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Aggregation Model That Describes the Physical Properties of the Sodium Dodecyl Sulfate/Poly(propylene glycol) System in Aqueous Solution E. Rodenas* and M. L. Sierra Departamento de Quı´mica Fı´sica, Universidad de Alcala´ de Henares, 28871 Alcala´ de Henares, Madrid, Spain Received July 13, 1995. In Final Form: December 18, 1995X
Micellar ionization degrees, from conductivity measurements, and micellar aggregation numbers, from steady-state quenching fluorescence of the sodium dodecyl sulfate/poly(propylene glycol) (SDS/PPG) (MW ) 425 and 1000) systems in aqueous solution, have been obtained. From the experimental results we conclude that small aggregates form on the polymer chain at a surfactant concentration c1 smaller than the surfactant cmc. The aggregation numbers of these aggregates sharply increase with SDS concentration and, at a critical surfactant concentration (c2) higher than the SDS cmc, the aggregates become large enough to incorporate the polymer chains into the surfactant micelles, forming SDS/PPG mixed micelles in aqueous solution, that are similar to the cetyltrimethylammonium bromide (CTAB)/PPG and surfactant/ medium chain alcohols mixed micelles.
Introduction The interactions between anionic surfactants and uncharged water soluble polymers, such as PEO (poly(ethylene oxide))1-16 and PVP (poly(vinylpyrrolidone)),1,5,8,17-19 have been widely studied. According to the results, it is well established that when surfactant is added to a polymer solution small surfactant aggregates form on the polymer chain.1 The surfactant concentration at which the aggregates start to form, called the critical aggregation concentration (cac), is normally lower than the surfactant critical micelle concentration (cmc). As surfactant concentration increases, the polymer chain becomes saturated with surfactant aggregates and, above this concentration, simple surfactant micelles form in the aqueous solution, in equilibrium with the polymer/ * To whom correspondence should be addressed. Fax no. 34 1 885 47 63. X Abstract published in Advance ACS Abstracts, March 1, 1996. (1) Goddard, E. D. Colloids Surf. 1986, 19, 255-300. (2) Nagarajan, R. Colloids Surf. 1985, 13, 1-17. (3) Schwuger, M. J. J. Colloid Interface Sci. 1973, 43, 491-498. (4) Cabane, B. J. Phys. Chem. 1977, 81, 1639-1645. (5) Turro, N. J.; Baretz, B. H.; Kuo, P.-L. Macromolecules 1984, 17, 1321-1324. (6) Franc¸ ois, J.; Dayantis, J.; Sabbadin, J. J. Eur. Polym. 1985, 21, 165-174. (7) Tondre, C. J. Phys. Chem. 1985, 89, 5101-5106. (8) Lissi, E. A.; Abuin, E. J. Colloid Interface Sci. 1985, 105, 1-6. (9) Ruckenstein, E.; Huber, G.; Hoffmann, H. Langmuir 1987, 3, 382-387. (10) Witte, F. M.; Engberts, J. B. F. N. J. Org. Chem. 1987, 52, 47674772. (11) Brackman, J. C.; Engberts, J. B. F. N. J. Colloid Interface Sci. 1989, 132, 250-255. (12) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Phys. Chem. 1991, 95, 462-467. (13) van Stam, J.; Almgren, M.; Lindblad, C. Prog. Colloid Polym. Sci. 1991, 84, 13-20. (14) Xia, J.; Dubin, P. L.; Kim, Y. J. Phys. Chem. 1991, 96, 68056811. (15) Lo¨froth, J.-E.; Johansson, L.; Norman, A.-C.; Wettstro¨m, K. Prog. Colloid Polym. Sci. 1991, 84, 73-77. (16) Brown, W.; Fundin, J.; Miguel, M. G. Macromolecules 1992, 25, 7192-7198. (17) Arai, H.; Murata, M.; Shinoda, K. J. Colloid Interface Sci. 1971, 37, 223-227. (18) Fishman, M. L.; Eirich, F. R. J. Phys. Chem. 1971, 75, 31353140. (19) Shirahama, K.; Mukae, K.; Iseki, H. Colloid Polym. Sci. 1994, 272, 493-496.
surfactant complexes.20,21 The presence of both types of aggregates has been detected by different techniques such as conductivity,3,10,15,20-23 surface tension,3,4 equilibrium dyalisis,17,18 fluorescence,5,24 or dye solubilization,3,17,25 and at a fixed polymer content, two break points are found in the physical property-surfactant concentration curves. When the polymer of low molecular weight poly(propylene glycol) (PPG, MW ) 425, 1000) is used with the cationic surfactant cetyltrimethylammonium bromide (CTAB), the results obtained for the systems formed at low surfactant and polymer concentrations, when mixed micelles in aqueous solution are formed, showed that the polymer behaves as a medium chain alcohol, forming CTAB/PPG mixed micelles with smaller aggregation numbers and higher ionization degrees than simple CTAB micelles in aqueous solution.26 The polymer (PPG) again behaves as a medium-chain alcohol in the presence of high polymer and surfactant contents in the L phase of the CTAB/PPG/H2O ternary system.27 The same conclusion was reached when this polymer was used in the presence of the anionic surfactant sodium dodecyl sulfate (SDS) at high surfactant and polymer concentrations, according to the phase diagram of the SDS/PPG/H2O ternary system.28 In this paper the SDS/PPG mixed micelles in aqueous solution have been studied, trying to elucidate whether PPG behaves the same with SDS as with CTAB or it behaves as other larger uncharged water soluble polymers do in other surfactant/polymer systems.1 (20) Fadnavis, N.; Engberts, J. B. F. N. J. Am. Chem. Soc. 1984, 106, 2636-2640. (21) Fadnavis, N.; van den Berg, J.-J.; Engberts, J. B. F. N. J. Org. Chem. 1985, 50, 48-52. (22) Zana, R.; Binana-Limbele, W.; Kamenka, N.; Lindman, B. J. Phys. Chem. 1992, 96, 5461-5465. (23) Kamenka, N.; Burgaud, I.; Zana, R.; Lindman, B. J. Phys. Chem. 1994, 98, 6785-6789. Kamenka, N.; Burgaud, I.; Treiner, C.; Zana, R. Langmuir 1994, 10, 3455-3460. (24) Winnik, F. M.; Winnik, M. A.; Tazuke, S. J. Phys. Chem. 1987, 91, 594-597. Winnik, F. M.; Ringsdorf, H.; Venzmer, J. Langmuir 1991, 7, 905-911. Winnik, F. M.; Ringsdorf, H.; Venzmer, J. Langmuir 1991, 7, 912-917. (25) Nilsson, S.; Holmberg, C.; Sundelo¨f, L.-O. Colloid Polym. Sci. 1995, 273, 83-95. (26) Sierra, M. L.; Rodenas, E. J. Phys. Chem. 1993, 97, 1238712392. (27) Sierra, M. L.; Rodenas, E. Langmuir 1994, 10, 4440-4445. (28) Sierra, M. L.; Rodenas, E. Langmuir 1996, 12, 573.
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Figure 1. Specific conductivity of the SDS/PPG (MW ) 425) systems with the surfactant concentration, at a fixed PPG concentration: (b) SDS, (4) [PPG] ) 10-3 M, (0) [PPG] ) 10-2 M, (O) [PPG] ) 0.1 M. The SDS/PPG conductivity curves are displaced 3 units from the Y-scale to improve visibility.
Figure 2. Specific conductivity of the SDS/PPG (MW ) 1000) systems with the surfactant concentration, at a fixed PPG concentration: (4) [PPG] ) 10-4 M, (0) [PPG] ) 10-3 M, (O) [PPG] ) 10-2 M. Each of the conductivity curves for the systems at [PPG] ) 10-3 and 10-2 M are displaced 3 units from the Y-scale.
Experimental Section SDS (Sigma) and poly(propylene glycol) (MW ) 425 and 1000) (Aldrich) were used without further purification. Pyrene (Merck) and N-cetylpyridinium chloride (Merck) were recrystallized several times, from methanol (Scharlau, gradient HPLC grade) for the pyrene and MeOH/Et2O (Scharlau, purissimo) for the N-cetylpyridinium chloride. Cetylpyridinium was first dissolved in the minimum amount of MeOH and then precipitated adding Et2O. Specific conductivities were determined in a Crison 525 conductimeter with cell constant 1.000 cm-1. All the measurements were thermostated at 25.0 ( 0.1 °C. Steady-state fluorescence measurements were carried out in a Perkin-Elmer LS-5B spectrofluorometer, thermostated at 25.0 ( 0.1 °C. Pyrene was excited at 336 nm, and its emission was monitored at 375 and 386 nm, corresponding to the first and third vibronic peaks of the emission spectrum of pyrene.
Results Conductivity Study. Specific conductivities of the SDS/PPG system in aqueous solution and at a fixed PPG concentration, at different surfactant concentrations, are represented in Figures 1 and 2 for the systems formed
Langmuir, Vol. 12, No. 6, 1996 1601
with PPG (MW ) 425) and PPG (MW ) 1000), respectively. The figures show two break points in the conductivityconcentration curves (c1 and c2), the same as those shown by other polymer/surfactant systems.1 According to the literature, the first break (c1) corresponds to the critical aggregation concentration (cac), at which small surfactant aggregates form on the polymer chain, and appears at a lower SDS concentration than its cmc [(7-8) × 10-3 M].29 The second break (c2) should correspond to the saturation of the polymer chains; it appears at a higher SDS concentration than its cmc and increases with the polymer concentration in the system, as it has been previously reported for other polymer/surfactant systems,3,5,9,14,16,30,31 although this increase is not linear with polymer concentration. The micellar surface ionization degree of the aggregates located on the polymer chain (R1) can be calculated as the ratio of the slopes above and below c1, taking into account that in the literature micellar ionization degree (R) has been obtained as the ratio of the slopes of the conductivityconcentration curves above and below the break point (cmc).32 Also, we have calculated the micellar ionization degree of the aggregates formed at a surfactant concentration higher than c2, R2, as the ratio of the slopes above c2 and below c1. Table 1 shows c1, c2, R1, and R2 for each SDS/PPG system. R1 and R2 are both higher in all cases than the R value for the SDS micelles in aqueous solution (R ) 0.38)33 and increase with the PPG concentration. It is noticeable that in the SDS/PPG (MW ) 1000) system, [PPG] ) 10-4 M, only one break point was found and the cmc and R values obtained correspond to those for SDS micelles in aqueous solution. This means that the presence of this small amount of polymer in the solution has no effect on the micellar system. In the case of the SDS/PPG (MW ) 425 and 1000) systems with a molar ratio [SDS]/[PPG] ) 1, the conductivity-concentration curves only show one break point (Figure 3), which corresponds to the cmc of the systems that are nearly the same as the SDS cmc, although the micellar ionization degrees are higher than the R value for the SDS micelles in aqueous solution and higher in the SDS/PPG (MW ) 1000) system that in the SDS/PPG (MW ) 425) system. The same behavior was found in the systems formed with the cationic surfactant CTAB.26 The cmc values and the micellar surface ionization degrees for both systems are given in Table 2. Fluorescence Study. Steady-state quenching fluorescence measurements have been carried out in the SDS/ PPG systems in aqueous solution, using pyrene as probe and N-cetylpyridinium chloride as a static quencher.34 In this way probe and quencher are located in the same environment of the micelles, since CPyCl acts as a quencher of the probe pyrene, as in the CTAB/PPG mixed micellar system.26 The aggregation numbers have been calculated taking into account the theoretical treatment given in the literature,35,36 which considers both probe and quencher to be distributed between the aqueous and micellar pseudophases, according to the Poisson statistics. Therefore, pyrene fluorescence intensity in the absence (29) Mukerjee, P.; Mysels, K. J. Critical Micelles Concentration of Aqueous Surfactant Systems; NSRDS-NBS 20420; Washington, D.C., 1971. (30) Hoffmann, H.; Huber, G. Colloids Surf. 1989, 40, 181-193. (31) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Colloid Interface Sci. 1990, 137, 137-146. (32) Evans, H. C. J. Chem. Soc. 1956, 579-586. Hoffmann, H.; Ulbricht, W. Z. Phys. Chem. N.F. 1977, 106, 167-184. Hoffmann, H.; Tagesson, B. Z. Phys. Chem. N.F. 1978, 110, 113-134. Rubio, D. A. R.; Zanette, D.; Nome, F.; Bunton, C. A. Langmuir 1994, 10, 1151-1154. (33) Pe´rez-Benito, E. Tesis Doctoral, Alcala´ de Henares, 1991. (34) Malliaris, A.; Lang, J.; Zana, R. J. Chem. Soc., Faraday Trans. 1 1986, 82, 2709-2713.
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Table 1. c1 and c2 Values and Micellar Surface Ionization Degrees between c1 and c2 and above c2, for the SDS/PPG (M ) 425 and 1000) Systems in Aqueous Solution [PPG (MW ) 425)] 103c1 103c2
(M) (M)
R1 R2
[PPG (MW ) 1000)]
10-3 M
10-2 M
0.1 M
6.64 12.8 0.498 ( 0.082 0.771 ( 0.107
6.49 17.7 0.685 ( 0.077 0.730 ( 0.048
7.38 18.6 0.786 ( 0.056 0.837 ( 0.022
Figure 3. Specific conductivity of the SDS/PPG systems, where [SDS]/[PPG] ) 1, vs the SDS/PPG concentration: (O) SDS/PPG (MW ) 425), (0) SDS/PPG (MW ) 1000). The SDS/PPG conductivity curves are displaced 3 units from the Y-scale. Table 2. Cmc and Micellar Surface Ionization Degree (r) for SDS/PPG (MW ) 425 and 1000), [SDS]/[PPG] ) 1, in Aqueous Solution 103cmc R
(M)
SDS/PPG (MW ) 425)
SDS/PPG (MW ) 1000)
7.27 0.665 ( 0.039
8.30 0.784 ( 0.045
and in the presence of quencher is related to the average aggregation number (N) by
()
ln
I0 [Q]N )n j) I [Dn]
[1]
where n j is the average quencher occupation number and N denotes the surfactant aggregation number. I0 represents the pyrene emission intensity in the absence of quencher, I the pyrene emission intensity in the presence of quencher, and [Dn] is the micellized surfactant concentration. The experimental results fit well the theoretical treatment, shown in Figure 4, in which ln(I0/I) versus quencher concentration, [Q], is plotted. According to the polymer/surfactant complexation model given by other authors,1,2,4,8,11,12 SDS aggregates on the polymer chains are formed at SDS concentrations between c1 and c2, and once the PPG chains are saturated with micellar aggregates, simple SDS micelles in aqueous solution start to form, i.e. at a surfactant concentration above c2. Therefore, in order to obtain the aggregation numbers for the SDS aggregates located on PPG chains, in the SDS concentration range between c1 and c2, we have considered the micellized surfactant concentration, [Dn], as [Dn] ) [D] - c1 in expresion 1, where [D] is the (35) Infelta, P. P.; Gra¨tzel, M.; Thomas, J. K. J. Phys. Chem. 1974, 78, 190-195. Infelta, P. P. Chem. Phys. Lett. 1979, 61, 88-91. Yekta, A.; Aikawa, M. N.; Turro, N. J. Chem. Phys. Lett. 1979, 63, 543-548. Tachiya, M. Chem. Phys. Lett. 1979, 75, 179. Kalyanasundaram, K. Photochemistry in Microheterogeneous Systems; Academic Press: New York, 1987. (36) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977, 99, 2039-2044.
10-4 M 8.10 0.407 ( 0.038
10-3 M
10-2 M
5.50 13.5 0.688 ( 0.145 0.580 ( 0.067
9.07 38.4 0.781 ( 0.056 0.617 ( 0.037
Figure 4. Natural logarithm for the I0/I ratio vs the quencher concentration for the SDS/PPG systems. MW ) 425: [SDS]/ [PPG] ) 1 (b) (20/20) × 10-3 M; [PPG] ) 10-3 M, (O) [SDS] ) 9.33 × 10-3 M, (0) [SDS] ) 23.3 × 10-3 M; [PPG] ) 10-2 M, (2) [SDS] ) 7.2 × 10-3 M; [PPG] ) 0.1 M, (4) [SDS] ) 23.3 × 10-3 M. MW ) 1000: [PPG] ) 10-4 M, (k) [SDS] ) 30 × 10-3 M.
total surfactant concentration. The aggregation numbers obtained at different SDS/PPG concentrations, together with the ones obtained in the systems where the surfactant to polymer ratio is [SDS]/[PPG(MW ) 425)] ) 1 are all given in Table 3, until the double line, and plotted in Figures 5 and 6 (filled symbols) for SDS/PPG(MW ) 425) and SDS/PPG(MW ) 1000), respectively. It is shown in Table 3 that, in all the cases, the aggregation numbers are lower than those for simple SDS micelles in aqueous solution and, although N increases sharply with the SDS concentration, in no case do the values approach those of the SDS micelles in aqueous solution. On the other hand, the curves for each PPG molecular weight have a 0 intercept on the X-axis, corresponding to the SDS concentration at which aggregates begin to form (c1), that agrees with the c1 values obtained by conductivity. Only in the system formed with PPG(MW ) 1000) at a [PPG] ) 10-4 M do the aggregation numbers reach values almost equal to those of simple SDS micelles in aqueous solution, which agree the conductivity results, i.e. the presence of the polymer in the system at the lowest concentration did not affect the physical properties of the SDS micelles in aqueous solution, and this is now confirmed with the results obtained by fluorescence. If we now consider the aggregates formed above c2, in order to obtain their aggregation numbers, it is necessary to add a second term to eq 1 to denote n j (the average quencher occupation number) to separately consider the micellar aggregates located on the PPG chains and the micellar aggregates formed in aqueous solution.
()
ln
I0 [Q] )n j) I C2 - C1 D - C2 + N1 N2
[2]
The term (c2 - c1)/N1 represents the number of aggregates located on the PPG chains formed at a surfactant
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Physical Properties of the SDS/PPG System
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Table 3. Aggregation Numbers for the SDS/PPG Systems in Aqueous Solution at [SDS]/[PPG] ) 1, between c1 and c2 and above c2 Considering [Dn] ) [D] - c1 [PPG (MW ) 425)] 103[SDS] (M) 6.33 7.20 7.33 8.33 9.33 10.0 11.3
NSDSa
1/1
10-3 M
[PPG (MW ) 1000)]
10-2 M
0.1 M
10-4 M
10-3 M 5(1
6(1 15 ( 5 29 ( 8 41 ( 5
15 ( 2
3(1
22 ( 2
20 ( 5
7(1
47 ( 4
22 ( 2
8(1
48 ( 4
10 ( 1 15 ( 1 19 ( 2
13.3
50.0 53.3 73.3 150 a
1(1
62 21 ( 3
44 ( 7
3(1 33 ( 3
18.3 23.3 30.0 33.3
10-2 M
7(1 10 ( 2
25 ( 4
59 ( 2
65
18 ( 24 32 ( 4
54 ( 4
15 ( 2
61 ( 5 26 ( 8
71 29 ( 8 37 ( 13
72 ( 14 73 ( 14
50 ( 7 51 ( 3
27 ( 4 29 ( 3
72 ( 7 74 ( 20
69 ( 8 74 ( 9
31 ( 22 42 ( 13
80
Pe´rez-Benito, E. Tesis Doctoral, Alcala´ de Henares, 1991.
Figure 5. Aggregation numbers for the SDS/PPG (MW ) 425) system vs SDS concentration. Filled symbols denote the N values of the aggregates formed between c1 and c2 of each system, and open symbols correspond to the N values of the micelles formed above the c2, for each system, calculated considering [Dn] ) [D] - c1: (b, O) [PPG] ) 10-3 M, (9, 0) [PPG] ) 10-2 M, (2, 4) [PPG] ) 0.1 M.
concentration equal to c2, and (D - c2)/N2 represents the number of micelles formed in aqueous solution at an SDS concentration above c2. According to the model given by other authors,1,2 N2 should be the aggregation number of the SDS micelles in aqueous solution in equilibrium with the PPG/small SDS aggregates complex and N1 represents the aggregation number of the SDS aggregates located on the PPG chains at an SDS concentration equal to c2, when the polymer is supposed to be saturated of small aggregates. These N1 values have been obtained by extrapolation from the aggregation numbers of the SDS micelles formed on the polymer chains, given in Table 3 (till the double line) and plotted in Figures 5 and 6 (filled symbols) for the SDS/PPG(MW ) 425) and SDS/PPG(MW ) 1000) systems, respectively. The extrapolated N1 values used in this treatment, according to Figures 5 and 6, are given in Table 4. With these data and eq 2, the N2 values were calculated from the fluorescence quenching results and are given in Table 5. A small variation in the extrapolated N1 values give N2 values within the experimental error margin. The pyrene emission intensity ratio II/IIII is nearly the same for all the SDS/PPG systems, with different SDS
Figure 6. Aggregation numbers of the SDS/PPG (MW ) 1000) system vs SDS concentration. The same notation as in Figure 5: (2) [PPG] ) 10-4 M, (b, O) [PPG] ) 10-3 M, (9, 0) [PPG] ) 10-2 M. Table 4. Extrapolated N1 Values for the SDS/PPG Systems, at a Surfactant Concentration Equal to the Systems’ c2 N1
SDS/PPG (MW ) 425) SDS/PPG (MW ) 1000)
[PPG] ) 10-3 M
[PPG] ) 10-2 M
[PPG] ) 0.1 M
46 33
32 28
16
and PPG concentrations. This ratio is not sensitive to the different possible micellar structures, small aggregates located on the polymer chain, and free micelles in the solution. All the system show the same value of II/IIII ≈ 1.14, close to the value of II/IIII of ca. 1.15 for SDS micelles. Taking into account the ratios given by other authors36,37 for various solvents of different dielectric constant, it is possible to know the apparent surface dielectric constant of these micelles, ∼26, similar to that of SDS micelles in aqueous solution. Discussion The conductivity-surfactant concentration curves for the SDS/PPG (MW ) 425) system, where [SDS]/[PPG] ) (37) Dong, D.; Winnik, M. A. Photochem. Photobiol. 1982, 35, 17-21.
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Table 5. Aggregation Numbers (N2) for the Micelles in Aqueous Solution Formed above c2 for the SDS/PPG Systems, According to Eq 2 [PPG (MW ) 425)] 103[SDS] 13.3 23.3 23.4 53.3 53.4 73.2 73.3
(M)
10-3
M
10-2
43 72
M
[PPG (MW ) 1000)]
0.1 M
10-3 M
10-2 M
25
110
34
89
41
35
88
66
33 80 62 59 78
1, show only one break, the same as in the mixed micellar system CTAB/PPG,26 which coincides with the cmc of the simple SDS micelles in aqueous solution. The presence of PPG in the SDS/PPG system in aqueous solution, at a molar ratio [SDS]/[PPG] ) 1, has no effect on the cmc of the SDS, although the conductivity results show more ionized aggregates and the aggregation numbers are smaller than those of simple SDS micelles in aqueous solution, according to Tables 2 and 3. This is the same behavior as that presented by the system formed with the cationic surfactant CTAB26 with a molar ratio of [CTAB]/ [PPG] ) 1. Although no reduction of the cmc values has been found, this does not mean that the PPG does not affect surfactant micellisation. Other surfactant/polymer systems do not show either a decrease of their surfactant cmc’s values, but some other physical properties can be modified, such as the endothermic and exothermic peaks, as shown by microcalorimetry,38,39 or the microenvironment sensed by the spin probes used in the ESR measurements in the presence and in the absence of polymers.40 In addition, micellar ionization degrees rise with the PPG molecular weight. The same effect has been found in both cationic surfactant/polymer systems22 as well as in anionic surfactant/polymer systems,10 and the same effect is produced by incorporating medium-chain alcohols into the micelles.41-43 All of these findings show that PPG can behave like medium chain alcohols, and can incorporate into micelles like the medium chain alcohols do when the surfactant to polymer molar ratio is [SDS]/ [PPG] ) 1. The hydrophobic part of the molecule would be located in the hydrophobic core of the micelle and the two terminal alcohol groups would be located in the interface, close to the ionic headgroups. This kind of incorporation creates smaller aggregates, as when mediumchain alcohols are incorporated into micelles,44 previously reported by other authors for different surfactant/polymer systems.8,15,25,39,45 In fact, the aggregation numbers in these SDS/PPG systems, molar ratio [SDS]/[PPG] ) 1, are lower over the whole range of surfactant concentrations used than the aggregation numbers for each SDS concentration in aqueous solution, given in ref 33. In the case of SDS/PPG (MW ) 425 and 1000) systems formed at a fixed PPG concentration and different SDS concentrations for which two break points have been obtained in the κ-concentration curves, it is observed that the formed aggregates are smaller,5,8,14,45-47 as it is shown (38) Brackman, J. C.; van Os, N. M.; Engberts, J. B. F. N. Langmuir 1988, 4, 1266-1269. (39) Brackman, J. C.; Engberts, J. B. F. N. Chem. Soc. Rev. 1993, 85-92. (40) Witte, F. M.; Engberts, J. B. F. N. J. Org. Chem. 1988, 53, 30853088. (41) Zana, R.; Yiv, S.; Strazielle, C.; Lianos, P. J. Colloid Interface Sci. 1981, 80, 208-223. (42) Valiente, M.; Rodenas, E. J. Colloid Interface Sci. 1989, 127, 522-531. (43) Pe´rez-Benito, E.; Rodenas, E. Langmuir 1991, 7, 232-237. (44) Pe´rez-Benito, E.; Rodenas, E. An. Quı´m. 1990, 86, 126-131. (45) Witte, F. M.; Engberts, J. B. F. N. Colloids Surf. 1989, 36, 417426. (46) Shirahama, K.; Tohdo, M.; Murahashi, M. J. Colloid Interface Sci. 1982, 86, 282-283.
in Table 3, and more ionized,14 shown in Figures 1 and 2 and Table 1, than simple SDS micelles, as it has been already described.1,2,4,8 From the aggregation numbers obtained at a surfactant concentration equal to c2, which is supposed to be the surfactant concentration at which the polymer chains are saturated of micelles, it is possible to calculate the number of micelles on a polymer chain from the expression [M]/[PPG] ) [Dn]/N[PPG], where [M] denotes the micelles concentration. Interestingly not even one single micelle per polymer chain was found, which means that several polymer chains must interact with each micelle. This is an interesting result that does not aggree the complexation model described in the literature. In addition, according to such treatment, surfactant micelles in aqueous solution should form above c2. But as the concentration of PPG increases, the formed SDS micelles have higher micellar surface ionization degrees (Table 1) and smaller aggregation numbers than those of simple SDS micelles in aqueous solution (shown in Table 5). This means that SDS and PPG are still interacting, even above c2, which contradicts the model postulated for other polymer/surfactant systems.1,2 These results require a new complexation model for the SDS with the low molecular weight polymer PPG, MW ) 425 and 1000. Since the micellar aggregation numbers at surfactant concentrations between c1 and c2 rise sharply with SDS concentration, it can be supposed that the aggregates near c2 are large enough to be able to incorporate the PPG chains into the micelles, the same as medium chain alcohols do,41-43 and so form SDS/PPG mixed micelles, like the ones obtained in the CTAB/PPG system in aqueous solution.26 The appearance of a second break in the conductivity-concentration curve would indicate in this case the transition from the aggregates located on the polymer chain to the SDS/PPG mixed micelles where PPG chains are incorporated into SDS micelles. With this aggregation model, only mixed micelles are formed at a surfactant concentration above c2, so the average aggregation numbers for these aggregates can be calculated with the fluorescence data, according to eq 1, where [Dn] ) [D] - c1 over the whole range of surfactant concentration. The N values obtained are represented in Figure 5 and 6 (open symbols) for the systems formed with PPG (MW ) 425) and PPG (MW ) 1000), respectively, and are given in Table 3 below the double line. The differences between the N2 values (Table 5), and these N values in Table 3 are not very significant. Thus, we conclude that at low surfactant concentrations, between c1 and c2, which correspond to the two breaks in the conductivity-concentration curves, small aggregates are formed on the polymer chains. Once the micelles are large enough, at a surfactant concentration equal to c2, the polymer incorporates into the SDS micelles, forming SDS/PPG mixed micelles with a higher ionization degree and with smaller aggregation numbers than the simple SDS micelles in aqueous solution. Acknowledgment. Financial support of this work by DGCYT, PB-1080, and the Ministerio de Educacio´n y Ciencia of the Spanish Government (Ma Luisa Sierra) are gratefully acknowledged. We also thank to C. F. Warren of the ICE at UAH for her linguistic assistance. LA9505778 (47) Piculell, L.; Lindman, B. Adv. Colloid Interface Sci. 1992, 41, 149-178.
