J . Phys. Chem. 1993,97, 13792-13802
13792
Phase Behavior of Aqueous Mixtures of Dodecyltrimethylammonium Bromide (DTAB) and Sodium Dodecyl Sulfate (SDS) Kathleen L. Herrington and Eric W. Kaler' Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
David D. Miller Eastman Kodak Company, Research Labs, Building 82, Rochester, New York 14650-2109
Joseph A. Zasadzinski and Shivkumar Chiruvolu Department of Chemical and Nuclear Engineering and Materials Engineering, University of California, Santa Barbara, Santa Barbara, California 931 06 Received: July 22, 1993" Strong electrostatic interactions between the oppositely charged head groups of cationic and anionic surfactants in aqueous mixtures provide an added degree of flexibility in tailoring microstructure. Here, we trace the phase behavior and microstructural evolution in mixtures of surfactants with symmetric tail groups: sodium dodecyl sulfate and dodecyltrimethylammonium bromide. Mixtures of single-chained cationic and anionic surfactants are studied using conductivity, cryo-transmission electron microscopy, video-enhanced microscopy, and timeresolved fluorescence quenching. We find that micelles of anionic surfactants grow upon addition of cationic surfactant. These rodlike micelles are transformed abruptly into vesicles over a very narrow composition range. For this symmetric system, formation of hydrated crystals of 1:1 anion/cation surfactant dominates the phase behavior. We develop a theoretical thermodynamic cell model to predict important properties of the mixed micellar solutions such as monomer and micellar composition and counterion binding as well as the equilibria between the crystalline and micellar phases. The cell model provides a good account of both the micelle/ precipitate phase equilibria and the micellar solution properties as probed by electrical conductivity.
Introduction Aqueous mixtures of anionic and cationic surfactants exhibit many unique properties that arise from the strong electrostatic interactions between the oppositely charged head groups. For example, mixtures of oppositely charged surfactants have dramatically lower critical aggregation concentrations (CACs), as determined from surface tension measurements, than do single pure surfactants. In addition, mixtures are often more surface active than either pure surfactant.I-* Finally, mixing the two surfactants together can produce interesting microstructures not formed by the pure components (e.g. vesicles and/or rodlike micelles) and can dramaticallydecreasethe concentration at which liquid crystalline phases form.Z4 These properties can be exploited in many applications. The surfaceproperties may be useful in detergency applications,rodlike micellar solutions have found use as drag-reduction agents in pipeline flow,5 and vesicles have been proposed for use as agents for controlled drug release,6 micro reactor^,^ and model membranes.* In order to develop these applications, it is essential that the relationship between surfactant geometry (e.g. branching of the tail groups, asymmetry between tail groups, and the type of polar head group) and phase behavior be understood. We have presented the phase behavior and properties of the system cetyltrimethylammonium tosylate (CTAT) and branched sodium dodecylbenzenesulfonate (SDBS) in water.2-4 In these mixtures, vesicles are quite stable with large vesicle phases present in the pseudoternary phase diagram for both cationic and anionicrich mixtures. Quasielastic light scattering measurements show that vesicles form at the CAC (ca. l e 3 wt 5%) in mixtures of CTAT and SDBS.Z A crystalline precipitate, presumably the 1:l salt of the amphiphilic ions, is present only in equimolar mixtures. Here we take another step toward understanding the Abstract published in Aduonce ACS Absrracrs, November 15, 1993.
0022-3654/93/2091- 13192304.00/0
effect of surfactant structure on phase behavior by considering the pair sodium dodecyl sulfate (SDS) and dodecyltrimethylammonium bromide (DTAB), surfactants with linear tail groups of equal length. The phase behavior for more concentrated solutions of DTAB and SDS is dominated by a crystalline precipitate and liquid crystalline phase^.^ Lucassen-Reynders et al.1 showed that the CAC occurs approximately 2 decades in concentration below the pure component critical micelle concentrations (CMCs) for a wide range of mixing ratios of DTAB to SDS, and that large equimolar aggregates formed at this concentration. The phase behavior and degree of counterion binding, probed by ion-selective electrodesand tracer self-diffusion,were investigated as a function of mixing ratio at a total surfactant concentration of 0.05 M (between 1 and 1.5 wt % total surfactant).IO At thisconcentration, the equimolar precipitate (DTA+:DS-) formed at mixing ratios between 88.7/11.3 and 39.6160.4 DTABISDS (all mixing ratios are on a weight basis). There was little micellar growth as SDS was added to DTAB-rich micellar solutions. Essentially all of the added dodecyl sulfate ions (DS-) were incorporated into the mixed micelles, and the degree of bromide ion binding decreased as DS- was added. In SDS-rich mixtures, all of the added dodecyltrimethylammonium ions (DTA+) were present in mixed micelles and the degree of sodium binding decreased to zero as the mixing ratio approached the SDS-rich precipitationboundary. This was attributed to micellar growth with added DTAB. Solutions in therange 33.5166.5-39.6160.4 DTAB/SDS appeared turbid, and examination by cryo-transmissionelectron microscopy (cryo-TEM) revealed the presence of vesicles at these mixing ratios. At a mixing ratio of 35.5165.5, the micrographs showed threadlike micelles coexisting with perforated vesicles.I0 Limited theoretical work has been directed at modeling the important properties of mixtures of anionic and cationic surfactants."-15 Regular solution theory, combined with the 0 1993 American Chemical Society
Phase Behavior of DTAB and SDS pseudo-phase-separation model, has been used to predict the monomer concentrations, micellar composition, and CAC for anionicandcationic surfactant mixtures.12J3 Although reasonable predictions are made for the dependence of the CAC on the solution composition, the theory is strictly applicable only to molecules of similar size and functionality, which is clearly not the case for mixtures of oppositely charged surfactants.l6 Further, some of the reported interaction parameters are determined from data that describe precipitate/monomer equilibria rather than micelle/monomer equilibria. The phase equilibria between monomer, micelles, and precipitate in mixtures of SDS and dodecylpyridinium chloride has been reported and interpreted in terms of a model that combines regular solution theory for the micellar phase and a solubility product for the precipitate phase." The thermodynamic machinery in which an expression for Gibbs free energy for micellar aggregates is combined with the mass action law has been developed for calculating micellar properties, size distribution, and phase ~eparati0n.I~ This model was used to make qualitative predictions of trends for micellar solutions of anionic and cationic surfactants. A statistical thermodynamic cell model has been used to predict the phase equilibrium between various phase~.15J~-~o Of these approaches, the cell model structure provides a careful and convenient way to account for the main contributions to the aggregate free energy. In addition, the cell model is well-suited for calculations for liquid crystalline phases. In this model, the nonidealities due to electrostatic interactions are calculated using the nonlinearized PoissonBoltzmann (PB) equation. In this paper, we explore the phase behavior and microstructure of mixtures of DTAB and SDS. The microstructures present in the different phases are probed by time-resolved fluorescence quenching (TRFQ), cryo-TEM, video-enhanced differential interference contrast microscopy (VEM), and electrical conductivity. Finally, we present a predictive thermodynamic cell model that can quantitatively account for the observed phase equilibria between micelles and an insoluble crystalline precipitate as well as for the properties of the mixed micellar solutions including micellar composition, counterion binding, and free monomer concentration. Model predictions are tested using the results of electrical conductivity measurements. The TRFQ technique is a well established method for determining aggregation numbers of surfactant A new extension of this technique can detect the presence of small micelles in turbid solutions of vesicles and liposomes.22 Such detection using scattering techniques is frustrated by the overwhelming signal from large vesicular or liposomal structures. TRFQ has been used to track the evolution of micelles tovesicles semiquantitatively in aqueous solutions of bis(tetradecy1)dimethylammonium surfactant cation with mixtures of bromide and acetate counterions.22 The TRFQ technique showed that micelles of bis(tetradecy1)dimethylammonium acetate spontaneously transform into mixtures of micelles and unilamellar vesicles as bromide replaces acetate counterion. The fraction of aggregates in vesicle form grows at the expense of micelles as the bromide/ acetate ratio increases. At high bromidecontent, only unilamellar and multilamellar structures exist. Cryo-TEM, in which thin aqueous films are rapidly frozen and examined while in a vitrified state, is a powerful technique for imaging microstructures in the size range 1-1000 nm and has been used to elucidate the structural transitions during both the detergent solubilization of phospholipids23.24 and membrane fusion.25 Here, the microstructural changes that accompany the DTAB/SDS micelle-vesicle phase transition are followed using both TRFQ and cryo-TEM.
Theory Cell Model. The Gibbs free energy of a mixed micellar solution of cationic and anionic surfactants is described within the
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13793
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Figure 1. Schematicof the cell geometry used to model a mixed micellar solution. RI is set equal to the length of a fully extended surfactant tail plus the distance to the surface of charge of the head group. R2 is the cell boundary and is determinedby a mass balance on the availablewater and counterions. R* is the point at which the electrostatic potential equals e/kT. All counterionswithin the shell RI < r < R* areconsidered bound to the micelle.
framework of a thermodynamic cell model developed by o t h e r ~ . I ~ JPhase ~ - ~ ~behavior and optimal aggregate properties are calculated by directly minimizing the Gibbs free energy,19 rather than by equating chemical potentials of each phase.l5J7J* The cell model is used to predict key properties of mixed micellar solutions such as the free monomeric surfactant concentrations, the micellar composition, the micelle surface charge density, and the degree of counterion binding. The equilibria between the solid crystalline and mixed micellar phases are predicted for DTAB and SDS using the cell model combined with an expression for the Gibbs free energy of the precipitate phase that makes use of solubility data reported in the literature.' The cell model includes the essential free energy contributions that govern the aggregation process. The factors that favor aggregation are the hydrophobic free energy of transferring the hydrophobic surfactant tails from water into theaggregate interior, Ghyd, the ideal entropy of mixing all molecules within the cell, Gmicrand the ideal entropy of mixing of the surfactant tails within the aggregate, G i X . These contributions are balanced against those opposing aggregation: the electrostatic work of establishing a potential distribution and a charged interface, Gel, the entropy loss due to ordering the ions in solution, Gchg, the ideal entropy of mixing for monomeric surfactant, water, and counterions, Gid, and the surface energy of the oil/water interface present at the aggregate surface, G,. The resulting free energy of aggregation per cell, Gas, is with
(1b) = Ghyd + Gmix + G, + Gel + Gchg + G i d + G, Here ni is the number of molecules of species i in the cell, p,Osw is the standard chemical potential of species i in water, and the summation is over components i in the aqueous region of the cell. The spherical cell of radius R, used for micelles is shown in Figure 1. The micelles are centered within the cell and are assumed to be monodisperse and spherical with a radius, R1, equal to a fully extended alkyl chain, calculated using Tanford's relation,26 plus the distance to the surface of charge of the polar head group, using values reported by Stitger.27 Ionic species and water are excluded from the hydrophobic micellar core, and the polar head groups of the aggregated surfactant ions are restricted to the core/water interface. A brief discussion of each of the abovecontributions to theaggregate free energyisin the Appendix. AGagg
Herrington et al.
13794 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 The phase equilibria between micelles and the crystalline precipitate for mixtures of DTAB and SDS can be predicted by minimizing the global free energy of the two-phase system: G cnipIDVw + ncellAGagg+ npptAGppt (2) where the summation is over components in the aqueous mixture, nail is the number of micellar cells, the free energy for micellar aggregates per cell is given by AG,, npplis the moles of precipitate, and AG,,is the molar freeenergychangeof precipitate formation. The minimization is subject to the appropriate mass balances for each species (assuming all of the water is in the micellar phase)
Xi"@+ xippt + x i m o n = 1
(3)
and electroneutrality constraints pori DS-
+ cBr = cEYA++ cNS+ cDs.XP&-= cDTA~:-A+
(aqueous solution) (4a) (precipitate)
(4b)
where Xij is the fraction of total surfactant i molecules in the aggregate type j ("mon" refers to monomeric surfactant, "ppt" to the precipitate, and "agg" to the micelle) and q is the molar concentration of species i. To find the free energy change of precipitate formation, consider a two-phase mixture consisting of a solid precipitate in equilibrium with monomeric surfactant dissolved in water. The free energy is
G = nwpwogw + c(nipIDVw+ niRT In ai) + npptAGppt
(5)
where the activity of species i in solution is ai and the summation is over the total surfactant and counterion molecules in the twophase mixture. Precipitate begins to form when the free energy of precipitate formation just compensates the entropic loss of constraining the molecules within a crystalline lattice. AGpptis calculated from the solubility parameter, Ksp,that characterizes the equilibrium between monomeric surfactant ions and the solid precipitate:l6 AGppt= -R T In KspK, = -R T In [XDSXDTA+] - R T In y+2
(6) where KIPis defined relative to a mole fraction standard state and 7~ is an activity coefficient. Using the literature value of Ksp determined from surface tension measurements1 and neglecting nonideality a t the very low CACs (-0.001 wt 5%) of mixtures of DTAB and SDS, the calculated value of AGpptis -74 455 J/mol. In eq 5, deviations from idealityentersolely through theactivity coefficients of the ionic monomeric surfactant solution. In the cell model, the presence of the highly charged micelle is assumed to dominate all deviations from ideality. The PB equation is solved numerically to yield the potential distribution around the charged micelle and, subsequently, the ion concentration distributions. Others have noted that it seems inappropriate to include a Debye-Huckel-type activity correction to account for ion correlations in the micellar phase since the PB equation is derived with the assumption that there are no correlations between ions.17 However, for the precipitate phase in equilibrium with monomeric surfactant, the only nonidealities are thosedue to ion correlations in the monomeric surfactant solution. In the following calculations, activity coefficients are used in the calculation of AGppt with eq 6 but are not used in calculating AGaU. Activity coefficients are estimated with the Debye-Huckel form:" log yt = -0.5139 lz+z-l[--
