Micellization of Sodium Dodecyl Sulfate with a Series of Nonionic n

Langmuir 2000, 16, 9983-9990

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Micellization of Sodium Dodecyl Sulfate with a Series of Nonionic n-Alkyl Malono-bis-N-methylglucamides in the Presence and Absence of Gelatin P. C. Griffiths,* J. A. Roe, R. L. Jenkins, J. Reeve, and A. Y. F. Cheung Department of Chemistry, Cardiff University, P.O. Box 912, Cardiff CF10 3TB, U.K.

D. G. Hall NEWI, Plas Coch, Wrexham, U.K.

A. R. Pitt and A. M. Howe Research & Development, Kodak Limited, Headstone Drive, Harrow, Middlesex HA1 4TY, U.K. Received February 2, 2000. In Final Form: September 25, 2000 The critical micelle concentrations (cmc’s) for binary mixtures of sodium dodecyl sulfate (SDS) and nonionic n-alkyl malono-bis-N-methylglucamides (CnBNMG) have been measured by surface tension. Synergistic interactions over the entire mole fraction range are observed when the nonionic alkyl chain length n is either 10 or 12. A switch from antagonistic behavior at low SDS solution mole fractions to synergistic behavior at high SDS solution mole fractions is observed for the C14BNMG/SDS mixture. The dodecyl sulfate unimer concentrations in binary mixtures of C12BNMG/SDS are well described by regular solution theory (Rubingh, D. N. Solution Chemistry of Surfactants; Plenum: New York, 1979), using the experimentally determined cmc values. On addition of gelatin, the cmc is depressed for the binary C10BNMG/ critical . SDS and C12BNMG/SDS combinations, but only above a critical SDS solution mole fraction, RSDS critical Therefore, interaction between the gelatin and the mixed micelles is only seen above RSDS . No critical value is found for the C14BNMG/SDS system. Here, cmc’s are unchanged by the corresponding RSDS presence of gelatin for any mixture, thus indicating no interaction between the mixed C14BNMG/SDS critical increases. For the micelle and gelatin. On increasing the nonionic alkyl chain length from 10 to 12, RSDS latter system where both components possess dodecyl tails, the dodecyl sulfate unimer concentration is critical critical but remains unchanged for solutions below RSDS , relative to the noreduced for solutions above RSDS gelatin case. The composition of the bound micelle is very different from that formed in the absence of gelatin. Furthermore, whereas the compositions of the micelle and solution are vastly different in the absence of gelatin, they are very similar in the presence of gelatin. Not only does the nonionic surfactant promote binding of SDS to gelatin, but at the highest SDS mole fraction studied, it induces pre-cmc(1) nonmicellar SDS binding.

Introduction Surfactant mixtures have many practical applications, as they both are less expensive and often perform better than a single surfactant in a particular application. This improved performance often arises through synergistic interactions between the two surfactants. Frequently, the solution also contains polymeric materials. The behavior of the polymer/surfactant mixture can be quite different from that of the separate polymer and surfactant solutions. The origins and implications of these differences are the subject of our current research. There are few studies on ternary systems, especially when the polymer is “selective”; that is, an interaction is only observed with one of the two surfactants. Clint1 proposed an ideal mixing model for binary surfactant solutions from which the unimer concentrations of the two surfactants can be easily calculated from a knowledge of the critical micelle concentrations (cmc’s) of the mixture and the two pure surfactants. Ideal mixing theory has been quite successful in explaining the properties of surfactants having similar structures, but it is (1) Clint, J. H. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1372.

usually unable to account for the characteristics of mixed solutions of dissimilar structural features. Theoretical treatments were therefore developed on the basis of regular solution theory (RST) with provisions for specific interactions between the two types of surfactants forming the micelles. Rubingh’s2 treatment is the most commonly used and includes a term β to account for specific interactions between two surfactants. Although this treatment has been used successfully,3,4 it is largely empirical and β has little physical meaning. Its ease of use has led to numerous studies in which β has been overinterpreted, a point addressed by Blankschtein in a recent review.5 Various other models have also been formulated, ranging from the semiempirical that require no or few molecule-dependent variables, for example Motomura et al.,6 to the molecular-thermodynamic and (2) Rubingh. D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1, p 337. (3) Turro, N. J.; Kuo, P. L.; Soamasundaran, P.; Wong, K. J. Phys. Chem. 1986, 90, 288. (4) Rosen, M. J.; Hua, X. Y. J. Colloid Interface Sci. 1983, 95, 443. (5) Blankschtein, D.; Shiloach, A.; Zoeller, N. Curr. Opin. Colloid Interface Sci. 1997, 2 (3), 294. (6) Motomura, K.; Yamanku, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948.

10.1021/la000151f CCC: $19.00 © 2000 American Chemical Society Published on Web 11/21/2000

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predictive treatments of Blankschtein et al.7-11 The molecular-thermodynamic theories, while somewhat unwieldy to the noncognisenti, do account reasonably well for the cmc, micelle size/shape, and aggregation number behaviors for a range of simple model systems. In this work, we present systematic data on a rather more complicated polymer than has been studied to date. Gelatin is often used in combination with surfactants, especially in the photographic industry,12 due to its thermoreversible gelling, emulsifying, and stabilizing ability. An understanding of the properties and behavior of such solutions is therefore of great commercial and scientific importance. The interaction between a number of sodium alkyl sulfates and gelatin results in the formation of surfactant micelles adsorbed onto gelatin at a surfactant concentration, cmc(1), which is substantially lower than the conventional critical micelle concentration, cmc.13,25 The binding isotherms for this series have been measured by PGSE-NMR. All the isotherms have a similar shape, which is displaced to lower surfactant concentrations as the hydrophobicity of the surfactant increases. The activity of the unimer increases monotonically above cmc(1), attaining a limiting value equivalent to the cmc under the prevailing ionic strength and pH conditions. This inherently defines cmc(2), the saturation condition, as being the surfactant activity above which the formation of free micelles is thermodynamically favored relative to that of gelatin-bound micelles. Small-angle neutron scattering (SANS) studies on gelatin/sodium dodecyl sulfate (SDS) solutions14 suggest that these adsorbed micelles have a comparable size to nonadsorbed SDS micelles, although the SANS estimates are strongly model dependent. In contrast, fluorescence-quenching studies point to a slightly lower aggregation number than in the absence of the gelatin.15 At gelatin concentrations above the critical overlap concentration, C*, the onset of an association with SDS micelles is accompanied by an increase in solution viscosity as the anionic micelles provide transient bridges between gelatin molecules.16 Below C*, the solution viscosity falls on addition of micellar SDS, indicating that micelles promote intrapolymer associations. Not all combinations of polymers and surfactants show such interactions. For instance, nonionic polymers show very little interaction with nonionic surfactants.17 Furthermore, cationic surfactants interact only weakly with nonionic polymers. Nagarajan18 discusses the polymer-surfactant complexation in terms of an area (apol) of the micelle surface that becomes “shielded” by the polymer upon complexation; hence, some water is displaced by the polymer (7) Blankschtein, D.; et al. Langmuir 1998, 14, 1618. (8) Sarmoria, C.; Puvvada, S.; Blankschtein, D. Langmuir 1992, 8, 2690. (9) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1992, 96, 5567. (10) Puvvada, S.; Blankschtein, D. In Mixed Surfactant Solutions; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992; p 96. (11) Puvvada, S.; Blanckstein, D. J. Phys. Chem. 1992, 96, 5579. (12) Rose, P. I. Gelatin. In Theory of the Photographic Process, 4th ed.; James, T. H., Ed.; Macmillan Publishing Co.: New York, 1977; p 51. (13) Nikas, Y. J.; Blankschtein, D. Langmuir 1994, 10, 3512. (14) Cosgrove, T.; White, S. J.; Zarbakhsh, A.; Heenan, R. K.; Howe, A. M. Langmuir 1995, 11, 744. (15) Griffiths, P. C.; Roe, J. A.; Abbott, R. J.; Howe, A. M. Imaging Sci. J. 1997, 45, 224. (16) Greener, J.; Contestable, B. A.; Bale, M. D. Macromolecules 1987, 20, 2490. (17) Lindman, B.; Thalberg, K. In Interactions of Surfactants with Polymers and Proteins; Goddard and Ananthapadmanabhan, Eds.; CRC Press: Boca Raton, FL, 1993. (18) Nagarajan, R. Colloid Surf. 1985, 13, 1-17.

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binding to the micelle surface. However, while polymer binding decreases the free energy of formation of the micellar core-water interface, it also increases the free energy of the system due to the steric repulsions between the polymer segments and the surfactant headgroups at the micelle surface. Compared to anionic surfactants, cationic and nonionic surfactants tend to have larger headgroups, which allows less penetration of water into the region next to the hydrophobic tails, and the potential benefits of shielding by the polymer are much smaller. Furthermore, binding of the polymer would induce much more steric repulsion at the micelle surface. This approach leads to a simple prediction that, for SDS/Triton X-100/ PEO mixtures, bound mixed micelles will form at high SDS mole fractions (shielding), but no binding will occur at low SDS mole fractions (steric repulsion). In a similar vein to Nagarajan,18 Ruckenstein et al.19 discuss the complexation of SDS/Triton X-100/PEO in terms of changes in interfacial tension between the surfactant aggregate and aqueous phase caused by the binding of the polymer, rather than the shielded area, apol. Ruckenstein’s approach predicts the same phase behavior as Nagarajan’s, namely, (1) that surfactants with sufficiently small headgroups can micellize on a nonionic polymer at a lower surfactant concentration than the polymer-free cmc value, (2) that the bound micelle is smaller than the free micelle, (3) that surfactants with large headgroups do not form bound micelles, and (4) that surfactants with moderate headgroup sizes can form polymer-bound micelles but only when some critical reduction in micelle surface-water interfacial tension occurs. Only the last prediction was not verified. Both models suggest that a strong interaction is observed where a significant amount of water will be displaced on polymer binding, whereas no interaction is observed where little or no water will be displaced. The surface hydration of a micelle is a parameter that can be easily determined.20 In this paper, we study the interaction of gelatin with a small range of model binary surfactant systems based on the combination of a nonionic n-alkyl malono-bis-Nmethylglucamide and SDS. In contrast to SDS, the nonionic surfactant does not interact with gelatin. Our approach is to probe how both the alkyl chain length and concentration of the nonionic surfactant affect the SDS/ gelatin interaction. Experimental Section Materials. The gelatin used in this study is referred to as “standard” gelatin, with molecular weight ∼150 000 g/mol. This is a polydisperse alkali-processed bone gelatin and was supplied by Kodak Ltd. This material has been deionized and its pH raised from its isoelectric point of 4.9 to 5.8 with NaOH. The ionic strength is estimated to be ≈1-2 mM for a 5 wt % gelatin solution. Sodium dodecyl sulfate (SDS), 98% purity from Aldrich Chemical Co. Ltd., was purified by repeated recrystallization from absolute alcohol until no dip could be seen in the surface tension behavior around the cmc (surface tension/log concentration data). The n-alkyl malono-bis-N-methylglucamides (the structure of the dodecyl malono-bis-N-methylglucamide is given in Chart 1) were supplied by Kodak Ltd. and purified by HPLC using a reversed phase column consisting of 18 µm silica particles coated with C18 alkyl chains. An 80% methanol (HPLC grade)/20% (double distilled water) mobile phase was employed. A typical HPLC trace showed three or four components, depending on the (19) Ruckenstein, E.; Huber, G.; Hoffmann, H. Langmuir 1987, 3, 382-387. (20) Griffiths, P. C.; Howe, A. M.; Bales, B. L.; Goyffon, P.; Rowlands, C. C. J. Chem. Soc., Perkin Trans. II 1997, 12, 2473.

Micellization of Sodium Dodecyl Sulfate

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Chart 1 Structure of Dodecyl Malono-bis-N-methylglucamide (DBNMG)

particular surfactant, corresponding to unreacted starting material(s), the target surfactant, and the single-headed analogue derived from decarboxylated starting material. Mass spectrometry and 1H and 13C NMR were used to identify the various components. Given the amount of material required for this work and the cost/time associated with purifying surfactants by HPLC, the entire mole fraction range was first characterized using the impure surfactant. The purified surfactant was then used to study that mole fraction range where interesting or unusual behavior was observed. Essentially, the purification had very little effect on the general behavior; it merely changed slightly the cmc values. This is in contrast to the behavior commonly observed in single-surfactant systems, where the presence of an impurity can drastically alter the observed behavior. Equipment. Surface tension measurements were made at 20 °C using a Du Nouy ring surface tension balance incorporating a CI Electronics zero displacement microbalance with a platinum ring of 4 cm circumference. The dodecyl ion selective electrodes used in this study (Methrohm Ltd.) consist of a PVC membrane developed and optimized for the titrimetric determination of anionic surfactants. This electrode was used in conjunction with a silver/silver chloride reference electrode. While this single point determination is not the intended use of the surfactant electrode, the response to SDS was linear over 4 decades of concentration, with a gradient (-61 mV per decade) in reasonable agreement with the Nernstian prediction, (-55 mV per decade). All measurements were SDS ) 8 mM, the response attained a performed at 20 °C. At Ctot plateau value, which is the limit of measurement. This linear response has been used as a calibration plot to determine the SDS unimer concentration in surfactant mixtures. The electrode has a certain characteristic that must be taken into consideration when used in this manner, namely a slow drift in measured response. Steady readings are obtained only after at least 30 min of immersion. However, we found that taking a reading after 5 min led to a highly reproducible, linear response to SDS standards. We therefore adopted this procedure throughout the experimental session, alternating standards and unknowns. The electrode was rinsed with distilled water (at room temperature) between measurements. Binding isotherms for two systems derived after waiting at least 30 min per point were found to be identical within experimental error to those derived from the 5 min procedure. The electrode shows no response to the pure nonionic surfactant below C ) 5 × cmc, that is, 2 mM, but does show a weak response above this surfactant concentration. Wherever possible, we have restricted the electrode work to those solutions below this nonionic surfactant concentration. In any case, any small errors introduced into the results by this impurity are insignificant given the SDS detected. changes in Cunimer

Results 1. Critical Micelle Concentrations. The cmc’s of mixtures of SDS and Cx-BNMG are given in Figures 1-3

Figure 1. Surface tension derived critical micelle concentrations for binary mixtures of sodium dodecyl sulfate and decyl malono-bis-N-methylglucamide (C10BNMG), in the absence (O) and presence (b) of 0.25 wt % gelatin. The solid line is the ideal mixing prediction, calculated from ref 1.

Figure 2. Surface tension derived critical micelle concentrations for binary mixtures of sodium dodecyl sulfate and dodecyl malono-bis-N-methylglucamide (C12BNMG), in the absence (O) and presence (b) of 0.25 wt % gelatin. The solid line is the ideal mixing prediction, calculated from ref 1.

for the mixtures of SDS with C10BNMG, C12DBNMG, and C14DBNMG, respectively. Values are presented for solutions in the absence (open symbols) and presence (filled symbols) of 0.25 wt % gelatin. The predicted cmc’s of the various binary surfactant solutions, based on ideal mixing, are shown as continuous lines for comparison. The cmc’s of SDS/C10BNMG mixtures (Figure 1) in the absence of gelatin are lower than the ideal prediction for all mole fractions studied. This synergistic interaction is typical of many anionic/nonionic surfactant mixtures.2 In the presence of gelatin, the micellization concentration of the mixtures is different from the simple surfactant case only at solution mole fractions of SDS, RSDS > 0.5. Below this critical value,21 we merely detect the formation of free micelles, that is, those that are not adsorbed onto (21) Dubin, P. L.; Oteri, R. J. Colloid Interface Sci. 1983, 95, 453.

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forms mixed micelles that are elliptical. However, these data were recorded on an impure sample of the nonionic and therefore warrant repeating.) There are several approaches to modeling or quantifying the thermodynamics describing the mixing of binary surfactants. The simplest is regular solution theory (RST).2 The nonideality of surfactant interactions (both antagonism and synergism) may be conveniently introduced by modifying the cmc values using activity coefficients, fi

1 cmcmixed

n

)

∑ i)1

Ri

fi(cmcpure ) i

(1)

The fi values are more conveniently introduced by the empirical parameter β, which for a binary surfactant system can be extracted following an expansion of eq 1

fCnBNMG ) exp β(1 - xSDS)2 Figure 3. Surface tension derived critical micelle concentrations for binary mixtures of sodium dodecyl sulfate and tetradecyl malono-bis-N-methylglucamide (C14BNMG), in the absence (O) and presence (b) of 0.25 wt % gelatin. The solid line is the ideal mixing prediction, calculated from ref 1.

gelatin. For clarity, the region RSDS < 0.5 has been omitted. Hence, we conclude that only above some critical SDS mole fraction, Rcritical SDS , do the micelles interact with gelatin. A clear maximum in cmc(1) is evident between Rcritical and RSDS ) 1.0, in the vicinity of RSDS ) 0.95. A SDS possible reason for this maximum is discussed in more detail for the SDS/C12BNMG/gelatin system in a later section. The behavior of the SDS/C12BNMG mixtures (Figure 2) is similar to that of the SDS/C10BNMG; synergy is observed in the cmc behavior over the whole mole fraction range. However, due to the much lower value of the cmc of the C12-BNMG, there is no broad minimum in the cmc, either in the presence or in the absence of gelatin, in contrast to the SDS/C10BNMG case. The addition of gelatin has much less effect on the reduction in micellization concentration for mixtures with C12BNMG in the region below the maximum in the cmc(1), that is, RSDS > 0.91. The critical SDS mole fraction necessary for an interaction also increases from 0.5 with C10BNMG to >0.8 with C12BNMG. As for the SDS/C10BNMG case, a clear maxiand RSDS ) 1.0. mum in cmc(1) is evident between Rcritical SDS The micellization process in SDS/C14BNMG binary mixtures (Figure 3) is noticeably different from that in the previous two systems, with micellization occurring at concentrations greater than that predicted from ideal behavior for low SDS mole fractions, RSDS e 0.5. Although the surfactant mixtures display antagonism at low RSDS, synergy is observed at higher SDS mole fractions, RSDS g 0.7. The effects in the region of antagonism are significant; here the unimer concentration of the nonionic surfactant, CCunimer , exceeds the cmc value of the pure surfactant. 14BNMG Furthermore, for all mole fractions studied (except RSDS ) 1), the aggregation concentrations of the SDS/C14BNMG mixtures in the presence of gelatin are unchanged from the gelatin-free cases; that is, no interaction with gelatin has occurs. Presumably, it can be assumed that Rcritical SDS increased to ≈1.0. This may be due to the greater hydrophobicity of the C14BNMG surfactant or a change in geometry of the mixed micelle. (Preliminary small-angle neutron scattering results suggest that SDS/C14BNMG

fSDS ) exp βxSDS2

(2)

The micelle composition at the cmc, xSDS, can be extracted from an iterative solution of xSDS2 ln(RSDScmcmixed/xSDScmcpure SDS ) (1 - xSDS)2 ln[(1 - RSDS)cmcmixed/(1 - xSDS)cmcCpure ] nBNMG

)1

(3)

Notwithstanding the point raised in the Introduction regarding the overinterpretation of β parameters, several distinct trends do emerge from the β values. For the SDS/ C10BNMG binary mixtures, β is negative, thus showing a favorable interaction between the two surfactants. In this system β is reasonably constant, showing a slight minimum around xSDS ≈ 0.5. For the SDS/C12BNMG binary mixtures, the β values are more negative than those for the SDS/C10BNMG binary mixtures for all mole fractions, thus indicating a more favorable interaction between SDS and C12BNMG surfactants. For the SDS/ C12BNMG system, β values vary more than those for the SDS/C10BNMG system over the same range of composition. Additionally, the minimum of β is somewhat more pronounced for the SDS/C12BNMG mixture and occurs at xSDS ≈ 0.4. For the SDS/C14BNMG mixtures, β ranges from positive (i.e. antagonism) for RSDS e 0.6 to negative (synergism) at higher values of RSDS; the RST clearly does hold. The interesting point here is an apparent maximum synergy when the tail sizes of the nonionic and anionic surfactants match. It would be interesting to see whether the phenomenon is general by investigating the interaction of CnBNMG with alkyl sulfates of different tail lengths. The cmc behavior of the SDS/C12BNMG system is reminiscent of the hydration of the micelle surface.24 Essentially, the concentration of hydrogen-bonding species within the headgroup region22 determines the polarity, which may be measured by a solubilized EPR spin probe. The amount of water bound to the headgroups decreases linearly until xSDS ) 0.3, where it goes through a minimum, (22) Bales, B. L.; Shahin, A.; Lindblad, C.; Almgren, M. J. Phys. Chem. B 2000, 104, 10347. (23) Griffiths, P. C.; Stilbs, P.; Paulsen, K.; Howe, A. M.; Pitt, A. R. J. Phys. Chem. B 1997, 101, 915. (24) Bales, B. L.; Roe, J. A.; Griffiths, P. C.; Howe, A. M.; Pitt, A. R. J. Phys. Chem. B 2000, 104, 264.


before increasing slightly. The obvious correlation between the hydration of the micelle surface and the nature and strength of the interaction between the surfactants (as characterized by the β values) suggests that the amount of water at the micelle-water interface is a significant factor in determining the overall free energy of micellization, and hence xSDS. Whether the interactions arise due to the shielding effect described by Nagarajan,18 a critical reduction in interfacial tension,19 or the entropy change associated with the displacement of this water is currently being investigated. 2. Unimer Concentration Behavior. Figure 4a shows the variation of SDS unimer concentration as a function of micelle mole fraction for SDS/C12BNMG mixtures for the purified nonionic surfactant (electrode studies). Also presented are the original PGSE-NMR data,23 which were derived from the C12BNMG surfactant containing the anionic impurity (see Materials in the Experimental Section). As found in the original study,23 and subsequently confirmed by SANS,26 there is a simple general relationship between the composition of the micelle and the free unimer concentration, irrespective of the total concentration of the two surfactants or their molar ratio. However, the data clearly show that, for any given micellar mole fraction, the system containing the purified nonionic surfactant gives a lower free SDS unimer concentration SDS ) than the one containing the impure nonionic (Cunimer surfactant. This suggests that the anionic impurity effectively displaces SDS molecules from the micelle, which is consistent with its greater hydrophobicity (the cmc of the impurity is approximately 1.0 mM). The same model is used to describe the EPR-sensed polarity of the micelle surface, as described previously.24 The solid lines plotted through the ion selective electrode data for the SDS/C12BNMG in Figure 4b are the unimer concentrations calculated using the RST, based on the cmc-derived β. The agreement between the RST calculations and experiment is good for all solutions studied. It appears therefore that while the RST does not stand up to the thermodynamic arguments discussed in the previous sections, it does provide a reasonably reliable framework for quantifying (at least empirically) the mixing behavior for this binary surfactant system. Interestingly, β appears total for the mole fractions to be independent of Csurfactant , studied. The limiting value of unimeric SDS, Cunimer,lim SDS increases with RSDS as expected, given that the mixed cmc increases, and therefore the unimer concentrations intotal and Csurfactant , xSDS can be esticrease. From Cunimer,lim SDS mated (to a first approximation) for these various mixed surfactants by assuming that the nonionic surfactant is entirely micellized. (This is reasonable in this instance, as the cmc of the nonionic is about one twentieth that of the SDS. This assumption is only likely to introduce a maximum error of ∼5%.) Whereas the micelles formed at low total surfactant concentrations are heavily populated by the more hydrophobic surfactant, the composition of the micelle at higher total surfactant concentrations corresponds to the solution composition within experimental error. The mixed surfactant data of Figure 4b are replotted in Figure 5 along with the corresponding behavior for solutions containing 0.25 wt % gelatin. Two data sets have (25) Griffiths, P. C.; Stilbs, P.; Howe, A. M.; Whitesides, T. H. Langmuir 1996, 12, 5302. (26) Griffiths, P. C.; Abbott, R. J.; Stilbs, P.; Howe, A. M. J. Chem. Soc., Chem. Commun. 1998, 1, 53. (27) Griffiths, P. C.; Whatton, M. L.; Kwan, W.; Abbott, R. J.; Pitt, A. R.; Howe, A. M.; King, S. M.; Heenan, R. K. J. Colloid Interface Sci. 1999, 215, 114.

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Figure 4. (a) SDS unimer concentration as a function of micellar mole fraction for SDS/C12BNMG mixtures for the purified surfactant: (3) RSDS ) 0.50; (0) RSDS ) 0.80; (4) RSDS ) 0.90; (O) RSDS ) 0.95. Also shown are the original PGSENMR data.28 The SDS is varied but the C12BNMG concentration is held constant at (b) 9.1 mM, (9) 15 mM, and (1) 25 mM; a simple general relationship27 exists between the composition of the micelle and the free unimer concentration, irrespective of the total concentration and molar ratio. (b) SDS unimer concentration as a function of total SDS concentration for SDS/ C12BNMG mixtures: (O) RSDS ) 0.90; (b) RSDS ) 0.80. The solid lines correspond to the RST prediction2 using the β value calculated from the cmc behavior.

(RSDS) been selected, corresponding to one below Rcritical SDS critical (R ) 0.90). For R < R and one above Rcritical SDS SDS SDS SDS , the SDS unimer concentration for the mixed surfactant solution is unchanged by the presence of gelatin. Therefore, there is no interaction between the mixed micelles and gelatin, at least over the concentration region 0 < Ctotal < 10 mM. This is consistent with the cmc behavior. Significantly, there is no obvious discontinuity or differSDS ≈ 0.6 mM, the ence in the two data sets around Cunimer cmc(1) for the binary SDS/gelatin solution. In other words, when C12BNMG is present, the interaction between SDS

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and gelatin has been “turned-off” even though there is sufficient (unimeric) SDS present for an interaction to be observed in the binary SDS/gelatin solution. This is a striking conclusion. The same conclusion is reached for the C14BNMG/SDS system, where the cmc data show that no interaction occurs at any mole fraction, even though SDS ) RSDS cmcmixed) the unimeric SDS concentration (Cunimer must exceed that required for an interaction to be observed in the binary SDS/gelatin solution. SDS When RSDS > Rcritical SDS , Cunimer is lower when gelatin is present for all total surfactant concentrations above cmc(1), although the isotherms have a very similar form. SDS for the gelatin-free and gelatinThe difference in Cunimer SDS containing solutions becomes perceptible around Cunimer ≈ 0.7-0.8 mM. From this observation, we cannot tell unequivocally whether the nonionic surfactant is present in the bound micelle or if the bound micelle is “pure” SDS, since cmc(1)mixed ≈ cmc(1)binary SDS/gelatin ≈ Cunimer SDS . The change observed in the micellization concentration on the addition of gelatin suggests that it would be highly improbable for the C12BNMG to be absent from the bound micelle. At higher Ctotal, the SDS unimer concentrations appear to converge. This last point further suggests that the composition of the bound micelle must be comparable to the solution composition in order that no preferential depletion from solution of one of the two surfactants occurs. The depletion would lead to a drift in solution composition and, hence, different limiting behavior, as shown in Figure 5b. Not surprisingly, the RST does not predict the unimeric SDS concentrations for the binary surfactant/gelatin system. We now consider the region of the cmc plot (Figure 2) that shows a maximum in cmc(1) with solution mole SDS behavior in the fraction, that is, RSDS > 0.90. The Cunimer presence of 0.25 wt % gelatin for RSDS ) 0.90, 0.95, and 1.0 is plotted in Figure 7. A noticeable difference occurs SDS < 3.0 mM. For RSDS ) over the region 0.3 mM < Cunimer 1.0 (the binary SDS/gelatin case), cmc(1) ) 0.60 mM, lower than both the RSDS ) 0.90 [cmc(1) ) 0.80 mM] and RSDS ) 0.95 [cmc(1) ) 1.0 mM] cases. One might expect the unimer concentration around and slightly above the cmc SDS will arise in to follow a similar ordersthe lowest Cunimer the RSDS ) 1.0 solution, as this interaction starts at the lowest SDS concentration, followed by RSDS ) 0.90. Finally, SDS . RSDS ) 0.95 would be expected to have the highest Cunimer This is not the order observed; at any given total SDS SDS is lowest in the RSDS ) 0.95 case, concentration, Cunimer increasing first to the RSDS ) 0.90 case and finally to the RSDS ) 1.0 case. SDS Knowing cmc(1) < cmc and Cunimer , cmc, the micellization process must arise from micelles binding to the gelatinsthere can be no nonadsorbed micelles. The bound micelles have a composition that is very different from those formed in the absence of gelatin, at the same SDS stoichiometry and total concentration. Taking the Cunimer values at a total SDS concentration of 2 mM, then xSDS ) 0.92 for RSDS ) 0.95, while xSDS ) 0.86 for RSDS ) 0.90, again assuming that all the nonionic surfactant is micellized. In other words, at concentrations at or slightly above cmc(1), the bound micelle mole fraction much more closely resembles the solution mole fraction. This is in contrast to the gelatin-free surfactant behavior where the micelle composition is more heavily weighted toward the nonionic component; for example, when RSDS ) 0.90, xSDS SDS ) 0.47. The limiting Cunimer is comparable to that found 25 in other studies and appears to be independent of solution mole fraction. This confirms the suggestion made in Figure

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Figure 5. (a) SDS unimer concentration as a function of total SDS concentration for SDS/C12BNMG mixtures, when RSDS < critical RSDS : (O) surfactants only; (b) surfactants plus 0.25 wt % gelatin. The solid line corresponds to the RST prediction2 using the β value calculated from the cmc behavior. (b) SDS unimer concentration as a function of total SDS concentration for SDS/ critical C12BNMG mixtures, when RSDS < RSDS : (O) surfactants only; (b) surfactants plus 0.25 wt % gelatin. The solid line corresponds to the RST prediction2 using the β value calculated from the cmc behavior. The cmc(1) for the binary surfactant/gelatin case is also shown.

5b that the bound micelle has a composition comparable with that in solution and that little or no drift in solution composition occurs. Significantly, the amount of SDS bound to the gelatin SDS (CSDS total - Cunimer) increases drastically when the nonionic surfactant is present: at 2 mM total SDS, there is 0.5 mM bound SDS for RSDS ) 1.0, 1.4 mM for RSDS ) 0.95, and 1.0 mM for RSDS ) 0.90. The behavior in Figure 6 is replotted in Figure 7 in terms of the fraction of total SDS present SDS /CSDS in the unimer form, Cunimer total, which effectively is the SDS / activity coefficient. By definition we would expect Cunimer SDS Ctotal ) 1.0 for Csurfactant < cmc(1), provided no pre-cmc(1) SDS /CSDS binding occurs. For RSDS ) 1.0 and 0.90, Cunimer total ) 1.0


Figure 6. SDS unimer concentration as a function of total SDS concentration for 0.25 wt % gelatin/SDS/C12BNMG mixtures: (O) RSDS ) 1.0; (0) RSDS ) 0.95; (b) RSDS ) 0.90. An approximate value for cmc(1) is shown; see text for details. The solid line corresponds to y ) x.

SDS Figure 7. Fraction of SDS present as the unimer form, Cunimer / SDS Ctotal, as a function of unimer SDS concentration for 0.25 wt % gelatin/SDS/C12BNMG mixtures: (O) RSDS ) 1.0; (4) RSDS ) 0.95; (b) RSDS ) 0.90. Approximate values for the cmc(1) correspond to the intercept of the solid lines. The broken line SDS is simply a linear regression of the data over 0.05 < Cunimer < 1 mM.

up to Csurfactant ) cmc(1), decreasing for Csurfactant > cmc(1) as expected. No pre-cmc(1) binding therefore occurs. However, for RSDS ) 0.95 (no data were recorded for RSDS SDS ) 0.975), Cunimer /CSDS total < 1.0 for surfactant concentrations well below the cmc(1) value obtained by surface tension. At CSDS total ) cmc(1) for this surfactant molar ratio, the SDS SDS /CSDS activity coefficient (Cunimer total) is about 0.30 ((0.05). Clearly, there is a significant drop in SDS unimer activity and this may be due to pre-cmc(1) binding.

Langmuir, Vol. 16, No. 26, 2000 9989

Figure 8. Surface tension data for binary mixtures of sodium dodecyl sulfate and dodecyl malono-bis-N-methylglucamide (C12BNMG) with RSDS ) 0.975, in the presence of (O) 0.25 wt % gelatin and (b) 0.75 wt % gelatin.

We now discuss the origin of the decrease from unity in the surfactant activity coefficient for SDS/C12BNMG when RSDS ) 0.95. Is this decrease a feature of the surfactant interaction which is enhanced by the presence of the gelatin; is this related to the formation of two types of micellesone SDS-rich type bound to gelatin and one nonionic-rich type not bound to gelatin;26 or is this a new feature of the gelatin/SDS interaction induced by the presence of small amounts of nonionic surfactant? The latter could arise due to site specific binding. The site specific hypothesis has been tested by measuring cmc(1) for the RSDS ) 0.975 system at two quite different gelatin concentrations, 0.25 and 0.75 wt %. As shown in Figure 8, cmc(1) is clearly not dependent on the gelatin concentration, confirming that no site specific binding is occurring. The minimum in surface tension around cmc(1) is very noticeable in the 0.75 wt % gelatin data set. On complexation with surfactant, there must be a strong enhancement in the adsorbed amount, leading to the low surface tension. With increasing surfactant concentration, the gelatin complexes are solubilized and, therefore, displaced from the surface. The surface becomes populated by less active species, and hence, the surface tension increases. cmc(2) can be estimated at 13((1) mM for 0.25 wt % gelatin and 30((3) mM for 0.75 wt %. Given that the cmc for the binary surfactant system is ∼3 mM, these saturation concentrations correspond to 10 ((2) mM and 27 ((4) mM bound surfactant respectively, that is, the expected constant value when normalized to the gelatin concentration. Therefore, it appears that the reduced activity coefficient of the SDS over this very narrow mole fraction range could arise due to a specific interaction between the two surfactants. Consider then the electrode data of Figure 5b from which the SDS surfactant activity can be extracted. For a mole fraction of RSDS ) 0.95 and at the mixed cmc (1.7 mM), that is, in the absence of gelatin, the SDS surfactant activity coefficient is approximately 0.80 ((0.05). The 20% drop in activity coefficient in the absence of gelatin is far smaller than the 70% drop in the presence

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of gelatin (activity coefficient ) 0.30), suggesting that gelatin does indeed alter the specific interaction between the two surfactants. The origins of this phenomenon are currently under investigation. Summary The cmc’s of sugar-based surfactants with different alkyl tail lengths, CnBNMG (n ) 10, 12, and 14), have been measured in binary mixtures with the anionic surfactant SDS in the absence and presence of 0.25% gelatin. The results have been compared with ideal mixing theory and discussed within the framework of regular solution theory. For the binary mixtures, the n ) 10 and 12 compounds show a synergistic interaction with SDS. The n ) 14 compound is strongly antagonistic at low SDS mole fractions but synergistic at high SDS mole fractions. In the case of binary C12BNMG/SDS mixtures, the micelles formed at Ctotal ≈ cmc are more heavily populated by the more hydrophobic surfactant, C12BNMG. As Ctotal increases, the micelle composition drifts toward the is comparable to solution composition. Cunimer,limiting SDS . For this pair of surfactants, no growth or RSDScmcRmixed SDS change in micelle shape occurs26 with increasing RSDS. However, when the alkyl lengths of the nonionic and anionic surfactants are different, the SANS data suggest (28) Griffiths, P. C.; Stilbs, P.; Paulsen, K.; Howe, A. M.; Pitt, A. R. J. Phys. Chem. B 1997, 101, 915.

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a significant change in shape of the micelle. For this reason, no further discussions of these binary mixtures are presented here. On addition of gelatin, the effective “hydrophobicity” of SDS is greatly enhanced by its binding to gelatin; cmc ≈ 8 mM, whereas the binary SDS/gelatin cmc(1) ≈ 0.6 mM. The difference in hydrophobicity between the two surfactants is then greatly reduced, and any preferential populating of the micelle by the more hydrophobic surfactant is minimal. The bound micelle composition is then much closer to the solution composition. The amount of SDS bound to gelatin as a function of RSDS goes through a maximum around the same composition range that displays a maximum in the cmc behavior. Around this range, there is a substantial drop in SDS unimer activity. The exact mechanism by which a small amount of added C12BNMG can induce this behavior is still unclear and is the subject of ongoing investigations. Acknowledgment. EPSRC and Kodak Research and Development are acknowledged for financial support. Prof. Dan Blankschtein, and members of his group, have made several helpful comments on this manuscript during preparation, and we are very grateful to them for doing so. LA000151F

Micellization of Sodium Dodecyl Sulfate with a Series of Nonionic n

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