Letter pubs.acs.org/Langmuir
Predicting the Orientation of Lipid Cubic Phase Films Samuel J. Richardson,† Paul A. Staniec,‡ Gemma E. Newby,‡,∥ Nick J. Terrill,‡ Joanne M. Elliott,† Adam M. Squires,*,† and Wojciech T. Gózd́ ź*,§ †
Department of Chemistry, University of Reading, Reading, Berkshire, RG6 6AD, United Kingdom Diamond Light Source Ltd, Diamond House, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom § Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland ‡
S Supporting Information *
ABSTRACT: Lipid cubic phase films are of increasingly widespread importance, both in the analysis of the cubic phases themselves by techniques including microscopy and X-ray scattering, and in their applications, especially as electrode coatings for electrochemical sensors and for templates for the electrodeposition of nanostructured metal. In this work we demonstrate that the crystallographic orientation adopted by these films is governed by minimization of interfacial energy. This is shown by the agreement between experimental data obtained using grazing-incidence small-angle X-ray scattering (GI-SAXS), and the predicted lowest energy orientation determined using a theoretical approach we have recently developed. GI-SAXS data show a high degree of orientation for films of both the double diamond phase and the gyroid phase, with the [111] and [110] directions respectively perpendicular to the planar substrate. In each case, this matches the lowest energy facet calculated for that particular phase.
■
INTRODUCTION This Letter demonstrates that thin films of lipid cubic phase adopt orientations predicted by a model that minimizes their interfacial energy. Lipid cubic phases are complex nanostructures showing periodicity in three dimensions.1 Also referred to as “inverse bicontinuous cubic” (QII) phases, they each consist of an intricately curved fluid lipid bilayer, on either side of which lie two interpenetrating branched networks of water channels 2−5 nm in diameter. Three QII phases are known, with structures based on the primitive, double diamond and gyroid mathematical minimal surfaces. These are known as the QIIP, QIID, and QIIG with respective space groups Im3m (229), Pn3m (224), and Ia3d (230). Of these, the QIIP is rarer; the QIID is usually found in coexistence with excess water, while the QIIG is formed at lower hydrations.2,3 The resemblance of the lipid bilayer to a cell membrane has led to an interest in lipid cubic phase research as models for intermediates in biological membrane fusion processes4 and for the encapsulation of membrane proteins,5 in particular for membrane protein crystallization.6,7 Lipid cubic phases also have applications as vehicles for drug8 or flavor9 delivery, and as templates in the production of mesoporous metal.10 Coatings of lipid cubic phase are stable under water,11 or in air in a humidified environment.12 Preparing lipid cubic phases specifically as films or coatings rather than bulk materials is necessary for certain analytical methods used to study them, including voltammetry,13−15 atomic force microscopy,11 and grazing-incidence small-angle X-ray scattering (GI-SAXS).12 © 2014 American Chemical Society
These coatings also have technological applications, especially when used to coat electrodes; recent articles have reported cubic phase electrode coatings in electrodeposition, to produce ultrahigh surface area platinum coatings;10 in biofuel cells;16 and in biosensors.17,18 The orientation of the cubic phase coating, and the nature of the interface at the boundary of the cubic phase, have been studied, both theoretically and experimentally, by a number of groups including ourselves.19,20,11,12 Diffusion of molecules such as drugs or flavours in and out of a lipid cubic phase would likely depend on the nature of the interface;21 it has been proposed that, in order to avoid free edges at the center of the bilayer being exposed to water, the bilayer forms a closed surface, closing off one of the two water channel networks,21 but at the moment there is only indirect experimental evidence for this.10,11 The shape of this closed surface depends on the crystallographic orientation of the plane of the surface relative to the cubic phase unit cell. Furthermore, if the cubic phase is used as a template for the production of nanostructured metal films, then these would themselves have properties dependent on orientation; light transmission, for example, has been shown to vary depending on direction of propagation through nanostructured gyroid meta-materials.22 One of the coauthors23 has developed a theoretical framework for the investigation of the structure of an interface Received: August 30, 2014 Revised: October 20, 2014 Published: October 25, 2014 13510
dx.doi.org/10.1021/la503313n | Langmuir 2014, 30, 13510−13515
Langmuir
Letter
between cubic bicontinuous phases and an isotropic fluid. The method was used to estimate the relative energetic stability of different facets within lipid cubic phase microcrystals and microdroplets of QIID morphology. By estimating the surface energy associated with the (111), (100), and (110) planes, they predicted that the most stable facet is the (111); this was indeed the first formed in experiments on droplets.19 In this work, we demonstrate that, in addition to facets of microscopic lipid cubic phase droplets, the macroscopic orientation of thin films of QIID lipid cubic phases, measured using GI-SAXS, can be predicted using the same considerations. We also extend the theoretical framework to the gyroid QIIG phase, and show that again the QIIG phase films adopt an orientation corresponding to a low-energy facet.
conditions in the x and y directions and a fixed boundary condition in the z direction, where the field ϕ on one side of the cuboid is composed of the bulk cubic phase, and on the other side it is ϕ = ±1 as in the external phase (i.e., in the absence of lipid). We use the nodal approximation (eq 2) for triply periodic gyroid phases to build the initial configuration ϕinitial (x1, x2, x3) G for the field ϕ(r) in the cuboids:
MODEL AND COMPUTATIONAL METHOD Energetic Model. The free-energy functional for systems inhomogeneous on the mesoscopic length scale can be written in the form24,25
where the coordinate frame is chosen such that xi are parallel to the edges of the cubic unit cell of the bulk phase. The length L of the periodic cubic element described by the nodal approximation (eq 2) is taken as the size of the unit cell of the bulk bicontinuous cubic gyroid phase, which is known from previous calculations.24 The structure is then rotated into one of three different orientations relative to the lab geometry (x,y,z), where z is perpendicular to the plane of the sample. The initial configurations for the three cuboids used to determine the structure of the gyroid phase are oriented with directions [111], [100], and [110] (defined relative to the unit cell coordinate frame (x1, x2, x3)) lying orthogonal to the film surface, and they are shown in Figure 1a,b,c, respectively. These
⎛ 2π ⎞ ⎛ 2π ⎞ ⎛ 2π ⎞ ϕGinitial(x1 , x 2 , x3) = sin⎜ x1⎟ cos⎜ x 2⎟ + sin⎜ x3⎟ ⎝L ⎠ ⎝L ⎠ ⎝L ⎠ ⎛ 2π ⎞ ⎛ 2π ⎞ ⎛ 2π ⎞ cos⎜ x1⎟ + sin⎜ x 2⎟ cos⎜ x3⎟ ⎝L ⎠ ⎝L ⎠ ⎝L ⎠
■
F[ϕ(r)] =
(2)
∫ d3r(|Δϕ(r)|2 + g[ϕ(r)]|∇ϕ(r)|2 + f [ϕ(r)]) (1)
Here, g and f are different functions, defined below, of an order parameter ϕ(r), a function that varies periodically with position r, and which characterizes the geometry of the system. In the case of a cubic phase made of lipids and water, ϕ2(r) relates to the local concentration of water. At the center of the lipid bilayer, ϕ(r) = 0. The bilayer divides the space into two disconnected networks of water channels, one of them on one side of the bilayer, where ϕ(r) > 0, and the other one on the other side of the bilayer, where ϕ(r) < 0. The sign of ϕ(r) allows the two disjoint channels of water to be distinguished from one another. The fluid in each channel, however, has the same physical nature. For this reason, in the case of lipids in water, the functional in eq 1 must be an even function of ϕ(r). We assume after previous work by Gozdz26 the form of f [ϕ(r)] = (ϕ(r)2 − 1)2(ϕ(r))2 and g[ϕ(r)] = g2ϕ(r)2 + g0, with g2 = 4.01 − g0 and g0 = −3. In the mean-field approximation the stable or metastable phases of the system correspond to the minimum of the functional (eq 1). In order to minimize the functional, we discretize the field ϕ(r) on the cubic lattice. The discretization and minimization procedures are described in detail in refs 23 and 24. Computational Method. At the interface with the isotropic phase, the structure of the gyroid phase is deformed in such a way that the water channels on one side of the bilayer are closed in order to avoid free edges in the lipid bilayer. We shall minimize the functional (eq 1) in the presence of the interface with the water-rich phase for three different orientations of the unit cell of the gyroid phase. We assume that ϕ(r) is periodic in the directions parallel to the surface of the film, while in the perpendicular direction the gyroid and the external (vapor or water) phases are present at the opposite sides of the interface. For each orientation we construct an appropriate cuboidal cell. We chose the coordinate frame with the x and y directions parallel, and the z direction normal to the surface of the film. The size of the cuboid in x and y directions is determined by the value of the unit-cell length of the bulk gyroid phase and the orientation of the film. The sizes of the computational cells are different for each orientation due to different symmetries in each case. We apply periodic boundary
Figure 1. Computational cells used for different orientations of the gyroid phase of lattice parameter L with respect to the film surface: (a) [111] √6L × √2L × √3L, (b) [100] L × L×L, and (c) [110] √2L × L×√2L. Green and yellow colors show different sides of the surface ϕ(r) = 0, representing the middle of the bilayer. The film surface is parallel to the front face, and the surface normal vectors, [111], [100], and [110], respectively, lie along the z direction.
three orientations, the same three used in the previous work on the diamond phase,23 were chosen in order to ensure an order parameter film that was periodic in the two dimensions of the film surface, free from terraces and steps. The size of the cuboids in the x and y directions is equal to the value of the period of the cubic phase in the corresponding direction. This size is kept constant. In the z direction, the thickness of the cuboid is varied in the range Zmin < Z < Zmax. Zmin is the size of the smallest cuboid in the z direction, equal to the period of the cubic phase in this direction, and Zmax = 4Zmin.
■
EXPERIMENTAL METHOD All compounds were used as received. Phytantriol was a gift from Adina Cosmetic Ingredients (Tunbridge Wells, Kent, UK); glycerol was purchased from Fisher Scientific. Silicon 13511
dx.doi.org/10.1021/la503313n | Langmuir 2014, 30, 13510−13515
Langmuir
Letter
wafer substrates were made hydrophobic as described by Rittman et al.12 Briefly: circular wafers (diameter = 2 cm) of silicon were cleaned in piranha solution, dried, and placed in a solution of toluene (50 mL), octyltrichlorosilane (0.2 mL), and triethylamine (0.3 mL) and left overnight. Finally, wafers were rinsed with toluene and ethanol and left to dry in air. Phytantriol and glycerol were separately dissolved at a ratio of 1:4 (w/w) [phytantriol or glycerol]:ethanol. These were then combined in ratios of 1:4 (w/w) glycerol solution:phytantriol solution. The glycerol/phytantriol/ethanol solutions (100 μL) were deposited onto the silicon substrates by spin coating during a 40 s rotation at 1000 rpm, 5000 rpm, or 10 000 rpm. This was sufficient time for the ethanol to evaporate, by visual inspection (the films were colored, due to interference, and color changes were observed during ethanol evaporation), to leave films that were 1:4 (w/w) glycerol:phytantriol. The process produced films of thickness between approx. 500 and 1500 nm, as confirmed by ellipsometry (see Supporting Information, SI1). Ethanol (50 μL) was then applied to the edge of the wafer during a second 30 s rotation at 5000 rpm in order to remove any excess buildup of phytantriol/glycerol at the edges that would otherwise interfere with the GI-SAXS measurements. The samples were then left for at least 15 min before analysis. The samples were analyzed inside a sealed polyimide chamber. Polyimide weakly scatters X-rays at small angles; however, this occurs only at a relatively high q range and did not interfere with our data, resulting in a broad ring at the edge of the detector. Humidity was controlled with the combination of hydrating sources placed inside the chamber (tissue paper or cotton pipe cleaners soaked in water) and a controllable dry helium line in. The humidity was monitored using a handheld humidity sensor placed near the sample. GI-SAXS measurements were performed on beamline I07 at the Diamond Light Source using a beam size of 300 μm × 500 μm and energy of 12.5 keV. A Pilatus 2 M detector was used to collect data over a q range of 0.01 Å−1 to 0.50 Å−1. The sample-to-detector distance and beam center were determined using a sample of silver behenate calibrant. One-second exposure GI-SAXS images were taken of the films every 10 s as the humidity was varied by controlling the helium flow manually, to increase the relative humidity (RH) by approximately 1% every 30 s. Samples were humidified from the micellar through the gyroid to the diamond phase. In some cases, the humidity was then reduced to go back through the phase sequence. The appearance of the gyroid scattering pattern was the same in both directions (see Supporting Information Figure SI5).
The energy varies periodically with Z (see Supporting Information SI2). The points in Figure 2 represent the lowest
Figure 2. Lowest values of the free energy for configurations with a given topology (genus) for the three different orientations shown in Figure 1. Interfaces perpendicular to the [111], [100], and [110] directions are represented respectively as diamonds, squares, and circles.
energy configurations (for fixed topology) of the gyroid phase in the three orientations. When the film thickness is increased, at some point the surface of the bilayer has to be cut to incorporate an extra layer of the bicontinuous phase. When this happens, the topology (genus) of the surface formed by the lipid bilayer is changed. In general, the lowest energy is obtained for the orientation where the interface is normal to the [110] direction. Remarkably, this energy is very close to the bulk value26 of −0.19 over a range of values of Z, implying that there is very little energetic cost associated with the formation of an interface normal to the [110] direction. In contrast, the energies of interfaces with the other two orientations investigated are significantly higher. This suggests that the (110) orientation is the most favorable out of the three; moreover, as its energy is close to the bulk phase value, it is unlikely that there is any other orientation that is lower in energy, and therefore we would predict that thin films would adopt the (110) orientation. Surfaces for the configurations corresponding to local energetic minima for the three orientations are shown in Figure 3 (top). It is noticeable that in the (110) orientation, the open water channels adopt a triangular lattice resembling that adopted by the (111) surface of diamond phase films.23,11 For this orientation, within the period of the gyroid phase, as the thickness is increased in the [110] direction, a stable
■
RESULTS AND DISCUSSION Energetic Calculations. Calculations that we have performed on the diamond phase have already been published,23 and demonstrated that the lowest energy interface would lie normal to the [111] direction. Here, we have performed the calculations for the gyroid phase when the plane of the film is orthogonal to the [100], [110], and [111] directions with respect to the unit cubic cell, in other words, with the plane parallel to the (100), (110) and (111) Miller planes, respectively. The functional (eq 1) was minimized with respect to ϕ(r) with the imposed boundary conditions and for a given Z, the size of the computational cell in the z direction. In this way a function of Z, F(Z), equal to the minimum of the functional (eq 1) for a given Z, is obtained for the range of Zmin < Z < Zmax.23
Figure 3. Energy minimized interface structures with the surface orthogonal to (from left to right) the [110], [100], and [111] directions within the gyroid (top) and the diamond (bottom), respectively. 13512
dx.doi.org/10.1021/la503313n | Langmuir 2014, 30, 13510−13515
Langmuir
Letter
humidity. For each sample, the humidity was increased and/or decreased to give three repeats of the two different QII phases. In every case, the spot patterns were consistent with the (110) and (111) planes lying parallel to the substrate for the QIIG and QIID phases, respectively (see Supporting Information SI6). It is probable that, when thicker films are formed, at some point the relative surface energy contribution no longer dictates orientation. Indeed, we have recently shown that, in coatings of cubic phases of glycerol monooleate tens of microns thick inside glass capillary tubes, the cubic phase shows no orientation relative to the interfaces with glass and water.27 We also note that, in our previous paper,12 the first to show GISAXS data from oriented QII phases, in some cases a second orientation was observed coexisting with the (110) and (111) for the QIIG and QIID, respectively (although these two orientations were observed for all samples). In that paper, samples were “drip-cast” along the wafer, and the film thickness was much less controlled or uniform than the spin-coated films described here. It has been proposed that the orientation of the QII film, rather than reflecting the most thermodynamically favorable surface as we suggest here, can instead be explained by an epitaxial relationship with a preceding phase, which is itself oriented.12 In particular, oriented QII phases have previously been formed on hydration via the lower-water-content lamellar (Lα) phase, which is itself typically oriented with the constituent bilayers lying parallel to the substrate.12 Mechanisms for pathways from Lα to QII phases28 and between the QIIG and QIID phases29−31 have been proposed, which suggest a clear orientational relationship between the two. Here, our data allow us to rule out such an alternative hypothesis for the QIIG phase; we have obtained data on a phytantriol/glycerol mixture, whose phase behavior is described in more detail in a forthcoming paper to be published separately. Importantly, from the point of view of the current discussion, due to the glycerol the system does not form an Lα phase at room temperature, so QII film formation does not proceed via the Lα phase. Instead, the QIIG phase is formed directly from an inverse micellar (LII) phase, which is isotropic, and whose scattering pattern is characterized by a uniform broad ring. Figure 5 shows both the inverse micellar ring and the spots corresponding to the highly oriented QIIG film, in the same
interface can be created at four different values of the thickness of the gyroid phase. The structure of the gyroid phase for these configurations is shown in the Supporting Information (SI3). Two of these correspond to one of the sides of the bilayer being exposed, and the other two to the other side; the actual interface looks identical in each case. Grazing Incidence Small-Angle X-ray Scattering. 2D GI-SAXS patterns were obtained from three different humidified phytantriol/glycerol films with different thicknesses between approx. 500 and 1500 nm. Representative patterns are shown in Figure 4, at two different water vapor relative
Figure 4. GI-SAXS image of phytantriol and 20% (w/w) glycerol films on hydrophobic silicon wafer at RH = 36% (top) and 90% (bottom). The top image was obtained by humidifying from the micellar phase. Simulated spot patterns (small circles) are superimposed onto images for the QIIG (top) and QIID (bottom) phases with the (110) and the (111) plane orientated parallel to the substrate, respectively, together with partial rings to show where isotropic reflections would lie for different sets of (hkl) planes, with √(h2 + k2 + l2) values labeled. The beam center is marked with an X near the bottom left of each image; the film is vertical as shown, and the substrate normal horizontal.
humidity values, which induce formation of the QIID and QIIG phase (integrated radial profiles shown in Supporting Information SI4). The QIID phase is formed at higher relative humidity than the QIIG.2 The GI-SAXS patterns show highly oriented materials, characterized by low mosaicity, as shown by the presence of spots rather than arcs or rings. In each case, the spot pattern obtained is effectively a “fiber-averaged” one, consistent with a sample showing uniaxial orientation with a single crystallographic direction perpendicular to the plane of the substrate, and therefore with a consistent facet plane parallel to the substrate and QII phase surface. The orientations are confirmed by simulated spot positions superimposed on the GI-SAXS patterns in Figure 4; the calculations for these have been published elsewhere12 and included in the Supporting Information (SI5). All samples adopted cubic phases where the plane parallel to the surface was the (111) plane for QIID, and the (110) plane for QIIG. These correspond to the lowest energy facet for each phase from the theoretical calculations. The experiment was repeated over three samples, which consistently formed QIIG and QIID phases in order of increasing
Figure 5. GI-SAXS image of phytantriol and 20% (w/w) glycerol film on hydrophobic silicon wafer taken at RH = 41%. The coexistence of LII (inner broad ring) and QIIG (dots) can be observed.
exposure, with no Lα reflections. As the QIIG phase is being formed from an unoriented precursor, its orientation must instead be due to thermodynamic considerations such as those we present in this article. For the QIID phase, the situation is more ambiguous, as it is itself formed from an oriented QIIG phase. Furthermore, experimental data on the QIIG to QIID transformation27,32 13513
dx.doi.org/10.1021/la503313n | Langmuir 2014, 30, 13510−13515
Langmuir
Letter
suggest that a ⟨110⟩ axis in the former can be converted into a ⟨111⟩ axis in the latter. Thus, while it is possible that the orientation of the QIID phase can be explained simply by the thermodynamic arguments of minimizing its surface free energy, just as for the QIIG phase, we cannot rule out the possibility that the epitaxial relationship with the oriented preceding QIIG phase also plays a role; both considerations would lead to the ⟨111⟩ orientation in the QIID phase. In summary, the very good agreement between theory and experiment for two different cubic phases suggests that the orientation adopted by QII films is dictated by energetic stability considerations. Furthermore, as the calculations are carried out assuming a continuous bilayer as previously hypothesized, our results provide further evidence supporting this structural model for the interface. We note the significance of the fact that this is true in a humidified vapor environment as well as under water, implying that the bilayer topology is likely preserved in both cases.
Properties; Academic Press: New York, 1997; Vol. 44, Chapter 1, pp 3−24. (2) Barauskas, J.; Landh, T. Phase Behavior of the Phytantriol/Water System. Langmuir 2003, 19, 9562−9565. (3) Qiu, H.; Caffrey, M. The Phase Diagram of the Monoolein/ Water System: Metastability and Equilibrium Aspects. Biomaterials 2000, 21, 223−234. (4) Mishra, A.; Lai, G. H.; Schmidt, N. W.; Sun, V. Z.; Rodriguez, A. R.; Tong, R.; Tang, L.; Cheng, J.; Deming, T. J.; Kamei, D. T.; Wong, G. C. L. Translocation of HIV TAT Peptide and Analogues Induced by Multiplexed Membrane and Cytoskeletal Interactions. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 16883−16888. (5) Conn, C. E.; Drummond, C. J. Nanostructured Bicontinuous Cubic Lipid Self-Assembly Materials as Matrices for Protein Encapsulation. Soft Matter 2013, 9, 3449−3464. (6) Landau, E. M.; Rosenbusch, J. P. Lipidic Cubic Phases: A Novel Concept for the Crystallization of Membrane Proteins. Proc. Natl. Acad. Sci. U. S. A. 1996, 93, 14532−14535. (7) van ‘t Hag, L.; Darmanin, C.; Le, T. C.; Mudie, S.; Conn, C. E.; Drummond, C. J. Meso Crystallization: Compatibility of Different Lipid Bicontinuous Cubic Mesophases with the Cubic Crystallization Screen in Aqueous Solution. Cryst. Growth Des. 2014, 14, 1771−1781. (8) Chen, Y.; Ma, P.; Gui, S. Cubic and Hexagonal Liquid Crystals as Drug Delivery Systems. BioMed. Res. Int. 2014, 2014, e815981. (9) Sagalowicz, L.; Leser, M. E. Delivery Systems for Liquid Food Products. Curr. Opin. Colloid Interface Sci. 2010, 15, 61−72. (10) 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. 2013, 25, 1160−1164. (11) Rittman, M.; Frischherz, M.; Burgmann, F.; Hartley, P. G.; Squires, A. Direct Visualisation of Lipid Bilayer Cubic Phases Using Atomic Force Microscopy. Soft Matter 2010, 6, 4058−4061. (12) 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 Small-Angle X-ray Scattering. Langmuir 2013, 29, 9874−9880. (13) Rowiński, P.; Bilewicz, R.; Stébé, M.-J.; Rogalska, E. Electrodes Modified with Monoolein Cubic Phases Hosting Laccases for the Catalytic Reduction of Dioxygen. Anal. Chem. 2004, 76, 283−291. (14) Bilewicz, R.; Rowiński, P.; Rogalska, E. Modified Electrodes Based on Lipidic Cubic Phases. Bioelectrochemistry 2005, 66, 3−8. (15) Nazaruk, E.; Szlęzak, M.; Górecka, E.; Bilewicz, R.; Osornio, Y. M.; Uebelhart, P.; Landau, E. M. Design and Assembly of pH-Sensitive Lipidic Cubic Phase Matrices for Drug Release. Langmuir 2014, 30, 1383−1390. (16) Nazaruk, E.; Smoliński, S.; Swatko-Ossor, M.; Ginalska, G.; Fiedurek, J.; Rogalski, J.; Bilewicz, R. Enzymatic Biofuel Cell Based on Electrodes Modified with Lipid Liquid−Crystalline Cubic Phases. J. Power Sources 2008, 183, 533−538. (17) Razumas, V.; Kanapieniené, J.; Nylander, T.; Engström, S.; Larsson, K. Electrochemical Biosensors for Glucose, Lactate, Urea, and Creatinine Based on Enzymes Entrapped in a Cubic Liquid Crystalline Phase. Anal. Chim. Acta 1994, 289, 155−162. (18) Bilewicz, R.; Rowiński, P.; Rogalska, E. Modified Electrodes Based on Lipidic Cubic Phases. Bioelectrochemistry 2005, 66, 3−8. (19) Latypova, L.; Gózd́ ź, W.; Pieranski, P. Symmetry, Topology and Faceting in Bicontinuous Lyotropic Crystals. Eur. Phys. J. E 2013, 36, 1−24. (20) Pieranski, P.; Sotta, P.; Rohe, D.; Imperor-Clerc, M. Devil’s Staircase-Type Faceting of a Cubic Lyotropic Liquid Crystal. Phys. Rev. Lett. 2000, 84, 2409−2412. (21) Larsson, K. Aqueous Dispersions of Cubic Lipid−Water Phases. Curr. Opin. Colloid Interface Sci. 2000, 5, 64−69. (22) 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, OP23−OP27.
■
OUTLOOK We have shown that the crystallographic orientation adopted by QIIG and QIID films can be predicted by an energetic model minimizing interfacial energy, which we have developed previously to describe facets in QIID phase microcrystals. Our findings confirm suggested models for the nature of the interface between lipid cubic phase films and their external environment, which is relevant to processes involving diffusion of molecules into and out of the cubic phase, in particular in electrochemical sensors17,18 and in drug, flavor, or aroma delivery. Our results also have implications for control of orientation of materials produced from cubic phases, in particular, membrane protein crystals,6 and functional platinum materials produced using QII films as templates.10
■
ASSOCIATED CONTENT
S Supporting Information *
Ellipsometry showing film thickness; energy variation with Z within one period; different stable facets normal to [110]; radial profiles; calculations for spot pattern generation; additional 2D GI-SAXS patterns. This material is available free of charge via the Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (A.M.S.). *E-mail:
[email protected] (W.T.G.). Present Address ∥
ESRF, 6, rue Jules Horowitz BP 220, 38043, Grenoble, France.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS S.J.R. was funded by the Diamond Light Source and a University of Reading Faculty Studentship. W.T.G. would like to acknowledge the support from NCN Grant No. 2012/05/B/ ST3/03302. Synchrotron experiments were carried out under Experiment SI8418.
■
REFERENCES
(1) Luzzati, V.; Delacroix, H.; Gulik, A.; Gulik-Krzywicki, T.; Mariani, P.; Vargas, R. The Cubic Phases of Lipids. In Current Topics in Membranes; Epand, R. M., Ed.; Lipid Polymorphism and Membrane 13514
dx.doi.org/10.1021/la503313n | Langmuir 2014, 30, 13510−13515
Langmuir
Letter
(23) Latypova, L.; Gózd́ ź, W. T.; Pierański, P. Facets of Lyotropic Liquid Crystals. Langmuir 2014, 30, 488−495. (24) Brazovskii, S. A. Phase Transition of an Isotropic System to a Nonuniform State. Sov. Phys. JETP 1975, 41, 85. (25) Ciach, A.; Pękalski, J.; Gózd́ ź, W. T. Origin of Similarity of Phase Diagrams in Amphiphilic and Colloidal Systems with Competing Interactions. Soft Matter 2013, 9, 6301−6308. (26) Gózd́ ź, W. T.; Hołyst, R. Triply Periodic Surfaces and Multiply Continuous Structures from the Landau Model of Microemulsions. Phys. Rev. E 1996, 54, 5012−5027. (27) Seddon, A. M.; Hallett, J.; Beddoes, C.; Plivelic, T. S.; Squires, A. M. Experimental Confirmation of Transformation Pathways between Inverse Double Diamond and Gyroid Cubic Phases. Langmuir 2014, 30, 5705−5710. (28) Siegel, D. P.; Banschbach, J. L. Lamellar/Inverted Cubic (Lα/ QII) Phase Transition in N-Methylated Dioleoylphosphatidylethanolamine. Biochemistry 1990, 29, 5975−5981. (29) Sadoc, J.-F.; Charvolin, J. Infinite Periodic Minimal Surfaces and Their Crystallography in the Hyperbolic Plane. Acta Crystallogr. A 1989, 45, 10−20. (30) Squires, A. M.; Templer, R. H.; Seddon, J. M.; Woenkhaus, J.; Winter, R.; Narayanan, T.; Finet, S. Kinetics and Mechanism of the Interconversion of Inverse Bicontinuous Cubic Mesophases. Phys. Rev. E 2005, 72, 011502. (31) Schröder-Turk, G. E.; Fogden, A.; Hyde, S. T. Bicontinuous Geometries and Molecular Self-Assembly: Comparison of Local Curvature and Global Packing Variations in Genus-Three Cubic, Tetragonal and Rhombohedral Surfaces. Eur. Phys. J. B 2006, 54, 509− 524. (32) Rappolt, M.; Di Gregorio, G. M.; Almgren, M.; Amenitsch, H.; Pabst, G.; Laggner, P.; Mariani, P. Non-equilibrium Formation of the Cubic Pn3m Phase in a Monoolein/Water System. Europhys. Lett. 2006, 75, 267−273.
13515
dx.doi.org/10.1021/la503313n | Langmuir 2014, 30, 13510−13515
