Cross-Section Structure of Cylindrical and Polymer-like Micelles from

Young, C. Y.; Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. ...... Daniel J. Iampietro, Laura L. Brasher, and Eric W. Kaler , Ann...
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Langmuir 1996, 12, 2433-2440

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Cross-Section Structure of Cylindrical and Polymer-like Micelles from Small-Angle Scattering Data. 2. Experimental Results Peter Schurtenberger,* Go¨tz Jerke, and Carolina Cavaco† Institut fu¨ r Polymere, ETH Zu¨ rich, CH-8092 Zu¨ rich, Switzerland

Jan Skov Pedersen Department of Solid State Physics, Risø National Laboratory, DK-4000 Roskilde, Denmark Received September 8, 1995. In Final Form: February 26, 1996X We report a small-angle neutron scattering (SANS) study of the cross-section structure of polymer-like lecithin reverse micelles in deuterated cyclohexane. We demonstrate that the application of the indirect Fourier transformation and square-root deconvolution methods to data from SANS measurements with cylindrical polymer-like micelles allows for a direct verification of the previously postulated geometrical model of flexible tubular structures with a well defined water core and a surfactant shell. By combining contrast variation experiments and data analysis performed on an absolute scale, we quantitatively deduce information on properties such as the extension of the aqueous core and the degree of water penetration into the headgroup and solvent penetration into the tail region.

Introduction It has previously been shown for a number of surfactant solutions that it is possible to find conditions where micelles grow dramatically with increasing surfactant concentration into giant cylindrical aggregates. These giant micelles normally have a high degree of flexibility, and their overall structure is generally well described by polymer theory.1,2 Numerous reports have for example demonstrated that considerable micellar growth occurs from the minimum sphere to very large anisotropic micelles in aqueous surfactant solutions at high salt concentrations.1,3-24 Several attempts have been made * To whom correspondence should be addressed. Telephone: +41-632 3104. Fax: +41-1-632 1073. E-mail: [email protected]. ethz.ch. † Current address: ITN, Physics Department, E.N. 10, 2685 Sacavem, Portugal. X Abstract published in Advance ACS Abstracts, April 15, 1996. (1) Cates, M. E.; Candau, S. J. J. Phys.: Condens. Matter 1990, 2, 6869-6892. (2) Schurtenberger, P.; Cavaco, C. J. Phys. Chem. 1994, 98, 54815486. (3) Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1976, 80, 1075-1085. (4) Gravsholt, S. J. J. Colloid Interface Sci. 1976, 57, 575. (5) Young, C. Y.; Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1978, 82, 1375-1378. (6) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Carey, M. C. J. Phys. Chem. 1980, 84, 1044-1057. (7) Porte, G.; Appell, J.; Poggi, Y. J. Phys. Chem. 1980, 84, 3105. (8) Ikeda, S.; Ozeki, S.; Tsunoda, M. J. Colloid Interface Sci. 1980, 73, 27. (9) Ikeda, S.; Hayashi, S.; Imae, T. J. Phys. Chem. 1980, 84, 744. (10) Hayashi, S.; Ikeda, S. J. Phys. Chem. 1980, 84, 744-751. (11) Appell, J.; Porte, G. J. Colloid Interface Sci. 1981, 81, 85. (12) Porte, G.; Appell, J. J. Phys. Chem. 1981, 85, 2511. (13) Ozeki, S.; Ikeda, S. J. Colloid Interface Sci. 1982, 87, 424-435. (14) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1983, 87, 1264-1277. (15) Hoffmann, H.; Rehage, H.; Platz, G.; Schorr, W.; Thurn, H.; Ulbricht, W. Colloid Polym. Sci. 1982, 260, 1042-1056. (16) Hoffmann, H.; Kalus, J.; Thurn, H.; Ibel, K. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 1120. (17) Appell, J.; Porte, G. J. Phys. Lett. 1983, 44, L-689. (18) Candau, S. J.; Hirsch, E.; Zana, R. J. Phys. (Paris) 1984, 45, 1263-1270. (19) Imae, T.; Ikeda, S. J. Colloid Interface Sci. 1984, 98, 363372. (20) Candau, S. J.; Hirsch, E.; Zana, R. J. Colloid Interface Sci. 1985, 105, 521-528.

to demonstrate the existence of cylindrical micelles and to characterize the micellar structure using small-angle scattering experiments.25-33 In these studies, the data analysis primarily relied on model fitting procedures33 or on an interpretation of different q regimes based on asymptotic expressions such as a Guinier approximation or the Debye equation for the low-q part, the use of simple crossover relations for the incorporation of flexibility in the intermediate-q range, or a Guinier approximation for the high-q part.23,29-32 Recently,33 we successfully demonstrated that an alternative characterization of the local structure of cylindrical polymer-like micelles can be obtained through the indirect Fourier transformation (IFT) method.34,35 The high-q part of the polymer-like scattering intensity reflects the local cylindrical symmetry of the micelles, and the cross-section scattering intensity at q ) 0, Ics(0), is directly related to the mass per length ML.36 While IFT uses the assumption that the crosssectional contribution to the total scattering can be decoupled from the rest, it has the advantage that it does (21) Olsson, U.; So¨dermann, O.; Gue´ring, P. J. Phys. Chem. 1986, 90, 5223. (22) Candau, S. J.; Hirsch, E.; Zana, R.; Adam, M. J. Colloid Interface Sci. 1988, 122, 430-440. (23) Marignan, J.; Appell, J.; Bassereau, P.; Porte, G.; May, R. P. J. Phys. (Paris) 1989, 50, 3553-3566. (24) Imae, T. Colloid Polym. Sci. 1989, 267, 707-713. (25) Lin, T.-L.; Chen, S.-H.; Gabriel, N. E.; Roberts, M. F. J. Phys. Chem. 1987, 91, 406-413. (26) Porte, G.; Marignan, J.; Bassereau, P.; May, R. J. Phys. (Paris) 1988, 49, 511-519. (27) Hjelm, R. P.; Thiyagarajan, P.; Alkan, H. J. Appl. Crystallogr. 1988, 21, 858-863. (28) Hjelm, R. P.; Thiyagarajan, P.; Sivia, D. S.; Lindner, P.; Alkan, H.; Schwahn, D. Prog. Colloid Polym. Sci. 1990, 81, 225-231. (29) Hjelm, R. P.; Thiyagarajan, P.; Alkan-Onyuksel, H. J. Phys. Chem. 1992, 96, 8653-8661. (30) Schurtenberger, P.; Scartazzini, R.; Magid, L. J.; Leser, M. E.; Luisi, P. L. J. Phys. Chem. 1990, 94, 3695-3701. (31) Schurtenberger, P.; Magid, L. J.; King, S.; Lindner, P. J. Phys. Chem. 1991, 95, 4173-4176. (32) Long, M. A.; Kaler, E. W.; Lee, S. P.; Wignall, G. D. J. Phys. Chem. 1994, 98, 4402-4410. (33) Pedersen, J. S.; Egelhaaf, S. U.; Schurtenberger, P. J. Phys. Chem. 1995, 99, 1299-1305. (34) Glatter, O. J. Appl. Crystallogr. 1977, 10, 415-421. (35) Glatter, O. J. Appl. Crystallogr. 1980, 13, 577-584. (36) Glatter, O. In International Tables for Crystallography; Wilson, A. J. C., Ed.; Kluwer Academic Publishers: Dordrecht, 1992; Vol. C, pp 89-105.

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not rely on the low-q part of the data used in the model fitting approach and that no specific model assumptions have to be made regarding the structure of the micelles except for the locally cylindrical symmetry. Therefore contributions from polydispersity of the overall size and interaction effects are minimized, which should result in a more reliable determination of the local micellar structure in micellar samples at finite concentrations. In the preceding article37 (Part 1 of this series), we have tested the applicability and limitations of the indirect Fourier transformation (IFT)34 and square-root deconvolution (SQDEC)38,39 method for a quantitative characterization of the local structure of cylindrical micelles and microemulsions using a series of simulated scattering data. Particular emphasis was given to the influence of sampling resolution and background, polydispersity, flexibility, ellipticity, and finite micellar length. Here we present experimental results from a detailed small-angle neutron scattering study of polymer-like lecithin reverse micelles. While numerous aqueous surfactant systems are known to exhibit polymer-like properties, there are only a few reports on polymer-like surfactant aggregates in organic solvents.30,31,40-47 In contrast to aqueous micellar systems, reverse micelles or water-in-oil microemulsions at moderately high values of surfactant concentration and low values of the molar ratio of water to surfactant, w0, are generally believed to have either a droplet-like structure or only a small degree of anisotropy. A notable exception is the system lecithin/organic solvent/water, where formation of gel-like, viscoelastic, reverse micellar solutions can be observed.48 Their unusual polymer-like properties were explained by a water-induced one-dimensional micellar growth into long and flexible cylindrical reverse micelles, i.e., a characteristics sphere-to-flexible cylinder transition normally observed in aqueous solutions only.30,31,43-47 The formation of giant tubular and polymer-like reverse micelles has been demonstrated with a combination of light scattering and small-angle neutron scattering (SANS) at low surfactant concentrations, which allowed verification of the locally cylindrical structure of these reverse micelles and an estimate of the persistence length and overall dimensions.46,49 SANS experiments with polymerlike lecithin reverse micelles in cyclohexane provide an ideal test for the applicability of IFT and SQDEC methods. In cyclohexane, the water-induced formation of giant cylindrical micelles occurs at relatively high values of w0, which according to the previously postulated model for the micellar structure should lead to a tubular arrangement with a well defined water core and a surfactant shell. (37) Pedersen, J. S.; Schurtenberger, P. Submitted to J. Appl. Crystallogr. (38) Glatter, O. J. Appl. Crystallogr. 1981, 14, 101-108. (39) Glatter, O.; Hainisch, B. J. Appl. Crystallogr. 1984, 17, 435441. (40) Terech, P.; Schaffhauser, V.; Maldivi, P.; Guenet, J. M. Langmuir 1992, 8, 2104-2106. (41) Zhou, Z.; Georgalis, Y.; Liang, W.; Li, J.; Xu, R.; Chu, B. J. Colloid Interface Sci. 1987, 116, 473-484. (42) Eastoe, J.; Steytler, D. C.; Robinson, B. H.; Heenan, R. K.; North, A. N.; Dore, J. C. J. Chem. Soc., Faraday Trans. 1994, 90, 2497-2504. (43) Schurtenberger, P.; Scartazzini, R.; Luisi, P. L. Rheol. Acta 1989, 28, 372-381. (44) Schurtenberger, P.; Magid, L. J.; Penfold, J.; Heenan, R. Langmuir 1990, 6, 1800-1803. (45) Ott, A.; Urbach, W.; Langevin, D.; Schurtenberger, P.; Scartazzini, R.; Luisi, P. L. J. Phys.: Condens. Matter 1990, 2, 5907-5912. (46) Schurtenberger, P.; Magid, L. J.; Lindner, P.; Luisi, P. L. Prog. Colloid Polym. Sci. 1992, 89, 274-277. (47) Schurtenberger, P.; Peng, Q.; Leser, M.; Luisi, P. L. J. Colloid Interface Sci. 1993, 156, 43-51. (48) Scartazzini, R.; Luisi, P. L. J. Phys. Chem. 1988, 92, 829-833. (49) Schurtenberger, P.; Magid, L. J.; King, S. M.; Lindner, P. J. Phys. Chem. 1991, 95, 4173-4176.

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Figure 1. Schematic representation of the expected radial cross-section excess scattering length density profiles for lecithin reverse micelles in deuterated cyclohexane with a molar ratio of water to lecithin w0 ) 14 with either H2O (∆FH2O(r), solid line) or D2O (∆FD2O(r), dashed-dotted line) as based on a simple model of tubular aggregates with a well defined water core and surfactant shell. Also shown is the result of a simple geometrical model that includes solvent penetration into the tail region as the dotted line.

One thus has the possibility to dramatically modify the radial cross-section excess scattering length density profile ∆F(r) by using deuterated cyclohexane as the solvent and either H2O or D2O. This is demonstrated in Figure 1, where a schematic drawing of ∆F(r) versus the crosssection radius r is shown for w0 ) 14 and both H2O and D2O. From an application of the IFT and SQDEC methods to small-angles neutron scattering (SANS) data obtained on an absolute scale, one should be able to resolve the corresponding variations in ∆F(r) and obtain quantitative agreement with the known scattering length densities of the water core and the lecithin headgroup and tail regions. Materials and Methods Soybean lecithin was obtained from Lucas Meyer (Epikuron 200) and used without further purification. Fully deuterated cyclohexane-d12 (99.5% isotopic purity) and D2O (>99.7% isotopic purity) were purchased from Dr. Glaser AG. Samples were prepared as described previously.47,50 The small-angle neutron scattering (SANS) experiments were performed with the SANS instrument at the DR3 reactor at Risø National Laboratory, Denmark.51 A range of scattering vectors q from 0.004 to 0.5 Å-1 was covered by four combinations of neutron wavelength (3.5 and 10 Å) and sample-to-detector distances (1-6 m). The wavelength resolution was 18% (full-width-at-half-maximum value). The samples were kept in quartz cells (Hellma) with a path length of 2 mm. The raw spectra were corrected for background from the solvent, sample cell, and other sources by conventional procedures.52 The two-dimensional isotropic scattering spectra were azimuthally averaged, converted to an absolute scale, and corrected for detector efficiency by dividing by the incoherent scattering spectra of pure water.53 The average excess scattering length density per unit mass ∆Fm of the micelles was calculated from the known (50) Schurtenberger, P.; Cavaco, C. Langmuir 1994, 10, 100-108. (51) Pedersen, J. S. J. Phys. IV 1993, 3, 491-498. (52) Cotton, J. P. In Neutron, X-Ray and Light Scattering: Introduction to an Investigative Tool for Colloidal and Polymeric Systems; Lindner, P., Zemb, T., Eds.; North-Holland: Amsterdam, 1991. (53) Wignall, G. D.; Bates, F. S. J. Appl. Crystallogr. 1987, 20, 2840.

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chemical composition of soybean lecithin using the measured partial specific volume of the “monomers” (lecithin plus water) in the aggregates. Throughout the data analysis corrections were made for instrumental smearing.51,54 For each instrumental setting the ideal model scattering curves were smeared by the appropriate resolution function when the model scattering intensity was compared to the measured one by means of leastsquares methods.34,38,55 Results and Discussion The results from measurements with lecithin reverse micelles in deuterated cyclohexane at three different values of the water-to-lecithin molar ratio w0 at a lecithin concentration of c ) 30 mM (which corresponds to a total (surfactant plus water) weight concentration of cw ) 26.3 mg/mL for w0 ) 6.0, cw ) 28.5 mg/mL for w0 ) 10.0, and cw ) 30.6 mg/mL for w0 ) 14.0) are summarized in Figure 2. A concentration slightly above the overlap threshold c* was chosen in order to work with a high ratio of (coherent) intensity to background but still under conditions where the static correlation length ξs is larger than the persistence length lp (for details of the w0 and c dependence of ξs, see ref 50). For ξs > lp > Rcs, where Rcs is the cross-section radius of the tubular reverse micelles, we then expect that the different asymptotic regimes (i.e., a Lorentzian q dependence due to chain overlap at low q values followed by an intermediate q-1 dependence of I(q) due to the cylindrical cross section) are well separated and that a decoupling approximation as described in ref 37 can be used. We see from Figure 2 that the exchange of H2O with D2O indeed results in a significant variation of the q dependence of the scattering intensity I(q). If H2O is used, both water and lecithin have comparable scattering length densities. The expected radial cross-section excess scattering length density profile ∆F(r) can then be approximated by a simple step function modified by the solvent penetration into the chain region at higher values of r, which will cause a smoother decay of ∆F(r) (Figure 1). This results in the typical monotonically decaying scattering pattern of a locally cylindrical particle with an intermediate q-1 dependence of I(q) followed by an exponential (Guinier) decay due to the cross-section form factor.33 However, when D2O is used instead of H2O, the reduced excess scattering length density in the water core of the tubular reverse micelles results in a pronounced shell contrast (see Figure 1), and a well defined first minimum of the cross-section form factor now becomes visible at high q values. Upon an increase of w0, the minimum in I(q) becomes more pronounced and moves to lower values of q. This is due to the fact that an increase of w0 induces a corresponding increase of the water core radius Rcore at approximately constant thickness of the surfactant shell, which is primarily given by the length of a lecithin molecule. Having seen that the scattering data qualitatively agree with our expectations based on the structural model of tubular reverse micelles, we can try to extract much more quantitative information on the local micellar structure by applying the indirect Fourier transformation (IFT) method to the experimental data.34,35 As described in detail in Part 1,37 the high-q part of the scattering intensity reflects the local cylindrical symmetry of the micelles, and the cross-section scattering intensity at q ) 0, Ics(0), is (54) Pedersen, J. S.; Posselt, D.; Mortensen, K. J. Appl. Crystallogr. 1990, 23, 321-333. (55) Bevington, B. R. Data Reduction and Error Analysis for Physical Sciences; McGraw-Hill: New York, 1969.

Figure 2. Normalized scattering intensity [dσ(q)/dΩ]/cwc versus scattering vector for lecithin reverse micelles in deuterated cyclohexane at a lecithin concentration c ) 30 mM, measurements with H2O (1) and D2O (O): (A) w0 ) 14.0; (B) w0 ) 10.0; (C) w0 ) 6.0.

directly related to the mass per length ML.36 For c , c*, we can derive a quantitative relation for the scattering cross section dσ(q)/dΩ using the decoupling approximation33

dσ(q) ) cwc〈M〉w∆Fm2Swc(q) Scs(q) dΩ

(1)

where cwc is the total weight concentration of lecithin and water in the micelles, ∆Fm is the average excess scattering

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length density per unit mass, Swc(q) and Scs(q) are the normalized scattering functions of the infinitely thin wormlike chains and of the cross section, respectively, and 〈M〉w is the weight average molar mass. For c > c*, we have to replace the single particle scattering function Swc(q) in the decoupling approximation (eq 1) by the (unknown) scattering function for entangled wormlike chains Swc,e(q), and 〈M〉w by an apparent molar mass 〈M〉w,app. However, whereas the low-q part will strongly deviate from the scattering function of a wormlike chain, at characteristic distances significantly smaller than the mesh size (≈ξs) of the entanglement network we will still find a single-coil scattering behavior. Therefore, provided that ξs > lp > Rcs, for lpq . 1 the high-q asymptotic behavior can then, as demonstrated in Part 1 for non-interacting wormlike cylinders, again be expressed by

dσ(q) π ) 2π dΩ q

()

∫0∞p˜ cs(r) J0(qr) dr ) πqIcs(q)

(2)

where the normalized cross-section distance distribution function p˜ cs(r) is given by

p˜ cs(r) )

2πcwc ML

∫0∞∆F(r′) ∆F(r+r′)r′ dr′

(3)

and J0(x) is the zeroth-order Bessel function. Note that p˜ cs(r) and Ics(q) contain a factor cwc/ML, which is important for absolute normalization. As demonstrated in Part 1, we can deduce a parametrized form of p˜ cs(r) through the IFT method. The resulting values of p˜ cs(r) and a comparison of fitted and experimental values of I(q) are shown in Figure 3 for the data obtained from w0 ) 10. The lower limit qmin ) 0.04 Å-1 of the fitted q range was chosen in accordance with the known persistence length of lp ) 120 Å.31,37 A very good fit of the experimental data can be achieved with the applied IFT method, and the thus obtained p˜ cs(r) functions closely resemble the simulated functions for filled and hollow cylindrical particles shown in Figure 3 of Part 1. Furthermore, a well defined shoulder with an initially linear region below r e 10 Å is also clearly visible and is most likely due to so-called diffuse longitudinal correlations, as described in detail in Part 1 (see Figure 14B in Part 1). The p˜ cs(r) functions vanish both in the “homogeneous cylinder” (H2O) and in the “shell” (D2O) contrast at approximately 70 Å, thus qualitatively confirming the previously postulated geometrical model which would predict a cross-section radius Rcs ≈ 30 Å. Having determined p˜ cs(r), we can calculate the integral parameters of the micellar cross-section using the corresponding relations for the cross-section radius of gyration Rcs,g

Rcs,g2

∫0∞r2p˜ cs(r) dr) ) ∞ (2∫0 p˜ cs(r) dr) (

(4)

the cross-section forward scattering intensity Ics(0)

∫0∞p˜ cs(r) dr

Ics(0) ) 2π

(5)

and the mass per unit length ML in the units g/cm given by

ML )

Ics(0) ∆Fm2

(6)

The resulting values are summarized in Table 1. We see

that an exchange of H2O with D2O results in a drastic decrease of Ics(0) by almost 40% due to the much lower value of ∆Fm for a “monomer” of 1 lecithin plus 10D2O molecules (∆Fm ) 6.00 × 1010 cm/g H2O, ∆Fm ) 4.58 × 1010 cm/g for D2O). Furthermore, Rcs,g increases by approximately 8% mainly due to the higher weighting of the surfactant shell (see eq 4 and Figure 1). In addition to the evaluation of these integral parameters of the micellar cross-section, we can also aim at a quantitative estimate of the radial cross-section excess scattering length density profile ∆F(r) from the p˜ cs(r) functions using the SQDEC method, as described in detail in Part 1. The resulting profiles ∆F(r) versus r in absolute units (cm-2) as well as the agreement between p˜ cs(r) determined from IFT and fitted using SQDEC are also shown in Figure 3C-E. Except for the initial part of the p˜ cs(r) function, which is strongly influenced by diffuse longitudinal correlations (see Part 1 for details) and which therefore was not used in the fitting procedure, the fit using the SQDEC method results in good agreement. Moreover, the thus obtained excess scattering length density profiles ∆F(r) for H2O and D2O are in close agreement with the expectations based on the geometrical model and the known scattering length densities of lecithin and water. The clear difference in ∆F(r) at low values of r and the subsequent perfect overlap at higher values of r provide us with a first direct estimate of the extension of the water core. The values of approximately 18 Å for the extension of the water into the headgroup region and approximately 22 Å for the hydrophobic tail region are in close agreement with the geometrical dimensions of the lecithin molecule and the relative volumes of water, headgroup, and tail region. Moreover, the entire data analysis has been performed in absolute units throughout, and no free parameters have been used to adjust the obtained ∆F(r) values such as to make them for example overlap in the tail region. Having established the procedures of the data analysis, we can proceed to the experimental data obtained for w0 ) 6 and w0 ) 14. The corresponding distance distribution functions and cross-section excess scattering length density profiles as deduced from IFT and SQDEC are shown in Figures 4 and 5. A comparison of Figures 3-5 clearly reveals that the increase of w0 has the expected qualitative effect on the p˜ cs(r) functions. Due to the increase of the water core, the difference between “homogeneous cylinder” and “shell” contrast becomes more pronounced, and both the peak and the maximum extension shift to higher values of r. Similarly, the differences in the ∆F(r) versus r profiles for H2O and D2O become more pronounced, and the extent of the water core is shifted from approximately 16 Å at w0 ) 6 to 22 Å at w0 ) 14. The degree of overlap in the chain region between the data sets from samples with H2O and D2O is extremely good and provides us with a very sensitive test of the applied data normalization procedure. The cross-section excess scattering length density profiles given in Figures 3-5 provide us for the first time with a direct verification of the previously postulated geometrical model of a tubular cross section with a well defined water core and a surfactant shell for the structure of polymer-like lecithin reverse micelles. In a next step, we can see whether we have achieved full quantitative consistency between the geometrical model of the micelles and the various results from our data analysis. We first start with the data obtained for w0 ) 14. The IFT method has yielded a value for the mass per length of ML ) 2.83 × 10-13 g/cm when using H2O. Together with the molar mass of a “monomer” (one lecithin plus 14 water molecules) of M1 ) 1019 g/mol this results

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Figure 3. Comparison of the experimental (O) and fitted (using the indirect Fourier transform method) normalized scattering intensity [dσ(q)/dΩ]/cwc (A and B), the corresponding distance distribution functions p˜ cs(r) (C and D), and the radial cross-section excess scattering length density profiles (as obtained by the square-root deconvolution method) (E) for lecithin reverse micelles in deuterated cyclohexane at w0 ) 10.0. (A and B): [dσ(q)/dΩ]/cwc versus q for measurements with D2O (A) and with H2O (B). The solid lines correspond to the intensity smeared by the instrumental resolution, and the dotted line corresponds to the ideal intensity (Note that the data obtained with different combinations of neutron wavelength and sample-detector distance and the corresponding fitted curves are slightly shifted due to resolution effects). Also shown by the arrow is the lower cutoff value of the q range used for the IFT. (C and D): p˜ cs(r) versus r as determined by IFT for measurements with D2O (C) and with H2O (D), respectively. Also shown as the full curves are fits to be the data by the square-root deconvolution procedure for p˜ cs(r), resulting in the radial cross-section excess scattering length density profile ∆FH2O(r) (solid line) or ∆FD2O(r) (dashed line) shown in part E. The light lines in part E indicate the errors in ∆F(r).

in a linear monomer number density of λL ) 1.7 Å-1 (lecithin molecules per angstrom) along the micellar contour. The surface area per lecithin headgroup a0 at the hydrocarbon chain-water interface for long chain

phosphatidylcholine molecules in a variety of different aggregate structures is approximately a0 ≈ 70 Å2,56,57 which together with λL allows for an estimate of the circumference of the cylindrical cross section at the hydrocarbon chain-

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Table 1. Cross-Section Radius of Gyration Rcs,g, Cross-Section Forward Scattering Intensity Ics(0), and Mass per Unit Length ML Obtained by IFT for Lecithin Reverse Micelles at Three Different Values of w0 H2O

D 2O

w0

Rcs,g (Å)

Ics(0) (108 cm/g)

ML (10-13 g/cm)

Rcs,g (Å)

Ics(0) (108 cm/g)

ML (10-13 g/cm)

6 10 14

20.2 22.3 23.7

6.08 8.06 11.7

1.75 2.24 2.83

21.5 24.0 26.4

4.54 4.94 5.95

1.84 2.36 2.94

water interface of λL a0 ≈ 119 Å and of the number of lecithin molecules radially arranged in the circumference of λLxa0 ≈ 14.2. From the known circumference of the cylindrical cross section at the hydrocarbon chain-water interface we can then finally calculate the water core radius Rcore ≈ λLa0/2π ≈ 19 Å, which is indeed in quite good agreement with the extension of the water into the headgroup region as estimated from the radial crosssection excess scattering length density profile ∆F(r) obtained with H2O and D2O (see Figure 5C). Having determined the water core radius Rcore, in a next step we can construct a more detailed estimate of the profile ∆F(r) versus r for w0 ) 14. The starting point for this is the known scattering length densities of H2O (∆FH ) -7.26 × 1010 cm-2), D2O (∆FD ) -0.3 × 1010 cm-2), the lecithin head group (∆Fhg ) -6.04 × 1010 cm-2), and the lecithin tail region (∆Ft ) -6.36 × 1010 cm-2). The phosphatidylcholine headgroup is known to extend approximately 5 Å into the water region, which results in a quite considerable penetration of water molecules into the headgroup region.57 For w0 ) 14, where we find Rcore ≈ 19 Å, this should result in a well defined water core with ∆FH2O(r)0) ) -7.26 × 1010 cm-2 for H2O or ∆FD2O(r)0) ) -0.3 × 1010 cm-2 for D2O and a relatively smooth transition to the expected value of approximately ∆FH2O(r)Rcore) ) ∆FD2O(r)Rcore) ) -6.2 × 1010 cm-2 at the hydrocarbon chain-water interface, where ∆FH2O(r) and ∆FD2O(r) correspond to the radial cross-section excess scattering length density profiles for samples with H2O and D2O, respectively. For the given distribution of fatty acid chain lengths in soybean lecithin the chains should extend on average over a length of approximately lc ≈ 17 Å.56-58 Due to the penetration of the solvent into the radially extended lecithin tails we do not expect a sharp steplike excess scattering length density profile for the chain region. A simple geometrical model for a hairy cylinder would predict that the profile should decay in a first approximation with ∆F(r) ≈ ∆Ft(r)[Rcore/r] from r ) Rcore to r ) Rcore + lc. Finally, the lecithin chains can extend by approximately 5-6 Å beyond lc,57 which then results in the radial excess scattering length density profile shown as the dotted line in Figure 1, which is comparable to the simulated profile for hairy flexible hollow cylinders given in Figure 14C of Part 1. A comparison of Figures 1 and 5C shows very good agreement on an absolute scale, thus confirming the data normalization and analysis procedures. Similar calculations based on the data summarized in Table 1 yield values of Rcore ≈ 16 Å for w0 ) 10 and Rcore ≈ 13 Å for w0 ) 6. The resulting excess scattering length density profiles shown in Figures 3E and 4C indicate that these values of the core radii are not large enough in order to obtain the corresponding bulk values of ∆FH and ∆FD, respectively, at r ) 0. Furthermore, all excess scattering length density profiles ∆FD2O(r) shown in Figures 3E, 4C, and 5C are much smoother at low values of r e Rcore and indicate that the water extends further (56) Small, D. The Physical Chemistry of Lipids. From Alkanes to Phospholipids; Plenum Press: New York, 1986. (57) Israelachvili, J. N. Intermolecular and Surfaces Forces, 2nd ed.; Academic Press: London, 1992. (58) Tanford, C. The Hydrophobic Effect, 2nd ed.; Wiley Interscience: New York, 1980.

Figure 4. Distance distribution function p˜ cs(r) (A and B) and the radial cross-section excess scattering length density profiles (as obtained by the square-root deconvolution method) (C) for lecithin reverse micelles in deuterated cyclohexane at w0 ) 6.0. (A and B): p˜ cs(r) versus r as determined by IFT for measurements with D2O (A) and with H2O (B), respectively. Also shown as the full curves are fits to the data by the square-root deconvolution procedure for p˜ cs(r), resulting in the radial crosssection excess scattering length density profile ∆FH2O(r) (solid line) or ∆FD2O(r) (dashed line) shown in part C. The light lines in part C indicate the errors in ∆F(r).

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Langmuir, Vol. 12, No. 10, 1996 2439

headgroups into the water core and protrusion of the surfactant molecules, which would result in higher values of ∆FD2O(r) at 0 for small values of Rcore and in a smoothly increasing profile ∆FD2O(r). A closer look at the results from the simulations of these effects in Part 1 together with the finding that the experimentally determined width of the tail region is constant for all values of w0 provides strong evidence against dominant contributions from cross-section polydispersity and ellipticity. We therefore believe that the experimentally determined profiles ∆F(r) indicate a considerable penetration of the water molecules into the interfacial region. Furthermore, in our interpretation of the results from IFT and SQDEC we always assume that the exchange of H2O with D2O changes the excess scattering length density of the water core only and has no subtle isotope effect on the lecithin headgroup conformation and packing, and thus on λL. We can test this hypothesis in a quantitative way. For a given value of w0, and under the assumption of constant λL, the change in the mass per unit length ML upon exchanging H2O with D2O should reflect the different values of M1 only. For w0 ) 14 and D2O, the expected value of ML is then ML(H2O) [M1(D2O)/M1(H2O)] ) 3.14 × 10-13 g/cm, where M1(D2O) and M1(H2O) are the molar mass of a “monomer” with either D2O or H2O. For w0 ) 10 we find ML(D2O) ) 2.29 × 10-13 g/cm, and for w0 ) 6 we find ML(D2O) ) 1.78 × 10-13 g/cm, which all agree with the measured values within 4-6%. Not only can we use the integral parameter ML in such a test but we can also directly verify that the difference in ∆F(r) for samples with H2O and D2O provides indeed a direct estimate of the extension of the water core. In a first approximation, the total mass per length ML,w of H2O in the micelles is given by

ML,w )

∫0∞∆FH O(r)r dr - ∫0∞∆FD O(r)r dr)

2π ( ∆Fm,w

2

2

(7)

where ∆Fm,w is the average excess scattering length density per unit mass of H2O and ∆FH2O(r) and ∆FD2O(r) are the experimentally determined radial cross-section excess scattering length density profiles for samples with either H2O or D2O in the core, respectively. In writing eq 7 we have neglected the small contribution to ∆FD2O(r) which arises from the D2O core (i.e., we have set ∆FD ) 0), which underestimates ML,w by approximately 4%. Similarly, we can estimate the total mass per length ML,Lec of lecithin in the micelles by

ML,Lec ) Figure 5. Distance distribution functions p˜ cs(r) (A and B) and the radial cross-section excess scattering length density profiles (as obtained by the square-root deconvolution method) (C) for lecithin reverse micelles in deuterated cyclohexane at w0 ) 14.0. (A and B): p˜ cs(r) versus r determined by IFT for measurements with D2O (A) and with H2O (B), respectively. Also shown as the full curves are fits to the data by the squareroot deconvolution procedure for p˜ cs(r), resulting in the radial cross-section excess scattering length density profile ∆FH2O(r) (solid line) or ∆FD2O(r) (dashed line) shown in part C. The light lines in part C indicate the errors in ∆F(r).

out into the tail region than expected from a simple core and shell model. For the sampling resolution (qmax and magnitude of background) obtained with the current data we can rule out that this is due to the regularizer (smoothness constraint) used in the fitting routines (see Part 1 for details). Smoothed profiles could be a result of cross-section polydispersity or ellipticity. However, it could also be due to a more pronounced extension of the

∫0∞∆FD O(r)r dr

2π ∆Fm,Lec

2

(8)

where ∆Fm,Lec is the average excess scattering length density per unit mass of lecithin. This provides us with an experimental determination of the number ratio of water to lecithin w0,exp in the micelles through

w0,exp )

ML,w M1(Lec) ML,Lec M1(H2O)

(9)

where M1(H2O) ) 18 is the molecular weight of water and M1(Lec) ) 767 is the molecular weight of lecithin. Using the radial cross-section excess scattering length density profiles shown in Figures 3E, 4C, and 5C, we thus obtain w0,exp ) 5.9 for w0 ) 6, w0,exp ) 9.3 for w0 ) 10, and w0,exp ) 13.6 for w0 ) 14. The remarkable agreement between w0 and w0,exp shows that the total mass ratio remains fully conserved in the application of IFT and SQDEC to the scattering data on an absolute scale and provides further

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strong support for the use of these methods in order to obtain quantitative information on the local structure of cylindrical micelles and microemulsions. We can compare our current results with the local dimensions of lecithin reverse micelles in cyclohexane obtained previously from SANS measurements on dilute solutions. The values of Rcs,g listed in Table 1 are in reasonable agreement with those previously deduced for w0 ) 8.0 at different concentrations using a cross-section Guinier approximation for data obtained at 2.5 × 10-2 Å-1 e q e 5.75 × 10-2 Å-1.31 The current values of Rcs,g are approximately 10% higher when taking into account the appropriate scaling of the tubular cross section with w0. Similarly, the previous estimates of ML at different values of w0 appear to be too small by approximately 40%.50 However, the current estimates are much more reliable due to the significantly larger q range used in the data analysis. Furthermore, preliminary measurements at different lecithin concentrations indicate a small but measurable degree of partitioning of water and lecithin between the micelles and solvent similar to a cmc effect in simple micelles. While at the concentrations used in this study the effect of this partioning is negligible and virtually all the material is in the micelles, at the very low concentrations used in the previous studies this could lead to an overestimation of the concentration cwc and thus to a subsequent underestimation of ML. We are currently investigating the effect of concentration on the local composition and structure of the reverse micelles and on their global size using a combination of SANS and light scattering.59 Conclusions We have seen from this study that the application of IFT and SQDEC methods to data from SANS measurements with cylindrical polymer-like micelles allows for an accurate and detailed characterization of the local structure of these aggregates. We have been able to directly verify the previously postulated geometrical model of flexible tubular structures with a well defined water core and a surfactant shell. Due to the fact that contrast (59) Schurtenberger, P.; Jerke, G.; Cavaco, C.; Lindner, P.; Pedersen, J. S. To be published.

Schurtenberger et al.

variation experiments and data analysis have been performed on an absolute scale, we have been able to quantitatively deduce information on properties such as the extension of the aqueous core and the degree of water penetration into the headgroup region and of solvent penetration into the tail region. From the analysis of simulated scattering data presented in Part 1 it is clear than an unambiguous determination of the exact radial density profile will be impossible due to the combined effects of resolution effects, shape fluctuations, and diffuse longitudinal correlations which obscure the information on short length scales. However, a comparison of the simulation results presented in Part 1 with the experimental data allows us to conclude that the observed smooth behavior of the radial cross-section excess scattering length density profiles ∆FH2O(r) and ∆FD2O(r) is mainly caused by a relatively diffuse oil-water interface due to protrusion/ extension of the individual surfactant molecules and penetration of water and oil in the headgroup and tail region, respectively. It is clear from this study that a combination of SANS experiments with well defined model systems, and the application of IFT and SQDEC methods represent a powerful tool for an investigation of the local structure of micelles and microemulsions, which has helped us to gain new and important information. Moreover, if combined with numerical simulations of chain order at interfaces (see for example refs 60 and 61) it will allow us to address open questions on issues such as the chain conformation of surfactants in spherical or tubular microemulsions. Acknowledgment. We gratefully acknowledge financial support from the Swiss National Science Foundation (Grants 21-37274-93 and 20-40339.94). The neutron scattering experiments reported in this paper were performed at the DR3 reactor at Risø National Laboratory and were supported by the Commission of the European Community through the Large Installation Plan. LA9507444 (60) Bjo¨rling, M.; Linse, P.; Karlstro¨m, G. J. Phys. Chem. 1990, 94, 471-481. (61) Sarmoria, C.; Blankschtein, D. J. Phys. Chem. 1992, 96, 19781983.