Towards a modellisation of the solvation energy in multi-component solvents. The interesting case of a charged solute imbedded in a polymer-containing electrolyte solution

In this paper we propose a mean-field theory to calculate the solvation free energy of a charged solute imbedded in a complex multi-component solvent. We considered a solvent made up of a mixture of small (electrolyte solution) and large (polymer) components. The presence of macromolecules ensures reduced mixing entropy among the different solvent components, an effect due to polymer connectivity. The reduced entropy favours strong preferential distribution of a particular solvent even in the presence of weak preferential solute–solvent interactions. In addition, two energy terms must be considered: (a) the interaction between the solute electrostatic potential and the electrolyte solution and (b) the formation of a polymer–solute interface. Because of the different dielectric permittivity of the solvent components, the electrolyte and polymer distribution functions are strongly coupled: ions, indeed, are more solvated in regions of higher local dielectric permittivity arising from the inhomogeneous mixing of solvent and polymer. We combined together the different energy terms in the framework of the de Gennes free energy functional for polymer solutions along with a generalised Poisson–Boltzmann equation developed for inhomogeneous dielectric media. Moreover, the preferential electrolyte solvation in regions of greater polarity was considered by an extension of the Born equation. Setting the polymer dielectric permittivity smaller than the solvent one and making null the specific polymer–solute interactions, we calculated enhanced electrolyte concentration and reduced polymer concentration near the solute surface on raising the solute surface charge density. The theory shows also the breakdown of the widely used separation between electrostatic and surface tension-dependent contributions to solvation energy when non-ideal mixed solvents are considered. In fact, according to the model, the surface tension of such mixed solvents strongly depends on the solute surface charge density: at high potentials the interfacial tension may increase rather than decrease on raising the polymer volume fraction. The theoretical results have been compared with experimental data on polymer+electrolyte solution surface tension and with solubility data of colloidal particles. The comparison evidences the complex behaviour of multi-component solvents going well beyond the trivial weighted average of the dielectric permittivity and surface tension of the isolated chemical components. Deviations from the simple behaviour predicted by an average picture of multi-component solvents could be understood by developing more sophisticated, but still simple, approaches like that proposed in this paper.Contribution to the Jacopo Tomasi Honorary Issue. This paper is dedicated to Jacopo Tomasi. I learned much of the difficult art of transforming complex problems into simple models after reading his early works on solvation energy.     

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.     

Poly(styrene-b-2-vinylpyridine-1-oxide) diblock copolymers: 3. Microemulsions in water/propan-2-ol/toluene mixtures

Pseudo-ternary phase diagrams have been constructed for the three-component solvent system (toluene+water+propan-2-ol) containing diblock copolymers of poly(styrene-b-2-vinylpyridine-1-oxide). Microemulsions have been shown to form on the water-rich side of the phase diagram, in the region of the phase boundary without polymer. Dynamic light-scattering experiments have led to droplet size values in the region of 100 nm, with the size depending strongly on the propan-2-ol/water concentration, as well as the amount of solubilised toluene in the core. Viscometry experiments have been carried out to measure polymer aggregation numbers in the microemulsion droplets, and interfacial tension measurements have shown that in the absence of propan-2-ol (effectively a cosurfactant) the limiting value of the oil/water interfacial tension, even an saturation adsorption of the copolymer is 20 mNm^–1. However, addition of propan-2-ol reduces the interfacial tension to the very low values generall commensurate with microemulsion formation.     

Noninteracting versus interacting poly(N-isopropylacrylamide)-surfactant mixtures at the air-water interface

Two polymer-surfactant mixtures have been studied at the air-water interface using neutron reflectivity and surface tension techniques. For the noninteracting system poly(N-isopropylacrylamide) (PNIPAM)/octaethyleneglycol mono n-decyl ether (C10E8), the adsorption behavior is competitive and driven purely by surface pressure (pi). When pi(polymer) > pi(surfactant), the surface layer consists of almost pure polymer, and for pi(polymer) < pi(surfactant), the polymer is displaced from the surface by the increasing pressure of the surfactant. Beyond the CMC, the polymer is completely displaced from the surface. For the interacting system PNIPAM/sodium dodecyl sulfate (SDS) where the two species interact strongly in the bulk beyond the critical aggregation concentration (CAC), the surface behavior is more original. Earlier neutron reflectivity studies investigated PNIPAM adsorption behavior where the SDS was contrast-matched to the solvent. In the present study, complementary measurements of SDS adsorption where PNIPAM is contrast-matched to the solvent give a complete view of the surface composition of the mixed system. At a constant polymer concentration, with increasing SDS, three main regimes are obtained. For C(SDS) < CAC, adsorption is governed by simple competition and PNIPAM is predominant at the interface. At intermediate SDS concentration (CAC < C(SDS) < x2, where x2 indicates the predominance of free SDS micelles), interfacial behavior is governed by bulk polymer-surfactant interaction. Adsorbed polymer is displaced from the interface to form PNIPAM-SDS complex in the bulk. SDS adsorption remains weak since most of the SDS molecules are used to form bulk polymer-surfactant aggregates. Further increase in SDS concentration results in continued displacement of PNIPAM and an abrupt increase in SDS adsorption. This is a result of saturation of bulk polymer chain with adsorbed micelles. Interestingly, beyond x2, PNIPAM is not completely displaced from the surface. A mixed PNIPAM-SDS adsorbed layer with enhanced packing of the SDS monolayer is formed.     

Interfacial tension and wetting in colloid-polymer mixtures

We calculate the interfacial tension and the wetting behavior in phase separated colloid-polymer mixtures both for ideal and excluded volume interacting polymers. Within the recently developed extension of the free volume theory to include polymer interactions the interfacial tension of the free interface is calculated by adding a van der Waals squared gradient term. The wetting behavior at a hard wall is calculated following a Cahn-Fisher-Nakanishi approach taking the one- and two-body colloid-wall interactions into account. Comparing results for interacting polymers with those for ideal polymers we find that for interacting polymers the interfacial tension does not increase as steeply as a function of the gas-liquid colloid density difference. Furthermore, the wetting transition shifts to higher polymer concentrations, even to above the triple line. The predictions for both the interfacial tension and the wetting are compared to recent experiments.     

Stabilization of self‐assembled microdroplets using short chain alcohols

The condensation of water vapor on a volatile polymeric solution leads to a porous surface after evaporation of both solvent and water. However, the stabilization of the water microdroplet is of great importance, which can be achieved using specific polymer or adding a third substance to the polymer solution. Short chain alcohols (methanol, ethanol, and n‐propanol) are utilized to fabricate a self‐assembled porous honeycomb film of linear, low molecular weight polystyrene using the breath figure technique. A combination of breath figure processing and the effect of alcohol on a water droplet can stabilize the pattern and make pores on the surface of the polymer film. The quality of the porous honeycomb film is strongly dependent on the type of alcohols and the concentration of polymer. In a specific range of polymer and alcohol concentration, pores cover all the surface of the polymer film. This method offers the possibility of producing a honeycomb structure with no trace of additive residual after the fabrication process and avoiding polymer modification. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 709–718     

Interfacial tension of evaporating emulsion droplets containing amphiphilic block copolymers: effects of solvent and polymer composition

Evaporating droplets of volatile organic solvent containing amphiphilic block copolymers may undergo hydrodynamic instabilities that lead to dispersal of copolymer micelles into the surrounding aqueous phase. As for related phenomena in reactive polymer blends and oil/water/surfactant systems, this process has been ascribed to a nearly vanishing or transiently negative interfacial tension between the water and solvent phases induced by adsorption of copolymer to the interface. In this report, we investigate the influence of the choice of organic solvent and polymer composition for a series of polystyrene-b-poly(ethylene oxide) (PS-PEO) diblock copolymers, by in situ micropipette tensiometry on evaporating emulsion drops. These measurements suggest that the sensitivity to the organic solvent chosen reflects both differences in the bare solvent/water interfacial tension as well as the propensity of the copolymer to aggregate within the organic phase. While instabilities coincident with an approach of the interfacial tension nearly to zero were observed only for copolymers with PEO content greater than 15 wt.%, beyond this point the interfacial behavior and critical concentration needed to trigger surface instability were found to depend only weakly on copolymer composition.     

Interfacial properties of compressible polymer solutions

A chemomechanical model for the interfacial concentration and density in compressible polymer solutions is formulated using variational principles. The nonlinear model with boundary conditions obtained from phase equilibrium calculations gives the coupled concentration and density profiles. The couplings between chemical and mechanical balances are identified and efficient ways to calculate the interfacial structure is identified. A specific model appropriate to high‐pressure processing of the polyolefins is developed using the modified Sanchez Lacombe equation of state. Bakker's formula for the interfacial tension is adapted to compressible polymer solutions. The structure and tension of a flat interface is characterized using the developed model and material properties of three molecular weight hydrogenated polybutadiene; the main variables of interest were the pressure, polymer molecular weight, and temperature. The relation between the pressure profile across the interface and the interfacial tension is characterized. Scaling power laws for interfacial tension and interfacial thickness as a function of pressure are obtained and contrasted with the corresponding laws observed and predicted for incompressible polymer solutions. It is found that the modified Sanchez Lacombe‐based power law prediction predictions for compressible solutions in terms of pressure quenches are similar to those from those obtained by the Flory‐Huggins incompressible model for temperature quenches. The present results provide the basis for the future study of the kinetics of pressure‐induced phase separation in compressible polymer solutions. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 640–654, 2009     

The influence of pH on phosphatidylcholine monolayer at the air/aqueous solution interface

The measurements of the interfacial tension at the air/aqueous subphase interface as the function of pH were performed. The interfacial tension of the air–aqueous subphase interface was divided into contributions of individuals. A simple model of the influence of pH on the phosphatidylcholine monolayer at the air/hydrophobic chains of phosphatidylcholine is presented. The contributions of additive phosphatidylcholine forms (both interfacial tension values and molecular area values) depend on pH. The interfacial tension values and the molecular areas values for LH⁺, LOH⁻ forms of phosphatidylcholine were calculated. The assumed model was verified experimentally.     

A self-consistent field study of a hydrocarbon droplet at the air-water interface

A molecularly detailed self-consistent field (SCF) approach is applied to describe a sessile hydrocarbon droplet placed at the air-water interface. Predictions of the contact angle for macroscopic droplets follow from using Neumann's equation, wherein the macroscopic interfacial tensions are computed from one-gradient calculations for flat interfaces. A two-gradient cylindrical coordinate system with mirror-like boundary conditions is used to analyse the three dimensional shape of the nano-scale oil droplet at the air-water interface. These small droplets have a finite value of the Laplace pressure and concomitant line tension. It has been calculated that the oil-water and oil-vapour interfacial tensions are curvature dependent and increase slightly with increasing interfacial curvature. In contrast, the line tension tends to decrease with curvature. In all cases there is only a weak influence of the line tension on the droplet shape. We therefore argue that the nano-scale droplets, which are described in the SCF approach, are representative for macroscopic droplets and that the method can be used to efficiently generate accurate information on the spreading of oil droplets at the air-water interface in molecularly more complex situations. As an example, non-ionic surfactants have been included in the system to illustrate how a molecularly more complex situation will change the wetting properties of the sessile drop. This short forecast is aimed to outline and to stress the potential of the method.     

Investigation of the interfacial properties of water-in-diluted-bitumen emulsions using micropipette techniques

The interfacial properties of water-in-diluted bitumen emulsions were studied using micropipette techniques. It was observed that, as bitumen concentration in the bulk phase (C0) increased, the interfacial tension on the water droplet surfaces decreased. In addition, there was a small effect on the interfacial tension when different solvent mixtures were used. Mixtures of toluene and heptane in different ratios were used as solvents for bitumen dilution. Crumpling of the interface was influenced by bitumen concentration and type of solvent. No crumpling was found for bitumen content less than 0.01% for all solvents used. Crumpling was observed at higher bitumen concentrations when deionized water (pH 5.4-5.6) was used. Setting "heptol[A]" to be the mixture of toluene and heptane, with the volume percent of toluene being A, the following were concluded. Crumpling disappeared at C0 > 1% and when heptol[100] was used, and also at C0 > 10% and when heptol[30] was used. Crumpling was strongly affected by the water pH. In the case of heptol[50], at a higher pH, the crumpling region that normally occurred at C0 > 0.01% disappeared. The micropipette technique proved to be useful in studying the interfacial properties of micrometer-sized emulsion drops.     

The Fast Relaxation Process between Hydrophobically Modified Associating Polyacrylamide and Different Surfactants at the Water‐Octane Interface

In our previous work (Macromolecules 2004, 37:2930), we found that the hydrophobic blocks of polyacrylamide modified with 2‐phenoxylethyl acrylate (POEA) and anionic surfactant sodium dodecyl sulfate (SDS) may form mixed associations at octane/water interface. However, the process involving the exchange of surfactant molecules between monomers and mixed associations in interface is so fast that we cannot obtain its characteristic time. In this article, the interfacial dilational viscoelastic properties of another hydrophobically associating block copolymer composed of acrylamide (AM) and a low amount of 2‐ethylhexyl acrylate (EHA) (<1.0 mol%) at the octane‐water interfaces were investigated by means of oscillating barriers method and interfacial tension relaxation method respectively. The influences of anionic surfactant SDS and nonionic surfactant Triton X‐100 on the dilational viscoelastic properties of 7000 ppm polymer solutions were studied. The results showed that the interaction between P(AM/2‐EHA) and SDS was similar to that of P(AM/POEA) and SDS. Moreover, we got the relaxation characteristic time of the fast process involving the exchange of s Triton X‐100 molecules between monomers and mixed associations.

We also found that the interfacial tension response of hydrophobically associating water‐soluble copolymers to the sinusoidal oscillation of interfacial area at low bulk concentration is as same as that of the typical surfactants: the interfacial tension decreases with the decrease of interfacial area because of the increase of interfacial active components. However, the interfacial tension increases with the decrease of interfacial area at 7000 ppm P(AM/2‐EHA), which is believed to be correlative with the structure of absorbed film. The results of another hydrophobically associating polymer P(AM/POEA) and polyelectrolyte polystyrene sulfonate (PSS) enhanced our supposition. The phase difference between area oscillation and tension oscillation has also been discussed considering the apparent negative value.     

Vinyl acetate emulsion polymerization. I. Effect of ionic strength and temperature on monomer solubility in the ionically stabilized polymer particle

Solubility of monomer in the polymer was strongly affected by ionic strength; with increasing ionic strength, solubility was found to increase. At constant temperature, this was entirely due to the decrease in interfacial tension, as the condensation of surfactant proceeded at the interface. The temperature affected both the polymer–solvent interaction parameter as well as the interfacial tension. These are the two parameters on which solubility depends. The variations of interfacial tension with temperature was found to be complex, but entirely dependent on the entropic consideration of adsorption. The polymer–solvent interaction parameter–inverse temperature dependence was found to be linear, as expected.     

The influence of electric field-induced orientation on the retraction of a liquid crystal droplet immersed in a flexible polymer matrix

We measured the apparent interfacial tension between a liquid crystal and a flexible polymer by deformed droplet retraction method. An external electric field is applied to change the director orientation in liquid crystal droplet. The deformation and recovery of a single liquid crystal droplet dispersed in a polydimethylsiloxane (PDMS) matrix were realized by a transient shear flow and observed by polarized optical microscope. In order to control the director orientation in LC droplet, the electric field is applied perpendicular and parallel to the flow field, respectively. The different orientation induced by electric field in liquid crystal droplet has different behavior during droplet retraction and affect the apparent interfacial tension between liquid crystal and flexible polymer.     

A mechanistic study of the formation of polymer nanoparticles by the emulsification-diffusion technique

 The mechanism of formation of polymer nanoparticles prepared by the emulsification–diffusion method was evaluated under different preparation conditions and by turbidimetry measurements. Biodegradable poly (D,L-lactic acid) was used as the polymer model. The results show that each emulsion droplet will form several nano-particles and that the interfacial phenomena during solvent diffusion determine the size properties of the resulting colloid particles. These phenomena cannot be entirely explained by the convection effects caused by interfacial turbulence. We suggest that nanoparticle formation is due to diffusion alone, and we propose a mechanism based on the “diffusion-stranding” mechanism for spontaneous emulsification. In this mechanism, the diffusion of solvent causes local supersaturation near the interface, and nanoparticles are formed, due to the phase transformation and polymer aggregation that occur in these regions. This interpretation is supported by the turbidity measurements made at different polymer concentrations and stirring rates. Received: 30 October 1996 Accepted: 27 March 1997     

Surface activity and emulsification properties of hydrophobically modified dextrans

Neutral polymeric surfactants were synthesized by covalent attachment of hydrophobic groups (aromatic rings) onto a polysaccharide backbone (dextran). By changing the conditions of the modification reaction, the number of grafted hydrophobic groups per 100 glucopyranose units (substitution ratio) was varied between 7 and 22. In aqueous solution, these polymers behaved like classical associative polymers as demonstrated by viscometric measurements. The associative behavior was more pronounced when the substitution ratio increased. The surface-active properties of the modified dextrans were evidenced by surface tension (air/water) and interfacial tension (dodecane/water) measurements. In each case the surface or interfacial tension leveled down above a critical polymer concentration, which was attributed to the formation of a dense polymer layer at the liquid-air or liquid-liquid interface. Dodecane-in-water emulsions were prepared using the polymeric surfactants as stabilizers, with oil volume fractions ranging between 5 and 20%. The oil droplet size (measured by dynamic light scattering) was correlated to the amount of polymer in the aqueous phase and to the volume of emulsified oil. The thickness of the adsorbed polymer layer was estimated thanks to zeta potential measurements coupled with size measurements. This thickness increased with the amount of polymer available for adsorption at the interface. The dextran-based surfactants were also applied to emulsion polymerization of styrene and stable polystyrene particles were obtained with a permanent adsorbed dextran layer at their surface. The comparison with the use of an unmodified dextran indicated that the polymeric surfactants were densely packed at the surface of the particles. The colloidal stability of the suspensions of polystyrene particles as well as their protection against protein adsorption (bovine serum albumin, BSA, used as a test protein) were also examined.     

Welding immiscible polymers with a supercritical fluid

Polymer adhesion between two immiscible polymers is usually poor because there is little interpenetration of one polymer into the other at the interface. Increasing the width of the interfacial zone can enhance adhesion and mechanical properties. In principle, this can be accomplished by exposing heterogeneous polymer materials to a high-pressure fluid. The fluid can act as a common solvent and promote interpenetration. It also increases chain mobility at the interface, which helps to promote "welding" of the two polymers. A combination of the gradient theory of inhomogeneous systems and the Sanchez-Lacombe equation of state was used to investigate this phenomenon, especially the effect of the high compressibility of supercritical (SC) fluid on the compatibilization of two incompatible polymers. We calculate the interfacial density profile, interfacial thickness, and interfacial tension between the two polymers with and without the SC fluid. We find that the interfacial tension is decreased and the interfacial thickness is increased with high-pressure SC fluid for the ternary systems we have investigated. As the critical point is approached and the SC compressibility becomes large, no enhancement or deleterious effects on compatibilization were observed.     

Simulation of droplet formation and coalescence using lattice Boltzmann-based single-phase model

A lattice Boltzmann method-based single-phase free surface model is developed to study the interfacial dynamics of coalescence, droplet formation and detachment phenomena related to surface tension and wetting effects. Compared with the conventional multiphase models, the lattice Boltzmann-based single-phase model has a higher computational efficiency since it is not necessary to simulate the motion of the gas phase. A perturbation, which is given in the same fashion as the perturbation step in Gunstensen's color model, is added to the distribution functions of the interface cells for incorporating the surface tension into the single-phase model. The assignment of different mass gradients along the fluid-wall interface is used to model the wetting properties of the solid surface. Implementations of the model are demonstrated for simulating the processes of the droplet coalescence, the droplet formation and detachment from ceiling and from nozzles with different shapes and different wall wetting properties.