H and 19F NMR Study of the Counterion Effect on the Micellar

Tetraethylammonium and Lithium Perfluorooctylsulfonates. 2. ... tetraethylammonium counterions (TEA+) due to the proton chemical shift is found to be ...
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J. Phys. Chem. B 1999, 103, 8259-8266

8259

1H

and 19F NMR Study of the Counterion Effect on the Micellar Structures Formed by Tetraethylammonium and Lithium Perfluorooctylsulfonates. 2. Mixed Systems Dobrin Petrov Bossev, Mutsuo Matsumoto, Tomohiro Sato, Hiroshi Watanabe, and Masaru Nakahara* Institute for Chemical Research, Kyoto UniVersity, Uji, Kyoto 611-0011, Japan ReceiVed: April 28, 1999

Mixtures of tetraethylammonium perfluorooctylsulfonate (TEAFOS) and lithium perfluorooctylsulfonate (LiFOS) in water (D2O) are studied as a function of the LiFOS fraction (φLi) at a total concentration of 100 mM and 30 °C by means of 1H and 19F NMR and viscosity measurements. The counterion binding in the double layer structure of the FOS micelles is analyzed through the chemical shifts and self-diffusion coefficients that are sensitive to the Stern and diffuse double layers, respectively. At φLi ) 0, the fraction of bound tetraethylammonium counterions (TEA+) due to the proton chemical shift is found to be 0.45; it implies that one TEA+ counterion is bound to and bridging roughly two micellized FOS- ions. This value is markedly smaller than that (0.73) obtained by the diffusion data because of the short-range sensitivity of the chemical shift. The binding fraction due to the diffusion data is higher because it involves both the Stern and diffuse double layers. The concentration of the TEA+ counterions preferentially localized within the Stern layer remains constant at 45 mM when φLi is varied between 0 and 0.55. It is shown that the preferential saturation of the Stern layer with TEA+ counterions in this region of φLi is prerequisite for the formation of the threadlike FOS structure and the high solution viscosity. At higher values of φLi, the threadlike structure disintegrates and the viscosity drops as a result of an overall shortage of TEA+ counterions in the solution.

1. Introduction In our previous study (part 1),1 we have shown that a number of static and dynamic NMR properties of the micelles formed by tetraethylammonium perfluorooctylsulfonate (TEAFOS) are significantly different from those of the lithium perfluorooctylsulfonate (LiFOS). Although these surfactants consist of an identical hydrophobic chain part and headgroup, threadlike micelles are grown by TEAFOS, in contrast to the spherical micelles formed by LiFOS. As a consequence, even qualitatively different fluorine NMR spectra are exhibited by these surfactants above their respective cmc (critical micellar concentration); cmc ≈ 1 and 7 mM (M ) mol dm-3) for TEAFOS and LiFOS, respectively. The 19F spectrum of LiFOS is composed of a single set of averaged peaks as a result of a fast exchange between the monomer and micellar states. On the other hand, the TEAFOS surfactant forms kinetically more stable micelles and the 19F spectrum is split into two distinguished sets of peaks, “monomer” and “micellar”. These separate signals have been subjected to detailed structural analysis. The marked differences in the structure between TEAFOS and LiFOS are attributed solely to the antagonism in the counterion nature. It is the hydrophobic TEA+ counterions that are more strongly bound to the micelles so as to effectively reduce the electrostatic surface charge density of the micelles.2,3 Thus, the counterion binding strongly affects the ionic micellar structure as well as the double layer structure. Here we investigate the counterion effect by varying the fraction of LiFOS (φLi) in the mixtures of TEAFOS and LiFOS at a constant total concentration of 100 mM. * To whom the correspondence should be addressed. E-mail: nakahara@ scl.kyoto-u.ac.jp. Telephone and fax: +81-(774)-38-3070.

The theory of the counterion binding to micelles has been steadily improved throughout the past decades.4 Together with the refinement of the classical or continuum theory of the electric double layer,5,6 a number of computer simulations have recently been done to get an adequate molecular picture.7,8 However, the experimental analyses employ rather macroscopic models to shed light on the counterion binding because it is difficult to distinguish between the different regions of the counterion atmosphere. Atomic force microscopy and ζ-potential measurements are applicable only to fixed macroscopic surfaces,6 and the conductivity method gives rather collective information.2,3 In this paper we have applied 1H and 19F NMR spectroscopy to the mixed surfactant systems in order to elucidate the fine structure of the electric double layer formed by the TEA+ counterions around the FOS- micelles. So far, NMR has been used to investigate the counterion binding of such counterions as alkali metal and carboxylate ions to the micelles on the basis of the self-diffusion coefficients of the counterions and the micelles.9-13 In this method, the selfdiffusion coefficient of the counterions has been treated by a two-state model, bound and free counterions.14 The binding coefficient is comparable to the dissociation degree obtained by the conductivity method. The diffusion of the counterions reflects their association to the micelles without specific information on the counterion/micelle interactions. On the other hand, the counterion chemical shift can provide much more selective information on the nature of these interactions. The chemical shift of the counterions in ionic micellar systems has also been treated by the two-state model.15-17 The chemical shift of the limiting free state is easy to obtain, though that of the bound state remains unknown. For this reason there is no report

10.1021/jp991398s CCC: $18.00 © 1999 American Chemical Society Published on Web 09/11/1999

8260 J. Phys. Chem. B, Vol. 103, No. 39, 1999 on the binding coefficient of the counterions according to the NMR chemical shift. To solve this problem, we have mixed TEAFOS with LiFOS at a constant total concentration; the TEA+ and Li+ counterions competitively adsorb on the micellar surface. In the mixed systems, we have measured the chemical shift and the selfdiffusion coefficient of the TEA+ counterions as a function of the φLi value. By doing this we can separately determine the otherwise unknown chemical shifts and self-diffusion coefficients of the completely free and bound counterions. These extreme values are necessary for the counterion distribution analysis. Our subsequent strategy is to combine the results from the self-diffusion coefficient and the chemical shift of the counterions in order to differentiate between the Stern and diffuse double layers in the electric double layer formed around the ionic micellar surface. The self-diffusion coefficient of the counterions is a powerful probe of the average or overall binding of the counterions to the micelles within the Stern and diffuse double layers. Thus the counterion binding evaluated through the self-diffusion coefficient is associated with both layers. On the other hand, the TEA+ chemical shift is sensitive to the shortrange interactions of the TEA+ ions with the micelles. Hence, we can uniquely distinguish the counterions trapped in the Stern layer on the basis of the chemical shift. In this way we can sufficiently benefit from the two independent sets of NMR data and explore the mechanism of the counterion binding to the micelles beyond such a classical method as the electric conductivity one. We have monitored also the change of the collective property of the micellar solution, viscosity, in the mixed systems as a function of the φLi value. This observation is helpful to detect changes in the micellar shape and correlate them to the structure of the electric double layer. 2. Experimental TEAFOS (purity, 98%) was purchased from Aldrich and used without further purification. LiFOS was synthesized and purified as described in our previous paper.1 Deuterated water (99.8%) was supplied by CEA. The solutions were prepared at a total concentration of 100 mM by weight method. All of the solutions were heated in a boiling water bath, shaken vigorously, and sonicated in order to ensure their homogeneity. The concentrations were recalculated in molar units, assuming the densities of H2O and D2O at 30 °C to be 1.00 and 1.10 g cm-3, respectively. The change in the density of the solutions upon mixing was safely neglected at the concentrations studied. All of the NMR measurements were performed on a multipurpose FT spectrometer (JEOL EX-270, wide-bore type, 6.35 T) at 30 °C. The 1H and 19F chemical shifts were measured relative to aqueous (D2O) solution of sodium 3-(trimethylsilyl)1-propanesulfonate (purity, 99%; Merck) and trifluoroacetic acid (purity, 99.8%; Merck), respectively, sealed in small capillaries. When the chemical shifts were measured, the magnetic field was locked to the 2H signal of the solvent. The intensities of the 19F peaks were measured relative to the reference. The self-diffusion coefficients of the TEA+ counterions (1H) and the FOS- ions (19F) were measured by the FT PGSE technique. The experimental procedure and the calibration of the field gradient were described previously.1 The self-diffusion coefficients were reproducible within 2% error. The viscosity of mixed TEAFOS/LiFOS systems with a fraction of LiFOS (φLi) below 0.6 was measured at 26 °C by a rheometer RMS 605 (Rheometrics) using a parallel plate

Bossev et al.

Figure 1. Viscosity of the TEAFOS/LiFOS mixtures in H2O at a total concentration (c) of 100 mM and temperature of 26 °C as a function of the LiFOS fraction (φLi).

geometry with a diameter of 25 mm. At φLi g 0.6 the viscosity was measured at the same temperature by a capillary viscosimeter (calibrated with neat H2O). 3. Results It is known that TEAFOS and LiFOS form threadlike and spherical micelles, respectively.18,19 Figure 1 shows how the solution viscosity varies with the LiFOS fraction (φLi) in the TEAFOS/LiFOS mixtures. The large size of the threadlike micelles formed by TEAFOS explains the high viscosity at φLi ) 0. On the other corner of this plot at φLi ) 1, the viscosity is roughly close to that of water because of the ordinary spherical micelles formed by LiFOS. When these two surfactants are mixed so that the total surfactant concentration is kept at 100 mM, the viscosity increases exponentially by 2 orders of magnitude with increasing φLi. At φLi ≈ 0.55, the viscosity of the mixture exhibits a clear maximum, apparently due to some unusual enhancement effect. At higher fractions of the Li+ ions, the viscosity drops sharply by about 4 orders of magnitude. Later in this paper we discuss the possible mechanism of the unexpectedly large increase in the viscosity at intermediate φLi values. What we want to emphasize now is that in the mixed TEAFOS/LiFOS system the threadlike shape of the micelles is preserved at 0 e φLi e 0.6 with an abrupt transition to spherical micelles at φLi ≈ 0.6. To see how the dynamics of the FOS micelles is affected by the changes in the counterion atmosphere, we have recorded the 19F spectrum of the FOS- ions as a function of φLi at a total concentration of 100 mM. The 19F spectrum of the monomeric FOS- ions, identical for both TEAFOS and LiFOS below cmc, is presented in Figure 2a. As shown previously,1 the terminal methyl peak (CF3-) is the most intense and sensitive to the surfactant aggregation, so that its chemical shift and selfdiffusion coefficient can be used for a detailed structural analysis. The FOS solution at φLi ) 1 exhibits a typical case of a fast exchange between the monomer and micellar states with a single set of averaged peaks; see Figure 2e. In contrast, the spectrum at φLi ) 0 consists of two sets of peaks at concentrations above the cmc value (∼1 mM); see Figure 2b. As discussed previously,1 the “micellar” peak in the spectrum of TEAFOS is entirely associated with the threadlike micelles that are responsible for the high solution viscosity. We have unveiled that the “monomer” peak reflects not only monomers but also small aggregates at concentrations above the cmc.1 When the TEAFOS/LiFOS ratio is varied, the 19F spectrum undergoes gradual changes as depicted in Figure 2b-e. It is

1H

and

19F

NMR Study of TEAFOS and LiFOS Mixtures

J. Phys. Chem. B, Vol. 103, No. 39, 1999 8261

Figure 3. Intensities of the “monomer” and “micellar” terminal methyl peaks of FOS- ions in TEAFOS/LiFOS mixtures as a function of φLi. The intensities are shown in M, calibrated to the total concentration.

Figure 4. 19F chemical shifts of the “monomer” and “micellar” terminal methyl peaks in TEAFOS/LiFOS mixtures as a function of φLi. The filled triangle represents the chemical shift of the pure monomeric state measured in neat LiFOS solution at concentrations below cmc.

Figure 2. (a) 19F spectrum of the monomeric FOS- ions in neat LiFOS solution at concentrations below cmc; (b-e) gradual changes in the position and intensity of the 19F terminal methyl peaks of the FOSions in TEAFOS/LiFOS mixtures at a total concentration of 100 mM for selected φLi values. All measurements are carried out in D2O at 30 °C.

seen there that both the intensities and chemical shifts of the “monomer” and “micellar” peaks are dependent on the φLi value. The intensities of the “monomer” and “micellar” peaks are calculated in molar units and plotted against φLi in Figure 3. The intensity of the “monomer” peak decreases steadily approaching zero, whereas the intensity of the “micellar” peak increases with increasing concentration of Li+ ions. At φLi ) 1 the separate “monomer” peak disappears as a result of the fast exchange between monomer and micellar states; i.e., no more presence of long-lived threadlike micelles. In Figure 4, the 19F chemical shifts of the “monomer” and “micellar” peaks are plotted against φLi. At φLi ) 0 (TEAFOS only), the chemical shift of the “monomer” peak differs from that of the genuine monomeric state whose chemical shift is -84.585 ppm obtained at concentrations below the cmc. This is also an indication of the presence of small aggregates with a

short lifetime and without significant influence on the solution viscosity. With increasing φLi, the “monomer” peak shifts to a downfield, i.e., toward the position of the genuine monomers (the filled triangle in Figure 4). This peak disappears in the absence of TEA+ ions at φLi ) 1. The 19F chemical shift of the “micellar” peak moves also to a downfield with increasing φLi. In the limit of φLi f 1, the stability of the FOS micelles decreases because of the shortage of the coordinating TEA+ counterions. Thus, the “micellar” peak is observed as an average between the genuine monomers and micelles, and its chemical shift approaches an intermediate value between these two states. Consequently, the chemical shift of the “micellar” peak, -86.851 ppm, at φLi ) 1 is different from the chemical shift of the genuine micellar state, -87.038 ppm, because of the significant presence of the monomers (∼7 mM).1 The self-diffusion coefficients D of the “micellar” peak of FOS- ions and that of TEA+ counterions are also measured as a function of φLi. These results are shown in Figure 5a. The D value of the “micellar” peak of the FOS- ion remains quite low at (0.8-1.3) × 10-12 m2 s-1 in the φLi range of 0-0.6 and increases steeply in the region of φLi > 0.65. The drop of the dynamic property illustrates the micellar transition from threadlike to spherical structure; compare Figures 1 and 5a. On the other hand, the D value of TEA+ counterions decreases almost linearly with increasing φLi and then increases, marking a well pronounced minimum at φLi ) 0.6. The D value of TEA+ counterions is very close (but not identical as clarified later) to that of the “micellar” peak of FOS- ions at φLi > 0.6. This

8262 J. Phys. Chem. B, Vol. 103, No. 39, 1999

Bossev et al. micelles increases with the total surfactant concentration. Hence, the position of the methylene peak is shifted toward a higher magnetic field because of the increase in the fraction of bound counterions. In the mixed systems, the chemical shift of the TEA+ counterions continues to move toward a higher magnetic field with increasing φLi and reaches a plateau (∼3.147 ppm) for φLi > 0.6; see the circles in Figure 6.20 The difference between the chemical shift of TEA+ ions in mixed systems and that of the free TEA+ ions in the neat TEAFOS system increases with φLi. In addition to the self-diffusion results shown in Figure 5a, this is another direct indication of the increasing and preferential binding of the TEA+ ions with increasing φLi. 4. Discussion Micellar Structure Transition. As seen in Figure 1, the viscosity of the TEAFOS/LiFOS mixtures steeply increases with an initial increase in φLi. This effect implies that the formation of threadlike micelles is enhanced in this region. A similar nonadditive increase in the viscosity has been observed by Hoffmann et al. in the mixtures of TEAFOS and perfluorooctylsulfonic acid (HFOS) at the same total concentration of 100 mM.21 This parallelism between the TEAFOS/HFOS and TEAFOS/LiFOS mixtures may be expected when we take into account the similarity in the ionic nature between the Li+ and H3O+ ions. For the explanation of the synergetic phenomenon, the viscosity (η) of this system can be expressed as in the case of the so-called living polymers organized in a transient network22

Figure 5. The measured self-diffusion coefficient of the “micellar” peak of FOS- ions (a) and the calculated self-diffusion coefficient of the micellized FOS- ions according to eq 4 (b) are plotted against φLi in D2O at 30 °C. The average D value of TEA+ ions is also shown for comparison.

Figure 6. Proton chemical shift of TEA+ ions as a function of φLi in TEAFOS/LiFOS mixtures at c ) 100 mM. For comparison, the chemical shift of TEA+ ions in neat TEAFOS solution is shown as a function of the inverse surfactant concentration.

implies an almost complete binding of all TEA+ counterions to the micelles. To obtain complementary information about the preferential binding of the TEA+ counterions, we show in Figure 6 how their proton chemical shift depends on φLi. For comparison, it is also shown how the chemical shift of TEA+ ions depends on the concentration in the neat TEAFOS system. As expected, below cmc the chemical shift of TEA+ ions is independent of the concentration; note the inverse concentration on the upper x-axis in Figure 6. Above cmc, the fraction of the TEAFOS

η ) Gτ

(1)

where G is the shear modulus of the network and τ is the lifetime of the network strands. The parameter G is a static (equilibrium) characteristic of the network, whereas the lifetime τ accounts for the network dynamics. We have already shown that this model well describes the rheology of aqueous solution of neat TEAFOS.19 Let us consider how the modulus of elasticity, G, changes with φLi in the region of φLi < 0.6. For this purpose we consider the obtained NMR parameters in the TEAFOS/LiFOS mixture. As discussed in our previous paper, the 19F “micellar” peak in neat TEAFOS solution represents the threadlike structures that are responsible for the high viscosity. As shown in Figure 3, the intensity of the “monomer” peak decreases with increasing φLi, accompanied by an effective increase in the intensity of the “micellar” peak. Thus, the effective concentration of the threadlike structure increases in the solution when φLi is varied from 0 to 0.55. This means that G increases too. This hypothesis is supported also by the chemical shift of the “monomer” peak. The “monomer” peak shifts toward the chemical shift of the genuine monomeric state with increasing φLi, indicative of a possible disruption of the small aggregates into monomers, as seen in Figure 4. As a result, a certain amount of FOS- ions is transferred to the threadlike micelles. Although the increase of G contributes to an increase in the viscosity, this contribution appears to be too small ( 0.55, as seen in Figure 4. The change in the position of the “micellar” peak at φLi > 0.55 is likely to be due to the increased fraction of the monomers exchangeable with the micelles. In fact, the cmc value of LiFOS is 7 mM in comparison to a lower value of 1 mM for TEAFOS. It is interesting to see how the viscosity of the TEAFOS/ LiFOS mixture correlates with the dynamic properties of the mixed systems. We can calculate the self-diffusion coefficient of the micelles as a function of φLi on the basis of the selfdiffusion coefficient obtained from the “micellar” peak; see Figure 5a. When the measured self-diffusion coefficient is controlled by an exchange between the monomers and micelles, we can write

D ) pDmon + (1 - p)Dmic

(2)

where Dmon and Dmic are the self-diffusion coefficients of the monomeric and micellized FOS-, respectively, and p is the fraction of the monomers exchangeable with the micelles. The value of p can be determined independently according to the static information from the chemical shifts. The chemical shift of the “micellar” peak of FOS- ions can be described approximately by the abovementioned two-state model as follows:

δ ) pδmon + (1 - p)δmic

(3)

where δmon and δmic are the chemical shifts of FOS- ions in the monomeric and micellar states, respectively. By substituting the fraction p from eq 3 into eq 2 for the self-diffusion coefficient of the micellar state, we obtain

Dmic )

(δmon - δmic)D - (δ - δmic)Dmon (δmon - δ)

(4)

The values of Dmon and δmon are 5.41 × 10-10 m2 s-1 and -84.563 ppm, respectively, according to our previous paper.1 The chemical shift of the micellar state δmic is also found to be -87.234 ppm for the threadlike micelles formed by TEAFOS and -87.038 ppm for the spherical LiFOS micelles.1 In part 1 of this study, we have discussed that this difference may be attributed to different shapes of the respective micelles and/or to the different degrees of counterion binding. These values are known only at the limits of φLi ) 0 and 1, and we take the following approach to estimate these parameters at intermediate φLi values. We assume that δmic is constant and equal to -87.234 ppm at φLi < 0.55 where the threadlike micelles are considered to be formed; see Figure 1. At φLi > 0.55, δmic can be assumed to change linearly with φLi from -87.234 to -87.038 ppm. These assumptions are necessary and plausible because the difference δ - δmic is relatively small and because Dmon is relatively large. Thus the term (δ - δmic)Dmon in eq 4 is sensitive to the value of δmic. The Dmic value thus calculated is tabulated in Table 1 and plotted against φLi in Figure 5b (empty circles), together with the self-diffusion coefficient of the TEA+ counterions. In the region of threadlike micelles, 0 < φLi < ∼0.6, the self-diffusion coefficient of the micellized FOS- ions is found to be as low

TABLE 1: The Self-Diffusion Coefficient of the “Micellar” Peak (D) and that of the FOS- Micelles (Dmic) Calculated According to Equation 4 as a Function of OLi φLi

D

Dmic

D+a

0.00 0.13 0.27 0.38 0.50

0.084 0.087 0.088 0.102 0.125

0.084 0.086 0.078 0.077 0.061

2.20 1.68 1.15 0.75 0.414

0.64 0.71 0.80 0.89 1.00

V disintegration of the threadlike micelles V 0.239 0.136 0.452 0.318 0.78 0.58 0.89 0.61 0.99 0.62

0.251 0.425 0.71 0.79

a The measured self-diffusion coefficient of the TEA+ ions (D+) is also shown. The self-diffusion coefficients are in 10-10 m2 s-1.

as (6-8) × 10-12 m2 s-1. These values are in the same order of magnitude as those obtained for the threadlike micelles formed by nonionic24 and ionic surfactants25 and polymers in water.26,27 There is a minimum of the micellar self-diffusion coefficient at φLi ≈ 0.55 which correlates with the maximum of the viscosity at this point. However, the diffusion minimum is too shallow to explain the dramatic increase in the viscosity in the corresponding region of φLi. This weak correlation is due to the difference in time and length scales between these dynamical properties. The micellar self-diffusion is monitored here at the molecular or aggregate level without alien probe molecules, whereas the solution viscosity is a hydrodynamic property with extremely long time and length scales.28 At φLi > 0.6, the self-diffusion coefficient of the FOS micelles increases. This is a clear indication of the breakdown of the threadlike micellar network into isolated spherical micelles. At high φLi values, the intrinsic self-diffusion coefficient of the micelles thus calculated is naturally lower than the average selfdiffusion coefficient of the TEA+ counterions. This resolves the “puzzle” in Figure 5a that the apparent self-diffusion coefficient of the “micellar” peak is greater than that of TEA+ counterions at φLi > 0.65. This is because, as discussed above, the “micellar” peak is affected by the free state because of a rapid exchange and involves some monomers in this region of φLi and thus effectively increases its self-diffusion coefficient. Structure of the Electric Double Layer. So far, the counterion binding to the micelles has been determined solely on the basis of the self-diffusion coefficient of the counterions. The effective binding coefficient obtained in this way gives no further details about the fine structure of the electric double layer. Our idea is to investigate whether and how the counterion binding is dependent on the two methods employed for the selfdiffusion coefficient and chemical shift of the TEA+ counterions. The parallel application of these different techniques allows us to get insight into the structure of the counterion atmosphere. The self-diffusion coefficient of the TEA+ ions shown in Figure 5 is an average between that of the free and bound states. Hence, we can evaluate the fraction of counterion bound to the micelles by neglecting the presence of small aggregates as follows:29 + D+ ) (1 - fD)D+ free + fDDbound

fD )

+ D+ free - D + D+ free - Dbound

(5a) (5b)

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Figure 7. The fractions of bound TEA+ ions evaluated through the self-diffusion coefficient (fD) and through the chemical shift (fδ) as a function of φLi in D2O at 30 °C (see eqs 5 and 6).

where D+free and D+bound are the self-diffusion coefficients of the free and bound counterions, and fD is the fraction of the bound counterions due to the diffusion measurements. The value of D+free can be measured in a dilute solution of tetraethylammonium chloride (TEACl) where only the free TEA+ ions exist; D+free ) 7.89 × 10-10 m2 s-1. Since D+bound can be assumed to be equal to the self-diffusion coefficient of the micelles shown in Figure 5b, fD can be evaluated according to eq 5b as a function of φLi. It is shown in Figure 7 that the thus calculated fD value increases steadily with increasing φLi in the region of 0 < φLi < 0.6. At φLi > 0.6, fD ≈ 1 indicating that almost all of the counterions are bound to the micelles. This implies that the hydrophobic TEA+ counterions are saturated and preferentially bound to the micelles. Now we examine to what extent the diffusion-based counterion binding fraction, fD, differs from the counterion binding fraction determined from the chemical shift of the TEA+ counterions. The proton chemical shift is especially sensitive to the short-range interactions between the counterions and the micellar surface. Thus, the chemical shift can be used as a selective probe for the species adsorbed onto the micellar surface. The 1H chemical shift of the TEA+ counterions can be analyzed independently in a way similar to the self-diffusion coefficients, and we have

δ ) (1 - fδ)δfree + fδδbound fδ )

δfree - δ δfree - δbound

(6a) (6b)

where δfree and δbound are the chemical shifts of the free and bound TEA+ counterions, and fδ is the fraction of the bound counterions due to the chemical shift. The fraction fδ is not necessarily equal to the dynamical fD because of the difference in the detection characteristic. The chemical shift of the methylene peak of the free TEA+ ions (δfree) is found to be 3.264 ppm,1 whereas the chemical shift of the bound TEA+ counterions (δbound) cannot be obtained in solutions composed of the single surfactant TEAFOS only. To determine this value, here we use the TEAFOS/LiFOS mixtures. At 0.6 < φLi < 1, almost all of the TEA+ counterions are completely bound according to the diffusion measurement; see fD in Figure 7. This is supported also by the chemical shift. Figure 6 exhibits a plateau value of 3.147 ppm at φLi > 0.6. Hence, δbound can be taken to be equal to this value. At φLi < 0.6, the binding fraction

Figure 8. Schematic illustration of the double layer structure around the micelles in a neat solution of TEAFOS (φLi ) 0). The fδ value represents the counterion bound within the Stern layer exclusively, whereas the fD value involves a portion of the diffuse double layer as well as the Stern layer.

Figure 9. Concentration of the TEA+ counterions bound in the Stern layer (cS) evaluated through the chemical shift as a function of φLi (see eq 7). The concentration of the remaining portion of TEA+ counterions (cD) is also shown.

(fδ) obtained through the chemical shift is much lower than that from the diffusion coefficients. At φLi ) 0, for example, the fδ value is 0.45 in contrast to fD ) 0.73. This large difference arises from the fine structure of the electric double layer which consists of the two parts, Stern and diffuse layers. The Stern layer is assumed to be a monolayer of counterions firmly bound to the micellar surface by not only Coulombic but also some additional interactions. The chemical shift probes exclusively the short-range interactions within the Stern layer. On the other hand, the fraction fD includes the counterions in the diffuse double layer as well as those in the Stern layer. Thus, we can separate the counterions located within the Stern layer from those in the diffuse double layer by the present combined method. The picture of the electric double layer thus established is illustrated in Figure 8. To get insight into the mechanism of the preferential binding of the TEA+ counterion, we calculate the concentration of TEA+ counterions localized within the Stern layer (cS) as a function of φLi. We have

cS ) cfδ(1 - φLi)

(7)

where c () 100 mM) is the total concentration of the FOSions and c(1 - φLi) is the concentration of the TEA+ ions in the TEAFOS/LiFOS mixture. The remaining portion of the

1H

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Figure 10. Schematic representation of the changes in the double layer structure at different φLi values. Note the preferential binding of TEA+ counterions. At high φLi values the micellar surface is incompletely covered by TEA+ counterions; this is a reason for the disintegration of the threadlike network.

TEA+ ions (cD) which are located within the diffuse double layer can be calculated simply as

cD ) c - c S

(8)

where cS from eq 7 is inserted. Figure 9 shows how cS and cD depend on φLi. The concentration of the TEA+ ions in the Stern layer is ∼45 mM and independent of φLi at 0 < φLi < 0.55. This value of cS shows that one TEA+ counterion is bound to roughly two FOS- ions in the micellar state; i.e., this hydrophobic counterion bridges two micellized FOS- ions. At a fixed value of c, the cD value decreases linearly with φLi. This implies that the TEA+ ions in the diffuse double layer are proportionally replaced by Li+ ions with increasing φLi and that the Stern layer remains unaffected at this stage. At φLi > 0.55, all of the TEA+ counterions are bound within the Stern layer and the concentration of the Stern layer decreases with increasing φLi as a result of the shortage of TEA+ ions in the micellar solution. We illustrate the structural changes in the counterion atmosphere obtained from these considerations in Figure 10. The Stern layer is saturated with TEA+ ions at a ratio of about one TEA+ ion per two micellized FOS- ions. In fact, the hydrated TEA+ ions are rather bulky and hydrophobic which would explain the limited accommodation of TEA+ ions in the Stern layer. Steric restrictions might be in action. As the origin of the driving force for the preferential binding of the TEA+ ions in the Stern layer, the hydrophobicity must be a key factor. Here, we return to the drastic changes in the viscosity of the TEAFOS/LiFOS system in relation to the structure of the electric double layer described above. The region of φLi where the viscosity is high (0 < φLi < 0.55) exactly corresponds to unruffled Stern layer, as seen in Figures 1 and 10. The sudden drop in the viscosity at φLi > 0.55 correlates with the deficiency of TEA+ ions to form a completed Stern layer. We conclude that the complete coverage of the micellar surface by the TEA+ ions is essential for the formation of threadlike structure by the FOS- surfactant. It seems that the surplus of TEA+ ions beyond the Stern layer, which is given by cD in Figure 10 at 0 < φLi < 0.55, reduces the viscosity. These excessive TEA+ ions probably enhance the structural fluctuation in the transient network to decrease τ in eq 1, a feature not exhibited by the free hydrated Li+ ions. Conclusions We have detected the transition from threadlike to spherical micelles in TEAFOS/LiFOS mixtures by means of 1H and19F NMR chemical shifts and self-diffusion coefficients. The counterion binding due to the chemical shift is attributed solely to the formation of the Stern layer, whereas the self-diffusion

coefficient gives us the overall binding coefficient that involves both Stern and diffuse double layers. In this way the structure of the electric double layer is elucidated. The TEA+ counterions bind strongly onto the micellar surface within the Stern layer where roughly two FOS- ions are bridged by one TEA+ ion. The remaining portion of TEA+ counterions is in the diffuse double layer. When Li+ ions are introduced into the solution at the fixed total concentration, they replace gradually the TEA+ counterions in the diffuse double layer, while the compact Stern layer of TEA+ ions remains unaffected. This is a demonstration of the preferential binding of the TEA+ ions onto the FOS micellar surface in the TEAFOS/LiFOS systems. The formation of threadlike micelles in the region of 0 < φLi < 0.55 is connected with the integrity of the Stern layer composed of TEA+ ions. Collapse of the Stern layer results in the disintegration of the threadlike micelles into isolated spherical ones. The nonlinear enhancement in the solution viscosity with increasing φLi from 0 to 0.55 correlates with the gradual replacement of TEA+ ions by Li+ ions in the diffuse double layer. References and Notes (1) Bossev, D. P.; Matsumoto, M.; Nakahara, M., J. Phys. Chem. B, 1999, 103, 8251. (2) Hoffmann, H.; Ulbricht, W. Z. Phys. Chem. Neue Folge 1977, 106, 167. (3) Hoffmann, H.; Tagesson, B. Z. Phys. Chem. Neue Folge 1978, 110, 113. (4) Israelachvili, J. In Intermolecular & Surface Forces, Academic Press: New York, 1994; chapter 12. (5) Manning, G. S. Z. Annu. ReV. Phys. Chem. 1972, 23, 2543. (6) Adamson, A. In Physical Chemistry of Surfaces, 3rd ed.; Wiley: New York, 1976; chapter IV. (7) Shelley, J. C.; Sprik, M.; Klein, M. L. Langmuir 1993, 9, 916. (8) MacKerell, A. D., Jr. J. Chem. Phys. 1995, 99, 1846. (9) Stilbs, P.; Lindman, B. J. Phys. Chem. 1981, 85, 2587. (10) Jansson, M.; Stilbs, P. J. Phys. Chem. 1985, 89, 4868. (11) Jansson, M.; Stilbs, P. J. Phys. Chem. 1987, 91, 113. (12) Li, P.; Jansson, M.; Bahadur, P.; Stilbs, P. J. Phys. Chem. 1989, 93, 6458. (13) Lindman, B.; Puyal, M.-C.; Kamenka, N.; Rymden, R.; Stilbs, P. J. Phys. Chem. 1984, 88, 5048. (14) The self-diffusion coefficient of the free state of the TEA+ ions can be easily obtained in diluted solutions of simple electrolytes and that of the bound state can be assumed to be equal to the micellar self-diffusion coefficient. (15) Gustavsson, H.; Lindman, B. J. Chem. Soc., Chem. Commun. 1973, 93. (16) Gustavsson, H.; Lindman, B. J. Am. Chem. Soc. 1975, 97, 3923. (17) Gustavsson, H.; Lindman, B. J. Am. Chem. Soc. 1978, 100, 4647. (18) Knoblich, A.; Matsumoto, M.; Murata, K.; Fujiyoshi, Y. Langmuir 1995, 11, 2361. (19) Watanabe, H.; Osaki, K.; Matsumoto, M.; Bossev, D. P.; McNamee, C. E.; Nakahara, M.; Yao, M. L. Rheol. Acta 1998, 37, 470. (20) The peak from the methyl protons of the TEA+ counterion exhibited the same behavior. (21) Hoffmann, H.; Wu¨rtz, J. J. Mol. Liq. 1997, 72, 191.

8266 J. Phys. Chem. B, Vol. 103, No. 39, 1999 (22) Cates, M. E. Macromolecules 1997, 20, 22289. (23) Watanabe, H.; Sato, T.; Osaki, K.; Matsumoto, M.; Bossev, D. P.; McNamee, C. E.; Nakahara, M., submitted to Rheol. Acta. (24) Kato, T.; Terao, T.; Seimiya, T. Langmuir 1994, 10, 4468. (25) Morie´, N.; Urbach, W.; Langevin, D. Phys. ReV. E 1995, 51, 2150. (26) Persson, K.; Wang, G.; Olofsson, G. J. Chem. Soc., Faraday Trans. 1994, 90, 3555. (27) Persson, K.; Griffiths, P. C.; Stilbs, P. Polymer 1996, 37, 253.

Bossev et al. (28) Wakai, C.; Nakahara, M. J. Chem. Phys. 1997, 106, 7512. (29) At φLi < 0.55 there are also small aggregates present in the solution.1 Strictly speaking, an additional term should be involved in eq 5a to take into account the counterion binding to the small aggregates as is done in part 1 of this study at φLi ) 0 (neat TEAFOS). The requisite self-diffusion coefficient of these small aggregates, however, could not be measured at intermediate φLi because the low intensity of the “monomer” peak hampered the diffusion measurements. Thus, eq 5a is an approximation in this case.