pubs.acs.org/Langmuir © 2010 American Chemical Society
On the Concept of Critical Surface Excess of Micellization Federico I. Talens-Alesson* Talenco Consulting, Urbanitzaci o Sant Salvador, Fase 1, Parcel.la 52 08790 Gelida, Barcelona, Spain Received July 19, 2010. Revised Manuscript Received September 1, 2010 The critical surface excess of micellization (CSEM) should be regarded as the critical condition for micellization of ionic surfactants instead of the critical micelle concentration (CMC). There is a correspondence between the surface excesses Γ of anionic, cationic, and zwitterionic surfactants at their CMCs, which would be the CSEM values, and the critical association distance for ionic pair association calculated using Bjerrum’s correlation. Further support to this concept is given by an accurate method for the prediction of the relative binding of alkali cations onto dodecylsulfate (NaDS) micelles. This method uses a relative binding strength parameter calculated from the values of surface excess Γ at the CMC of the alkali dodecylsulfates. This links both the binding of a given cation onto micelles and the onset for micellization of its surfactant salt. The CSEM concept implies that micelles form at the air-water interface unless another surface with greater affinity for micelles exists. The process would start when surfactant monomers are close enough to each other for ionic pairing with counterions and the subsequent assembly of these pairs becomes unavoidable. This would explain why the surface excess Γ values of different surfactants are more similar than their CMCs: the latter are just the bulk phase concentrations in equilibrium with chemicals with different hydrophobicity. An intriguing implication is that CSEM values may be used to calculate the actual critical distances of ionic pair formation for different cations, replacing Bjerrum’s estimates, which only discriminate by the magnitude of the charge.
Introduction Molecular models for ionic surfactant micelles1-3 describe them as possessing a Stern layer with closely bound counterions and a diffuse layer sufficiently charged electrically to balance the net charge of the micelle and Stern-layer bound cations. These models deal with the diffuse layer as having a concentration profile which is a mathematically continuous function. Some authors consider the diffuse layer split between an inner region held within the hydrodynamic boundary layer of the micelle and an outer region influenced only by the electrostatic forces around the micelle.2 Computer simulations4 have proposed ionic pairing at the micellar surface and suggested that most counterions would be bound to one surfactant headgroup, with progressively smaller proportions being bound to two or even three surfactant head groups. A more recent model proposes that micelles form when the critical distance for ionic pair association is reached between a counterion and a cluster of surfactant molecules.5 This model calculates the counterions available for binding onto the micelle by comparing their average distance in the solution with the critical distance for ionic pairing. The original model considered the micellar surface composed of ionic groupings [M:Sx]n-x. The stoichiometry is deduced from data on binding of monovalent, divalent, and trivalent cations onto NaDS micelles.1,3,6-8 This *E-mail:
[email protected]. (1) Rathman, J. F.; Scamehorn, J. F. J. Phys. Chem. 1984, 88, 5807–5816. (2) Lin, C.-C.; Jafvert, C. Langmuir 2000, 16, 2450–2456. (3) Srinivasan, V.; Blankschtein, D. Langmuir 2003, 19(23), 9946–9961. (4) Bruce, C. D.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. J. Phys. Chem. B 2002, 106, 3788–3793. (5) Talens-Alesson, F. J. Phys. Chem. B 2009, 113, 9779–9785. (6) Hafiane, A.; Issid, I.; Lemordant, D. J. Colloid Interface Sci. 1991, 1, 167–178. (7) Paton, P. Aplicacion de los Sistemas Tensioactivo Anionico/Aluminio(III) a la Depuracion de Aguas Residuales: Fundamento Fisicoquimico. (Spa.) Ph.D. Thesis. University of Barcelona, Spain, 1998. (8) Talens, F.; Paton, P.; Gaya, S. Langmuir 1998, 14(18), 5046–5050.
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limits the number of ions available to form the ionic groupings of the micelle, and explains why enough Al3þ can adsorb to cause electroneutrality and flocculation, whereas this would not happen in the presence of monovalent or divalent cations8 such as Naþ or Zn2þ. This approach removes the need to consider the existence of a Stern layer. The predictions for differently charged cations are correct, but the model cannot account for specific ion characteristics in competitive binding of equally charged ions. This approach should be considered original, because although some work has recently considered the effect of ionic pair formation onto micellar transition,9 and the Bjerrum criterion was used to estimate overall shielding of a micelle by counterions,10 the concept has not been used to explain micellization itself, or to predict the competitive binding of counterions onto ionic micelles. In this paper the model5 is refined in two ways: by introducing a parameter estimated from the values of surface excess of surfactants at their critical micelle concentration (CMC), and by including a balancing region (BR) to replace the diffuse layer. Figure 1 shows schematics of the model. This BR is assumed to be very thin and contain at most one counterion between the micelle and the bulk phase at any point. It does not allow for concentration profiles .This addresses the fact that the intermediate region between the micelle and the bulk phase has a discrete particle population. Let us consider an hypothetical M(DS)2 micelle formed by 60 DS- monomer with 20 Mþ2 counterions bound assuming an Mþ2:DS stoichiometry of 1:3.5 The micelle formed by these ionic groups would have a net charge of -20, and only 10 counterions in the BR would be required to balance the charge. Such a system cannot be described using a concentration profile. The enhanced model is validated with data on micellar enhanced ultrafiltration6 (MEUF) and micellar flocculation,7,8 taking as bulk phase concentrations to be matched by the predictions those in the permeate or clarified solution. It must (9) Abezgauz, L.; Kuperkar, K.; Hassan, P. A.; Ramon, O.; Bahadur, P.; Danino, D. J. Colloid Interface Sci. 2010, 342, 83–92. (10) Treiner, C.; Mannebach, M. H. Colloid Polym. Sci. 1990, 268(1), 88–95.
Published on Web 10/20/2010
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Figure 1. A scheme of the binding model proposed here: some cations are bound forming ionic pairs with groups of surfactant polar head groups. Other cations within a thin layer designated as the BR provide the charge required for neutralization of the micelles. Large gray spheres represent surfactant monomers, small black and white spheres represent monovalent cations, and small gray spheres represent divalent cations.
be taken into account that filtration times in MEUF data sets must be short enough so that ion exchange in the surfactant gellayer deposited on the membrane11 does not distort the results.
Data Sets Data Set from Hafiane et al.6 Surfactant was NaDS at an initial 50 mM concentration. The initial cation concentrations were 1, 2.5, 5, 7.14, 10, 16.6, and 25 mM, except in the case of Cr3þ, in which there were no experiments at the two higher concentrations. Other cations investigated included Hþ, Liþ, Rbþ, Csþ, Cu2þ. The temperature was 22 ( 2 °C. The type of membranes was polysulfone. These authors give their data in permeate concentrations for the various cations and the surfactant. In this paper, these data are used to calculate binding ratios. Data Set from Paton7,8 for the Systems NaDS/ZnSO4/ Al2(SO4)3 and NaDS/NaCl/Al2(SO4)3. NaDS concentration was 0.050 M, Al2(SO4)3 concentrations ranged from 0.0005 M to 0.006 M, and the concentrations used to illustrate the versatility of the model in the Supporting Information are ZnSO4 (0.031 and 0.075 M) and (NaCl 0.250 M). Temperature was 25 °C. The concentrations are concentrations in the clarified solution after filtration over paper of the micellar flocculates.
Theoretical Basis Critical Surface Excess of Micellization (CSEM) as the Critical Micellization Condition. Figure 2 shows molar ratios Mþ/Naþ data6, with Mþ being Hþ, Liþ, Rbþ, or Csþ. Hþ and the kosmotrope Liþ behave very similarly to Naþ. Chaotropes Rbþ and Csþ show higher affinity for the micelles than Naþ. Rbþ has the lowest molar ratios in the permeate, and therefore competes most successfully with Naþ. The behavior is consistent with the series of hydrated radii3 1.69, 1,48, 1.72, 2.18, and 2.43 A˚ for Csþ, Rbþ, Kþ, Naþ, and Liþ, respectively. The lowest hydrated radius matches the highest preference to bind. These hydrated radii are calculated from measures of either ionic activity coefficients or hydration entropy.13 Comparing the hydrated radii with ionic radii14 of 1.52 and 1.69 A˚ for Rbþ and Csþ, respectively, there is no obvious reason for the difference observed between Csþ and Rbþ, as both are practically nonhydrated. The trend observed in the binding of monovalent cations is consistent with the values of surface excess Γ given at 33 °C by (11) Sandar, B.; DasGupta, S.; De, S. Sep. Purif. Technol. 2009, 66, 263–272. (12) Lu, J.-R.; Morrocco, A.; Su, T.-J.; Thomas, R. K.; Penfold, J. J. Colloid Interface Sci. 1993, 158, 303–316. (13) Collins, K. D. Methods 2004, 34, 4300–311. (14) Handbook of Chemistry and Physics, 86th ed.; Lide, D. R., Ed.; Taylor & Francis: Boca Raton, FL, 2005.
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Figure 2. Molar ratios between Liþ, Hþ, Rbþ, and Csþ against
Naþ in the bulk phase (permeate)6 plotted against the initial molar ratios between the initial or nominal concentrations in the solution.
Lu et al.12 for the alkaly metal dodecylsulfates at their CMCs: 3.20, 3.33, 3.91, 4.54, and 4.27 μmol m-2, for LiDS, NaDS, KDS, RbDS, and CsDS, respectively. The corresponding CMCs are 8.46 10-3 M, 8.1 10-3 M, 6.71 10-3 M, 5.9 10-3 M and 5.9 10-3 M. While the surface excess Γ peaks for Rbþ, in agreement with the relative binding preferences shown in Figure 2, the CMC values do not. This suggests that the connection between CMC and binding is indirect via Γ. We prove this connection by calculating a characteristic distance between counterions dEV as described in the Supporting Infornation and previous work.5 If dEV is calculated for the values of critical surface excess for LiDS, NaDS, KDS, RbDS, and CsDS by Lu et al.,12 the values are respectively 0.36, 0.353, 0.326, 0.302, and 0.312 nm, showing that Rbþ is the one causing the closest packing. The values are similar to the theoretical 0.3477 value given by Bjerrum’s correlation for the critical distance for ionic pair formation between monovalent counterions in water at 33 °C. The small discrepancies show that assuming ionic pairing as the critical phenomenon for micelle formation is correct. The results also suggest that the actual values for the critical distance of ionic pair formation for a given cation can be estimated from the CSEM value for its dodecylsulfate salt. Anionic, cationic, and zwitterionic surfactants all show this agreement. For dodecyl trimethyl ammonium bromide (CTAB) with a CSEM value of 3.21 μmol m-2 at a CMC of 0.00825 M,15 the calculation gives a dEV of 0.358 nm. For ammonium perfluorooctanoate, CSEM values of 3.96 and 4.37 μmol m-2 have been given16 at a CMC of 2.6 10-2 M. From those values, dEV of 0.321 and 0.306 nm can be calculated. For sodium decanesulfonate, with a CSEM of 4.21 μmol m-2 at a CMC of 0.00234 M in the presence of 0.0684 M NaCl, dEV is 0.314 nm.17 The same (15) Zhao, J.-X.; Xin, F. Y.; Jiang, R.; Yan, H. M.; Jing, J. C. Colloids Surf., A 2006, 275, 142–147. (16) Downes, N.; Ottewill, G. A.; Ottewill, R. H. Colloids Surf., A 1995, 102, 203–211. (17) Granet, R.; Piekarski., S. Colloids Surf. 1988, 33, 321–336.
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authors listed CSEM and CMC for several other i-alkyl decane sulfonates, which are also consistent with dEV around 0.357 nm. In the case of zwitterionic phosphatidilcholines18 with general formulas diCxPC, CMCs at pH 7.4 are given ranging from 5.45 10-2 M for diC5PC to 2.1 10-4 M for diC8PC, with CSEM between 2.3 μmol m-2 and 2.5 μmol m-2. From these data, dEV around 0.41 nm can be calculated. This seems to support the idea that micelle formation must be triggered at the air-water interface, where the probability of ion pairing is higher than in the bulk phase. For example, at the CMC of NaDS, dEV in the bulk phase using eq 4 in the Supporting Information is 2.9 instead of 0.37. This shows the lower probability for ionic pair association away from the airwater interface. This takes a step further the discussion by Zhao et al.,19 on the occurrence of ionic pairs between cationic and anionic gemini surfactants near the interface: ionic pairing involving surfactants must not happen near the air-water interface, but at the air-water interface itself. Once ionic groupings form, they would subsequently assemble at or near the interface into fully formed micelles and drift into the solution. Conversely, micelles may migrate toward the interface and break up there. This would explain the well-known phenomenon of exchange of material between the micelles and the rest of the solution. This presents researchers with the intriguing question of what is the effect of the presence of other interfaces. Solid interfaces with the ability to compete successfully with the air-water interface for superficial adsorption of surfactant may become the source of micelles. Additionally, the ratio between the surface available for micelle formation and the volume of the solution could define whether two differently shaped containers with the same amount of surfactant in the same volume of solvent would contain micelles or not. Shape-changing containers causing the presence or absence of micelles may be combined with traces of substances whose detectability levels change whether they are free in solution or contained within a micelle. This could lead to a new generation of triggering devices, and is an example of the potential implications of the concept presented here. Model Equations. It is important to remember that none of the concentrations are local: they are all given as mole per liter in the whole volume of the system. The charge of the counterions in the BR surrounding the micelles must be equal to the charge contributed by micellar surfactant minus the charge contributed by ion-paired counterions. The difference between the total concentration of a counterion and the sum of its concentration in the BR (micelle-shielding) and the concentration of ion-paired counterions at the micelle surface would therefore be its bulk phase (or permeate) concentration. We impose the following hypotheses: • Binding onto micelles is proportional to the corrected molar fraction in eq 1. • The concentration of a counterion in the BR should be the product of the molar fraction of said counterion in the bulk phase times the total counterion concentration at the BR (Figure 1b). All-Monovalent Systems. For all-monovalent systems, we calculate the effective molar ratio of a competing counterion in the bulk phase introducing in a generic expression for binding ratio a relative binding strength parameter γ defined in the (18) Martınez-Landeira, P.; Lopez-Fontan, J. L.; Ruso, J. M.; Prieto, G.; Sarmiento, F. Colloids Surf., A 2003, 216, 91–96. (19) Zhao, J.-X.; Liu, J.-Y.; Jiang, R. Colloids Surf., A 2009, 350, 141–146.
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Supporting Information, to give eq 1: γi ½Miþ bulk n P γj ½Mjþ bulk
effective ¼ XMi þ
ð1Þ
j¼1
The charge required by the BR to counter the net charge of the micelle is X ionic-pair zð2Þ ½z ( BR ¼ z ( ð½Stotal - ½SCMC Þ i ½Mi The bulk phase concentration of the counterion i, which must match the experimental values is given in eq 3: 0 1 B
½Miþ free
½Mi bulk ¼ ½Mi total - ½z ( BR B @ P
j ¼ 1, n
C C=zM - ½M þ ion-pair i i
A ½Mjþ free
ð3Þ The superscript “free” denotes all counterions that are not forming ionic pairs, that is, the difference between the initial concentration and the concentration given in eq 4. Here the concentration of ions held by the micelles forming ionic pairs is proportional to the adjusted molar fraction in eq 2, and to the number of three-monomer surfactant ionic groupings assumed for spherical NaDS micelles.5 ½SDStotal - ½SDSCMC γi ½Miþ free þ ion-pair ð4Þ ½Mi ¼ P 3 γj ½Mjþ free j ¼ 1, n Monovalent-Polyvalent Systems. For a two counterion system, composed of a polyvalent counterion 1 and a monovalent counterion 2, the excess concentration in solution of polyvalent counterion 1 available to bind forming ionic pairs onto the micelle by forcing out of said pairs the monovalent counterions 2 originally present is defined (eq 5) as ½M1 excess ¼ ½M1 total - 2
1024
!33 42 jz jjz je 5 NA 8πε0 εr kT þ
-
ð5Þ
2
The concentration is defined as the excess over the critical concentration (second hand right term) for which the average distance of ions of a given charge-sign matched Bjerrum’s critical distance. We define a “Bjerrum” ionic pair binding ratio for the association of ions onto the micelle forming ionic pairs as ½M1 excess ð6Þ ½SDStotal - ½SDSCMC 3 The binding ratio β1Bj can be at most 1. We impose that every 3 mol of micellar NaDS (in solutions with spherical micelles) create an adsorption site.5 Therefore, if the value is higher than 1, then the value of the binding ratio will be 1 and the excess of counterion 1 will remain in solution. The ionic pair binding ratio for the monovalent counterion 2 is defined as βBj 1 ¼
Bj βBj 2 ¼ 1 - β1
ð7Þ
The charge required to neutralize the net charge of the micelle after the ionic-pair binding is complete is Bj zBR ¼ ð1 - z1 βBj 1 - z2 β2 Þð½SDSTotal - ½SDSCMC Þ
ð8Þ
The sign convention assumes that the counterion is positive and the surfactant is negative. Langmuir 2010, 26(22), 16812–16817
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Figure 3. Experimental and predicted values of bulk phase (permeate) concentrations for the competitive binding of Hþ, Liþ, Rbþ, and Csþ against Naþ by Hafiane et al.6
The total concentration needed to meet zBR is contributed by both the polyvalent and monovalent counterions as z2 ½M2 BR ¼ zBR - z1 ½M1 BR
ð9Þ
The concentration of the polyvalent cation has a bootstrap derived from the equations for the contribution of Ca2þ and Naþ to the CMC of NaDS in the presence of CaCl5: ½M1 BR ¼
z31 ½M1 bulk z31 ½M1 bulk þ z32 ½M2 bulk
ð10Þ
where ½M1 bulk ¼ ½M1 Total - ½M1 excess - ½M1 BR
ð11Þ
½M2 bulk ¼ ½M2 Total - ½M2 excess - ½M2 BR
ð12Þ
and
Equation 10 describes the way the higher charge cation would compete advantageously for the BR (Figure 1c) against the monovalent cation. The restriction for the concentration of monovalent counterions in the BR is ½M2 BR ¼
z32 ½M2 bulk z31 ½M1 bulk þ z32 ½M2 bulk
ð13Þ
The equation system is solved by iteration, seeding values for the concentration of one of the cations within the BR and using eq 10 as the bootstrap for the other cation.
Model Results and Discussion The results in Figure 3 come from calculations using eq 3 plotted against experimental values from Hafiane et al.6 The “reference” is an X = Y line plotted to stress the agreement of the predictions with the actual results. The predictions are accurate, confirming the link between cation binding, surface excess, and micellization. The section of a NaDS polar headgroup16 is about 25 A˚2, and its radius is about 2.8 A˚. A cation sitting on top of the headgroup could hardly reach the neighboring head groups. It seems reasonable to assume that the ionic pair structure is the time average of a counterion shared by head groups of three or four adjacent surfactant monomers (Figure 4a) and that more hydrated counterions will be less efficient at binding (Figure 4b). Langmuir 2010, 26(22), 16812–16817
Figure 4. Schematic representation of the competition of hydrated and nonhydrated ions for a surfactant headgroup cluster.
If the percentage of air-water interface covered by DS- heads with an individual section of 25 A˚2 is calculated for each surfactant’s CSEM, RbDS covers 68.3%, whereas LiDS covers 48.2% only. The CSEM and CMC values by Lu et al.12 show that Rbþ creates a more compact surface layer before micellization starts, but also requires a lower bulk concentration in equilibrium to do so. This suggests that, because the ionic groups are tighter, more of them are needed at the air-water interface before aggregation into micelles takes place. The higher mass of Csþ compared with Rbþ seems to be the only difference in their relative ability to displace Naþ. Lower diffusivity may compensate for lower hydration during competition for the surfactant heads (Figure 4c). The various factors may dictate the proportion of each counterion onto the micelle (Figure 4d). This brings the question of the influence of counterion charge on the micellization of an ionic surfactant. Al(DS)3 has a CMC8 of 5 10-4 M. This is about 1/17 of the CMC of NaDS, although it could be expected to be 1/27 because the cation is trivalent and its dEV would be larger than that of a monovalent cation by its charge to the power of 3. The CMCs20 of Mn(DS)2, Cu(DS)2, Co(DS)2 are 1.1 10-3 M, 1.0 10-3 M, and 8.8 10-4 M. The values are between 1/8 and 1/10 of the CMC of NaDS, closer to the theoretical ratio of 1/8. The values suggest that the effect of greater charge does not completely overrule other (“lyotropic”) effects in the triggering of ionic pair formation. Although the dEV distances obviously become larger than the ionic and hydrated radii, the same charge ions still lead to different CMC values. This suggests that measures of CSEM for polyvalent cations could also provide differentiated values for their critical distances for ionic pair formation, as charge alone cannot explain why different M(DS)2 surfactants should have different CMCs or why the equilibrium between CMC and CSEM should be displaced. Nevertheless, the trends are qualitatively consistent with the model presented here and support the underlying concept. Figure 5 shows data6 for the system NaDS/Cu2þ and the predictions from the model for a monovalent-divalent system. (20) Hato, M; Shinoda, K. Bull. Chem. Soc. Jpn. 1973, 46, 3889–3890.
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Figure 5. Experimental and predicted values for the bulk phase (permeate) concentrations of Cu2þ and Naþ, and predicted concentration of Cu2þ bound onto NaDS micelles due to ionic pairing [Cu]Bj.
Figure 6. Exclusion of polyvalent cations from the BR. Gray represents surfactant polar head groups. Black represents monovalent cations, and white represents divalent cations. Left: When there are few divalent cations bound to the micelle, there can be a significant concentration of divalent cations in the BR. Right: Higher local density of positive charge due to binding of divalent cations would suppress the presence of divalent cations from the BR.
In this case, the predictions do not include relative binding parameters, as those should be derived from available CSEM data, and not CMCs. The symbols represent the predicted [Cu2þ] bound onto NaDS triads in the micelles. Predictions are very accurate up to [Cu2þ] = 15 mM. At this concentration, saturation of the ion-pairing capacity of the micelle toward Cu2þ is almost reached as the 15 mM of Cu2þ bound into ionic pairs requires 45 mM of micellar surfactant. As the charge distribution on the micelle is nonuniform, the localized repulsive forces between bound divalent cations bound and those divalent cations trying to enter the BR may override the attractive force of the anionic micellar background. This may give preference to monovalent cations to incorporate into the BR (Figure 6). Lin and Jafvert2 had proposed that about 60% of the monovalent ions required to neutralize the micelle are closely bound to it, within the hydrodynamic boundary layer of the micelle. The distribution predicted by the model by Bruce et al.4 indicates that within their first headgroup shell 72% counterions are bound to one surfactant head, 23% are bound to two surfactant heads, and 6% are bound to three surfactant heads, with the first shell accounting for 16816 DOI: 10.1021/la102868z
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Figure 7. Prediction of bulk phase (permeate) concentrations of Naþ (left Y axis) and Cr3þ (right Y axis).
25% of the counterions and the first two shells accounting for 50%. Both views are not incompatible with the view that about two-thirds of the counterions required to neutralize a micelle is directly involved in being part of dynamic surfactant-counterion ionic groups, or in the process of replacing or being replaced by another counterion within a given cluster. Figure 7 shows data6 for NaDS/Cr3þ and model predictions. The discrepancies for Cr3þ are very small. The high charge of Cr3þ implies that the BR will not exist when a trivalent cation fully replaces Naþ because the charge of the three-monomer DS- clusters would be neutralized.7,8 Therefore the predictions in the case of high concentrations of Cr3þ are in practice based on the predicted ionic pairing at the surface and are as accurate as those for the binding of Al3þ described in the earlier version of this model.5
Conclusions The model tends to small over predictions of the bulk phase concentration of Cr3þ, unlike Cu2þ. The CMC data for divalent dodecylsulfate salts20 suggest that a correction factor derived from their CSEMs would be required. However, the good agreement of the model predictions with the data shows that the charge factor is sufficiently strong to be considered much more important than the lyotropic factor associated with the chaotropy-kosmotropy of the counterions. The improved model proposed in this paper, based on a binding parameter derived from surface excess data and a prediction of the cation concentration available for binding, derived from the Bjerrum condition for ionic pair association, provides remarkable predictions of counterion binding onto micelles over a range of monovalent, monovalent/polyvalent, and even polyvalent/polyvalent systems. The agreement of the predictions with more complex systems is shown in the Supporting Information. On the strength of such agreement with experimental data, it is proposed that the mechanism of ionic pair association seems to govern both the binding of counterions onto ionic micelles and the onset of micellization, as suggested by the fact that the values for surface excess at the CMC are consistent with the distances predicted by Bjerrum’s expression. Therefore, the surface excess would be the critical condition for the formation of micelles. Furthermore, the results indicate that surface excess data can be used to estimate the critical distance for ionic pair formation for any dodecyl sulfate Langmuir 2010, 26(22), 16812–16817
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salts. A potentially significant technological implication is that the presence or absence of micelles in a given volume of solution at a given concentration may depend on the ratio of the area of the air-water interface to the volume of solution. Another question raised by this work is whether alterative micellization surfaces may compete with the air-water interface to be the micellar generator, and whether a systematic approach to design such surfaces may have an impact on applications such as detergency.
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Supporting Information Available: Definition of the characteristic distance dEV. Calculation of the relative binding strength parameter γ. Prediction of binding of Al3þ onto SDS micelles in the presence of 0.250 M NaCl: comparison with binding of Al3þ in the absence of added electrolyte. Prediction of competitive binding of Al3þ and Zn2þ onto SDS micelles. This material is available free of charge via the Internet at http://pubs.acs.org.
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