786
Langmuir 1990,6, 786-791
Table 111. Comparison of Mo Clusters in Acetylene Reduction. monomer* dimer trimer ethane 0.0010 0.0011 O.oO08 ethylene' 0.0018 reducing equiv 0.0040 0.0080 0.0032 a Comparisons made at a common loading of about 10 clusters/ rarticleand at pH 7. Values in the table are product quantum yields. Data from Zun-Sheng Cai, Ph.D. Thesis, University of Missouri, 1987. Ethylene formed through the Mo cluster.
are dependent on factors such as Mo loading, pH, and light intensity. Under similar conditions of loading, pH, and intensity, the Mo, is more efficient for total electron transfer than either the monomer or trimer (see Table 111). The monomer and dimer are about equally effective for the 4-e process and somewhat better than the trimeric material. In general, the potential enhancement of multielectron reduction efficiency by closely spaced Mo reducing centers as enforced by the dimer and trimer cores is not realized. The relatively low efficiency of these processes even
in the presence of a good electron donor such as PVA indicates that electron transfer to acetylene does not compete effectively with other fates of conduction band electrons. Whether the rate-limiting step is reduction of the Mo clusters by Ti(II1) or substrate binding and subsequent electron transfer cannot be determined from this study. Buildup of the blue Ti(II1) color centers during the photolysis does indicate that the rate of production of charge carriers exceeds the rates of the subsequent steps and suggests that lower intensities should increase the quantum efficiency. Acknowledgment. This work was supported in part by grants from the National Science Foundation (CBT8813146), the University of Missouri Research Council, and the Weldon Spring Endowment administered by the University of Missouri. Assistance from Professor R. Kent Murmann with preparation and purification of the Mo(IV) and MOW)aquo ions is also greatly appreciated. Registry No. TiO,, 13463-67-7; Mo,O:+, 54429-28-6; Mo30d4+,97252-76-1;poly(viny1 alcohol), 9002-89-5;acetylene, 74-86-2;ethane, 74-84-0;ethylene, 74-85-1.
From Cetyltrimethylammonium Bromide Micelles to 2-Butoxyethanol Aggregates Stabilized by Cetyltrimethylammonium Bromide Molecules: A Small-Angle Neutron-Scattering Study Francois Quirion*Pt and Maurice Driffords INRS-Energie, Varennes, Qu6bec, Canada J3X 1S2, and CEN de Saclay, 91911 Gif-sur- Yvette, Cedex France Received June 12, 1989. In Final Form: October 24, 1989 Mixed micelles of cetyltrimethylammonium bromide (CTAB) and 2-butoxyethanol (BE) are investigated through small-angle neutron scattering, and the micellar parameters are compared to those obtained for CTAB micelles in D,O at 26 OC. Although the mole ratio of BE to CTAB is kept constant at 5 or 10, the micellar parameters are not constant with respect to the total concentration (MBECTAB = M TAB + MBE). Our results show that at low concentrations the mixed aggregates resemble micelles of C%AB while at higher concentrations they behave like BE aggregates stabilized by CTAB molecules. This is supported by quasi-elastic light scattering. For the two ratios studied, it is suggested that the micellar parameters depend only on the total concentration. Around MBECTAB = 0.5, there is a transition that is consistent with an increase of the counterion binding. We suggest a dry headgroup shell for CTAB micelles while for the mixed aggregates there might be some hydration associated to BE (ND2,JNBE
-
2).
Introduction Aqueous solutions of surfactant and cosurfactant are able to dissolve large quantities of oil to form stable microemulsions. These systems have been studied extensively over the past 15 years, and reviews'*2 have been published on the subject. INRS-Energie. CEN de Saclav. (1) Prince, L. MI Microemulsions: Theory and Practice; Academic Press: New York, 1977.
0743-7463/90/2406-0786$02.50/0
Because of its name, the cosurfactant is often viewed as a passive ingredient that helps the surfactant to solubilize oil. This is in contradiction with the detergentfree microemulsions, where the role of the surfactant is played by an alcohol such as l - b ~ t a n o l 2-propan01,~~~ ,~ and 2-butoxyethano1.B Recently, Quirion et a17 have studied aqueous solutions of 2-butoxyethanol (BE) through (2) Holt, S. L. J. Dispersion Sci. Technol. 1980, 1,423. (3) Roux-Desgrangp, G.; Grolier,J.-P. E.; Villamanan,M. A.; Casanova, C . Fluid Phase Equilcb. 1986, 25, 209.
0 1990 American Chemical Society
Small-Angle Neutron-Scattering Study small-angle neutron scattering (SANS), and they concluded that BE forms aggregates similar to micelles. Durand et aL8*' came to the same conclusion for 1,2hexanediol and 1,2,3-octanetriol in water. Roux et a1.l' suggested that molecules such as 2-amino-2-methylpropanol, diethylmethylamine, and triethylamine are able to self-associate in water to form microheterogeneities similar to micelles. When such molecules are combined to a long-chain amphiphile, it is not evident which behavior will dominate over the other. For instance, Lianos and Zana" have studied the mixed micelles of cetyltrimethylammonium bromide (0.1 M CTAB) and 1butanol (0.8 M) with fluorescence probing, and they suggested that the micelles contain 15 molecules of CTAB and about 70 molecules of 1-butanol. From this composition, it becomes difficult to say that 1-butanol plays a passive role in the micellar solution. Using apparent molar volumes and heat capacities, Roux-Desgranges et d.12s u g gested that at low concentrations 1-butanol is partially solubilized in the micelles of sodium dodecyl sulfate (SDS) while at higher concentrations 1-butanol forms microaggregates stabilized by SDS. Surfactant solutions containing 1-pentanol as a cosurfactant can also form aggregates that resemble 1pentanol rather than the surfactant aggregates. From a SANS study of tetradecyltrimethylammonium bromide (TTAB) with added 1-pentanol, Zana et al.13 suggested that at low TTAB concentrations the micelles were swollen by an inner core of 1-pentanol. At higher concentrations of TTAB, Lianos and Zana" found that the micelles are gradually swollen by an inner core of 1-pentanol as the concentrations of 1-pentanol and TTAB are increased with a constant mole ratio of about 9. This is consistent with the SANS study of Hayter et al.;' who found extensive penetration of 1-pentanol within the micelles as the concentration of 1-pentanol is increased at a fixed concentration of sodium octanoate. The swelling of micelles by 1-pentanol is inherent to the behavior of 1-pentanol in water. As its solubility is exceeded, 1-pentanol forms a macroscopic phase which is gradually dispersed into small droplets in the presence of a surfactant. As the ratio of 1-pentanol to surfactant decreases, the nature of the aggregates changes toward micelles of surfactant, For micellar solutions containing a cosurfactant that is completely soluble in water, it is difficult to predict its partition between the bulk and the micelles. Rao and Verrall" and Kat0 et a1.l' have measured the ultrasonic properties of CTAB in the presence of BE over a wide range of concentration where CTAB and BE are able to (4) Lund, G.; Holt, S. L. J.Am Oil Chem. SOC.1980, 71, 264. (5) Lara, J.; Perron, G.; Desnoyera, J. E. J. Phys. Chem. 1981, 85, 1600. (6).Kilpatrick, P. K.; Davis, H. T.; Scriven, L. E.; Miller, W. G. J. Colloid Interface Sci. 1987, 118, 270. (7) Quirion, F.; Magid, L. J.; Drifford, M. Langmuir 1990, 6, 244-
-
349 _".
(8)Durand, R. R.; Hajji, S. M.; Coudert, R.; Cao, A.; Taillandier, E. J . Phys. Chem. 1988,92,1222. (9) Hajji, S. M.; Errahmani, M. B.; Coudert, R.; Durand, R. R.; Taillandier, E. J. Phys. Chem. 1989,93, 4819. (10) Roux, G.; Roberts, D.; Perron, G.; Desnoyers, J. E. J. Solution Chem. 1980,9,629. (11)Lianos, P.; Zana, R. Chem. Phys. Lett. 1980, 72, 171. (12) Roux-Desgranges, G.; Roux, A. H.; Grolier, J.-P. E.; Viallard, A. J. Solution Chem. 1982, J I , 357. (13) Zana, R.; Picot, C.; Duplessix, R. J. Colloid Interface Sci. 1983, 93,43. (14) Lianos, P.; Zana, R. J. Colloid Interface Sci. 1984,101, 587. (15)Hayter, J. B.; Hayoun, M.; Zemb, T. Colloid Polym. Sci. 1984, 262, 798. (16) b o , N. P.; Verrall, R. E. J. Phys. Chem. 1982,86,4777. (17) Kato, S.; Jobe, D.; Rao, N. P.; Ho, C.-H.; Verrall, R. E. J.Phys. Chem. 1986,90, 4167.
Langmuir, Vol. 6, No. 4, 1990 787 form aggregates in water. At low BE to CTAB ratios and below the microphase transition of BE, they observed only the exchange of BE between the bulk and the mixed micelles. At higher ratios and above the microphase transition of BE, they observed two relaxation frequencies that they associated to the behavior of BE in water, suggesting that the a gregates are similar to those of BE. Quirion and Magidgshave investigated this system through SANS for solutions of CTAB = 0.03 m with increasing BE concentration. As the ratio of BE to CTAB increases, the mole fraction of BE in the aggregates increases while the radius, the counterion binding, and the mean aggregation number of CTAB into the aggregates decrease. They suggested that the aggregates change continuously from CTAB micelles to BE aggregates stabilized by CTAB molecules. From these studies, it seems that the nature of the aggregates is related to the relative concentration of surfactant and cosurfactant. Quirion and Desnoyed' have studied the behavior of micellar solutions with a constant mole ratio of BE to CTAB of 5,10, and 20. A t low concentrations, the apparent molar volumes and heat capacities of these mixtures behave like CTAB in water while at higher concentrations the trends are similar to BE in water despite the fact that the ratio of BE to CTAB is constant. We have investigated aqueous solutions of BE and CTAB with a constant mole ratio of 5 or 10 through SANS measurements in order to obtain estimates of the size, the charge, and the composition of the aggregates. We also measured the SANS of CTAB in D,O to compare the nature of the mixed aggregates with the micelles of CTAB.
Experimental Section BE (Fisher)was fractionally distilled before use. CTAB (Aldrich) was recrystaked from acetone-methanol (80-20 v/v). Purity was checked by means of surface tension measurements, and there was no evidence of a minimum at the cmc. Mutual diffusion coefficients (DI2)were obtained by quasielastic light scattering using the green line (5145 A) of an argon ion laser coupled to a Malvern correlator. The technique is well described elsewhere." Electromotive forces were measured with a bromide-specific electrode, and surface tensions were determined by the ring method. Neutron small-angle scattering spectra were measured on the D-16 diffractometer at the high-flux reactor of the Institut Laue Langevin, Grenoble, France. Spectra were taken at two angles (6" and 13") on a 16 X 64 multidetector covering values of momemtum transfer (8)between 0.05 and 0.45 A-1. The wavelength used was 4.52 A. Samples were prepared in heavy water (D20) and measured in 2-mm pathlength optical quartz cells placed at a sample to detector distance of 1.09 m. Spectra were recorded at 26 f 1 "C and corrected for absorption and detector efficiency. They were put on an absolute scale using the incoherent scattering of waterz1and analyzed from 0.05 to 0.25 A-' with a nonlinear nonweighted least-squares fitting procedure based on Bevington's CUR FIT.^^ SANS Analysis The experimental scattered intensity (I(Q)EX) has a coherent contribution (I(@,) and a flat incoherent backgroung (B). B can be calculated from the incoherent scattering of the solution or from the Porod limit at high ~
~~~~
(18)Quirion, F.; Magid, L. J. J. Phys. Chem. 1986,90, 5193.
(19) Quirion, F.; Desnoyers, J. E. J. Colloid Interface Sci. 1987,115, 176. (20) Candau, J. S. In Surfactant solutions: New methods of inuestigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; Vol. 22, p 147. (21) Harris, N. H. Ph.D. Thesis, Oxford University, 1980. (22) Bevington, P. R. Data reduction and error analysis for the physical sciences; McCraw-Hill: New York, 1969; Chapter 11.
788 Langmuir, Vol. 6, No. 4, 1990 QVz3The Porod limit has the advantage of giving the experimental background (BEX),so we do not need an additional parameter to account for the residual incoherent scattering. We evaluated BE, from the slope of 1(Q)ExQ4vs Q4 in the range 0.35 < Q < 0.4 A-'. BEX was subtracted from Z(Q)EX to get Z(Q),. For monodisperse particles, Z(Q), is given by
JA(F(Q))2S(Q) = I(Q)Ex-BEx
Z(Q),
(1)
A = N p b p - PS)~V;
(2)
Np = ( M c T -~CmC)/NcTAB
(3)
I
Vp
= NmmVcTA + NBEVBE = 47Rp3/3
5 -
(4)
(5) PP = (NCTAB~CTA +NBE~BE)/~P where J is a scaling parameter that allows for uncertainties in the calibration for absolute intensity, A is the amplitude, F(Q) is the form factor, and S(Q) is the structure factor. F(Q)is related to the shape and the size of the particles in solution. For a homogeneous sphere of radius Rp, the form factor is
F(Q)= 3[sin (QRp)- QRp cos (QRP)I/(QRP)~ (6) For S(Q), we used the rescaled mean spherical approximation (RMSA) derived by Hayter et al.24*25The Coulombic repulsions between the particles enhance the structure of the solution, which results in a maximum in the scattered intensity. For charged aggregates, these repulsions depend on the ionic strength, the size, the volume fraction, and the net charge of the aggregates (2). The amplitude is related to the scattering length density (p), the volume of the aggregates (V,), and the number particle density of the aggregates (Np).For dry aggregates, it is calculated with NCTmand N B E assuming constant values of the molecular volume (V) and scattering length ( b ) of the species. For BE in the aggregates, we used the molecular volume of pure BEz6 (VBE). When BE is added to solutions that contain DzO, the hydroxyl proton is substituted for deuterium. Protonation of the solvent and the distribution of BE between the aggregates and the solvent were taken into account for the evaluation of the scattering length density of the solvent (ps). The volume fraction of BE in the solvent was calculated with the molecular volume of BE at infinite dilution in water.z6 Using a bromide-specific electrode, we obtained 7.8 X M for the cmc of CTAB in water at 25 "C. For and BECTAB-5 and BECTAB-10, we obtained 3.9 X M, respectively. These values correspond to 7.5 X and 7.5 X an aqueous molarity of CTAB of 7.8 X lo4, respectively. However, measurements in aqueous solutions of BE showed that the cmc of CTAB decreases with increasing concentrations of BE. Moreover, the addition of BE to D20 might decrease the dielectric constant (e) of the solvent. We checked these effects by using cmc = 0 or by decreasing e by lo%, and in both cases the effect on the fitted parameters was negligible. Thus, we assumed constant values (cmc = 7.8 X and e = 77.6). For CTAB, we used the partial molecular volume in the ~
I
I
-
OV
O C 0
a(a-1)
0.25
Figure 1. SANS spectra: V, MCTm = 0.044; 0,McTm = 0.053 and M B = 0.264; 0 , M, AB = 0.053 and M, = 0.512; in D,O a t 26 -: intensity cdculated with eqs 1-6 using the optimal set of parameters obtained through the least-squares pro-
"8
cedure.
micellar phase2' ( VCTm). Since the model assumes that the bromide counterions do not contribute significantly to the scattered intensity, we subtracted the molecular volume of the hydrated bromide ionz8( VBr) from VcTm to get VcTA. Table I summarizes the molecular volumes and scattering lengths that were used for the calculation of the amplitude, and Figure 1 shows the experimental and calculated intensity for McTm 0.05 with mole ratios of BE to CTAB of 0,5, and 10.
-
Results Aqueous Solutions of CTAB. Experimental intensities for aqueous solutions of CTAB were fitted without the RMSA from 0.07 to 0.25 A-1 where S(Q) is almost unity. Values of J and NCTmobtained from the fits are summarized in Table I1 for CTAB in D,O with and without added KBr at 26 "C. J remains about constant at a value of 1.15, suggesting a systematic error in the calibration procedure or in the calculation of the amplitude. Using NCTAB and VCTA, we calculated the radius of the sphere having the same volume as the micelles (Rp). Extrapolation at the cmc leads to 132 and 25.9 A for NCTAB and RP in fair agreement with 115 and 26.5 A obtained by Quirion and Magid2' with a prolate ellipsoid model coupled with the RMSA for which the volume of the bromide ions was included in the micellar volume. Assuming that 25.9 A corresponds to the minor semiaxis (a) of a prolate ellipsoid, we estimated the axial ratio ( b / a ) with b / a = (Rp/aI3 (7) where b is the major semiaxis. We also calculated the
~~
(23) Cabane, B. In Surfactant solutions: New methods of inuestigation; Zana, R., Ed.; Marcel Dekker: New York, 1987; Vol22, p 57. (24) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42,109. (25) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982,46, 651. (26) Roux, G.; Perron, G.; Desnoyers, J. E. J. Solution Chem. 1978, 7, 639.
I
(27) Quirion, F.; Desnoyers, J. E. J. Colloid Interface Sci. 1986, 112, 565. (28) Desnoyers, J. E.; Jolicoeur, C. In Modern aspects of electrochemistry;Bockris, J. OM., Conway, B., Eds; Plenum Press: New York, 1969 VOl. 5, p 1. (29) Quirion, F.; Magid, L. J. J.Phys. Chem. 1986,90, 5435.
Small-Angle Neutron-Scattering Study
Langmuir, Vol. 6, No. 4, 1990 789
Table 11. Results of the SANS Analysis with a Dry Model for CTAB in D,O at 26 OC with and without Added K B P McTAB,
mol L-'
0.0113
0.0279
0.0444
0.0584 1.11 138 26.25 1.04 53.5
0.0649 1.16 143 26.59 1.08 53.0
0.0672 1.15 153 27.16 1.15 51.8
MK mol L-'
B,,!
cm-1
J
NCT
Rp,C3B b lad AHG~'A2
Fitting parameters are J and NCTm. pp = -0.39 X 10- A-2, ps = 6.37 X 10" Porod limit at high Q. From eq 4 with NBE= 0. From eq 7. e From eqs 8-10.
0.0114 0.034 0.0595 1.09 227 31.00 1.72 47.5
0.0265 0.033 0.0653 1.18 220 30.67 1.66 47.7
A-*, cmc = 7.8 X lo4,
c
0.0422 0.032 0.0762 1.18 221 30.72 1.67 47.7
= 77.6. Obtained from the
Table 111. Results of the SANS Analysis with a Dry Model for Aqueous Solutions of BE and CTAB with a Constant Mole Ratio of 5 and 10 at 26 OC' mol L-' mol L-' Be:? cm-I McTAB,
M J
NCTAB
5:;
A
0.0107 0.0545 0.0641 1.11' 106 43 25.30
2 A
cy;;
pp3
A-2
76 -2.14 6.33
0.0527 0.2639 0.1Ooo 0.80 48 114 23.03 18 139 0.12 6.25
0.1448 0.7241 0.1808 1.00 40 79 21.10 16 140 -0.27 6.00
0.0112 0.1117 0.0695 l.llC 79 55 23.69 89 -2.10 6.29
0.0525 0.5117 0.1424 0.83 29 92 20.47 15 182 0.71 6.08
0.1345 1.3367 0.2430 1.56 26 44 17.88 9 155 -0.58 5.48
10 t = 77.6. Obtained from the Porod limit at high Q. J a Fitting parameters are J, NCTm, N B E , and 2. cmc of CTAB = 7.8 X was fixed to the value obtained for MCTAB= 0.0113 in Table 11. From eq 4. e From eq 8 using the area of a sphere of radius R,. 'From eq 5. PS,
area per headgroup (AHG) at the interface between the polar heads and the core. For a prolate ellipsoid, the surface area (S)is related to the eccentricity ( E )and the axial ratio:
AHG= SINCTM S = 2 ~ ( -a tHG)'([l+ [(b/a) sin-' ( E ) ] / E )
E = [(b/a)2- l]'/'/(b/a)
(8)
(9)
(10)
where t is the thickness of the headgroup shell. TabonyBG and Zana et al.13 studied the spherical micelles of TTAB, and they report an experimental tHG of 2.0 and 1.6 A,respectively. Assuming a prolate ellipsoid with found t,G = 2.1 A for CTAB-d, a dry shell, Berr et in D20 at 50 "C. If one assumes that the interface between the polar heads and the core is located in the middle of the CH,-N bond, a thickness of 2 A is consistent with the geometric diameter of a trimethylammonium group. Table I1 reports bla and A H G calculated with a = 25.9 A and tHG = 2 A. AH, decreases slightly with surfactant concentration, and the extrapolation to the cmc gives 54.3 A' in good agreement with 55.4 A2, which we obtained from the surface tension of CTAB in water at 25 "C. In the presence of KBr, the micelles have a prolate shape with an axial ratio of 1.7 which results in a smaller area per headgroup (AHG = 47.7 A2). This is consistent with the screening of the Coulombic repulsions between the headgroups in the presence of added salt. Aqueous Solutions of BECTAB. Using the model described above, we obtained J, NCTAB, N B E , and 2 as fitting parameters at a constant mole ratio of BE to CTAB of 5 and 10 (BECTAB-5 and BECTAB-10) at 26 "C. The results are presented in Table 111. From these parameters, we calculated the fractional charge of the aggregates (a= Z/NC,), the mole fraction of BE in the aggregates ( X B E , M ) , the area per headgroup of CTAB (30) Tabony, J. Mol. Phys. 1984,51,975. (31)Berr, S. 5.; Caponetti, E.; Johnson, J. S.,Jr.; Jones, R. H.; Magid,
L. J. J . Phys. Chem. 1986,90, 5766.
0
MBECTAB (mol I-')
1.5
Figure 2. Suggested trends of the micellar parameters obtained from the SANS analysis: 0 , BECTAB-5; 0,BECTAB-10; 0 , CTAB micelles at the cmc (see text) in D 0 at 26 "C. 0: results of Quirion and Magid for mole ratios of b E to CTAB of 5 and 10 (from ref 18).
(ACTAB),and Rp. They are plotted against the molarity of BECTAB ( M B E C T . B = M B E + MCTAB) in Figure 2. The first observation is that the trends are the same for BECTAB-5 and BECTAB-10. Moreover, at a given total concentration, the absolute value of the parameters seems to be independent of the mole ratio of BE to CTAB. This behavior has been observed by Kat0 et al.,17 who measured the ultrasonic properties of BECTAB at mole ratios of BE to CTAB ranging from 6 to 63. In the range 0.5 < MBECTAB < 6.0, their relaxation frequencies fall on the same line irrespective of the ratio of BE to CTAB. On this basis, we have drawn a possible trend for each parameters assuming that the micellar properties depend only on MBECTAm Data obtained by Quirion and Magid" are compared to these trends, and the
Quirion and Drifford
790 Langmuir, Vol. 6, No. 4, 1990
agreement is very good except for XBE,M, where the slopes are the same but the absolute values are shifted. As MBECTAB approaches zero, NCTAB, Rp, and a tend to the values of CTAB at the cmc. As the concentration increases, N C T A B and R, decrease monotonically, suggesting that the internal packing of the CTAB chains is changed in the presence of BE to allow for a smaller radius. This structural change has certainly an effect on tHG, but we have no means to evaluate it. For this reason, ACTAB was calculated with the area of the sphere at a distance RP from the center. A t MBECTAB = 0, ACTAB extrapolates to about 65 A', in good agreement with 63.8 A' calculated with the overall radius of CTAB micelles at the cmc. AH,, and CY increase in As M B E C T q B increases, XB accordance with other studieJB4 dealing with the effect of alcohols on the micelles of ionic surfactants. In the and a start to decrease, range 0.4 < MBECTAB < 0.6, A,, suggesting an increase in the counterion binding which would allow for a tighter packing of the ionic headgroups. For the same systems, Quirion and De~noyers'~ have observed an increase of the apparent molar heat capacity of CTAB in the range 0.2 < MBECTAB < 0.4, which they associated to an increase in the counterion binding. The shift of the concentration at which the transition occurs is probably due to the solvent isotope effect.
Discussion Aqueous Solutions of CTAB. Our values of N C T A B and bla agree to within 10% with those obtained by Quirion and Magid" with a prolate ellipsoid model coupled with the RMSA. This accordance shows that for relatively low concentrations of CTAB the analysis of SANS data at low Q with the RMSA or at higher Q without the RMSA leads to the same results within experimental error. We found good agreement between values of AH, from SANS and from surface tension measurements. However, these values differ substantially from other values reported in the literature. For a spherical object, the area depends on the distance from the center and one has to evaluate the location of the interface between the headgroup and the core in order to compare AH, with the results obtained by surface tension measurements. For instance, using the overall radius, Tabony30 reports AHG = 66 A' for the micelles of TTAB while calculation with the core radius leads to 55.3 A,. Similarily, Candau and Zana3' obtained 77 A' by using the hydrodynamic radius of TTAB in 0.1 M KBr. For these spherical micelles, they suggest a hydration layer of 1.9 A. Subtracting this value along with the thickness of the headgroup layer ( 2 A) leads to A,, = 56.3 A' at the cmc. From the micellar parameters obtained by Berr et aL31 (with a dry shell model), we calculated AH, = 56.6 A' for CTAB-$ in D,O at 50 "C. All these values are in good agreement with those we obtained from SANS analysis and surface tension. This supports our choice of 2 A for the thickness of the headgroup shell. From SANS measurements of TTAB in D,O, Tabony30found that the headgroup shell was almost dry. Berr et al.31conducted a similar study on the micelles of CTAB-dg in D,O at 50 OC. Although they suggest a wet headgroup shell, they were not able to distinguish between (32) a n a , R.;Yiv, S.; Strazielle, C.; Lianoe, P. J. Colloid Interface Sci. 1981, 80,208. (33)Oakenfull, D.J. Colloid Interface Sci. 1982,88, 562. (34)Bahadur.. P.: . Sastrv, N. V.: Chand, S. Tenside Detergents 1984, 21,84.
(35) Candau, S.J.; Zana, R. J. Colloid Interface Sci. 1981,84, 206.
t
1
e e
\e
= I
'I-
a
tMBECTAB (mol I")
2.5 Figure 3. Apparent mutual diffusion coefficients (D,) obtained by quasi-elastic light scattering for BECTAB-10 in 0 a t 25 O C : -, trend of D,,for BE in H,O a t 25 "C reported %y Quirion e t al. (from ref 7 ) . 0
k
the fit obtained with a dry shell and the fit obtained with a wet shell. From A,, = 54.3 A' and tHG = 2 A, we calculated 118 A3 for the volume of the shell that contains one headgroup. This leaves enough space for the trimethylammonium (102.3 A3),31 but it cannot accomodate one D,O molecule (30.0 A3). On this basis, we agree with Tabony that the trimethylammonium layer is almost dry. The hydration layer would be associated with the counterion layer adsorbed at the surface of the micelles but its contrast with the solvent would be too low to contribute significantly to the scattered intensity. Aqueous Solutions of BECTAB. From our results for aqueous solutions of BECTAB, we find that the aggregates change from micelles of CTAB at low concentrations to aggregates of BE stabilized by CTAB molecules. From emf measurements of BECTAB-5 and BECTAB10, we found that the cmc of CTAB is not affected by the presence of BE. This supports the idea that at low concentrations the aggregates resemble those of CTAB in water. Figure 3 shows the apparent mutual diffusion of BECTAB-10 in water at 25 "C. Our coefficients (D,,) results are compared with the D,, of BE in water reported by Quirion et al.' D,, decreases continuously in the same fashion that BE does. For MBECTAB < 0.7, the trend of D,, suggests the presence of aggregates for BECTAB-10 but not for BE in water. This is consistent with the presence of mixed micelles of BE and CTAB. At higher concentrations, both curves have the same trends. The higher values of D,, for BECTAB-10 are probably related to Coulombic repulsions due to the presence of CTAB molecules into the aggregates. This behavior is consistent with aggregates of BE stabilized by CTAB molecules. The changes in the micellar parameters are continuous except for XBE,M, a, and ACTAB, where a break is observed around MBBCTAB = 0.55. This break is consistent with an increase in counterion binding that may be related to a dielectric effect in the interfacial region of the aggregates that contain a large amount of BE. For TTAB at 0.05 M in the presence of BE, Bahadur et found that the specific conductance goes through a maximum around M B E = 0.7, and the decrease of the conductance at higher concentrations is consistent with an increase in the counterion binding. As expected, the increase in the counterion binding is associated to a decrease of the area per headgroup of CTAB due to weaker electrostatic repulsions. Thus, the leveling of X B E , M at M,EcTA, > 0.55 could be related to a decrease of the free volume available for BE molecules, which would be
Langmuir, Vol. 6, No. 4, 1990 791
Small-Angle Neutron-Scattering Study the consequence of the tighter packing within the aggregates. From the micellar parameters at MBECTAH < 0.55, we have calculated the mole fraction of' BE in the aqueous phase (XBE,w) in order to evaluate the partition coefficient of BE (KBE) between the aggregates and the solvent. XBE,, and XBE,, increase linearily with MBECTAB, and we used the slopes to get KBE. KBE=
(dXBE,M/dMBECTAB) (dXBE,W/
(11)
gested that the mole ratio of water to CTAB within the aggregates was about 9 for MBECTAB around 8 M with a ratio of BE to CTAB of about 6. From the values of N,y,H, N H E , and R obtained with the wet model, we get 3.9 and 3.6 for the ratio of D20 to CTAB at MBECTAB 0.31 and 0.56 for RE to CTAB ratios of 5 and 10, respectively. Both studies report rough estimates of the hydration of the mixed aggregates, and the agreement is fair. The differences are probably related to concentration and solvent isotope effects.
dMBECTAB)
This relation is valid if both XBE "I and XBE extrapolate to zero at MBEcT,B = 0. This is not the case for XBE,M, but com arison of our results with those of Quirion and Magid' ?l shows that the slope is the same. Moreover, the fact that all other micellar parameters extrapolate to those of CTAB in D20 suggests that the micelles contain almost no BE at infinite dilution. With this in mind, our values for XBE,, are probably not absolute, but the trend seems to be realistic. The error on the slopes is large, and eq 11 leads to KBE = 148 f 40, in fair agreement with 126 f 26 obtained by Quirion and Magid." On the basis of the low solubility of CTAB in BE, Kat0 et al.17 suggested that the mixed micelles must be "relatively water-rich". Assuming that the water molecules are homogeneously distributed within the aggregates, we /-,, have evaluated the hydration number of BE ( R = ND NBE). For this, we have to assume that the scattered intensity is absolute (J = I), and we introduce the parameter R as a variable. Vp and pp are calculated by adding the contribution of D20 to the volume and the scattering length deiisity of the aggregates. Using this procedure, we obtained R = 2.1 and 1.4 and NBE = 89 and 74 for MCTAB = 0.05 in the presence of MBE = 0.26 and 0.51, respectively. The other micellar parameters were identical with those found with the dry model except for XBE,M. The extent of hydration found with the wet model scales quite well with the hydration of BE aggregates reported by Quirion et al.7 ( R = 4-6). Assuming that our values of R are correct, our results suggest that in the presence of CTAB the aggregates of BE are dehydrated to some extent. However, one must keep in mind that these values are only rough estimates. There is no way to distinguish between the dry and the wet model because it is impossible to get the real value of the correction factor (4 related to the absolute scaling of the scattered intensity. From their ultrasonic data, Kat0 et al." have sug-
Conclusion Within experimental error, the analysis of SANS spectra of CTAB micelles in the range of Q where S(Q) is almost unity leads to the same aggregation numbers and axial ratios as the analysis at lower Q with the RMSA. Interpretation of the area per headgroup coupled with a headgroup thickness of 2 A suggests that the shell containing the trimethylammonium groups cannot accomodate water. For mixtures of BE and CTAB at a constant mole ratio of 5 or 10, the aggregates change gradually from CTAB micelles (low concentrations) to BE aggregates stabilized by CTAB molecules (high concentrations). At a given total concentration, the micellar parameters seem to be the same for both ratios. Around a total concentration of 0.5 M, the composition and the fractional charge of the aggregates and the area per headgroup of CTAB show a break consistent with an increase in the counterion binding. Analysis with a wet model suggests that the mixed aggregates are hydrated to some extent. These results show that in some conditions the inherent properties of the cosurfactant dominate over those of the surfactant. With this in mind, a cosurfactant is inot necessarily a helping ingredient, and the name "cosurfactant" represents a limitation of the role of these molecules in micellar solutions. We believe that the properties of aqueous micellar solutions of surfactant and cosur,factant are governed by their respective behavior in water.
Acknowledgment. We are grateful to Dr. Jim Tabony, %who adapted the D-16 diffractometer for SANS measurements, and to Dr. Arnaud DeGeyer, who put the spectra on an absolute scale. F.Q. thanks the Natural Science and Engeneering Research Council of Canada and the Quebec-France exchange program for financial support. Registry No.
BE,111-76-2;CTAB,57-09-0.
