pubs.acs.org/Langmuir © 2009 American Chemical Society
Size Determination of Shear-Induced Multilamellar Vesicles by Rheo-NMR Spectroscopy B. Medronho,*,†,‡ C. Schmidt,§ U. Olsson,‡ and M. G. Miguel† †
Department of Chemistry, University of Coimbra, 3004-535, Coimbra, Portugal, ‡Physical Chemistry, Center of Chemistry and Chemical Engineering, Lund University, Box 124, 221 00 Lund, Sweden, and § Department of Chemistry, University of Paderborn, Warburger Strasse 100, D-33098 Paderborn, Germany Received September 29, 2009. Revised Manuscript Received November 24, 2009 A model for analyzing the deuterium (2H) NMR line shapes of D2O in surfactant multilamellar vesicle (MLV, “onion”) systems is proposed. The assumption of the slow exchange of water molecules between adjacent layers implies that the 2H NMR line shape is simply given by a sum of Lorentzians if the condition of motional narrowing is also fulfilled. Using the classical two-step model for the NMR relaxation in structured fluids allows us to calculate how the NMR line shape depends on the MLV size. The model is tested on two different MLV systems for which the NMR line shapes are measured as a function of the applied shear rate using rheo-NMR. The MLV sizes obtained are in good agreement with previous data from rheo-small-angle light scattering.
Introduction Self-assembled soft matter systems such as surfactant systems often exhibit complex rheological behavior.1 Most often they are strongly shear-thinning, but a number of shearthickening systems have also been documented. The reason for this complexity is that the applied shear flow may induce structural changes in these systems, which in turn result in changes in viscosity.2 Hence, to understand the rheological behavior we need to look inside the sample in the rheometer and monitor the structural changes that occur. For this reason, rheometers that are transparent to visible light, X-rays,3,4 or neutrons5 have been developed, allowing for the measurement of birefringence and dichroism6,7 or for scattering and microscopy experiments while shearing the sample or even following the rheological response. More recently, there has also been the development of rheo-NMR,8-10 where NMR probes containing a small shear cell, typically for wide-bore magnets, have been constructed to allow for various modern NMR experiments on samples being sheared.11-13 Such rheo-NMR probes are now also commercially available. As far as shear effects on surfactant self-assembled systems are concerned, the lamellar liquid-crystalline phase has
received particular attention.14,15 Many surfactant-water systems form a lamellar-phase region that occupies a large area in the phase diagram. When an external shear force is applied to a lyotropic lamellar phase changes in the lamellar topology can be observed. These range from the simple flow alignment of the lamellae to more complex processes such as the formation of structural defects.16,17 Although well documented and reported in several systems, the shear-induced formation of multilamellar vesicles, MLVs, is still a subject of considerable research not only from the fundamental point of view, where the mechanism and driving force of formation are still under debate, but also from the consideration of applications, where these closed packed objects can work as microreactors18,19 and encapsulate drugs or relevant biological material.20-22 The shear rate controls the size of MLVs.16 When shear is increased, layers are stripped off, decreasing the size of MLVs but increasing their number density, and the total bilayer area can be considered to be as a conserved quantity.23 Because the size of MLVs may vary from hundreds of nanometers to tens of micrometers, several techniques have been used to determine their dimensions, including common microscopy,16,23,24 freeze-fracture electron microscopy,25 and scattering
*Corresponding author. E-mail:
[email protected]. (1) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999. (2) Butler, P. Curr. Opin. Colloid Interface Sci. 1999, 4, 214. (3) Plano, R. J.; Safinya, C. R.; Sirota, E. B.; Wenzel, L. J. Rev. Sci. Instrum. 1993, 64, 1309. (4) Nakatani, A.; Waldo, D. A.; Han, C. C. Rev. Sci. Instrum. 1992, 63, 3590. (5) kalus, J.; Neubauer, G.; Schemlzer, U. Rev. Sci. Instrum. 1990, 61, 3384. (6) Fuller, G. G. Annu. Rev. Fluid. Mech. 1990, 22, 387. (7) Fuller, G. G. Optical Rheometry of Complex Fluids; Clarendon: Oxford, U.K., 1995. (8) Samulski, E. T. Polymer 1985, 26, 177. (9) Nakatani, A. I.; Poliks, M. D.; Samulski, E. T. Macromolecules 1990, 23, 2686. (10) Nakatani, A. I.; Samulski, E. T. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1986, 27, 169. (11) Callaghan, P. T. Rep. Prog. Phys. 1999, 62, 599. (12) Callaghan, P. T. Rheo-NMR: A New Window on the Rheology of Complex Fluids; John Wiley and Sons: Chichester, U.K., 2002; Vol. 9. (13) Schmidt, C. Rheo-NMR Spectroscopy. In Modern Magnetic Resonance; Webb, G. A. et al., Ed.; Springer: New York, 2006; Vol. 3.
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(14) Mortensen, K. Curr. Opin. Colloid Interface Sci. 2001, 6, 140. (15) Berni, M. G.; Lawrence, C. J.; Machin, D. Curr. Opin. Colloid Interface Sci. 2002, 98, 217. (16) Diat, O.; Roux, D.; Nallet, F. J. Phys. II 1993, 3, 1427. (17) Diat, O.; Roux, D.; Nallet, F. Phys. Rev. E 1995, 51, 3296. (18) Meyre, M.-E.; Lambert, O.; Desbat, B.; Faure, C. Nanotechnology 2006, 17, 1193. (19) Bernheim-Grosswasser, A.; Ugazio, S.; Gauffre, F.; Viratele, O.; Mahy, P.; Roux, D. J. Chem. Phys. 2000, 112, 3424. (20) Mignet, N.; Brun, A.; Degert, C.; Delord, B.; Roux, D.; Helene, C.; Laversanne, R.; Francois, J. C. Nucleic Acids Res. 2000, 28, 3134. (21) Pott, T.; Roux, D. FEBS Lett. 2002, 511, 150. (22) Freund, O.; Mahy, P.; Amedee, J.; Roux, D. J. Microencapsulation 2000, 17, 157. (23) Medronho, B.; Fujii, S.; Richtering, W.; Miguel, M. G.; Olsson, U. Colloid Polym. Sci. 2005, 284, 317. (24) Leon, A.; Bonn, D.; Meunier, J.; Al-Kahwaji, A.; Greffier, O.; Kellay, H. Phys. Rev. Lett. 2000, 84, 1335. (25) Gulik-Krzywicki, T.; Dedieu, J. C.; Roux, D.; Degert, C.; Laversanne, R. Langmuir 1996, 12, 4668.
Published on Web 12/01/2009
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techniques.16,26-30 Previous rheo-NMR investigations have considered the qualitative changes in line shapes and widths that occur during the processes of vesicle formation30-32 and destruction32 and that accompany the size changes of MLVs. More recently, Lutti et al. using pulsed gradient NMR diffusometry were able to determine the dimensions of MLVs in situ under shear.33 In this letter, the 2H NMR line shapes of heavy water in MLV systems are analyzed quantitatively on the basis of the classical two-step model of NMR relaxation.34-36 Because the molecular reorientation dynamics of confined or assembled molecules is strongly dependent on the aggregate size and shape, relaxation data can be used to determine the aggregate size in self-assembled systems.37-41 The simple model proposed here explains the observed MLV line shapes and allows us to determine the MLV size, illustrating that rheo-NMR can be an alternative method of measuring the MLV dimensions in sheared lamellar systems.
Materials and Methods Sample Preparation. Triethylene glycol mono n-decyl ether (C10E3) and tetraethylene glycol mono n-dodecyl ether (C12E4), both with a purity higher than 99.8%, were purchased from Nikko Chemical Co. (Tokyo, Japan). Deuterium oxide (D2O) was obtained from Sigma Chemicals (Steinheim, Germany). Samples containing 40 wt % surfactant were prepared by weighing the desired amounts of surfactant and water into vials, mixing them in a vortex mixer, and centrifuging them in order to remove air bubbles. All samples were prepared with D2O as a probe for deuterium NMR spectroscopy. Deuterium NMR Spectroscopy. The 2H rheo-NMR experiments were carried out using a cylindrical Couette cell with 14 and 15 mm inner and outer diameters, respectively. This cell is integrated into an NMR probe for a wide-bore superconducting magnet. The axis of the shear cell is aligned parallel to the external magnetic field; that is, both the velocity gradient and flow direction are perpendicular to the magnetic field. Shear is applied by rotating the outer cylinder with an external motor located below the NMR magnet.42 The spectra were recorded with a Tecmag Apollo 300 MHz NMR spectrometer operating at the deuterium resonance frequency of 46.073 MHz. Spectra were obtained by Fourier transformation of the signal following a single pulse. Typically 4 to 16 scans were accumulated for each spectrum and a recycle delay of 1 s was used. The temperature of the sample was maintained constant with an accuracy of (0.2 °C using an air-flow system. (26) Courbin, L.; Delville, J. P.; Rouch, J.; Panizza, P. Phys. Rev. Lett. 2002, 89, 148305. (27) Nettesheim, F.; Zipfel, J.; Olsson, U.; Renth, F.; Lindner, P.; Richtering, W. Langmuir 2003, 19, 3603. (28) Bergenholtz, J.; Wagner, N. J. Langmuir 1996, 12, 3122. (29) Le, T. D.; Olsson, U.; Mortensen, K. Phys. Chem. Chem. Phys. 2001, 3, 1310. (30) M€uller, S.; B€orschig, C.; Gronski, W.; Schmidt, C.; Roux, D. Langmuir 1999, 15, 7558. (31) Lukaschek, M.; M€uller, S.; Hasenhindl, A.; Grabowski, D. A.; Schmidt, C. Colloid Polym. Sci. 1996, 274, 1. (32) Medronho, B.; Shafaei, S.; Szopko, R.; Miguel, M. G.; Olsson, U.; Schmidt, C. Langmuir 2008, 24, 6480. (33) Lutti, A.; Callaghan, P. T. J. Magn. Reson. 2007, 187, 251. (34) Wennerstrom, H.; Lindblom, G.; Lindman, B. Chem. Scr. 1974, 6, 97. (35) Wennerstrom, H.; Lindman, B.; Soderman, O.; Drakenberg, T.; Rosenholm, J. B. J. Am. Chem. Soc. 1979, 101, 6860. (36) Halle, B.; Wennerstrom, H. J. Chem. Phys. 1981, 75, 1928. (37) Jonstromer, M.; Nagai, K.; Olsson, U.; Soderman, O. J. Dispersion Sci. Technol. 1999, 20, 375. (38) Leaver, M.; Furo, I.; Olsson, U. Langmuir 1995, 11, 1524. (39) Leaver, M. S.; Olsson, U.; Wennerstrom, H.; Strey, R. J. Phys. II 1994, 4, 515. (40) Soderman, O.; Henriksson, U.; Olsson, U. J. Phys. Chem. 1987, 91, 116. (41) Skurtveit, R.; Olsson, U. J. Phys. Chem. 1992, 96, 8640. (42) Grabowski, D. A.; Schmidt, C. Macromolecules 1994, 27, 2632.
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For each series of experiments, reproducible initial conditions were achieved by filling the shear cell with the sample and increasing the temperature until the isotropic signal of the sponge phase was reached. The sample homogenization and adjustment of the magnetic field homogeneity (shimming) took place at around 49 °C for the C10E3-water system and at around 65 °C for the C12E4-water system under shear at a constant rate of 10 s-1. Under these conditions, the sponge phase, L3, is stable and the typical 2H NMR fingerprint is a narrow singlet. The temperature was then decreased slowly (0.5 °C/min) into the region where the lamellar phase is stable and then MLVs were generated by shear. Typically, 2 h was enough to reach the steady state, which was determined by monitoring the time evolution of the 2H line shape.
Results and Discussion In Figure 1, we present the 2H NMR line shapes obtained for a sheared sample at three different temperatures corresponding to three different bilayer structures in the C10E3-water system. The different bilayer structures are illustrated in the Figure. At 49 °C, in the sponge phase, the system forms a multiply connected bilayer structure for which a narrow singlet is obtained (Figure 1, top). At 42 °C planar bilayers are stable; this results in a lamellar phase that is oriented by shear flow in the so-called c orientation where the bilayer normal points in the direction of the velocity gradient, which in the present Couette cell is perpendicular to the external magnetic field. This structural anisotropy results in a quadrupolar splitting of ΔνQ = 670 Hz (Figure 1, middle). Finally, when the sample is sheared at 25 °C the lamellae are arranged in multilamellar vesicles (MLVs) for which the NMR spectrum again consists of a singlet, but with a line width significantly larger than that of the sponge phase (Figure 1, bottom). The difference between the line widths of the sponge and MLV states is mainly due to the difference in the local bilayer principal curvature, as illustrated in Figure 1. Water molecules are perturbed by the bilayer interface, at which they have a preferred orientation. They exchange rapidly with the locally isotropic bulk, but there still remains a residual anisotropy that gives rise to the quadrupolar splitting in the planar lamellar state. This residual anisotropy can be averaged to zero if the interface is curved so that all orientations of the interface normal with respect to the external magnetic field can be experienced. In the sponge phase, the structural length scale is ξ ≈ 1.5δ/φ, where φ = 0.44 is the bilayer volume fraction and δ = 3 nm is the bilayer thickness, yielding ξ ≈ 10 nm.43 The MLV radius, however, is approximately 2 orders of magnitude larger. Hence, water molecules confined within one of the outer layers of the MLVs need a much longer time to experience, by diffusion, all local orientations of the bilayer than in the sponge phase, where the structural length scale is much smaller. As a consequence, the line width is much smaller in the sponge phase. Shear is known to be a controlling parameter of MLV size. The radius has been found to scale approximately as RMLV ≈ γ_ 1/2 in many systems, where γ_ denotes the shear rate.16,30 In Figure 2, we present a set of spectra obtained from the C10E3 system at _ As γ_ increases, the resonance lines become different values of γ. narrower, indicating that the line width is indeed sensitive to variations in RMLV. The line shape from the MLV state can be modeled in a more detailed but still simple way. If the exchange of water molecules between the different layers is slow (residence time in one layer much longer than the inverse of the line width) and if, for any (43) Cates, M. E.; Roux, D.; Andelman, D.; Milner, S. T.; A., S. S. Europhys. Lett. 1988, 5, 733.
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each corresponding to an individual water layer, n. Here, T2,n is the transverse relaxation time, T2, associated with layer number n, and ν0 is the resonance frequency. The Lorentzians will have different line widths because the layers have different radii, Rn, and they will have different weights, fn, in the sum because the layers contain different numbers of water molecules, depending on their radius. The sum runs up to n = N, where N is the total number of layers. Assuming a constant bilayer spacing, d, the MLV radius is given by RMLV = Nd and we have fn ≈ Rn2 = n2d2. The molecular motions responsible for the relaxation are the fast local reorientational motions that on the average are slightly anisotropic because of the presence of the bilayer interface and the slow isotropic reorientation associated with the diffusion of water molecules within the spherical water layer. This separation of timescales was recognized by Wennerstr€om and co-workers, who developed the so-called two-step model of NMR relaxation.34-36 The residual anisotropy remaining after partial averaging by the fast motions is quantified by an order parameter, S, that can be obtained from the quadrupolar splitting in the lamellar phase34 ΔνQ ¼
3 jχSj 4
ð2Þ
Here, χ is the quadrupolar coupling constant. The 2H line width in the MLV state is much larger than in the sponge phase. This tells us that the transverse relaxation is mainly due to the slow motion and that it is sufficient to consider the zero-frequency spectral density of the slow motion, js(0), in the expression for T2 so that 1 9π2 jχSj2 js ð0Þ ¼ T2 40
2
Figure 1. Experimental H NMR line shapes of D2O in the C10E3-water system for three different lamellar topologies: (a) a sponge phase at 49 °C under constant shear at a rate of 10 s-1, (b) an aligned lamellar phase prepared at 42 °C and 0.1 s-1, and (c) shear-induced MLVs at 10 s-1 and 25 °C. A schematic picture of each structure is shown together with the radius of curvature.
If the slow reorientation of water molecules is due to diffusion within a spherical shell of radius R, then we have js ð0Þ ¼
R2 3D
given vesicle shell, the reorientational motion due to lateral diffusion is in the motional-narrowing regime (line width , ΔνQ), then the NMR spectrum is given by a sum of Lorentzian functions LðνÞ ¼
N X n ¼1
fn
2T2, n 1 þ 4π2 ðν -ν0 Þ2 T2, n 2
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ð1Þ
ð4Þ
where D is the diffusion coefficient. With eqs 2 and 4 in eq 3, we now have a simple expression for T2,n 1 2ΔνQ 2 d 2 2 1 n þ ¼ T2, n T2, inhom 15D
Figure 2. Set of experimental NMR spectra from MLVs of the C10E3-water system prepared at different rates: 40 ( 3 3 3 ), 20 (-), and 10 s-1 (---).
ð3Þ
ð5Þ
Here, we have also introduced a constant term, 1/T2,inhom = πΔν1/2,inhom, to take into account the effect of magnetic field inhomogeneity on the line shape. The added line width at half height, Δν1/2,inhom, is taken as the line width, 30 Hz, of the resonance obtained from the sponge phase at higher temperature and was further assumed to be independent of temperature. With eq 5 in eq 1, we now have the final expression for the line shape that can be compared with experiments. If ΔνQ, d, and D are known, then the only free parameter is N or RMLV = Nd. Using this model, NMR spectra were calculated and compared with experiment. In the calculations, we have used D = 10-9 m2 s-1 for both systems. Also, the d spacing is the same in the two systems, d = 6.5 nm. The quadrupolar splittings are 670 Hz in the C10E3 system and 576 Hz in the C12E4 system. In Figure 3, we present experimental 2H NMR spectra from MLVs prepared at different shear rates for the C10E3-water (left column) and C12E4-water (right column) systems. In each case, we also compare with a computed spectrum, calculated using eqs 1-5. In the calculations, RMLV was varied until reasonable agreement with experiment was obtained, as judged by eye. DOI: 10.1021/la903682p
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Figure 3. Experimental 2H NMR spectra (-) of shear-induced MLVs at different rates for the C10E3-water (left column) and C12E4-water (right column) systems and their corresponding best fits (---) obtained as weighted sums of Lorentzian functions from the different shells.
As can be seen in Figure 3, the agreement between experimental and calculated spectra is good, however, with a minor systematic deviation. For the best fit, the simulated spectrum is narrower in the central part and broader at the wings of the band. The central and the wide parts can be fitted individually to give a sort of error bar. One contribution to the systematic deviation may be that we underestimate Δν1/2,inhom because this contribution is estimated to be 49 °C but the line-shape analysis is performed at 25 °C. Another contribution may arise if the simplifying assumption that the water molecules remain confined to a single layer during the experimental timescale is not fulfilled. The lifetime, τ, of a water molecule within a given layer is approximately given by τ ¼
dw 2P
ð6Þ
where dw ≈ 3.5 nm is the water layer thickness and P is the water permeability of the bilayer, which for phospholipid bilayers has values of 10-6-10-5 m/s.44,45 With these values, we estimate τ ≈ 1 ms. This is about an order of magnitude lower than the inverse of a typical line width, and we therefore expect some exchange of water, typically among 10 water layers (cf. N ≈ 200), on the timescale of the experiment. This “smearing” effect is larger among the inner layers, partially because the line width is smaller (44) Lasic, D. D. Liposomes: From Physics to Applications; Elsevier: Amsterdam, 1993. (45) Engelbert, H. O.; Lawaczeck, R. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 754.
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Figure 4. Radius of the MLVs, RMLV, determined from the lineshape simulation as a function of the shear rate for (top) C10E3-water and (bottom) C12E4-water systems. The MLV radii obtained from previous rheo-small-angle light scattering are shown for comparison.
and partially because the relative radius difference, (Rnþ1 - Rn)/ Rn, is larger, with a larger relative difference in T2. Hence, the exchange of water between adjacent layers is expected to broaden the narrower contributions to the resonance. The model can also be extended to include this smearing effect, but for simplicity, we neglect this here, as we have also neglected the size polydispersity of the MLVs. In Figure 4, we have plotted the obtained MLV radius as a function of the shear rate for both the C10E3 system (Figure 4a) and the C12E4 system (Figure 4b). Here we also compare with sizes determined previously using small-angle light scattering, SALS.23,30 As can be seen, the two methods agree reasonably well. In the SALS experiments, the MLV sizes are obtained at lower shear rates from the form factor maximum, whereas at higher shear rates they are estimated from a structure factor peak. The difference in size, obtained from the two methods, is at most ca. 30%, and we conclude that the simple model described here can be applied to analyze rheo-NMR data from MLVs and related systems. In summary, we present a simple model describing the 2H line shape of water in MLV systems, from which the MLV size can be determined. Good agreement with the experimental line shape is obtained, and the MLV sizes determined with this method are also in reasonable agreement with sizes determined earlier using SALS. NMR relaxation is one method of determining aggregate sizes of self-assembled colloids. Because rheo-NMR has recently become commercially available, NMR relaxation experiments may become useful for determining transient and steady-state structures and structural transformations under shear. Another issue that was not dealt with here (because the water lateral Langmuir 2010, 26(3), 1477–1481
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diffusion is fast) concerns the rotation of colloidal objects in shear flow. Because NMR relaxation, in principle, probes reorientational motion, such experiments can be of particular interest for studying the dynamics of colloidal particles in shear flow. Acknowledgment. This work was supported by grants from the Swedish Research Council (VR), the Swedish Foundation for International Cooperation in Research and Higher Education
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(STINT), and the German Academic Exchange Service (DAAD). The Colloid Group in Coimbra University is supported by grants from the Fundac-~ao para a Ci^encia e Tecnologia (FCT) (project refs POCTI/QUI/45344/2002 and POCTI/QUI/58689/2004). B.M. thanks the Fundac-~ao para a Ci^encia e Tecnologia (FCT) (project ref SFRH/BD/21467/2005). We are grateful to Dr. Luis Pegado, Prof. Alberto Canelas Pais, and Dr. Jo~ao Almeida for their help with Matlab.
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