Regular Solution Theory Research Articles

Adsorption mechanism of new mixed anionic/cationic collectors in a spodumene-feldspar flotation system

The mixed anionic collector sodium oleate (NaOL) and cationic collector dodecyl ammonium chloride (DTAC) demonstrate high selectivity for the flotation of spodumene from feldspar, and the optimal molar ratio of NaOL and DTAC is 9:1. To detect the underlying mechanism, surface tension measurements, adsorption measurements, zeta potential measurements and Fourier transform infrared (FTIR) analyses were performed. The surface and thermodynamic parameters (CMC, γCMC, Γmax, Amin, ΔGm0) obtained from surface measurements show higher surface activity and a denser molecular arrangement in mixed NaOL/DTAC than in single NaOL or DTAC. Further analysis of the interaction parameters and activity coefficients (βm, βσ, fm, and fσ) obtained from the theory of regular solutions shows that there is a synergistic effect both in the mixed micelle and at the water/air interface. Moreover, the maximum synergistic interaction was found at XDTAC=0.5 in mixed NaOL/DTAC. The adsorption measurements show that more NaOL is adsorbed on the spodumene surface than on feldspar and that the cationic collector can improve the adsorption of NaOL on the spodumene surface by a small amount, but not for feldspar. The zeta potential measurement and Fourier transform infrared analyses show that in the mixed NaOL/DTAC system, the anionic collector NaOL first reacts with aluminum sites on the mineral surface. Then, the cationic collector DTAC forms an electroneutral complex with the anionic collector NaOL and co-adsorbs on the Stern layer because of the chemisorption of NaOL. Based on these analyses, an adsorption model of the mixed collector NaOL/DTAC on the mineral surface was drawn.

Mixed micellization between amphiphilic drug propranolol hydrochloride and cetyltrimethylammonium bromide surfactant in aqueous medium

Abstract The interaction between an amphiphilic drug (propranolol hydrochloride (PPL)) and cationic surfactant (cetyltrimethylammonium bromide (CTAB)) in aqueous solution has been investigated at different mole fractions. The CMC (pure and mixture), mixed micellar composition (X1id, X2id, X1m and X2m), interaction parameter (βm) and the degree of counterion binding (α) have been computed and discussed. The micellar interaction parameter (the βm-parameter) was determined from the CMC values of the pure drug and surfactant (CMC1 and CMC2) and the mixed system (CMCmix) using the Rubingh's model (regular solution theory). For all mixtures of PPL/CTAB, the results indicate a fairly strong attractive interaction (negative βm-values), which confirming synergistic interactions between drug-surfactant. Also, activity coefficients (f1m and f2m) are always less than unity suggesting non-ideality in the mixtures. Finally, the standard Gibbs energy of micellization (ΔGmic0) and the excess free energy of micellization (ΔGmicex) values were evaluated and discussed with increasing drug concentration.

Термодинамическое описание фазовых равновесий в системе Cu2O–CeO2–Ce2O3–La2O3

Thermodynamic modeling of liquidus lines for binary oxide phase diagrams and liquidus surfaces for ternary oxide phase diagrams that make up the Cu2O–CeO2–Ce2O3–La2O3 system was performed using the theories of ideal ionic solutions and subregular ionic solutions. Solidus line, limiting the existence of a solid solution in the CeO2–La2O3 system, was calculated using the theory of regular ionic solutions. The values of parameters of the used theories and the temperature dependence of the equilibrium constants of transition from solid to liquid, used to calculate the phase diagrams of the investigation systems, were determined during this work. Most of the systems (Cu2O–CeO2, Cu2O–Ce2O3, Cu2O–La2O3, CeO2–Ce2O3, Ce2O3–La2O3, Cu2O–CeO2–Ce2O3, Cu2O–Ce2O3–La2O3) are eutectic type diagrams with one eutectic point for each diagram. For the above systems including Cu2O as a component, it was concluded that these systems are characterized by sufficiently low eutectic equilibrium temperatures. The CeO2–La2O3 system is characterized by the presence of a solid solution and a point on the liquidus line, having a zero crystallization interval. Phase diagrams Cu2O–CeO2–La2O3 and CeO2–La2O3–Ce2O3 are characterized by a vast area of the equilibrium of oxide melt with the solid solution |CeO2, La2O3|ss.

Mild solutions of semilinear elliptic equations in Hilbert spaces

This paper extends the theory of regular solutions (C1 in a suitable sense) for a class of semilinear elliptic equations in Hilbert spaces. The notion of regularity is based on the concept of G-derivative, which is introduced and discussed. A result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property, that is, it maps continuous functions into G-differentiable ones. The validity of this smoothing assumption is fully discussed for the case of the Ornstein–Uhlenbeck transition semigroup and for the case of invertible diffusion coefficient covering cases not previously addressed by the literature. It is shown that the results apply to Hamilton–Jacobi–Bellman (HJB) equations associated to infinite horizon optimal stochastic control problems in infinite dimension and that, in particular, they cover examples of optimal boundary control of the heat equation that were not treatable with the approaches developed in the literature up to now.

Thermodynamic investigation of binary surfactant mixtures of Tween 85/Triton X100 and 85/Triton X165 in water solution – Binary mixed micelles formation

Binary surfactant mixtures of Tween 85/Triton X100 and Tween 85/Triton X165 have been investigated in water solution over the temperature range from 273.15K to 323.15K. At the temperatures of 273.15K and 283.15K between different building units of binary mixed micelles, synergistic interactions exist whose size is not affected by difference in length of the polyoxyethylene chains.At higher temperatures, the longer polyoxyethylene chain of Triton X165 shows a more stabilizing effect in mixed micelle with Tween 85 than in mixed micelles of Tween 85/Triton X100. For the investigated binary mixed micelles, regular solution theory approximation about zero value of excess entropy of binary mixed micelle formation cannot be accepted.

Solubility of Nifedipine and Lacidipine in Supercritical CO2: Measurement and Correlation

Solubilities of two calcium channel blockers, nifedipine and lacidipine, were measured in supercritical carbon dioxide at T = (313, 323, and 333) K over the pressure range (12.0–36.0) MPa using a dynamic-analytical apparatus. The solubility values obtained are in the range of (0.18–7.05) × 10−5 mol·mol−1. The solubilities of the two solids show similar trends with a crossover region of the respective isotherms in the range 18.0–21.0 MPa. The experimental solubility data were correlated with several different models. The semi-empirical density-based models provided satisfactory correlation results with AARD values lower than 10%. According to the results of the Mendez-Santiago and Teja models, the measured solid solubility data are quite consistent at all experimental conditions, which indicates the reliability of the data. The compressed gas model of the Peng–Robinson equation of state, combined with the two parameter van der Waals mixing rule (PR-EoS-VDW2) model, gives better correlation results than the PR-EoS-VDW1 model. The expanded liquid model based on Scatchard–Hildebrand regular solution theory can be used for solubility prediction, but the correlation results for nifedipine and lacidipine by the model are inferior to the compressed gas models in this work.

Synergisms in Binary Mixtures of Anionic and pH‐Insensitive Zwitterionic Surfactants and Their Precipitation Behavior with Calcium Ions

AbstractThis work aims to investigate synergy in anionic and zwitterionic surfactant mixtures, as they result in better interfacial properties and micellization behavior. Various mixtures of the pH‐insensitive zwitterionic surfactant 3‐(decyldimethylammonio) propanesulfonate (Zwittergent 3–10) and sodium dodecylsulfate (SDS) were prepared in aqueous solution at a range of pH values between 2 and 13. The thermodynamic parameters during mixed surfactant adsorption at the air/water interface are obtained and the results show the mixed surfactant systems having superior properties to the constituent surfactants. Experimentally, the mixed surfactant solutions clearly improve the surface activities by lowering the critical micelle concentration (CMC) and lowering the surface tension at the air/water interface. The synergisms are investigated through the interaction parameters estimated from regular solution theory that is used to quantitatively describe the nonideality of surfactant mixtures. High negative interaction parameters are obtained from these surfactant mixtures. Experimental precipitation phase boundaries of SDS in the presence of CaCl2 were also investigated in mixtures containing pH‐insensitive zwitterionic surfactant at different pH levels from 2 to 13 and SDS mole fractions of 0.25, 0.50, 0.75, and 1.00. Changes in the precipitation phase boundaries are due to the changes in the speciation or activities of the major components both below and above the CMC. As a result, the precipitation phase boundaries are pH dependent. In addition, mixed micellization and counterion binding to the micelle also change the precipitation phase boundary above the CMC. The activity‐based solubility product of calcium dodecylsulfate is also determined from the precipitation phase boundaries below the CMC. X‐ray diffraction patterns and SEM images confirm that only calcium dodecylsulfate precipitates in the soap scum for all pH and surfactant compositions studied.

Synergism and Performance for Systems Containing Binary Mixtures of Anionic/Cationic Surfactants for Enhanced Oil Recovery

AbstractThe surfactant structure–performance relationship and application properties in enhanced oil recovery (EOR) for binary mixtures of anionic and cationic surfactants are presented and discussed. A polyoxyethylene ether carboxylate anionic surfactant was blended with a quaternary ammonium chloride cationic surfactant and tested for a high‐temperature, low‐salinity, and high‐hardness condition as found in an oil reservoir. These mixtures were tailored by phase behavior tests to form optimal microemulsions with normal octane (n‐C8) and crude oil having an API gravity of 48.05°. The ethoxy number of the polyoxyethylene carboxylate anionic surfactant and the chain length of the cationic surfactant were tuned to find an optimal surfactant blend. Interfacial tensions with n‐C8 and with crude oil were measured. Synergism between anionic and cationic surfactants was indicated by surface tension measurement, CMC determination, calculation of surface excess concentrations and area per molecule of individual surfactants and their mixtures. Molecular interactions of anionic and cationic surfactants in mixed monolayers and aggregates were calculated by using regular solution theory to find molecular interaction parameters βσ and βM. Morphologies of surfactant solutions were studied by cryogenic TEM. The use of binary mixtures of anionic/cationic surfactants significantly broadens the scope of application for conventional chemical EOR methods.

Surface properties and morphology of mixed POSS-DPPC monolayers at the air/water interface

From the point of view of the possible medical applications of POSS (polyhedral oligomeric silsesquioxanes), it is crucial to analyse interactions occurring between POSS and model biological membrane at molecular level. Knowledge of the interaction between POSS and DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine) allows prediction of the impact of POSS contained in biomaterials or cosmetics on a living organism. In the study presented, the surface properties and morphology of Langmuir monolayers formed by mixtures of POSS and the phospholipid (DPPC) at the air/water surface are examined. We selected two POSS derivatives, with completely different chemical structure of substituents attached to the corner of the silicon open cage, which allowed the analysis of the impact of the character of organic moieties (strongly hydrophobic or clearly hydrophilic) on the order of POSS molecules and their tendency to form self–aggregates at the air/water surface. POSS derivatives significantly changed the profile of the π–A isotherms obtained for DPPC but in different ways. On the basis of the regular solution theory, the miscibility and stability of the two components in the monolayer were analysed in terms of compression modulus (Cs−1), excess Gibbs free energy (ΔGexc), activity coefficients (γ) and interaction parameter (ξ). The results obtained indicate the existence of two different interaction mechanisms between DPPC and POSS which depend on the chemical character of moieties present in POSS molecules.

Three-gradient regular solution model for simple liquids wetting complex surface topologies.

We use regular solution theory and implement a three-gradient model for a liquid/vapour system in contact with a complex surface topology to study the shape of a liquid drop in advancing and receding wetting scenarios. More specifically, we study droplets on an inverse opal: spherical cavities in a hexagonal pattern. In line with experimental data, we find that the surface may switch from hydrophilic (contact angle on a smooth surface θY < 90°) to hydrophobic (effective advancing contact angle θ > 90°). Both the Wenzel wetting state, that is cavities under the liquid are filled, as well as the Cassie–Baxter wetting state, that is air entrapment in the cavities under the liquid, were observed using our approach, without a discontinuity in the water front shape or in the water advancing contact angle θ. Therefore, air entrapment cannot be the main reason why the contact angle θ for an advancing water front varies. Rather, the contact line is pinned and curved due to the surface structures, inducing curvature perpendicular to the plane in which the contact angle θ is observed, and the contact line does not move in a continuous way, but via depinning transitions. The pinning is not limited to kinks in the surface with angles θkink smaller than the angle θY. Even for θkink > θY, contact line pinning is found. Therefore, the full 3D-structure of the inverse opal, rather than a simple parameter such as the wetting state or θkink, determines the final observed contact angle.

Thermodynamic analysis of an asymmetric system: Aqueous sodium dehydrocholate- hexadecyltrimethylammonium bromide mixed micelles

Presuming that the thermodynamic behavior of a system is symmetric, as in the Regular Solution Theory (RST or Rubingh’s method), may mask relevant characteristics and lead to erroneous conclusions derived from inexact computed properties (micelle composition, intramicellar interaction energy, activity coefficients and excess free energy of mixed micellization). This work addresses a system which seems prima facie strongly non-ideal and asymmetric due to the very different structures of the surfactants: the aqueous solutions of the catanionic system sodium dehydrocholate (NaDHC) and hexadecyltrimethylammonium bromide (HTAB). It has been analyzed with two procedures: the RST and the EOMMM (Equation Oriented Mixed Micellization Modeling). The latter finds the Margules parameters and the micelle compositions that globally minimize the total free energy of micellization. It does not assume symmetry and assures the fulfillment of the Gibbs-Duhem relation.

Antidepressant drug amitriptyline hydrochloride (AMT) interaction with anionic surfactant sodium dodecyl sulfate in aqueous/brine/urea solutions at different temperatures

Conductivity method was carried out at various temperatures ranging from 293.15K to 313.15K to examine the monomeric as well as micellar phases of aqueous/brine/urea solutions of mixed systems composed of anionic surfactant sodium dodecyl sulfate (SDS) and cationic drug amitriptyline hydrochloride (AMT). AMT is used to treat mental/mood problems such as depression. NaCl decreases critical micelles concentration (cmc) of pure components as well as their mixed systems may be mainly ascribed to the salting-out effect of the hydrophobic moiety of components while urea increases the cmc value because of enhancement in the surface charge of the micelles/mixed micelles. The interaction among the monomers in the micelles/mixed micelles in the urea solution is slightly less than the NaCl and aqueous solutions. Synergism is modeled by employing the regular solution theory (RST) with a negative interaction parameter and nonideal behavior. Molecular thermodynamic models of Rubingh, Rodens and Motomura allow the calculation of the total excess free energy of micellization (ΔGex) with negative values in all the three situations. The aggregation number, micropolarity, and apparent dielectric constant of solution mixtures were evaluated and discussed in detail by fluorescence measurement in three different media.

Prediction of solid-liquid equilibrium in paraffinic systems with new solid solution model

A thermodynamic model for the prediction of wax precipitation with the new solid solution model is established. For liquid phase, regular solution model and Flory free-volume equation are adopted to consider the two contributions of activity coefficient: enthalpy contribution, the energetic interactions between the components, and entropy contribution, the differences in size and shape between the molecules. For solid phase, the derived solid solution model accounting for the two parts of the solid non-ideality is proposed, where an improved regular solution model is developed for the description of residual part (enthalpy contribution), on the basis of the combination of regular solution theory and local composition theory; while Wilson equation with the consideration of the end effects between molecules is used for combinatorial part (entropy contribution). The improved model is tested against the experimental data of binary, ternary, quaternary and multi-paraffins systems. All experimental data are obtained at atmospheric pressure with temperature varying from 260 K to 350 K. Results show that present model could precisely predict the experimental WATs (wax appearance temperature)/WDTs (wax disappearance temperature) and precipitation curves.

Effect of isopropanol on the micellization of binary mixture containing amino sulfonate amphoteric surfactant in aqueous solution: Mixing with sodium dodecylbenzene sulfonate

The effect of isopropanol (IPA) on the micellization behavior of binary surfactant mixtures of an amphoteric sodium 3-(N-dodecyl ethylenediamino)-2-hydropropyl sulfonate (C12AS) with an anionic sodium dodecylbenzene sulfonate (SDBS) was investigated in the water–IPA mixed solvent media (the concentration of IPA in bulk solution varies within the range of 0–100g/L). The values of critical micelle concentration (cmc) of individual surfactants and their mixtures were determined by both the conductometry and the UV–vis spectrometry. Based on the regular solution theory, pseudophase separation model, and some thermodynamic models, the effect of IPA on the micellization parameters and the thermodynamic parameters was theoretically discussed. The addition of IPA in aqueous solution not only changes the polar of solution but also influences the solvation of ionic surfactant, consequently resulting in the change in the mixed cmc values and the molar fraction of components in mixed micelle. The synergistic effect between two surfactants may be decreased with increasing IPA. Thermodynamic data show that the presence of IPA may be not an advantage to the spontaneous process of micellization, and influences the contribution of entropy in the process of micellization. Specially, these cases can be obviously observed at a high concentration of IPA in aqueous solution. These results help us to understand the advantage and the disadvantage of the effect of cosolvent (specially IPA) on the micellization of mixed surfactants and to design the surfactant formulas relative to cosolvent.

Interactions between molecular solutes and task-specific ionic liquid: Measurements of infinite dilution activity coefficients and modeling

Infinite dilution activity coefficients of 35 molecular compounds in novel ionic liquid (IL) 1-(2-hydroxyethyl)-1-methylpyrrolidinium dimethylphosphate are presented in a wide range of temperature. Basic thermal characteristics and liquid density of the IL at ambient pressure are also reported. The measured activity coefficients are discussed in terms of molecular interactions between the solutes and the IL's cation and anion. An impact of strongly basic anion and the cation functionalization is elucidated. Application of the studied IL in aromatic-aliphatic separations and extractive desulfurization is evaluated on the basis infinite dilution selectivity and capacity. The experimental data are treated in terms of three distinct approaches: linear solvation-energy relationship (LSER), regular solution theory and conductor-like screening model for real solvents (COSMO-RS). In particular: temperature-dependent LSER correlation able to accurately reproduce gas-liquid partition coefficients derived from activity coefficients is presented, the solubility parameters of pure IL are derived on the basis of treatment of measured data with the Scatchard-Hildebrand equation and the predictive capacity of the COSMO-RS approach in calculating limiting activity coefficients for the considered systems is tested.

Effect of isopropanol on the micellization of binary mixtures containing amino sulfonate amphoteric surfactant in aqueous solution: Mixing with octadecyltrimethyl ammonium bromide

In aqueous solutions containing isopropanol (IPA), within the range of 0–100g/L, the micellization behaviors of binary surfactant mixtures of amphoteric sodium 3-(N-dodecyl ethylenediamino)-2-hydropropyl sulfonate (C12AS) and cationic octadecyltrimethyl ammonium bromide (OTAB) were investigated by three techniques including tensiometry, conductometry and isothermal titration microcalorimetry (ITC). Based on extant theories and models (such as, the regular solution theory, the pseudophase separation model, the Rubingh’s model, etc.), the effects of IPA on the molar fraction of components in mixed micelles, the interaction parameters between the two surfactants, and associated thermodynamic parameters have been discussed. The addition of cosolvent IPA results in a change in the conformation of C12AS, as well as affecting the interaction behavior between the two surfactants and a decrease in the hydrophobic effect. The synergistic effects between the two surfactants varies partly with the concentration of IPA. The observations can be used to explain the cause for the abnormal dependence of the molar fraction of components in mixed micelles and the interaction parameters on the concentration of the cosolvent IPA. Thermodynamic parameters further show the effect of IPA on the entropy-driven process of micellization.

Prediction of wax precipitation with new modified regular solution model

In present work, an improved regular solution model is established, based on the concept of regular solution and local composition theory. The local volume fractions φij are considered to include the influence of interaction energy between molecules on molecules' local distribution. A new expression for molar excess Gibbs free energy (gE) is developed for the calculation of activity coefficients. Regular solution (RS), Wilson (W) and modified regular solution (MRS) are used for the non-ideality of solid phase and regular solution is adopted for liquid phase. Compared with the experimental data of binary, ternary and quaternary n-alkane systems, the advantage of RS-MRS is illustrated, with the best predictions of wax appearance temperature (WAT) and solid precipitation curve, which proves that the non-random molecules distribution caused by interaction energy between molecules is essential for gE. It is the application of φij that enhances the prediction accuracy of RS-MRS.

Effect of 1-ethyl-3-methylimidazolium bromide on interfacial and aggregation behavior of mixed cationic and anionic surfactants

Aggregation behavior and interaction of sodium dodecyl sulfate (SDS), tetradecyl trimethyl ammonium bromide (TTAB) and their mixtures with an excess of anionic surfactant in the presence of imidazolium-based ionic liquid, 1-ethyl-3-methylimidazolium bromide (EMIm Br) were investigated using surface tension, electrical conductivity, dynamic light scattering (DLS), transmission electron microscopy (TEM) and cyclic voltammetry measurements. Different physicochemical properties such as critical micelle concentration (CMC), degree of counterion dissociation (αdiss), interfacial properties, the standard Gibbs energy of adsorption and the size of aggregates were determined. The effects of ionic liquid (IL) as additive on the interactions between the surfactants; TTAB, SDS and their mixtures were analyzed on the basis of regular solution theory, both for mixed monolayers at the air/liquid interface (βδ) and for mixed micelles (βM). Interaction parameter values suggested that the formation of aggregates is due to the synergistic interactions in the case of SDS/TTAB systems and becomes more affected by adding IL. It was shown that an excess of cationic surfactant and IL resulted in an increase in the nano-aggregate sizes. The synergism observed for three component systems (surfactant–water–IL) revealed the effect of attractive electrostatic interaction, formation of a three-dimensional hydrogen bond network and hydrophobic forces on mixed micelle formation.

Conductometric study of the mixing behaviour of sodium benzoate and salicylate with an anionic surfactant sodium lauroylsarcosinate

ABSTRACTEffects of two anionic hydrotropes – sodium benzoate (NaBz) and sodium salicylate (NaSal) – on the mixed-micelle formation with an amino-acid-based surfactant – sodium lauroylsarcosinate (SLS) – in water were investigated by the conductometric method. Specific conductivity was measured for SLS/NaBz/water and SLS/NaSal/water systems to determine the critical micelle concentration (cmc). Using the regular solution theory for non-ideal mixing, the pairwise interaction parameter, β12, and micellar composition, χ, were estimated in the mixed micelle. The cmc values of the surfactant–hydrotropes mixtures were generally lower than those predicted from the ideal mixing theory. The β12 values are generally negative for the two systems at all mole fractions with an average value of −2.83 for the SLS/NaBz and −3.31 for SLS/NaSal systems, respectively, indicative of a strong attractive interaction between the SLS/NaBz and SLS/NaSal mixed micelle. The calculated thermodynamic parameters of micellisation all indicated spontaneity in mixed-micelle formation for the systems studied.

Correlation of interaction parameters in Wilson, NRTL and UNIQUAC models using theoretical methods

The activity coefficient models of Wilson, Nonrandom Two Liquid Theory (NRTL) and Universal Quasi-chemical Theory (UNIQUAC) are of the most applied chemical thermodynamic models in phase equilibria calculations and materials behavior prediction and/or correlation. The reliable and accurate evaluation and determination of interaction/adjustable parameters defined in these models, which are necessary for any future applications of models in binary and multicomponent systems, requires the knowledge on experimental data of binary systems. By using such experimental data and regression and fitting of data, in literature, these interaction parameters are obtained for a substantial number of systems. Here, a new theoretical methodology has been developed and examined for estimation of these parameters without the use of experimental data. The presented method equates the activity coefficients calculated by a Compressible Regular Solution Theory (CRS) to those calculated using the three aforementioned models and the interaction parameters are obtained by optimally solving the constructed system of equations. For CRS theory, the application of Sanchez and Lacombe Equation of State (LS-EoS), Constantinou and Gani Group Contribution Method and Hoftyzer and van Krevelen Group Contribution Method was considered while for models of Wilson, NRTL and UNIQUAC, the interaction parameters were searched by implementation of an evolutionary optimization technique. The obtained results are compared to those reported in literature and desirable agreement was found. The method is simple, fast, implementable in computer routines; straightforward and accurate and can be used to estimate these binary interaction parameters for systems of interest. Some phase calculations are also included to demonstrate the applicability of method.