J . Phys. Chem. 1991, 95.4832-4837
V2 05 loadings I wt% Figure 14. Calculated XPS intensity ratio (fv/fsi) as a function of the amount of V2OS.The parameter in this figure is the number of (010)
and the specific surface area of the support, respectively. The calculated Iv/Isiis also given in Figure 14 for various values of N. The parameters used in this calculation are given in Table 111. The values of dv, t , and dsi are derived from the crystallographic data of V20529and cristobalite,m and Xsi~i,and Xsi,v are calculated according to the literat~re.~'When N varies from 10 to 2, Iv/Isiincreases by a factor of about 3. The ratios Iv/Isiexperimentally obtained for V2OS/SiO2(CVD-723)-calcined are about 3 times higher than those for V205/Si02(Imp)at high loadings. Therefore, the average thickness of the V2O5 overlayers of V20S/Si02(CVD-723)are estimated to be less than 20% that of V205/Si02(Imp). If the thickness of V2O5 on 18.4 wt % ' V205/Si02(Imp) is assumed to be 210 A, that of 16.9 wt 96 V20S/Si02(CVD-723)dcinedis less than 40 A. This estimate is compatible with the XRD results.
layers accumulated (N). TABLE IIk h8-m U d in I h l c u l r t i ~Of~ Iv/Za IMFP of V photoelectron in V205 XV,V 1.0 nm IMFP of Si 2p photoelectron in V205 hsi,v 1.5 nm IMFP of Si 2p photoelectron in S O z ,Isisi 1.9 nm number of Si atoms in unit volume of SiOz dsi 21.8 number of V atoms in unit volume of Vz05 dv 22.3 thickness of ideal V205(010) monolayer r 0.437 nm weight of ideal Vz05(010) monolayer A 1.47 X
Acknowledgment. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan. We greatly appreciate partial support by the Asahi Glass Foundation and by the Foundation for the Promotion of Material Science and Technology of Japan. g m-2
in unit volumes of V2O5 and SiO,, respectively. B can be expressed by eq 7,where w, A, and S are weight ratio of V2OSloaded and e = W/(SAN) (7) Si02, the weight of an ideal V2OS(010) monolayer of unit area,
Rdstry NO. VO(OCzH5)3, 1686-22-2;VIOS,13 14-62-1.
(29)Bachmann, H.G.;Ahmcd, F.R.; Barnes, W. H. 2.Krisrallogr. 1961, 115, 110. (30) Wyckoff, R. W. G. Crysral Srrucrures, 2nd ed.; lishers: New York, 1963; Vol. 1, p 318.
(31) Penn, D. R. J. Electron Specrrosc. Relar. Phenom. 1976, 9, 29.
Uttrasonlc Absorption Studies of Surfactant Exchange between Micelles and Bulk Phase In Aqueous Micellar Solutions of Nonionic Surfactants with Short Alkyl Chains. 1. 1,2-HexanedIol and 1,2,3-0ctanetriol M. Frindi, B. Micbels, Laboratoire de SpectromOtrie et d'lmagerie Ultrasonores, 4, rue Blaise Pascal, 67000 Strasbourg, France
and R. Zana* Institut Charles Sadron (CRM-EAHPJ, CNRS- ULP Strasbourg, 6, rue Boussingault, 67083 Strasbourg CPdex, France (Received: December 17, 1990) 1,2-Hexanediol (1,2-HD) and 1,2,3-octanetriol (1,2,3-OT) are known to self-associate in a manner very similar to that of conventional surfactants to give rise to micellelike aggregates (Hajii, S.;et al. J . Phys. Chem. 1989,93,4819). This paper reports on fluorescenceprobing, with pyrene as a probe, of these aggregates and on a study of the kinetics of monomer exchange between aggregates and bulk phase by means of the ultrasonic relaxation method in the frequency range 0.5-100 MHz. Thus the polarity sensed by pyrene solubilized in the aggregates is lower than for conventional nonionic surfactants of the C,E, type. The critical micellization concentrations determined by fluorescence probing are in agreement with the reported values. The ultrasonic relaxation amplitude A and frequencyfi have been found to vary with concentration as expected from the expressions derived for conventional surfactants on the basis of the Aniansson and Wall treatment for the kinetics of surfactant exchange. The full use of these expressions permitted us to obtain the values of the rate constants k+ and kfor the incorporation of a surfactant monomer into, and the dissociation of a monomer from, a micelle, respectively, as well as the standard deviation characterizing the distribution of micelle aggregation numbers (polydispersity) and the volume change upon incorporation. These results are discussed and compared to those obtained for conventional surfactants.
systems are now rather well-known. In particular it is widely
*Towhom correspondence should be addressed. 0022-3654/91/2095-4832602.50/0
( 2 ) degiorgio, V. Physics of Amphiphiles: Micelles Vesicles and Micre emulsions; Degiorgio, V., Corti, M.,Eds.; North Holland: Amsterdam, 1985, and references therein.
0 1991 American Chemical Society
Ultrasonic Absorption Studies of Surfactant Exchange growth occurs faster in the range T, - 40 < T < Tc but remains nevertheless moderate.'-" Concerning the dynamic properties of micellar aqueous solutions of C,E, surfactants, timaresolved fluorescence quenching studies have permitted us to show that nonionic micelles can merge temporarily upon collision, thus allowing transport of material from micelle to micelle on the microsecond time scale, in range T,- 40 < T < Tc,ell This process is greatly slowed upon decreasing the temperature. It is qualitatively similar to that evidenced in solutions of ionic surfactants at high concentration of surfactant and/or added salt or in the presence of counterions strongly bound by the micelle^,'^-'^ that is, in a situation where the intermicellar repulsions are much reduced. Nevertheless in ionic systems collisions with merging occur at a slower rate, in the millisecond time ~ c a l e . ' ~ -A' ~similar process is also known to occur between water droplets in water in oil microemulsions.1618 Whereas much is known about the kinetics of surfactant exchange between micelles and bulk in aqueous micellar solutions of ionic surfactants both from the qualitative and quantitative viewpoint^,^^*^ there have been very few studies of this process for nonionic systems. Thus, the Aniansson and Wall treatment21 of the kinetics of surfactant exchange and its improved vers i o n ~ have ~ ~ been ~ ~ extremely ~ - ~ ~ successful for the analysis of studies of aqueous ionic surfactant systems. Although these treatments are now widely accepted it is not known whether they fully apply to nonionic systems, even though the original Aniansson and Wall treatment should, in principle, strictly apply only to nonionic micelles. For our part we have reported two ultrasonic absorption studies of nonionic systems.2s.26 One dealt with 1butanol in water, at the limit of Its main conclusion was that 1-butanoldoes associate in water, but the restricted range of concentration where aggregates exist did not permit a test of Aniansson and Wall theory. The second study dealt with some C,E, surfactants with short alkyl chains (n = 6 and 8).% It was shown that the observed excess ultrasonic absorption arose from the surfactant exchange between micelles and bulk. The results were again too preliminary to allow for a test of Aniansson and Wall theory. This situation led us to look for other surfactants or surfac~
(3) Corti, M.;Degiorgio, V. J . Phys.Chem. 1981, 85, 1442. (4) Zulauf, M.; Rosenbuch, J. P. J . Phys. Chem. 1983,87, 856. (5) Wyn Brown; Pu, Z.; Rymden, R. J . Phys. Chem. 1988. 92, 6086. (6) Nilsson, P.-G.; Wcnnerstrhn, H.; Lindman, B. Chem. Scr. 1985, 25, 67. (7) Wilcoxon, J. P.; Kaler, E. W. J . Chem. Phys. 1987,86, 4684. (8) Manid. L. J.: Triolo. R.: Camnetti. E.: Johnson. S . J.. Jr. Surfactants in kdlutioh; 'Mittal, K. L:, Lindman, B.; Eds.;Plenum Press: Niw York, 1987; Vol. 4, p 155. (9) Zana, C., Weill, C. J . Phys. Lett. 1985,16, L-953. (IO) Binana-Limbelt, W.; Zana, R. J . Colloid Interface Sei. 1988, 121, 81. (11) Binana-Limbclt, W.; van Os, N. M.; Rupert, L. A. M.; Zana, R. J . Colloid Interface Sei., in press. (12) Lcssner, E.; Teubner, M.; Kahlweit, M. J . Phys. Chem. 1981, 85, 3167. (13) Kahlweit. M. J . Colloid Interface Sei. 1982, 90, 92. (14) Lang, J.; Zana, R. J . Phys. Chem. 1986, 90,5258. ( I 5) Malliaris, A.; Lang, J.; Sturin, J.; a n a , R. J. Phys. Chem. 1987.91, 1475. (16) Thomas, J. K.; Atik, S. J . Am. Chem. Soc. 1981. 103, 3543. (17) Fletcher, P. D.; Robinson, B. H. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 863. (18) Jada. A.; Lang, J.; Zana, R.; Makloufl, R.; Hirsch, E.;Candau, S . J. J . Phys. Chem. 1990, 91, 387 and references therein. (19) Lang, J.; Zana, R. Surfactants Solutions. New Methods of Inoestigarion: a n a . R., Ed.; Dekker: New York, 1987; Chapter 8. (20) A n i a w n , E. A. G.;Wall, S.; Almgren, M.; Hoffmann, H.; Kielmann, 1.; Ulbricht. W.; Zana, R.; Lang, J.; Tondn, C. J. Phys. Chem. 1976, 80,905. (21) Aniansaon. E.A. G.;Wall, S. J . Phys. Chem. 1974, 78, 1024; 1975, 79, 851. (22) Almgren, M.; Aniansson, E.A. G.; Holmaker, K. Chem. Phys. 1977, 19, I . (23) Hall, D. J. 1. Chem. Sa.,Faraday Trans I 1981, 77, 1973. (24) Wan-Radhi, W.; Palepu, R.; Bloor, D. M.; Hall, D. G.; Wyn-Jones, E. To be published. (25) Zana, R.; Michels. 8.J . Phys. Chem. 1989, 93, 2643. (26) Borthakur, A.; Zana, R. J . Phys. Chem. 1987, 91, 5957.
The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 4833 tant-like compounds which would permit such a test. Recall that the ultrasonic absorption techniques in use in our laboratories explore the range 1 ps-1 ns25and therefore can only be used for investigating the kinetics of exchange of surfactants with a fairly short alkyl chain. This study and the following ones will be dealing with such Surfactants. Recently, Taillandier et aI?'58 have showed that 1,Zhexanediol (1,2-HD) and 1,2,3-octanetriol(1,2,3-OT)are surface-active and self-associative in aqueous solutions, similar to the behavior of nonionic surfactants. These studies revaled that the existence of a critical concentration, very much like a cmc, below which the compounds are molecularly dispersed and above which aggregates are formed. The "cmc's", as obtained by various techniques, are 0.73 f 0.04 M and 0.28 f 0.04 M for 1,2-HD and 1,2,3-OT, r e ~ p e c t i v e l y .The ~ ~ ~factor ~ ~ of 3 f 0.3 between the cmc's of the twqcompounds is the same as that found for C,E, surfactants when the alkyl chain is decreased by one methylene group.'*2 Further the micelle aggregation numbers determined by light scattering were 20 for 1,2-HD and 44 for 1,2,3-OT.27 These values, which appeared to depend only little on concentration,28 again as for C,,E, surfactants,"' are comparable to those reported for short-chain ionic surfactants.29J0 Finally, it should be recalled that Kato31 and Kwan and R ~ s e have n ~ ~reported on the micellization of various alkanediols and their adsorption at the air-water interface. All these results clearly indicate that 1,2-HD and 1,2,3-OT can be considered as short chain nonionic surfactants, even though their polar heads are rather unusual. The values of both their cmc's and aggregation numbers appear to be in the right range for a successful investigation of the kinetics of surfactant exchange between micelles and bulk by ultrasonic absorption. Such a study was therefore performed and the results are reported below. Also reported are the results of investigations of the same systems by means of fluorescence probing.
Experimental Section 1,2-HD (98%, Aldrich) was purified as described.28 Two samples of 1,2,3-OT were used. The first one, a gift from Prof. E. Taillandier (University of Paris Nord) was used in preliminary investigations. The second sample was prepared as described in the l i t e r a t ~ r e . ~Its ~ elemental analysis and NMR spectrum (Brucker AC-200 F) indicated that the sample was at least 98% pure. The sample of purified pyrene was the same as in a previous investigation.2s The fluorescence measurements used pyrene as probe?*% The fluorescence emission spectra were obtained with aerated solutions at very low pyrene concentrations ( E 1-2 X lod M), which ensured the absence of excimer, by using a Hitachi F4010 spectrofluorimeter at an excitation wavelength of 335 nm. The spectra were used to determine the ratio 11/13of the intensities of the first and third vibronic peaks of monomeric pyrene. Recall that Il/Z3 is sensitive to the microenvironment of pyrene and can be used to detect the changes of polarity sensed by pyrene when, upon micellization or aggregates formation, pyrene becomes partly or wholly solubilized within the The changes of 11/13 with the surfactant concentration C were thus used to obtain the cmc of 1,2-HD at various temperatures and to compare the polarity sensed by pyrene in 1,2-HD and 1,2,3-OT aggregates to that in micellar solutions of other surfactants. (27) Durand, R.; Hajji, S.; Coudert, R.; Cao, A.; Taillandier, E. J . Phys. Chem. 1988, 92, 1222. (28) Hajji, S.;Errahmani, M.; Coudert. R.; Durand, R.; Cao. A,; Taillandier, E. J . Phys. Chem. 1989, 93, 4819. (29) Lianos, P.; Zana, R. J . Colloid InterJace Sei. 1981, 81, 100. (30) Hayter, J.; Zemb, T. Chem. Phys. Lett. 1982, 93, 91. (31) Kato, Y. Chem. Pharm. Bull. 1962, 10, 771. (32) Kwan, C.-C.; Rosen, M. J. J . Phys. Chem. 1980,84, 547. (33) Zana, R. Surfactant Solutions. New Methods of Inuestigation: Zana. R., Ed.; Dekker: New York, 198% Chapter 5. (34) Kalyanasundaram, K.; Thomas, J. K. J . Am. Chem. Soc. 1977,99, 2039. (35) Nomura, M.; Mitaku.S. Rep. Prog. Polym. Phys. Jpn. 1986.29,733. (36) Lianos, P.; Lang, J.; Strazielle, C.; Zana, R. J . Phys. Chem. 1982, 86, 1019.
4834 The Journal of Physical Chemistry, Vol. 95, No. 12, 199'1 The ultrasonic absorption measurement^^^.^^ were performed by using the standard pulse techniqueZ6in the frequency range 3.91-1 15 MHz and the resonator method in the range 0.49-5 MHz.25-37 The absorption was measured as a function of concentration, temperature, and frequency and expressed as a/f (a = ultrasonic absorption coefficient in m-';f= frequency in hertz). Special care was taken in the measurements as a function of frequency to have the same temperature within 0.1 OC in the two series of experiments by the resonator method and the pulse technique, performed on two different campuses, because the excess absorption of the solutions with respect to water was found to be strongly dependent on temperature (see below). However, the temperature was controlled to within 0.01 OC in each series of measurements. The error is estimated to be f10% and f5% in the frequency ranges 0.49-1 1.68 and 15-1 55 MHz, respectively. Recall that in aqueous solutions of ionic surfactants the relaxation process giving rise to the excess ultrasonic absorption is usually associated to the exchange of surfactant monomers S between micelles and bulk phase19,24s38-42
s,& S1-I + s k+,
where u is the standard deviation of the distribution of aggregation numbers and N the average micelle aggregation number, which can be taken as the value obtained from light scattering or any other appropriate method. In the case of ionic surfactant solutions, the cmc (concentration of free surfactant) decreases upon increasing C and this introduces difficulties in the analysis of the ultrasonic absorption data.24 Another problem is associated with the contribution of counterions to the micellization process and a more complete expression involves both the micelle ionization degree and an activity term.24 These difficulties disappear or are reduced to a negligible level in the case of nonionic surfactants. Equation 2 predicts a linear increase OffR with C from which kand u can be obtained, provided N is known. The expression of the amplitude A of the ultrasonic relaxation has also been g i ~ e n : ' ~ . ~ ~ du Avo2 k--(C - cmc) RT fR2 N
1.4 1.6 C I MI?)
Figure 1. Variation of 11/13at 8 OC (A),25 OC (0),and 40 OC ( 0 )for pyrene in aqueous solutions of 1,2-HD.
where S,andSkl are two aggregates of aggregation number i and i - 1, k+/ and k-, being the rate constants for the incorporation of a surfactant into the aggregate Si-l and for the dissociation of one surfactant from the aggregate Si. Aniansson and Wall2' have derived the expression of the relaxation frequency fR on the assumption of a fairly narrow Gaussian distribution of micelle aggregation numbers and taking k+i = k+, and k-, = ik- in the range of micelles proper. The second assumption reduces the spectrum of relaxation frequencies to a single value given by2'
Frindi et al.
where d is the density of the solution (g ~ m - ~u)is, the velocity of ultrasound in the solution (cm s-l), T is the temperature, R is the gas constant (8.32 X lo7 erg mol-Ideg-l), and AVOis the volume change associated with the reaction of incorporation of a surfactant into the micelle of aggregation number N (cm3 mol-'). With the concentrations C and cmc expressed in mol liter-' and fR in Hz, A is expressed in m-' s2. Equation 3 predicts a linear increase of the quantity AfR2 with C - cmc. It can thus be used for checking the validity of the theory and also for determining the cmc and the value of AVO,since k - / N is obtained from the (37) Eggers, F.; Funck, T. Rev. Sei. fnstrum. 1973,44969. Dormoy, Y . ; Michels, E. Acustica 1981, 49, 119. (38) Graber, E.;Lang, J.; Zana, R. Kolloid 2.2.Polym. 1970, 238,470. (39) Zana, R.;Yiv, S.Can. J . Chem. 1980,58, 1780. (40) Lang, J. J . Phys. Chem. 1982,86,992. (41) Diekmann, S.Ber. Bunsen-Ges. Phys. Chem. 1979,83, 528. (42) Rassing, J.; Sam, P. J.; Wyn-Jones, E . J . Chem. Soc., Faraday Trans. 2 1974, 70, 1247. (43) Teubner, M. J . Phys. Chem. 1979,83, 2917.
Figure 2. Variation of 11/13at 25 OC for pyrene in aqueous solutions of 1,2,3-OT. TABLE I: Values of (f,/f3)o1,2,IOT in Water
and cmc's (mol/L) for 1,2-HD and
8 25 40
1.12 1.11 1.08
1,2-HD 0.84 f 0.04 0.73 f 0.03 0.69 f 0.03 0.60 f 0.03 0.61 0.03
1,2,3-OT 0.253 0.28 f 0.02
From the 11/13vs C plot. bFrom the AfR2 vs C plots. From refs 27 and 28.
slope of the fR vs (C - cmc)/cmc plot. The ultrasonic velocities were determined by means of the ultrasonic r e s o n a t ~ r ? ~The . ~ ~densities of the solutions investigated were calculated from the reported values of the apparent molal volume of 1,2-HD and 1,2,3-OT in aqueous solutions28and found to be equal to 1.00 g ~ m - within ~ , 1%.
Results 1 . Fluorescence Probing. Figures 1 and 2 represent the variations of 11/13for which Kalyanasundaram and Thomas" have shown that, for aqueous solutions of sodium dodecyl sulfate, in the 11/13vs C plot, the cmc corresponds approximately to the concentration where 11/13has dropped to a low and nearly constant value. In the present work, the cmc's obtained by the extrapolations shown in Figures 1 and 2, as in the above cited study," are in good agreement with the reported values at 25 OC, as can be seen in Table I. The cmc of 1,2-HD decreases upon increasing T as in the case of C,E, surfactants.44 The values of 11/13for concentrations above the cmc, ( I l / 13)Dcmcare also listed in Table I. They all are in the range 1.02-1.12, revealing that pyrene senses a nonpolar environment. For comparison, we have determined as part of this work (II/ 13)Dcmcfor CloEBand CIzE8, two typical C,E, surfactants, and (44) Meguro, K.; Takasawa, Y.;Kawahashi, N.; Tabata, Y.;Ueno, M.J . Colloid Interface Sei. 1981, 83, 50.
The Journal of Physical Chenristry. Vol. 95, No. 12, 1991 4835
Ultrasonic Absorption Studies of Surfactant Exchange
TABLE II: Values of Ultrasonic Velocity of Investigated Solutions and of Ultrasonic Fitting Parameters A, B,and fna
1 015 a/f2(m-1s2)
10 f ( M H z f o 0
63. Ultrasonic relaxation spectra for solutionsof 1,2-HDat 25 OC; 0.6 M (A); 0.7 M (U); 1 . 1 M (0). 1,2,3-OT 0.20
0.60 0.80 0.95 1.05
1529 1535 1533 1530
m-l s2 101'A, m-I 1,2-HD at 10 "C 53 25 43.9 6910 48.4 8940 50.4 8615
0.50 0.60 0.70 0.80 0.90 1.00 1.10
1547 1549 1550 1549 1547 1543 1542
1,2-HD at 25 O C 28.8 10.3 18.8 218 29.7 2460 40.6 3640 38.8 3430 71.7 3290 57.6 2880
0.20 0.25 0.30 0.35 0.40
1519 1524 1526 1524 1522
1,2,3-OT at 25 OC 28 23 1530 26.9 10100 25.1 11180 33 8770 31.2
9.6 3.1 4.9 6.0 10.9 11.2 5.6 7.1 8.7 9.6 11.3 1.20 0.81 1 .oo 1.37 1.90
'Experimental errors: v, 1 m s-l; A, *IO%; B, &15%;J~,5%. 400
0.8 1 .o concentration (M/L)
Figure 4. Variation offR with concentration for 1,2-HD (0)and 1,2,3OT (+) at 25 O C and 1,2-HD (0)at 10 O C .
found a value of 1.19. Thus, pyrene senses a more oillike environment in 1,2-HD or 1,2,3-0T than in C&, micellar solutions. 2. Ultrasonic Absorption. The ultrasonic absorption spectra have been determined at 10 and 25 OC in the range 0.5-1.1 M for 1,2-HD and at 25 OC in the range 0.2-0.4 M for 1,2,3-OT. For the sake of illustrating the results, we have shown in Figure 3 the ultrasonic absorption spectra of three 1,2-HD solutions in a semilogarithmic representation. In all instances eq 4, valid for (4) a single relaxation process, could be fitted to the experimental results. In eq 4, A is the relaxation amplitude, B a constant, and f~the ultrasonic frequency. A threeparameter (A, B, fR) weighted least-squares fitting procedure was adopted in which the quantity Y2
was minimi~ed.'~ The sum was taken over all experimental data. In Figure 3 the solid lines going through the experimental results have been obtained as just described. In general, the rms deviation ( ~ ~ / p where ) ' / ~ p is the number of experimental data was about 5%, that is, of the order of or less than the experimental uncertainty. This provides convincing evidence that the ultrasonic absorption spectra are characteristic of a single relaxation frequency. Table 11 lists the values of u, A, B, and fR of the various solutions investigated. Figure 4 shows the fR vs c plots at 25 OC. It is seen
Figure 5. Variation of AfR2with 1,2-HD concentration at 10 O C (0)and 25 OC (0).
that the results at C > cmc fall on straight lines, as to be expected from eq 2, whereas the data at C < cmc show positive deviations from these lines, which are quite large in the case of 1,2-HD. The systems at C < cmc are also characterized by small to very small relaxation amplitudes. The results are discussed in detail below (see Discussion). At this stage we only note that similar results have been reported for solutions of other surfactants, ionic and nonionic, with high cmc'sm9 as in the present study. Another remark must be made concerning the values of the fitting parameter B. For 1,2-HD as well as 1,2,3-OT solutions the values of B are seen to be larger than for pure water (35 X and 21.5 X m-I s2 at 10 and 25 OC,respectively). A similar result has often been found with solutions of ionic and nonionic s ~ r f a c t a n t s . * ~ ~ ~ *It~ ~indicates ~ ~ ~ . 5 that 0 - ~ some ~ process contributes to the high-frequency ultrasonic absorption of the investigated systems. Hydration and secondary as~ o c i a t i o n ~have ' . ~ ~been proposed to explain this high-frequency behavior, which is beyond the scope of the present study. (46) Adair, D.; Reinsborough, V.; Trenholm, H.; Valleau, J. Can. J. Chem. 1976, 54, 1162. (47) Adair, D.; Reinsborough, V.; Zamora, S.Adv. Mol. Rekax. Inleract. Processes 1977, 11, 63. (48) Gettins, J.; Jobling, P.;Walsh, M.;Wyn-Jones, E. J . Chem. Soc., Faraday Trans. 2 1980, 76,794. (49) Jones, P.; Wyn-Jones, E.;Tiddy, G. J. Chem. Soc.. Faraday Trans. I 1987,83, 2735. (50) Takeda, K. J . Sci. Hiroshima Uniu., Ser. A: Phys. Chem. 1976, 40. 87.
(45) Djavanbakht, A.; Lang, J.; Zana, R.J. Phys. Chem. 1977,81,2620.
(51) Rassing, J.; Wyn-Jones, E.Chem. Phys. Leu. 1973, 21, 93. (52) Graber, E. ThLe de 3 O Cycle, University of Strasbourg, 1969.
4836 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991
Frindi et al.
TABLE III: Valm of k-/u*, k - / N , k; k+, u, rad A V, for 1,2-HD and 1,2,3-OT micellar solutions 1Odk-/ 2," 1O-'k-/N.O 104k-, 1O+'k+, 1,2-HD (10 "C) 1,2-HD (25 "C) 1,2,3-OT (25 "C)
15f4 21 f 6 3.4 f 0.6
5.3 f 0.5 5.3 f 0.5 1.4 f 0.2
11 f 3 b
11 f 3 b 6.3 f I C
A Vo, cm3 mol-'
8 f l 6fl 13 f 3
1.5 f 0.4 1.8 f 0.4 2.5 f 0.7
7.8 f 1 7.1 f 1 (5.0)d 7.0 f 1 (5.8)d
.From the intercept and slope of the plots offR vs (C - cmh)/cmc,. *Calculated by assuming N = 20, independent of temperature (ref 28). CCalculatedby assuming N = 44 (ref 28). dThe values in parentheses are from ref 28.
--20 E v
Figure 7. Variation offR with (C- cmc,)/cmc, at 10 O C (0)and 25 "C ( 0 ) .
for I,2-HD solutions
1. Ultrasonic Relaxation Data at C < cmc. We have seen above that the solutions of 1,2-HD and 1,2,3-OTat C < cmc show the presence of a relaxation process with a relaxation frequency generally higher than that for solutions at concentrations above the cmc but not too large (see Figure 4). Similar results have been reported for aqueous solutions of various ionic surfactantsand for solutions of nonionic surfactants in organic solvent^.'^ These systems, as well as 1,2-HD and 1,2,3-OTaqueous solutions, are all characterized by fairly large cmc or "operational" cmc values. Besides, in the case of nonionic surfactants in organic solvents self-association is known to take place even below the operational cmc. This suggested that the relaxation process o b served at C < cmc may be associated to the reversible formation of oligomeric species such as dimers or trimers. Recall that the mechanism of micelle formation postulated by hiansson and Wall2' assumes a stepwise association of monomers S to aggregates S,:
(53) Rassing, J.; Sams,P. J.; Wyn-Jones, E. J . Chem. Soc., Furaduy Truns. 2 1973,69, 180.
The assumptions made in the derivation of eq 2 approximately reduce the species present in the system to monomers, a few oligomeric species (dimers, trimers, ...), and fully grown micelles having aggregation numbers within a narrow range, centered around N. Moreover only reaction 6d involving full micelles is assumed to contribute to the ultrasonic absorption of the system. This last approximation is good to very good for systems having a low to very low cmc. Indeed, the concentrations below the cmc are then very small and result in negligibly small amounts of oligomers, and therefore in very low excess ultrasonic absorption. Such may not be the case in systems with high to very high cmc's, for example between 0.3 and 1 M, corresponding to short-chain surfactants (4-7 carbon atoms depending on whether the surfactant is ionic or nonionic). Then at concentrationsslightly below the cmc, the amount of oligomers (essentially dimers and trimers) may be significant. Moreover, for oligomers k-, is probably larger than for the fully grown micelles, as the free energy change associated with the dissociation of a monomer from an oligomer is smaller than that from a full micelle.m As for the association
The Journal of Physical Chemistry, Vol. 95, NO. 12, 1991 4837
Ultrasonic Absorption Studies of Surfactant Exchange rate constant k+,, it remains close to the value for a diffusioncontrolled processIg (see below). The relaxation frequency fR‘ associated with the reversible formation of oligomers (i = 2,3) is of the form fR‘
= Gk+lC,+ k-,
where 6 is a numerical constant. It follows from the above that at C < cmc may be larger than fR (eq 2) at concentrations above the cmc but not too large. Besides, the volume change AVJ associated to the formation of oligomers (in cm3/mol of surfactant) is likely to be much smaller than AVOin eq 3 because the alkyl chains in oligomers still retain contacts with water contrary to the chains in full micelles. Thus, at C < cmc the relaxation amplitude A, which is proportional to (AVd/fR?2, would be quite small with respect to that in the micellar range. As C is increased beyond the cmc, the oligomer concentration may be reduced as oligomers are used up to form micelles. Their contribution to the ultrasonic absorption would thus rapidly vanish. This assumption would account for the observation of a single relaxation process, associated with exchange reactions involving full micelles, at C > cmc. Nishikawa et al.scs7 have reported four ultrasonic absorption investigations of aqueous solutions of various alkanediols. The compounds investigated were either with a very short chain (e.g. 1,2-butanediol)or with OH groups not located on the two terminal carbon atoms (e.g. 2-methylpentane-2,4iol) and their operational “cmc’s’’ were extremely high (well above 1 M). This resulted in a relaxational excess absorption below the cmc due to oligomer formation, characterized by high fR values, larger than at C > cmc, and the fR vs C plots showed a minimum, as in the case of 1,2-HD (see Figure 4). This fact was not recognized by the authors who attributed the relaxation processes observed in the whole C range (below and above the cmc) to a reversible association between the diol and non-hydrogen-bondedwater molecules and neglected the diol self-association in the interpretation of the results. 2. Kinetics of Exchange of I,2-HD and 1,2,3-OT between Micelles and Bulk Phase. As pointed out above the variations of fR and AfR2 with C a r e qualitatively as expected on the basis of the treatment of Aniansson and Wall2’for the kinetics of micelle formation. This result gives further support to the conclusion that 1,2-HD and 1,2,3-OT can be considered as nonionic surfactants, as much as the nonionic Triton X-100 for example. We can now turn to quantitative aspects of the kinetics of surfactant exchange in aqueous micellar solutions of 1,2-HD and 1,2,3-OT. First consider the values of k - / N . Recall that N / k represents the average residence time of a given surfactant in the The ratio between the values of N / k - for 1,2,3-0T and 1,2-HD is 3.5 and that is close to the value found for several series of ionic surfactant^.^^ Recall that this ratio is given by exp[AGo(CH2)/kT] where AGo(CH2) is the free energy change associated with the transfer of one methylene group from water to the most probable micelle (1.l-1 .2kr),21and should be equal to 3-3.3. Also we note that the k-/Nvalue for 1,2-HD is close
to that found for the dissociation of I-pentanol, which has the same alkyl chain as 1,2-HD, from cetyltrimethylammonium bromide micelles.s8 (The self-association of I-pentanol cannot be investigated in water where its restricted solubility prevents the formation of micelles.) This finding is similar to that made for ionic surfactants in solution: k-/N depends mainly on the alkyl chain length and only little on the nature of the head group.Ig The values of k- are quite large, characteristic of surfactants with a short alkyl chain. Note that the relative error on k- is larger than on k-/N, as the former also includes the error on N . At this stage, we note a surprisingly large difference between the reported Nvalues of 1,2-HD (20) and 1,2,3-OT (44).28 For such shortchain surfactants, one would have expected values of 15 and 25 for 1,2-HD and 1,2,3-OT, on the basis of the oil drop assuming alkyl chains with 5 and 7 carbons for these two surfactants, respectively. The values of k+ are all large and around (2 f 0.6) X IO9 M-’ s-’, which is smaller than the rate constant for a diffusion-controlled bimolecular association by a factor of only 5. Again this result is similar to that found for ionic surfactant^.'^*^^ Notice that the error on k+ is large, as it is the sum on the errors on k-/N, N , and the cmc. Finally, the standard deviation a, which characterizes the micelle polydispersity, is seen to be almost 2 times larger for 1,2,3-OT than for 1,2,-HD. As for ionic surfactants, a increases with N, and a 2 / N falls in the range 1-4.19
Conclusions The results presented above clearly show that 1,2-HD and 1,2,3-OT aggregates in water are similar to micelles of conventional nonionic surfactants. The polarity of the hydrophobic cow of these micellelike aggregates as sensed by the p p n e fluorescence is even lower than for C,,E, surfactants. Also, the Aniansson and Wall treatment for the kinetics of surfactant exchange between micelles and bulk holds for 1,2-HD and 1,2,3-OT and the rate constants associated to this process have for these two surfactants the same characteristics as for ionic surfactants. Thus the values of the rate constants for the incorporation of a surfactant monomer into a micelle are close to those for a diffusion-controlledprocess. The relative values of the residence times of 1,2-HD and 1,2,3-OT in micelles are again as found for ionic surfactants. Finally, the characteristics of the micelle polydispersity are also comparable to those for ionic surfactants. Note Added in Proof. Since this paper was accepted for publication, two new values of the aggregation number N of 1,2-HD micelles at the cmc have become available: N = 40 f 10 at 25 O C , from light scattering measurements in our laboratory, and N = 35 f 4, from vapor pressure measurements (Coudert, R. University of Tours, private communication). The values of k-/N, k-/a2,and AVOfor 1,2-HD in Table 111 are not modified, whereas the values of k-, k+, and a become larger, respectively equal to 1.9 X lo* s-I, 2.6 X IO9 M-’ S-I, and 11 at 10 OC and to 1.9 X IO9 s-’, 3.1 X IO9 M-’s-I, and 8 at 25 O C . The conclusions of the paper are not affected. Registry No. 1,2-HD, 6920-22-5; 1,2,3-OT, 112196-85-7; pyrene,
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