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Langmuir 1996,11,487-492
Mixed Micelles of Dodecyltrimethylammonium Bromide and Didodecyldimethylammonium Bromide K. M. Lusvardi, A. P. Full, and E. W. Kaler* Center for Molecular a n d Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received August 12, 1994. I n Final Form: October 26, 1994@ Mixed micelles of dodecyltrimethylammonium bromide (DTAB) and didodecyldimethylammonium bromide (DDAB) are investigated with small-angle neutron scattering (SANS). The roughly spherical DTAB micelle elongates, and the fraction of condensed bromide ions increases, as the DDAB-DTAB mixing ratio increases at a constant total surfactant concentration. The aggregate composition matches that predicted by an ideal mixing model. SANS contrast variation experiments using partially deuterated DTAB (DdTAB)confirm the modeling parameters determined from fully hydrogenatedsurfactant samples and provide consistent structural information about the interfacial region.
Introduction Micelle formation in mixtures of surfactants is of considerable interest from both fundamental and practical points of view, especially because surfactants used in applications are often mixtures of homologous compounds or are contaminated by impurities. Mixed micelles of two or more components are also important in biology, and mixed micelles of monoalkyl surfactants and phospholipids have been carefully explored.'-3 There is a good analogy between mixtures of phospholipids and smaller surfactants (e.g., glucosides or bile salts) and mixtures of simple double-tailed and single-tailed surfactants such as didodecyldimethylammonium bromide (DDAB) and dodecyltrimethylammonium bromide (DTAB). DDAB and DTAB have nearly identical head group areas and tail lengths and so form a simple model mixed-micelle system. Mixed surfactant solutions contain a variety of structures. Solutions of anionic single tailed and anionic double tailed surfactants form rodlike micelles that are much larger than the spherical micelles of single-tailed surf a c t a n t ~ Micelles .~ of other double-tailed surfactants show the structural transitions from spheres, to prolate ellipsoids, to rods, but not to disks despite having lamellar mesophases adjacent to the isotropic region of their phase diagram.5,6 Knowledge of the structural changes that occur in mixtures of simple synthetic surfactants provides insight to the more complex micelle to vesicle or lamellar transitions important in uivo. The mixed micelle behavior of two surfactants is often approximated by assuming that the micelles are a separate thermodynamic phase in equilibrium with surfactant monomer. In systems that mix ideally, such as surfactant mixtures with the same head groups but differing methylene chain lengths, solution properties such as the mixed cmc, the unaggregated monomer concentrations, and the micellar composition as a function of total surfactant concentration can be predicted.' More recently, many studies have focused on mixed surfactant solutions
* Author to whom correspondence should be addressed. Abstract published in Advance A C S Abstracts, February 1,
1995. (1) Sinensky, M.; Kleiner, J. J . Cell. Physiol. 1981,108, 309. (2)Lichtenberg, D.;Robson, R. J.;Dennis, D. A. Biochzm. Biophys. Acta 1983,737,285. (3)Isomaa, B.Ecol. BUZZ. 1984,36,26. (4)Kaler, E. W.; Puig, J. E.; Miller, W. G. J . Phys. Chem. 1984,88,
2887. (5)Lin, T.-L.; Chen, S.-H.; Gabriel, N. E.; Roberts, M. F. J . Phys. Chem. 1987,91,406. (6)Magid, L. J. Colloids Surf. 1986,19,129. (7)Clint, J. H. J . Chem. Soc., Faraday Trans. 1 1976,71, 1327.
of oppositely charged surfactants.8-11 These mixtures exhibit unique properties that arise from the strong electrostatic interactions between the oppositely charged head groups and can spontaneously produce interesting microstructures such as vesicles or rodlike micelles, again in analogy to biological structures. In these mixed surfactant solutions, the assumption of ideal mixing fails and other models are needed to predict cmc values and structure. Altering the DTAB-DDAB mixing ratio provides a means for studying structural changes induced by changes of the average tail volume per molecule, since head group areas and tail lengths are nearly equivalent for DTAB and DDAB. Modeling of small-angle neutron scattering (SANS) spectra of pure DTAB solutions suggests that DTAB forms nearly spherical micelle^.'^-'^ However DDAB, which contains twice the volume of the DTAB tail, forms bilayers in water.12 The rheological behavior of mixed DTAB-DDAB micelles as studied by Weers et a1.16 suggests that, as DDAB is added to DTAB micellar solutions, spherical micelles undergo a transition from spheres to rods as a function ofcomposition. To investigate quantitatively the evolution of aggregate structure with increasing DDAB concentrations, we have made SANS measurements of samples containing different DTABDDAB mixing ratios a t constant total surfactant concentrations. As a stringent test of the model of structure suggested by our interpretation of this data, parameters deduced from model fits of spectra from fully hydrogenated surfactant samples are used to predict the experimental spectra from samples containing partially deuterated DTAB (DdTAB).
Experimental Section DTAB and DDAB (from TCI America with 98% purity) were recrystallized three times from acetone containing a small amount of anhydrous ethanol. Deuterated dodecyl bromide (from ( 8 ) Kaler, E. W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. N. J.Phys. Chem. 1992,96,6698. (9)Herrington, K. L.;Kaler, E. W.; Miller, D. D.; Zasadzinski, J. A.; Chiruvolu, S. J . Phys. Chem. 1993,97,13792. (10)Marques, E.; Khan, A.; da Graca Miguel, M.; Lindman, B. J . Phys. Chem. 1993,97,4729. (11)Koehler, R. D.; Kaler, E. W. Structure and Flow in Surfactant Solutions;Herb, C. A,, Prud'homme, R. K., Eds.; ACS Symposium Series 578;American Chemical Society: Washington, D.C.; 1994 p 120. (12)Evans, D. F.;Mitchell, D. J.; Ninham, B. W. J . Phys. Chem. 1986,90,2817. (13)Full, A. P.; Kaler, E. W. Langmuir 1994,10, 2929. (14)Berr, S. S.J . Phys. Chem. 1987,91,4760. (15)Hayter, J. B.;Penfold, J. Colloid Polym. Sci. 1983,261,1022. (16)Weers, J. G.; Scheuing, D. R. J . Colloid Interface Sci. 1991,145, 563.
0743-746319512411-0487$09.00/0 0 1995 American Chemical Society
Lusuardi et al.
488 Langmuir, Vol. 11, No. 2, 1995 Cambridge Isotope Laboratory with 98% deuteration) and trimethylamine (from Aldrich with 97% purity) were used t o synthesizedeuterated DTAB by the method outlined by Simister et al.17 Primary and secondary amines were removed from the trimethylamine by reaction with acetic anhydride. Excess trimethylamine was then distilledinto a mixture ofdodecyl bromide and anhydrous methanol and refluxed for 4 h at 0 "C. At the completion of the reaction, nitrogen was passed through the solution to remove excess trimethylamine and solvent. Anhydrous ether was then used to extract trimethylamine from the surfactant residue and the surfactant was purified further by the recrystallization procedure used above. After recrystallization,the surfactant was dissolved in water and passed through a Millipore Waters C18 Sep-Pak column to remove any trace impurities. No minima were detected in plots of surfacetension vs concentrationvia the Wilhelmy plate technique (KrussModel K-10 tensiometer). Deuterium oxide (Cambridge Isotope Laboratory, 98% deuterated) was used as received. Small-angle scattering experiments were performed on the NG-7 spectrometerat the Cold Neutron Research Facility ofthe National Institute of Standards and Technology (NIST). The neutron wavelength was L = 5 A with M I L = 0.15, and the magnitude of the scattering vector q ranged from 0.015 to 0.22 A-1 (q = 4x/A sin(OI2)where O is the scattering angle). The samples were held in quartz cells with 2 mm path lengths and maintained at either 25.0 or 60.0 0.1"C. The scatteringspectra were corrected for background, detector sensitivity,solvent and empty cell scattering, and sample transmission. The spectra were then radially averaged and placed on an absolute scale through direct calibration of the beam flux. The error (dn associated with each intensity data point reflects the counting statistics of the 2-D detector.
The critical micelle concentrations of mixtures of DTAB and DDAB have been determined using electrical conductivity measuremenW and agree well with predictions based on the assumption that mixed micelles constitute a condensed pseudophase that exhibits ideal solution behavior. With this model, the mixed cmc (cM), unaggregated monomer concentrations (cy and c:), and the mole fraction of surfactant 1(DTAB)in the mixed micelle ( X I ) as a function of total surfactant concentration are calculated from the cmc's of the pure components and the bulk mole fraction of component 1 in the surfactant mixture by7
*
Theory The observed scattered intensity from a dispersion of interacting particles is given by15J8J9
XI
=
ac
- cy
c - c;
-cy
where a is the mole fraction of surfactant 1 in the total mixed solute, cy1and C M are ~ the cmc's of pure surfactants 1 and 2, Acmeis C M ~- C M ~ ,and c is the total surfactant concentration. where F(q)is the single particle amplitude factor, S(q)is Several particle geometries were tested in calculating the interparticle structure factor, and n p is the particle model spectra, but only a suspension of prolate ellipsoidal number density. The structure factor depends only on particles produces model spectra that match experimental the potential of interaction and reflects the spatial spectra. The structure factor, S(q),for the ionic mixed arrangement of the micelles. The averaged square and micelles was calculated using a repulsive Yukawa pothe squared average of F(q)reflect micelle size and shape tential. This potential is approximately valid for KU less and the intermicellar distribution of scattering centers. than 6 , where K is the inverse Debye length and o is the B is a constant term that represents the residual incohereffective diameter.20The effective diameter was calculated ent scattering, which is mainly due to hydrogen in the by equating the second virial coefficient of a dispersion of sample. ellipsoids to that of a hard sphere dispersion.21 Structure For a solution of monodisperse spheres, (lF(q)I2)factors were calculated using either the rescaled mean l(F(q))I2 is identical to zero, thus eq 1 simplifies to spherical approximation (RMSA)22s23 or the hypernetted chain (HNCY4closure relations to solvethe one-component Ornstein-Zernicke equation. The RMSA somewhat underestimates the peak height in strongly coupled sysFor asymmetrical or polydisperse particles, an approxit e m ~however, ; ~ ~ its analytic solution provides a faster mate expression can be derived assuming that there is no correlation of particle orientation or size with p o ~ i t i o n . ' ~ J ~ means for calculating S(q)and makes iterative nonlinear least-squares fitting of a model spectrum to the experiThis "decoupling approximation" allows the application mental spectrum more convenient. The best fit paramof the structure factor expressions for spherical particles eters using RMSA compare well (within 1%) with those to describe solutions of polydisperse or elongated particles. calculated using the hypernetted chain (HNC) closure. The particles are redefined a s equivalent spheres for the The parameters reported are calculated using RMSA. calculation of S(q) (see below) and eq 1can be rewritten A core-and-shell geometry was used to calculate the in a form similar to that of eq 2 as model intensity. The hydrocarbon core is assumed to contain a fraction ofthe methylene groups of the surfactant (3) tails and the surrounding shell to contain the remaining where (17) Simister, E. A,; Thomas, R. K.; Penfold, J.;Aveyard, R.; Blinks, B. P.; Cooper, P.; Fletcher, P. D. I.; Lu, J. R.; Sokolowski, A. J . Phys. Chem. 1992,96, 1383. (18)Kotlarchyk, M.; Chen, S.-H. J . Chem. Phys. 1983, 79, 2461. (19) Hayter, J. B. I n Physics of Amphiphiles: Micelles, Vesicles, Microemulsions; Degiorgio, V., Corti, M., Eds.; North-Holland: New York; 1985.
(20) Venvey, E. J. W.; Overbeek, J. T. G. Theory ofthe Stability of Lysophobic Colloids; Elsevier: Amsterdam, 1948. (21) Isihara, A. J . Chem. Phys. 1960, 18, 1446. (22) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 651. (23) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. (24)Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; Academic: London, 1986. (25) Krause, R.; D'Aguanno, B.; MBndez-Alcaraz, J. M.; Nagele, G.; Klein, R.; Weber, R. J. Phys.: Condens. Matter 1991,3, 4459.
Langmuir, Vol. 11, No. 2, 1995 489
Mixed Micelles of DTAB and DDAB
shell, A, and the axial ratio,
A=
Rc,maj Rc,min
+ A -- Rt,maj + A Rt,min
(11)
are calculated. The volume fraction of surfactant, 9, coupled with the micelle dimensions determines the number density of micelles,
np =
39 4 n @ , m i n ~ t ,maj
Once the micelle dimensions have been specified, the scattering amplitude for a n ellipsoidal particle with a coreand-shell distribution of scattering length densities is given by18
Figure 1. Cross section of a core-and-shellprolate ellipsoidal micelle. The micelle shell is defined to include the ideallymixed surfactant head groups, a fraction of the methylene tails, associated counterions, and waters of hydration. The core is made up of the remaining portion of the surfactant tails. The scattered intensity is a weighted average of the contributions of the two regions (see text). where methylene groups, the surfactant head group ions, associated counterions, as well a s the water molecules that hydrate the ions (Figure 1). The solvent contains the remaining water, disassociated counterions, and unaggregated surfactant molecules. The ionic strength of the solvent used to calculate K depends on the concentration of dissociated counterions and unaggregated surfactant (cy and c y ) in the aqueous continuum.26 The aggregation number (N-), the fraction of associated counterions (d), the number of methylenes per surfactant monomer in the core (p), and the incoherent scattering background ( B ) , are the free-fitting parameters that determine the model intensity. In these scattering experiments, the spectra were placed on an absolute scale through direct calibration of the beam flux;therefore a scale factor was not used as a n additional fitting parameter. The first three parameters above completely specify the core-and-shell geometry of the elliptical micelle where the volume of the core is
and the volume of the shell is
V C HV~C, HV~ ,D V ~D ~ D, Vci, ~ ~and , Vsolare the molecular volumes of the CH3 and CH2 groups, the DTAB and DDAB head group, the counterion, and the solvent, r e ~ p e c t i v e l y . ~n ~ C H, z~, ~ the number of methylenes in a dodecyl surfactant tail, is set equal to 11, and Whg and oCi, the number of water molecules hydrating the head group ions and counterions, are set to 1 and 4, respecti~e1y.l~ When the minor axis of the core, Rc,min,is set equal to the extended length of the fraction of the surfactant tail in the core,28 the major axis, Rc,maj,is calculated by accommodating the remaining volume of the core. Since the total particle volume is specified through the fitting parameters and molecular volumes, the thickness of the (26)Cant& L.; Corti, M.; Degiorgio, V. Faraday Discuss. Chem. SOC. 1987,83,287. (27)Berr, S. S.; Coleman, M. J.;Jones, R. R. M.; Johnson, J. S., J r . J . Phys. Chem. 1986,90,6492. (28)Tanford, C. J . Phys. Chem. 1972,76,3020.
p is the cosine of the angle between q and the direction
of the major axis. ec,esh, and esolare the scatteringlength densities of the core, shell, and solvent, respectively, and jl is the first-order Bessel function. The amplitude factor is averaged over all orientations by
A parameter optimization routine is used to determine the best set of parameters by minimizingz2.I3 Confidence limits for the estimated model parameters are determined by a statistical analysis technique called b o o t ~ t r a p p i n g . ~ ~ , ~ ~ In this method, Monte Carlo simulations are used to create new spectra from the spectrum measured experimentally.31 This is accomplished by randomly selecting a measured error value (dT)without regard to its q value, and then adding or subtracting dZ to the original Zexp. The q value of the new Zexp is the same as the original Zexp so that the general shape of the simulated spectra is preserved. A new set of parameters is then determined by minimizing x2 for the newly simulated Zexp. Repeating this procedure 100 times produces a distribution of parameter values from which a confidence interval is determined. The 95% confidence intervals are reported without regard to the distribution of other parameters.
Results All compositions are reported as mole fraction of aggregated DTAB ( X I ) at constant total surfactant concentration (mol/L). The one-phase boundary for mixtures of DTAB and DDAB in D2O (Figure 2) grows as the temperature increases from 25 to 60 "C (beyond the isotropic micellar boundaries various lyotropic liquid crystalline phases form). DTAB-DDAJ3 mixed micelle samples were made a t total surfactant concentrations of 0.2 and 0.4 M and at four mixed surfactant concentrations, x1 = 0.70,0.80,0.90,1.0, for SANS measurements (Figure 2). In addition, DdTAB-DDAB mixed micelles were made (29)Efron, B.;Tibshirani, R. Statistical Sci. 1986,I (l), 54. (30) LBger, C.; Politis, D. N.; Romano, J. P. Technometrics 1992,34 (4),378. (31)Press, W.H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes: TheArt ofscientific Computing (Fortran Version); Cambridge University: New York, 1990;Chapter 14.
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490 Langmuir, Vol. 11, No. 2, 1995
DT
Figure 2. The phase behavior of DTAB and DDAB by weight in deuterium oxide at 25 and 60 "C. The lines are the limits of the isotropic phase (la); samples with compositions in the shaded area contain several phases. Open circles represent the concentrationsmeasured at 0.2 M and open squares those measured at 0.4 M.
Discussion
10 -
x
." v1
C
1 :-
e
c
c.
.I I
.o1
i1
1
8
x
0.70
0.80 i
0.90
1
.oo
i
1
.01
to values determined for the hydrogenated sample at X I = 0.90 and 0.80. Excellent fits are obtained with only one fitting parameter, B , the incoherent scattering (Table 2). In the case of X I = 0.70, the fits for the DdTAB-DDAB mixture are much worse because the model fails at this composition. Similar trends are observed in the results from fitting scattering spectra a t a total surfactant concentration of 0.4 M a t 25 "C. However, while the model adequately describes the spectra for x1 = 1.00 and 0.90, it underestimates the peak heights and low q intensity for X I = 0.80 and 0.70. The modeling for x1 = 1.00 and 0.90 suggests lower fractions of associated counterions and larger aggregation numbers than for equivalent 0.2 M compositions (Table 1).For pure DTAB micelles, the size increase is slight; however, as DDAB is incorporated into the micelle, the size increases more significantly. In Figure 6, the spectra for 0.4 M solutions a t X I = 1.00, 0.90, 0.80, and 0.70 are shown a t 60 "C. Table 1shows that the micelle axial ratios and sizes are smaller than those a t 25 "C and the fraction of associated counterions is lower. The number of methylene groups in the core of a pure DTAB micelle decreases with increasing temperature, but the same trend of tighter packing in the core with increasing DDAB concentrations also holds a t 60 "C. Again the model begins to fail for x1 = 0.70.
.I
1
q(llh
Figure 3. SANS spectra of 0.2 M surfactant solutions at 25 "Cshowingthe effect of decreasing DTAB concentrationon the mixed DTAB-DDAB micelles. Symbols represent the measured intensity and lines represent the modeled intensity. x1 is the mole fraction of DTAB in the mixed micelles.
a t X I = 0.70,0.8(4,0.90, at 0.2 M total surfactant in order to test more rigorously the fitting parameters determined for the purely hydrogenated samples. The small-angle neutron scattering spectra for mixed DTAB-DDAB micellar solutions (Figure 3) at 0.2 M and 25 "Cshow interaction peaks characteristicof dispersions of charged particles. As the percentage of DTAB in the mixed micelles decreases, the position of maximum intensity (am,) shifts to lower q concurrently with a n increase in the maximum intensity. Modelingthe spectra as monodisperse prolate ellipsoids with a core-and-shell scattering length density profile (Figure 3 and Table 1) suggests that the aggregation number and axial ratio of the micelle increases with decreasingDTAB concentration. The modeling also suggests that the fraction of associated counterions increases except in the case of X I = 0.70, where this composition approaches the phase boundary. The number of methylene groups in the core, p, increases with decreasing DTAB concentration, suggesting that less methylene groupsprotrude into the shell when the doubletail DDAB is incorporated into the micelle. Shown in Figures 4 and 5 are fits of the scatteringcurves in which the contrast in the core and shell are changed by incrementally by substituting DdTAB for DTAB in the mixed micelle. The parameters Nagg,6, and p are fixed
Ideal mixing, combined with the pseudo-phase-separation model, is useful for predicting micellar composition and the amount of unaggregated surfactant for total surfactant concentrations above the cmc. Because the amount of unaggregated surfactant and the micellar composition contribute to the structure factor and scattering amplitude calculations, respectively, the fitting problem is indeterminate unless assumptions about the micellar composition and free monomer concentration are made a priori. Given the values of the mixed cmc values and the similarity of the hydrophobic tails and hydrophilic head groups, the assumptionof ideal mixing is appropriate. Model SANS spectra corresponding to several particle geometries were compared to the experimental spectra. Only prolate ellipsoids with a core-and-shell scattering length density profile captured the shape of the experimental spectra in the q-range measured for the mixed DTAB-DDAB micelles. For pure DTAB micelles a t 0.2 and 0.4 M, a model of monodisperse spheres gave good fits with equivalent fitting parameters to the ellipsoidal model except that the constant background B was 7% of the overall intensity. This is unrealistically large and indicates that the micelles either deviate from sphericity or are not monodisperse. For low values of the polydispersity (
