Experimental Confirmation of Transformation Pathways between

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Experimental Confirmation of Transformation Pathways between Inverse Double Diamond and Gyroid Cubic Phases Annela M. Seddon,†,‡ James Hallett,†,‡ Charlotte Beddoes,†,‡ Tomás S. Plivelic,∥ and Adam M. Squires*,§ †

H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom Bristol Centre for Functional Nanomaterials, Nanoscience and Quantum Information Building, University of Bristol, Tyndall Avenue, Bristol BS8 1FD, United Kingdom § School of Chemistry, Whiteknights Campus, University of Reading, Reading, Berkshire RG6 6AD, United Kingdom ∥ MAX IV Laboratory, Lund University, 22100 Lund, Sweden ‡

S Supporting Information *

ABSTRACT: A macroscopically oriented double diamond inverse bicontinuous cubic phase (QIID) of the lipid glycerol monooleate is reversibly converted into a gyroid phase (QIIG). The initial QIID phase is prepared in the form of a film coating the inside of a capillary, deposited under flow, which produces a sample uniaxially oriented with a ⟨110⟩ axis parallel to the symmetry axis of the sample. A transformation is induced by replacing the water within the capillary tube with a solution of poly(ethylene glycol), which draws water out of the QIID sample by osmotic stress. This converts the QIID phase into a QIIG phase with two coexisting orientations, with the ⟨100⟩ and ⟨111⟩ axes parallel to the symmetry axis, as demonstrated by small-angle X-ray scattering. The process can then be reversed, to recover the initial orientation of QIID phase. The epitaxial relation between the two oriented mesophases is consistent with topologypreserving geometric pathways that have previously been hypothesized for the transformation. Furthermore, this has implications for the production of macroscopically oriented QIIG phases, in particular with applications as nanomaterial templates.

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INTRODUCTION The gyroid and related triply periodic continuous structures are the subject of widespread fundamental research in both the physical and life sciences. They occur naturally, for example, in the exoskeletons of sea urchins,1 in butterfly wings,2 and as cellular structures and intermediates.3−6 They can also be formed synthetically, in systems including biological lipids,7 block copolymers,8 surfactants,9 and zeolites.10 Block copolymers11,12 and, more recently, lipids13 have been used as templates for metal deposition to form bicontinuous cubic nanowire networks. Such morphologies have been predicted to show unusual photonic or phononic metamaterial behavior such as negative refractive index.14 Metals with gyroid nanostructures produced using block copolymer templates have indeed shown novel and tunable optical properties.11,12 Biological lipids, in addition to the gyroid, form two further symmetries rarely observed in type I liquid crystals or diblock copolymers;15 these are the double diamond (QIID) and primitive (QIIP) phases. The three QII (inverse bicontinuous cubic) phases are shown in Figure 1. In each case, the lipid molecules form an intricately curved fluid bilayer, on either side of which lie two interpenetrating continuous networks of water channels.16 In particular, the QIID phase has recently been used as a template to produce bicontinuous cubic nanomaterials with single diamond morphology.13 Materials with single diamond morphology have been predicted to display exceptionally large photonic and phononic bandgaps.17,18 Although we are aware that these materials would have to have lattice parameters an order of magnitude © 2014 American Chemical Society

higher than lipid-derived structures in order to show photonic effects in the visible spectrum, we would nonetheless expect unusual or enhanced physical properties from lipid-templated nanomaterials with the same single diamond morphology. Due to the ease with which it is possible to access different bicontinuous cubic structures in addition to the gyroid, lipid systems represent attractive candidates for the fundamental understanding of these topologies and their interconversion,19 as well as for templating applications. However, one issue that needs to be addressed is the alignment of the nanostructure; light transmission has been shown to vary depending on the crystallographic orientation of the nanomaterial,11 and, in a polydomain nanomaterial that would be expected to be formed using a template with no overall orientation,13 internal domain boundaries may be expected to cause further complications.20 One part of the motivation for the work described in this Letter is to address the issue of macroscopic orientation in different lipid cubic phases, with implications for their use as templates. The interconversion of bicontinuous cubic materials and their underlying mathematical surfaces have been the subject of considerable theoretical research. Mechanisms for the QIID to QIIG transformation have also been studied extensively. The underlying triply periodic minimal surfaces (TPMS) lying at the center of the bilayer are topologically related by a mathematical Received: February 12, 2014 Revised: May 7, 2014 Published: May 8, 2014 5705

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EXPERIMENTAL METHODS

We prepared glycerol monooleate at a 40:60 w/v ratio in water and butanediol (60:40 v/v). The oriented QIID phase coating was produced using a process described in more detail in our previous paper.28 Briefly: into tubing connected to a syringe, we loaded 50 μL of this sample, separated by a 40 μL air gap from the water that filled the remainder of the tubing and the syringe itself. The tubing was connected to an X-ray capillary tube, and the sample was pushed into the capillary tube using the syringe pump until the interface between the air gap and the sample lay approximately in the beam position. A further oscillator flow was then set up with a flow rate of 10 μL/s and an amplitude of 50 μL. This was left for approximately 2 min during which time a coating of oriented QIID phase was deposited within the capillary tube. The process is shown schematically in Figure 1 of ref 29, which we have reproduced in the Supporting Information (S2). We have previously suggested that, as the sample−air interface repeatedly passes in front of the beam position, the sample is gradually deposited on the capillary wall; furthermore, as the air gap is smaller than the amplitude of the oscillatory flow, with each pass a little water is introduced into the sample, and a little butanediol is washed away, driving the transformation into the QIID phase. Finally, water is pushed into the capillary tube, to expel all remaining sample from the liquid in the middle of the tube, leaving only an oriented QIID coating that adheres to the capillary tube walls. We then replaced the water with a solution of 18% w/w solution of poly(ethylene glycol), PEG-6000, which dehydrated the sample and caused a QIID to QIIG transformation. In one experiment this was kept and analyzed in more detail, while in another the PEG was replaced by water, rehydrating the sample back to the QIID phase. SAXS experiments were carried out at beamline I911-4 at MAX IV Lab, University of Lund, with a beam size at the sample of 0.3 × 0.3 mm (full width at half-maximum, fwhm). The wavelength was 0.91 Å and data were collected over a q range of 0.006−0.18 Å−1. Images were recorded in a bidimensional CCD detector (165 mm diameter, from Marresearch, Inc.) over a range of exposure times between 30 and 60 s. For time series data, a 60 s gap was left between the collection of each image in the series. Azimuthal and radial plots were generated and analyzed using ImageJ with the YAXS macro code written in-house.28 The positions of the simulated peaks were calculated as described in the work of Squires et al.28

Figure 1. Different descriptions of the inverse bicontinuous cubic phases. Top: Skeletal graphs representing the centers of the water channels. Bottom: Skeletal graphs with surfaces that approximate the underlying triply periodic minimal surfaces lying at the center of the bilayer. The three inverse bicontinuous cubic phases shown are (from left) QIIG QIID and QIIP (crystallographic space groups Ia3d, Pn3m, and Im3m respectively). The two networks of rods and the two sides of the surface have been shaded differently for claritythe shading is not intended to represent any physical difference. Reproduced with permission from ref 19. Copyright 2005 American Physical Society.

process known as the Bonnet transformation, which preserves the Gaussian curvature, and angles, distances, and areas on the surface.21 Although this mechanism may in theory interconvert the TPMSs, in reality it is unlikely that transitions between actual QII phases occur via such a mechanism, because it would require regions of the bilayer to pass through one another.20 Nonetheless, the topological relationship suggests that it is possible in principle to find a pathway from one QII phase to another, while preserving the integrity of the bilayer throughout. Descriptions of such pathways have been developed in terms of the “skeletal graphs” describing the water channels,22,23 the minimal surfaces at the centers of the bilayer,24 or combinations of these.19 However, until now, the samples that have been employed in investigations of phase transitions in QII phases are bulk polydomain samples with no overall orientation. In this Letter, we demonstrate that studies of phase transformations between two oriented phases allow the determination of their relative orientation, which provides evidence for a specific mechanism of the transformation. The phase diagram of the lipid glycerol monooleate25 shows that it is possible to move from the QIID phase to the QIIG phase by reducing the relative hydration of the sample to below approximately 35% (w/w) water. Chung and Caffrey26 have demonstrated that this transition could be induced by the addition of an osmotic stressing agent, in that case high molecular weight poly(ethylene glycol) (PEG) above approximately 8% (w/w). In our previous work, we have successfully prepared highly oriented samples of the QIID phase using shear;27 as such, we hypothesized that subsequently dehydrating this oriented QIID phase in the absence of shear would lead to the formation of an a QIIG phase whose orientation relative to the preceding QIID phase should be consistent with a proposed mechanism of transformation between these phases.19 We also postulated that by rehydrating the sample, the oriented QIID phase could be recovered.

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RESULTS AND DISCUSSION We have previously shown that a macroscopically oriented QIID phase can be formed by dilution of a sponge (L3) phase under flow,27 and that the orientation can be selected with either the ⟨100⟩ or ⟨110⟩ axis aligned in the flow direction, depending on the flow conditions used.28 Here we began with a QIID phase of glycerol monooleate aligned about the ⟨110⟩ axis, prepared as in the work of Squires et al.28 The oriented sample adopted a QIID phase with lattice parameter a = 9.21 ± 0.04 nm, consistent with previously published phase behavior for glycerol monooleate.25 The 2-D pattern obtained from small-angle X-ray scattering (SAXS) confirms the sample orientation (Figure 2a), as we have previously demonstrated.28 We then induced a transformation into a QIIG phase by replacing the water with an 18% w/w solution of poly(ethylene glycol), PEG-6000, which has previously been shown to exert sufficient osmotic stress to dehydrate a glycerol monooleate sample into the QIIG phase.26 This QIIG phase also shows orientation (Figure 2b) that we argue reflects an epitaxial relationship with the QIID phase based on the pathway of the transformation. This will be discussed later. The experiment shown in Figure 2 was carried out reversibly, with water replaced by 18% w/w PEG solution, which was then replaced with water again, causing a transformation back into the QIID phase, which showed the same orientation as at the 5706

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orientation in an unoriented sample, and is comparable with the typical flow rate used to fill a capillary using a micropipet, for example, in our previously published control experiments on unoriented cubic phase films; the use of a single column of liquid prevents liquid−air interfaces from passing across the sample, which we have previously hypothesized induces orientation through a “combing” mechanism.28 In another experiment, the transformation was carried out in the QIIG phase, and the sample was kept in this state by keeping the capillary filled with PEG solution. The same Q IIG orientation was seen in both experiments (Figure 3b, compared to Figure 2b), demonstrating that the process is reproducible. The alignment was found to persist when the sample was analyzed several hours later. During this time, we obtained data with the beam passing tangentially (approximately parallel to the capillary wall) and radially (approximately perpendicular) as shown in Figure 3 by moving the capillary vertically across the beam, in order to rule out the alternative possibility that the QIIG phase orientation is due to the sample/capillary interface. The SAXS patterns demonstrated the same symmetry regardless of the direction of the beam relative to the capillary wall (Figure 3). The agreement demonstrates that the sample is uniaxially aligned about the initial flow direction (i.e., the capillary axis); all directions perpendicular to this axis are equivalent, whether they are parallel or perpendicular to the sample−glass interface. This indicates that the sample/capillary interaction, while sufficiently strong to prevent the lipid from being washed away, does not induce orientation relative to the capillary wall. We note that such out-of-plane orientation has been observed in GI-SAXS experiments, which were performed on much thinner samples (100 nm compared to approximately 10 μm in the present work) on a hydrophobically modified silicon substrate, in humidified air.29 Having demonstrated that the orientation in the QIIG phase arises from an epitaxial relationship with the preceding QIID phase, we now discuss analysis of the oriented QIIG scattering pattern. We model the peaks in the azimuthal plots of the √6, √8, √16, and √22 reflections assuming uniaxial orientation about the capillary axis, using an approach as described in detail in ref 28. The modeled peaks are shown as vertical dashed and dotted lines superimposed on the azimuthal plots in Figure 4. The pattern cannot be accounted for by a single orientation, but can by allowing two coexisting orientations, with the ⟨111⟩ and ⟨100⟩ axes aligned tangent to the capillary axis, i.e., the ⟨110⟩ axis of the preceding QIID phase. The azimuthal and

Figure 2. (a) 2D pattern of QIID coating in a capillary filled with water, at start of experiment. (b) 2D pattern of QIIG formed by replacing water with 18% (w/w) PEG-6000. (c) 2D pattern of QIID after PEG6000 solution was replaced with water again. (d) Stacked radial profiles, taken 60 s apart, beginning at the bottom with the QIID phase, moving upward through the QIIG phase to the final regeneration of the QIID phase.

start of the experiment (Figure 2c). The entire process was carried out with a single column of liquid passing from the syringe, through the plastic tubing and through the glass capillary tube, going from pure water to approximately 18% PEG and back to water again. (The 600 μL of aqueous solution represented a column of liquid 34 cm long, in a tube of diameter 1.5 mm, so any mixing within the time scale of the experiment was not sufficient to prevent the induction of the phase transitions between QIID and QIIG.) A time series of radial profile data for the entire process is shown in Figure 2d. This approach eliminates other potential influences that could cause orientation in the QIIG phase, to ensure that any orientation observed does indeed reflect an epitaxial relationship with the orientation of the preceding QIID phase: the flow rate of 0.5 μL s−1, corresponding to an average linear flow rate of approximately 0.3 mm s−1, is too low to itself induce

Figure 3. In order to test orientation relative to the capillary wall, scattering patterns were obtained with the beam passing tangentially (a) and radially (b). (c) shows a schematic depiction of the pathway of the beam relative to the capillary for each pattern in panels a and b. The corresponding azimuthal data are shown in the Supporting Information (S1). 5707

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Figure 4. Azimuthal profiles of the √6(a), √8(b), √16(c), and √22 (d) reflection of the oriented QIIG phase; vertical lines show simulated positions and approximate relative intensities of expected reflections assuming uniaxial orientation about a ⟨100⟩ axis (black dotted lines) and a ⟨111⟩ axis (red dashed lines), which is horizontal relative to the image in Figure 2b, corresponding to an azimuthal angle of 0 or 180 deg.

simulated plots in Figure 4 show that consideration of both of these orientations is necessary, and sufficient, to account for all of the reflections within the most prominent rings, at {211} (√6), {220} (√8), {400} (√16), and {332} (√20). In particular, the peaks at 0 and 180° in the √16 reflection cannot be accounted for by orientation about a ⟨111⟩ axis, while the peaks at approximately 10°, 170°, 190° and 350° cannot be accounted for by orientation about a ⟨100⟩ axis. Fogden, Hyde, and Schröder-Turk24,30 have described two different pathways that can potentially interconvert QIID and QIIG phases while keeping the surface at the center of the bilayer as a minimal surface that retains its integrity throughout. One of these−the tetragonal pathway−has also been described by Squires et al.19 in terms of the skeletal graph representation (for the centers of the water channels) and a linear combination of nodal surfaces (to approximate the bilayer midplane), and is shown in an animation in the Supporting Information. In this tetragonal pathway the unit cells are related to one another by a 45° rotation about a common ⟨100⟩ axis, shown as vertical in the figure. We can consider two groups of equivalent ⟨110⟩ axes in the QIID phase: those lying in a plane perpendicular to this axis (horizontal dashed lines), and those that do not (diagonal, dotted lines). The former group is converted into ⟨100⟩ directions in the QIIG phase, and the latter into ⟨111⟩ axes (Figure 5, right). Since they are all equivalent, there is no particular reason why the ⟨110⟩ axis of orientation in the initial QIID phase (i.e., the capillary axis) should be converted into one rather than the other, and it is likely that both occur. This is indeed what we observe in the experimental data. The second pathway described by Fogden and Hyde24 is the rhombohedral pathway proceeding via the QIIP structure. This is predicted to preserve the relative axes of the respective QIID and QIIG cubic unit cells30 so that a QIID phase aligned about a ⟨110⟩ would become a QIIG phase also aligned about a ⟨110⟩ axis. The predicted azimuthal peak positions for such a QIIG phase are shown in the Supporting Information (S3), and are clearly not consistent with our experimental data. This result is

Figure 5. A double diamond (left) is transformed into a gyroid (right). In the top left image, the thick black cubic frame shows the orientation of the diamond unit cells, while the shaded region shows the pretranslational gyroid unit cell, which transforms into the gyroid unit cell (shaded cube, top right). The four horizontal ⟨110⟩ directions in the double diamond are transformed into ⟨100⟩ directions in the gyroid (dashed lines), while the remaining eight are transformed into ⟨111⟩ directions (dotted lines). Bottom figures taken from19

consistent with theoretical work, suggesting that the tetragonal pathway is energetically more favorable than the rhombohedral one,30 lending additional support to the models employed to describe lipid bilayer membranes using minimal surfaces.

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CONCLUSIONS In conclusion, we have demonstrated experimentally for the first time the formation and epitaxial relationship between oriented QIID and QIIG phases of a lipid. The information we have presented here could only be obtained from macroscopically oriented samples, and not from bulk polydomain samples typically employed in investigations of lipid phase transitions,19 5708

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(9) Ulf, O.; Kell, M. Shear melting and orientation of a lyotropic cubic phase. J. Phys. II France 1995, 5 (6), 789−801. (10) Gier, T. E.; Bu, X. H.; Feng, P. Y.; Stucky, G. D. Synthesis and organization of zeolite-like materials with three-dimensional helical pores. Nature 1998, 395 (6698), 154−157. (11) Vignolini, S.; Yufa, N. A.; Cunha, P. S.; Guldin, S.; Rushkin, I.; Stefik, M.; Hur, K.; Wiesner, U.; Baumberg, J. J.; Steiner, U. A 3D optical metamaterial made by self-assembly. Adv. Mater. 2012, 24 (10), OP23−7. (12) Salvatore, S.; Demetriadou, A.; Vignolini, S.; Oh, S. S.; Wuestner, S.; Yufa, N. A.; Stefik, M.; Wiesner, U.; Baumberg, J. J.; Hess, O. Tunable 3D extended self-assembled gold metamaterials with enhanced light transmission. Adv. Mater. 2013, 25, 2713−2716. (13) Akbar, S.; Elliott, J. M.; Rittman, M.; Squires, A. M. Facile production of ordered 3D platinum nanowire networks with “single diamond” bicontinuous cubic morphology. Adv. Mater. 2012, 25, 1160−1164. (14) Hur, K.; Francescato, Y.; Giannini, V.; Maier, S. A.; Hennig, R. G.; Wiesner, U. Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks. Angew. Chem., Int. Ed. Engl. 2011, 50 (50), 11985−9. (15) Erukhimovich, I.; Kriksin, Y.; Ten Brinke, G. The diamond and other non-conventional morphologies in two-scale multiblock AB copolymers. Soft Matter 2012, 8 (7), 2159−2169. (16) Zabara, A.; Negrini, R.; Onaca-Fischer, O.; Mezzenga, R. Perforated bicontinuous cubic phases with pH-responsive topological channel interconnectivity. Small 2013, 9, 3602−3609. (17) Gorishnyy, T.; Maldovan, M.; Ullal, C.; Thomas, E. Sound ideas. Phys. World 2005, 18 (12), 24−29. (18) Maldovan, M.; Urbas, A. M.; Yufa, N.; Carter, W. C.; Thomas, E. L. Photonic properties of bicontinuous cubic microphases. Phys. Rev. B 2002, 65, 165123. (19) Squires, A. M.; Templer, R.; Seddon, J.; Woenkhaus, J.; Winter, R.; Narayanan, T.; Finet, S. Kinetics and mechanism of the interconversion of inverse bicontinuous cubic mesophases. Phys. Rev. E 2005, 72 (1), 011502. (20) Seddon, J. M.; Templer, R. H. Cubic phases of self-assembled amphiphilic aggregates. Philos. Trans. R. Soc. London, Ser. A: Phys. Eng. Sci. 1993, 344 (1672), 377−401. (21) Andersson, S.; Hyde, S.; Larsson, K.; Lidin, S. Minimal surfaces and structures: From inorganic and metal crystals to cell membranes and biopolymers. Chem. Rev. 1988, 88 (1), 221−242. (22) Sadoc, J. F.; Charvolin, J. Infinite periodic minimal-surfaces and their crystallography in the hyperbolic plane. Acta Crystallogr., Sect. A 1989, 45, 10−20. (23) Benedicto, A. D.; O’Brien, D. F. Bicontinuous cubic morphologies in block copolymers and amphiphile/water systems: Mathematical description through the minimal surfaces. Macromolecules 1997, 30 (11), 3395−3402. (24) Fogden, A.; Hyde, S. T. Continuous transformations of cubic minimal surfaces. Eur. Phys. J. B 1999, 7 (1), 91−104. (25) Briggs, J.; Chung, H.; Caffrey, M. The temperature-composition phase diagram and mesophase structure characterization of the monoolein/water system. J. Phys. II 1996, 6 (5), 723−751. (26) Chung, H.; Caffrey, M. The curvature elastic-energy function of the lipid−water cubic mesophase. Nature 1994, 368 (6468), 224−226. (27) Seddon, A. M.; Lotze, G.; Plivelic, T. s. S.; Squires, A. M. A highly oriented cubic phase formed by lipids under shear. J. Am. Chem. Soc. 2011, 133 (35), 13860−13863. (28) Squires, A. M.; Hallett, J. E.; Beddoes, C. M.; Plivelic, T. S.; Seddon, A. M. Preparation of films of a highly aligned lipid cubic phase. Langmuir 2013, 29 (6), 1726−1731. (29) Rittman, M.; Amenitsch, H.; Rappolt, M.; Sartori, B.; O’Driscoll, B. M. D.; Squires, A. M. Control and analysis of oriented thin films of lipid inverse bicontinuous cubic phases using grazing incidence smallangle X-ray scattering. Langmuir 29 (31), 9874−9880. (30) Schroeder-Turk, G. E.; Fogden, A.; Hyde, S. T. Bicontinuous geometries and molecular self-assembly: Comparison of local

and it allows us to confirm previously suggested pathways for the phase transformations. Furthermore, our experiments offer a route to films of gyroid materials, with in-plane orientation. In a separate study, we have demonstrated a method of forming films of QIID or QIIG phase in air, with a high degree of out -of plane orientation.31 Taken together, this suggests the possibility in the future of complete biaxial (3D) orientation of gyroid samples with lattice parameters an order of magnitude smaller than block copolymers, and therefore with considerable implications in uses as templates for effective metal or inorganic nanomaterials.

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ASSOCIATED CONTENT

S Supporting Information *

Azimuthal plots corresponding to 2D plots in Figure 3. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; phone: +44(0) 118 378 4736. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.H. and C.B. are supported by a EPSRC Doctoral Training Centre Grant EP/G036780/1. We thank MAX IV Lab and the Diamond Light Source for beamtime.

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REFERENCES

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