Molecular-thermodynamic theory of micellization of multicomponent surfactant mixtures: 1. Conventional (pH-Insensitive) surfactants

A molecular-thermodynamic (MT) theory was developed to model the micellization of mixtures containing an arbitrary number of conventional (pH-insensitive) surfactants. The theory was validated by comparing predicted and experimental cmc's of ternary surfactant mixtures, yielding results that were comparable to, and sometimes better than, the cmc's determined using regular solution theory. The theory was also used to model a commercial nonionic surfactant (Genapol UD-079), which was modeled as a mixture of 16 surfactant components. The predicted cmc agreed well with the experimental cmc, and the monomer concentration was predicted to increase significantly above the cmc. In addition, the monomer and the micelle compositions were predicted to vary significantly with surfactant concentration. These composition variations were rationalized in terms of competing steric and entropic effects and a micelle shape transition near the cmc. To understand the packing constraints imposed on ternary surfactant mixtures better, the maximum micelle radius was also examined theoretically. The MT theory presented here represents the first molecular-based theory of the micellization behavior of mixtures of three or more conventional surfactants. In article 2 of this series, the MT theory will be extended to model the micellization of mixtures of conventional and pH-sensitive surfactants.     

Micelle–monomer equilibria in solutions of ionic surfactants and in ionic–nonionic mixtures: A generalized phase separation model

On the basis of a detailed physicochemical model, a complete system of equations is formulated that describes the equilibrium between micelles and monomers in solutions of ionic surfactants and their mixtures with nonionic surfactants. The equations of the system express mass balances, chemical and mechanical equilibria. Each nonionic surfactant is characterized by a single thermodynamic parameter — its micellization constant. Each ionic surfactant is characterized by three parameters, including the Stern constant that quantifies the counterion binding. In the case of mixed micelles, each pair of surfactants is characterized with an interaction parameter, β, in terms of the regular solution theory. The comparison of the model with experimental data for surfactant binary mixtures shows that β is constant — independent of the micelle composition and electrolyte concentration. The solution of the system of equations gives the concentrations of all monomeric species, the micelle composition, ionization degree, surface potential and mean area per head group. Upon additional assumptions for the micelle shape, the mean aggregation number can be also estimated. The model gives quantitative theoretical interpretation of the dependence of the critical micellization concentration (CMC) of ionic surfactants on the ionic strength; of the CMC of mixed surfactant solutions, and of the electrolytic conductivity of micellar solutions. It turns out, that in the absence of added salt the conductivity is completely dominated by the contribution of the small ions: monomers and counterions. The theoretical predictions are in good agreement with experimental data.     

Mixed micelle behavior of poly(ethylene glycol) alkyl ethers with series of monomeric cationic, phosphonium cationic, and zwitterionic surfactant

The steady state fluorescence measurements have been carried out for the binary mixtures of poly(ethylene glycol) alkyl ethers (C _i E _j ) with series of monomeric cationic (MC), zwitterionic (ZI), and phosphonium cationic (PC) surfactants over the whole mole fraction range by using pyrene as fluorescence probe. The cmc values for all the binary mixtures, thus, determined have been further evaluated by using the regular solution theory. The various micellar parameters such as regular solution interaction parameter (β), micropolarity (I ₁/I ₃), and mean micelle aggregation number (N _agg) have been determined. A strong influence of hydrophobicity of both nonionic as well as cosurfactant (CS) components has been observed on the nature of mixed micelles. The presence of bulky head groups of PC surfactants significantly contributes towards the unfavorable mixing.     

HEXADECYLTRIMETHYLAMMONIUM BROMIDE + TETRADECYLTRIMETHYL-AMMONIUM BROMIDE MIXED MICELLES IN AQUEOUS GLYCOL OLIGOMERS

The conductances of hexadecyltrimethylammonium bromide (HTAB) + tetradecyltrimethylammonium bromide (TTAB) mixtures over the entire mole fraction range of HTAB (α_HTAB) were measured in pure water as well as in the presence of various aqueous ethylene glycol oligomers containing 5, 10 and 20 wt% of each additive in their respective binary mixtures at 30°C. From the conductivity data, the critical micellar concentration (cmc), degree of counter ion association (χ) and the standard free energy of transfer of the surfactant hydrocarbon chain from the medium to the micelle (ΔG^O _HP ) for HTAB and TTAB were computed. From the conductivity data of mixed surfactants systems, apart from cmc and χ, the regular solution theory parameters were also computed in order to explore the non-ideality in the mixed micelle formation in the presence of additives. The micellar parameters of both kind of surfactants and their mixtures show a significant dependence on the amount as well as on the number of repeating units of glycol oligomers. However, the non-ideality of mixed micelle formation remains unaffected in the presence of additives. These results have been explained on the basis of the medium effects of aqueous additive and it has been concluded that there are no significant interactions of glycol oligomers with the micelles of single and mixed surfactants.     

Synergistic Behavior of Binary Mixed Micellar Solution

Conductivity measurement has been used to study the properties of aqueous solutions of the nonionic polyoxyethylene sorbitan(20)monooleate (T₈₀) and the cationic 1,1′ lauryl amido propyl ammonium chloride (LAPACl) and their mixtures in the presence of 0.1 M HCl and at 303 K. The values of the critical micelle concentration (CMC) of the individual surfactants and their mixtures were determined from the conductometric measurements. Based on Rubingh's theory (approximation of the theory of regular solutions), the compositions of micelles (X₁), and the parameters of interaction between the molecules of cationic and nonionic surfactants (β) were calculated for mixture of systems LAPACl+α T₈₀ and T₈₀+α LAPACl. The mixture LAPACl+α T₈₀ showed synergistic interactions up to α=0.2 whereas those of T₈₀+α LAPACl registered antagonistic behavior. The study disclosed that for cationic/nonionic surfactants mixtures, the priority is for mixtures of cationic base with small mole fraction of nonionic surfactant and not the reverse.     

Ebulliometric determination and prediction of (vapor + liquid) equilibria for binary and ternary mixtures containing alcohols (C1–C4) and dimethyl carbonate

(Vapor + liquid) equilibrium (VLE) data for a ternary mixture, namely {methanol + propan-1-ol + dimethyl carbonate (DMC)}, and four binary mixtures, namely an {alcohol (C₃ or C₄) + DMC}, containing the binary constituent mixtures of the ternary mixture, were measured at p = (40.00 to 93.32) kPa using a modified Swietoslawski-type ebulliometer. The experimental data for the binary systems were correlated using the Wilson model. The Wilson model was also applied to the ternary system to predict the VLE behavior using parameters from the binary mixtures. The modified UNIFAC (Dortmund) model was also tested for the predictions of the VLE behavior of the binary and ternary mixtures. In addition, the experimental VLE data for the ternary and constituent binary mixtures were correlated using the extended Redlich–Kister (ERK) model, which can completely represent the azeotropic points. For the ternary system, a comparison of the experimental and the predicted or correlated boiling points obtained using the Wilson and ERK models showed that the ERK model is more accurate. The valley line, i.e., the curve which divides the patterns of vapor–liquid tie lines, was found in the (methanol + propan-1-ol + DMC) system. This valley line could be represented by the ERK model. Finally, the composition profile for simple distillation of this ternary mixture was obtained by analysis of the residue curves from the estimated Wilson parameters of the constituent binary mixtures.     

An Approximate Linear Solvation Energy Relationships Model Based on Snyder’s Selectivity Parameters. Chromatographic Behavior of Some 1-Aralkyl-4-Arylpiperazines

In order to elucidate the influence of the mobile phase composition on the retention of some 1-aralkyl-4-arylpiperazines, Snyder’s selectivity and polarity concept for building a simple linear solvation energy relationships model of chromatographic behavior was used. Maximum variability of mobile phase selectivity was achieved by using ternary mixtures of solvents from three different corners of the Snyder selectivity triangle: methanol as a strong proton donor, acetone as a strong proton acceptor and dimethyl formamide as a dipole interactor. Water was added to keep elution strength constant. Mobile phase composition was varied using Simplex–lattice mixture design. Selectivity parameters were calculated on the basis of linear relationships between volume fractions of pure solvents and their χ _e , χ _d , χ _n values. For seven-substituted 1-aralkyl-4-arylpiperazines R _M values were measured and correlated with previously calculated selectivity parameters. Mathematical models obtained are discussed according to the structural properties of the studied compounds.     

Interaction of the Amphiphilic Drug Amitriptyline Hydrochloride with Gemini and Conventional Surfactants: A Physicochemical Approach

Pyrene fluorescence measurements were carried out on various binary mixtures of the antidepressant amphiphilic drug amitriptyline hydrochloride (AMT) with conventional (TTAB and CTAB) and gemini surfactants (14-4-14 and 16-4-16). In all cases mixed micellar aggregates were formed and the mixed critical micelle concentration (cmc) of various mixtures was computed from the I ₁/I ₃ versus total surfactant concentration plots. In the region where mixed micelles are formed, the interaction of the amphiphlic drug and four surfactants showed synergistic behavior. The results were analyzed using an interaction parameter, β, which characterize the interaction in the mixed micelle and is introduced by a regular solution theory. The β values are negative in all binary mixtures, and their magnitudes increase with increasing hydrophobicity of the amphiphile. The micellar mole fraction of AMT in the mixed micelle (x ₁) and in the ideal sate (x _ideal) were evaluated and their values (x ₁ > x _ideal) suggest that the contribution of the AMT component is greater in binary mixtures as compared to that in the ideal state. Activity coefficients (f ₁ and f ₂) and excess Gibbs energy (G _ex) were also calculated. The values of micelle aggregation numbers (N _agg) and various other parameters like the Stern–Volmer constant (K _sv), micropolarity and dielectric constant of mixed systems have also been evaluated from the ratios of respective peak intensities (I ₁/I ₃ or I ₀/I ₁).     

The behaviour of surfactants in concentrated acids 6. Micellization and interfacial behaviour of n-hexadecyltrimethylammonium bromide in mixtures of methane sulphonic acid and concentrated sulphuric acid

The surface and interfacial activity of cationic surfactants depends on the polarity of the bulk phase. If concentrated sulphuric acid is mixed with water, physical properties such as density, and surface and interfacial tension go through a maximum as the molar composition is changed. Also the properties of surfactants, i.e. surface activity and CMC, do not vary linearly in such aqueous mixtures. However, if concentrated sulphuric acid is mixed with methane sulphonic acid we find a linear relationship.The adsorption isotherms of n-hexadecyltrimethylammonium bromide at the surface (interface) of mixtures of H₂SO₄ and CH₃SO₃H/air (n-hexane) and the CMC were determined for various compositions of the acid phase and approximated by the Von Szyskowski equation. The change in the energy of micelle formation, — Δ_MG, and the energy of adsorption, — Δ_AG°, were calculated as a function of solvent composition. The surface concentration as a function of bulk concentration, the maximum surface coverage and the percentage surface concentration were also calculated.We found a linear dependence of the CMC, and of the lowering of σ and γ at the CMC, on the mole fraction of the acid phase. Also the constant A of the Von Szyskowski equation decreases and the logarithm of B increases linearly with the mole fraction of methane sulphonic acid. Therefore it is possible to calculate all the data needed for the characterization of systems of different acid composition. A special pattern was found for acid mixtures with X_CH3SO3H < 0.1. This can be explained by the transformation of micelle structure and the possibility that micelles can solubilize hydrocarbons in this region.     

The low concentration aggregation of sodium oleate–sodium linoleate aqueous mixtures

Sodium oleate (NaOL, C₁₈H₃₃O₂Na)–sodium linoleate (NaLin, C₁₈H₃₁O₂Na) mixtures were studied in the micellar and in the air/water interface states at 298.15 K. Three aggregation steps were found: a premicellar aggregation, the critical micelle concentration (CMC), and a structural change of micelles. Micelles, both at the CMC and at the structural change concentration, are richer in oleate than the overall mixture composition. Micelles are strongly non-ideal and the interaction is repulsive. The non-ideal behavior and the dependence of the micelle ionization degree with micelle composition are explained on the basis of the interaction of the π electrons of the surfactants’ chains with water at the hydrocarbon/water micellar interface. The air/solution adsorbed monolayer is also non-ideal, but the interaction is attractive and there is a preferential composition with a mole fraction of sodium oleate of about 0.7. The surface pseudophase behaves as if oleate were the solvent and linoleate a strongly soluble solute. This behavior and the dependence of the average area per adsorbed molecule were explained on the basis of the interaction of the double bonds with water. At the air/solution interface, the linoleate molecule area was similar to that of a heterogemini surfactant having a spacer with seven carbon atoms.     

Mixed Micellization Behavior of 12-2-12 Gemini Surfactant with Some Alkyltrimetyl Ammonium Bromide Surfactants

Mixed micellization behavior of dimeric cationic surfactant ethanediyl-1,2-bis (dimethyldodecylammonium bromide) (12-2-12) with a series of monomeric cationic surfactants dodecyltrimethyl ammonium bromide (DTAB), tetradecyltrimethyl ammonium bromide (TTAB), and cetyltrimethyl ammonium bromide (CTAB) has been studied in aqueous and aqueous polyvinylpyrrolidone (PVP) solutions at 298.15, 308.15, and 318.15 K, respectively, using conductometric method. Various thermodynamic parameters like mixed micelle concentration (C_m), micelle mole fraction (X₁), interaction parameter (β), and free energy of mixing (ΔG_ex) of the mixed systems have been determined and analyzed using Rubingh's regular solution theory. The results indicate that in aqueous solutions the binary mixtures of 12-2-12 with DTAB/TTAB behave nonideally with mutual synergism whereas that with CTAB shows almost ideal behavior at 298.15 K. At 318.15 K, all these binary mixtures exhibit antagonistic behavior. The effect of variation in chain length of alkyltrimethyl ammonium bromide surfactants on the interactions with 12-2-12 have also been evaluated and discussed.     

Thermodynamic and Dynamic Properties of Micellar Aggregates of Nonionic Surfactants with Short Hydrophobic Tails

The densities and viscosities of binary aqueous mixtures of poly(ethylenoxide)hexanols [C₆H₁₃(OCH₂CH₂)_mOH, C₆E_m] (m= 3, 4, and 5) have been studied in the micellar composition range. For the same surfactants the self-diffusion coefficients in mixtures with heavy water have been determined by the spin-echo pulsed field gradient method. The volumetric data are interpreted by means of the phase separation model, and values of the CMC, volume change, and standard free energy change of micellization are obtained. From the viscosity data the hydration numbers of the surfactant hydrophilic head in the micellar state are computed; they are in agreement with those obtained from HDO self-diffusion data. The surfactant self-diffusion data are used to calculate the apparent micelle radius and the aggregation number. The micellization parameters obtained for the different surfactants are compared and discussed.     

Mixed micelles of homologous perfluoropolyether anionic surfactants in water

The mixtures of sodium and ammonium salts of three homologous perfluoropolyether carboxylic acids having Cl-terminated perfluoroalkyl group (Cl-PFPE) and differing in the average molecular weight (MW) were examined. The surfactants, namely n2, n3 and n4, have two, three and four PFPE units, respectively. Each surfactant was studied alone and in mixture with the other surfactants with the same counterion. NMR chemical shifts were measured for each surfactant and for the mixtures in different concentrations. For a given mixture the micelle composition, X_i, can be determined from the observation of the chemical shifts of the micellar components. It was found that Cl-PFPE surfactant mixtures form in water mixed micelles which contain the surfactants in equilibrium with monomeric species. The analysis of NMR chemical shift variations allowed evaluating the partition of the various surfactants in the mixed aggregates as a function of the total concentration. Composition of mixed micelles resembles ideal mixing predictions particularly at high surfactant concentrations.     

Determination of autoprotolysis constants of ternary water—dioxane—methanol solvent systems at 25°C

The thermodynamic autoprotolysis constant K₅ (the sum of the autoprotolysis constants of H₂O and CH₃OH) of various ternary water—dioxane—methanol and the corresponding binary solvent systems (water—dioxane, water—methanol) were determined by potentiometric measurements with a combined glass—calomel electrode. In the ternary mixtures, the results show that the composite medium effect on the pK₅ values, expressed by a parameter b = dpK₅/d_u (u being avariable expressing the solvent composition), depends on the ratio of the organic solvent concentrations. In these mixtures, superposition of the various effects detected in the corresponding binary solvents allows the calculation of the pK₅ value of any ternary mixture by means of a simple equation.     

Acid-base equilibria in ternary water/methanol/dioxane solvent systems : Determination of pKa values of some aliphatic monocarboxylic acids

The thermodynamic acidity constants of n-butanoic, n-pentanoic, n-hexanoic, and n-heptanoic acids were determined at 25°C in ternary water/dioxane/methanol mixtures. The results obtained show that the composite medium effect, expressed by a parameter b = dpK′/du (u being a variable expressing the solvent composition), depends on the ratio of the organic co-solvent concentrations. In the ternary mixtures, superposition of the various effects detected in the corresponding binary solvents (water/dioxane and water/methanol) enables simple interpolation formulae to be used to estimate the pK_a values in solution with any ratio of the three solvents.     

Viscometric study on the compatibility of some water-soluble polymer-polymer mixtures

Dilute solution viscosity behavior of three water-soluble polymer mixtures has been studied at 20 °C. The ternary systems assayed are distilled water/sodium carboxymethylcellulose (CMC)/polyacrylamide (PAM), distilled water/methylcellulose (MC)/CMC, and distilled water/polyvinylpyrrolidone (PVP)/MC. The intrinsic viscosity and the viscometric interaction parameters have been determined for the binary (distilled water/polymer) and ternary (distilled water/polymer1/polymer2) systems. Degree of compatibility of these polymer systems was estimated on the basis of five criteria: (i) the sign of Δb_m, (ii) the sign of Δb_m^′, (iii) the sign of Δ[η]_m, (iv) sign of thermodynamic parameter α, and (v) the sign of modified thermodynamic parameter β. Based on the sign convention involved in these criteria, compatibility/miscibility was observed in CMC/PAM and MC/CMC systems and incompatibility/immiscibility in PVP/MC system. The FTIR analyses also support the obtained results. The miscibility/compatibility of all these systems is in accordance with the interactions between the unlike polymer chains rather than the polymer-solvent interactions.     

Mixed micellization of gemini surfactant with nonionic surfactant in aqueous media: a fluorometric study

Herein we report on the study of the interactions between alkanediyl-α,ω-type cationic dimeric (gemini) surfactant and the nonionic Triton X-100 in aqueous medium. The critical micelle concentrations of binary mixtures were determined by fluorometric study. Using the regular solution theory for the analysis of the experimental data, the attractive nature of interactions and synergistic behavior of gemini surfactant and Triton X-100 mixture were demonstrated. The micelle aggregation number was measured using steady state fluorescence quenching method. The micropolarity, binding constant and dielectric constant of mixed systems were determined from the ratio of peak’s intensity (I ₁/I ₃) in the pyrene fluorescence emission spectrum.     

Topological investigations of binary and ternary mixtures: excess isentropic compressibilities

The speed of sound, U_ij 1,3-dioxolane (D) in binary mixtures (ij) with benzene, cyclohexane, n-hexane or n-heptane and U_ijk for 1,3-dioxolane in ternary mixtures (ijk) with the same hydrocarbons have been measured as a function of composition at 298.15 K. The observed data have been utilised to evaluate excess isentropic compressibility of binary, (κ_s^E)_ij and ternary (κ_s^E)_ijk mixtures using density and speed of sound values of the binary and ternary mixtures. The Moelyn-Huggins concept of interaction between the molecular surfaces of the components of a binary mixture [Polymer 12 (1971) 389] has been extended to evaluate excess isentropic compressibility of the studied binary and ternary mixtures. It has been observed that κ_s^E values predicted by a graph-theoretical approach using connectivities of third degree for binary mixtures compare reasonably well with their corresponding experimental values and κ_s^E for ternary mixtures are of the same sign and order of magnitude.