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Self-Assembly of Organic Monolayers below the Freezing Threshold Lutz Wiegart,† Sean M. O’Flaherty,‡ Saskia Schmacke, § Henri Gleyzolle,† and Bernd Struth*,
European Synchrotron Radiation Facility (ESRF), B.P. 220, 38043 Grenoble, France, ‡Oxford Instruments :: :: Americas, 945 Busse Road, Elk Grove Village, Illinois 60007, §Fakultat Physik/DELTA, Technische Universitat Dortmund, Maria-Goeppert-Mayer Str. 2, D-44227 Dortmund, Germany, and HASYLAB at DESY, Notkestrasse 85, Hamburg, Germany )
†
Received December 5, 2008. Revised Manuscript Received February 11, 2009 One measure that arctic fish and amphibians use to minimize damage to cellular membranes during cooling and freezing processes is the production of cryo-protective substances. We have mimicked this biological “trick” by using the surface of a cryo-protectant as a liquid subphase for the preparation of organic membranes. Following this innovative approach, quasi two-dimensional amphiphilic monolayers were cooled to -40 C at a liquid/gas interface. To date, the low temperature region of the generic phase diagram for alkane chain molecules has been only “virtually” accessible by tuning the molecular chain length. By extending the temperature range well below the freezing point of water, we gained new insights into membrane stability, morphology, and reorganization at low temperatures. Upon cooling relaxed monolayers at a surface pressure of 4.5 mN/m, we find a transition from a mesophase with tilted chains at ambient temperature toward a crystalline phase with upright chains at low temperatures. Structure factor calculations reveal that the chain alignment in the crystalline phase differs from the classical herringbone configuration.
Introduction Low temperature phases of organic monolayers such as fatty acids at the liquid/gas interface are widely explored via tuning of the alkane chain length of the amphiphilic molecules.1 The generic phase diagram for long chain fatty acids2 is based on the concept that the increasing length of the alkane chain, more precisely an increase of the number of methylene (CH2) groups, leads to an upward shift of the temperature axis.3 However, due to the common use of water or water based buffers as a subphase, there are only few studies extended to low temperatures marginally below 0 C.4 In the present work, we aim to investigate the selfassembly, phase behavior, and morphology of a fatty acid organic membrane far below the freezing point of pure water. Extending the lower limit of the temperature range is possible by using a cryo-protective subphase. Dimethyl sulfoxide (DMSO), which is widely exploited in cryobiology to preserve tissues and cells during cooling and vitrification,5 was used as our cryo-protector. The subphase, an eutectic mixture of DMSO and water, exists in a liquid phase to below -60 C.6 The membrane molecule under investigation was eicosanoic acid, consisting of a single, saturated C19 carbon chain attached to a hydrophilic carboxyl headgroup. Contrary to conventional Langmuir techniques, no mechanical compression was applied to the membranes. Morphology and phase behavior were thus exclusively studied as a response to the change in molecular interactions provoked by shifting the energy equilibrium of the system via the temperature. The physical characteristics of the membrane were monitored by means of surface sensitive grazing incidence X-ray *Corresponding author. E-mail:
[email protected]. (1) Knobler, C. M.; Desai, R. C. Annu. Rev. Phys. Chem. 1992, 43, 207–236. (2) Kaganer, V. M.; Peterson, I. R.; Kenn, R. M.; Shih, M. C.; Durbin, M.; Dutta, P. J. Chem. Phys. 1995, 102, 9412–9422. (3) Bibo, A. M.; Peterson, I. R. Adv. Mater. 1990, 2, 309–311. (4) Durbin, M. K.; Malik, A.; Richter, A. G.; Ghaskadvi, R.; Gog, T.; Dutta, P. J. Chem. Phys. 1997, 106, 8216–8220. (5) Gordeliy, V. I.; Kiselev, M. A.; Lesieur, P.; Pole, A. V.; Teixeira, J. Biophys. J. 1998, 75, 2343–2351. (6) Rasmussen, D.; Mackenzie, A. Nature (London) 1968, 220, 1315–1317.
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diffraction (GIXD)7,8 and grazing incidence diffuse X-ray scattering (GIXOS), with the latter technique providing information similar to specular reflectivity with the advantage of much shorter acquisition times.9
Materials and Methods Eicosanoic acid (CH3(CH2)18COOH, CAS 506-30-9) was used as purchased from Sigma Aldrich in solution with chloroform at a concentration of 0.6 mmol/L. Monolayers were prepared by spreading this solution on the liquid surface using a Hamilton microliter syringe. Dimethyl sulfoxide (DMSO, (CH3)2SO, CAS 67-68-5) in a 68.1/31.9% w/w mixture with ultrapure water (Elga Purelab Classic) was employed as the liquid subphase. The surface pressure of the monolayers during the spreading and accompanied relaxation process was monitored by means of a conventional tensiometer (Nima ST 9005) using a paper Wilhelmy plate. Relaxed monolayers (surface pressure stable over ∼30 min) were prepared at a surface pressure of 4.5 mN/m in a specifically designed sample chamber, consisting of an inner cell containing the 68 mm diameter trough for the sample and an outer cell providing an insulation vacuum from the environment. The inner sample chamber was flushed with helium gas to minimize parasitic air scattering. At low temperatures, cold helium gas was transferred from a liquid helium dewar via a vacuum insulated pipe in order to avoid temperature gradients between the liquid surface and the ambient atmosphere in the inner cell. Cooling of the trough containing the sample was achieved by Peltier elements. The temperatures of the sample and the helium atmosphere were monitored by Pt100 temperature sensors, and the Peltier elements were controlled by a PID controller. Grazing incidence diffuse scattering and diffraction experiments were performed at beamline ID10B (ESRF, France) using an X-ray energy of 8.004 keV (λ = 1.5490 A˚). The incident angle on the liquid surface was adjusted to 2.094 mrad, corresponding to about 80% of the subphase’s critical angle for total external reflection. The X-ray signal was recorded with a 150 mm long position sensitive linear (7) Kuzmenko, I.; Rapaport, H.; Kjaer, K.; Als-Nielsen, J.; Weissbuch, I.; Lahav, M.; Leiserowitz, L. Chem. Rev. 2001, 101, 1659–1696. :: (8) Kaganer, V. M.; Mohwald, H.; Dutta, P. Rev. Mod. Phys. 1999, 71, 779–819. (9) Wiegart, L.; Struth, B.; Tolan, M.; Terech, P. Langmuir 2005, 21, 7349–7357.
Published on Web 4/17/2009
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detector. For the GIXD measurements, the beam was collimated before the detector by a Soller collimator, while for the measurements of the diffuse scattering (GIXOS) a pair of vertical slits separated by a 680 mm long flight path were used.
Results and Discussion The evolution of the layer structure of the fatty acid film during cooling provides first insights into its stability at low temperatures and temperature induced morphological changes. The diffuse scattering signal was therefore recorded in a GISAXS-like geometry10 at a small, constant in-plane angle as a function of the wavevector transfer qz perpendicular to the sample surface. The diffuse scattering from the monolayer at the liquid surface contains the oscillations caused by changes in the electron density contrast along the surface normal11 and allows thus the reconstruction of the electron density profile. Figure 1 shows the GIXOS spectra obtained for an eicosanoic acid monolayer at a surface pressure of 4.5 mN/m for temperatures between 22 and -20 C. The samples were cooled at a rate of 0.5 C/min, and sufficient time was allowed for all monitored temperatures to reach a steady state prior to data acquisition. The mathematical formalism describing the diffuse scattering signal has been addressed elsewhere.9 The signal is proportional to conventional specular reflectivity, divided by the Fresnel reflectivity and multiplied by the respective transmission functions12 for the grazing incidence geometry. The reflectivity has been calculated according to the Parratt algorithm.13 The fatty acid monolayer was modeled within this framework using a single layer approximation which represents both the rather small carboxyl headgroup and the alkane chains. In particular, no subphase layering, DMSO adsorption, or intercalation of DMSO within the alkane chains was allowed to minimize the number of parameters to be refined. The GIXOS spectra show no indication of surfactant induced freezing of the subphase, which is observed, for example, for alcohol monolayers on supercooled water14 and which could become noticeable via a significant increase of the surface roughness. The shift of the peaks in the GIXOS spectra toward lower wavevector transfers qz with decreasing temperature points toward a decreasing tilt angle between the alkane chain and the surface normal. The parameters obtained from the fit of the GIXOS spectra are summarized in Table 1. δ/δsub denotes the electron density δ of the layer normalized to the electron density δsub of the subphase calculated according to ref 15. The layer thickness and the roughness of the monolayer/gas interface are denoted as d and σmon/gas, respectively. The roughness σsub/mon of the subphase/monolayer interface is about 3.3 A˚ for all curves. The values reported in Table 1 show a general trend toward an increasing layer thickness and a simultaneously decreasing electron density upon cooling. Recalling the preparation technique used for the monolayer and the absence of mechanical compression, it is evident that, averaged over the rather large footprint area seen by the detector, the number of molecules in the layer and thus the product of layer thickness and electron density should be constant. The latter is reported in the last column of Table 1, showing only marginal variations from the average value of 16.01 A˚, except at -20 C where this ratio is seen to increase to 17.4. However, diffraction data, discussed below, reveal an intact (10) Fradin, C.; Braslau, A.; Luzet, D.; Smilgies, D.; Alba, M.; Boudet, N.; Mecke, K.; Daillant, J. Nature (London) 2000, 403, 871–874. (11) Sinha, S. K. J. Phys. III 1994, 4, 1543–1557. (12) Vineyard, G. H. Phys. Rev. B 1982, 26, 4146–4159. (13) Parratt, L. G. Phys. Rev. 1954, 95, 359–369. (14) Popovitzbiro, R.; Wang, J. L.; Majewski, J.; Shavit, E.; Leiserowitz, L.; Lahav, M. J. Am. Chem. Soc. 1994, 116, 1179–1191. (15) http://www.ncnr.nist.gov/resources/sldcalc.html.
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Figure 1. Measured GIXOS spectra (open symbols) and fits to a one-box model (solid lines) for an eicosanoic acid monolayer on a DMSO/water subphase at temperatures of 22 C (a), 10 C (b), 5 C (c), 0 C (d), -5 C (e), -10 C (f ), and -20 C (g). Spectra are shifted along the y-axis for clarity. The dashed line is intended as a guide to the eye to look approximately along the shifting position of the maximum. Table 1. Parameters Obtained by Fitting the Spectra Shown in Figure 1a δ/δsub
T [C]
d [A˚]
σmon/gas [A˚]
δ/δsub d1 [A˚]
22 (a) 0.896 18.06 2.3 16.18 10 (b) 0.855 18.74 2.6 16.02 5 (c) 0.849 18.74 2.6 15.91 0 (d) 0.852 18.55 2.6 15.80 -5 (e) 0.846 18.84 2.5 15.94 -10 (f ) 0.845 19.19 2.5 16.21 -20 (g) 0.850 20.47 2.3 17.40 a The fit parameters of the layer describing the eicosanoic acid monolayer are the electron density normalized to the one of the subphase, δ/δsub, the layer thickness d, and the rms roughness at the monolayer/gas interface σmon/gas. The roughness σsub/mon of the subphase/monolayer interface is 3.3 A˚ for all curves. The product δ/δsub d is calculated to check the conservation of the electron density within the layer as explained in the text.
Table 2. Positions of the Observable In-Plane Reflections in the Weakly Ordered Mesophase at 22C and in the Crystalline Phase As Shown in Figures 2 and 3 T [C] qxy [A˚-1] qxy [A˚-1] qxy [A˚-1]qxy [A˚-1]qxy [A˚-1] qxy [A˚-1] qxy [A˚-1] 22 -20 -40
1.436 1.510 1.517
1.476 1.693 1.705
2.500 2.515
2.829 2.847
3.019 3.038
3.383 3.408
3.865
monolayer at even lower temperatures. Despite the above-discussed limitations of the model, the increase in layer thickness by 2.4 A˚ corresponds exactly to the reduction of the tilt angle of the alkane chains found in the diffraction experiments described below. Primed with knowledge concerning the formation of stable monolayers at low temperatures, their in-plane structure was investigated using GIXD. At ambient temperature, the diffraction pattern was restricted to two broad reflections of lowest order, indicative of a weakly ordered rectangular mesophase (see inset in Figure 2). The reflections are centered around qz = 0 A˚-1 and qz = 0.597 A˚-1 leading to a tilt angle of the alkane chain of t = 25.9 and an alkane chain cross section A^ = 19.54 A˚2. The structure found here on the DMSO/water subphase is therewith comparable to the one reported by Peterson et al.16 on (16) Peterson, I. R.; Kenn, R. M.; Goudot, A.; Fontaine, P.; Rondelez, F.; Bouwman, W. G.; Kjaer, K. Phys. Rev. E 1996, 53, 667–673.
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pure water at 24.4 C and a surface pressure of 4.8 mN/m (t = 26.8, A^ = 19.575 A˚2). The lateral correlation length ξ can be calculated from the fwhm Δqxy of the in-plane diffraction peaks (ξ = 0.9 2π/Δqxy, with the wavevector transfer qxy parallel to the surface plane),17 and it was about 20 nm for the mesophase at 22 C. Upon reaching temperatures marginally below 0 C, a distinct change in the diffraction pattern was observed consisting of a significant increase of the peak intensities and a sharpening of the diffraction peaks, indicative of a crystalline phase. The number of observable reflections increased from six at -20 C (see diffraction pattern in Figure 2) to seven upon further cooling to -40 C (see Figure 3). The in-plane peak positions of the data presented in Figures 2 and 3 are reported in Table 2. The diffraction peaks shown in Figure 3 are obtained by integrating along the qz direction in the interval 0 e qz e 0.1 A˚-1. Bragg rod analysis9,18 was employed to determine the tilt angle of the alkane chains with respect to the surface normal and the tilt direction within the 2d lattice whichs exhibit a rectangular unit cell over the entire temperature range. Upon cooling, the tilt angle of the alkane chain reduces from 25.9 to 0 in accordance with the increasing monolayer thickness found in the diffuse scattering measurements. At 22 C, the tilt direction of the chains is toward the nearest neighbor (n.n.) which changes to the next nearest neighbor (n.n.n.) direction upon cooling to 10 C. Both phases exhibit rather broad mesophase-like diffraction peaks. At 0, two phases were identified in the diffraction pattern, one with broad diffraction peaks and n.n.n. tilt direction and one with sharp diffraction peaks, as in a crystalline phase, and n.n. tilt direction. Upon further cooling, the tilt angle of the latter phase was reduced to 0, while the mesophase with n.n.n. tilt direction disappeared. Along with the appearance of the two phases at 0 C, the unit cell area is discontinuously decreased as at the rotator-crystalline phase transition in normal bulk alkanes.19 It is noteworthy that although the phase transition toward a crystalline phase occurs around the freezing point of water, the formation of ice crystallites as the origin of the observed reflections can be ruled out both from their position and intensity distribution in reciprocal space. The transition temperature found in this study is not supposed to be generic but to vary as a function of the strength of molecular interactions, determined, for example, by the length of the alkane chains. In particular, a lower temperature found for a similar transition in phospholipid monolayers of DPPA20 suggests the importance of molecular interactions rather than a subphase peculiarity around 0 C. At -40 C, traces of a tilted mesophase, like the one observed at 0 C, were found in the low qxy region in addition to the {11} and {02} reflections of the crystalline phase (see inset of Figure 3 and Supporting Information Figure S1). Because of the Bragg rods of the {11} and {02} reflections both being centered at qz = 0 A˚-1, an assignment of these reflections to the same phase can be ruled out.21 The reappearance of a tilted mesophase at -40 C, which was not observed between -5 and -20 C, might be an indication that the crystalline domains grow via metastable mesophases, a kinetic process which is slower at lower temperatures and thus more likely to be observed at -40 C than at higher temperatures. A different explanation involves the formation of monolayer (17) Guinier, A. X-ray diffraction in crystals, imperfect crystals, and amorphous bodies; W.H. Freeman: San Francisco, 1963. (18) Als-Nielsen, J.; Kjaer, K. In Phase Transitions in Soft-Condensed Matter; Riste, T., Sherrington, D., Eds.; Plenum Press: New York, 1989; pp 113-138. (19) Doucet, J.; Denicolo, I.; Craievich, A. J. Chem. Phys. 1981, 75, 1523–1529. (20) Wiegart, L. Ph.D. Thesis, Universite Joseph-Fourier, Grenoble (France), 2007, http://tel.archives-ouvertes.fr/tel-00164719/fr/. (21) Wiegart, L.; Struth, B. Phys. B 2005, 357, 126–129.
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Figure 2. In-plane diffraction pattern for an eicosanoic acid monolayer at -20 C (peak intensities have been scaled for visibility, and lines connecting data points serve as a guide to the eye). Indexing of the diffraction peaks is in accordance with a centered rectangular lattice. Inset: the two in-plane reflections of lowest order observable at 22 C.
Figure 3. Reflections obtained at a sample temperature of -40 C. Inset: diffraction pattern for the low q-region resolved in qxy and qz. The {11} and {02} reflections of the crystalline phase were separated from the one of a tilted mesophase {11}meso (arrow) by integration in the region 0 e qz e 0.1 A˚-1.
phases with low packing densities in the voids between the crystalline domains. Such heterogeneities and phase coexistence could be a direct consequence of the absence of compression, leaving the average surface area per molecule unchanged, while the packing density in the crystalline domains is strongly increased. Due to the finite tilt angle at the rotator-crystalline phase transition, the phase sequence was identified as L2-L20 -L200 -CS22 (see Figure 4). The observation of the L200 -CS phase transition in our experiments suggests that for the temperature driven selfassembly the slope of the corresponding phase boundary (22) Riviere, S.; Henon, S.; Meunier, J.; Schwartz, D. K.; Tsao, M. W.; Knobler, C. M. J. Chem. Phys. 1994, 101, 10045–10051.
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Figure 4. Sketch of the low temperature region of the generic phase diagram according to Riviere et al.22 (solid lines). In accordance with the work of Bommarito et al.,33 the L2-L20 -L200 triple point for the relaxed monolayer corresponds to a surface pressure of π = 3.0 mN/m (compared to the 10-15 mN/m obtained by compression isotherms). The dotted arrow indicates the phase sequence identified in the presented study during cooling. Note that the temperature scale is abandoned, as our measurements were not made to identify the phase boundaries.
(sketched as a dashed line) is opposite to the one reported in the generic phase diagram obtained by compression isotherms.22,23 Although it was predicted by the original phase diagram for fatty acids,24 our measurements are the first observation of a phase transition upon cooling from tilted mesophases to an upright crystalline phase without applying mechanical compression to the monolayer. Measuring the peak width is limited by the resolution offered by the experimental setup and implies a correlation length of at least 120 nm for the crystalline domains at -40 C. This domain growth was induced by a temperature decrease only and can therefore be considered as an entropy-driven self-assembly process. The sharpening of the reflections was accompanied by a discontinuous decrease of the 2d unit cell area A0 (parallel to the surface plane) and an increase of the packing density within the monolayer. The evolution of the unit cell area per molecule from 21.72 A˚2 at 22 C to 18.45 A˚2 at -40 C is comparable to that found for bulk alkanes during the rotator-crystalline phase transition19 (see Figure 5). The low temperature phase exhibits a denser packing, characterized by the alkane chain cross section, than both that reported for eicosanoic acid on pure water in high pressure phases4 and that reported for normal alkanes in the bulk.19,25 Our analysis revealed alkane chain cross sections equivalent to those of 3d single crystals of similar fatty acids.26 The large number of reflections observed enabled structure factor calculations allowing the relative angle between the C-C planes of the two hydrocarbon chains and their absolute orientation within the nonprimitive rectangular unit cell to be determined. While for the diffraction pattern measured at -40 C the position of the {11} reflection can be well resolved by integrating over a small qz range, its intensity cannot be determined in a reliable way. Structure factor calculations were thus limited to the diffraction pattern measured at -20 C, where a sufficient number of reflections, originating exclusively from the crystalline phase, was observed. Calculations were performed with the relative intensities normalized on the {11} reflection. It was assumed that the alkane chains were in an all-trans conformation. Rather than attempting to fit individual atomic positions, the (23) Schwartz, D. K.; Knobler, C. M. J. Phys. Chem. 1993, 97, 8849–8851. :: (24) Stallberg-Stenhagen, S.; Stenhagen, E. Nature (London) 1945, 156, 239– 240. (25) Denicolo, I.; Doucet, J.; Craievich, A. F. J. Chem. Phys. 1983, 78, 1465– 1469. (26) Kaneko, F.; Sakashita, H.; Kobayashi, M.; Kitagawa, Y.; Matsuura, Y.; Suzuki, M. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1994, 50, 247–250.
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Figure 5. Upper panel: temperature dependent unit cell area per molecule (A0, open diamonds) and tilt angle (filled diamonds) for eicosanoic acid on DMSO/water. Area per molecule as a function of temperature for C21 bulk alkanes (open circles, data adopted from ref 19). Inset sketch: C-C plane orientation within the nonprimitive rectangular unit cell derived from structure factor calculations; arrows: orientation for herringbone packing (sketch not drawn to scale). Lower panel: comparison of the measured intensities (scaled for visibility) with the ones calculated for the classical herringbone ordering and for the optimized chain alignment.
orientation of the C-C planes of the two alkane chains were varied resulting in a very small number of free parameters.20 For a nonprimitive rectangular unit cell containing two upright alkane chains, these free parameters are as follows: the Debye-Waller factor mean displacement u, the chain twist angle Φ (defining the absolute alignment of the chains within the unit cell27), and the relative twist angle ΔΦ between the two chains (see inset in Figure 5). Good agreement between the calculated and the observed intensities for all reflections was obtained with a relative twist angle ΔΦ of about 90 between the C-C planes of the two alkane chains and twist angle Φ e 20 (see lower panel in Figure 5). The latter angle, which determines the absolute orientation of the molecules in the unit cell, is thus smaller than the 45 typically found for the herringbone ordering in crystalline phases of compressed Langmuir monolayers28 (see inset in Figure 5). However, better fitting of the peak intensities by the optimized chain alignment presented above is evident. This is supported by the R-value of the structure factor calculation, which for herringbone ordering is about 40% larger. The R-value was thereby defined as the sum of the R-values of the individual reflections: R = Σ|Iobs([h,k]) - Icalc([h,k])|/Iobs([h,k]), where Iobs and Icalc are the observed and the calculated intensities for the reflection with the set of Miller indices h and k, respectively, and the sum is extended over all sets of Miller indices [h,k]. The mean displacement u of the in-plane Debye-Waller factor Dhk = exp(-G2hku2), with the reciprocal lattice vector Ghk of the reflection with Miller indices h and k, was obtained as (27) Hautman, J.; Klein, M. L. J. Chem. Phys. 1990, 93, 7483–7492. (28) Kuzmenko, I.; Kaganer, V. M.; Leiserowitz, L. Langmuir 1998, 14, 3882– 3888.
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u = 0.18 ( 0.03 A˚. The determination of reliable peak intensities for the reflections at large in-plane wavevector transfers is hampered by the low count rates and the limited number of data points on the diffraction peaks. Nevertheless, our results point toward a chain alignment which differs from the classical herringbone ordering, being somewhat intermediate between herringbone and the parallel chain alignment reported by Pignat et al. for the high pressure phase of eicosanoic acid on ultrapure water.29 Possible origins for this derivation might arise from the particular preparation of the monolayer without any mechanical compression or an interaction between the carboxyl head and the DMSO molecules in the subphase. The structural evolution observed during the cooling process seems to be reversible: upon reheating the sample to ambient temperature, the same diffraction pattern as at the beginning of the cooling cycle was obtained. We have presented the first structural investigation of an organic monolayer at the liquid/air interface far below the freezing threshold of water. Insights into self-assembly and phase behavior at such low temperatures were made possible thanks to the novel approach of using cryo-protective subphases. It is apparent that the phase diagram, describing order and functionality of organic membranes, is extendable to very low tempera(29) Pignat, J.; Daillant, J.; Leiserowitz, L.; Perrot, F. J. Phys. Chem. B 2006, 110, 22178–22184.
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tures by using cryo-protective subphases. Besides the prevention of chain freezing, in which unsaturated alkane chain molecules play an important role,30,31 the inhibition of crystalline ice formation is a key issue for the preservation of intact cell membranes for low temperature extremophiles.32 Beyond the results presented in this study, the use of cryo-protective subphases may open new routes for the study of membrane and proteins relevant in this context. Acknowledgment. The authors thank the ESRF (Grenoble, France) for access to the X-ray beam. L. Wiegart acknowledges grants for a Ph.D. thesis from CEA Grenoble and the ESRF. Supporting Information Available: Plot showing the separation of the two diffraction peaks of the crystalline phase ({11}) and a tilted meso-phase ({11}meso) from the diffraction pattern shown in Figure 3. This material is available free of charge via the Internet at http://pubs.acs.org. (30) Tomczak, M. M.; Hincha, D. K.; Estrada, S. D.; Wolkers, W. F.; Crowe, L. M.; Feeney, R. E.; Tablin, F.; Crowe, J. H. Biophys. J. 2002, 82, 874–881. (31) Mod, R. R.; Skau, E. L. J. Phys. Chem. 1956, 60, 963–965. (32) Storey, K. B. Comp. Biochem. Physiol., Part A: Mol. Integr. Physiol. 1997, 117, 319–326. (33) Bommarito, G. M.; Foster, W. J.; Pershan, P. S.; Schlossman, M. L. J. Chem. Phys. 1996, 105, 5265–5284.
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