Aerosol-OT Forms Oil-in-Water Spherical Micelles in the Presence of

Jun 15, 2009 - tetrafluoborate (bmimBF4), a polar room temperature ionic liquid, is explored through optical microscopy in polarized light, SAXRD and ...
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J. Phys. Chem. B 2009, 113, 9216–9225

Aerosol-OT Forms Oil-in-Water Spherical Micelles in the Presence of the Ionic Liquid bmimBF4 Sergio Murgia,*,† Gerardo Palazzo,‡ Marianna Mamusa,† Sandrina Lampis,† and Maura Monduzzi*,† Dipartimento di Scienze Chimiche, UniVersita` di Cagliari and CSGI, ss 554 biVio Sestu I-09042 Monserrato (CA), Italy, and Dipartimento di Chimica, UniVersita` di Bari and CSGI, Via Orabona 4, I-70126 Bari, Italy ReceiVed: April 1, 2009; ReVised Manuscript ReceiVed: May 18, 2009

The phase diagram sodium bis(2-ethylhexyl) sulfosuccinate (NaAOT)/water/1-butyl-3-methylimidazolium tetrafluoborate (bmimBF4), a polar room temperature ionic liquid, is explored through optical microscopy in polarized light, SAXRD and NMR PGSTE techniques. The analysis of SAXRD and self-diffusion data reveals that the bmim+ cation is strongly adsorbed at the interface. Data are accounted for by Hill’s model for cooperative binding. The overall process is described as a comicellization of AOT- and bmim+ involving roughly two cations for AOT- ion. The bmim+ is severely involved in the structural arrangement of the interface. Indeed, a huge modification of the interfacial geometry resulting in the occurrence of micelles having positive curvature is inferred from the analysis of the self-diffusion coefficients. The analysis of the water diffusion data in the L1 phase (according to the effective cell model) allows one to exclude the presence of oblate and/or discoid micelles. Finally, the study of the oil diffusion in samples doped with p-xylene permits one to assess furthermore not only the formation of AOT aggregates of the oil-in-water type but also the occurrence of dynamic percolation phenomena. 1. Introduction Ionic liquids (ILs) are a class of easily tunable electrolytic solvents constituted by large and asymmetric organic cations and small inorganic anions weakly bonded in 1:1 ratio. They are homogeneous nonflammable liquids with negligible vapor pressure endowed of good solvent properties, high ionic conductivity and high chemical, thermal and electrochemical stability. Because of their unique physicochemical features the exploitation of ILs in a broad range of practical applications has been proposed, spanning from solar cell preparation1 to telescope construction.2 Since commonly considered environmentally green, they are currently used as suitable substitutes for traditional solvents in various chemical organic/inorganic synthesis and catalytic reactions. Their biocompatibility has also been successfully tested in some biocatalytic processes.3 With regard to their claimed environmentally benign nature it is however worth noticing that ILs are not intrinsically “green” (some of them are toxic), but they can be properly designed to fulfill this requirement taking advantage of the astonishing diversity of potentially possible ILs, which has been estimated in terms of millions.4 Among others, one interesting application of ILs concerns their use in micellar, microemulsion and liquid crystal formulations.5,6 Particularly, it has been shown that they can suitably replace each of the microemulsion components, that is the immiscible polar/apolar media as well as the surfactant. Apart from obvious analogies with the conventional component they are replacing, the use of ILs confers peculiar features to self-assembled systems, often leading to notable advantages in the preparation of nanostructures.7,8 Also when added as additive * Corresponding authors. Phone: +390706754453. Fax: +390706754388. E-mail: [email protected]. † Dipartimento di Scienze Chimiche, Universita` di Cagliari and CSGI. ‡ Dipartimento di Chimica, Universita` di Bari and CSGI.

the electrolytic/surfactant nature of ILs may produce significant alterations in the polymorphism typically manifested by traditional surfactant molecules in a suitable solvent. Indeed, the aggregate supramolecular architecture is characterized by two distinct contributions, the interfacial curvature and the interfacial topology. The former is related to the local geometry while the latter describes the global geometry in terms of the interfacial connectivity degree. Both these contributions are strongly influenced by the local constraint given by the packing parameter p ) V/a0l of the surfactant (V is the hydrophobic chain volume, a0 is the headgroup area and l is the chain length, taken as 80% of the fully extended chain).9 Therefore, as a result of the ionic liquid/surfactant interactions substantial modifications in the molecular self-assembly can realistically be expected.10,11 To gain insight on the role played by the ionic liquid in the structural organization of the interface, we have focused on the addition of 1-butyl-3-methylimidazolium tetrafluoborate (bmimBF4) to a well-known surfactant/water system, i.e. the sodium bis(2-ethylhexyl) sulfosuccinate (NaAOT)/water (W) system. The NaAOT in water (cmc ) 2.2 × 10-3 mol L-1)12 is known to form, already at low concentration, an extended lamellar phase.13 Upon further surfactant additions first a bicontinuous cubic phase and then a reverse hexagonal phase form.13 The peculiar absence of micelles having positive curvature has been ascribed to the NaAOT geometrical parameters (l ) 8.5 Å, a0 ) 60 Å2, V ) 480 Å3, and therefore p ≈ 0.9) that are incompatible with an efficient packing into disconnected spheroidal aggregates and that justify its celebrated ability to form reverse micelles upon addition of oil.14,15 The water-in-oil (w/o) microemulsions (L2 phase) formed by AOT with different kinds of oils has extensively been investigated for twenty years. A wide literature is available concerning the microstructural features, the water droplet size, the polydispersity, and particularly the static and dynamic percolation phenomena that occur in the microemulsion regions at high

10.1021/jp902970n CCC: $40.75  2009 American Chemical Society Published on Web 06/15/2009

Oil-in-Water Spherical Micelles surfactant concentration. Most studies pointed out that the microstructure of AOT w/o microemulsions is reasonably well described in terms of spherical w/o droplets,16 although various experiments, carried out as a function of several parameters such as surfactant concentration, temperature, type of oil, and following different dilution criteria, provided evidence of anomalous behavior with respect to a hard-sphere system. So far, discrepancies have been discussed within a context of critical phenomena, microstructural transitions and percolation theory.17-20 Water-in-oil spherical droplets with a hard-sphere behavior are likely to occur in a very limited region of the L2 phase, namely, at low volume fraction of the disperse phase, φd ) φW + φS < 0.1 (subscripts W and S refer to water and surfactant, respectively), i.e. close to the oil corner. Both conductivity and water self-diffusion have demonstrated the occurrence of important modifications of the w/o droplet organization due to transient fusion-fission processes among the droplets. These processes become more and more important with increasing φd, and are oil and temperature dependent.21 At high values of φd, spherical droplets densely packed within a body-centered cubic lattice as demonstrated by SANS measurements.17 The attractive interactions prolong the lifetime of the particles’ encounters and produce a cluster of droplets, thus generating water networks throughout the L2 phase. This clustering, which is associated with changes of various macroscopic parameters, such as viscosity and electrical conductivity, can be understood in terms of “percolation”.20,22,23 It has been suggested that, below the static percolation threshold, dynamic percolation can also take place. In this case water channels can form when the surfactant interface, separating adjacent water cores, breaks down during collisions or through the transient merging of droplets. The observation of the microstructural transitions, in terms of static or dynamic percolation, can be strictly dependent on the time scale of the experimental technique. The kinetic constants regulating the lifetime of the clustering interaction, and thus the exchange of material, may range over a wide time scale.24 Percolation can also be affected by other factors such as the type of counterions as observed in the case of the ternary microemulsions formed by CaAOT (investigated by conductivity and NMR self-diffusion measurements) where the percolation threshold occurs at a much lower φd than in the corresponding NaAOT system.25 The NaAOT/W/bmimBF4 ternary phase diagram is here investigated using optical microscopy, SAXRD and NMR techniques. The highlight is on the crucial role of the large bmim+ cation, particularly on its partition between the bulk and the AOT interface. 2. Materials and Methods Materials. The 1-butyl-3-methylimidazolium tetrafluoborate (bmimBF4, purity g97%, MW ) 226.03 g/mol, F ) 1.21 g/mL, η ) 154 mPa s) was purchased from Fluka, while sodium bis(2ethylhexyl) sulfosuccinate (aerosol-OT, NaAOT, purity ) 99%, MW ) 444.60 g/mol, F ) 1.138 g/mL) and p-xylene (p-xyl, purity ) 99%, MW ) 106.17 g/mol, F ) 0.861 g/mL) reagents were respectively purchased from Sigma-Aldrich and Carlo Erba. All the reagents were used as received. For sample preparation distilled water (W) further purified by means of a Millipore system (conductivity ) 0.054 µS/cm) was used. Sample Preparation. Samples were prepared by weighing and then homogenizing the components through a vortex shaker into glass tubes. Throughout the paper, sample compositions, unless differently stated, are given as weight percentage. Samples used for the phase diagram characterization were stored

J. Phys. Chem. B, Vol. 113, No. 27, 2009 9217 at 25 °C in the dark for seven days before any measurement was taken. After a period of about a week a white crystalline precipitate starts to form at the bottom of the NMR tubes and the pH drops from 5 to 2 (indicator strip). The precipitate was found almost insoluble in a number of different polar/apolar solvents. Interestingly, the binary W/bmimBF4 ) 50/50 sample was in much the same way affected by the pH reduction. These findings were rationalized considering that the tertrafluoborate anion in water slowly hydrolyzes26 producing fluoric and boric acid, respectively accountable for the decreased pH and the precipitate (H3BO3 is hardly soluble). However, independently of the precipitate formation, no significant changes in the selfdiffusion coefficients of all the investigated species were observed, thus indicating the substantial retention of the samples’ nanostructure. Optical Microscopy. Liquid crystalline phases were observed through the optical microscope Zeiss Axioplan II in polarized light, at 25 °C. The observed patterns were compared with the typical textures of liquid crystals formed by other surfactants.27 Small Angle X-ray Diffraction (SAXRD) Experiments. X-ray diffractograms were recorded with a S3-MICRO SWAXS camera system (HECUS X-ray Systems, Graz, Austria). Cu KR radiation of wavelength 1.542 Å was provided by a GeniX X-ray generator, operating at 50 kV and 1 mA. A 1D-PSD-50 M system (HECUS X-ray Systems, Graz, Austria) containing 1024 channels of width 54.0 µm was used for detection of scattered X-rays in the small-angle region. The working q-range was 3 × 10-3 Å-1 e q e 0.6 Å-1, where q ) 4π sin(θ) λ-1 is the modulus of the scattering wave vector. Calibration in the smallangle region was performed with a silver stearate standard. The distance between the sample and detector was 272 mm. The diffraction patterns were recorded at 25 °C. A PC-controlled Peltier element was used for temperature stabilization and control of the sample. A few milligrams of sample was enclosed in a stainless steel sample holder using a polymeric sheet (Bratfolie, Kalle) window. To minimize scattering from air, the camera volume was kept under vacuum during the measurements. Scattering patterns were recorded for 1000 s. Errors on the lattice parameter values calculated are less than 2% (standard deviation). NMR Self-Diffusion Experiments. 1H, 19F and 23Na NMR measurements were carried out at 25 °C through a Bruker Avance 300 MHz (7.05 T) spectrometer at the operating frequencies of 300.131, 282.36, 79.39 MHz respectively. A standard BVT 3000 variable temperature control unit with an accuracy of (0.5 °C was used. Self-diffusion coefficients were determined using a Bruker DIFF30 probe equipped with specific inserts for the 1H, 19F and 23Na nuclei, and supplied by a Bruker Great 1/40 amplifier that can generate field gradients up to 1.2 T m-1. The pulse-gradient stimulated echo (PGSTE) sequence was used. Self-diffusion coefficients were obtained by varying the gradient strength (g) while keeping the gradient pulse length (δ) and the gradient pulse intervals constant within each experimental run. The data were fitted according to the Stejskal-Tanner equation:

I δ ) exp -Dq2 ∆ I0 3

[

(

)]

(1)

where I and I0 are the signals intensities in the presence and absence of the applied field gradient, respectively, q ) γgδ is the so-called scattering vector (γ being the gyromagnetic ratio of the observed nucleus), t ) (∆ - δ/3) is the diffusion time, ∆ is the delay time between the encoding and decoding

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Figure 1. Ternary diagram of the NaAOT/W/bmimBF4 system at 25 °C. Also displayed are the samples analyzed through SAXRD (open symbols) and NMR PGSTE (closed symbols) techniques.

gradients, and D is the self-diffusion coefficient to be extracted.28 The errors on the fitting were always less than 1%, those on the measurement always less than 5% (standard deviation). 3. Results and Discussion 3.1. The Phase Diagram. The various phase regions in the NaAOT/W/bmimBF4 ternary system were initially determined by visual inspection (naked eyes or through polarized lens) of samples prepared adding to the NaAOT/bmimBF4 and NaAOT/W binary samples tiny amounts (20 µL) of the third component. For each binary system a series of nine samples was prepared with water (W) or ionic liquid (IL) concentrations spanning between 10 and 90 wt %. When required, appropriate ternary samples were prepared to better describe the phase region boundaries (errors within 2 wt %). Then, the nanostructure of the aggregates in the different regions were investigated by means of optical microscopy in polarized light, SAXRD and NMR techniques. It should be noted that in this work the terms indicating the number of components refer to the molecular species. As shown in Figure 1, the ternary diagram is characterized by a wide (L1) and a small (X) isotropic fluid region, a large lamellar (LR), a small cubic (CG) and a reverse hexagonal (H2) liquid crystalline phase region. The L1 comprises a composition range where the formation of an isotropic, slightly viscous liquid was observed. It is worth noticing that even in the presence of

Murgia et al. the ionic liquid all the liquid-crystalline nanostructures observed in the NaAOT/W binary system are retained.13 It was not possible to define the nanostructure of the samples in the region indicated by the X symbol unambiguously. The boundaries related to the liquid-crystalline phases are indicated with a dashed line since the optical and rheological properties of such phases made it difficult to safely exclude the simultaneous presence of a second phase, and therefore to define the monophasic region boundaries. Areas of the phase diagram not included within the labeled regions should be understood as multiphasic. These areas were not investigated in detail. 3.2. bmim+ Partition Between the Bulk and the Interfacial Film. Analysis of the Lattice Parameters of Lr and H2 Phases. The influence of bmimBF4 on the lattice parameters of lamellar, cubic, and hexagonal phases was studied along IL dilution lines. The investigated samples are indicated by the star-shaped open symbols in Figure 1, while Figures 2 and 3 show the optical microscopy images in polarized light and the SAXRD diffractograms related to these samples, respectively. The values of the lattice parameter a determined from the SAXRD analysis of the ternary samples and, for comparison, of the related binary NaAOT/W samples are reported in Table 1. Concerning the LR phase, the lattice parameter a is related to the bilayer thickness (2L) through the relation

a)

2L Φeff

(2)

where Φeff denotes the effective volume fraction of the lamellae. In the case of the NaAOT/water binary system, Φeff can be unambiguously identified with the NaAOT volume fraction (ΦAOT). Accordingly, a value of 2L ) 21 Å is calculated in good agreement with previous report.29 Loading with bmimBF4 scarcely affects the lattice parameter. If all the ionic liquid is present in the aqueous phase, eq 2 foretells that a plot of the lattice parameter against the reciprocal ΦAOT is a straight line with null intercept and slope equal to 21 Å. Actually this is not the case, as shown in Figure 4A. This evidence suggests that the surfactant volume fraction underestimates the actual lamellae volume fraction; this is often an indication of the presence of water filled defects in the membrane (this means that a fraction of the water is part of the lamellar volume). We can exclude this hypothesis because defective lamellae are characterized by a broad SAXRD peak at low q-values30,31 and peculiar textures under polarized light,32,33 while in the present case only features of classical lamellar phase are discernible. Another possibility is that a fraction of the bmimBF4 is somehow bound to the

Figure 2. (a) Maltese crosses and mosaic mixed lamellar phase pattern (NaAOT/W/bmimBF4 ) 63.6/21.5/14.9), magnification 100×. (b) Fanlike hexagonal pattern (NaAOT/W/bmimBF4 ) 90.0/4.3/5.7), magnification 40×.

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lamellae thus increasing their effective volume. Hence Φeff ) bound . Under the assumption that the ideal swelling ΦAOT + Φbmim behavior (eq 2) holds and that the bilayer thickness remains roughly constant, the lamellar volume fraction can be estimated from the ratio between the lattice parameter found in the absence of bmimBF4 and the measured a-values

Φeff ) ΦAOT +

bound Φbmim

a° ) Φ°AOT a

(3)

where a° and Φ°AOT denote the lattice parameter and the NaAOT volume fraction of the binary NaAOT/water system, respectively. The values of the effective volume fraction estimated, according to the above equation, from the spacing of the LR phase increase upon bmimBF4 loading as shown in Figure 4B (closed squares). This indicates a partition of the bmimBF4 between the polar and the apolar lamellar domain. For the inverse hexagonal phase samples, the cross sectional hex ) is related to the lattice radius of the aqueous cylinders (rW 34 parameter according to 1/2 rhex W ) a(1 - Φeff)

( ) √3 2π

1/2

(4)

The quantity Φeff in the above equation indicates the volume fraction of the continuous phase surrounding the aqueous core

of reverse cylinders. The radius of the aqueous core of cylindrical reverse micelles is expected to depend only on the ratio between the internal volume V ) (1 - Φeff) and its surface area S (rW/2 ) V/S) according to

rhex W )

2(1 - Φeff) 2(1 - Φeff)VAOT ) nAOTR ΦAOTR

(5)

where nAOT ) ΦAOT/VAOT is the number of NaAOT molecules, and VAOT and R respectively represent the NaAOT molecular volume and the mean polar head area at the polar/apolar interface. Equating eqs 4 and 5 gives

a(1 - Φeff)1/2

( ) √3 2π

1/2

)

2(1 - Φeff)VAOT ΦAOTR

(6)

In analogy with the calculations performed in the case of the lamellar phases, it is possible to evaluate Φeff by comparing the H2 lattice parameter in samples with and without addition of bmimBF4, as long as the water/NaAOT ratio remains constant.

Figure 3. SAXRD diffractograms of the various liquid-crystalline phases found in the ternary diagram. NaAOT/W/bmimBF4 sample compositions are 63.6/21.5/14.9, 75.4/21.0/3.6 and 90.0/4.3/5.7 for the lamellar, cubic and hexagonal phases, respectively.

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Φeff = 1 -

(

)

aΦAOT 2 (1 - ΦAOT) a°Φ°AOT

Murgia et al.

(7)

To evaluate the above equation we have assumed that the polar head area is roughly unaffected by the presence of the ionic liquid (at constant water/NaAOT ratio). The values of Φeff (normalized to the NaAOT volume fraction), calculated according to eq 7, are shown in Figure 4 as open circles. Also in the case of reverse hexagonal phase, the calculated ratio Φeff/ΦAOT is larger than one. This suggests the presence of a component different from NaAOT in the aggregate, as already observed for the LR phase. Analysis of the Self-Diffusion Coefficients in the L1 Phase. Six samples, indicated by the closed symbols in Figure 1, were prepared along the W/bmimBF4 ) 50/50 (wt %) dilution line. The surfactant concentrations, which range between 3.2 and 38.4 wt % with increments of about 7 wt %, were chosen in order to cover the whole region of existence of the L1 phase along that dilution line. The inner structure of such isotropic fluid phase was characterized studying the self-diffusion coefficients of the various ionic/molecular species via 1H, 23Na and 19F PGSTE NMR measurements. Figure 5 shows the surfactant and the ionic liquid molecular structures along with the 1H NMR spectrum and the main NMR signal assignments of the sample having composition NaAOT/W/bmimBF4 ) 38.4/30.8/30.8. Figure 6 displays a representative example of the 1H NMR signals decay observed upon the magnetic field gradient increase in a PGSTE NMR experiment. Fitting these data to eq 1 gives the water, AOT- and bmim+ self-diffusion coefficients. Analogous decays were obtained from the NMR signal of the other examined nuclei (23Na and 19F) and, in general, for all the investigated samples. Results are reported in Table 2. A decrease of all the self-diffusion coefficients upon surfactant loading is generally observed. The AOT- self-diffusion coefficient (DAOT) is systematically lower than the diffusion of water, BF4- and Na+ by at least 1 order of magnitude. In the case of the more diluted sample (ΦAOT ) 0.03), obstruction effects can be neglected, and a hydrodynamic radius of 15 Å can be obtained directly through the Stokes-Einstein equation (D ) kBT/6πηRh; η ) 1.88 mPa s for a water/bmimBF4 ) 50/50 mixture35). The comparison with the hydrodynamic radius of 5 Å for the NaAOT monomer, deduced from the surfactant selfdiffusion coefficient (DAOT ) 3.54 × 10-10 m2 s-1) measured in deuterated water below the NaAOT critical micelle concentration ([NaAOT] ) 2.0 × 10-3 M < cmc), indicates that, in the range of composition explored, the NaAOT self-assembles into micellar aggregates. Since the water diffusion, DW, is always much higher than DAOT, the presence of reverse aggregates with the water molecules confined inside the aggregates can be excluded (because in this case DW should match DAOT and this is clearly not the case). Figure 7 shows the evolution of the reduced self-diffusion coefficients (D/D°) of water, BF4-, bmim+ and Na+ upon loading with NaAOT; the reference self-diffusion coefficient D° was taken as the diffusion measured in the binary solution water/bmimBF4 ) 50/50 for water and the ionic liquid ions, while for the sodium ion it was extrapolated at null NaAOT concentration from the data of Table 2. In the case of water, the reduced diffusion decreases only weakly upon loading with NaAOT. This evidence suggests that the aggregates present in solution are disconnected, and with oil-in-water type curvature. Such a conclusion is fully supported by the more detailed analysis of the self-diffusion coefficients that will be presented in the next section.

Figure 4. (A) Dependence of the lamellar spacing on the reciprocal volume fraction of NaAOT; the dashed line represents the prediction for monodimensional swelling (eq 2). (B) Effective volume of the interfacial film (normalized to the NaAOT volume) as a function of the bmimBF4 concentration (volume fraction). Closed squares: data from lamellar spacing calculated from eq 3. Open circles: data from the lattice parameter of H2 phase calculated from eq 7. Closed stars: data from the self-diffusion coefficients of AOT- and bmim+ measured in the L1 phase calculated from eqs 9 and 10 (see text). Also shown are the data obtained for the L1 phase doped with p-xylene (open stars, see text). The curve represents the best-fit according to Hill’s cooperative binding (eq 13).

TABLE 1: Type of Liquid-Crystalline Phase, Sample Composition, AOT- and bmim+ Volume Fraction (ΦAOT,bmim), Effective Volume Fraction (Φeff, See the Text) and Lattice Parameter (a) Obtained from the SAXRD Analysis phase NaAOT/W/bmimBF4 ΦAOT Φbmim a/Å LR LR LR LR Ia3d Ia3d H2 H2 H2 H2 H2 H2 H2 a

75.0/25.0/70.2/23.7/6.1 66.8/22.7/10.5 63.6/21.5/14.9 80.2/19.8/75.4/21.0/3.6 89.7/10.3/95.3/4.7/90.0/4.3/5.7 83.9/4.0/12.1 79.2/3.7/17.1 76.6/3.5/19.9 70.2/3.2/26.6

0.73 0.68 0.65 0.62 0.74 0.73 0.89 0.94 0.9 0.84 0.8 0.77 0.71

0.06 0.11 0.15 0.05 0.04 0.05 0.11 0.16 0.19 0.25

28.8 29.6 29.9 30.1 59 72.6 26.1 25.2 24.5 24.3 24.2 23.4 23.2

Φeff

Φeff/ΦAOT

a

0.73 0.71a 0.70a 0.70a

1.00 1.04 1.08 1.13

0.94b 0.95b 0.96b 0.96b 0.97b 0.97b

1.00 1.06 1.14 1.20 1.26 1.37

Calculated according to eq 3. b Calculated according to eq 7.

The trends of the reduced coefficients of BF4- and Na+ are very similar to that observed for water (we observe identical D/D° values up to 20 wt % NaAOT). On the other hand, D/D° for bmim+ clearly deviates from this common trend.

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J. Phys. Chem. B, Vol. 113, No. 27, 2009 9221 imply that a fraction of this cation is strongly bound to the AOTmicelles. A simple way to treat both the binding and the obstruction effects is according to the so-called Lindman’s law36

Dobs ) b(1 - P)D° + PDmic

(8)

where P represents the fraction of bound molecules (moving with the micelles). According to eq 8, the observed self-diffusion coefficient, Dobs, is the population average of the self-diffusion coefficients in the two sites: the micelle (Dmic) and the continuous bulk. This last quantity is expressed in eq 8 as the product of the self-diffusion coefficient in the absence of micelles, D°, times the obstruction factor b. We can anticipate here the results of the analysis described in the next section, where the presence of discoid micelles is ruled out. In view of that, the equation b ) (1 + Φeff/2)-1 describing the obstruction factor for spheres37 can be used, and eq 8 is rewritten explicitly for the bmim+ as Figure 5. 1H NMR spectrum of the sample with composition NaAOT/ W/bmimBF4 ) 38.4/30.8/30.8. NaAOT and bmimBF4 molecular structures along with the main NMR signals assignments are shown.

( (

Φeff 2 P) Φeff 1+ 2 1+

) )

-1

-1

Dbmim D°bmim DAOT D°bmim -

(9)

where we have assumed that Dmic ) DAOT. Of course, the effective volume fraction of the micelles depends on the fraction of bmim+ bound to the micelles themselves: bound ΦAOT + Φbmim Φeff Φbmim ) )1+ P ΦAOT ΦAOT ΦAOT

Figure 6. Semilogarithmic fitting of the water, AOT- and bmim+ NMR signals decay while varying the gradient field strength in a 1H NMR PGSTE experiment.

Basically, the observed decrease of the D/D° ratio can be attributed to two mechanisms. The micelle excludes a fraction of the total volume for the diffusing molecule, and this leads to a lengthening of the diffusion paths. This is often referred to as the “obstruction effect”, and strongly affects also the diffusion of the micelles themselves. The second factor is related to specific interactions with the micellar wall. For example, cations could adsorb on the negatively charged micellar surface and some water molecules are certainly involved in the hydration of the AOT- polar heads; clearly a fraction of the observed species is bound to the slow-diffusing micelles, and this leads to a further decrease in the measured self-diffusion coefficient. The fact that water, the anion BF4-, and the cation Na+ share the same D/D° values indicates that their diffusion is mainly affected by the obstruction factor (being unlikely that they share the same interactions with AOT-). On the other hand, the systematically low D/D° values observed in the case of bmim+

(10)

Equations 9 and 10 were used in an iterative procedure to evaluate the effective volume fraction from the self-diffusion coefficients of bmim+ and AOT-. In the initial step Φeff in eq 9 was assumed to be equal to the NaAOT volume fraction and a first value of P was evaluated. Using such a value eq 10 allows obtaining a new value of Φeff that can be inserted in eq 9 to obtain a new P-value, and so on. Within three to five iterations, the above-described procedure converges giving the values of Φeff/ΦAOT shown in Figure 4B as closed stars. It is clear that the cation bmim+ accounts for a considerable fraction of the micellar volume. More importantly, the values of Φeff/ΦAOT obtained from the bmim+ self-diffusion coefficients merge with the data obtained from the analysis of SAXRD lattice parameters described previously. This indicates that the excess volume of micelles (L2), lamellae (LR) and cylinders (H2) is due to some bmim+ molecules bound to the AOT- molecules. The shape of the plot Φeff/ΦAOT versus Φbmim in Figure 4B is peculiar because any indication of saturation is absent. On the contrary, the steepness of the plot increases with Φbmim. This feature excludes a description of bmim+ binding to AOT- according to a classical Langmuir’s isotherm. Indeed, a Scatchard plot38 of the results of Figure 4B ((Φeff/ΦAOT - 1)/Φbmim against (Φeff/ΦAOT - 1)) is a nonlinear growing function (data not shown). The steepness of the plot Φeff/ΦAOT versus Φbmim indicates a cooperative binding process. The simplest way to treat this process is through Hill’s binding equilibrium39,47

nbmim+ + AOT- ) AOT - bmimn

(11)

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Murgia et al.

TABLE 2: Self-Diffusion Coefficients (D, m2 s-1) of the Various Ionic/Molecular Species (IL ) bmimBF4) Present in the Samples Studied in the L1 Region NaAOT/W/IL -/50/50 3.2/48.1/48.7 10.0/44.9/45.0 17.0/41.6/41.4 24.1/38.0/37.9 31.3/34.3/34.4 38.4/30.8/30.8 a

ΦAOT

Φbmim 0.45 0.43 0.40 0.37 0.34 0.31 0.28

0.03 0.10 0.17 0.25 0.31 0.38

Φeffa 0.08 0.18 0.30 0.41 0.50 0.58

DW 1.22 1.20 1.05 9.33 8.22 6.93 5.80

× × × × × × ×

Dbmim -9

10 10-9 10-9 10-10 10-10 10-10 10-10

DBF4 -10

3.67 × 10 3.22 × 10-10 2.72 × 10-10 2.17 × 10-10 1.68 × 10-10 1.26 × 10-10 9.3 × 10-11

5.48 5.11 4.58 4.17 3.62 2.72 2.14

× × × × × × ×

DAOT

DNa

-10

10 10-10 10-10 10-10 10-10 10-10 10-10

7.5 4.4 3.6 2.9 2.5 2.1

× × × × × ×

10-11 10-11 10-11 10-11 10-11 10-11

4.67 4.25 3.65 2.86 2.11 1.96

× × × × × ×

10-10 10-10 10-10 10-10 10-10 10-10

Calculated according to eqs 9 and 10.

with an equilibrium constant

Keq )

ΦAOT-bmim n ΦAOTΦbmim

(12)

The ratio Φeff/ΦAOT can be expressed according to the above equilibrium as n Φeff nfKeqΦbmim )1+ n ΦAOT 1 + KeqΦbmim

(13)

where f ) 0.66 is the ratio between the bmim+ (V ) 316 Å3)40 and AOT- molecular volumes. Equation 13 has been successfully fitted to the Φeff/ΦAOT versus Φbmim data of Figure 4B (continuous curve) furnishing as best fit parameters Keq ) 5 ( 1 and n ) 2.23 ( 0.07. Accordingly, when the results of Figure 4B are represented in a Hill plot, all data follow the same linear trend (see Figure 8). Summarizing, the evidence obtained from independent experiments and data analysis performed on samples within the LR, H2, and L1 phases consistently indicate that a fraction of bmim+ is bound to the AOT- molecules thus being a relevant fraction of the aggregates. It is worth noting that the assumptions underlying eqs 3, 7 and 9 are independent, so that the fully consistent behavior shown in Figure 4 can be interpreted as a proof of a real cooperative binding of bmim+ to AOT-. 3.3. Morphology of the L1 Phase. Water Diffusion. As previously stated, the molecular diffusion in a complex fluid is affected either by the obstruction effect due to the presence

Figure 7. Reduced self-diffusion coefficients (D/D°) of the components in the L1 phase system as a function of the NaAOT volume fraction (ΦAOT).

Figure 8. Hill plot of the data in Figure 4; symbols as in Figure 4. According to Hill, the fraction of sites occupied θ is introduced (in the present case θ ) (Φeff/ΦAOT - 1)/n, see eqs 12 and 13). In terms of θ (and assuming f ∼ 1) eq 13 becomes θ ) KeqΦbmimn/(1 + KeqΦbmimn). Such a relation can be linearized by writing θ/(1 - θ) ) KeqΦbmimn and taking the logarithm of both sides Ln[θ/(1 - θ)] ) Ln[Keq] + n Ln[Φbmim]. In the present case the ordinate Ln[θ/(1 - θ)] equals Ln{(Φeff - ΦAOT)/[(n + 1)ΦAOT - Φeff]} with n ) 2.23 according to the best fit of Figure 4. The linearity of the plot and its slope (2.00 ( 0.07, very closed to the guessed n-value) are a graphical confirmation of the cooperative process. The reader is referred to standard biochemistry textbooks (such as ref 47) for a detailed description of the cooperative binding.

of aggregates or by the interactions of the molecules with the aggregates themselves. In the presence of a strong binding to the micelles, Lindman’s law (eq 8) represents a simple and effective treatment. However, in many cases the situation is more delicate since the interaction with the micelles is weak and can be hardly described by a binding process. The presence of the micellar surface can alter locally the diffusive properties, and this will result in a change of the measured self-diffusion coefficient also without any special affinity for the micelle. These situations can be described through the so-called “effective cell model” (ECM).41 The ECM gives a theoretical description of the molecular diffusion in a system of colloidal sized particles. The model is based upon the widely used concept of dividing a macroscopic system into small subsystems, or cells, in such a way that they together may represent the macroscopic properties. The reader is referred to ref 41 for a complete description of the model. The effective diffusion coefficient for a component i will in this model depend on both the diffusion of the cell and the diffusion within the cell. The equation for the total effective diffusion coefficient Di of component i in a micellar system may be written as42

Oil-in-Water Spherical Micelles

(

Di ) Dicell 1 -

J. Phys. Chem. B, Vol. 113, No. 27, 2009 9223

)

Dmic + Dmic Dio

(14)

where Dcell is the effective self-diffusion coefficient in a cell i centered around the micelle, Doi is the self-diffusion coefficient of component i in the bulk solution, and Dmic the selfdiffusion coefficient of the micelle. For water diffusion, in is nearly the same as the measured the present case, Dcell i total self-diffusion coefficient (DW), since Dmic is very low. The key parameter of the model is the local variation of the product of the self-diffusion coefficient and the concentration of the component (CiDi). Simple cases are those where the cell is divided into two subvolumes. One subvolume is close to the micelle and is characterized by concentration C1 and self-diffusion coefficient D1, and the rest of the cell has bulk concentration C2 and self-diffusion coefficient D2. The general equation has the form41

Dcell ) D2

U

(

1- 1-

)

C1 Φ C2 eff

(15)

where the function U depends on the C1D1 and C2D2 products and on the symmetry (shape of the micelles). For spherical micelles eq 15 assumes the simple form:41

Dcell ) D2

(

1

)

C1 Φ C2 eff 1 - [C1D1 /(C2D2)] β) 1 + [C1D1 /(2C2D2)] 1- 1-

1 - βΦeff 1 + (βΦeff /2)

(16)

In the case of weak binding (C1 < C2) and taking into account that D2 is the bulk diffusion (D2 ) D°) the following equation holds:

1 - βΦeff Dcell (1 - Φeff) ) U ) D° 1 + βΦeff /2

(17)

Note that in the absence of any adsorption (C1 ) 0 f β ) 1) eq 17 describes only the obstruction effect and reduces to the definition of b used in eq 9. Further rearrangement gives42

1-U ) βΦeff 1 + U/2

(18)

Equation 18 is the closed solution for spherical micelles but is also numerically indistinguishable from the solution obtained in the case of prolate micelles and cylindrical micelles.41,43 On thecontrary,oblateanddiscoidmicellesbehaveverydifferently.41-43 Thus eq 18 could be used to check if disklike micelles are present in solution. The function U was evaluated according to eq 17, using the DW values of Table 2. The ratio (1 - U)/(1 + U/2) is plotted as a function of Φeff in Figure 9; according to the prediction of eq 18, it is a linear function of the effective volume fraction with null intercept. The slope of the linear regression gives β ) 1.24, which is indicative of a low affinity of water for the surface of the micelles. It should be stressed

Figure 9. Analysis of the water diffusion according to the ECM (eq 18, see text). Dependence of the function (1 - U)/(1 + U/2) on the effective micelle volume fraction (Φeff). U was calculated from the water diffusion using eq 17 and the micellar volume fraction from the AOT- and bmim+ diffusion using eqs 9 and 10. Closed symbols refer to the NaAOT/W/bmimBF4 system; open symbols refer to the NaAOT/W/ bmimBF4/p-xylene system (in this last case the micellar volume fraction accounts also for the p-xylene volume fraction).

that for oblate micelles with axial ratio larger than 4-5 a marked nonlinearity of the plot is expected.42 Thus we can exclude the presence of disklike micelles in the present system, a conclusion that is somehow surprising because at these concentrations NaAOT in water forms only bilayers. On the other hand, the plot of Figure 9 does not help to discriminate between spherical and cylindrical micelles. To achieve this goal we have to somehow complicate the system and use the prediction of the ECM in the case of a strongly adsorbing component able to efficiently diffuse along the micellar contour, i.e. a component with high C1 and D1. Oil Diffusion in Samples Doped with p-Xylene. Often the hydrodynamic size of the micelle permits one to distinguish between spherical and cylindrical micelles.44 Unfortunately this approach holds only for dilute micellar solutions, since the selfdiffusion coefficient of the micelle is strongly affected by the obstruction effect and reliable corrections are available only for simple intermicellar interactions (e.g., hard spheres) and low volume fractions (