5472
J. Phys. Chem. 1983, 87, 5472-5478
complexes of monensin present lower stability constants than predicted by cation solvation alone, as well as higher dissociation rates and lower formation rate constants. These lower formation rates have been observed, for example, in metal complexes with cryptands and the naturally occurring macrocyclic antibiotic valinomycin, as we have pointed out in a previous work.1°
Registry No. AgMon, 87568-70-5;monensin, 17090-79-8;silver ion, 14701-21-4 (2,2,2)c~ptand,23978-09-8.
Supplementary Material Available: Experimental data from the stability constant and rate constant measurements (3 pages). Ordering information is given on any current masthead page.
Aggregation of Sulfosuccinate Surfactants in Water L. J. Magid," K. A. Daw, P. D. Butler, and R. B. Qulncy Department of Chemlstry, Unlversl~of Tennessee, Knoxville, Tennesse 37996- 1600 (Received: February 7, 1983; In Final Form: March 8, 1983)
We have investigated the aggregation of sodium di-n-alkyl sulfosuccinates in water (HzO and DzOat 45 "C). A self-consistentpicture of the dependence of sodium ion binding on surfactant concentration is obtained from emf measurements,conductimetry,and small-angle neutron scattering (SANS) measurements. The concentration dependence of the micellar aggregation number for the sulfosuccinates and related double-tailed surfactants depends markedly on surfactant solubility. A sphere-to-disk transition in micellar shape, which might have been expected as a precursor to formation of a lamellar mesophase, was not observed as the surfactant concentration was increased. Introduction The aggregation in aqueous solutions of ionic surfactants having two alkyl chains is frequently ~haracterizedl-~ by a broadened critical micelle concentration (cmc) region, lower aggregation numbers, and a higher degree of counterion dissociation compared to that of single-chain surfactants. Many of these surfactants show limited solubility (to form an isotropic micellar solution) in water; the first lyotropic liquid crystalline mesophase encountered as the surfactant concentration in water increases is lamellar. Thus, one might expect, on the basis of the predictions of , ~ douIsraelachvili et ala's packing constraint t h e ~ r ythat ble-tailed surfactants would undergo a sphere-to-disk shape transition as the boundary between isotropic micellar solution (L,) and the biphasic dispersion of Ll plus lamellar liquid crystal (LC) is approached. (Disk micelles are the lamellar mesophase precursors, just as rod micelles are the hexagonal mesophase percursors). It is also of interest to ask whether there is a relationship between surfactant solubility (extent of the L1 region) and the dependence of average aggregation number on surfactant concentration. Reliable micellar aggregation numbers can be obtained at finite surfactant concentrations from small-anglescattering measurements provided micelle-micelle interactions are accounted for properly. R e c e n t l p it has become possible to calculate the static structure factor explicitly for the case of spherical macroions interacting through a screened Coulomb potential. In this paper we present SANS data for DzOsolutions of sodium di-n-alkyl sulfosuccinates (I), where the alkyl (1) Miller, M. L.; Dixon,J. K.J.Colloid Interface Sci. 1968,13,411-7. (2) Evans, H. C. J. Chem. SOC.1966, 579. (3) Tausk, R. J. M.; Karmiggelt, J.; Oudshoorn, C.; Overbeek, J. Th. G. Biophys. Chem. 1974,1,175-83. (4) Magid, L. J.; Shaver, R. J.; Gulari, E.; Bedwell, B.; Alkhafaji, S. Prepr., Diu.Pet. Chem., Am. Chem. SOC.1981,26,93-109. (5) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J.Chem. SOC., Faraday Trans. 2 1976, 72, 1525-68. (6) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109-18. (7) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 651. (8) Hayter, J. B.; Penfold, J. Chem. SOC.,Faraday Trans. 11981,77, 1851-63.
0022-3~54/a3/20a7-5472$01.5o/o
ROCCHzCHCOR
I
SO3Na
1
tails are either n-hexyl or n-octyl groups. We are able to evaluate the concentration dependence of their aggregation numbers and to draw certain conclusions regarding the internal structure of their micelles. Experimental Section Surfactants. The c6 and closulfosuccinates were prepared by the sulfonation (NaHS03)of the corresponding di-n-alkyl maleates in a mixed solvent consisting of 1,2propanediol, water, and chloroform (reaction time of 6 h at reflux). The maleates were prepared according to the method of Kitahara and K ~ n - n o . ~After sulfonation, solvents were removed by vacuum distillation, and the resulting light yellow solid was taken up in dry methanol, treated with activated charcoal, and fiitered through Celite. (This filtration also removes unreacted NaHS03.) The methanol was then evaporated and the surfactant recrystallized from methanol-water. The c8 sulfosuccinate, received as an approximately 50% dispersion in 1,2propanediol from American Cyanamid, was purified in the same manner. Anal. Calcd for c8: C, 54.04; H, 8.39. Found: C, 53.67; H, 8.64. Anal. Calcd for Clo: C, 57.57; H, 9.06. Found: C, 57.35; H, 9.07. For the C6 sulfosuccinate, elemental analysis of different batches indicated the presence of 1-2 mol of HzO per mole of surfactant. However, the cmc's determined by surface tension at 25 "C and by emf measurements and conductimetry at 45 "C agree well with previous determinations at other temperatures.l The surface tensions of our c6 sulfosuccinate solutions having concentrations close to the cmc show no evidence of the minimum observed with impure sulfosuccinates.1° (9) Kon-no, K.; Kitahara, A. J. Colloid Interface Sci. 1971,35,636-42.
0 1983 American Chemical Society
Aggregation of Sulfosuccinate Surfactants in Water
The Journal of Physical Chemistry, Vol. 87, No. 26, 1983
Phase Diagrams. Surfactant-water samples were prepared by weight and sealed in glass ampules. Phase boundaries were identified visually. Particularly in the case of the c6 material, supercooling of solutions and biphasic dispersions was found to be facile; all transition temperatures reported here were obtained by warming rather than cooling the samples. EMF Measurements. Two electrode systems were used (1)an Orion 94-11 sodium electrode with an Orion 90-02 double junction reference electrode; (2) a Fisher 13-639-20 sodium electrode with a Corning Ag/AgCl double junction reference electrode (Fisher 13-641-621). Regeneration of the sodium electrodes was performed as needed (1) according to Orion's specifications and (2) by soaking the electrode in methanol followed by 0.1 M NaC1. In the case of the Corning reference electrode, the inner filling solution was 4 M KC1; the outer filling solutions were (1)0.1 M NH4C1or (2) 0.1 M ",NO,. Surfactant solutions were prepared by adding aliquots of a surfactant stock solution to distilled water; potential readings were recorded after allowing 3-5 min for the resulting solutions to equilibrate at 45.0 f 0.1 "C. All solutions were stirred magnetically during the measurements. Conductimetry. The water used to prepare the solutions was obtained from distillation using a Kontes WS still, followed by a simple redistillation in which an Ascaritefilled drying tube was used to prevent the introduction of COP The water's specific conductivity was (1.0-1.3) X lo4 S cm-l at 45.00 f 0.01 OC (oil thermostat). A 500-mL Kraus-Erlenmeyer conductivity cell (cell constant was 0.5418) was used; samples were diluted in the cell by adding weighed aliquots of water. Resistance measurements were made at 1 and 3 kHz (no frequency dependence was noted) using a Beckman RC-18A conductivity bridge, having an accuracy of f0.05%. SANS Measurements. Neutron-scattering measurements were performed with the 30-m (source-to-detector) SANS instrument of the National Center for Small Angle Scattering Research, located at the High Flux Isotope Reactor, Oak Ridge National Laboratory. Scattered intensities were recorded in the Q range 0.02-0.20 A-l; Q = (47r/X) sin 0 , where 20 is the scattering angle and X (4.75 A) is the neutron wavelength. The samples were contained in quartz spectrophotometric cells of 5-mm path length; the cells were thermostated at 45.0 f 0.1 "C by means of circulation from an external bath. Scattering from samples and the D20 solvent (Norell) was corrected for detector background and sensitivity, empty cell scattering, (computed) incoherent scattering, and sample transmission. Solvent intensity was subtracted from that of the sample at each position. These differences were converted to radial-average intensities vs. Q and absolute cross sections dX/d!l [=I(&)] in cm-' were computed from calibrations based on the known scattering from pure water or from a vanadium single crystal. The quality of the fits of our scattering curves achieved by applying Hayter and Penfold's m o d e P for the computation of the solutions' structure factors may be assessed by considering the average percent deviation per data point. This ranged from 2.3% to 12.3%, except at the highest surfactant concentrations studied. For 0.4 M c6 sulfosuccinate, the value was 31%.
80
Results and Discussion Phase Diagrams. Figure 1shows partial phase diagrams for the Cg, C8, and Clo sulfosuccinates in water. The (10)Williams, E. F.; Woodberry, N. T.; Dixon,J. K. J. Colloid Sci. 1957,12,452-9.
5473
- i
hydrofed solid t soln
od0
I 10
I
20
-1
1
I
30
40
"
1 250
450
w t % Sulfosuccinate
Figure 1. Phase diagrams for the sulfosuccinates in water solutions:
Clo (H); C8 (0);C8 (A).L1 is an isotropic solution region; L1 4- LC is a biphasic dispersion, and the liquid crystal (LC) is lamellar.
melting points (to a biphasic dispersion) of the hydrated solid surfactants were 16,32, and 49.5 "C respectively; the first-formed liquid crystal is lamellar.'l The surfactant L, + LC biphasic dispersion concentrations at the L, transition at 45 "C are as follows: Cg, 1.2 M (extrapolated); C8, 0.050 M and Clot0.0014 M. There is an isotope effect on this boundary: in the C8 case with D20 as solvent, the corresponding concentration is 0.041 M. Determination of cmc's and Counterion Binding. Emf measurements made by using the Fisher Na+ electrode for the c6 and C8 sulfosuccinates are presented in Figure 2. The breaks in the emf (mV) vs. log concentration plots occur at 0.0120 and 0.001 14 M, respectively; these breaks are associated with micellization of the surfactant. In the case of the CBsulfosuccinate, the slope of the line below the break is much greater than the theoretical slope for a 1:l electrolyte at 45 "C (a value of 63.1 mV is expected from the Nernst equation). We have observed this behavior previously4 with sodium p-(1-heptylnony1)benzenesulfonate, which is also a double-tailed surfactant of very limited solubility in water. For the c6 sulfosuccinate, the analogous slope is close (vide infra) to the Nernstian value, indicating that little if any premicellar association (at least to aggregates which bind sodium ions) is occurring. I t should be noted that in our hands the Orion 94-llA sodium ion selective electrode gave anomalous results with both surfactants: enormous shifts in potential for pre-cmc concentrations vs. the same concentrations of NaCl and/or slopes in both the pre- and post-cmc concentration regimes which were not reproducible from one set of measurements to the next. The percent counterion binding for the c6 sulfosuccinate was evaluated according to the method of Kale et a1.12 Since the surfactant did cause a shift in potential (compared to a calibration plot obtained with NaC1) of ca. 5 mV, the pre-cmc region was used to obtain Eo'and N in the equation E = Eo' + N log a (1) Activities were computed according to log a = log c (Ac1l2)/(1+ c1I2) with A equal to 0.5317 at 45 "C; concentrations are in mol/L. Counterion activities above the cmc were then determined according to
-
and the parameter
cy
a = 10*t("Eo')/N (2) (which is the fraction of dissociated
(11)Balmbra, R. R.;Clunie, J. S.; Goodman, J. F. Proc. R. SOC.London, Ser. A 1965,285,534-41. (12)Kale, K.M.;Cussler, E. L.; Evans,D. F. J.Phys. Chern. 1980,84, 593-8.
The Journal of Physical Chemlstty, Vol, 87,No. 26, 1983
5474
Magid et ai. 3.0 I
1
60
I
mV 40
LJ
20’ .X10-3
1 x 15-2
1 x 10.’
a(Mol/L)
I
oov
00
Cb
00
0 01
I 0 02 c(Mol/L)
I 0 03
0 04
b
/
t
1 x 10-4
1 10-3
1 x 10-2
c(MoI/L)
09
Figure 2. Emf vs. surfactant activity or concentration: (a) C6 sulfosuccinate; (b) CBsulfosuccinate. TABLE 1: Fraction o f Dissociated Counterions in Aqueous C, and C, Sulfosuccinate Solutions concn, 0.013 0.014 0.016 0.017 0.020 0.022
M
1 5
0 9 2 9
0.001 7 1 0.002 0 1 0.002 54 0.002 96 0.003 46 0.004 05
o(
concn,
M
C, Sulfosuccinate 0.63 0.026 0 0.65 0.029 1 0.63 0.032 8 0.62 0.035 8 0.60 0.038 8 0.60 C, Sulfosuccinate 0.46 0.004 67 0.44 0.005 32 0.41 0.005 77 0.39 0.006 27 0.37 0.006 79 0.36 0.007 50
01
0.61 0.57 0.54 0.53 0.53
0.34 0.33 0.32 0.31 0.30 0.29
counterions) was computed from (cNa+- cmc)/(c, - cmc), where C, represents the total surfactant concentration. The results are presented in Table I. Since the solutions of the c8 sulfosuccinate which were investigated were quite dilute, concentrations rather than activities were used in eq 1and 2. The values of a obtained are found in Table I; despite the markedly non-Nernstian response of the electrode to this surfactant, these values agree reasonably well with other estimates of a! (vide infra). Plots of specific conductivity vs. concentration for the c6 and c8 sulfosuccinates are given in Figure 3. Measurements were also made for the Clo sulfosuccinate, but they are not reported here, since the solutions’ conductivities showed aging effects. Its micellar region, if indeed
c(Mol/L)
Figure 3. Specific conductivity vs. concentration, with operational cmc’s marked: (a) c6 sulfosuccinate; (b) C8suifosuccinate.
it forms proper micelles at all, occurs over a very limited range of concentration (see Figure 1). We believe that the Clo compound, because of its very low solubility in water, is markedly sensitive to traces of electrolyte impurities, including Na+ ions which may be leached from glass. We4 and others13 have noted such anomalies previously in conductimetric measurements on aqueous sodium p - (1heptylnonyl)benzenesulfonate. At least two operational cmc’s may be identified for both the c6 and c8 sulfosuccinates on the basis of the specific conductivity data; in both cases the lower of the two values corresponds to the cmds obtained from the emf data. The identification of multiple break points is the result of the continuous decrease in degree of counterion dissociation with increasing surfactant concentration which is observed for these double-tailed surfactants. Values of a! were derived from the conductivity data by using Evans’ equation2 (ii - m)2 1000s2 = (1OOOS1 - ANa+)
a413
ii-m +ANa+ ii
(3)
where SI and S2are the slopes below and above the operational cmc, respectively, hNa+is the equivalent conductivity of the sodium ion (73.7 at 45 “C), ii is the average micellar aggregation number, and m is the average number of bound counterions. Hence, in Evan’s terminology, a! is (13) Frames, E. I.; Puig, J. E.; Talmon, Y.; Miller, W. G.; Scriven, L. E.; Davis, H. T. J.Phys. Chem. 1980,84, 1547-56.
The Journal of Physical Chemistry, Vol. 87, No. 26, 1983
Aggregation of Suifosuccinate Surfactants in Water
0
1
0
0 0 0 0
****
3.6
I 0 02
I 004
I 0 06
0
0
.
A
a
*
5475
0.30 M 0.20 M 0.10 M 0.07 M 0.04 M
\
1
0 08
0 10 0 OO
fi
(MOI/L~'~
0 0
Figure 4. Equivalent conductlvity vs. square root of concentration for
0
the C, suifosuccinate.
0 0
0
0
equal to 1 - (m/ri). Values of ii in the cmc region were derived from the dependence of ii on surfactant concentration, as determined from analysis of the SANS curves; the values are 25 and 34, respectively, for the C6and C8 sulfosuccinates. For the c6 sulfosuccinate,the operational cmc's (and cy values) are 0.0135 (0.523) and 0.0178 (0.460) M; for the C8 sulfosuccinate we obtain 0.001 12 (0.402) and 0.00256 (0.341) M. The cy values obtained here show qualitative agreement with those derived from the emf measurements and from literature conductivity data.14 Other investigators1 have noted that the equivalent conductivity vs. d 2plot for the C8 sulfosuccinate at 30 "C shows a shallow maximum in the cmc region; the cmc estimated from this plot was 6.4 X lo4 M. We see a slight inflection in the 45 "C data (Figure 4) at approximately the same concentration, but the main break occurs at 0.0012 M. SANS Measurements. Scattering curves for the c6 and C8 sulfosuccinates studied are presented in Figure 5. As and others8J7Jshave observed previously, the curves exhibit a pronounced interaction peak except at very low surfactant concentrations. The peak moves to higher Q as the surfactant concentration increases, because the intermicellar distance is decreasing. Provided the micelles are spherically symmetric, the absolute intensity I(&) is given by 1(Q)= PS(Q)P(Q)
(4)
where P is a proportionality constant which depends on the micelle number density and the units used for the scattering lengths, S(Q)is the static structure factor for micelle-micelle interactions, and P(Q ) is the single-particle scattering function. The structure factor S ( Q )was calculated according to the model of Hayter and co-workersG8which assumes the micelles to be monodisperse charged hard spheres (of (14) Mucharski, S.; Gerhardt, W.; Martens, C. Pol. J. Chem. 1980,54, 551-60. (15) Magid, L. J.; Triolo, R.; Johnson, J. S.; Koehler, W. C. J. Phys. Chem. 1982,86, 164-7. (16) Magid, L. J.; Triolo, R.; Gulari, E.; Bedwell, B. to be published in the "Proceedings of the International Symposium on Surfactants in Solution, Lund, Sweden, July 1982", in press. (17) Benedouch, D.;Chen, S.-H.; Koehler, W. C.; Lin, J. S. J . Chem. Phys. 1982, 76, 5022. (18) Hayter, J. B.; Zemb, T. Chem. Phys. Lett. 1982, 93,91-4.
0
.
.**
,.
o *
0.0343 M 0.0305 M 0.0214 M 0.0161 M 0.0110M
o
(b)
0
Q(A-') Flgure 5. SANS curves for (a) CB sulfosuccinate and (b) C8 sulfosuccinate.
diameter a) interacting via a screened Coulombic potential of the form
V ( x ) = P-17 exp(-h.x)/x
x
>1
(5)
The quantity equals kBT; y is a dimensionless parameter which is a function of the dielectric constant, the diameter u, the micellar surface potential, and the inverse x is Debye screening length K [K = (8~~*e21/103~izBT)1/2]; equal to r / u , with r being the center-to-center distance between the micelles. To describe the internal structure of the micelle we chose a core (of radius R,) plus shell (of thickness R2- R,) model. F(Q) [where P ( Q )= ( F ( Q ) ) 2 is ] then given by
F(Q) = V i b i - p2)Fo(QRJ + V z ( ~-2 p&Fo(QRz) (6) where pl, pz, and ps are the scattering length densities of the core, shell, and solvent, respectively; V,, = 41rR,3/3 and F o b ) = 3(sin x - x cos x ) / x 3 . The use of an additional shell (which corresponds to the model that Hayter and Penfold8 employed for sodium dodecyl sulfate) gave poorer fits. The core radii for the c6 and C8 sulfosuccinates were chosen to be 9.0 and 11.5 A, respectively, which correspond to the length of extended CH3(CH2),,chains. This assigns the carboxyl groups to the shell, which seems reasonable in view of their polarity and ability to hydrogen bond to water. The cross-sectional area per alkyl tail is 21.3 A2. The aggregation numbers for even the smallest c6 and c8
5476
The Journal of Physlcal Chemistry, Vol. 87, No. 26, 1983
Magid et al.
0 0088
0 0066
0 0044
-a
0 0022
W
I
I
I
I
+ W
$
00000
D
g 00200
. \
(b) 00150
0O f 0 0
0.0010 -
0.0050
0 0000
Q *DIAMETER 0.0136
Flgure 7. MSA fits (eq 5) to the experimental scattering curves for (a) 0.011 and (b) 0.0343 M CBsulfosuccinate. Fitted lines as in Figure 6.
0.010 2
and scattering length density (which happens to equal p1 in the model) per carbon for the CH3(CH2),chains and assign a portion (n + 1 - ALFA) of these carbons to the micellar core, with the remaining ALFA carbons per chain residing in the shell. Since VI is fixed by R1,ALFA will increase as ri increases. Both carboxyl groups, the CH(SOs-)CH2 moiety, and the bound counterions are also assumed to be located in the shell. Solvent is introduced explicitly into the shell via hydration of the sulfonate head group (hydrn no. = 4) and the Naf counterions (hydn no. = 6); some of this water may in fact be associated with the carboxyl groups as well. The values of p z and Rz depend on ri, ri - m, and ALFA and are computed by employing group volumes1gand scattering lengths.20 Figures 6 and 7 show typical results obtained by fitting eq 5 to the experimental data, with the parameters ri and m being determined with a least-squares criterion. Table I11 gives the values of ri and ri - m,as well as those of several of the dependent variables. A cmc of 0.013 M was used for the C6sulfosuccinate,since this value is consistent with both the conductivity and emf data and with the surface tension data of others.lJOFor the C8 sulfosuccinate, the conductivity and emf data suggest a cmc of ca. 0.001 M. However, attempts to fit the scattering curves for 0.011 and 0.0161 M surfactant using that cmc failed to converge.
0.0068
0.0034
0.0000
QDIAMETER Flgure 6. MSA fits (eq 5) to the experimental scattering curves at selected concentrations of Cssulfosucclnate: (a) 0.070, (b) 0.20, and (c) 0.40 M. Solid line: Z(0). Short dashed line: P ( 0 ) .Long dashed line: S(0).
sulfosuccinate micelles are too large for the core of the micelles to contain the terminus of each alkyl tail. Thus, we have assumed that the actual alkyl-group arrangement deviates substantially from the radial array of the classic Hartley micelle (because of the presence of one or more gauche conformers per alkyl tail, in addition to other types of chain meanderings). The independent variables in the Hayter and Penfold model are the micellar aggregation number (ri) and charge (ii - m). We compute an average volume (using the group volumes of Immirzi and Perinilg)
(19) Immirzi, A.; Perini, B. Acta Crystallogr., Sect. A 1977,33, 216-8. (20) Kostorz, G.; Lovesey, S.W. Treatise Mater. Sci. Technol. 1979, 15, 5-7.
Aggregation of Sulfosuccinate Surfactants in Water
The Journal of Physical Chemistry, Vol. 87, No. 26, 1983 5477
TABLE 11: Results of Core + Shell Model for the C, and C, Sulfosuccinates concn, M R2, a n n-rn ALFA
0.040 0.070 0.10 0.20 0.30 0.40
a
0.0110 0.0161 0.0214 0.0305 0.0343 Cmc = 0.013M.
17.1 18.0 18.8 20.8 22.6 23.4
20.5 21.2 21.9 23.3 24.1 Cmc = 6.4X
lo-",,
A-Z
10-,p*,A - 2
28.3 33.4 37.9 50.4 62.6 68.6
C, Sulfosuccinatea 12.0 14.5 15.6 16.9 15.5 14.4
3.9 4.2 4.4 4.8 5.1 5.1
-0.560 -0.560 -0.560 -0.560 -0.560 -0.560
3.02 2.92 2.89 2.85 2.87 2.88
41.7 45.6 50.6 60.1 66.5
C. Sulfosuccinateb 10.7 10.4 11.4 12.2 12.1
5.0 5.3 5.5 5.9 6.1
-0.506 -0.506 -0.506 -0.506 -0.506
2.91 2.87 2.81 2.74 2.72
M.
Thus, the lower cmc, 6.4 X M, suggested by the first inflection in the equivalent conductivity vs. plot, was used. Note that in the fits in Figure 6, the first peak in the structure factor occurs at higher Q than the peak in I(Q); the displacement to higher Q increases with increasing surfactant concentration. As Hayter and Penfolds have noted, the peak in I(Q)is due to the relative forms of P(Q) and S(Q),rather than simply coinciding with the first peak in S(Q). The values of a (1- m/ri) obtained from the scattering data range from 0.424 to 0.210 for the c6 sulfosuccinate in the concentration range 0.04-0.40 M; for the c8 sulfosuccinate values from 0.257 to 0.182 are obtained over the range 0.011-0.0343 M. For both surfactants, the value at the lowest concentration agrees reasonably well with the values obtained by condudimetry and emf measurements; a monotonic decrease in counterion dissociation is observed over the entire concentration range investigated. As the surfactant concentration is increased, both the c6 and cs sulfosuccinate micelles grow; this growth may be considered to proceed by incorporation of monomers (as ion pairs), since the micellar charge remains essentially constant as ri increases. Hayter and Zemb18 have found the same behavior with sodium octanoate micelles. In the case of the c8 sulfosuccinate, the highest concentration that we investigated was quite close to the solubility limit (0.041M) for the isotropic micellar solution. However, there is no evidence of a sphere-to-disk transition in micellar shape occurring (note the good fit achieved for 0.0343 M surfactant, Figure 7b). To test this possibility, we repeated the fits for the cs surfactant using Hayter and Penfold's model for S(Q),but evaluating P(Q)for an oblate ellipsoid21(semiminor axis of 18.0 A, the extended length of the surfactant molecule; semimajor axis as a variable dependent upon aggregation number and charge). The sphere of radius equivalent to the ellipsoid was used to determine the value of u needed for use in computing the interaction potential and particle volume fraction. The fits obtained were much poorer than those obtained by assuming the micelles are spheres, so that oblate ellipsoids or disks possessing any significant anisotropy cannot be present in the solutions. The fit obtained for the 0.40 M c6 sulfosuccinate assuming spherical micelles is also rather poor, but no improvement is found by assuming the micelles are oblate ellipsoids. It is possible that neglecting polydispersity is responsible for the poor fit. The large values of ALFA suggest substantial disorder in the micelles' interiors, with no well-defined segregation
of alkyl carbons from the polar portions of the micelles. The surface roughness (with some alkyl groups and/or carboxyl groups protruding into the head-group region) of the micelles must be pronounced at the higher surfactant concentrations, since the micellar radii are a few angstroms larger than the extended length of the surfactant molecules (19.0 and 21.5 A,respectively, for the c6 and cs sulfosuccinates). A more detailed model for the micellar shell, in particular the time-averaged spatial distribution of alkyl-group carbons relative to the carboxyls and the head-group region and the question of the depth of water penetration, will have to await the use of selectivity deuterated surfactant (in internal contrast variation experiments). Hayter and Zernbls observed an approximately linear increase of the aggregation number with increasing concentration of micellized sodium octanoate in D20 at 28 "C, with Afi/A(c - cmc) equal to 13.3. Sodium dodecyl sulfate, which like sodium octanoate is very soluble in water, also shows only a weak dependence of aggregation number on surfactant concentration.8 The dependence is much larger for the double-tailed surfactants that we have investigated, as the data in Figure 8 demonstrate. Some of the scattering curves for sodium p - (1-pentylhepty1)benzenesulfonate, 6-PhCI2SNa, at 45 "C have been published previously; I5,l6we have recently determinedz2the aggregation numbers in this paper. In addition, Lianos et aLZ3 have obtained the concentration dependence of ri for
(21) Guinier, A.; Fournet, G. ''Small-Angle Scattering of X-Rays"; Wiley: New York, 1955; p 19.
(22) Triolo, R.; Magid, L. J.; Johnson, J. S.,unpublished results. (23) Lianos, P.; Lang, J.; Zana, R. J. Colloid Znterfuce Sci., in press.
80
60
ii 4 0
20
9
10
0 10
0 20 c(MoI/L)
0 30
0 40
Figure 8. Micellar aggregation number vs. concentration of miceiiized surfactant: C8 sulfosuccinate (0); &PhC,,SNa (H);CBsuifosuccinate (0).
5478
J. Phys. Chem. 1083, 87, 5470-5481
micelles of n-dodecyl-n-octyldimethylammonium bromide in water at 20 "C using a fluorescence probe technique; Aii/A(c - cmc) is 840. The concentration dependence of ii follows the micellar solubility (concentration limit for the isotropic micellar solution given in parentheses) for these double-tailed surfactants: c6 sulfosuccinate (130, 1.2 M at 45 "C); 6PhC12SNa (393,0.25 M at 30 "C); C12C8N(CH3)2Br (840, 0.07 M at 20 "C); C8 sulfosuccinate (930,0.041M at 45 "C). Conclusion Micellization of the c6 and C8 sulfosuccinates leads, at surfactant concentrations of a few times the cmc, to spherical micelles with radii comparable to the lengths of the extended surfactant molecules (19.0 and 21.5 A, respectively). These micelles evidently grow by incorporation of monomeric ion pairs, since the micellar charge is approximately constant over the concentration range studied. The micellar interior is quite disordered, with some chain termini being located further than 9 (c6)and 11.5 (C,) A from the center; the micelle surface is rather rough, with some alkyl and/or carboxyl groups located at or beyond the minimum distance for the head groups from the micelle centers. On the basis of NMR measurement^,^^ the single-tailed surfactant SDS may be considered to have (24)Cabane, B.J.Phys. (Orsay, Fr.) 1981,42,847-59.
a similarly disordered micellar interior. However, SANS6 and NMR24predict a rough and smooth surface respectively for the SDS micelles. The extent of counterion dissociation just above the cmc is considerably larger than for single-tailed surfactants; it decreaes monotonically with increasing surfactant concentration. No evidence was found for a sphere-to-disk transition in micellar shape close to the L1 L1 LC boundary, but the concentration dependence of the aggregation number for a series of double-tailed surfactants was found to increase as the surfactants' solubility decreased (i.e., as the L1 L1 LC boundary moves to lower surfactant concentration.)
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Acknowledgment. This work was supported by the U.S. Army Research Office (Contract DUG-29-82-K-0115) and the Mobil Foundation. The NCSASR at Oak Ridge National Laboratory is funded by National Science Foundation Grant No. DMR-77-244-58, through Interagency Agreement No. 40-637-77 with the Department of Energy (DOE) and is operated by the Union Carbide Corp. under Contract No. W-7405-eng-26with the DOE. We thank H. R. Child and G. D. Wignd of the NCSASR; J. S. Johnson, Jr., Chemistry Division, ORNL; and R. Triolo, University of Palermo, for helpful discussions. Registry No. I (R = n-hexyl), 3006-15-3; I (R = n-octyl), 23524-64-3; I (R = n-decyl),1639-66-3.
Kinetic Study of the Adsorption-Desorption of the Uranyl Ion on a y-Al,03 Surface Using the Pressure-Jump Technique Naokl Mlkaml, Mlnoru Sasakl, Kazuakl Hachlya, and Tatsuya Yasunaga Department of Chemistry. Faculty of Science, Hiroshlma lJniversl@, Hiroshima 730, Japan (Received; February 8, 1983; I n Flnal Form: May 16, 1983)
In an aqueous 7-A1203suspension containing the uranyl ion, single relaxation was observed over the pH range 4.4-5.4, using the pressure-jump technique with conductivity detection. The reciprocal relaxation time increases with uranyl ion concentration, while it decreases with increasing pH and then approaches a constant value. From the kinetic and static results obtained, the relaxation was attributed to the adsorption-desorption of (U02)3(OH)5+ on the surface hydroxyl group. The intrinsic values of the adsorption and desorption rate constants were determined to be k p t = 1.6 X lo3 mol-' dm3s-l and k-lint = 1.1 x lo5mol-' dm3 s-l, respectively, at I = 1.5 X and 25 "C.
Introduction Adsorption of the uranyl ion on the metal oxide surface has been of interest to colloid scientists and chemical engineers concerned with not only the adsorption mechanism but also extractions from solution and sea ~ a t e r . l - ~ For the uranyl ion adsorption on SiOz, Stanton and Maatman have proposed a mechanism where the uranyl ion is adsorbed on bidentate surface sites.l In the above investigation, however, the experimental results have been analyzed without considering the surface potential, the importance of which has been pointed out by many in(1)Stanton, J. H.; Maatman, R. W. J. Colloid Sci. 1963, 18, 132. (2)Dugger, D. L.; Stanton, J. H.; Irby, B. N.; McConnell, B. L.; Cummings, W. W.; Maatman, R. W. J.Phys. Chem. 1964,68,757. (3)Davies, R. V.;Kennedy, J.; Mclloy, R. W.; Spence, R.; Hill, K.M. Nature (London) 1964,203,1110. (4)Keen, N. J. J. Brit. Nucl. SOC.1968, 7, 178. 0022-3654/03/2087-5476~Q1.5010
vestigators."1° This fact motivated us to reexamine this mechanism. However, it is difficult to prepare a well-defined sample of SiOz because the surface characteristics of Si02 are extremely sensitive to trace amounts of impurities such as A1 and Na.ll Thus, a sample of 7-AlZO, whose surface characteristics are well established was used in the present investigation.12-14 For elucidation of the ~~~
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(5)Davis, J. A.; Leckie, J. 0. J. Colloid Interface Sci. 1978,67,90. (6)Davis, J. A.; Leckie, J. 0. J. Colloid Interface Sci. 1980,74,32. (7)James, R. 0.;Stiglich, P. J.; Healy, T. W. Adsorp. Aqueous Solutions, Proc. Conf. 1981,19. (8)Ashida, M.; Sasaki, M.; Kan, H.; Yasunaga, T.;Hachiya, K.; Inoue, T.J. Colloid Interface Sci. 1978,67,219. (9)Ashida, M.; Sasaki, M.; Hachiya, K.; Yasunaga, T. J. Colloid Interface Sci. 1980, 74,572. (10)Mikami, N.; Sasaki, M.; Hachiya, K.; Astumian, R. D.; Ikeda, T.; Yasunaga, T.J.Phys. Chem. 1983,87, 1454. (11)Nippon Kagakukai, "Shin Jikken Kagaku Koza": Maruzen: Tokyo, 1977;Vol. 18,p 331.
0 1963 American Chemical Society
