A thermodynamic analysis of charged mixed micelles in water

A thermodynamic analysis is presented for electrically charged mixed micelles in water on the basis of the Gibbs-Duhem relation proposed by Hall in combination with the information on the degree of counterion binding. The proposed analyses are shown to work well for both ionic/nonionic mixed micelles and those consisting of ionic surfactants of like charges. Conclusions for ionic/nonionic mixed micelles are as follows. (1) The contribution from counterions is significant. (2) In media of low ionic strengths, the counterion concentration varies with the micellar mole fraction of the ionic species x. The dependency of the activity coefficients and the excess free energy on x is significantly influenced by this effect, but it can be corrected to a large extent in terms of the Corrin-Harkins relation. (3) The regular solution theory (RST) is not always valid even when the excess free energy is described well with the RST expression unless the observed range of the micelle composition is wide enough. (4) The RST overestimates x and underestimates the activity coefficient of the ionic species when applied to the mixed micelles to which it is inapplicable. For the ionic mixed micelles consisting of surfactants of like charges, the Lange-Shinoda approach is shown to be consistent with the present analysis in terms of the Gibbs-Duhem relation, but Motomura's approach is found to be not exact but approximate.     

A thermodynamic analysis of the hydrogen ion titration of micelles

A thermodynamic analysis of hydrogen ion titration is presented for association colloids with particular emphasis on surfactant micelles. When a particular type of the micellar Gibbs-Duhem relation (MGD), alpha(M)dmu(I)+(1-alpha(M))dmu(N)=0 [alpha(M): the degree of ionization of micelles; mu(I),mu(N): chemical potentials of ionized and nonionized species], holds, the free energy change accompanying the ionization of the micelle G(ex) can be evaluated from the titration data in the same manner as for covalently bonded colloids such as linear polyions. In the case where the regular solution approximation is valid for mixed micelles, the titration curve should be a straight line with a slope yielding the interaction parameter, and G(ex) is given as a function of alpha(M)(2). For dodecyldimethylamine oxide micelles for which the MGD relation has been shown to hold, values of the calculated electrostatic free energy G(el) were close to but significantly greater than experimental G(ex) values when the former were calculated on the basis of the Poisson-Boltzmann equation for either a sphere or a plate with smeared charges in a salt solution of infinite volume. When the critical micelle concentration (cmc) data are combined with the hydrogen ion titration data, we obtain a criterion to judge whether the above MGD relation holds or not. When the MGD relation holds, the monomer concentration C(1) can be evaluated from the hydrogen ion titration. For most cases examined, the C(1)/C(1)(alpha(M)=0) from the titration agrees well with cmc/cmc(alpha(M)=0), suggesting cmc=C(1) above the cmc. For tetradecyldimethylamine oxide, the MGD relation does not hold in the range of low ionic strength and even at 0.1 M NaCl it has been found that C(1)/C(1)(alpha(M)=0)相似文献   

Some Thoughts Regarding Theoretical Aspects of the Corrin-Harkins Relation and the Micellization Product of Ionic Micelles

The dependence of the stability of ionic micelles on the ionic strength of the medium is examined analytically without recourse to any explicit expression of the surface potential of micelles. The present study is based on the idea developed by Evans, Mitchell, and Ninham (D. F. Evans, D. J. Mitchell, and B. W. Ninham, J. Phys. Chem. 88, 6344 (1984)) that the interfacial free energy at the water/hydrocarbon core interface is independent of the ionic strength of the medium. The Corrin-Harkins (C-H) relation, a linear relation between the logarithm of the critical micelle concentration (cmc) and the logarithm of the counterion concentration n(C), is obtained in the range of n(C) where the salting-out effect is negligible, under the condition that the area per monomer on the micelle surface decreases very weakly with n(C). The "micellization product" of the charged pseudophase model of ionic micelles is discussed. The linear dependence of the surface potential of ionic micelles on n(C) is derived while a part of the effects of salt on the micelle size/shape is allowed. Copyright 2001 Academic Press.     

The Correlation of the Degree of Counterion Binding with the Composition of Ionic–Nonionic Mixed Micelles

Two simple expressions for calculating the degree of counterion binding of mixed micelles are presented. These approximate expressions for the spherical micelle are derived from the relationship of the degree of counterion binding with the surface charge density. One of them works quite well for the estimation of the degree of counterion binding of mixed micelles when the mole fraction of the ionic component in mixed micelles is high.     

Effects of interactions on the formation of mixed micelles of 1,2-diheptanoyl-sn-glycero-3-phosphocholine with sodium dodecyl sulfate and dodecyltrimethylammonium bromide

Mixed micelles of the phospholipid 1,2-diheptanoyl-sn-glycero-3-phosphocholine (DHPC) with sodium dodecyl sulfate (SDS) or dodecyltrimethylammonium bromide (DTAB) in aqueous solutions and the effects of interactions between the components were studied by fluorescence and NMR measurements. The regular solution theory (RST) was applied to analyze the experimental critical micelle concentration values determined from the fluorescence spectra of pyrene in the mixed micelles. Negative values for the interaction parameter (beta12) were obtained for both DHPC + SDS and DHPC + DTAB mixtures, with the value being more negative in the former case. The negative beta12 values for the two systems imply that the interaction between the phospholipid and the two ionic surfactants is attractive in nature, being more intense in the case of DHPC + SDS. The interaction parameter, beta12, varies with composition of the mixtures indicating changes in packing. The proton NMR shifts are quite different for the two systems and also vary with composition. An interpretation of these experimentally determined chemical shifts in terms of the degree of compactness attributed to electrostatic and steric interactions in the mixed micelle supports the conclusions derived from the fluorescence cmc experiments.     

Effects of micellar charge density on the coefficient of the Corrin-Harkins relation

Effects of the micelle composition (ionic species fraction alpha(M)) on the coefficient of the Corrin-Harkins relation (k(CH)) of ionic/nonionic mixed micelles were examined in the case of dodecyldimethylamine oxide. Long alkyl chain amine oxides exist either in the nonionic or the cationic (protonated form) species depending on the pH of solutions and hence the control of the micelle composition near the critical micelle concentration (cmc) is possible by adjusting the pH of the solutions. On the basis of the cmc data from the surface tension measurements and the hydrogen ion titration curves, we evaluated the k(CH) values as a function of the micelle composition alpha(M) for the first time. The obtained k(CH) values were compared with the degree of the counterion binding, theta, in the solutions without added salt. The k(CH) values increased with alpha(M), and were approximately identical with theta for alpha(M)>0.4. In the range alpha(M)<0.4, it is likely that theta is greater than k(CH). An empirical relation proposed by D. G. Hall et al. ("Mixed Surfactant Systems," Am. Chem. Soc., Washington, D.C. 1992) on the relation between theta and the micelle composition was also compared with these experimental results. Experimental values, k(CH) and theta, followed the empirical relation for alpha(M)>0.4; however, both k(CH) and theta increased steeply in the range alpha(M) 0.25-0.3.     

Micellar solutions of ionic surfactants and their mixtures with nonionic surfactants: Theoretical modeling vs. Experiment

Here, we review two recent theoretical models in the field of ionic surfactant micelles and discuss the comparison of their predictions with experimental data. The first approach is based on the analysis of the stepwise thinning (stratification) of liquid films formed from micellar solutions. From the experimental step-wise dependence of the film thickness on time, it is possible to determine the micelle aggregation number and charge. The second approach is based on a complete system of equations (a generalized phase separation model), which describes the chemical and mechanical equilibrium of ionic micelles, including the effects of electrostatic and non-electrostatic interactions, and counterion binding. The parameters of this model can be determined by fitting a given set of experimental data, for example, the dependence of the critical micellization concentration on the salt concentration. The model is generalized to mixed solutions of ionic and nonionic surfactants. It quantitatively describes the dependencies of the critical micellization concentration on the composition of the surfactant mixture and on the electrolyte concentration, and predicts the concentrations of the monomers that are in equilibrium with the micelles, as well as the solution’s electrolytic conductivity; the micelle composition, aggregation number, ionization degree and surface electric potential. These predictions are in very good agreement with experimental data, including data from stratifying films. The model can find applications for the analysis and quantitative interpretation of the properties of various micellar solutions of ionic surfactants and mixed solutions of ionic and nonionic surfactants.     

Interactions in binary mixed systems involving a sugar-based surfactant and different n-alkyltrimethylammonium bromides

In this paper, mixtures of sugar-based decanoyl-N-methylglucamide with three different n-alkyltrimethylammonium bromides (n=12 (DTAB), 14 (TTAB), and 16 (CTAB)) have been studied using conductance and fluorescence spectroscopic techniques. The critical micelle concentration values of pure and mixed systems were determined by both the conductance and the pyrene 1:3 ratio methods. The experimental results were interpreted using thermodynamic mixing approaches based on the pseudophase separation model. These analyses allowed us to determine the interaction parameters and the composition of the mixed micelles through the whole composition range. Since all the ionic surfactants used in this study have the same headgroup, the differences observed between the three mixed systems were attributed to the lengths of their hydrocarbon chains. It was established that, besides interactions of electrostatic character, additional short-range interactions must be considered. By using the static quenching method, the mean micellar aggregation numbers of mixed micelles were obtained. In the cases of the mixed systems with DTAB and TTAB it was observed that the aggregation number is initially reduced with the participation of the ionic component, remaining almost constant and close to the aggregation number of the pure ionic micelle. However, in the systems involving CTAB it is observed that the size of micelles initially increases and then decreases slightly for mixtures with a high content of the ionic component. The hydrophobic index pyrene 1:3 ratio was used to examine possible changes in the micellar micropolarity; however, no definitive conclusions could be derived from these experiments. In order to study the evolution of the local viscosity of the mixed micelles upon addition of the ionic surfactant, fluorescence polarization measurements were carried out with two different probes, fluorescein and coumarin 6. It was found that the participation of the ionic component in the mixed micelle induces the formation of less ordered structure than that of pure nonionic micelles. An attempt was made to correlate these effects with the interaction parameters obtained from the theoretical mixing model and, consequently, with the alkyl chain length of the ionic components.     

Computer Simulations of the Formation of Bile Salt Micelles and Bile Salt/DPPC Mixed Micelles in Aqueous Solutions

Brownian dynamics simulations for a coarse-grained model have been performed to study the formation of micelles from bile salts and mixed micelles with dipalmitoyl-phosphatidylcholine (DPPC) in aqueous solutions. The particular association behavior of bile salts as facial surfactants was shown to be caused by their special molecular architecture with a hydrophilic and a hydrophobic side. The experimentally observed smooth transition into the micellar region with increasing concentration is reproduced. Micelle size distributions have been evaluated at different bile salt concentrations. Typical structures of pure bile salt micelles could be identified. The composition and the structure of mixed micelles have been studied in their dependence on the bile salt/lipid concentration ratio in the aqueous solution. We have found that the bile salt fraction in the mixed micelles increases considerably with increasing bile salt/lipid concentration ratio and decreasing micelle size. The structural and thermodynamic features of micelle formation in the aqueous bile salt solutions with DPPC, which we have studied with the coarse-grained model, are in good qualitative agreement with experimental findings.     

Mixed micelle formation between amino acid-based surfactants and phospholipids

The mixed micelle formation in aqueous solutions between an anionic gemini surfactant derived from the amino acid cystine (C(8)Cys)(2), and the phospholipids 1,2-diheptanoyl-sn-glycero-3-phosphocholine (DHPC, a micelle-forming phospholipid) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC, a vesicle-forming phospholipid) has been studied by conductivity and the results compared with the ones obtained for the mixed systems with the single-chain surfactant derived from cysteine, C(8)Cys. Phospholipid-surfactant interactions were found to be synergistic in nature and dependent on the type of phospholipid and on surfactant hydrophobicity. Regular solution theory was used to analyse the gemini surfactant-DHPC binary mixtures and the interaction parameter, β(12), has been evaluated, as well as mixed micelle composition. The results have been interpreted in terms of the interplay between reduction of the electrostatic repulsions among the ionic head groups of the surfactants and steric hindrances arising from incorporation of the zwitterionic phospholipids in the mixed micelles.     

A simple rule for describing the composition dependence of the aggregation number of mixed micelles

The mean aggregation numbers of mixed micelles composed of hydrocarbon surfactants (nonionic/nonionic and ionic/nonionic surfactants) have been determined by the intensity light-scattering method, in order to compare them with the values calculated by using the equations derived. The equations have been derived for representative micellar shapes (disk-like, rod-like, and spherical shapes) by making the assumptions that (i) the surface area of the hydrocarbon core of a mixed micelle is built up by independent contributions from each surfactant monomer, and (ii) the dimension of the hydrocarbon core is determined by the number of carbon atoms of a surfactant. The closest agreement of the observed aggregation numbers with the calculated ones has been obtained for the mixed micelle of an oblate ellipsoidal shape as a geometrical model for a disk-like micelle. This suggests that an oblate ellipsoidal shape may be more probable for a micelle formed at a moderate range of surfactant concentration than a prolate ellipsoidal (a rod-like) and a spherical shape if the assumptions (i) and (ii) hold. The equations presented here are useful, since they make it possible to calculate an accurate aggregation number of the mixed micelle of any composition from the aggregation numbers of the pure micelles of the components and the number of carbon atoms of component surfactants as long as there is no highly specific interaction between different surfactant components.     

Effect of the protonation equilibrium on the interaction of mixed micelles with their counterions

Ionic/nonionic mixed micelle formation of dodecyldimethylamine oxide (DDAO) was studied by measuring the activities of DDAO⁺ ions and Cl⁻ ions using surfactant-selective electrodes and Ag/AgCl electrodes at three pH values in the absence of added salt. DDAO monomer exists as either a nonionic or a cationic species depending on the pH of the aqueous solution and hence the two species are not independent of each other. A new relation between the activity of the surfactant ions and that of the counterions is presented which differs from the corresponding relation valid for ionic/nonionic mixed micelles consisting of independent components. Received: 15 May 1998 Accepted in revised form: 30 September 1998     

Effects of micelle-to-vesicle transitions on the degree of counterion binding

Effects of micelle-to-vesicle transitions on the degree of counterion binding (beta) were investigated on three systems. For the concentration-dependent micelle-to-vesicle transition in the didodecyldimethylammonium bromide (DDAB)/water system, in the region of coexistent micelles and vesicles, less than 3 mM, the beta values increased significantly with DDAB concentration: beta (0.07 mM)=0.35 and beta (3 mM)=0.93. In the coexistent region, activities of the bromide ion, a(Br), were almost independent of the DDAB concentration, suggesting the pseudo-phase nature of both micelles and vesicles. In the concentration-dependent vesicle-to-lamellar transition region above 5 mM, where multilamellar vesicles were prevailing, on the other hand, the beta values were only little affected by this transition. This suggests that the increase in the layer number of DDAB multilamellar vesicles scarcely affects the beta values. This was also supported by the fact that the destruction of multilamellar vesicles by ultrasonication did not change the beta values. These results strongly suggest that the inner and outer monolayers of DDAB multilamellar vesicles are characterized by similar beta values. The second system, cetyltrimethylammonium bromide (CTAB)/DDAB mixtures, showed composition-dependent transitions depending on the mole fraction of DDAB X(DDAB): spherical micelles (0rodlike micelles (0.2vesicles (0.6相似文献   

A-B diblock copolymer micelles: effects of soluble-block length and component compatibility

Micellization of a diblock copolymer in dilute solution is studied by dissipative particle dynamics. The influence of the compatibility between blocks A and B and the interaction between the insoluble block and solvent on aggregation number P and micellar core radius Rc are examined. The micelle size distribution is obtained, and it is quite polydisperse. Different from the scaling theory for starlike micelles, the mean aggregation number based on weight average w decreases with increasing soluble-block length NA and the power law relation can be obtained, w approximately NA(-alpha). Similarly, the micellar core radius declines with NA, following Rc approximately NA(-beta) with beta=alpha/3. However, the exponent depends on the mutual compatibility between soluble and insoluble blocks. For the same composition, the incompatible diblocks form a smaller micelle and its aggregation number declines with a smaller exponent alpha. When NA approximately NB, the micelles deviate significantly from the spherical shape and solvophilic blocks are observed to be entrapped in the solvophobic core for compatible diblocks.     

Mixed micelles containing sodium oleate: the effect of the chain length and the polar head group

We have investigated the mixing behavior of binary mixtures of the alkylglucosides (CnG) octyl beta-D-glucoside and decyl D-glucoside in combination with sodium oleate (NaOl), and the amine oxide surfactants (AO) N,N-dimethyldodecylamine oxide, N,N-bis (2-hydroxyethyl)dodecylamine oxide, and 3-lauramidopropyl-N,N-dimethylamine oxide in combination with NaOl. From the equilibrium surface tension measurements, the critical micelle concentration (cmc) data were obtained as functions of the composition. Values of the cmc were analyzed according to both the regular solution model developed by Rubingh for mixed micelles and Maeda's formulation for ionic/nonionic mixed micelles. Two interaction parameters, beta and B1, were estimated from the regular solution model and Maeda's formulation, respectively. For NaOl/CnG mixed systems, a decrease in the hydrocarbon chain length of CnG resulted in a stronger interaction with NaOl from both beta and B1 values. For NaOl/AO mixed systems, the bulkiness of a polar head group of AO surfactants influenced the interaction between NaOl and AO. The dynamic surface tension measurements show that all surface tension values of surfactant solutions examined decreased with the time. We found that the time dependence of surface tension values for NaOl mixed systems was greatly influenced by the presence of NaOl rather than the other component.     

Influence of Additives on Capillary Absorption of Aqueous Solutions into Asymmetric Porous Ceramic Substrate

The effect of divalent and trivalent salts (CaCl(2), CaBr(2), MgCl(2), MgBr(2), LaCl(3), CeCl(3), La(NO(3))(3), and Ce(NO(3))(3)) on the micelle formation in C(8)-lecithin solutions was investigated using the techniques of static and dynamic light scattering. The critical micelle concentration (cmc), mean hydrodynamic radius (R(h)), gyration radius (R(g)), and weight-average molecular weight of the micelles were measured as functions of salt identity and concentration, amphiphile concentration, and temperature. It was found that the micelles in solutions of magnesium are less likely to form and less stable; their standard enthalpy is less exothermic as the ionic strength increases. On the contrary, the micelles in solutions of calcium and trivalent salts form easily, and are more stable; their standard enthalpy is also more exothermic as the ionic strength increases. Based on our model of the Gibb's free energy for the salt-added solutions, we obtained the following formula for the effect of salts on cmc: ln(cmc)'=ln(cmc)+k(1) I(1/2)+k(2)I, where (cmc)' and (cmc) are the critical micelle concentrations in salt-added and salt-free solutions, respectively, I is the ionic strength, and k(1) and k(2) are the salt effect parameters. The agreement between the formula and the experimental data for all the systems under study shows that the formula is more satisfactory than those suggested previously by other authors in describing the effect of salts on the cmc in the micellar solutions of not only zwitterionic but also nonionic surfactants. Copyright 2001 Academic Press.     

Markov chain model for the critical micelle concentration of surfactant mixtures

An extension of the Markov chain model (MC) for micellization is proposed, which allows the distribution of the surfactants between the monomer solution and the micelles in a mixed surfactant system to be predicted. The dependence of the critical micelle concentration (cmc) on the composition of the solution is investigated. The equilibrium thermodynamic relation between cmc and micelle composition is discussed. The case of ternary mixtures is analyzed, and theoretical triangular diagram is constructed according to MC. Available experimental data for binary and ternary mixtures agree well with the new MC theory. The dependence of MC parameters on the structure of the surfactants is discussed. Comparison of MC with the simple mixture (“regular solution”) model is presented. The parameters of the MC theory are related to the interaction parameter β _SM of the simple mixture model.     

Adsorption dynamics of binary mixture of Gemini surfactant and opposite-charged conventional surfactant in aqueous solution

The maximum bubble pressure technique has been used to study the adsorption kinetics of binary mixtures of an anionic Gemini surfactant C9pPHCNa with a cationic conventional surfactant C10TABr in aqueous solutions. The dynamic surface tension data were analyzed using the revised Ward and Tordai equations as well as the micelle dissociation kinetic model suggested by Joos et al. The apparent diffusion coefficient Da below the cmc, the adsorption barrier epsilona and the micelle dissociation constant kmic were obtained. The Da s at short times and at long times were respectively 0.2-16 x 10(10) and 0.08-0.9 x 10(10) m2s(-1), the latter corresponded to the adsorption barrier epsilona of 10-20 kJ mol(-1). The minimum epsilona appeared at the mole fraction of C9pPHCNa (alpha1, on a surfactant-only basis) in the bulk solution being 0.33. The kmic s of the mixed micelles were about 16-2300 s(-1). The most stable mixed micelles were formed at alpha1=0.2 rather than at alpha1=0.33 owing to great discrepancy of hydrophobicity between the two components. These results indicated that the composition of mixed solution was an important factor affecting the adsorption kinetics and the micelle stability.     

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.