Ideal Mixing of Polymer-Surfactant Complexes of Polyethylene Oxide and Sodium Dodecyl Sulfate Plus Sodium Dodecanoate

Journal of Colloid and Interface Science 213, 379 –385 (1999) Article ID jcis.1999.6115, available online at http://www.idealibrary.com on

Ideal Mixing of Polymer-Surfactant Complexes of Polyethylene Oxide and Sodium Dodecyl Sulfate Plus Sodium Dodecanoate Dino Zanette 1 and Vera L. A. Frescura Universidade Federal de Santa Catarina, Departamento de Quı´mica, 88040-900, Floriano´polis, SC, Brazil Received July 28, 1998; accepted January 28, 1999

complexes, hydrophobicities, specific interactions, and types of polymer and surfactant chains. So far, these theoretical explanations have been accompanied by poor experimental observations. Moreover, the field of polymer–surfactant system applications has been considerably extended by many types of polymers. Recently, Hansson and Lindman (7) in their 1995–1996 summary dealing with polymer–surfactant interactions emphasized the continuing interest in hydrophobically modified water-soluble polymers, polyelectrolytes, and anionic surfactants. A number of recent studies have been directed toward the clarification of different rheological properties and the characterization of sizes and mechanisms of surfactant binding to modified polymers (8 –12). In interactions among nonionic surfactants and hydrophilic polymers such as PEO, only weak interactions have been reported (13). However, in relation to matters of practical importance, possible models for interactions of Triton X surfactants and polyethylene glycols with different molecular weight, following the effects on the cloud point of the surfactants, have been suggested very recently (14). Although several works and reviews summarizing the present understanding of polymer–surfactant systems have been published, only minor studies have been carried out on interactions of mixtures of anionic surfactants with nonionic polymers. Therefore, in this field of our contribution, in a previous work (15), by using electrical conductivity, we reported the formation of polymer–mixed surfactant complexes in a ternary system formed of the anionic surfactants, SDS and sodium decyl phosphate (NaDeP), and with PEO. The plot of surfactant concentration corresponding to the onset of the mixed complexation (called critical aggregation concentration (cac)) versus the mole fraction of NaDeP, x NaDeP, indicates a system following an ideal mixing process. Additional evidence was obtained by following the kinetics of the acid-catalyzed hydrolysis of di-tert-butyl acetal. This reaction is sensitive to a mole fraction of phosphate in the mixed aggregate interface because it acts as a general acid catalyst. Interestingly, when PEO is absent, the binary system NaDeP/SDS behaves as an ideal mixture (15, 16). But, for the PEO–NaDeP system, therefore in the absence of SDS, we also

Mixtures of the anionic surfactants sodium dodecyl sulfate (SDS) and sodium dodecanoate (SDoD) were investigated regarding their ability to bind to a hydrophilic nonionic polymer, polyethylene oxide (PEO). By electrical conductivity measurements, the parameters with respect to the onsets of surfactant aggregation were determined in the presence of 0.06 M PEO (critical aggregation concentration) and in its absence (critical micelle concentration). It was found that both plots of these parameters for the multicomponent mixtures against molar fraction of SDoD showed an ideal mixing behavior. The same technique was used to estimate the degree of ionization as a fundamental parameter relating to the interfacial composition of mixed aggregates. In addition, in order to monitor changes in polymer–surfactant structures, we used steady-state quenching fluorescence measurements to characterize the sizes of PEO–SDS/SDoD complexes at different compositions of the complex mixture. © 1999 Academic Press Key Words: polymer–surfactant interaction; surfactant mixture; electrical conductivity; aggregation number; sodium dodecanoate; polyethylene oxide.

INTRODUCTION

It has long been established that surfactant mixtures exhibit a very different behavior in comparison to their components. The interaction between different surfactants can lead to synergistic effects, for instance, in their critical micelle concentration or in their individual solubility (1). The importance of practical formulations containing mixtures of surfactants and polymers has motivated many studies using different techniques and several systems. Because of their simpler structures, anionic surfactants and nonionic polymers are the most commonly investigated. Emphasis is given to the systems sodium dodecyl sulfate (SDS) with polyethylene oxide (PEO) or with polyvinyl pirrolidone (PVP). For these systems, several theoretical models have been developed to explain the interactions (2– 6). Nevertheless, intriguing questions concerning the mechanism of interaction and regarding the nature of the driving forces still exist. The weaknesses of the models are related to several variables which are not taken into consideration in the models, such as size and shape of the 1

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report that the electrical conductivity vs [NaDeP] profiles (square brackets, here and thoughout the text, indicate molarity) did not show the typical PEO–SDS association: the profiles exhibited only one breakpoint and the depression of the critical micelle concentration (cmc), assumed as a polymer–surfactant complex formation, was not observed (15, 17). Therefore, since the classical profiles are recuperated in mixtures of SDS– NaDeP and PEO, then this was interpreted assuming the binding to be driven by the SDS. This assumption is ratified by the fact that the “supposed” estimated cac of PEO–NaDeP mixtures and the cmc of NaDeP micelles are numerically identical. As an extension of the PEO–SDS/NaDeP ternary system, and, in order to extend the discussion on the effect of headgroup type on the phenomenon of binding, in this work we report the anionic surfactant mixture of SDS and sodium dodecanoate (SDoD) with respect to its ability to bind to PEO. For electrical conductivity measurements, we determined cac and cmc parameters for the multicomponent mixture, and both plots (including cac) against x SDoD show an ideal mixing behavior. This result was interpreted as strong evidence that polymer–surfactant complexes are formed by a mixture of SDS and SDoD surfactants. In addition, in order to monitor changes in polymer–surfactant structures, we used steady-state quenching fluorescence measurements to characterize the sizes of PEO–SDS/SDoD complexes at different compositions of the complex mixture. EXPERIMENTAL

Materials Sodium dodecanoate was prepared from neutralization of dodecanoic acid (Aldrich) and NaOH solution until pH 9.50 and was followed on a Beckman pH meter model F71 (equipped with a combined glass electrode). The resulting solution was dried by lyofilization. Stock solutions of borate buffer were prepared from reagent grade boric acid and were titrated with NaOH solution to pH 9.50 at 25.0°C. Sodium dodecyl sulfate was supplied by Sigma and was used as received. Polyethylene oxide, weight-average molecular weight 10000, was obtained from Aldrich and was also used as received. The stock solutions of PEO in 0.050 M sodium borate buffer, pH 9.50, were routinely prepared under magnetic stirring for at least 7 h, and the concentrations are given as molarity on a monomer basis (moles of monomer per liter of solution). 9-methylanthracene, MA, from Aldrich, was purified by sublimation. Tris(bipyridyl)ruthenium (II), Ru(bipy) 321 (18, 19) was the same as that previously used. All solutions were prepared from water which was distilled and demineralized in a Millipore Milli-Q Water System. Fluorescence Measurements Stock solutions of MA and Ru(bipy) 321 were prepared in spectroscopic acetonitrile. The probe concentration used was

1.0 3 10 26 M. Quencher concentrations were varied up to 2.5 3 10 24 M. The fluorescence intensities were measured using an SLM AMINCO SPF 500C spectrophometer equipped with a thermostated cell holder set at 25.0°C. The excitation wavelength was 450 nm and the fluorescence emission was followed at 630 nm. Molar micelle concentrations [M] were determined from plots of the logarithmic intensity ratio, ln(I o/I), where I o and I are the emitted light intensities in the absence and presence of quencher, respectively, versus the quencher concentration [MA], according to the method of Turro and Yekta (20). Average aggregation numbers n were estimated from the slope of above plots, n/C t 2 cmc, where C t is the total surfactant concentration. The values of n correspond to an average of three independent measurements. Electrical Conductivity Measurements Conductance measurements were carried out at 25.0°C in a water-jacketed flow dilution cell by use of an ATI.ORION conductivity meter, model 170, by using the same routines as previously described (19). Values of parameters, cmc, cac, and psp, obtained from the conductivity vs surfactant concentration plots, were defined by the intersection points of the lines above and below the corresponding breakpoints. RESULTS AND DISCUSSION

1. Conductivity vs Surfactant concentration Concentration Profiles Figure 1 shows the conductivity vs [SDoD 1 SDS] profiles in the presence of 0.060 M PEO and at 0.050 M borate buffer, pH 9.50. The buffer contribution to the total [Na 1] in solution corresponds to ca. 0.035 M. In the profiles are emphasized the onset of the surfactant association to polymer (cac) and the onset of a linear region in which it has long been assumed that polymer is saturated by monomer (psp) and that only regular micelles are developed (21, 22). For comparison with the other profiles, Fig. 1, curve A, shows a typical conductivity profile for SDoD without PEO. The cmc value is 18.0 3 10 23 M and the slopes of the linear conductivity vs [SDoD] plots, above (S 2 ) and below (S 1 ) for the cmc obtained from this curve, are listed in Table 1 (19). Attention should be paid to the profiles at x SDoD 5 1 (curve B) and at x SDS 5 1 (curve E). As may be observed, the profile at x SDoD 5 1 exhibits the conventional behavior with the same typical characteristics as those of the PEO–SDS system, extensively documented (19, 21–27), as follows: (i) two breakpoints in the electrical conductivity versus [surfactant] plots, different to that for the absence of PEO (Fig. 1, curve A), and (ii) the profile with cmc depression, as can be seen by comparing the cac in curve B and the cac in curve A. These two essential similar characteristics reinforce the fact that SDoD binds to PEO in a manner similar to the way that SDS does.

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FIG. 1. Plots of conductivity (in relative scale units) vs [Surfactant] for SDoD alone (A) and for mixtures of SDS/SDoD, at 0.06 M PEO, in 0.05 M borate buffer pH 9.50, at following x SDoD: (B) in the absence of SDS (x SDoD 5 1); (C) 0.8; (D ) 0.2; and (E) in the absence of SDoD (x SDoD 5 0). The inset magnifies the absence of linearity above cac for the curve x SDoD 5 0.8.

Furthermore, the occurrence of cmc depression, when in the presence of polymer, has been used as an argument for surfactant–polymer binding (6, 13). This same argument has also been used by Gao et al. (24) in NMR studies of an alkanoate binding to PEO, the v-phenyldecanoate. Also, as a third characteristic, we emphasize the linearity in the cac–psp range of both curves, B and E, a fact we have already insisted on as providing evidence of the development of polymer–surfactant complexes alone (25, 26). Table 1 summarizes the parameters obtained from conductivity plots. We have omitted the S 2 values for those profiles in which the cac–psp regions exhibit curvatures because of uncertainty in their determination. Furthermore, for the graphical estimation of cac and psp in those plots where the linearity is

absent, we applied the criterion of assuming the surfactant concentrations equivalent to the beginning and the end of the curved region, respectively. The styles of the conductivity vs SDS 1 SDoD mixture depend particularly on the amount of individual molar fractions. It is important to note the profile at 0.2 mole fraction of SDoD (Fig. 1, curve D), which still preserves the linearity in the cac–psp range. At this molar fraction, the complex composition must be substantially rich in SDS monomers, just like that described for ideal mixtures of anionic surfactants (28). We also note, however, that the conductivity profile at x SDoD 5 0.8 (curve C) is different in terms from the absence of linearity in the points of the region between cac and psp points (for great detail see inset of Fig. 1). A preliminary interpretation raises further questions concerning more than one type of aggregate under development in this region. As a consequence, such a curvature reflects changes in the composition of mixed aggregates with different degrees of dissociation. An intermediate breakpoint is not clear in these conductivity plots, but we have found evidence of a third discontinuity point, identified by conductivity and surface tension plots for the mixed system PEO–SDS/NaDeP, which is closely related to the cmc of NaDeP (not shown). Since the cmc is the minimum surfactant concentration at which micelles form, the possible existence of this intermediate conductivity point is the result of the expected SDoD monomer concentration increase in the cac–psp range, and the SDoD micelles composition must form with rich SDoD monomers. Further evidence is necessary in order to adequately describe the nonlinear behavior in the PEO–SDS/ NaDeP system. Surfactants with similar structures of like charge usually mix ideally because hydrophobic and hydrophilic parts sense the same environments in the mixed aggregates. Consequently, they are similar to those in the pure component micelle. This ideal mixing behavior can be simply modeled by Eq. [1] which assumes that the thermodynamics of mixed micelle formation obey ideal solution theory (29). In this equation, cmc is the predicted critical micellar concentration of the mixtures, and

TABLE 1 Conductivity Parameters Obtained in Mixtures of SDS and SDoD, in the Presence of 0.060 M PEO and 0.050 M Borate Buffer, pH 9.50, at 25°C x SDoD

S1

S2

S3

10 3cac (M)

10 3psp (M)

S 2 /S 1

S 3 /S 1

None 0.2 0.4 0.6 0.8 1.0 1.0 a

55.4 55.5 55.3 55.2 55.5 53.3 48.0

31.9 31.7 31.7

26.9 26.3 26.4 26.8 27.0 26.5

2.2 2.5 3.2 4.2 6.4 14.0 18.0

20.6 24.2 27.1 30.3 35.2 40.2

0.56 0.57 0.57

0.48 0.47 0.48 0.47 0.49 0.50

30.9 23.0

Note. The slopes (S) are given in V 21 cm 2 mol 21. a In the absence of PEO (from Ref. (19)).

0.58 0.48

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FIG. 2. Changes of cac (F) for the ternary system PEO–SDS/SDoD in the presence of 0.06 M PEO, and changes of cmc (■) for mixtures of SDS/SDoD, in the absence of PEO, at 0.05 M borate buffer pH 9.50; Dotted lines were estimated by using Eq. [1]; dashed lines are drawn, at 0.006 and 0.016 M of constant surfactant concentrations (SDS 1 SDoD), to follow, in the diagram, the analytical composition of PEO–SDS/SDoD ternary system in which the aggregation number was measured.

cmc SDoD and cmc SDS are the cmc values for the individual components. As can be seen in Fig. 2, Eq. [1] fits the data of SDS/SDoD mixtures (in the absence of PEO) very well. cmc 5

cmcSDScmcSDoD xSDoDcmcSDS 1 x SDScmcSDoD

[1]

The second set of data shown in Fig. 2 is related to the predicted ideal mixing behavior for the ternary system PEO– SDS/SDoD. The cac necessarily marks the beginning of formation of mixed PEO–SDS/NaDeP complexes and Eq. [1] provides also an excellent description of the onset of mixed complex formation over the entire range of surfactant composition. 2. Fraction of Micelle Ionization Electrical conductivity methods have largely been used to estimate the degree of micelle ionization (a) of ionic micelles (30, 31) and have also been extended to polymer–surfactant assemblies (25, 32–34). In particular, this is a fundamental parameter in the interpretation of micellar catalysis by ionic micelles (35, 36). In the pseudophase ion exchange formalism, to describe ionic distribution of a counterion, micellar surfaces are treated as selective ion exchangers saturated with counterions. Therefore, the “local” interface concentration of a reactive counterion strongly depends on the fraction micellar ionization and success of the treatment is strictly limited by knowledge of a (36). Although several techniques have been used to estimate the

degree of ionization for ionic micelles, the simplest is the conductometric whose method consists of an estimation from the ratio of slopes of linear plots above and below the cmc. It can also be applied to surfactant–polymer systems in which the ratio of slopes of linear regions above (S 2 ) and below (S 1 ) the cac (a 1) is attributed to the degree of ionization of PEO– surfactant complexes, and above (S 3 ) the psp and below the cac (a 2) it is related to free micelles (25, 32–34). This method requires linearity in the range of cac–psp. Criticisms have been made regarding the higher a values usually obtained by this method. Bunton et al. (37) have commented on the lower a values obtained by Zana (38) for alkyltrimethylammonium bromides, stating that this method treats the micelle as a large macroin whose contribution to the net conductivity is the same as that of the number of surfactant monomers that are equivalent in charge. Evans introduced a new method that takes into account the differential contributions considering the mobilities of macroions based on the application of Stoke’s law and the micellar aggregation number which was assumed to be directly related to the hydrodynamic radius (39). We have also applied Evans’ equation to estimate a of PEO–SDS complexes. We found a of 0.41 for PEO–SDS complexes, while for SDS micelles, by using the same methodology, a 5 0.27 (40). We note the difference in these a values in comparison with those listed in Table 1. Parallel comments, for the system polyvinyl pyrrolidone (PVP) and SDS (26), can be made. The slopes of conductivity plots can represent the equivalent conductance (in S cm 2 mol 21) of ionic species in solution. At [Surf.] , cac or cmc, the slope represents the equivalent conductance in terms of the ionic contributions of Na 1, DS 2, DoD 2, and borate (B 2) by their limiting ionic conductivity (l), i.e., S 1 5 l Na 1 l DS 1 l DoD, where l Na corresponds to the total Na 1 concentration contribution. Considering here that the conductivity data measurements were made in 0.05 M borate buffer, one approach concerns the fact that the buffer must play its role in all range of surfactant concentration used. This implies constant contribution of B 2 to the final conductivity. Thus, taking this into consideration, it was omitted in the expressions S 1 above and S 2 below. Table 1 lists the S 1 values and other parameters. It is interesting that S 1 values are practically independent of individual and mixed surfactant composition. These results are consistent with their similar limiting ionic conductivity values; that is, l DS 5 24 S cm 2 mol 21 (41) and l DoD 5 22 S cm 2 mol 21 (42). Let us now consider the system at [Surf.] . cac and , psp. The approach in this method involves the total contribution in conductivity of mixed micelles which above cac (or cmc when this is the case) is equal to the sum of the conductivities of the individual ionic species. On the other hand, it was assumed that the bound counterion neutralizes the monomer charge, and, in micellar form, does not contribute to the conductivity. From this approach, the slope S 2 5 a 1 ( l Na 1 l DS 1 l DoD). Since in the range of cac–psp only PEO–SDS/SDoD complexes are

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developed, the ratio S 2 /S 1 5 a 1 represents the fractional ionization of these mixed complexes. It is interesting to note from the above considerations that buffer and monomer contributions to conductivity are consistent with the analogous S 2 values obtained in the PEO–SDS (S 2 5 31.9), PEO–SDoD (S 2 5 31.9), and PEO–SDS/SDoD (S 2 5 31.7) systems (Table 1). Furthermore, this result is consistent with the ideal behavior of the PEO–SDS/SDoD complex formation described above and, also, the analogous a 1 values obtained, independent of micellar compositions, corroborate their expected similar properties. It has been extensively commented for nonionic polymer– surfactant mixtures that, above the psp, regular micelles are formed (21, 22, 24). This fact is also in agreement with our results. As can be seen, Table 1 lists similar S 3 values for the PEO– SDS/SDoD complex mixtures, and a 2 can be expressed from the S 3 /S 1 ratios as 0.48 6 0.01. Interestingly, this value is the same for SDS (x SDoD 5 0) and for SDoD (x SDoD 5 1) (Table 1), which is evidence for development of regular micelles above the psp. The higher a 1 values obtained in comparison to a 2 are consistent with several results already reported for nonionic polymer–surfactant complexes (32, 34, 40). 3. Size of PEO-SDS/SDoD Complexes It has already been stated that measurement of aggregation number of mixed ionic micelles, using conventional methods, is a difficult task (43). Milliaris et al. (44), in mixed surfactant systems, as an alternative method, have used fluorescence probing of pyrene fluorescence lifetime. They commented on the inadequacy for this purpose of methods such as light scattering, centrifugation, osmometry, and NMR because they require extrapolation of the data to the cmc in order to eliminate intermicellar interactions. In this work, the mean aggregation numbers (n) were esti-

TABLE 2 Main Aggregation Numbers (n) of Mixed SDS/SDoD, Measured at [SDS] 1 [SDoD] 5 0.006 and 0.016 M, Determined in the Presence of 0.060 M PEO at 0.050 M Borate Buffer, pH 9.50 N 10 3 C t , M

x SDoD

6.0

16.0

0.0 0.2 0.4 0.6 0.8 1.0

32 (3.8) 36 (3.3) 37 (2.6) 31 (1.5) — —

43 (13.8) 48 (13.3) 51 (12.6) 50 (11.5) 49 (9.1) 16 (1.5)

Note. In parentheses is the micellized surfactant concentration, C t 5 Cd 1 cac; Values of cac were obtained from theoretical plot shown in Fig. 2.

TABLE 3 Main Aggregation Numbers (n) of Mixed SDS–SDoD Surfactants, Measured at [SDS] 1 [SDoD] 5 0.010 and 0.020 M, at 0.050 M Borate Buffer, pH 9.50 N 10 3 C t , M

x SDoD

10.0

20.0

0.0 0.2 0.4 0.6 0.8 1.0

54 (6.0) 55 (4.8) 62 (4.2) 52 (2.2) — —

71 (16.0) 74 (14.8) 83 (14.2) 83 (12.2) 84 (9.8) 38 (2.0)

58 (11) a

58 (22) a

a From Ref. (48). In parentheses is the micellized surfactant concentration, estimated from the total surfactant concentration, C t 5 Cd 1 cmc. Values of cmc were obtained from theoretical plot shown in Fig. 2.

mated using the method of changes in the fluorescence intensity of Ru(bipy) 312 following the quenching of fluorescence by addition of 0.2 to 2.0 3 10 24 M of 9-methylantracene (MA) (20). Molar micelle concentrations [M] were determined from plots of logarithmic intensity ratio, ln(I o /I), versus the quencher concentration, [MA]. Average aggregation numbers were estimated from the slopes, (n/C t 2 cmc) for SDS–SDoD solutions, or (n/C t 2 cac) for PEO–SDS/SDoD mixtures, where C t is the total surfactant concentration. In all slope determinations, the linear correlation was higher than 0.998. In order to explore the variation in the composition of the PEO–SDS/SDoD ternary system, two sets of experiments were performed at constant surfactant concentrations, [SDS 1 SDoD] (see the indications of the dashed lines in the diagram of Fig. 2). We note that at the lower concentration, 0.006 M, just above the cac, it is possible to follow changes in the microstructure of the mixed system against the mole fraction of SDoD. In addition, at the chosen higher concentration 0.016 M, it is also possible to compare the effect of the total surfactant concentration on the average sizes. Table 2 lists the mean aggregation numbers for the PEO– SDS/SDoD system at different surfactant compositions at 0.06 M PEO, and Table 3 lists SDS–SDoD aqueous mixed micelles (in the absence of PEO). In order to facilitate the comparisons, in the presence and absence of PEO, because the parameters cac and cmc are different, the surfactant concentrations are expressed in terms of their total micellized surfactant concentrations (Cd 5 C t 2 cac or Cd 5 C t 2 cmc). In each set of results listed in Tables 2 and 3, the amounts of surfactant concentrations in solution are constant, so therefore it is obvious that as x SDoD increases, the amount of micellized surfactant concentration (Cd) decreases, leading up to values close to the cac or cmc (dashed lines in Fig. 2 were drawn to help this explanation). For x SDoD 5 0.2, for example, Figure 3

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FIG. 3. Typical plots of ln(I o/I) versus 9-methylanthracene quencher concentration (MA) in a fixed [SDS 1 SDoD] 5 0.016 M, in the presence of 0.06 M PEO, at following x SDoD: (F) 1.0 and (■) 0.2.

shows a typical linear [MA] vs ln(I o/I) plot at [Surf.] 5 0.016 M with a correlation of 0.9996. On the other hand, we note the lack of linearity for x SDoD 5 1.0, whose total surfactant concentration is only just above cac (cac 5 14.0 3 10 23 M). This observed shift above 1.0 3 10 24 M quencher can be interpreted as a failure of the general assumptions of the steady-state method. Therefore, since the fractions of both probe and quencher dissolved in water must be negligible, in this case, particularly in surfactant concentrations close to cac, the observed deviation definitely indicates that the method fails. If one considers an approach to the linear region only, the region below 1.0 3 10 24 M quencher, then a smaller aggregate with n equal to 16 can be estimated. The same consideration is extended to mixed micelles of SDS–SDoD (Table 3). As may be observed, when x SDoD 5 1.0 and Ct 5 0.02 M, then n 5 38.0, a value which again is expressively smaller than in the other lower SDoD molar fractions. A second consideration is related to the increase of n with surfactant concentration increase observed in both sets of measurements in Table 2. It is obvious that the differences do not exceed ca. 30% in 0.016 M surfactant. This can be explained in terms of polymer–surfactant complex size growth or in terms of development of regular micelles also in the region of cac– psp. Although we believe it to be a difficult task to distinguish the above two effects independently, because in the diagram of Fig. 2 it is necessary to take into consideration additional variables such as changes in the composition of mixed aggregates (x SDoD) and micellized surfactant concentration (Cd), the following remarks appear to be reasonable: (i) The same aggregation number dependency of the total surfactant concentration is observed also in the absence of PEO (Table 3). Curiously, the obtained n values are also ca. 25% larger in 0.020 M surfactant. (ii) When in the absence of PEO, in both sets of surfactant concentrations, a modest increase in n with

increase of the x SDoD is shown. Note that in these statements, we are not considering the n values obtained for surfactant concentrations in which the general assumptions of the steadystate method, [MA] vs ln(I o/I) plot, fail (see above comments). A slight increase of n for SDS micelles with increasing SDS concentration has also been determined before (45, 46). Witte and Engberts (45), also using the steady-state method, found a difference of ca. 20% of SDS micelle size between 0.020 and 0.050 M SDS. In addition, micelle growth, with surfactant concentration increase, has long been documented (47). This effect is interpreted in terms of salt-stabilization of aggregates by effectively screening electrostatic interactions in the micellar surface. It is obvious that this effect can be extended to polymer–surfactant complexes which also have charged interfaces. Therefore, the slight increases in n values noted in 0.016 M surfactant (Table 2) could be first related to complex size growth. However, we cannot exclude the argument on the linearity of conductivity plots in the cac–psp region by justifying the development of a simple type of aggregate (25, 26, 40). The premise of this argument rests on the fact that regular micelles and polymer–surfactant complexes are aggregates with different degrees of ionization whose contributions to the measured conductance are different (see profiles of Fig. 1). In this context, Fig. 1 demonstrates linearity only in a lower molar fraction of SDoD. Therefore, for higher x SDoD, in the presence of PEO, we also cannot exclude the contribution of mixed micelles to the increase in the main aggregation number observed at 0.016 M surfactant (Table 2). CONCLUSIONS

Changes in the molar fraction of surfactant in the mixtures of SDS and SDoD in the presence of polyethylene oxide obey an ideal mixing behavior. The onset of the surfactant cooperative binding to polymer (cac) is modeled by a simple equation (Eq. 1) which, in practical terms, describes a PEO–SDS/SDoD complex–monomer equilibrium. This behavior is consistent with the conductivity slope values, which are independent of the molar fractions of surfactant (Table 1). Increasing the x SDoD up to the limit of 0.5, the aggregation numbers of mixed surfactant–polymer complexes and regular mixed micelles are affected in the same way, but in all cases the complexes are smaller. ACKNOWLEDGMENTS We are grateful to CNPq, PADCT, and PRONEX for the financial support of this work.

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MIXTURES OF POLYETHYLENE OXIDE AND SDS PLUS SDoD 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

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