A proposal for the estimation of binary mixture activity coefficients from surface tension measurements throughout the entire concentration range

A method to estimate the concentration dependence of the bulk activity coefficients of both binary mixture components from experimental surface tension data covering the whole concentration range is presented. To this end, high-quality experimental surface tension data as a function of the concentration, paying special attention to the diluted regions, are needed. The method is based on the application of equilibrium conditions to the surface chemical potential arisen from the Volmer equation (the simplest non-ideal surface EOS) and to the bulk chemical potential coming from the three-suffix Margules equation for activity coefficients. It can be applied provided that positive aneotropy is not present and the second derivative of the surface pressure as a function of the mole fraction is not positive in any composition region, which means rather unrestrictive conditions. In order to test the method, a compilation of 25 systems for which surface tension and activity coefficient data are simultaneously available in the literature was performed, turning out that most of them involved water. It was found that surface tension data with enough concentration coverage and good quality are really scarce, which makes the development of this kind of methods difficult.     

An Assessment of the Aggregation and Adsorption Behavior of the Sodium Dodecylsulfate–Cetyltrimethylammonium Bromide Mixed Surfactant System in Aqueous Medium

Sodium dodecylsulfate and cetyltrimethylammonium bromide mixtures are important catanionic systems, as they have an inherent tendency to form vesicle structures. Despite extensive studies on the phase behavior and microstructures, there is dearth of basic information on the aggregation and adsorption behavior of this mixed system. In this work the critical micelle concentration, surface tension reduction effectiveness, surface excess, mixed micelle and monolayer compositions, activity coefficients, interaction parameters, counterion binding and Gibbs energy terms of this mixed system are determined by measuring its surface tension and conductance as a function of composition. The dependence of mixed micelle composition on surfactant concentration has been successfully demonstrated.     

New Thermodynamics for Evaluating the Surface‐phase Enrichment in the Lower Surface Tension Component

Regarding the surface phase of liquid mixtures as a thermodynamic phase, ideal surface phases are designed so that at fixed bulk‐phase composition, real and ideal surface phases have the same chemical composition and identical limiting slopes for the dependence of surface tension on mole fraction. Standard chemical potentials are introduced for surface phase components, and quasi‐exact expressions are worked out to compute ideal surface tensions and surface‐phase compositions of real liquid mixtures. Guidelines for choosing molecular models to estimate the molar surface area of pure constituents are given. Ideal and excess surface tensions are calculated by using literature data for aqueous ethanol solutions at 298 K. These results show treatment based on Butler’s equations grossly overestimate predicted surface tensions, thus leading to lower ethanol content in the surface phase. These inaccuracies are ascribed to the use of molar surface areas in model equations that are too small.     

Further investigation about Lagrangian theorem-based density functional approximation: test by non-uniform polymer melt

A Lagrangian theorem-based density functional approximation [S. Zhou, New J. Phys. 4 (2002) 36] for hard sphere fluid is employed to describe non-uniform polymer melt in the framework of density functional theory. A required bulk second order direct correlation function (DCF) within the whole density range is obtained by solving the polymer-RISM integral equation, the associated adjustable parameter is specified by a hard wall sum rule, and is found to be a negative value when the bulk density is low and the number of chain segment is large. However, the mathematically meaningless value can be physically meaningful by the observation that the present recipe can produce out density profile in very good agreement with simulation data not only at the contact region, but also at the region far away from the surface, and that the predicted global quantities such as surface excess and surface tension are also in good agreement with the simulation data. It is considered that the LTDFA has a property of self correction, which enables the LTDFA-based DFA for non-uniform polymer melt performs quite well even with a not very accurate second order DCF as input. Potential applications of the self correction peculiarity are discussed.     

Surface tension of polystyrene blends: Theory and experiment

Surface tension of linear–linear and star/linear polystyrene blends were measured using a modified Wilhelmy method. Our results show that for both polystyrene blend systems, the surface tension‐composition profile is convex, indicating a strong surface excess of the component with lower surface energy. Star/linear blends display more convex surface tension profiles than their linear–linear counterparts, indicative of stronger surface segregation of the branched‐component relative to linear chains. As a first step toward understanding the physical origin of enhanced‐surface segregation of star polymers, self‐consistent field (SCF) lattice simulations (both incompressible and compressible models) and Cahn‐Hilliard theory were used to predict surface tension‐composition profiles. Results from the lattice simulations indicate that the highly convex surface tension profiles observed in the star/linear blend systems are only possible if an architecture‐dependent, Flory interaction parameter (χ = 0.004) is assumed. This conclusion is inconsistent with results from bulk differential scanning calorimetry (DSC) measurements, which indicate sharp glass transitions in both the star/linear and linear/linear homopolymer blends and a simple linear relationship between the bulk glass transition temperature and blend composition. To implement the Cahn‐Hilliard theory, pressure‐volume‐temperature (PVT) data for each of the pure components in the blends were first measured and the data used as input for the theory. Consistent with the experimental data, Cahn‐Hilliard theory predicts a larger surface excess of star molecules in linear hosts over a wide composition range. Significantly, this result is obtained assuming a nearly neutral interaction parameter between the linear and star components, indicating that the surface enrichment of the stars is not a consequence of complex phase behavior in the bulk. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1666–1685, 2009     

New approach to defining thermodynamic surface tension of solids

Using either the chemical potential of the immobile component of a solid dissolved in a fluid phase or the corresponding component of the tensor of chemical potential in solid phase, a new concept of the grand thermodynamic potential of solid-fluid two-phase system is proposed. For a planar interfacial surface, this makes it possible to generalize the notion of thermodynamic surface tension σ introduced by Gibbs that has the meaning of the formation work of a unit surface. This tension is determined as the specific surface excess of the grand thermodynamic potential. This definition of the thermodynamic surface tension does not depend on the position of the dividing surface and is common for fluids and solids. It is shown that, at the arbitrary position of dividing surface, the difference between thermodynamic σ and mechanical @[gamma] surface tensions for solid surface is determined by the nonuniformity of the tensor of chemical potential in a solid, as well as by its anisotropy in the bulk of solid phase.     

Surface tension of binary liquid mixtures

Experimental measurements of the liquid-air interfacial tension are reported for the systems benzene + n-hexane at 20°C and acetone + isooctane at 25°C. The excess surface tension for both systems is negative while the surface tension itself for the second system, when plotted against composition, exhibits a flat minimum. An attempt is made to interpret this behavior in terms of basic thermodynamic quantities of the mixtures such as the excess free enthalpy, the heat of mixing, the excess volume, and the isothermal compressibility.     

Surface and bulk behavior of (dialkylsulfoxides + carbon tetrachloride) mixtures

Surface tensions, surface tension deviations, densities, and excess molar volumes of binary mixtures of carbon tetrachloride (CCl₄) with dimethylsulfoxide (DMSO), diethylsulfoxide (DESO), dipropylsulfoxide (DPSO), and dibutylsulfoxide (DBSO) have been determined over the entire composition range at (298.15 and 313.15) K. The results were fitted by the Redlich–Kister polynomial equation and the corresponding binary coefficients have been derived.The obtained excess quantities show that both charge-transfer complex formation between CCl₄ and dialkylsulfoxides (DASO) molecules and on the other hand sulfoxides’ chain length are crucial factors conditioning the excess thermodynamic properties of (CCl₄ + DASO) binary mixtures.     

Adsorption equilibria of binary gas mixtures on graphitized carbon black

Adsorption equilibria for binary gas mixtures (methane-carbon dioxide, methane-ethane, and carbon dioxide-ethane) on the graphitized carbon black STH-2 were measured by the open flow method at 293.2 K. The experimental pressure range was (0 to 1.6) MPa. The extended Langmuir (EL) model and the ideal adsorption solution theory (IAST) have been adopted to predict the equilibria of binary gas mixtures. The results indicate that gas mixtures adsorbed on the homogeneous surface of STH-2 exhibit the nonideal behavior, which is mainly induced by adsorbate-adsorbate interactions. The real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have been correlated with the Wilson equation. The investigation demonstrates that the nonideality of adsorbed phase is completely dissimilar with the bulk liquid phase. The adsorption of the heavier component would benefit the adsorption of the lighter component.     

Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: renormalized local functional theory

We investigate the critical behavior of a near-critical fluid confined between two parallel plates in contact with a reservoir by calculating the order parameter profile and the Casimir amplitudes (for the force density and for the grand potential). Our results are applicable to one-component fluids and binary mixtures. We assume that the walls absorb one of the fluid components selectively for binary mixtures. We propose a renormalized local functional theory accounting for the fluctuation effects. Analysis is performed in the plane of the temperature T and the order parameter in the reservoir ψ(∞). Our theory is universal if the physical quantities are scaled appropriately. If the component favored by the walls is slightly poor in the reservoir, there appears a line of first-order phase transition of capillary condensation outside the bulk coexistence curve. The excess adsorption changes discontinuously between condensed and noncondensed states at the transition. With increasing T, the transition line ends at a capillary critical point T=T(c) (ca) slightly lower than the bulk critical temperature T(c) for the upper critical solution temperature. The Casimir amplitudes are larger than their critical point values by 10-100 times at off-critical compositions near the capillary condensation line.     

全氟丁基磺酸钠与辛基三乙基溴化铵的相互作用

通过测定辛基三乙基溴化铵(C8H17N(CH2CH3)3Br,C8NE)与全氟丁基磺酸钠(C4F9SO3Na,C4F)组成的不同混合比的碳氢-碳氟正负离子表面活性剂混合体系的表面张力,得到不同摩尔比时C8NEC4F体系的临界胶束浓度(cmc)、cmc处的表面张力(γcmc)、总饱和吸附量、不同表面张力时表面吸附层的组成,利用Gibbs-Duhem方程求得cmc处的胶团组成。 采用规则溶液理论计算了胶团中分子间相互作用参数(βm),并求得cmc以上的胶团组成。 实验表明,C8NEC4F复配体系的cmc远远小于单体系的cmc,这也体现在该体系的βm负值很大,胶团内分子相互作用很强。 但是C4F与C8NE复配后γcmc较C4F单体系的变化幅度不是特别大(γcmc降低2~4 mN/m),这是由于C8NEC4F碳链的不对称性导致部分C8NE的碳链在溶液表面弯曲而覆盖了C4F端基CF3基团。 表面吸附层中氟表面活性剂相对于本体溶液是富集的,即使对于C8NE大大过量的体系,表面吸附层组成也在等摩尔附近;对于C4F过量的体系,C4F在表面吸附层中的比例比溶液中的略高。 随着表面张力的降低,表面吸附层的组成相对更偏向于氟表面活性剂。 cmc处的胶团组成随着体系中C4F含量的增大偏向于形成显著富含C4F的胶团,对于C8NE大大过量的体系,胶团组成接近等摩尔。 cmc之后的胶团组成接近等摩尔,主要归因于此时静电相互作用占主导,这和溶液配制过程中发现复配体系超过cmc一定浓度后就易生成沉淀的现象是相符的。     

The wettability of polytetrafluoroethylene by aqueous solution of cetyltrimethylammonium bromide and Triton X-100 mixtures

Measurements of the advancing contact angle (theta) were carried out for aqueous solution of cetyltrimethylammonium bromide (CTAB) and p-(1,1,3,3-tetramethylbutyl) phenoxypoly(ethylene glycol), Triton X-100 (TX100) mixtures on polytetrafluoroethylene (PTFE). The obtained results indicate that the wettability of PTFE depends on the concentration and composition of the surfactants mixture. There is a minimum of the dependence between contact angle and composition of the mixtures for PTFE for each concentration at a monomer mole fraction of CTAB, alpha, equal 0.2, which points to the synergism in the wettability of PTFE. In contrast to Zisman, there is no linear dependence between costheta and the surface tension of aqueous solution of CTAB and TX100 mixtures for all studied systems, but a linear dependence exists between the adhesional tension and surface tension for PTFE in the whole concentration range, the slope of which is -1, that suggests that the surface excess of the surfactant concentration at the PTFE-solution interface is the same as that at the solution-air interface for a given bulk concentration. It was also found that the work of adhesion of aqueous solution of surfactants to PTFE surface did not depend on the type of surfactant and its concentration. It means that the interactions across PTFE-solution interface were constant for the systems studied, and they were largely Lifshitz-van de Waals type. On the basis of the surface tension of PTFE and the Young equation and thermodynamic analysis of the adhesion work of aqueous solution of surfactant to the polymer surface it was found that in the case of PTFE the changes of the contact angle as a function of the mixture of nonionic and cationic surfactants concentration resulted only from changes of the polar component of solution surface tension.     

Importance of bulk and surface excess concentration in fast atom bombardment mass spectrometry of small peptides

The surface tension of hydrophilic and hydrophobic peptides in glycerol solution at various concentrations is measured by the du Nouy ring method. From these values the surface excess concentration is calculated by means of the Gibbs adsorption equation. The behaviour of the surface excess peptide concentration on the fast atom bombardment mass spectrometric response (protonated molecular ion) as a function of the bulk peptide concentration in glycerol is discussed in terms of parameters commonly used in surface chemistry. The experimental results showed a straightforward correlation between the sputtering of protonated molecular ions of peptides and surface excess peptide concentration. Further, there is good agreement with a model involving desorption/ionization in the first layers of the liquid matrix surface. It is additionally demonstrated that the surface excess concentration of each peptide will be different in glycerol solutions of identical bulk concentration and, as a consequence, any differences in protonated molecular ion yield will reflect differences in the surface activity of the peptides, which explains suppression phenomena in peptide mixtures such as tryptic peptide digest. Based on this finding, it can be assumed that a difference observed in the mass spectrometric response does not represent a substantial difference in ionization efficiency.     

Local composition in the vicinity of a protein molecule in an aqueous mixed solvent

This paper is focused on the composition of a cosolvent in the vicinity of a protein surface (local composition) and its dependence on various factors. First, the Kirkwood-Buff theory of solution is used to obtain analytical expressions that connect the excess or deficit number of cosolvent and water molecules in the vicinity of a protein surface with experimentally measurable quantities such as the bulk concentration of the mixed solvent, the preferential binding parameter, and the molar volumes of water and cosolvent. Using these expressions, relations between the preferential binding parameter (at a molal concentration scale) and the above excesses (or deficits) are established. In addition, the obtained expressions are used to examine the effect of the nonideality of the water + cosolvent mixtures and of the molar volume of the cosolvent on the excess (or deficit) number of cosolvent molecules in the vicinity of the protein surface. It is shown that at least for the mixed solvents considered (water + urea and water + glucose) the nonideality of the mixed solvent is not an important factor in the local compositions around a protein molecule and that the main contribution is provided by the nonidealities of the protein-water and protein-cosolvent mixtures. Special attention is paid to urea as cosolvent, because urea is one of only a few compounds with a concentration at the protein surface larger than its concentration in the bulk. The composition dependence of the excess of urea around a protein molecule is calculated for the water + lysozyme + urea mixture at pH = 7.0 and 2.0. At pH = 7.0, the excess of urea becomes almost composition independent at high urea concentrations. Such independence could be explained by assuming that urea totally replaces water in some areas of the protein surface, whereas on the remaining areas of the protein surface both water and urea are present with concentration comparable to those in the bulk. The Schellman exchange model was used to relate the preferential binding parameter in water + lysozyme + urea mixtures to the urea concentration.     

Surface behavior, aggregation and phase separation of aqueous mixtures of dodecyl trimethylammonium bromide and sodium oligoarene sulfonates: the transition to polyelectrolyte/surfactant behavior

The properties and phase diagrams of aqueous mixtures of dodecyltrimethylammonium bromide (C(12)TAB) with the sodium oligoarene sulphonates (POSn), POS2, POS3, POS4, and POS6 have been studied using surface tension and neutron reflectometry to study the surface, and neutron small angle scattering and fluorescence to study the bulk solution. The behavior of POS2 and POS3 is reasonably consistent with mixed micelles of C(12)TAB and POSn-(C(12)TA)(n). These systems exhibit a single critical micelle concentration (CMC) at which the surface tension reaches the usual plateau. This is contrary to a recent report which suggests that the onset of the surface tension plateau does not coincide with the CMC. In the POS3 system, the micelles conform to the core-shell model, are slightly ellipsoidal, and have aggregation numbers in the range 70-100. In addition, the dissociation constant for ionization of the micelles is significantly lower than for free C(12)TAB micelles, indicating binding of the POS3 ion to the micelles. Estimation of the CMCs of the POSn-(C(12)TA)(n) from n = 1-3 assuming ideal mixing of the two component surfactants and the observed values of the mixed CMC gives values that are consistent with the nearest related gemini surfactant. The POS4 and POS6 systems are different. They both phase separate slowly to form a dilute and a concentrated (dense) phase. Fluorescence of POS4 has been used to show that the onset of aggregation of surfactant (critical aggregation concentration, CAC) occurs at the onset of the surface tension plateau and that, at the slightly higher concentration of the phase separation, the concentration of POS4 and C(12)TAB in the dilute phase is at or below its concentration at the CAC, that is, this is a clear case of complex coacervation. The surface layer of the C(12)TA ion in the surface tension plateau region, studied directly by neutron reflectometry, was found to be higher than a simple monolayer (observed for POS2 and POS3) for both the POS4 and POS6 systems. In POS6 this evolved after a few hours to a structure consisting of a monolayer with an attached subsurface bilayer, closely resembling that observed for one class of polyelectrolyte/surfactant mixtures. It is suggested that this structured layer, which must be present on the surface of the dilute phase of the coacervated system, is a thin wetting film of the dense phase. The close resemblance of the properties of the POS6 system to that of one large group of polyelectrolyte/surfactant mixtures shows that the surface behavior of oligoion/surfactant mixtures can quickly become representative of that of true polyelectrolyte/surfactant mixtures. In addition, the more precise characterization possible for the POS6 system identifies an unusual feature of the surface behavior of some polyelectrolyte/surfactant systems and that is that the surface tension can remain low and constant through a precipitation/coacervation region because of the characteristics of two phase wetting. The well-defined fixed charge distribution in POS6 also suggests that rigidity and charge separation are the factors that control whether a given system will exhibit a flat surface tension plateau or the alternative of a peak on the surface tension plateau.     

Correlation between surface and bulk structures of alcohol-water mixtures

Adsorption isotherms of binary aqueous solutions of methanol, ethanol, 1-propanol, 2-propanol, tert-butanol, and 1-butanol are demonstrated, being calculated by using the Gibbs adsorption equation with experimental data of surface tension and vapor pressure found in the literature. For all of the alcohol-water mixtures, the maximum value in the adsorption isotherm, namely, the maximum surface excess is about that expected for the formation of a monolayer. Furthermore, the composition of the mixture for the maximum surface excess coincides with that corresponding to the minimum in the excess partial molar volume of the solutes. These results indicate that the hydrophobic hydration in bulk induces the surface excess of the alcohols and after a monolayer is formed, the hydrophobic hydration itself is no longer retained.     

Phase equilibria and interfacial tension of fluids confined in narrow pores

Correlation between phase behaviors of a Lennard-Jones fluid in and outside a pore is examined over wide thermodynamic conditions by grand canonical Monte Carlo simulations. A pressure tensor component of the confined fluid, a variable controllable in simulation but usually uncontrollable in experiment, is related with the pressure of a bulk homogeneous system in equilibrium with the confined system. Effects of the pore dimensionality, size, and attractive potential on the correlations between thermodynamic properties of the confined and bulk systems are clarified. A fluid-wall interfacial tension defined as an excess grand potential is evaluated as a function of the pore size. It is found that the tension decreases linearly with the inverse of the pore diameter or width.     

The properties of a binary mixture of nonionic surfactants in water at the water/air interface

The behavior of mixed nonionic/nonionic surfactant solutions, that is, p-(1,1,3,3-tetramethylbutyl)phenoxy poly(ethylene glycol)s Triton X-100 (TX100) and Triton X-165 (TX165) have been studied by surface tension and density measurements. The obtained results of the surface tension measurements were compared with those calculated from the relations derived by Joos, Miller, and co-workers. From the comparison, it appeared that by using these two approaches the adsorption behavior of TX100 and TX165 mixtures at different mole fractions can be predicted. The negative deviation from the linear relationship between the surface tension and composition of TX100 and TX165 mixtures in the concentration range corresponding to that of the saturated monolayer at the interface, the values of the parameters of molecular interaction, the activity coefficients, as well as the excess Gibbs energy of mixed monolayer formation calculated on the basis of Rosen and Motomura approaches proved that there is synergism in the reduction of the surface tension of aqueous solutions of TX100 and TX165 mixture when saturation of the monolayer is achieved. The negative parameters of intermolecular interaction in the mixed micelle and calculations based on MT theory of Blankschtein indicate that there is also synergism in the micelle formation for TX100 and TX165 mixture. It was also found that the values of the standard Gibbs energy of adsorption and micellization for the mixture of these two surfactants, which confirm the synergetic effect, can be predicted on the basis of the proposed equations, which include the values of the mole fraction of surfactant and excess Gibbs energy TX100 and TX165 in the monolayer and micelle.