On the curvature dependence of the interfacial tension in a symmetric three-component interface.

We consider a symmetric interface between two polymers A(N) and B(N) in a common monomeric solvent S using the mean-field Scheutjens-Fleer self-consistent field theory and focus on the curvature dependence of the interfacial tension. In multi-component systems there is not one unique scenario to curve such an interface. We elaborate on this by keeping either the chemical potential of the solvent or the bulk concentration of the solvent fixed, that is we focus on the semi-grand canonical ensemble case. Following Helfrich, we expand the surface tension as a Taylor series in the curvature parameters and find that there is a non-zero linear dependence of the interfacial tension on the mean curvature in both cases. This implies a finite Tolman length. In a thermodynamic analysis we prove that the non-zero Tolman length is related to the adsorption of solvent at the interface. Similar, but not the same, correlations between the solvent adsorption and the Tolman length are found in the two scenarios. This result indicates that one should be careful with symmetry arguments in a Helfrich analysis, in particular for systems that have a finite interfacial tension: one not only should consider the structural symmetry of the interface, but also consider the constraints that are enforced upon imposing the curvature. The volume fraction of solvent, the chain length N as well as the interaction parameter chi(AB) in the system can be used to take the system in the direction of the critical point. The usual critical behavior is found. Both the width of the interface and the Tolman length diverge, whereas the density difference between the two phases, adsorbed amount of solvent at the interface, interfacial tension, spontaneous curvature, mean bending modulus as well as the Gaussian bending modulus vanish upon approach of the critical point.

Adsorption and desorption of reversible supramolecular polymers.

We report numerical mean-field results on the quasichemical level of approximation that describe adsorption of reversible supramolecular polymers at a flat interface. Emphasis is laid on the regime of strong adsorption from a dilute solution. There are two differences with respect to macromolecular polymer adsorption: (i) adsorption sets in at relatively high monomer concentrations of the surrounding solution, and (ii) the surface is filled within a much narrower concentration range. Contrary to macromolecular polymers, supramolecular polymers can therefore be desorbed by dilution of the equilibrium solution by solvent within an experimentally accessible concentration window. Based on simple thermodynamic arguments, we provide a quantitative explanation why supramolecular polymers adsorb at relatively high concentrations. Moreover, we discuss the (by comparison) narrow concentration window wherein filling of the surface occurs. This is attributed to the cooperative nature of supramolecular polymer adsorption. The degree of cooperativity is quantified by means of the Hill parameter n.

Multiple shear-banding transitions in a supramolecular polymer solution.

We report on the nonlinear rheology of a reversible supramolecular polymer based on hydrogen bonding. The coupling between the flow-induced chain alignment and breakage and recombination of bonds between monomers leads to a very unusual flow behavior. Measured velocity profiles indicate three different shear-banding regimes upon increasing shear rate, each with different characteristics. While the first of these regimes has features of a mechanical instability, the second shear-banding regime is related to a shear-induced phase separation and the appearance of birefringent textures. The shear-induced phase itself becomes unstable at very high shear rates, giving rise to a third banding regime.

Symmetric liquid-liquid interface with a nonzero spontaneous curvature.

The curvature dependence of the symmetric interface between two immiscible polymer solutions in a common monomeric solvent is analyzed using a self-consistent field theory. Contrary to symmetry arguments we find that the surface tension depends in first order on a nonzero Tolman length. These interfaces further have a negative mean and a positive Gaussian bending modulus. The finite spontaneous curvature is attributed to the adsorption of the solvent at the interface.

Long-range depletion forces induced by associating small molecules.

This is the first report of experimental observations of depletion interactions in solutions of a (hydrogen-bonded) reversible supramolecular polymer. Depletion forces were measured directly by colloidal probe atomic force microscopy. The range of the depletion force is consistent with existing independent experimental data. The interaction can be tuned by adding monofunctional chain stoppers to the solution, a possibility which is unique to supramolecular polymers. The depletion force is shown to be strong enough to induce phase separation in a colloidal suspension.

Direct determination of liquid phase coexistence by Monte Carlo simulations.

A formalism to determine coexistence points by means of Monte Carlo simulations is presented. The general idea of the method is to perform a simulation simultaneously in several unconnected boxes which can exchange particles. At equilibrium, most of the boxes will be occupied by a homogeneous phase. The compositions of these boxes yield coexisting points on the binodal. However, since the overall composition is fixed, at least one of the boxes will contain an interface. We show that this does not affect the results, provided that the interface has no net curvature. We coin the name "Helmholtz-ensemble method," because the method is related to the well-known Gibbs-ensemble method, but the volume of the boxes is constant. Since the box volumes are constant, we expect that this method will be particularly useful for lattice models. The accuracy of the Helmholtz-ensemble method is benchmarked against known coexistence curves of the three-dimensional Ising model with excellent results.

Thinning of wetting films formed from aqueous solutions of non-ionic surfactant.

We investigated the thinning of wetting films formed from aqueous solution of non-ionic triblock copolymer Pluronic F127 on the surface of silica using a home-made thin film balance and time-resolved ellipsometry. Imaging ellipsometry was used to visualize the film structures at subsequent stages of their development. The results unambiguously show that the time required for the formation of steady films strongly depends on the electrolyte concentration. When increasing the latter from 10(-4) to 0.1 M, this time typically increases with several orders of magnitude, from a few minutes to several hours. Moreover, for sufficiently large amounts of salt, two characteristic relaxation regimes can be clearly identified. After initial quick thinning, further thinning slows down enormously. These typical kinetic regimes are thought to result from the coupled dependencies of the bulk and interfacial properties of F127 on salt concentration. Possible explanations of the phenomenon are discussed.

Mean chain length of adsorbed supramolecular polymers.

We present a theoretical study of reversible supramolecular polymers near an adsorbing surface. Mean chain lengths for free and adsorbed supramolecular polymers were calculated for a broad range of concentrations. As far as we know, this is the first report that describes a regime where the mean chain length decreases with increasing monomer concentration. It is shown that this anomalous behavior is caused by a change of the structure of the adsorbed layer.

Influence of NaCl on the behavior of PEO-PPO-PEO triblock copolymers in solution, at interfaces, and in asymmetric liquid films.

The solution behavior of the polymeric surfactant Pluronic F127 (PEO(99)PPO(65)PEO(99)) and its adsorption behavior on aqueous-silica and aqueous-air interfaces, as well as the disjoining pressure isotherms of asymmetric films (silica/aqueous film/air) containing F127, are studied. The interfacial properties of adsorbed F127 layers (the adsorbed amount Gamma and the thickness h) as well as the aqueous wetting film properties [film thickness (h) and refractive indexes] were studied via ellipsometry. The solution properties of F127 were investigated using surface tensiometry and light scattering. The interactions between the air-water and silica-water interfaces were measured with a thin film pressure balance technique (TFB) and interpreted in terms of disjoining pressure as a function of the film thickness. The relations between the behaviors of the asymmetric films, adsorption at aqueous air, and aqueous silica interfaces and the solution behavior of the polymeric surfactant are discussed. Special attention is paid to the influence of the concentrations of F127 and NaCl. Addition of electrolyte lowers the critical micelle concentration, diminishes adsorption on silica, and increases the thickness of the asymmetric film.

Dynamics of reversible supramolecular polymers: independent determination of the dependence of linear viscoelasticity on concentration and chain length by using chain stoppers.

The linear viscoelasticity of solutions of a hydrogen bonded reversible supramolecular polymer in the presence of a chain stopper was studied by rheometry and by dynamic light scattering using probe particles. The use of chain stoppers enabled the independent variation of the degree of polymerisation and the monomer concentration, and the effect of both parameters on rheology was investigated. Scaling exponents were obtained for the chain length and concentration dependence of the zero-shear viscosity and the terminal relaxation time, and these were compared to theoretical values. The results indicate that the reversible supramolecular polymer is semiflexible, and that both breaking and reptation of chains contribute to the stress relaxation. The parameters from macroscopic rheometry were compared to microscopic values obtained from probe particle diffusion. The particles probe the macroscopic viscoelastic parameters if their size is large compared to the correlation length in the system and to the (persistence) length of the polymer chains.

Wetting in a colloidal liquid-gas system.

We present first observations of wetting phenomena in depletion interaction driven, phase separated colloidal dispersions (coated silica-cyclohexane-polydimethylsiloxane). The contact angle of the colloidal liquid-gas interface at a solid substrate (coated glass) was determined for a series of compositions. Upon approach to the critical point, a transition occurs from partial to complete wetting.

Brownian particles in supramolecular polymer solutions.

The Brownian motion of colloidal particles embedded in solutions of hydrogen-bonded supramolecular polymers has been studied using dynamic light scattering. At short times, the motion of the probe particles is diffusive with a diffusion coefficient equal to that in pure solvent. At intermediate time scales the particles are slowed down as a result of trapping in elastic cages formed by the polymer chains, while at longer times the motion is diffusive again, but with a much smaller diffusion coefficient. The influence of particle size and polymer concentration was investigated. The experimental data are compared to a theoretical expression for the mean-square displacement of an embedded particle in a viscoelastic medium, in which the solvent is explicitly taken into account. Differences between the friction and elastic forces experienced by the particle and the macroscopic viscosity and elasticity are explained by the inhomogeneity of the medium on the length scale of the particle size.

Statistical thermodynamics of equilibrium polymers at interfaces.

The behavior of a solution of equilibrium polymers (or living polymers) at an interface is studied, using a Bethe-Guggenheim lattice model for molecules with orientation dependent interactions. The density profile of polymers and the chain length distribution are calculated. For equilibrium polymers at a nonadsorbing surface it is found that the depletion layer thickness has a maximum. In dilute solutions it is proportional to the average radius of gyration of the polymers, which increases with increasing concentration. Above the overlap concentration it corresponds to the bulk correlation length, which decreases with increasing concentration. Furthermore, it is found that the surface region is predominantly occupied by the shorter chains. Both in dilute solutions and in a melt of equilibrium polymers, a very simple relation is found between the surface excess of a component and the chain length.