Langmuir 1996, 12, 5033-5041
5033
Micellar Properties of Sodium Sulfopropyl Alkyl Maleates in Aqueous SolutionsA Time-Resolved Fluorescence Quenching Study Hans von Berlepsch,* Katrin Sta¨hler,† and Raoul Zana† Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Rudower Chaussee 5, D-12489 Berlin, Germany, and Institut Charles Sadron (CRM-EAHP), 6 rue Boussingault, 67083 Strasbourg Cedex, France Received April 24, 1996. In Final Form: July 11, 1996X The aggregation behavior of four sodium sulfopropyl alkyl maleates with alkyl chain carbon numbers 12, 14, 16, and 18 has been investigated in aqueous solution as a function of surfactant concentration, added sodium chloride concentration, and temperature by means of electrical conductivity and timeresolved fluorescence quenching (TRFQ). Critical micelle concentration and micelle ionization degree decrease upon increasing chain length, exhibiting the classical behavior for straight alkyl chain surfactants, whereas the Krafft temperature, TK, increases. The aggregation numbers have been found to decrease with increasing temperature between TK and 65 °C, with the magnitude of decrease becoming higher for longer hydrophobic chains. The surfactants show micellar growth with surfactant and salt concentration. Whereas the increase of the aggregation number N with ionic strength I is generally weak and follows in good approximation the power law relation N ∝ Iβ, with a unique exponent β = 0.13 below a surfactantdependent characteristic threshold ionic strength, I*, N steeply increases beyond I*. The values of N indicate that the micelles are probably spheroidal below I*. The micellar polydispersity is generally low for ionic strength I < I* and increases with I, in agreement with the theory of micellization.
I. Introduction Due to their ability to lower interfacial tensions, surfactants are important substances in many applications and in fields ranging from different branches of big industry up to the daily use in households. The uses of dispersants or emulsifiers are the most frequent ones. In emulsion polymerization, surfactants are used to control the size of the resulting polymer particles and to stabilize the latexes. Polymerizable emulsifiers that covalently bind to particles during their synthesis possess the advantage not to desorb during the later application of the polymers.1-4 The homologous series of sodium sulfopropyl alkyl maleates HC
COO(CH2)3SO3Na
HC
COOCnH2n+1
with
n = 12, 14, 16, 18
were synthesized5,6 in view of their use as polymerizable emulsifiers. Many physicochemical investigations to characterize these compounds were carried out recently.6-10 The homologue with the longest hydrophobic chain, sodium sulfopropyl octadecyl maleate (SSPOM), especially * To whom correspondence should be addressed. † Institute Charles Sadron. X Abstract published in Advance ACS Abstracts, September 15, 1996. (1) Greene, B. W.; Sheetz, D. P.; Fisher, T. D. J. Colloid Interface Sci. 1970, 32, 90. (2) Tsaur, S.-L.; Fitch, R. M. J. Colloid Interface Sci. 1987, 115, 450. (3) Tauer, K.; Goebel, K.-H.; Kosmella, S.; Sta¨hler, K.; Neelsen, J. Makromol. Chem., Macromol. Symp. 1990, 31, 107. (4) Urquiola, M. B.; Dimonie, V. L.; Sudol, E. D.; El-Asser, M. S. J. Polym. Sci., Part A: Polym. Chem. 1992, 30, 2619 and 2631. (5) Kanegafuchi, Kogaku, Kogyo, Kabushiki, Kaisha. G.B. Patent, 1 427 789, 1976; U.S. Patent, 3 980 622, 1976. (6) Goebel, K.-H.; Sta¨hler, K.; von Berlepsch, H. Colloids Surf., A: Physiochem. Eng. Aspects 1994, 87, 143. (7) von Berlepsch, H.; Strey, R. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 1403. (8) von Berlepsch, H. Langmuir 1995, 11, 3667. (9) von Berlepsch, H.; Hofmann, D.; Ganster, J. Langmuir 1995, 11, 3676. (10) von Berlepsch, H.; Dautzenberg, H.; Rother, G.; Ja¨ger, J. Langmuir 1996, 12, 3613.
S0743-7463(96)00407-6 CCC: $12.00
attracted our attention because of its unusual mesoscopic properties. Thus, on the one hand SSPOM forms a highly ordered lamellar gel state below its Krafft boundary, and on the other hand it forms strikingly stiff wormlike micelles in the presence of sodium chloride. In a light-scattering study10 we demonstrated that the micelles formed at low salt concentrations are small, having a mean aggregation number of about 180 at 50 °C, exhibit a slight shape asymmetry, and do not increase in size with salt concentration as long as a critical threshold concentration of salt, corresponding to the spheroid-to-rod transition, is not reached. Data about the temperature dependence of micelle size, polydispersity, and chain length dependence for this class of polymerizable surfactants were still missing. Besides, sodium dodecyl sulfate (SDS) micelles and several other ionic surfactant micelles are known11,12 to grow slowly as a function of surfactant and salt concentration below the sphere-to-rod threshold. It was therefore interesting to know whether the shorter chain members of the maleate surfactant series show such an increase as well. The present study tries to answer some of these questions. The micelle sizes were characterized by the micelle aggregation numbers determined by the time-resolved fluorescence quenching technique.13-15 This method permits the determination of the micelle aggregation number at a given surfactant concentration, as it is insensitive to intermicellar interactions and micellar shape, contrary to, for instance, light or neutron scattering. However, the interpretation of the fluorescence data and the derived aggregation numbers is not always unambiguous. The results usually depend on the micellar models used in data analysis. In particular, whether the micelles are assumed polydispersed or not not only gives different aggregation numbers but may also lead to (11) Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1976, 80, 1075. (12) Croonen, Y.; Gelade´, E.; Van der Zegel, M.; Van der Auweraer, M.; Vandendriessche, H.; De Schryver, F. C.; Almgren, M. J. Phys. Chem. 1983, 87, 1426. (13) Zana, R. In Surfactant Solutions. New Methods of Investigation; Zana, R., Ed.; Marcel Dekker: New York, Basel, 1987; p 241. (14) Grieser, F.; Drummond, C. J. Phys. Chem. 1988, 92, 5580. (15) Gehlen, M. H.; De Schryver, F. C. Chem. Rev. 1993, 93, 199.
© 1996 American Chemical Society
5034 Langmuir, Vol. 12, No. 21, 1996
misleading conclusions about the size increase with surfactant concentration.16-19 It follows from the thermodynamics of self-assembling systems that the weightaveraged aggregation number must increase appreciably with the concentration of micellized surfactant if the polydispersity is large and must be nearly independent of concentration for small polydispersity. Size increase and polydispersity are interrelated, and a controversial debate about the correct interpretation of data is running. Therefore, careful experiments appeared necessary, and the present study provides further experimental data. II. Experimental Section and Theory II.1. Materials. The synthesis of the sodium sulfopropyl alkyl maleate involves two steps.6 In the first step the partial esterification of maleic anhydride with the long chain alcohol results in the corresponding half-ester. The second step is the esterification of the remaining carboxyl group with propanesultone. For purification the surfactants have been at least three times recrystallized from a water-acetone mixture. Thinlayer chromatography showed no impurities, indicating at least 99% purity. Sodium chloride (p.a.) was purchased from Prolabo. The fluorescence probes used were the ruthenium(II) derivatives Ru(bipy)2(bipy2C17)2+2Cl- and Ru(bipy)2(bipy2C10)2+2(ClO4)-, where bipy stands for bipyridine and bipy2Cn is a bipyridine on which have been covalently fixed two alkyl (C10 or C17) chains in order to make it more hydrophobic. 9-Methylanthracene (9MeA) was used as quencher. All solutions were prepared with Milli-Q quality water (conductivity < 1 µS cm-1 at 20 °C). II.2. Experimental Conditions. For the calculation of aggregation numbers from the fluorescence decay data, the critical micelle concentrations (cmc’s) as a function of temperature T and salt concentration cNaCl are necessary. These characteristics together with the Krafft temperatures (TK) and the micelle ionization degrees (R) for the different homologues were taken from refs 6 and 8 or measured during this study. All these quantities have been obtained from conductivity studies, as described in ref 6. The fluorescence decay curves were recorded by the singlephoton counting technique20 using the same apparatus as in previous studies. The fluorescence was excited at the wavelength 450 nm by a flash lamp with a fwhm value of about 3 ns.24 The emission was monitored above 530 nm with a high-pass cutoff filter. The decay curves were recorded mostly over about 4 lifetimes of the ruthenium probe (τ ) 550 ns at 40 °C), and the analysis of decay curves, using a nonlinear weighted least-squares fitting procedure, started about 20 channels after the peak maximum and included all channels (maximum number of channels: 512 or 1024) up to that channel where the statistics for the observed points became too poor (number of counts below 100). The total time window was broad enough, because both probe and quencher do not migrate and the intramicellar quenching rate constant, kq, is normally high enough compared with the reciprocal of the probe lifetime τ that the condition 10 > τkq > 1 was fulfilled. The total error in the aggregation number is estimated to be lower than (10%. When shorter time windows were used (at higher quencher concentrations for the shorter chain surfactants), the decay curves have been deconvoluted with the instrument response, which has been measured on a fluorophore-free surfactant solution. At the highest salt concentrations when the aggregation numbers were large, the asymptotic part of decay curves was sometimes not reached (τkq = 1), leading to larger errors in the decay parameters, estimated (16) Almgren, M.; Lo¨froth, J.-E. J. Chem. Phys. 1982, 76, 2734. (17) Reekmans, S.; Bernik, D.; Gehlen, M.; Van Stam, J.; Van der Auweraer, M.; De Schryver, F. C. Langmuir 1993, 9, 2289. (18) Nagarajan, R. Langmuir 1994, 10, 2028. (19) Zana, R. Langmuir 1995, 11, 2314. (20) Demas, J. N. Excited State Lifetime Measurements; Academic Press: New York, 1983. (21) Binana-Limbe´le´, W. Doctoral Thesis, University Louis Pasteur, Strasbourg, France, 1988. (22) Lang, J.; Lalem, N.; Zana, R. J. Phys. Chem. 1991, 95, 9533. (23) Zana, R.; Levy, H.; Papoutsi, D.; Beinert, G. Langmuir 1995, 11, 3694. (24) Fuchs, C.; Henck, R. J. Appl. Phys. 1986, 60, 427.
von Berlepsch et al. to be (15%. In all measurements the number of counts in the maximum of the decay curve was at least 104. The probe concentration was always kept proportional to the concentration of micellized surfactant, 1 µM for a 5 mM surfactant solution. For selected surfactant and salt concentrations the quencher concentration was varied, in order that the average number of quencher molecules per micelle was between ∼0.5 and ∼2.0. Most of the fluorescence measurements were performed at the standard temperature of 41 °C, but some temperature scans between the corresponding Krafft temperatures and 65 °C have been performed. Prior to the fluorescence measurements the solutions were thoroughly deoxygenated by repeated freezepump-thaw cycles and equilibrated to the measuring temperature. II.3. Time-Resolved Fluorescence Quenching (TRFQ). In TRFQ experiments the fluorescence decay after a short excitation pulse is analyzed by appropriate kinetic models. The relevant information on the investigated system is obtained from the values of the fitting parameters. The basic expression for the fluorescence intensity25-27
I(t) ) I(0) exp{-A2t - A3[1 - exp(-A4t)]}
(1)
where
A2 ) τ-1 + kq[Q](k+ + keK[M])/A4(1 + K[M]) (2) A3 ) RK[M](1 + K[M])-1(kq/A4)2
(3)
A4 ) kq + k- + ke[M]
(4)
has been derived under the assumption of a δ-pulse excitation at time t ) 0, monodispersity of surfactant micelles, and a probe immobility during the time scale of the fluoresence experiment, whereas the quencher can migrate from one micelle to another, and the assumption that the quencher molecules are distributed among micelles in a Poissonian way. Here [Q] and [M] are the molar concentrations of quencher and micelles, respectively, τ is the fluorescence lifetime, kq is the intramicellar quenching rate constant, ke is the rate constant for micelle collisions, k- and k+ are the quencher exit and entry rate constants from or into the micelles with K ) k+/k-, and R ) [Q]/[M]. For charged micelles where collisions can be neglected (ke[M] , kq) and when the quencher and probe molecules do not exchange via the bulk phase within the lifetime of the probe (k- , kq), eqs 2-4 reduce to the much simpler expressions
A2 ) τ-1, A3 ) [Q]/[M], A4 ) kq
(5)
and the average micelle aggregation number is given by
N ) A3(c - cmc)/[Q] ) A3/η
(6)
where the quencher-to-surfactant molar ratio, η ) [Q]/(c - cmc), has been introduced. The experimental criterion for considering the quencher as immobile is constancy of the fit parameter A2 at varying quencher concentrations. In the above theory the micelles are considered as monodisperse. Polydispersity effects have to be included in the interpretation of fluorescence decay data for systems where the micelles are able to grow, because this is usually associated with a broadening of the size distribution. Introducing polydispersity leads to some modifications but leaves eq 1 unchanged.16,28 The apparent aggregation number obtained by using eq 1 becomes dependent on the quencher concentration and has to be considered as a quencher-averaged aggregation number, hereafter denoted Nq, given by (25) Infelta, P. P.; Gra¨zel, M.; Thomas, J. K. J. Phys. Chem. 1974, 78, 190. (26) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (27) Dederen, J. C.; Van der Auweraer, M.; De Schryver, F. C. Chem. Phys. Lett. 1979, 68, 451. (28) Warr, G.; Grieser, F. J. Chem. Soc., Faraday Trans. 1 1986, 82, 1813.
Sodium Sulfopropyl Alkyl Maleates
Langmuir, Vol. 12, No. 21, 1996 5035
Table 1. Krafft Temperatures, Critical Micelle Concentrations, and Micelle Ionization Degrees of Sodium Sulfopropyl Alkyl Maleates SSPDM TK (°C) cmc (mM) at 30 °C at 40 °C at 50 °C R f
I*, respectively. Also the SSPOM data fit reasonably into the general picture if deviations up to about 15% are accepted. Fourthly, the threshold ionic strength increases exponentially as the surfactant chain length decreases. The characteristic screening length (1/κD*) ∝ (I*)-1/2, increases by a factor of about 2.1 per two CH2 groups. This finding is consistent with the higher micellar ionization degree, R, or larger effective micelle surface charge as n is decreased (cf. Table 1). To shield the micellar charges, larger amounts of counterions are required. The similarity in shape of the different plots in Figure 6 led us to construct a “universal” master curve by shifting the plots along the Nq axis, applying different normalization factors. The resulting curve is shown in Figure 7. The graph expresses once more the phenomenological fact that the weak micelle growth for the investigated family of surfactants below I* may be described to a very good approximation by the power law
5038 Langmuir, Vol. 12, No. 21, 1996
von Berlepsch et al.
Figure 7. Master plot of the data in Figure 6, using the same symbols but without distinguishing between open and filled ones.
Nq ) κ2Iβ
(10)
with a chain length-independent universal exponent β ) 0.128. κ2 is an empirical constant. A more general expression with a nonzero intercept was also checked but does not lead to a better fit of the experimental data (β then differs by less than 0.1%). The data above the respective I* have been fitted by an exponential law. A power law with a much higher exponent is equally possible, but the experimental data are not accurate enough to permit an unambiguous choice. It should be noted here once more that care has to be taken in interpreting tendencies in size increase when only quencher-averaged micellar aggregation numbers, are considered, as done until now, because micelle sizes and polydispersity are not independent quantities. Polydispersity effects are discussed below and do not affect the present picture qualitatively. TRFQ investigations similar to the ones above have been carried out for other homologous series of ionic surfactants, especially for alkyltrimethylammonium halides and SDS, and we now compare our results with some of them. Roelants and De Schryver38 investigated three alkyltrimethylammonium chlorides (C12, C14, C16) and found a similarly stronger size increase versus concentration or added salt for the longer chain length homologues compared with the shorter ones. Almgren and Lo¨froth,39 Croonen et al.,12 Bales and Almgren,40 and Quina et al.41 found that SDS micelles grow with salt and surfactant concentrations but with an exponent β of about 1/4.12,40,41 This characteristic exponent for SDS has been confirmed in other studies by using different experimental methods (cf. Figure 2 in ref 41) and appears experimentally well established. Values between 0.06 and 0.42 for an analogous power law dependence of weight-averaged molecular masses on ionic strength have been obtained for other alkyldimethyl- and trimethylammonium halides from static light scattering and have been summarized.42 Our β value ranges within these data. Whereas the transition range from spheroidal to rodlike aggregates is well investigated experimentally and many data are available, the theoretical description of the effect was largely qualitative until now. The difficulties in the theory arise especially from the treatment of electrostatic interactions. One instructive theoretical paper by Rao (38) Roelants, E.; De Schryver, F. C. Langmuir 1987, 3, 209. (39) Almgren, M.; Lo¨froth, J.-E. J. Colloid Interface Sci. 1981, 81, 486. (40) Bales, B. L.; Almgren, M. J. Phys. Chem. 1995, 99, 15153. (41) Quina, F. H.; Nasser, P. M.; Bonilha, J. B. S.; Bales, B. L. J. Phys. Chem. 1995, 99, 17028. (42) Ikeda, S. Colloid Polym. Sci. 1991, 269, 49.
Figure 8. Quencher-averaged aggregation numbers, Nq, as a function of quencher-to-surfactant ratio, η, for SSPDM (O, 10 mM), SSPTM (3, 10 mM), SSPHM (0, 5 mM), and SSPOM (4, 5 mM) at 41 °C. The straight lines are weighted linear leastsquares fits (cf. section III.2.3).
Figure 9. Quencher-averaged aggregation numbers, Nq, as a function of quencher-to-surfactant ratio, η, for 5 mM SSPOM solutions at different temperatures (0, 41 °C; O, 50 °C; 4, 50 °C, cNaCl ) 50 mM). The straight lines are weighted linear least-squares fits.
and Ruckenstein43 deals with this problem. The authors used in the framework of molecular thermodynamic models44-47 two approaches, the optimal micelle size approach and the size distribution model for a theoretical description. These approaches allow only a numerical solution and give no analytical expression for a growth law in the transition regime; nevertheless, they predict the experimentally observed trends, that is the decrease in threshold concentration with decreasing head group size and with increasing degree of counterion binding to the micellar surface. III.2.3.3. Dependence on Quencher Concentrations Polydispersity Effects. Information about the aggregate size distribution function may be obtained via eq 7 from a study of the quencher concentration dependence of the quencher-averaged aggregation numbers, Nq, at a given surfactant concentration. The variation of Nq with η ) [Q]/(c - cmc), the [quencher]/[micellized surfactant] molar ratio is represented in Figures 8-10. Figure 8 shows the results for salt-free solutions of all four homologues at 41 °C, and Figures 9 and 10 show the data obtained for two different temperatures and after the addition of different amounts of salt, respectively. The data points have been fitted by straight lines, applying a weighting factor (43) Rao, I. V.; Ruckenstein, E. J. Colloid Interface Sci. 1987, 119, 211. (44) Ruckenstein, E.; Nagarajan, R. J. Phys. Chem. 1975, 79, 2622. (45) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1525. (46) Gelbart, W. M.; Ben-Shaul, A.; McMullen, W. E.; Masters, A. J. Phys. Chem. 1984, 88, 861. (47) Nagarajan, R.; Ruckenstein, E. Langmuir 1991, 7, 2934.
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Langmuir, Vol. 12, No. 21, 1996 5039
Figure 10. Quencher-averaged aggregation numbers, Nq, as a function of quencher-to-surfactant ratio, η, for 10 mM SSPDM solutions at different NaCl concentrations (0, salt-free; 4, 30 mM; O, 250 mM) at 41 °C. The straight lines are weighted linear least-squares fits. Table 3. Weight-Averaged Aggregation Numbers, Nw, and Polydispersity Indices, σ/Nw, for Various Solutions Calculated by Means of Eq 7 T ) 41 °C c (mM) Nw σ/Nw
SSPDM
SSPTM
SSPHM
SSPOM
10 96 0.094
10 136 0.309
5 153 0
5 239 0.126
c ) 5 mM SSPOM T ) 41 °C cNaCl (mM) Nw σ/Nw cNaCl (mM) Nw σ/Nw
0 239 0.126
T ) 50 °C 0 203 0
c ) 10 mM SSPDM; T ) 41 °C 0 30 96 144 0.094 0.166
T ) 50 °C 50 295 0.278 250 177 0.288
proportional to [Q] to all data points, which takes into account the increasing accuracy in the fitted decay parameters used to calculate Nq with increasing [Q]. The error bars are thus getting smaller with increasing [Q]. The considerable scatter in the Nq data does not justify the use of a nonlinear fit, and the second-order term ∝η2, in eq 7 was neglected. This is equivalent to assuming a symmetrical size distribution function. We found always negative or zero slopes, indicating some polydispersity. But the degree of polydispersity quantified by the relative standard deviation, σ/Nw, has to be considered again with some caution because of the obvious experimental uncertainties. The computed weight-averaged aggregation numbers and polydispersities are listed in Table 3. The polydisersity indices of the salt-free solutions of the different homologues are generally small, indicating a low polydispersity, but with a somewhat higher value for SSPTM. The temperature dependence was only studied for SSPOM and is likewise weak, as long as cNaCl < c*NaCl. In the regime of strong micelle growth, above c*NaCl, the polydispersity increases significantly. The polydispersity increase is also perceptible for SSPDM in the presence of salt, and this effect is already visible below c*NaCl due to the generally lower level of error for this homologue. A correct interpretation of aggregation numbers and polydispersity has to be checked for consistency with the thermodynamics of micellization. This is done in the following, starting with the influence of temperature. Israelachvili et al.45 have derived an expression for the standard deviation of the aggregation number distribution function, σ, valid for a nearly Gaussian distribution of
spherical micelles. Suppressing constant prefactors, the expression reads σ ∝ T1/2γ1/2N2/3, with γ the interfacial tension at the micelle hydrophobic core-water interface and N the optimal aggregation number. Under the assumption that N is close to Nw and neglecting the temperature dependence of the interfacial tension term, the relation for the relative standard deviation, σ/Nw ∝ T1/2Nw-1/3, follows. Inserting the above listed Nw values for SSPOM at 41 and 50 °C, a total increase of σ/Nw by only about 7% is predicted. The expected effect is smaller than the error range of aggregation numbers and under the present experimental conditions not detectable. The dependence of the weight-averaged aggregation number, Nw, on ionic strength is now considered. The three available values for SSPDM at different salt concentrations have been found to obey the power law eq 10, with an exponent β ) 0.136, only 7% larger than that for the Nq versus I plot, owing to the low polydispersity of the systems (small slope of the Nq versus η curves). The generally low polydispersity below I* permits us to generalize this result without making a large error and to conclude that the growth law as represented by eq 10 also holds for the weight-averaged aggregation number for the present family of surfactants. This relation is needed for the discussion. A connection between micellar size increase and polydispersity follows from the thermodynamics of selfassembling systems.48 Recently, Nagarajan has drawn attention to this fact in discussing the consistency of the interpretation of dynamic fluorescence quenching data.18 He derived the following expression:
∂ ln Nw ) [Nz/Nw - 1] ∂ ln
∑NXN +
Nz(Rw - Rz) ∂ ln Xc (11)
where XN is the concentration of micelles with aggregation number N, ∑NXN is the total concentration of surfactant present as micelles, and Xc is the total concentration of counterions, including the counterions of the nonmicellized surfactant in solution, micelles, and added salt. Nw and Nz, as well as Rw and Rz, are the weight- and z-averaged mean values of the aggregation number and effective degree of ionization, respectively, defined as
Nw )
∑N2XN, ∑NXN
∑N3XN and ∑N2XN ∑RNN2XN, R ) ∑RNN3XN Rw ) z ∑N2XN ∑N3XN Nz )
(12)
The size dispersion of micelles is characterized by the variance σ2, defined as 2
σ
(
)
(N - Nw)2NXN Nz ∑ ) ) Nw2 -1 Nw ∑NXN
(13)
The derivation of eq 11 involves no specific model for the electrostatic interaction. This relation indicates that, for monodispersed ionic micelles (i.e., Nw ) Nz and Rw ) Rz), Nw is invariant with total surfactant concentration and total counterion concentration. On the contrary, for polydispersed micelles Nw must increase with the total surfactant concentration. Equation 11 was applied to our results with the following simplifications. First, the contribution of the micelles in the expression of the total (48) Hall, D. G.; Pethica, B. A. In Non-ionic Surfactants; Schick, M., Ed.; Marcel Dekker: New York, 1967.
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Figure 11. Master plot of quencher-averaged aggregation numbers, Nq, as a function of the micellized surfactant concentration (c - cmc), for SSPDM (O), SSPTM (3), and SSPHM (0) at 41 °C. The solid line is a power law fit: Nq ∝ (c - cmc)0.093.
counterion concentration is neglected, that is the above defined ionic strength I of small ions (eq 9) is used instead of Xc. Second, we consider either the concentration dependence, neglecting the second term, or the ionic strength dependence, neglecting the first term on the righthand side of eq 11, and obtain two relations characterizing the size and charge polydispersity, respectively:
[ ] [ σ Nw
2
=
]
∂ ln Nw
∂ ln(c - cmc)
(14)
I
and
Nz(Rw - Rz) =
[
]
∂ ln Nw ∂ ln I
(c-cmc)
(15)
To check eq 14 we plotted the concentration dependences of Nq (SSPDM, SSPTM, and SSPHM results of Figure 6) in normalized form against the micellized surfactant concentration (c - cmc) and obtained the plot represented in Figure 11. The data could be fitted again by a power law, but with the somewhat smaller exponent 0.093. The dependence of Nw on concentration is expected to be stronger than that for Nq but has not been estimated. Thus, using Nq instead of Nw, we find via eq 14 a lower limit for the polydispersity index, σ/Nw, amounting to about 0.30. Comparison with the experimentally estimated polydispersities given in Table 3 shows good agreement for SSPTM. The other two experimental values, excluding those of SSPOM, appear too low. The SSPOM data have not been included in Figure 11 because the aggregation number in this case does not depend within experimental error on surfactant and salt concentration, respectively, and a vanishing polydispersity would follow from theory. The experimental values (Table 3) confirm this prediction. Nevertheless, all deviations are not too large and the experimental data show some scatter, so that rough agreement seems to be given. To estimate the charge polydispersity, we go back to Figure 7. If we consider the measured ionic strength dependence of Nq, assuming only a change in salt concentration, then we obtain from the power law exponent β via eq 15 and, using the general relationship Nz ) Nw + (σ2/Nw), the numerical estimate (Rw - Rz) = 0.136/Nw. The SSPDM data for the ionic strength dependence of Nw listed in Table 3 give values for the difference of weightand z-averaged mean ionization degrees of the order of 10-3, in agreement with Nagarajan’s18 conclusion that this effect should be very small, as long as the aggregation number does not increase dramatically with I. Our result shows indeed that R may be considered a constant independent of ionic strength in the regime of low micellar growth, where charge polydispersity plays no role. III.2.3.4. Size Dependence of Quenching Rate Constant. The first-order quenching rate constant, kq, depends on the surfactant and added salt concentrations (section
Figure 12. Intramicellar quenching rate constant, kq, as a function of reversed quencher-averaged aggregation number for SSPDM (O, 10 mM), SSPTM (3, 10 mM), SSPHM (0, 5 mM), and SSPOM (4, 5 mM) at 41 °C. Symbols represent data obtained by varying salt concentration.
III.2.2). The reason for this behavior is the size dependence of the intramicellar quenching process. When kq is plotted versus the reverse aggregation number, as done in Figure 12, we find a nearly linear relation as long as the aggregation number is not too large. A qualitatively similar behavior has been found for several systems, among others by Almgren and Lo¨froth39 for SDS using the tris(2,2′-bipyridyl)ruthenium(II)/9-MeA pair. Various theoretical models have been developed for describing the diffusion-controlled quenching process.49-51 The results depend on the distribution function of the probe and quencher in the micelle and on micelle shape, and it is often difficult to distinguish between different models on the basis of experimental data. For spherical or nearly spherical micelles and when probe and quencher are confined to a surface layer, a kq ∝ R-2 dependence is predicted, and if the reactants are distributed throughout the core, a kq ∝ R-3 ∝ 1/Nq relation holds, with R an equivalent sphere radius.51 Our data appear to favor the three-dimensional diffusion model. This seems to be consistent also with the simplified view that the ruthenium probe is fixed more or less in the surface layer whereas 9-MeA can diffuse more or less throughout the micelle core due to its high hydrophobicity. Deviations from the linear kq versus 1/Nq relation at large Nq in Figure 12 may be explained as indicating the transition to rod-shaped micelles, for which kq ∝ 1/N2 is suggested.52 The factor of proportionality in these relations is a measure of the effective microviscosity, sensed by the quencher in its motion within the micelle core. The temperature dependence of the product Nqkq represented in Figure 3 thus reflects the temperature dependence of reverse microviscosity, with ∆Eq its activation energy. The comparison of the tabulated Nqkq values listed in Table 2 for different chain lengths reveals an increase in microviscosity by a factor of about 1.3 for two additional CH2 groups in the alkyl chain. A similar effect was recently found for zwitterionic surfactants53 with varying carbon number of the intercharge group and has been connected with changes in their conformation. In present case the effect is likewise significant, but its interpretation is unclear. To correlate aggregation numbers with micelle radii and shape is problematic in the present case because of missing reliable data about specific volumes and the (49) Go¨sele, U.; Klein, A.; Hauser, M. Chem. Phys. Lett. 1979, 68, 292. (50) Tachiya, M. Chem. Phys. Lett. 1980, 69, 605. (51) Van der Auweraer, M.; De Schryver, F. C. Chem. Phys. 1987, 111, 105. (52) Almgren, M.; Alsins, J.; Mukhtar, E.; Van Stam, J. J. Phys. Chem. 1988, 92, 4479. (53) Kamenka, N.; Chevalier, Y.; Zana, R. Langmuir 1995, 11, 3351.
Sodium Sulfopropyl Alkyl Maleates
Langmuir, Vol. 12, No. 21, 1996 5041
Figure 13. Weight-averaged molecular masses of micelles, Mw, for sodium sulfopropyl alkyl maleates as a function of critical micelle concentration. T ) 41 °C, c ) 5 mM.
conformation of the surfactant molecules. All conclusions would be more or less speculative, and thus we discussed only the aggregation number dependence of kq. Nevertheless, to know these parameters would be important, and some general trends are visible, indeed. To discuss them, we first refer to our X-ray and lightscattering studies8,10 on SSPOM solutions. We obtained from SAXS for the radius of the rods in the hexagonal HR phase r ) 2.46 nm, a value which was confirmed roughly by the static light-scattering measurement for the wormlike micelles in dilute solutions, at a high content of NaCl (cNaCl > 100 mM). This radius should also be the minimum radius of a hypothetical spherical micelle. It is then obvious that with an aggregation number around 200 the spherical model fails. A model of a prolate spherocylindrical micelle with hemispherical ends and using a density value of ρo ) 1.1855 g/cm3 10 lead to an axial ratio of about 1.7. An upper limit for the radius of a spherical micelle may be computed from the extended length of an alkyl chain with 24 carbon atoms, the total number of carbon atoms of the SSPOM molecule, by using Tanford’s formula: 54 0.15 ( 0.1265(24) ) 3.19 nm. A nearly identical effective radius has been derived from a fit of the static lightscattering data. Dynamic light scattering gave a value which was by about 20% larger. These experimental results led us to conclude that the SSPOM micelles at low salt concentration and 50 °C are spheroidal with an axis symmetry well below 2. We think that the same should be true also for the other homologues. Computer modeling methods and small-angle-scattering experiments should be helpful to get more reliable micelle radii. SANS studies are in progress. To summarize the results in this section, we represent in Figure 13 a log-log plot of the weightaveraged molecular masses of micelles, Mw, versus the cmc for the four homologues. The plot is linear, and Mw may thus be expressed empirically by
log Mw ) κ3 - κ4 log(cmc)
(16)
An identical equation has been found to also hold for the micelle molecular masses, determined by static light scattering by Huisman55 on several sodium alkyl sulfates independently of alkyl chain length. The empirical constants for the sodium sulfopropyl alkyl maleates are κ3 ) 3.712 and κ4 0.319. Combining eqs 16 and 8 leads to a power law dependence for the weight-averaged aggregation number as a function of ionic strength with an exponent β given by the product β ) κ4(1 - R). Quina et al.41 have recently report the latter relation and predicted from the numerical values of the constants κi, taken from Huisman’s work and others, the power law exponent of 0.25 for SDS and values ranging between 0.19 and 0.27 for other alkyl sulfate homologues. Because our κ4 is comparable with that of the sodium alkyl sulfate series (0.336 for SDS41), we get β values between 0.18 and 0.27 for increasing alkyl chain length, i.e. much higher than experimentally estimated (0.128) and of the same order as for the alkyl sulfates. It seems to us that the above expression of β is not of complete general character, contrary to the suggestions of Quina et al. IV. Conclusions Time-resolved fluorescence quenching studies of micellar solutions of four sodium sulfopropyl alkyl maleates confirm the general and well-known trends in the micellization of ionic surfactants. The investigations also revealed special properties of this new family of polymerizable surfactants. The four amphiphiles investigated exhibit with increasing concentration or after addition of salt micelles of increasing sizes and a spheroid-to-rod transition. Both the concentration and salt dependence of the aggregation number follow the same curve if plotted against the ionic strength. Thus, the ionic strength of the solution controls the increase of aggregate size. The threshold concentration for the steep elongational growth decreases with increasing alkyl chain length. An unexpected result is the fact that the law of growth below the threshold ionic strength, I*, is to a good approximation a power law with the same exponent, about 0.13, irrespective of chain length. This value is half that reported for SDS. Obviously, the exponents have to be considered as specific to the surfactants and necessitate a deeper theoretical interpretation. The micelle polydispersity below I* is always low and increases markedly only above I*, in agreement with general concepts of micellization. The agreement between the predicted polydispersity index derived from the increase of aggregate size by thermodynamic relations and the measured one is satisfying. It is better than in former TRFQ studies but not perfect. Acknowledgment. The authors thank K.-H. Goebel for providing part of the surfactants. H.v.B. was supported by a grant from a MPG/CNRS special fund and gratefully acknowledges the hospitality encountered during his stay at the Institute Charles Sadron. LA960407A
(54) Tanford, C. The Hydrophobic Effect, 2nd ed.; Wiley Interscience: New York, 1980.
(55) Huisman, H. F. Proc. K. Ned. Akad. Wet. 1964, B67, 367.
