ESR line shapes in lyotropic systems: the micellar and liquid

in line shape of the hexagonal phase spectra is qualitatively reproduced by the rotational diffusion of a highly anisotropic prolate symmetric top. In...
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5964

J . Phys. Chem. 1990, 94, 5964-5972

ESR Line Shapes in Lyotropic Systems. The Micellar and Liquid-Crystalline Phases of the Dodecyltrimethylammonium Chloride/Water System Goran Wikander, Per-Olof Eriksson,* E. Elliott Burnell,+ and Goran Lindblom Department of Physical Chemistry, University of Umel, S-901 81 VmeA, Sweden (Received: November 1, 1989; In Final Form: March 19, 1990)

ESR spectra of a paramagnetic spin probe, 5-doxylstearic acid, solubilized in the micellar and lyotropic liquid-crystalline phases of the dodecyltrimethylammonium chloride (CI2TACl)/watersystem have been recorded and analyzed by employing spectral line shape simulation techniques. The partial averaging of the magnetic interactions by fast local anisotropic motions in the aggregates has been accounted for by the introduction of scaled magnetic interactions, quantified by an order matrix. The effects of aggregate rotation and amphiphile surface diffusion in phases with curved aggregates are simulated by rotational diffusion models. The spectra from the micellar phase are well reproduced with an isotropic rotational diffusion model, giving reasonable estimates of the micellar size. In the hexagonal phase, with increasing water content and temperature, the ESR spectrum undergoes a transition from a static limit, similar to the spectrum from the lamellar phase, through an intermediate motional region, to a new static limit consistent with rapid lateral diffusion around the cylinder aggregates. The transition in line shape of the hexagonal phase spectra is qualitatively reproduced by the rotational diffusion of a highly anisotropic prolate symmetric top.

Introduction A wealth of information has been obtained about the properties of amphiphilic systems by magnetic resonance techniques. Much of the success stems from the fact that the motions associated with the aggregation of amphiphilic molecules are often on a time scale that influences the magnetic resonance spectrum. In the motional narrowing regime,2 information about molecular ordering and aggregate symmetries can be obtained directly from simple spectral f e a t ~ r e s . ~ -Dynamic ~ properties are then accessible through measurement of different spin-relaxation ratel0 or from the direct measurement of the self-diffusion coefficient with the pulsed magnetic field gradient NMR On the other hand, in the intermediate motional regime, where the motions are on the time scale of the modulated interaction, the spectral line shape is a complicated function of the static and dynamic properties of the s y ~ t e m . l ~ -A’ ~direct evaluation of molecular quantities from simple spectral features is then often impossible and a full lineshape analysis is necessary. Since the magnitude of the anisotropic magnetic interactions are larger in ESR than in NMR, the two techniques are sensitive to motions on different time scales. For example, in amphiphile systems with curved aggregates, aggregate tumbling and lateral diffusion around the curved aggregate surfaces are usually in the motional narrowing regime in N M R whereas they are in the intermediate motional regime in ESR. On the other hand, local fast molecular reorientations are often in the motional narrowing regime both in NMR and ESR. Micellar solutions have been investigated extensively by E S R using amphiphilic spin probes.’8-20 The correlation time for the tumbling of the solubilized spin probe has often been calculated by employing equations6 valid for a single isotropic motion. Neglect of the motional averaging by local fast molecular reorientations has led to anomalously fast tumbling rates for the micellar aggregate.I9 On the other hand, E S R spectra of lyotropic liquid-crystalline phases, especially lipid bilayer systems, have been analyzed in terms of an order parameter, introduced to quantify the local partial averaging of the anisotropic interaction^.^^^^^^^^^ In hexagonal phases it has generally been found that lateral diffusion around the rodlike aggregates is too slow to average the static interaction^.^^-^^ Thus, for unaligned samples, similar line shapes are obtained for lamellar and hexagonal phases. Complete averaging through lateral diffusion to a new static limit has only been observed at high temperatures in an amphiphile/water system.*’ Present address: Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver BC, V6T 1Y6,Canada.

0022-3654/90/2094-5964$02.50/0

In this study, we have undertaken an extensive E S R investigation of all the phases in the binary system dodecyltrimethyl-

( I ) Abbreviations: ESR, electron spin resonance; NMR, nuclear magnetic resonance; LI, micellar phase; II cubic phase with closed aggregates; HI, hexagonal phase, I*, bicontinuous cubic phase; L,, lamellar phase; C,,TACI, dodecyltrimethylammonium chloride. (2) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, U.K., 1961. (3) Shui Pong Van; Birrell, G. B.; Griffith, 0.H. J . Magn.Reson. 1974, 15, 444. (4) Gaffney, B. J.; McConnell, H. M. J . Magn. Reson. 1974. 16, I . (5) Berliner, L. J.; Ed.Spin Labeling Theory and Applications; Academic Press: New York, 1976. (6) Schreier, S.; Polnaszek, C. F.; Smith, I . C. P. Biochim. Biophys. Acta 1978, 515, 395. (7) McLaughlin, A. C., Cullis, P. R., Berden, J . A,, Richards, R. E. J . Magn.Reson. 1975, 20, 146. (8) Seelig, J. Q. Rev. Biophys. 1977, IO, 353. (9) Seelig, J. Biochim. Biophys. Acta 1978, 515, 105. (10) Vold, R. R. In Nuclear Magnetic Resonance in Liquid Crystals; Emsley, J. W., Ed.; D. Reidel: Dordrecht, The Netherlands, 1985; p 253. ( 1 1 ) Stejskal, E. 0.; Tanner, J. E. J . Chem. Phys. 1965, 42, 288. (12) Roeder, S. B. W.; Burnell, E. E.; An-Li Kuo; Wade, C. G. J . Chem. Phys. 1976.64, 1848. Lindblom, G.; Johansson, L. B.-A; Arvidson, G. Biochemistry 1981, 20, 2204. (13) Lindblom, G.; Larsson, K.; Johansson, L.; Fontell, K.; Forsen, S. J . Am. Chem. SOC.1979, 101, 5465. Lindblom, G.; Wennerstrom, H. Biophys. Chem. 1977, 6, 167. (14) Eriksson, P. 0.; Khan, A.; Lindblom, G.J . Phys. Chem. 1982, 86, 387. ( I 5 ) Freed, J. H. In Spin Labeling Theory and Applications; Berliner, L . J., Ed.; Academic Press: New York, 1976; p 53. (16) Muller, K.; Meier, P.; Kothe, G. Prog. Magn. Reson. Spectrosc. 1985, 17, 211. (17) Barbara, T. M.; Greenfield, M. S.; Vold, R. L.; Vold, R. R. J . Magn. Reson. 1986, 69, 3 1 1. (18) Waggoner, A. S.; Keith, A. D.; Griffith. 0. H. J . Phys. Chem. 1968, 72, 41 29. Povich, M. J.; Mann, J. A,; Kawamoto, A. J . Colloid Interface Science 1972, 41,145. Esposito, G.; Giglio, E.;Pavel, N . V.; Zanobi, A. J . Phys. Chem. 1987, 91, 356. Hearing, G.; Luisi, P. L.; Hauser, H. J . Phys. Chem. 1988, 92, 3574. (19) Ernandes, J. R.; Schreier, S.; Chaimovich, H. Chem. Phys. Lipids 1976, 16, 19. Yoshioka, H. Chem. Lett. (Jpn.) 1977, 1477. Baglioni, P.; Ferroni, E.; Martini, G.; Ottaviani, M. F. J . Phys. Chem. 1984, 88, 5107. Baglioni, P.; Ottaviani, M. F.; Martini, G. J . Phys. Chem. 1986, 90, 5878. (20) Lasic, D. D.; Hauser, D. J . Phys. Chem. 1985,89, 2648. (21) Seelig, J . J . Am. Chem. SOC.1970, 92, 3881. (22) Hubbel, W. L.; McConnell, H. M. J. Am. Chem. Soc. 1971,93,314. (23) Boggs, J. M.; Hsia, J. C. Proc. Natl. Acad. Sci. U.S.A. 1973, 70, 1406. (24) Seelig, J.; Limacher, H. Mol. Crysr. Liq. Crysr. 1974, 25, 105. (25) Taylor, M. G.; Smith, I . C. P. Chem. Phys. Lipids 1981, 28, 119. (26) Nesrullajev, A.; Panatta, A . Mol.Crysf. Liq. Cryst. 1988. I59, 77.

0 1990 American Chemical Society

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y/

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40 X

20%

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Figure 2. Experimental ESR spectra (-) of 5-doxylstearic acid at 25

C12TACI % W Figure 1. Phase diagram of the dodecyltrimethylammonium chloride (C12TACl)/water system. The various phases are marked in the dianormal gram: LI,micellar phase, I,, cubic phase (closed aggregates); HI, hexagonal phase; I*. cubic phase (bicontinuous); L,, lamellar phase. The stars indicate the compositions and temperatures for the spectra displayed in Figures 2-6. Adapted from ref 28.

ammonium chloride (C12TACl)/water.28 With increasing amphiphile concentration micellar (LJ, cubic (I1), normal hexagonal (HI), cubic (I2), and lamellar (La) phases are formed (Figure 1). The ESR line shape of a solubilized nitroxide label has been simulated by applying simple models for the amphiphile lateral diffusion and aggregate rotation. The analysis demonstrates the importance of taking into account local fast anisotropic molecular motion in the aggregates. The averaging effect of the local motions are described by the introduction of an order parameter.

Materials and Methods Dodecyltrimethylammonium chloride (C12TACI)was purchased from Eastman Kodak Co., and was purified by mixing with active charcoal in a methanol solution. The solution was filtered and the solvent was removed under vacuum. 5-Doxylstearic acid was purchased from Molecular Probes Inc., Eugene, OR, and was used without further purification. For the ESR samples, a suitable amount of a chloroform/methanol (2:l vol/vol) solution of 5doxylstearic acid was transferred to glass tubes. The solvent was removed under vacuum and appropriate amounts of vacuum-dried amphiphile and water were added to the glass tubes. The sample tubes were flame sealed and the content was thoroughly mixed by repeated centrifuging and heating for several days. The samples were stored for at least 3 weeks before any ESR experiments were done. Small aliquots of the samples were transferred to capillary tubes which were subsequently sealed. The ESR samples were equilibrated for at least 24 h before the recording of the spectra. The label/amphiphile molar ratio was 1/1O00 in all samples. ESR spectra were recorded with a Varian Model E-109 X-band (9 GHz) spectrometer equipped with an E-238-type (TMllomode) cavity and a Model V-6040 variable-temperature regulator. The (27) Schara, M.;Pusnik, F.; Sentjurc, M.Croatica Chem. Acta 1976,48, 147. (28) Balmbra, R. R.; Clunie, J. S.; Goldman, J. F.Nuture (London) 1969, 222, 1 1 59.

"C solubilized in the micellar phase (L,)and the cubic phase with closed aggregates (II) of the C12TACl/watersystem. The composition (in wt % CI2TACI)is given next to each spectrum. Calculated ESR spectra (-) are superimposed on the experimental. The parameters for the spectral simulations are given in Table I.

spectrometer was interfaced to a Zenith 11 1-32 personal computer. The interfacing and the program for handling of data were similar to that outlined by Lipscomb and sal^.^^ Computer simulations for the ESR line-shape analysis were performed on a CYBER 180/750 at the computer center of the University of UmeA, using the program given by Freed and co-workers in ref 15, modified to include scaled magnetic interactions (cf. below).

Experimental Results The ESR spectra at 25 OC of 5-doxylstearic acid solubilized in the different phases of the CI2TACl/watersystem (Figure 1) are displayed in Figure 2 (the micellar phase, LI, and the cubic phase at high water content, 11) and in Figure 3 (the hexagonal phase, HI, the bicontinuous cubic phase, 12, and the lamellar phase, La). In Figures 4-6 the ESR spectra at varying temperatures of samples in the water-rich end of the HI phase region (Figure 4), in the I2 phase (Figure S), and in the La phase (Figure 6) are shown. The line shapes of the spectra in Figures 2-6 can be rationalized qualitatively in terms of aggregate motion and amphiphile lateral diffusion, as described in the following. The L1 Phase. The spectral line shape from the L1 phase (Figure 2) is isotropic due to the rotational tumbling of the micellar aggregates and the lateral diffusion of the amphiphiles. The line width increases with increasing amphiphile concentration, indicating slower aggregate tumbling and/or slower amphiphile diffusion at higher concentration. The ZIPhase. The spectrum from the I, phase (Figure 2, top) bears strong resemblances with the spectra from the L! phase. This phase has previously been shown by the N M R diffusion technique to consist of closed, presumably micellar, aggregate^.'^,^ The isotropic averaging observed in ESR can thus be ascribed to motions similar to those in the L I phase. The L, Phase. At low water content in the C12TACl/water system, an La phase forms (Figure 1). The ESR spectrum is "anisotropic" at 25 'C (Figure 3, top), typical of a random distribution of immobilized spin probes. However, the anisotropy of the hyperfine coupling, 1.6 mT (All - A, in Figure 3) is considerably smaller than in a dry powder of the nitroxide: 2.7 mT. (29) Lipscomb, J. D.; Salo, R. W.Comput. Enhanced Spectrosc. 1983, I , 11. (30) Bull, T.; Lindman, B. Mol. Cryst. Liq. Cryst. 1974, 28, 155

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rI - - - - - I I I

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I

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Figure 3. Experimental ESR spectra (-) of 5-doxylstearic acid at 25 OC solubilized in the hexagonal phase (HI), the bicontinuous cubic phase (I2) and the lamellar phase (La)of the C12TACl/water system. The composition (in wt % C12TACI)is given next to each spectrum. The elements of the partially averaged (axially symmetric) hyperfine-coupling tensor, parallel ( A , , )and perpendicular ( A , ) to the normal of the aggregate surface are marked on the spectrum from the lamellar phase. Calculated ESR spectra are superimposed on the experimental. The parameters for the spectral simulations are given in Table IV. (-e)

This indicates the presence of anisotropic molecular motions in the La phase, which are fast on the time scale of the static anisotropy of the hyperfine coupling, 108-109 S-I. The fast motions modulate the anisotropy of the hyperfine coupling tensor, A, and the g tensor. The residual anisotropic interactions give rise to a "quasi-static-limit" spectrum. An increase in the temperature does not render the line shape isotropic (Figure 6). This is consistent with an L, phase composed of bilayers with negligible curvature. Thus, lateral diffusion along the planar bilayer is ineffective in averaging the anisotropic magnetic interactions. The I2 Phase. As shown by NMR diffusion and X-ray res u l t ~ , ' the ~ *I2~ phase ~ ~ ~consists ~ of continuous amphiphile aggregates arranged in a three-dimensional network. The aggregates extend over colloidal distances, rendering the phase structure bicontinuous, i.e., continuous in both lipid and water domains. The lateral diffusion around the curved aggregate reorients the amphiphile molecules isotropically. The ESR spectrum of the l2 phase is "anisotropic" at 25 "C (Figure 3) and is similar to the spectrum of the L, phase at that temperature (Figure 3). However, with increasing temperature, the ESR spectrum changes through an intermediate line shape into an 'isotropic" line shape at 65 O C (Figure 5 ) , in contrast to the temperature dependence of the spectra from the L, phase (Figure 6). Thus, on the time scale defined by the residual anisotropy of the A and g tensors4 (1 X 1 08-4 X IO8 s-l), the reorientation through lateral diffusion in the 12 phase is slow at 25 "C, intermediate between 35 and 5 5 "C, and fast at 65 "C and above. (31) Fontell, K . f r o g . Chem. Fats Other Lipids 1978, 16, 145.

Wikander et al. The H I Phase. This phase is built from rodlike aggregates (cf. Figure 7C), arranged in a hexagonal array. The polar headgroups of the amphiphile molecules cover the cylinder surface, facing the surrounding water, while the hydrocarbon chains fill up the interior of the aggregates. The ESR spectra at 25 OC from the HI phase at varying concentrations are shown in Figure 3 together with spectra from the I2 and L, phases. At high amphiphile content at 25 "C, the ESR spectrum of the HI phase is anisotropic, resembling the spectrum of the L, phase (Figure 3). As the amphiphile concentration decreases, the static anisotropic features are gradually smeared out and at 60% ClzTACl(Figure 3, bottom) the spectrum resembles the spectrum of the (isotropic) L, phase (Figure 2). However, the spectrum of 60% CI2TACIis not an isotropic spectrum; this can be understood from the series of spectra with increasing temperature at this composition (Figure 4) since above 40 OC anisotropic features reappear with the opposite sign of the anisotropy (see further below). That the spectrum from the HI phase at 60% C,,TACl and 25 OC is an anisotropic spectrum (in the intermediate motional regime) is consistent with results from NMR of the hexagonal phase. The 2H spectrum of C U , C U - ~ H ~ - C ~is~anisotropic TACI throughout the whole hexagonal phase and the quadrupolar splitting increases only slightly with c~ncentration,~~ from 12.2 kHz at 65% to 12.7 kHz at 78% C12TAC1. Since the time scales are much faster in ESR than in NMR, it is impossible that the motion giving rise to the spectral line shape in ESR a t 60% C12TACl would be isotropic a t the same time as the N M R spectrum shows the presence of anisotropic constraints on the molecular motion. The time scales are defined by the anisotropy of the g and A tensors in ESR and the quadrupolar splitting in NMR. Reorientation through lateral diffusion around the cylindrical aggregates in the HI phase is fast on the NMR time scale throughout the whole HI phase whereas it is slow to intermediate on the ESR time scale. The changes in line shape with concentration and temperature in the HI phase (Figures 3 and 4) can be rationalized by assuming a concentration- and temperature-dependent lateral diffusion coefficient. The lateral diffusion around the cylinder aggregates reorients the spin probe, thereby modulating the anisotropic interactions. At high amphiphile concentrations, the reorientation is slow compared with the residual anisotropic interactions. The spin label then effectively experiences a local lamellar-like environment and a spectrum similar to that from the La phase results (Figure 3,80%). At increasing water content the lateral diffusion gets faster and starts to affect the line shape. Below 70%ClzTACI the reorientation through lateral diffusion is in the intermediate motional regime at 25 "C (Figure 3, bottom). With increasing temperature the lateral diffusion gets faster, and at 60 "C and above the interactions are averaged to a new static limit, with opposite sign of the anisotropy (Figure 4). Computer Simulations of the ESR Spectra

We have performed line-shape simulation^^^^^^ of the ESR spectra, using the program given by Freed in ref 15 where a full description of the theory can be found. The program solves the stochastic quantum mechanical Liouville equation for a nitroxide spin label in a magnetic field. It handles a number of different models for the motion of the spin probe, of which the isotropic and axially symmetric Brownian rotational diffusional models are relevant here. To a good approximation the principal axis system of the static g and A tensors of solid 5-doxylstearic acid coincide! The principal values which we have used in this study are4 g,, = 2.0088, gYy = 2.0061, g,, = 2.0027, A,, = 0.626 mT, A,,,, = 0.585 mT, and A,, = 3.346 mT. The various axis systems used in the following (32) Stael von Holstein, J.; Eriksson, P. 0.;Tiddy, G . J. T.; Lindblom, G . To be published. (33) Freed, J. H.; Bruno, G . V.; Polnaszek, C. F. J . fhys. Chem. 1971, 75, 3385. Polnaszek, C. F.; Bruno, G . V.; Freed, J. H. J . Chem. f h y s . 1973,58, 3185. Polnaszek, C. F. "An Electron Spin Resonance Study of Rotational Reorientation and Spin Relaxation in Liquid Crystal Media." Ph.D. Thesis, Cornell University, 1976. Polnaszek, C. F.; Freed, J. H. J . Phys. Chem. 1975, 79, 2 2 8 3 .

ESR Line Shapes in Lyotropic Systems

The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 5967

9ooc

80°C

70'C

60'

C

5OoC

40'. C

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Figure 4. Experimental ESR spectra (-) of 5-doxylstearicacid solubilized in the hexagonal phase (HI) of the C12TACl/watersystem as a function of temperature. The composition of the sample (40% w/w water, 60% w/w amphiphile) corresponds to the high-water end of the hexagonal phase-region are superimposed on the experimental. The parameters for the spectral simulations are given in Table IV. (Figure 1). Calculated ESR spectra (e-)

n

800C

70'C

EODC

50'C

4OOC

3OoC

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.*_ mT

Figure 5. Experimental ESR spectra of 5-doxylstearicacid solubilized

in the bicontinuous cubic phase (I2) of the CI2TACl/watersystem as a function of temperature. Sample composition, 84% C,,TACI.

are illustrated in Figure 7. Apart from the principal axis system of the A and g tensors (xyz) and the laboratory-fixed system defined by the direction of the magnetic field, Bo. we also introduce a third coordinate system (XYZ)with the Z axis along the normal to the aggregate surface (the director) and the X and Y axes oriented as shown in Figure 7 for different types of aggregates. In the simulations of the ESR line shapes we assume that local anisotropic motions of the spin probe (e.g., rotations around the

V

c . )

1 mT

Figure 6. Experimental ESR spectra of 5-doxylstearicacid solubilized in the lamellar phase (L,) of the C12TACl/watersystem as a function of temperature. Sample composition, 90% CI2TACI.

molecular long axis, tilting, and isomerizations) are fast compared to the static anisotropic interactions and lead to a partial averaging of the anisotropic interactions,4-s*2132 in analogy with assumptions made when interpreting NMR spin relaxation data from lyotropic The interactions are projected along the normal

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The Journal of Physical Chemistry, Vol. 94, No. 15, 1990

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Figure 7. Illustration of the orientation of the various coordinate systems used in the study. (A) The molecular-fixed principal coordinate system of the A and g tensors ( x y z ) and the aggregate-fixed director system ( X Y Z ) . (B) The director system in the micellar aggregates. (C) The director system in the hexagonal phase. (D) The director system in the lamellar phase. The elements of the rotational diffusion tensor, Rlland R , are indicated in B-D. The A and g tensors are axially symmetric in the director system with A,, and qll referring to Z and A , and g, referring to X and Y.

to the aggregate surface, here referred to as the local director (Figure 7). The orientational distribution around the local director (Z) is assumed to possess at least threefold symmetry, rendering the residual anisotropy of the g and A tensors axially symmetric.36 The assumption that the interface is axially symmetric is not strictly true for the HI phase and possible the I2 phase. However, for the level of sophistication of our simple model, this will probably be a good approximation even for these phases. The scaling of the anisotropic magnetic interactions is described by an order parameter matrixz2v3'

where cos 6, and cos Oa are the direction cosines of the angles between the local director, Z, and the a and 0 axes in the principal axes system of the A and g tensors and ,6 is the Kronecker delta. The brackets indicate a time average over the fast local motions. If the order matrix is axially symmetric about the Z axis (Le., S, = Syy= -I/#,,), then the averaged interactions are given bf13*

(3) where All, A , , gll and g, are the elements of the (axially symmetric) averaged A and g tensors, parallel and perpendicular t o the local director (Zin Figure 7). The factor in eq 2, where a b = l/3(AXx+ A , + A,,) and a. = '/3(All + 2A,), is a correction for the difference in polarity between the hydrocarbon interior (34) Charvolin, J.; Rigny, P. J . M a p . Reson. 1971, 4 , 4 0 ; J . Chem. Phys. 1973.58, 3999. ( 3 5 ) SMerman, 0.; Walderhaug, H.; Henriksson, U.;Stilbs, P. J . Phys. Chem. 1985, 89, 3693. (36) Wennerstrom, H.; Lindblom, G . ; Lindman, B. Chem. Scr. 1974, 6, 97, Bloom,M.; Burnell, E. E.; Roeder, S. B. W.; Valic, M. 1. J . Chem. Phys. 1977. 66. 301 2. (37) Saupe,A. Z . Nuturforsch. 1964, 190, 161. Mason, R. P.; Polnaszek, C. F.; Freed, J. H. J . Phys. Chem. 1974, 78, 1324. (38) Buckingham, A. D.; McLaughlan, K. A. Prog. Nucl. Mogn. Reson. Spectrosc. 1967, 2, 63.

of the amphiphile aggregates and the system used in ref 4 for the determination of the static A-tensor elements.39 The order matrix, referred to the principal A and g tensor axis system, has five independent elements. The off-diagonal elements do not influence the spectrum of the spin probe. In addition, the introduction of a non axially symmetric order parameter matrix (Sxx# Syy)did not improve the fits reported in this paper. Thus we shall set S , = Syy = -1/2Srrand use eqs 2 and 3 throughout. Spectra from unaligned L, samples are powder patterns. In an axially symmetric powder pattern, All and A, can be determined directly from the s p e c t r ~ m ,as ~ ?shown ~ in Figure 3. With the use of eq 2, the order parameter S,, can then be obtained. When extracting an order parameter from a powder spectrum it is assumed that the local motion is in the motional narrowing regime, Le., that the local motion is much faster than the static anisotropic interactions. Recently, Korstanje et pointed out that for biological lipids the motional narrowing approximation for the local motion is not generally valid. As a consequence, the order parameter is overestimated when calculated from simple spectral features (Figure 3, top). However, for amphiphile molecules, the local motions are generally faster. For the C12TACl/water system a recent multifield NMR relaxation study3sof the L1 and cubic phases yielded correlation times for the local motion on the order of 10-ll-lO-lo s. This is well into the motional narrowing region on the ESR time scale, thus justifying our assumption about fast local motions in the aggregates. On the other hand, as shown below, at low water content in the H I phase and in the L, phase the local dynamics are probably not completely in the motional narrowing limit. Depending on the geometry of the amphiphile aggregate, slower global motions take place, viz., aggregate rotation and lateral surface diffusion of the amphiphiles. These motions modulate the residual anisotropy of the A and g tensors, which remains after partial averaging by the local motions. The global motions are described here by simple rotational diffusion models.41 For spherical micelles, in the motional narrowing regime, the combined motion of aggregate tumbling and lateral surface diffusion is equivalent to an isotropic rotational diffusion, with a single rotational diffusion coefficient given b~~~ R = R,,,

+ DL/r2

(4)

where R,,, is the rotational diffusion coefficient for aggregate tumbling, DL is the lateral surface diffusion coefficient of the amphiphile, and r is the aggregate radius. For stick boundary conditions RrOtis given by the Stokes-Einstein equation43

where kB is the Boltzmann constant, Tis the absolute temperature, and q is the viscosity of the medium. The ESR spectra from the LI phase are thus simulated with an isotropic rotational diffusion model representing the combined effect of aggregate tumbling and amphiphile surface diffusion. These motions are assumed to modulate scaled anisotropic interactions. The scaling arises from fast local motions of the amphiphile in the aggregate which partially average the anisotropy of the static g and A tensors. The scaling is quantified by an order parameter, S,, (eq 1). As a first approximation, S,, was taken from the ESR spectrum of the L, phase in the same system. All and A, are measured directly from the powder pattern line shape of the L, phase spectrum (Figure 3, top) and S,, is obtained by using eq 2. The line-shape-calculating program then simulates an ESR line shape assuming an isotropic rotational diffusion which (39) Meirovitch, E.; Freed, J. H. J . Phys. Chem. 1984,88,4995. (40) Korstanje, L. J.; Van Faassen, E. E.; Levine, Y. K. Biochim. Biophys. Acto 1989, 980, 225. (41) Huntress, W. T. Adu. Mogn. Reson. 1970, 4, 1. (42) Halle, B. Mol. Phys. 1987, 61, 963. (43) Cantor, C. R.; Schimmel, P. R. Biophysicol Chemistry, part 11; W. H. Freeman: New York, 1980.

ESR Line Shapes in Lyotropic Systems modulates the scaled magnetic interactions. From the optimal value of the rotational diffusion coefficient, R, the micellar radius, r, can then be calculated by using eqs 4 and 5 , provided the value of DL is known. In the HI phase the partially averaged magnetic interactions are projected perpendicular to the long axis of the cylindrical aggregates (along Z in Figure 7C). For a very large cylindrical aggregate, aggregate rotation around both the long and the short axes can be neglected.43 However, lateral surface diffusion of the amphiphiles is approximately independent of aggregate size and will modulate the residual anisotropic interactions. The averaging effects of the lateral diffusion are described here by the rotational diffusion of a highly anisotropic symmetric top with R , 0 as long as the factor ( S , z ~ I is ) 2held ~ , constant (cf. Table 111). Thus, it is not posible to independently determine S,, and T, from the line-shape fits. However, if the size of the micelle is fixed at a value obtained by an independent technique (NMR), a value of S,, can be extracted (cf. above). The value of S,, so obtained (0.50) is close to the value obtained from the La phase (0.60). It is reasonable to expect that the order parameter is somewhat smaller in the LI phase than in the La phase due to different packing constraints in the curved (micellar) and planar (lamellae) aggregates. The increase in the correlation time of the micellar tumbling with increasing concentration can be attributed, apart from a real increase in the micellar size, to increased aggregate interactions. In eq 5 this would correspond to a higher viscosity, 1. Recently Johansson et al.49determined the micellar aggregation number, N , for micelles of C,,TACI as a function of concentration, using fluorescence quenching techniques. It was found that N was approximately constant up to 30% amphiphile ( N i= 60) but increased when approaching the cubic phase border ( N = 69). Our results show a monotonic increase in the aggregation number with concentration (Table I). Thus, the increase in T~ with concentration can probably be ascribed to increased interactions between the aggregates with increasing concentration rather than to a real increase in micellar size. Previously, it was common to analyze ESR line shapes of amphiphile probes solubilized in micellar aggregates with a single isotropic rotation modulating the static (unscaled) anisotropic interactions.19 No account was then taken for fast local dynamics in the aggregate. In our analysis this would correspond to S,, = 1.0 (see Table 111). This has generally resulted in rotational correlation times too short to be compatible with the tumbling of the micelle and the results have instead been interpreted by assuming other motional processes in the system.19 The application of such a single-motion analysis to our results yields unreasonably small micellar radii, viz. 10-13 A (Table 111). The I , Phase. As has been shown by the N M R diffusion t e c h n i q ~ ethis ' ~ ~phase ~ ~ is built from closed, micellar, aggregates. This cubic phase has counterparts in other amphiphile/water system^.^' Recently, a structure for this cubic phase was suggesteds2 with eight rod-shaped micelles per unit cell where the rotation of six of the micelles is partially constrained due to steric effect. Strong support for this structure was obtained from the observation of residual anisotropic interactions in the NMR spectra (50) Tanford. C. J . Phys. Chem. 1972, 76, 3020. (51) Ekwall, P. In Aduances in Liquid Crysfals; Brown, G. H., Ed.; Academic Press: New York, 1975; Vol. 1, p 1. Arvidson, G.; Brentel, I.; Khan, A.; Lindblom, G.; Fontell, K. Eur. J . Biochem. 1985, 152, 753. Tiddy, G. J . T. Phys. Rep. 1980, 57, 1. Eriksson, P. 0.; Lindblom, G.; Antidson, G. J . Phys. Chem. 1987, 91, 846. (52) Fontell, K.; Fox, K.; Hansson, E.Mol. Crysr. 159. Cryst. 1985, I , 9.

The Journal of Physical Chemistry, Vol. 94, No. 15, I990 5971

ESR Line Shapes in Lyotropic Systems

nll/s-l lE11

1E9

1E8

5E7 2.5E7

-v p- -

1E7

3E8

V

1ml

Figure 8. Model calculation of the ESR line shape. arising from motional averaging through lateral diffusion around a cylindrical aggregate, typical for a hexagonal phase. The spectra were calculated by applying an anisotropic rotational diffusion model where R , R,. This could correspond to a cubic structure built from a network of rodlike aggregates where the reorientation through lateral diffusion around the rods corresponds to R,,and reorientation through lateral diffusion along the curved rods corresponds to R,. The best fit to the experimental spectrum at 25 OC, with S,, = 0.60, was obtained with Ril = 19 X IO6 s-I and R , = 2.5 X lo6 d. The calculated spectrum is displayed in Figure 3 together with the experimental spectrum. With R , = Dt/$ this would correspond to a radius of curvature, r, of 30 A, giving an estimated unit cell dimension of 60 A. Here, the lateral diffusion coefficient is taken as DL = 3DCub= 2.3 X IO-" s-I where Dcub is the measured translational diffusion coefficient in the bicontinuous cubic phaseI4 and the (56) Oradd, G.; Wikander, G.; Lindblom, G.; Johansson, L. B.-A. To be published.

Wikander et al. factor of 3 is a geometrical correction (cf. above). Analogously,

RIIwould correspond to a radius of the rods of 11 A. This is in

qualitative agreement with the measured dimension of the cubic unit cell ( d = 79 A) and the radius of a cylindrical aggregate of Cj2TACl(1 8 A), respectively. The uncertainty in these fitted R values is large and the agreement should only be taken as a rough test of the model. A proper description of the motional narrowing of the ESR line shape in the I2 phase would require explicit consideration of the local dynamics and a detailed description of the reorientation through lateral diffusion.

Concluding Remarks In this study we have demonstrated that the ESR line shape of a spin probe solubilized in the Li phase and the cubic and HI liquid-crystalline phases in the C12TACl/water system can be reproduced by properly taking into account (i) the partial averaging of anisotropic magnetic interactions by local fast motions in the aggregate, quantified by an order parameter, and (ii) the effects of global slow motions, viz., aggregate rotation and lateral diffusion along curved aggregates, simulated by simple rotational diffusion models. The calculated micellar rotational correlation time corresponds to an aggregate radius in reasonable agreement with the results obtained from other experimental techniques, being dependent upon a proper choice of the value of the order parameter. In the HI phase the anisotropic interactions are modulated by the lateral diffusion of amphiphiles around the cylinder aggregates and (possibly) aggregate rotation. The transition, due to increased lateral diffusion around the cylindrical aggregates, from a static limit with slow lateral diffusion to a new static limit consistent with fast lateral diffusion around the aggregates, is qualitatively reproduced by an anisotropic rotational diffusion, modulating the scaled anisotropic interactions. The apparent variation of the order parameter with hydration and temperature in the HI and L, phases indicates that at low water content the local dynamics is not completely in the motional narrowing limit. A proper analysis of these spectra requires an explicit description of the local dynamics, superimposed on a slower global reorientation through lateral diffusion. Work along these lines is currently under way in our laboratory. Note Added in Proof: Recent results32from 2H and 14N NMR show that a separate phase with biaxial symmetry forms a t amphiphile concentrations above 80% w/w in the region indicated as the HI phase region in Figure 1. Acknowledgment. Thanks are due to Prof. Jack H. Freed for providing a copy of the line-shape simulation program, to Jan Kristoffersson for performing some of the ESR measurements, and to Per-Olof Westlund for constructive criticism of the manuscript. This work was supported by grants from the Swedish Natural Science Research Council (NFR). The stay of E.E.B. at University of UmeP was made possible by grants from NFR.