318
Langmuir 2000, 16, 318-323
Variation in Degree of Counterion Binding to Cesium Perfluorooctanoate Micelles with Surfactant Concentration Studied by 133Cs and 19F NMR Hiroshi Iijima† and Tadashi Kato* Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Minamiohsawa, Hachioji, Tokyo 192-0397, Japan
Olle So¨derman Division of Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00, Lund, Sweden Received March 8, 1999. In Final Form: August 16, 1999 The concentration dependences of 133Cs and 19F chemical shifts for aqueous solutions of cesium perfluorooctanoate are analyzed by using a two-state model to ascertain the results in our previous study on the same system which demonstrates micellar growth along two dimensions based on the analysis of small-angle X-ray and neutron scattering. The distribution of counterions has also been calculated by using a cell model combined with the Poisson-Boltzmann equation. The results are consistent with the increase in the degree of counterion binding with increasing surfactant concentration, which may be related to the two-dimensional growth of micelles.
Introduction The cesium perfluorooctanoate (CsPFO)-water system has been known as a unique system that exhibits a discotic nematic phase over wide ranges of concentration and temperature without any additives.1-10 In a previous study,11 we measured small-angle X-ray and neutron scattering (SAXS and SANS, respectively) from aqueous solutions of CsPFO including a dilute region much lower than the isotropic/nematic phase boundary. The results are consistent with micellar growth along two dimensions (disklike micelles) rather than along one dimension (rodlike micelles). This conclusion is not surprising because the building block of the discotic nematic phase is disklike micelles. However, theoretical arguments predict that surfactants would assemble spontaneously not into finite aggregates but into infinite bilayers when micelles grow * Corresponding author. Phone: +81-426-77-2528. Fax: +81426-77-2525. E-mail:
[email protected]. † Current address: Department of Polymer Physics, National Institute of Materials and Chemical Research, 1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan. (1) Boden, N.; Jackson, P. H.; McMullen, K.; Holmes, M. C. Chem. Phys. Lett. 1979, 65, 476. (2) Boden, N.; Corne, S. A.; Jolley, K. W. J. Phys. Chem. 1987, 91, 4092. (3) Boden, N.; Corne, S. A.; Holmes, M. C.; Jackson, P. H.; Parker, D. J. Phys. 1986, 47, 2135. (4) Holmes, M. C.; Reynolds, D. J.; Boden, N. J. Phys. Chem. 1987, 91, 5257. (5) Holmes, M. C.; Reynolds, D. J.; Boden, N. Mol. Cryst. Liq. Cryst. 1987, 146, 377. (6) Boden, N.; Jolley, K. W.; Smith, M. H. J. Phys. Chem. 1993, 97, 7678. (7) Leaver, M. S.; Holmes, M. C. J. Phys. II (France) 1993, 3, 105. (8) Holmes, M. C.; Smith, A. M.; Leaver, M. S. J. Phys. II (France) 1993, 3, 1357. (9) Boden, N. In Micelles, Membranes, Microemulsions, and Monolayers; Gelbert, W. M., Ben-Shaul, A., Roux, D., Eds; Springer-Verlag: New York, 1994; p 153. (10) Holmes, M. C.; Leaver, M. S.; Smith, A. M. Langmuir 1995, 11, 356. (11) Iijima, H.; Kato, T, Yoshida, H.; Imai, M. J. Phys. Chem. B 1998, 102, 990.
Figure 1. Degree of counterion binding β vs (C - cmc)1/2 obtained from the fits of SAXS (filled symbols) and SANS (open symbols) data using prolate (triangles) and oblate (circles) ellipsoid models.
along two dimensions.12,13 In fact, there has been no report indicating the existence of bidimensional aggregates based on the analysis of the curve profile of SAXS or SANS except for the mixed short-chain lecithin/long-chain lecithin aggregates.14 So our conclusion is not self-evident, and it is necessary to check the results by using other methods. In ref 11, it has been shown that the degree of counterion binding (β) increases substantially with increasing surfactant concentration (see Figure 1 where (C - cmc)1/2 is used so that all the data in a wide concentration range are included and the extrapolation to the cmc can be easily performed). The reason β can be obtained from SAXS and (12) Ben-Shaul, A.; Gelbert, W. M. In Micelles, Membranes, Microemulsions, and Monolayers; Gelbert, W. M., Ben-Shaul, A., Roux, D., Eds; Springer-Verlag: New York, 1994. (13) Israelachvili, Y. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525. (14) Lin, T.-L.; Liu, C.-C.; Roberts, M. F.; Chen, S.-H. J. Phys. Chem. 1991, 95, 6020.
10.1021/la9902688 CCC: $19.00 © 2000 American Chemical Society Published on Web 10/16/1999
Counterion Binding to Cesium Perfluorooctanoate Micelles
SANS measurements is as follows. For dilute solutions of micelles, the scattering intensity is expressed in terms of the single particle form factor F(q) and the structure factor S(q) related to the micelle structure and intermicellar interactions, respectively, where q is the absolute value of the scattering vector. Usually, S(q) is calculated by using the rescaled mean spherical approximation15,16 where the micelle is assumed to be a rigid sphere having a charge m(1 - β) (m: aggregation number of micelles) and only double-layer repulsion is taken into account. The form factor also depends on β through the scattering length density. Thus the scattering intensity can be expressed in terms of β and other parameters such as m. These parameters are determined from the least-squares fitting of the scattering intensity as a function of q. So β is no more than an adjustable parameter in the analysis of SAXS and SANS. On the other hand, NMR spectra reflect the microscopic environment of each nucleus. Thus, more direct information on counterion binding can be obtained from the NMR spectra of the counterion (Cs) and the fluorine atom of the R-CF2 group located in the vicinity of the counterions. Previously, one of the authors (H.I.) reported NMR data on salts of perfluorocarboxylic acids with different counterions and fluorocarbon chain length.17 In the present study, we analyze the NMR data for CsPFO micelles to check the counterion binding β obtained from our SAXS and SANS study reported before. First of all, the concentration dependence of the 133Cs chemical shift is analyzed to obtain information on the concentration dependence of β. Then, the absolute values of β at higher concentrations are determined by combining the 133Cs chemical shift and SAXS results. The effects of counterion binding to the environment of the R-CF2 group are examined by analyzing the concentration dependence of the 19F NMR chemical shift. Finally, we obtained the distribution of cesium ions outside the micelle by solving the Poisson-Boltzmann equation and compared it with the data on the 133Cs NMR chemical shift. 1.
133Cs
Chemical Shift and Counterion Binding
In the analysis of the 133Cs chemical shift, we employ a two-state model where the surroundings of the cesium ion is divided into the free (dispersed in bulk phase) and bound (attached to a micelle) states. Then, the observed chemical shift (δobs) of 133Cs is expressed as
δobs ) δfree
(1a)
for concentrations below the critical micelle concentration (cmc) and
δobs )
Cfreeδfree + Cboundδbound C
(1b)
for concentrations above the cmc, where C is the surfactant concentration, Cfree and Cbound are the concentrations of cesium ion in the free and bound states, respectively, and δfree and δbound are the corresponding chemical shifts. Above the cmc, the concentrations Cfree and Cbound can be expressed in terms of the degree of counterion binding β (15) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. (16) Hansen, J.-P.; Hayter, J. B. Mol. Phys. 1982, 46, 651. (17) Iijima, H.; Koyama, S.; Fujio, K.; Uzu, Y. Bull. Chem. Soc. Jpn. 1999, 72, 171. The experimental apparatus and assignment of the peaks are therein.
Langmuir, Vol. 16, No. 2, 2000 319 Table 1. 133Cs Chemical Shifts from External Cesium Chloride and Difference from that at 0.0044 mol kg-1 (, cmc ) 0.024 mol kg-1) in D2O as a Function of Surfactant Concentration C (mol kg-1)
δobs (ppm)
δobs - δfree (ppm)
0.0044 0.0126 0.0170 0.0181 0.0206 0.0222 0.0239 0.0261 0.0280 0.0300 0.0335 0.0349 0.0407 0.0508 0.0538 0.0611 0.0698 0.0710 0.0820 0.0827 0.0890 0.0980 0.0998 0.1541 0.1831 0.1960 0.3023 0.3705 0.3930 0.4925 0.6309 0.6350 0.7308 0.7776 0.9905
-11.14 -11.20 -11.24 -11.24 -11.25 -11.29 -11.41 -11.77 -12.13 -12.60 -13.10 -13.28 -14.01 -15.00 -15.17 -15.66 -16.13 -16.13 -16.58 -16.65 -16.91 -17.17 -17.15 -18.36 -19.12 -19.08 -20.23 -20.77 -20.99 -21.49 -22.10 -22.07 -22.43 -22.49 -23.00
0.00 -0.06 -0.10 -0.10 -0.11 -0.15 -0.27 -0.63 -0.99 -1.46 -1.96 -2.14 -2.87 -3.86 -4.03 -4.52 -4.99 -4.99 -5.44 -5.51 -5.77 -6.03 -6.01 -7.22 -7.98 -7.94 -9.09 -9.63 -9.85 -10.35 -10.96 -10.93 -11.29 -11.35 -11.86
and the concentration of monomers Cmon as
Cfree ) Cmon + (1 - β)(C - Cmon)
(2a)
Cbound ) β (C - Cmon)
(2b)
Substitution of eq 2 into eq 1 gives the following relation above the cmc.
δobs - δfree ) (1 - cmc/C)β(δbound - δfree)
(3)
In the derivation of eq 3, Cmon is assumed to be equal to the cmc, 0.024 mol kg-1 in D2O solutions. This assumption was also used in the analysis of the small angle scattering data and will be reconsidered later. The left-hand side of eq 3 can be obtained experimentally if the δfree value is replaced by the chemical shift observed in the range C , cmc. Table 1 contains 133Cs chemical shifts from external cesium chloride and δobs - δfree in D2O as a function of surfactant concentration where δfree is replaced by δobs at 0.0044 mol kg-1 which is much smaller than the cmc. The precision of δobs is (0.01 ppm. In Figure 2, the δobs - δfree is plotted against the reciprocal concentration of CsPFO. Equation 3 indicates that δobs - δfree is proportional to the reciprocal concentration when the product β (δbound - δfree) is independent of surfactant concentration. As can be seen from Figure 2, however, such a plot does not give a straight line in the CsPFO system, indicating that β (δbound - δfree) depends on concentration. So we have obtained the product β(δbound - δfree) from (δobs - δfree) at each concentration by using eq 3. The results are shown in Figure 3 where the absolute value of (δobs - δfree) (
