Phase Behavior in the System Pine Needle Oil Monoglycerides

J . Phys. Chem. 1994,98, 8453-8467

8453

Phase Behavior in the System Pine Oil Monoglycerides-Poloxamer 407-Water at 20 O C Tomas Landh’ Department of Food Technology, Chemical Center, University of Lund, P.O. Box 124, S - 221 00 Lund, Sweden Received: November 16, 1993; In Final Form: April 8, 1994‘

The phase behavior of a monoolein-rich (89.5 wt %) monoglyceride blend based on pine needle oil (denoted glycerol monooleate)-poloxamer 407 block copolymer-water system has been investigated and studied by small-angle X-ray diffraction. The phase diagram exhibits an extended cubic phase field, originating from the binary glycerol monooleate-water system, ranging from 18 to 67 wt 7% water with a maximum content of 20 wt 7’% of poloxamer 407. It is shown to possess four different reversed bilayer-based cubic one-phase regions as based on phase equilibria and X-ray data. X-ray data indicates that these are of crystallographic cubic aspects number 4, 8 (two cubic structures are proposed to have the same symmetry), and 12. The structures are further identified by reference to the minimal surface bisecting the three-dimensional bilayer in each structure. The cubic phase sequence is proposed to be G(Q230) D(Q224) P(QZz9) C(P)(QZz9),described by Schoen’s gyroid, Schwarz’ double diamond, Schwarz’ primitive, and Neovius’ periodic minimal surfaces, respectively. The lattice parameters vary approximately between 130 and 150 A, 75 and 102 A, 120 and 210 A, and 315 and 355 A for these phases, respectively, and are found to be most influenced by the proportion of water. At concentrations higher than 20 wt % poloxamer 407 the cubic phase P(Q229)is transformed to a reversed micellar (L2) phase. The phase diagram possesses two lamellar (La)phases, one which originates from the binary glycerol monooleate-water system which extends to about 15 wt % of poloxamer 407. The other is located in the water-rich region at 65-75 wt 7% of water, and approximately equal amounts of poloxamer 407 and glycerol monooleate. At higher dilutions (about 80 wt % water) an isotropic flow-birefringent L3 or sponge phase appears with domain sizes above 200 A. The fine structure of the different phases is discussed, with emphasis on the structure of the cubic phases, in terms of the mixing behavior and the molecular arrangement of the poloxamer 407 molecules and the glycerol monooleate-based bilayer.

- - -

Introduction Since the pioneering work of Luzzati and co-workers,l cubic liquid crystalline phases have been found in a variety of systems and at varying conditions.2 The intriguing structure of bicontinuous cubic phases and their disordered counterpart, the L3 phase, have aroused interest, especially due to their possible role in b i ~ l o g y .Technological ~~ applications of cubic phases are being investigated in such areas as drug delivery6 and separation technique^.^ In lipid-water systems six cubic structures have been found (Q2’2, Q223, Q2Z4, Q2z7, Q229, and 4239, four of which have been unambiguously determined (4223, Q224, Q227, and Q230).8-11 Luzzati and associates have given a detailed crystallographic analysis and description of cubic phases in lipid-water systems.8-*0 Besides the inter-connected-rod (ICR) model put forward by Luzzati, much attention has recently been given to the description of certain cubic phases by triply periodic surfaces (fully embedded in 3-D space) of either zero mean curvature5J2-I9 or constant mean curvature.20 Surfaces with everywhere vanishing mean curvature are called minimal surfaces, since they correspond to surfaces of minimum area under certain boundary conditions. Under certain symmetry conditions minima1 surfaces can be repeated in such a way that they divide the entire space into two subspaces. Such surfaces are known as periodic minimal surfaces (PMS’s) and are well known to mathematicians.21-26 In contrast, their constant mean curvature counterparts have just recently been r e c o g n i ~ e d .Both ~ ~ ~types ~ ~ of surfaces divide space into two interwoven and unconnected subspaces forming a bicontinuous structure28 in which the two subspaces are not necessarily congruent. Certain PMS’s have been found to describe reversed (type 11) cubic phases of the bilayer type in which the minimal

* Current address: Department of Biomaterials, SUNY at Buffalo, 332 Squire Hall, Buffalo, NY 14214. Abstract published in Aduance ACS Abstracts, June 1, 1994. 0022-3654/94/2098-8453!§04.50/0

surface is considered as the midsurface of the hydrocarbon region, and it has been established (see e.g. ref 5 and references cited therein) that the type I1 Q224,Q229,and Q230phases are well described by reference to the D (Schwarz’ diamond F-surface),21 P (Schwarz’ primitive surface),zl and G (Shoen’s gyroid)*4PMS surfaces, respectively. The corresponding periodic surfaces with constant mean curvature describe the apolar/polar interfaces of a bilayer (or a monolayer) cubic phase.28 Provided that the cubic phase field is large enough, results from differential geometric analysis of cubic phases predict a variation of the structure within the field.I7J8 Such cubic mesomorphism is well known from experiments and was first reported in the monoolein-water system by L a r s s ~ n Subsequent .~~ works mainly by Luzzati and associates,8.30 Larsson and cow0rkers,l3-~land C a f f r e ~ ~ 2 -have 3 ~ established the phenomenon of cubic mesomorphism in several monoglyceride- and monooleinprotein-water systems. Luzzati and co-workershave also reported cubic mesomorphism in a membrane lipid-water system,35 and it has also been observed in nonionic surfactant-water systems.36-37 In the latter systems cubic mesomorphism has been observed for both reversed, type 11, and normal, type I, cubic phases, as opposed to only type I1 in lipid-water systems. More recently, cubic mesomorphism has also been reported in didodecyldimethylammonium bromide (DDAB)-hydrocarbon-water systems38Jg and in the binary (didodecylphosphatidy1)ethanolamine-water system.40 Noteworthy is the observation of five different cubic phases in the DDAB-styrene-water system.41 The current work deals with the aqueous phase equilibria of a monoolein-rich (89.5 wt %) monoglyceride blend (denoted glycerol monooleate) when a nonionic triblock copolymer, poloxamer 407, is introduced. The monoglyceride blend which is based on pine needle oil exhibits an aqueous phase behavior similar to that of other monoolein-rich monoglyceride blends43q44 and to pure monoolein.13~29~42Poloxamer 407 is well known by the commercial name Pluronic F127 and is frequently used in 0 1994 American Chemical Society

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Landh

The Journal of Physical Chemistry, Vol. 98. No. 34, 1994

% (w/w) GMO

Figure 1. Schematic partial phase diagram for the monoolein-rich pine needle oil monoglyccride (GM0)-poloxamer 407-water system at 20 OC showingmonophaseregionsand thecubiocubicmultiple-phaseregions(shaded). Thephases indicated aretwo lamellarphases (La),twoliquid isotropic solution phases (Lzand La), and five cubic phases (Q, QI. two Qs, and Qi2). C denotes crystalline material. In addition the phase diagram psesses a micellar phase (not indicated) originating from the binary poloxamer 407-water system (see text). A broken line indicates larger uncertainty in the exact location of the phase boundary. The approximate variation of the lattice parameter (A) is indicated in the low-hydration QSphase region, The dots mark some of the samples analyzed in the text, labeled as in Table 1. See text for further details and phase assignments. cosmetic and pharmaceutical preparation^^^.'^ This work was undertaken as part of the development of colloidal dispersions of cubic phases for use as a drug delivery system, a work which called for a qualitativeunderstanding of the interactions between ampbipbilic polymers and lipids. In this paper we report on the general features of the glycerol monooleate-poloxamer 407-water phase diagram and focus on the understanding of the mixing behavior as well as on the extended reversed cubic phase field found in this system in which four different cubic monophasic regions are determined. The study of interactions between lipids (surfactants) and water-soluble polymers has been an active research area for a number of years, and the topic has been the subject of several 1eviews.4~-'0 However, most works are concerned with charged surfactants in diluted systems and except for the lipid-proteinwater systems mentioned above, the author is aware of few works concerning phase diagrams in lipid-polymer-water systems."

Experimental Section Materials. The monoglyceride blend which wedenoteglycerol monooleate (GMO) (85-06) (074832-FF 8-009) was prepared by molecular distillation of pine oil by Grindsted Products A/S (Braband, Denmark) from which it was purchased. It consist of 97% monoglycerides, 1.O% diglycerides, 1.O% glycerol, and 1 ,O% free fatty acids and has a fatty acid composition of the monoglycerides according toCl6a,O.5, CIS,^, 2.0, CIS,I,92.3, CIS, 2.4.3, Cis:,, trace, C20:r,0.5 wt %, as stated by the supplier. The purity of the monoglyceride was checked with thin-layer chromatography (TLC) (chloroform-acetone-acetic acid-methanol, 72.5/25/0.5/2 ~ 0 1 % ) .No significant changes of the chromatograms could be seen during the time of the experiments. A specially purified poloxamer 407 was obtained from BASF Corporation (Wyandotte). Poloxamer 407 is a block copolymer consisting of a polyoxypropylene (PPO) block with a polyoxyethylene (PEO) block at each side. It has an average molecular weight of 12 500 (mp 54 "C) and an approximate formula of PE099PP067PE099 (EPE) (approximately 70% PEO). Doubledistilled water was used in all experiments. All materials were used without further purification. Sample Preparationfor Phase Characterization. Cold GMO, which is a white solid crystalline compound (mp 37 "C), was ground with a mortar and pestle which had been cooled to -20 OC. The obtained powder was stored at -20 OC. Appropriate amounts of GMO, EPE, and water were weighed into glass

ampules (1&15 mmindiameter) whichwereimmediatelyflushed with nitrogen gas and flame sealed. Samples of a total weight of 1 gwereusedthroughoutthisstudy. Theampuleswereheated for 1 h at 50 'C and thereafter centrifuged at l5OOg for 1 h in a Sorvall Ecouospin desk centrifuge (DuPont) equipped with a swing-out rotor. If needed in order to obtain sample homogeneity thecentrifugation step was repeated after 24 h or more. In order to achieve phase separation in samples containing two or more cubic phases in equilibrium, and samples in which the sponge phase (L2). lamellar (La), and/or cubic ( Q ) phase coexisted, an ultracentrifuge (RC-5, Sorvall, DuPont Instruments) equipped with a fixed-angle rotor, operated at 20 OC and 25 OOOg for up to 24 h, was used. All samples were stored at room temperature and in the dark. The partial phase diagram in Figure 1 is based on more than 500 samples. Sample Homogeneity and Criteria for Equilibrium Conditions. To ensure thermodynamic equilibria the following criteria were used. At the time at which the X-ray diffraction pattern gave a constant lattice parameter, as judged from a series of exposures of the same sample with 2 4 4 8 h time elapse between the exposures, duplicate or triplicate samples were prepared along lines of constant ratio of the three binary mixtures and along lines with a fixed amount of one component. This procedure allows for evaluation of the effects of sample history on sample homogeneity and equilibrium. Equilibrium conditions were assumed to bereached when thesame final result (samediffraction pattern) was obtained, independent of mixing procedureand time for equilibration. This criteria was used prior to preliminary phase assignment and subsequent structural study. In addition, samplesof cubic phases, especially samples corresponding to twoor three-phase cubic regions, and those assigned as L, phase, were examined for reversible thermotropic phase transitions, a criterion which is necessary but not enough to ensure conditions close to thermodynamic equilibrium. We stress that the kinetics of phase transitions involving cubic phases is generally different upon heating as compared tocooling. After samples were judged to have reached equilibrium no sample showed any significant physical changes over a time period of more than 1 year. During the same period of time TLC indicated no chemical changes of the lipid constituent of the samples. VisualObsenations. Inspection of the optical texture of liquid crystalline samples provides a simple method to discriminate isotropic lipid mesophases such as the Q. L2, and L3 phases from anisotropic phases such as the L, and the hexagonal (H). It is also worth noting that theviscosityofliquidcrystalsoftenincreases

Phase Behavior in Lipid-Polymer-Water Systems in the order La < H < Q. Preliminary inspection of samples was carried out between crossed polarizers and examined for homogeneity and birefringence. Microscopic examinations of the specimens were carried out by using an Olympus Vanox polarizing microscope fitted with a camera and a heating stage (Mettler FP52). Analysis of Cubic Mesomorphism. Macroscopically cubic phases are most often viscous but exhibit varying degrees of stiffness. Generally, the higher the connectivity (Table 3), which as a first approximation may be assumed to increase with increased hydration along a sequence of reversed cubic phases, the lower the stiffness is. Therefore, when a significant difference in the stiffness is observed between neighboring samples within a cubic phase field it may be taken as an indication of mesomorphism. In the current system the difference in stiffness between such samples was found to be large enough to be observed macroscopically by simply striking the samples. However, it is well known that the history of the samples can have a profound kinetic influence on the phase behavior and the possibility of hysteresis must be considered, according to above. In the current system the time for cubic phase samples to reach equilibrium was generally increasing with increased hydration, indicating increased complexity of the structure. Samples with the highest amount of water reached equilibrium in some months while samples with low water content needed days to achieve equilibrium. Such observations may indicate, like the changes in stiffness, that the connectivity of the cubic phases is changed, and can thus be taken as further support of cubic mesomorphism. The coexistence of cubic phases is perhaps best indicated by means of microscopic examinations of the sample,36,37by which the cubic phases are easily distinguishable due to their difference in refractive index. We made use of some different “flooding” and “drying” techniques (see e.g. ref 52) for examination of the “phase sequence” as the hydration changes. Because of the long equilibrium times observed at high water content we have preferred to work with “drying” of equilibrated samples. These preliminary observations are useful in combination with a known extension of a cubic phase field and indicate a progression of cubic phases within the field as well as the location of the coexistence region(s) between them. Cubic mesomorphism can, however, only be verified once the coexistence region has been located, which requires observations of samples representing physically separated cubic phases. Small-Angle X-ray Diffraction. Small-angle X-ray scattering (SAXS) measurements were performed with a Guiner-type focusing camera according to Luzzati andco-workerss3(equipped with Philips X-ray tube type PW 2273120 operated a t 40 kV and 20 mA) with a bent quartz monochromator adjusted to isolate the Cu Kal radiation (A = 1.5405 A). A diffraction versus temperature (DPT) camera with Ni-filtered Cu K, radiation (wavelength X = 1.542 A, Philips X-ray tube type P W 2223120 operated a t 40 kV and 20 mA) designed after the principles of StenhagenS4and equipped with precise t e m p e r a t u r e ~ o n t r owas l~~ also used. The specimen to film distance and the time of exposure was 160 mm and 2-24 h in the DPT camera and 200 mm and 24-120 h in the Guiner camera. In both cameras the samples were mounted between thin mica windows in customized metal holders. Some experiments were performed with a Kiessig camera (Ni-filtered Cu K, radiation) operated at 16 mA, 40 kV with a specimen to film distance of 200 or 500 mm. All exposures were made on CEA Reflex (25150 FW/5 in. X 7 in.) X-ray film (Ceaverken AB, Strangnas, Sweden). The samples were thoroughly mixed by repeated centrifugation of the samples or mechanical agitation to reduce the appearance of spotty diffraction patterns which arises due to the tendency of crystals of cubic phases to grow into macroscopic monodomains. Films were analyzed with an image-analyzing system (JAVA, Germany) equipped with a Philips CCD video camera. This system allows

The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 8455

accurate measurements of both distances and relative integrated intensities (expressed as optical densities on an absolute gray scale ranging from 0 to 255) of the diffraction lines. Some films were analyzed with the aid of a photodensitometer (Kipp & Zonen, Delft, Netherlands). Structural Analysis. The characterization of lipid mesophases by X-ray diffraction is based on the long-range order of the organization which gives rise to Bragg reflections whose spacings are in characteristic ratios.’ As usual with liquid crystals, we refer to two regions of the X-ray spectra, one at s < 10 A-1 (s = 2 sin 8/X, 28 is the scattering angle) where diffraction indicates the long-range order, and one a t s > 10 A-1 where the presence of a diffuse band (or sharp reflections) indicates the short-range conformation of the hydrocarbon chains. Cubic phases show spacing ratios in accordance with the systematic absence of reflections that are not permitted by each cubic aspect according to the International Tables.s6a It is thus possible to identify a cubic phase by its extinction symbol which defines the cubic aspect a, Qa, of the structure.56b I t is also possible to tentatively identify the space group s, Qs.5bThe space group determination is yet in most cases ambiguous due to the relatively few reflections observed. However, using differential geometric analysis of the bilayer cubic phases we might test a space group for which symmetry a corresponding PMS exists. The test should be consistent with the predicted cubic mesomorphism relative to the reference system (the GMO-water system) and consistent with the phase equilibria study. Moreover, the test must take into account the existence of topological and geometrical constraints of the cubic phase. Thus, for bilayer-based type 11cubic phases, identified as of cubic aspects 4 and 8, the space groups Pn3m (224) and Im3m (229) were analyzed, respectively. The corresponding PMS’s are the D surface and the P or C(P) surface, respectively, where the C(P) or Neovius’ surface22 is the complementary surface to the P surface, according to Schoen’s notation.24 The cubic structures are referred to as D(Q2Z4), P(Q229),and C(P)(Q229),respectively. For cubic phases adopting a body-centered latticeof cubicaspect number 12 the space group Ia3d (230) is uniquely defined, and the bilayer-based type I1 phase is assumed to be described by the G surface. This defines phase G(Q230). Furthermore, if the cubic phase field extends over large ranges of composition we may as a first approximation assume that the progression of the cubic phases should follow the sequence G D P C(P) with decreasing volume fraction of bilayer, CPb. We will use CP for volume fraction with indices GMO, p, w, b, and aq, corresponding to lipid (GMO polar apolar parts), polymer, water, bilayer (total apolar volume fraction), and aqueous (total polar volume fraction) volume fractions, respectively. Some guidance can also be obtained from the intensity distributions of the diffraction pattern in comparison with earlier reported cubic phases (see e.g. refs 2,8, 10, and 11, and references cited within them). Calculation of the lattice parameters of the lipid mesophases were done in accordance with the equations of Luzzati.1 The structural identification of the isotropic L2 and L3 solution phases by means of X-ray was based on their lack of both long- and short-range order. The domain sizes of the these phases were estimated by using the DebyeScherrer equation for line broadenings7 assuming that the L3 phase shows X-ray scattering as proposed.s8 All analysis is based on the assumptions of ideal mixing of the components and densities equal to 1 g cm-3.

--

-+

+

Results Oneof theobjectives of this study is toinvestigate theassociation behavior of water soluble self-associating block copolymers in lyotropic lipid-based liquid crystals. In the current system there are essentially two possibilities for the mixing behavior. Case i. The EPE molecules form micelles which are located in the water regions of a phase, in which the aqueous volume

8456

The Journal of Physical Chemistry, Vol. 98, No. 34, 1994

fraction,

Landh

aaq,may be estimated as

where 0 . 2 a ~ represent ~0 the G M O headgroup contribution, as based on monoolein. Case ii. The PPO blocks are located in the apolar domains of the phase with the PEO blocks located in the aqueous regions, in which a,, may be estimated as

= 0.2@GMO

+ 0.7@p+ aW

(ii)

where 0.70, represents the PEO contribution. We will put I . . . . I. I ..I I . . . forward arguments that case ii is the most likely in the current 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 system. We note that it is generally believed that EPE forms s (A- I ) reversible micelles (cmc = 100 ppm in water) with very low aggregation numbers.59 The hydrodynamic radius of a monomeric 0.016 1 micelle has been estimated to be in the range of 65-100 A.60v61 Part of the phase diagram in the three-component system 0.014 GMO-EPE-water at 20 OC is shown in Figure 1. The smallangle X-ray data of the indicated samples are given in Table 1 (experiments 1-10). In the phase diagram six different phase 0.012 fields are indicated: two lamellar phase regions, one at low water content (about 7-17 wt % water) originating from the binary 0.01 GMO-water system which swells to approximately 15 wt % EPE, and one water-rich in between 65-77 wt % water and 10-19 wt % EPE; two isotropic solution phases are observed, designated LZ 0.008 and L3, occurring between 20 and 42 and 78 and 90 wt % water, respectively; two cubic phase fields are observed, one originating from the binary GMO-water phase and one, called Q, from the binary EPE-watei system. Within the first cubic phase field we 0 0.01 0.02 0.03 s (A.1) have found four different cubic monophase regions separated by Figure 2. (a) Densitometer tracks of the small-angle X-ray scattering the necessary two-phase regions. In the water-rich region of the curves in experiments 7 and 8, the L2 and L3 phase, respectively,showing binary EPE-water system micelles are formed whose solubilization the similarity in the line broadening effect and (b) densitometer track capacity of GMO is less than 0.5 wt %. Above the solubilization of the diffraction pattern for the diluted lamellar phase (experiment 10). capacity of the micellar solution an isotropic dispersion with the appearance of "oil" droplets is observed. of blue light, indicating that at least some of the structural units The Q Phase. When the amount of EPE exceeds 1 8 wt % the are larger than approximately 500 A. Furthermore, it is Q phase area appears with less than about 1 wt % GMO in the characterized by a flow birefringence and opalescence which investigated region (the Q phase extends between 18-80 wt % become increasingly pronounced with dilution. The liquid EPE in the binary EPE-water system). At higher amounts of crystalline nature of this phase was established by the presence GMO, anisotropic domains, sometimes appearing as bands, are of a diffuse 4.5 A reflection. In addition this phase exhibited a observed. On the basis of the observations made in the polarizing broad diffusion scattering curve similar to those found for Lz microscope we believe that samples within this region of the phase phases (see e.g. ref 62). The absence of a Bragg peak indicates diagram are two- and three-phase regions composed of Q, La, that it has a disordered structure with no long-rangeorder. Figure and L2 phases. However, it has not been possible to separate 2a shows a representative scattering curve for this isotropic solution these phases for SAXS experiments. phase together with a scattering curveof the L2 phase (experiments The formation and structure of the Q phase, in the binary EPE-water system has been subject to many i n v e ~ t i g a t i o n s . ~ 6 , ~ ~ .7~and ~ 8, respectively). The similar shapes of the scattering curves suggest that the structures of these two isotropic solution phases The structure has been proposed to consist of close packed micelles are related with respect to their loss of long-range order. Taken arranged in a face-centered fashion. The existence of the 4.5-A together, these characteristics are consistent with those of the diffuse Bragg reflection implies that the structure is liquid so-called L3 phase (sometimes termed "anomalous flow birecrystalline in nature. The small angle diffractograms of this fringent"or Lz*phase), which is frequently observed in surfactantisotropic phase were generally of poor quality and only two water system5*,63"* and the X-ray scattering obtained in this broadened Bragg reflections were observed whose reciprocal study are similar to those obtained for L3 phases in nonionic spacings were in the ratio d 2 d 5 (25 wt % poloxamer 407, 40 surfactant-water systems. Both thelocation in the phasediagram "C). This corresponds to a primitive lattice with a lattice and the correlation with the adjacent lamellar phase (and the parameter of approximately 130 A. We can, however, not cubic phase field) support this phase assignation. conclude whether a face centered structure is plausible or not. In order to estimate an average repeat distance of the L3 phase The results does, however, indicate that the structure of the Q we have made use of the Debye-Scherrer equation for line phaseis of cubic symmetry. Our results are consistent with recent broadening (see e.g. refs 57 and 62), in which the mean dimension, small-angle neutron scatteringm and NMR61 studies of the binary L h k / , of crystallites is given by L h k / = h/@1/2cos 8, where X, B l l z , EPE-water system. and 8 are the wavelength of the X-ray diffraction, the angular Lz and La Phases. At approximately equal amounts of G M O width a t half-maximum of the scattering profile (rad), and the and EPE and at 90 wt % of water an isotropic solution phase diffraction angle (the values of cos 8 is close to unity), respectively. appears after several weeks of equilibration (the time varied with In this case we assume that the transition from long-range order the amount of water, being longest (-8 weeks) at high amounts in the diluted L, phase (see below for its characterization) to a of water). This phase is surprisingly viscous and has a hydrogelmedium-range order in the L3 phase is accompanied with a line like appearance. It is transparent but shows a weak refraction


Phase Behavior in Lipid-Polymer-Water Systems

TABLE 1: Small-Angle X-ray Results of Experiments 1-10 at 20 OC, Indicated in Figure 1 composition (w/w %) experiment

CIICDICW'

1

68.6211.99129.39

d (A)* 55.91 48.38 36.53 34.17 30.54 29.14 27.74 26.80 70.35 57.50 49.76 40.54 35.52 33.30 87.74 62.55 51.12 43.88 39.01

63.1/1.0/35.9

60.08/5.12/34.8

4

33.27 30.99 138.52 97.18 79.96

38.661 14.09147.25

61.94 55.91 52.22 5ag

34.18/14.77/51.05

5bs

46.26 146.9 103.9 84.8 73.46 65.81 222.0 157.9 128.1 110.8 99.2 83.8 79.0

6

27.01 10.14162.86

7h 8h 9 10

40.01/25.08/34.91 9.2915.25185.46 72.831 13.52113.65 34.18/14.77/51.05

244.8 173.1 141.6 121.9 108.9

--

92.9 140 240 43.0 180.5 89.0 58.7 44.9

hklc

Id

211 220 321 400 420 332 422 431,5 10 110 111 200 21 1 220 22 1,300 110 200 21 1 220 310 222 32 1 400 110 200 21 1 220 310 222 321 400 330,411 110 200 21 1 220 310 110 200 21 1 220 310 222 321 400 330,410 110 200 21 1 220 310 222 321

650 125 16 21 80 90 5 13 495 255 32 94 64 58 405 265 280 7 5 0 25 15 508 172 213 0 6 5 29 0 14 470 135 360 5 30 105 380 255 105 85 0 30 35 0 45 630 197 78 10 0 18

a (A).

structuref

136.6 f 0.3

99.7 f 0.4

124.3 f 0.7

195.6 f 0.7

207.8

* 0.2

315.3 f 1.7

345.8 & 1.5 -250' 650-700' 43' N

00 1 00 1 002 003 004

574 277 106 43

178.5

* 2'

0 CI,cp, and cw are the weight fractions (w/w %) of GMO, poloxamer 407, and water, respectively. b d is the observed Bragg spacing in A. hkl is the lattice indices (hkl and I for tri- and monoperiodicity, respectively). The relative intensities, I, were measured as the area under the peak from the microdensitometer chart or on a computer when the JAVA system was used. Reflections observed for other experiments than those reported are indicated by "0" intensity. The intensities are normalized to a sum of 1000. a is the lattice parameter of the unit cell (in A). /See text for structural assignments. 8 Experiments 5a and b correspond to the top and the bottom phase, respectively, in a two-phase sample. In experiments 7 and 8 the observed spacings corresponds to the maxima in the scattered intensity and the structural units have been estimated as described in the text. Average repeat distance (in A).

*

broadening, analogously to similar suggestions made for an L2 piase.62 The average repeat distance of the L3 phase can thus be estimated as the length, Loo,, of the crystallite domain perpendicular to the (001) plane of the Laphase in the biphase region L, + L3 (not indicated in Figure 1). The camera effect (the Guiner camera was used for these experiments) is included in under the assumption of that the ideal width of the (001) Bragg peak of the L, phase is zero. is thus estimated by

'

subtracting the half-maximum angular width of the (001) peak of the L, phase from the corresponding value for the Lg phase. For a two-phase sample with a composition of 13.5/7.9/78.6 (GMO-EPE-water w/w %) j31p values of 0.006 and 0.002 rad was determined which corresponds to an average repeat distance of the L3 phase in the order of 3 9 0 A (the repeat distance for the L, phase was about 220 A). Assuming everything else constant, we may determine an average repeat distance in the order of

8458 The Journal of Physical Chemistry, Vol. 98. No. 34, 1994

Landh

3. Photographs shou mg the texture of (a) the rater-rich L, phdr: lerpcr~msni IO. crdrrcd polarirerr 90'. IOr (reproduced at 4% of original size)] and (b) water-pmr 1." phirc lerpcr:mcnr 9. crossed polariierr 90'. 20%)(reproduced at 4 5 5 of original \im)l.

65&700 A for experiment 8 = 0.00424.002, with a Bragg spacing corresponding to the maximum of the L3phasescattering curve is about 240 A (Figure Za)]. L.Phases. The lamellar phase in the water-rich region of the phase diagram was ascertained by its X-ray diffraction pattern which showed reflections in the ratio 1 2 3 4 (experiment 10, FigureZb) witharepeatdistanceof 160toabout 220A. Notably, thislamellar phaseshowsagreatvariationin textureastheamount of EPE is increased. At low polymer content its microscopic texture resembles thatof the hexagonal (type 1) phase. Increasing thepolymerconcentrationscausesagradualchangeinthe texture until the characteristic mosaic structure of the lamellar phase appears. Figure 3a shows a photograph exemplifying the appearanceofthe textureasobservedin the polarizing microscope. This and the fact that some samples showed a,diffuse X-ray scattering superimposed on the sharp reflections could be taken as an indication of an occasionally suppressed (or too weak) reflection. However, the same diffraction pattern was obtained when the samples are exposed in a point-collimated camera, allowing the study of orientation effects. Furthermore, if we assume a mixing behavior according to case ii we obtain the expected one-dimensionalswelling behavior of this phase as shown in Figure4. Thedatacorresponds toanaveragebilayerthickness of 31.8 0.5 A. We do not obtain a linear relationship if case i mixing is assumed and the bilayer thickness shows a larger variation(30.4f 3.1 A) ascompared tothecaseiimixing.Strictly, however, these data do not definitely exclude the existence of a hexagonal phase (or its coexistence with a lamellar phase). Further evidence for the lwation of the EPE will be critical for

*

200 210

1M)

E ,

1

0'

. , , . I . . ~ , 1 ~ ~ ~ , 1 ~ ~ ~ , 1 ~ ~ ~ ~ 1 , ~ ~ . ' , . .

0.79

0.8

0.81

0.82

0.83

0.84

0.85

0.86

ow Fiyre4. Observedrepeatdistancesd(h)vs theaqucousvolumefraction Q, for samples of the water-rich L . phase, showing its onedimensional

swelling behavior. a conclusive structure determination of this phase since the choice of distribution of the EPE according tocase i and ii mixing models clearly affects the structural assignment as well as the magnitude of the d spacings. However, we note that it is unlikely that the presence of a hexagonal phase would escape observation in theKiessigcameraand wemay assume that thisphaseislamellar. Samples of the lamellar phase originating from the binary G M G w a t e r system showed a mosaic structure in the polarizing microscope (Figure 3b) and small-angle X-ray diffractograms with reflections in the ratio 1:2corresponding to repeat distances ranging hetween 35 to 47 A (see e.g. experiment 9) which is in


Phase Behavior in Lipid-Polymer-Water Systems

.,.

I

~224

I

~230

Figure 5. Photograph (parallel polarirers OD, 25 'C) of a 'drying" experiment, showing, in addition to the water-rich L . and possibly the L, phase, the existence of three distinct isotropic phases [tentatively identified as cubic phases G(Q230). D(QZz4)and P(Qzz9)]separated by clear 'baundaries" as an effect of their difference in refractive indices. The original sample composition was 44/2/54 % (w/w) of GMO-EPE-water.

the same order of magnitude as observed in the binary G M O water system69 and in the monoolein-water system." This indicates that the PPO's are located in the bilayer according to case ii. The Cubic Phase Field Originating from the Binary GMW Water System. The binary GMO-water system exhibits two reversed cubic phases the G(Q'30) and the D(Q224) ranging between 18 and 33 and 35 and 38 wt W water, respe~tively.6~ This is inagreement with themonoolein-watersystem.I) In the ternary GMO-EPE-water system, we have found that this cubic phase field is extended over a considerably large range in composition with respect to both water ( 1 8 4 7 wt %) and EPE (maximum 20 wt %) content. In addition to the G(Q230) and D(Q224)phases, we show the existence of two more distinct cubic phases within the field. These might tentatively be assumed to be reversed and bilayer-based due to the location in the phase diagram. Thus, we will give data indicating the progression of four different reversed cubic phases, separated by the necessary two- and threephase regions, as imposed by Gihb's phase rule, assuming that EPE and GMO behaves as pure components. Sampleswithin this cubic phase field werealloptically isotropic and did not flow. However, their stiffness decreased discontinuouslyas thehydrationincreased. This was takenasapreliminary indication of a cubiocubic phase transitions. In the light microscope we frequentlyohservedsamples within thecubic phase field which showed easilyrecognizedboundariesbetweendifferent, yet isotropic regions. The boundaries are visible as both macroand microscopic discontinuities as an effect of the different refractive indices of the cubic phases. An example is seen in Figure 5 which shows a photograph of a "drying" experiment carried out at 25 OC of an equilibrated sample with an original composition of 44/2/54 % (w/w) (GMO-EPE-water). The curved boundaries appearing in the isotropic region are easily seen. As indicated in the figure three cubic phase regions (two boundaries) can be identified. The identification of the different cubic phases called for extensive X-ray experiments. Thestrategy was toperform X-ray experiments on samples with either constant GMO-water or GMO-EPE ratios or at constant amounts of water. Along such lines in the phase diagram which differed with maximum 2.5 wt %,sampleswhichdiffered withmaximum2.5 wt Wincomposition of either EPE or water, were examined. Such a detailed scheme

is necessary since thequality of the diffractograms of cubic phases often shows great variation with composition. In addition, many diffraction lines are of weak intensity and may occasionally, for various reasons, be suppressed. Therefore, it is important to find some"referencediffractograms",inaddition to those in the hinary GMO-water system, within every region which can be satisfactorily indexed and, most favorably, whose intensities are in agreement with the structure. In such a manner it is possible to study thevariationofintensitiesand thusapproximatelydetermine the two- and three-phase regions present even if the phases have not been physically separated. The situation is complicated in thecurrent system by theenhanced tendency ofthesecuhic phases togrow in macrodomains as compared to theGMSwatersystem. X-ray data for some representative experiments is presented in Tables 1 and 2. Phases Q12:G(Q230) andQ,:D(QZ2'). Theexistenceof thecubic phases G(Q230) and D(QZx) is clear since they are formed in the hinary GMO-water system69 and must he present in the ternary systemaswel1,eitherasone-ortwo-phaseregionsasaconsequence of Gihb's phase rule. Experiment 1 (Table I ) shows an example of a powder diffraction pattern of a cubic phase whose Bragg peaks index as the 211,220, 321,400,420, 332,422,431/510 reflections of cubic aspect 12, defining the phase QI~:G(Q2m). It is of some importance to give the arguments for the choice of cuhicaspect for theobserved spacingratios. Thus,a facecentered lattice F is ruled out hecause the observed spacing ratios in the direct lattice [ d I / 3 ( d 3 : d 4 d 7 d 8 : d l O d l I : d l Z d 1 3 ) ] is different from those of lattice F [ d l / 3 ( d 3 : d 4 d 8 d l l : d l Z d 1 6 d l 9 d 2 0 ) ] . Thelatticeis most likely not a primitivelattice P, since none of the observed reflections index as h k + I = 2n 1, where h, k , and I are the Miller indices. Therefore, the structure is consistent with a bodycentered lattice, I, and since no observed reflection violates the conditions hhl; 2h I = 4n, Okl = k, I = 2n and hOO = 4n, it suggests that the lattice is of cubic aspect 12. There is only one space group possible for this aspect, namelyla3d(230). The indexing of theohserved spacing ratios in experiment 1 is shown in Figure 6a as a plot of the reciprocal spacing, s = 2 sin B/X (A-1). vs d h 2 + k' + P . The direct lattice has a parameter a = 136.6 0.3 A (as = dh' + k2+ P)givenhythereciprocalgradientoftheplot. Thelinearity of the plot gives a measure of the reliability of the indexing. The indexing is quite convincing and the diffraction pattern of this

+

+

+

*

8460 The Journal of Physical Chemistry, Vol. 98, No. 34, 1994

TABLE 2 X-ray Data of the Cubic Phases P(Q2z9), D(Q2"), and C(P)(Q229) at 20 OC composition (WJW%) sample elf cpf cw' a (A)b 1ad 122.4 68.612.0129.4 2ae 2b 3 4

5

6a

64.615.0130.4 59.4110.1130.5 54.6115.0130.4 49.8 J20.0J30.2 62.412.5135.1

6b

I 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22a 22b 23 24 25 26 21 28

60.115.1134.8 57.6f1.4J35.0 54.9110.0135.1 52.3 f 12.6135.1 49.1114.9135.4 59.112.4138.5 55.5 f 1.5131.0 50.0J 10.0140.0 55.0J3.5J41.5 46.6 11.2146.1 43.8 f 12.4149.6 40.5 19.9149.6 38.7114.1141.2 36.8 f 11.9145.3 38.5 112.3149.2 34.2114.8151.0 3 6 4 9 . 9 154.0 35.011 1.0155.0 30.1114.0156.9 31.5J9.9J58.6 27.0JlO.lJ62.9 25.0 J 10.0165.0

116.6 15.2 121.6 130.5 139.0 111.6 83.5 124.3 130.2 135.0 140.1 143.9 123.2 134.9 150.0 131.8 166.3 167.0 193.8 193.2 193.4 197.2 207.1 315.3 206.6 212.3 316.0 350.3 345.8 351.0

P

structure

vs, m,m vs, s, s vs, m, s vs, m, s vs, m, s ws, w, m

vs, m, m vs, m, m vs, m, s vs, m, s vs, w, m s, m, m vs, w, m vs, m, m s, w, m vs, w, m vs, m, s s, w, m

m, w, m m, m, m vw, vs, m vw, vs, s vw, vs, m vw, vs, m q,cprand cware the weight fractions (WJW %) of GMO, poloxamer 407, and water, respectively. a is the lattice parameter of the unit cell (in A). The relative intensities, I, were visually estimated for the three first observed reflections (ws = very very strong, vs = very strong, s = strong, m = medium, w = weak, vw = very weak, and w w = very very weak). This sample most probably corresponds to a three-phase equilibrium between G , D, and P. e In samples with two phases in coexistence a and b stands for top and bottom phase, respectively. phase is usually easily recognized. Normally, eight reflections were observed whose intensities are in good agreement with earlier published results (see e.g. ref 8) and with those of the same phase in the GMO-water system.69 The identification of the cubic phase of aspect 4 (44) is exemplified by experiment 2. The direct spacing ratio observed [2/1/2(d2:d3:2/4:.\/6:1/8:.\/9:.\/10)] is in agreement with a primitive lattice for which there exists no general extinction conditions but seven cubic aspects each with special extinction conditions. The observed 110, 1 1 1, and 200 reflections rules out cubic aspects 3 , 5 , 6 ,and 7, identified by extinction symbols P41, P..n, Pn.n, and Pa., respectively. The absence of reflections 100 and 210 leaves only cubic aspect 4 identified by extinction symbol Pn.. for which two space groups Pn3m and Pn3 are possible. Therefore, the indexing cannot be unequivocal. However, we have chosen space group Pn3m since this corresponds to the space group of the D surface. Notice that, because of the additional symmetry of the bilayer draped over the minimal surface the space group is Pn3m rather than F43m (216) due to the loss of orientability of the surface. This has caused some confusion in the literature.20 The D surface was also chosen to describe the Q224 phase in the binary MO-water system,13as well as the GMOwater system.69 Since, space group 224 is the most symmetrical space group within the given cubic aspect it is in accordance with the suggestions of Luzzati and associates.8 The indexing of the observed spacing ratios in experiment 2 as cubic aspect 4 is shown in Figure 6b. The intensity distribution of the reflections are again similar to those found in the binary GMO-water system as well as other systems.8

Landh

Increasing amounts of EPE (1.5-2 wt %) causes a phase transition of both the G(QZ3O)and D(Qzz4)phases as is evident by the presence of two-phase samples and the observations of Bragg reflections which violates the permitted reflections of these space groups, even if two-phase samples of phases G(Q230)and D(Q224)are accounted for. The region just above the G(Q230) phase is not fully understood due to the presence of very complicated two- and three-phase regions (shaded in Figure 1). Furthermore, the strong tendency of the cubic phases in this region to grow large macrodomains limited the use of the Guiner camera. It is, however, most likely that the D(QZz4)phase region extends to the water-poor boundary of the cubic phase region. The region seems to be very narrow as the water content is decreased and we have only been able to find two-phase samples with either the D(Qz24)and P(Q229) (see below for its identification) or the G(Q23O) and D(Q224) phases in coexistence. We notice that the phase transition G(Q230) P(Qz29)is unlikely, due to the geometrical relation between the G and the P surfaces, while the D(QZz4) P(QZz9)transition is more likely to occur a t higher amounts of hydrophilic matter as is generally observed in e.g. monoolein-protein-water sy~tems.53~ However, since we encountered some samples in which three cubic phases coexisted, we conjecture a three-phase region, separated by the necessary two-phase regions, in which the G ( Q 2 9 , D(QZz4),and P(Q229) phases coexist. Phase Q s : P ( Q ~ At ~ ~about ) . 1.5 wt % of EPE a phase transition of the D(Q2Z4) phase to a cubic phase of cubic aspect 8 takes place. Consider e.g. experiment 3 for which spacing ratios in accordance to [.\/2(dl:1/2:2/3:~'4:2/5:.\/6:d7:d8:d9 4/12)]were observed. Since hZ+ k2 + Iz never can be equal to 7 and is accordingly forbidden for any cubic lattice, a primitive lattice is ruled out. Therefore the lattice is body-centered (the conventional choice of the smallest unit cell rules out an Flattice) for which thereexist fivecubic aspects. The presenceof reflections with indices h2 + k2 + P = 2,4, 10, 12,and 18 rule out aspect number 12 and those with h2 + kZ + l2 equal to the sets (2,4, 12,and 18), (2and lo), and ( 4 ) rule out space groups 1434 Ia3, and 14132, respectively. The remaining cubic aspect is thus number 8. This aspect defines a set of six space groups of which we tentatively chose space group Zm3m (229)in accordance to theexistenceof a corresponding PMS with this symmetry, namely the P surface of Schwarz. Furthermore, all Bragg reflections show intensities which are in good agreement with earlier reports8 of this cubic phase with one important exception, the Q229 phase observed by Ktkicheff and Cabane in the SDS-water system.71 However, the location of the latter cubic phase in the phase diagram suggests that it is of type I rather than type I1 which is considered here. Thus, it is not surprising that the observed intensities of the reflections differ significantly. As with the D surface, we notice the difference in symmetry of the oriented (space group Pm3n) and the unoriented P-surface (space group Zm3m). The choice of the P surface rather than the C(P) surface is discussed below. The diffractograms of the P(Qz29) phase were usually of good quality at water content between 30 and 45 wt % and reflections up to (330, 41 l), and occasionally higher, were observed. The indexing of the observed reflections is in general satisfactory if the 32 1 reflection is observed, since it rules out the other primitive aspects. Two examples of rather convincing indexing are shown in Figure 6c. For samples with water content higher than about 45 wt % (see e.g. experiment 4 ) the 321 reflection is of weak intensity and it is only occasionally identified. At the lowest water contents the growth of large macrodomains limits the structural evaluation. However, as with samples with high water content, a t least the three first sharp reflections were measured with good accuracy. The unusually large P(QZz9)phase region and the exceptionally large cell parameters (the largest lattice parameter found is about

-

-

Phase Behavior in Lipid-Polymer-Water

Systems


a 0.04 0.035

0.03

0.03

0.025

0.025

3.-N"

d

3

0.02

-

0.02 -

0.015 0.01 0.005 0 0

0.035

1.375

2.15 dh2 + k2 + 1'

4.125

5.5

0

0.5

1

1.5

2

2.5

3

3.5

h2+ k2 + l2 I

I

0.0112

Experiment 3

0.0084

0.025 d

.-

0.02 0.0056

0.015 0.01

0.005 v o

I

,

Experiment 4

1 o'oo21

I

I

0

2.25 3.375 4.5 0 0.975 1.95 2.925 3.9 h2+ k2 + l2 i h 2 + k2 + l 2 Figure 6. (a) Indexing of the observed spacing ratios in experiment 1 on a body-centered lattice of cubic aspect 12, given as 2 sin e/X vs d h z + k2 + P. The linearity, through origin, of the plot gives a measure of the reliability of the indexing. Part b shows indexing, as in a, of the observed spacing ratios in experiment 2 on a primitive lattice of cubic aspect 4. Part c shows indexing, as in a for the spacing ratios observed in experiments 3 and 4 indexed on a bodv-centered lattice of cubic asuect 8. Part d shows indexing, as in a of the observed spacing ratios in experiment 6 on a body-centered lattice of cubic a'spect 8. See text for furthe; details. supports, in addition to the structural assignment, a bilayer 21 8 A) observed, calls for a more detailed examination. In Figure arrangement described by the P surface. 1 (see also Table 2) the variation of the lattice parameter within Phase QgC(P)(Q229).At water content higher than 51 wt % this cubic phase region is indicated. As may be expected there is no simple relationship between the size of the unit cell and the and about 6-18 wt % EPE, cubic two-phase samples weie found in which the least dense phase, the top phase of the sample, composition. Although the amount of water is the most important parameter it is the amount of EPE which allows for the large corresponds to the P(Q229)phase (experiment 5a) with a lattice water swelling. At 35 wt % water the unit cell varies from parameter of about 208 A. For the bottom phase of the sample (experiment 5b) spacings were observed in the ratio 2 ( d l : d 2 : approximately 117 A at 2.5 wt % EPE to about 144 A at 15 wt d 3 : d 5 : 2 / 6 : d 7 : d 8 : d 9 ) which suggests a body-centered lattice. % EPE. For a similar change in the water content at constant The diffraction pattern was reminiscent of that obtained for the amount of EPE (10 wt %) we observe a change in the lattice topP(QZz9)phase, but with different intensity distribution. Since parameter from about 120 A (30 wt % water) to about 170 A the sample was a two-phase sample we cannot exclude contribu(45 wt % water). At water concentrations higher than about tions from the P(Q229)phase to the observed diffraction pattern. 40-45 wt %, e.g. at a ratio of GMO-water of 45/55, the lattice However, one phase sample, as in experiment 6, the observed parameter is not greatly influenced by the polymer content. The spacing ratio ( d 2 : d 4 : d 6 : d l O : d l 4 : d 1 8 ) also indicates a body"jump" in the variation of the lattice size observed at about a centered lattice. This suggests that the lattice is of cubic aspect ratioof 50/50% (w/w) GMO-water indicates a phase transition. However, we have no observations in support for a phase transition 8 and thus the same type as in the P(Q229) phase. The indexing within the P(Q229) phase region (no two-phase samples, similar of the diffractograms of this phase was, however, generally uncertain, due to the relatively few Bragg reflections observed. diffractograms, and intensity distribution, for the most intense The indexing of the observed reflections in experiment 6 as cubic Bragg peaks etc.). In addition, the theoretical evaluation of the X-ray data given below strongly supports this structural asaspect 8 is seen in Figure 6d. In order to observe the higher signment. Taken together we may conclude that the current reflections than 310 we had to expose samples for up to a week P(Q229) phase region is exceptionally large and as a consequence in the Guiner camera (in experiment 6 the time of exposure was 72 h),at whichdamagescaused by theX-rayand/orcompositional of the large concentration of water, the phase reaches an unusually large lattice parameter. We note that large lattice parameters changes became a limiting factor. The data available suggest, however, that the two phases have the same aspect but with a of a P(Q229) phase has been reported in the monoelaidin-water different distribution of matter per unit cell. As discussed in system.8 It should be pointed out that the structure of the Qzz9 detail below we will provide arguments that this seems to be the phase is still a matter of confusion. Since cubic phases can adopt case and we suggest that the fourth cubic phase is also bodycompletely different structural arrangements yet have the same centered and of cubic aspect 8. Furthermore, especially in view space group, the need for additional arguments for a bilayer of the theoretical evaluation of the X-ray data given below, we arrangments is urged. The theoretical interpretation given below 0

1.125

8462 The Journal of Physical Chemistry, Vol. 98, No. 34, 1994

propose a structure of the fourth cubic phase which is based on a triply periodic bilayer. Accordingly, the fourth cubic phase is most likely described by the C(P) surface defining phase Qs: C(P)(Q229). The transition between phase P(QZz9)to the C(P)(4229) phase is hence not described by a Bonnet transformation. With this assignment the lattice parameter for the C(P)(Q229) phase ranges from about 310 to 350 A with increased amounts of water (52-67 wt % at 10 wt % EPE). It is important to notice that the observed reflections are within the limits of resolution of the Guiner camera and for samples with highest water content we did not observe the first reflection due to the large lattice parameter.

Discussion The most crucial steps for the evaluation of the phase behavior presented in Figure 1 was the judgement of when conditions close to equilibrium applied, and the discernment of sample homogeneity (the study of large samples in polarized light is very valuable in this step). This urged the need of a reference system and the application of Gibb’s phase rule. In particular, this is critical in the determination and characterization of cubic phases and their mesomorphism since cubic phases are often observed to exhibit hysterisis. The existence of cubic mesomorphism can only be unambiguously verified if actual multiphase samples are identified. Such samples are invaluable and provide an extraordinarily accurate test for the state of equilibration. Since a cubiccubic two-phase region very often is macroscopically sharp (at least toward one of the two cubic phases) its physical location can be monitored from time to time and it can furthermore be controlled by e.g. temperature. Thus the reversibility, and hence the state of equilibration can be estimated. The phase diagram presented in Figure 1 clearly shows that it is by no means simple to predict aqueous polymer-lipid phase behavior, at least not in the present system. The presence of structures of such high complexity as the cubic phases and the L3 phase cannot be explained in the ordinary terms of complex formation used in polymer-surfactant systems. Instead there exists a competition between the aggregation of the poloxamer 407 molecules and the assembly of the G M O molecules. Clearly the competition is won by the assembly of the GMO in bilayers. In fact, the reversed cubic phases seems to function as an “ideal” solvent for the triblock copolymer. The resulting dominating feature of the phase diagram is the extended reversed cubic phase field discussed in detail below. The cubic phase manifests itself in the presence of its “melted” relatives, the Lz and L3 phases and we may regard their formation as a consequence of weakened interbilayer forces, balanced by an optimal mean curvature. L3 phases have recently received much attention and their structure has been a matter of dispute. It is now generally believed that the structure is best described by a three-dimensional continuous bilayer structure of high connectivity in which the bilayer is curved toward the most abundant phase (reversed curvature) and separates (on an average basis) two independent water (solvent) domains.6348 In this respect it is reminiscent of the reversed bilayer-based cubic phases and the L3 phase can be regarded as a melted cubic phase.65 However, even though the correlation with the adjacent cubic and lamellar phases strongly indicates that the structure is locally of bilayer type and presumably bicontinuous, such a conclusion cannot be made from the data presented here. The formation of both the L2 and L3 phases seems to require a distribution of the poloxamer blocks such as proposed in case ii, since it would be more difficult to explain the decrease of the interbilayer forces in case i. This has indeed been qualitatively verified in a recent study of the phase behavior in some ternary poloxamer-GMO-water systems in which a series of poloxamers with different hydrophilic (PEO) to lipophilic (PPO) ratios were investigated (Landh, T. to be published): low ratios decreased

Landh the extension of the cubic phase field. The presence of the L3 phase has furthermore provided insight in the formation of stable colloidal dispersions of cubic phases Le., fragmented particles of cubic phases, Cubosomes. The phase behavior in Figure 1 can readily be used to explain their formation since there exists an L3-P(QZ29)-water three-phase region (not indicated in Figure l ) , in which the cubic phase is easy to disperse due to the presence of the L3 phase. The formation of Cubosomes is reported in detail elsewhere. The fact that amphiphilic block copolymers do interact with polar lipids has been known for some time and poloxamer 407 has been shown to penetrate monolayers72 as well as bilayers liposome^).^^ Such behavior is difficult to explain without assuming an interaction between the PPO’s and the liposomal bilayer. However, poloxamer micelles could in principle be included in the structure of the mesophases and the PEO units could perturb the bilayer according to the model put forward by Kdkicheff and Cabane in the sodium dodecyl sulfate-PEO-water system.51 Although, it seems like their data are consistent with a complex specific interaction between the PEO and the SDS, we have to seek a better verification of the proposed case ii mixing behavior. Verification of the Case ii Mixing Behavior. It is convenient to begin analyzing the La phase originating from the binary GMOwater system. We analyze experiment 9 for the two cases i and ii of the mixing behavior and compare the observed values with the corresponding values obtained in the binary GMO-water system. We remind the reader that we are assuming ideal mixing and densities equal to 1.O g cm-3 for all components.45-70J4 We notice that the aqueous region in this lamellar phase cannot be large enough to host a monomeric EPE micelle unless a very elongated “micelle” built up by one layer of PPO’s surrounded by a “monolayer” of P E O s is formed. Such configuration seems to be very unlikely. For experiment 9 (d = 43.0 A) cases i and ii give a surface area per G M O a t the apolar/polar region of 48.05 and 44.92 A2, and a half bilayer thickness of 12.53 and 13.40 A, respectively. The corresponding values for the GMOwater system (at 85.0/15.0GMO-water (w/w) %, d = 43 A) are 41.17 Azand 14.6 A.69Clearly, both models give an increased surface area per GMO a t the interface. This is as expected due to the increased hydration of the G M O head groups. However, we cannot explain the large increase in case i, which would correspond to a contribution of 7 A2 per PEO and GMO. Such a large increase would cause a change of the curvature of the bilayers toward the aqueous region (type I) which is not consistent with the phase diagram, even if we assume an interaction according to Kdkicheff and C a b a r ~ e . A ~ ~further argument for case ii is that we have observed problems of homogeneity and hysteresis when samples of the water-poor lamellar phase are prepared from EPE stock solutions. This may be due to formation of micelles which are kinetically included in the structure. No such observation has been made when the same samples are prepared from nonhydrated EPE. These results and those made earlier for the diluted lamellar phase indicate that the PPO’s are located in the apolar environment of the GMO bilayer structure with the PEO’s in the polar regions. Provided this is correct, the PPO’s are on an average basis located closer to the apolar/polar interface rather than the midregion of the bilayer as can be concluded from the extension of the cubic phase region, since it only extends at increased water content and thus with decreased mean curvature a t the apolar/ polar interface. This is consistent with an increase of the average surface area at the apolar/polar interface of the bilayer. If the PPO’s would have been located a t the midregion of the bilayer we would have expected the cubic phase region to extend toward the dry part of the phase diagram. Even if the mixing behavior seems to be consistent with case ii in the lamellar phases, we stress that in the case of the most water-rich cubic phase regions


Systems


TABLE 3: Certain Characteristics per Unit Cell of Some Cubic Periodic Minimal Surfaces (PMSP ~ ~ PMS space groupb XC €Od Q ~

D P

G I-WP C(P) C(D) F-RD

224 229 230 229 229 224 225

-2 -4 -8 -12 -16 -36

-40

1.919 2.345 3.051 3.464, 3.510 g

3.007

_

4 6 3 8:4 12:4 123

Adapted after refs 20 and 24. The space group is given only for the unorientable surface. x is the Euler characteristic. €0 is the surface to volume ratio (area (bilayer) per unit cell with a lattice parameter equal where SOand Vuis the surface and volume to 1) given by €0 = So/( per unit cell. Cis thecoordination(connectivity)number (Le. thenumber of rods that are joined at the nodes in each of the graphs). f According to ref 77. 8 Note that the surface to volume ratio for the C(D) structure is not known to date. the average radius of the water networks are large enough to host a monomeric micelle of the polymer, in which case the possible formation of segregated cubic phases, and cubic phases built up by micelles embedded in a PMS’s, should be considered. However, as is shown below, estimation of the surface-area contributions at various parallel surfaces in reversed cubic phases, confirms the distribution of the PEO’s and the PPO’s according to case ii. Theoretical Considerations on the Structure of the P(Q22g)and C(P)(Q229) Phases. The wide range of water content over which the reversed cubic phase region exists calls for a more detailed analysis. We will in this subsection consider some theoretical arguments for the observed cubic phase sequence and tentatively identify their corresponding PMS’s. We focus on the arguments for the proposed mixing behavior and the structures of the two Q8 phases which are proposed to be described by the P and the C(P) PMS’s. Preliminary Geometric Analysis. The reader is referred to the results by Hyde, Ninham, and c o - ~ o r k e r s ~ ~ J as 8 J *well as those of Anderson and associatesZofor a detailed background of differential geometric analysis of surfactant aggregates. Table 3 lists some surface characteristics of the PMS’s structures of cubic symmetry that have been considered in the analysis. Two parameters characterize the complexity of the surface, the Euler characteristic, x, which is given by the Gauss-Bonnet theorem, and the coordination number, which is, in the ICR model of Luzzati, or in the “skeletal” graphs of S ~ h o e the n ~ number ~ of “rods” in each labyrinth which are joined a t the nodes. In the terminology of Schoen the “skeletal” or “labyrinth” graphs are the two interpenetrating graphs which are threaded in the subvolume labyrinths in such a way that the shape of the labyrinth is outlined. Each labyrinth graph is given a name and the corresponding PMS is given hyphenated names in accordance to the two graphs. Two graphs are dual, and if they are congruent they are said to be selfdual and is given the name of one of the two graphs (e.g. P and D). We note the important result obtained by Charvolin and Sadoc which shows that bilayer-based cubic phases only can be described by PMS’s in which the pair of graphs are ~elf-dual.’~Finally, a PMS is said to be the complement to another PMS if they contain the same set of straight lines and have the same space group; e.g., the complement of P:C(P). The surface area per G M O head group and the bilayer half thickness of the cubic phases in the ternary phase diagram can be estimated based on the cubic phases in the binary GMOwater system. The dimensionless surface area per unit cell of a PMS of cubic symmetry, to, (sometimes called surface to volume ratio) listed in Table 3 is given by

to= S 0 a 3 / ~ , a=2 s,/(v,)*/~ where a is the lattice parameter,& the area of the minimal surface, and Vuthe volume, of the unit cell. Equation 1 allows us to scale

_

the surface area per unit cell for cubic symmetries. The corresponding dimensionless surface area per unit cell for a surface _ parallel to the midsurface located a t a distance 1 (Le. half the bilayer thickness excluded the head group) irom the the midsurface is given by

which allows scaling as well. The D(Q2Z4) phase in the binary system has a lattice parameter of 99.7 A a t 36.0 wt % GMO.69 By using the exact formula for the bilayer volume ratio (ab = 1 - aaq)as a function of the bilayer half thickness to lattice parameter ratio ( l / a ) given by

(3) l / a can be solved by iteration. For ab = 0.512 (EO = 1.919, we obtain a half bilayer thickness of I = 13.78 A and a corresponding surface area per G M O at the apolar/polar interface of sGMO = 2&a2/PGMo = 31.67 A2, where pGMo is the number concentration of G M O per unit cell. The corresponding values for the G(Qz3o) phase ( t o = 3.051, x = -8) are for ab = 0.544 and a = 149.6 A, I = 14.00 A a n d S l = 30.89 A2.b9Notice that the surface area at the apolar/polar interface is increased with increased hydration even if a phase boundary is crossed. This is in agreement with earlier observations. A calculation of the surface area per oleic chain using the ICR model gives about 35 and 36 A2 for the G(Q230) and D(Q224)phases, respectively. Within the ICR model we can also calculate the rod radius which corresponds to some average radius of the aqueous networks in the corresponding PMS model. For the D(Q224) and G(Q230) phases we obtain 22.5 and 20.2 A, respectively. Thus both the PMS formalism and the ICR model give values in support of a mixing behavior according to case ii since the average size of the polar networks is too small to host a monomeric micelle of the EPE in both the G(Q230)and D(Q224) phases. We point out that in the case of the cubic phases a t higher hydrations, where the average radius of the water networks are large enough to incorporate a monomeric micelle of the polymer, the differences between the two mixing models are delicate. However, we have no results in support of a dissociation of the EPE- and the GMObased bilayer. An additional important point is indicated from these calculations, namely that the half bilayer thickness is only about 0.6 of the fully extended oleic chain length (about 24 A), which is usually used to estimate the bilayer half thickness in the GMO-water system. The calculated half thickness is in fact in good agreement with the chain length if we assume a packing of the G M O chains in the bilayer where the methyl endgroup of each GMO in one layer is located a t the position of the double bond of the opposite G M O layer. Bilayer-EPE Interactions in the P(Q229)Phase. Before we analyze the structure of the proposed C(P)(Q229) phase we seek a verification of the proposed mixing behavior according to case ii in the cubic phase field, particularly in the P(Q229) and C(P)(Q229)regions. Generally, it also has to be verified that the total surface area per unit cell is not dependent on some specific molecular interaction between the GMO and EPE. This may be done by estimating the different contributions to the surface area per species, which also provides additional information about their approximate location with reference to the bilayer. The different contributions to the surface area a t the midsurface, So, given by eq 1 and the surface area, S1 = tla2, of the parallel surface located at a distance 1 from the midsurface can approximately be decomposed into the contributions from GMO (SGMO) and from the polymer molecules (sp) by a plot of S / ~ G M O vs Pp/PGMO according to the formula

x = -2)

(4)

8464


a

60

Landh

~,

c , , , , , , , , , ~ , , , , , , , , , ~ , , ' , , , , '

0

So

- - -y

'1

- - - - - y = 32.363 + 341.62~R= 0.84097

= 37.542 + 118.19~R= 0.38513

0 so SI

2o 0

0.005

0.01

0.5

1

PJPGMO

0 so

= 37,542 + 0.59694~R= 0.38513

- - - - - y = 32.363 + 1.7253~R= 0.84097

E 0

0.015

- - -y

2

1.5

2.5

3

PF~PGMO

- - -y = 37.542 + 1.8184~R= 0.38513 - - - - - y = 32.363 + 5 . 2 5 5 6 ~R= 0.84097

c

A

--

-y = 38.856 + -0.030596~R= 0.19457 S I -----y=32.07+0.14175~R=0.68101

0 so 10

1 10

0

0.2

0.4 0.6 pPFQ/pGMO

0.8

1

5

10

15

20

25

30

35

P~/PGMo

Figure 7. (a) Plot of the total surface area (per unit cell) per GMO vs the number fraction per unit cell of poloxamer 407-GMO for the data in Table 2 corresponding to the P(Q2z9) phase. Open circles shows the plot corresponding to the total surface area calculated as the midsurface area of the hydrocarbon region. Filled circles shows the plot corresponding to the total surface area given by the area of the apolar/polar interface. The broken lines are the least-squares-fit linear regression, whose equations are shown (see eq 4 in the text). The plots indicates a larger contribution to the area of the apolar/polar interface per poloxamer 407 molecule. Part b is the same as in a but for the PPO/GMO number fraction per unit cell, showing the larger contribution to the midsurface area per PPO unit, indicating that its preferred location is more adjacent to the hydrocarbon midsurface, as compared to the PEO. Part c is the same as in a and b but the abscissa is given by the PEO/GMO number fraction, showing the relative small contribution per PEO unit to the midsurface area, indicating that their preferred location is in the polar regions of the phase. Part d is the same as in a but for the water-GMO number fraction, showing the negligible contributions per water molecule to the midsurface area (note the negative slope) and the relative small contribution per water molecule to the apolar/polar surface, as compared to the contributions both per PEO and PPO units, indicating the usefulness of eq 4. These results gives strong support that the proposed case ii mixing model seems to be qualitatively correct, and we can assume that the PPO units of the poloxamer are located in the apolar regions or at the apolar/polar interface of the bilayer, while the PEO units are located in the aqueous regions and at the GMO head groups, significantly increasing the hydration of the cubic phases as compared to the binary

GMO-water system. where ~ G M Oand pp are the number of molecules per unit cell of GMO and polymer respectively, and S is either SOor SI, for which we obtain corresponding values for SGMO and sp. Similarly, we can estimate the contributions per PPO and PEO (pp is then changed to pppo and p p ~ orespectively in eq 3) of the poloxamer at the two surfaces which thus can be taken as a measure of their respective location with reference to the bilayer. In this analysis we have used the data given in Table 2 for the P(QZz9)phase. Note that we have used @b according to case ii in the iterative calculation of l / a from eq 3. The results are shown in Figure 7 . The linearity of the plot for the polymer contributions, seen in Figure 7a, suggests that the surface area per unit cell does not depend on any specific molecular interaction between the G M O and poloxamer 407 molecules. The intercepts give 37.5 Az for the mean interfacial area per oleic chain at the midsurface of the bilayer and 32.4 A2 at the parallel surface defined by the apolar/ polar interface. These values should approximately correspond to the values for the D(Q224)phase in the binary GMO-water system which is calculated to 36 and 32 AZ, respectively. Linear relationships are also obtained if the EPE contribution is decomposed into PPO, and PEO contributions, as is seen in Figure 7, parts b and c, respectively. Since the contribution per PPO at the apolar/polar interface is significantly larger than the contribution at the midsurface, it gives further support for the assumption that the PPO's are located closer to the apolar/polar

interface than to the midbilayer surface. As is expected in case ii the PEO contribution is also larger at theapolar/polar interface, although significantly smaller than for the PPO's. The use of eq 4 can be validated by estimating the area contributions per water molecule. Such a plot is shown in Figure 7d. Within the accuracy of the data, the contribution at the midsurface is zero, and the contribution to the area of the apolar/polar interface is significant, although smaller than these from the PPO and PEO. These calculations supports our earlier assumptions and we may as a first approximation estimate the aqueous volume fraction to be = 0.2@, + 0.7@.,+ @w according to case ii. Furthermore, we can assume ideal mixing and set the densities of all components equal to 1.0 g cm-3.45~70J4 We are aware that this is a rather coarse estimation but it is satisfactory for the moment, and we have generally found that a refinement of the densities favor case 11.

Phase C(Pl(Q229)and the P(QZz9)to C(P)(QzB)Phase Transition. We have to substantiate the choice of the C(P) surface as the PMS describing the fourth cubic phase region. In doing so we emphasize that it is important to use the symmetry indicated by the X-ray data, as well as the need for reference data. As the latter we will use the P(Q229) phase. We begin by estimating the dimensionless surface area for the structure in the fourth cubic phase region by means of eq 3. We consider experiments 6 and choose a half bilayer thickness in accordance with those in the


Systems


0.98

lo5

0.96

L

0.94 0.92

0

3 -

P

0.9

1o4

M

0.88

D

1000 " 00

E

G

t

h

0.86

il

0.84

100

0.82 0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.45

0.8

0.5

0.55

0.6

0.65

0.7

0.75

0.8

@aq @aq

Figure 8. The curvature estimated as [I/(O for the D(Q224),P(Q229),and C(P)(Q229)phases (data fromTable 2) versusthe aqueousvolumefraction

aaq.Note the relief, at the phase transitions (arrows), of the strain accumulated as aaqincreases. binary GMO-water system (e.g. 13.8 A). If we assume the structure to be described by the P surface (i.e. to be Qs!) rather than the C(P) surface, we obtain t o = 3.1, which clearly is significant higher than 2.345 for the P surface (for ab = 0.25 ( I = 17 A, a = 300 A) and ab = 0.32 ( I = 13 A, a = 360 A) we obtain 60 = 2.80 and 3.44, respectively). t o may also be estimated from the surface area, SO. From Figure 7a SOis found to be about 40 A2 giving 50 = 3.15. (Note that the data for the plot in Figure 7a are for the P(Q229) phase.) These values can be assumed to underestimate the true value, since it is rather the balance between a, 1, and the composition which determines the interfacial topology. But we have consciously underestimated the values. For the moment we are satisfied with these approximate values of Eo since all other methods to estimate it will just introduce additional assumptions which we cannot verify. However, the structure of the fourth cubic phase is described by a PMS which is self-dual and most likely has a space group compatible with those defined by cubic aspect 8 with a dimensionless surface area which most probably is higher than 3.1. It is furthermore likely that the PMS candidate should have a higher coordination number than the P surface. There is currently only one known PMS which fulfills these criteria; the C(P) surface whose symmetry is Zm3m for the unorientable surface as imposed by its relation to the P surface. Other candidates of PMS's with high connectivity such as the C(D) s~rface2~3~6 (assuming that the indicated symmetry from X-ray is found to be wrong) cannot be considered since their surface to volume ratios are yet to be determined. However, we note that the C(D) has a higher coordination number than the C(P) surface which favors thelatter as the most probable PMS (see also below). In order to verify the use the P(Q229) phase as a reference for the evaluation of the C(P)(QZz9)the existence of a P(Q2z9) C(P)(Q229) phase transition must be supported, since they both belong to the same cubic aspect. First we assume that the PMS assignment is correct. Since the Euler characteristic per unit cell is negative for the PMS's considered we see that the area per unit cell of a parallel surface of a reversed bilayer-based cubic phase must be less than the surface area at the midsurface of the bilayer. Thus 61/40 gives a measure of the curvature of a cubic phase. Since in the current system the cubic phase structures may be assumed to be of type 11, because of their location in the phase diagram, El/[O must be less than 1. This measure of the curvature is preferred in the current ternary system since the progression of cubic phases is rather governed by a balance between a, I , and the composition. Moreover, molecular packing relationship is not simply applied to the current system. Figure 8 shows a plot of tl/Eoas function of +,,in which we have assumed the structures are corresponding to D, P, and C(P). As is seen the curvature

-

Figure 9. The number density of GMO (PGMO) vs the aqueous volume calculated according to case ii mixing, indicating a phase fraction (aaq), transition (arrow) at about 68 vol q,correspondingto the proposed P ( Q 9 C(P) (Q229)transition.

-

increases (&/to decreases) toward a phase transition where it abruptly changes. This observation can be phrased in terms of a strain, or frustration, which is built up in a structure as ab decreases and thus necessarily & / t o increases. The buildup is suddenly relieved at the "discontinuities" in the plot which corresponds to the cubic-cubic phase transitions. A phase transition can thus be said to occur in order to get the preferred curvature on the right track again. There are, however, no indications of differences between the two phase transitions as might have been expected due to the PMS's relations. Note that similar conclusions can be made if for example the area averaged mean curvature is plotted as function of aaq. We now seek an analysis which is not dependent on the PMS assignment but sensitive to the symmetry and topology of the cubic phases. We chose a plot of the number density of G M O per unit cell vs the lattice parameter in which we only assume the data to be described by cubic aspect 8. Such a plot is shown in Figure 9 and there is a clear indication of a phase transition taking place at about 68 vol 7% corresponding to the P(Q229) C(P)(Q229) phase transition. This is in agreement with Figure 8. By combination of eqs 1 and 2 and using the Gauss-Bonnet theorem an approximate relation for PMS's with cubic symmetries is given by

-

which suggest that if the lattice parameter is known as a function of composition, a plot of S1/2a2vs 2 d 2 / a 2will provide an estimate of the surface topology.I8-38 The intercept yields the value of €0 and the slope is equal to x. It should thus be possible to discriminate between the two cubic phases proposed to be described by the P and C(P) surfaces, since they have the same surface symmetry but different surface topology. A plot of eq 5 should thus give two distinct regions with different slopes, one corresponding to the P surface ( x = -4) and another corresponding to the C(P) surface (x = -16). Such an analysis is a priori assumed to be most accurate if the data are for samples with a constant GMO/EPE ratio corresponding to the most centered path in the cubic phase area, where it is fairly safe to assume a constant half bilayer thickness and an increasing surface area at the apolarlpolar interface as the hydration increases. Since the data is somewhat scattered, and since we are more interested in the general trends, we first plot all data for the two Q, phases as shown in Table 2 (the variation in 1 is about 3 A for these experiments). As seen in Figure 10a the result indicates two different slopes corresponding to the two observed cubic phases. The data for the P(Q229) phase supports our structural assignment

8466

Landh


1

1 0. I

0

3.5

1.5

rather simple geometrical arguments can be used to exclude certain possible arrangements. It is demonstrated that cubic mesomorphism is not a crystallographicoddity and that detailed phase behavior studies of cubic phase fields can reveal the existence of several monophasic cubic regions. The reversed cubic phase field in the current system extends through a wide range of water and polymer content as a result of a decrease in the bilayer curvature due to the preferred location of the PPO block just below the apolar/polar interface of the GMO bilayer. The fact that the molecular arrangement favors decreased curvatures is manifested in the extension of the cubic phase field and the observed cubic mesomorphism as well as in the appearance of an L3 phase at increased hydrations adjacent to the cubic phase field. The molecular arrangement is also reflected in the unusually broad extent of the cubic phase in polymer content, which is an affect of the amphiphilic nature of EPE. This allows for small changes in the bilayer curvature as the EPE content is increased. We note that the GMO-water system (as well as other monoglyceride-water systems) possesses an unusually large cubic phase field compared to "ordinary" surfactant-water and surfactant-il-water systems, where the extension of the cubic phase@) most often is narrow in one or two directions, indicating that the thermodynamic degree of freedom is small. It is then interesting to speculate why monoglycerides, especially monoolein, have such a "preference" to form bilayerbased cubic phases. In particular, it is tempting to compare the current system with mixtures of monoolein-water and amphiphilic biological polymers, such as proteins and glycoproteins. Such systems are known to possess a similar phase behavior as the one presented here. The experimentally observed sequence of the four reversed cubic phases is proposed to be, starting from the binary GMOwater line, G(Q230) D(Q224) P(Q229) C(P)(Q229). The boundaries between these phases is charackrized by two-phase samples, and the sequence is confirmed by X-ray experiments. The experimentally observed cubic mesomorphism is to an approximation theoretically verified by reference to the minimal surface bisecting the periodic bilayer. However, the complicated molecular arrangement and the poor X-ray data makes the determination of the C(P)(Q2Z9) phase more uncertain. We conclude, however, that the only PMS known today whose structure is in agreement with the estimated structural parameters is the C(P) surface. The existence of the proposed P C(P) phase transition is supported by the observation of two-phase samples and changes in physical behavior. In addition, the X-ray data and its theoretical evaluation show a significant difference between the two phases. The required transition between the two complementary surfaces is different from earlier observed intercubic phase transitions which have been proposed to be transitions between associate surfaces. The existence of a cubic phasedescribed by the C(P) surface was independently considered by Strom and Anderson.41 Further experiments are needed to make more definite conclusions concerning the possible existence of the C(P)-based cubic phase as well as the possible mesomorphism in the fourth cubic phase region. A forthcoming publication will treat these matters in more detail. In addition to experiments, the characterization of the C(D) surface is urged.

0.02

0.04 0.06 2n(lia)'

0.08

0.03

0.04 0.05 2n(~a)'

0.06

1 1

1

0.02

0.07

Figure 10. (a) The plot according to eq 5 in the text using the data in Table 2, for the P(Q229) and C(P)(Q229) phases. The different slopes

indicate that the data corresponds to two different structures. Ideally, the slope is a measure of the topology per unit cell ( x ) and the intercept gives the normalized surface to volume ratio (€0) of the PMS. The symmetry,Zm3m) theoretical lines for the P surface ( € 0 = 2.345, x = 4, and theC(P) surface ( € 0 = 3.51, x = -16,symmetryZm3m) areindicated. Part b shows magnification of the plot for the P(QZz9)phase, indicating that the most likely structure is a bilayer draped over the P surface. Indicated is also the theoretical line for the P surface as specified in a. See text for further details. and the linear character of the plot implies that it is of bilayer type. If the data is chosen between GMO/EPE ratios corresponding to 113 and 411 in order to reduce deviations due to the variation in the half bilayer thickness, the intercept yields 50 = 2.4. This is close to the expected value of 2.345 for the P surface (Figure lob). The data for the proposed C(P)(QZz9) phase suffers from severe scatter. However, we can estimate €0 to be on the order of 3.3 which should be compared with 3.5 1 for the C(P) surface. We can also conclude that the structure is described by a PMS with a higher Euler characteristic than for the P(Q229) phase. Thus, irrespective of the scattered data, we believe that the fourth cubic phase is indeed a bilayer-based cubic phase defined as phase C(P)(Q2Z9). Finally, we note that the data indicate that there may be yet another cubic phase structure at the highest amounts of water. It is obvious that further experiments are needed (which are in progress) to reveal the exact nature of this part of the cubic phase field.

Conclusions This study reveals some intriguing phase properties in the ternary GMO-poloxamer 407-water system. The importance of conducting complex phase behavior studies relative to a known phase behavior is emphasized. Furthermore, due to the fact that several molecular arrangements are possible within a given space group the importance of fine structure methods are becoming urgent. As shown, even estimations of low resolution based on

- - -

-

Acknowledgment. I thank KBre Larsson for fruitful ideas and discussions and Krister Fontell for valuable comments on the manuscript. Financial support from Lanstyrelsen of Malmohus Ian is gratefully acknowledged. References and Notes (1) Luzzati, V . In Biological Membranes; Chapman, D., Ed.; Academic Press: New York, 1968, pp 71-123. (2) Fontell, K. Colloid Polym. Sci. 1990, 268, 264. (3) Luzzati, V.; Gulik, A.; De Rosa, M.; Gambacorta, A. Chem. Scr. 1987, 278, 211.

Phase Behavior in Lipid-Polymer-Water Systems (4) Lindblom, G.; Rilfors, L. Biochim. Biophys. Acta 1989, 988, 221. (5) Larsson, K. J . Phys. Chem. 1989, 93, 7304. (6) EngstrGm, S.; Landh, T.; Ljunger, G. Proc. Inr. Conf. Pharm. Tech. Paris, Abstr. 1989, 5. (7) Anderson, D.; Strbm, P. In Polymer Association Structures: Liquid Crystals and Microemulsions; El-Nokaly, M., Ed.; American Chemical Society: Washington, DC, 1989; p 204. (8). Mariani, P.; Luzzati, V.; Delacroix, H. J . Mol. Biol. 1988,204,165. Luzzati, V.; Mariani, P.; Delacroix, H. Macromol. Symp. 1988, 15, 1. (9) Luzzati, V.; Vargas, R.; Gulik, A.; Mariani, P.; Seddon, J. M.; Rivas, E. Biochemistry 1992, 31, 279. (10) Vargas, R.; Mariani, P.; Gulik, A.; Luzzati, V. J. Mol. Biol. 1992, 225, 137. (1 I ) Delacroix, H.; Gulik-Krzywicki, T.; Mariani, P.; Luzzati, V. J. Mol. B i d . i993, 229, 527. (12) Larsson. K.: Fontell. K.: Kroa. N. Chem. Phvs. LiDids 1980.27.321. (1 3) Hyde, S.T.; Andersson, S.; J%icsson, B.; Larsson; K. 2. Kristallogr. 1984, 168, 213. (14) Longley, W.; McIntosh, T. J. Nature 1983, 303, 612. (1 5 ) Mackay, A. L. Nature 1985,314,604. Mackay, A. L. Physica 1985, 1318, 300. (16) Charvolin, J.; Sadoc, J. F.J . Phys. Fr. 1987, 48, 1559. (17) Hyde, S. T. J . Phys. Chem. 1989, 93, 1458. (18) Hyde, S. T. J. Phys. Fr. 1990, C7 (Suppl. 23), 209. (19) Scriven, L. E. Nature 1976, 266, 123. (20) Anderson, D. M.; Davis, H. T.; Scriven, L. E.; Nitsche, J. C. C. Adv. Chem. Phys. 1990, 77, 337. (21) Schwarz, H. A. Gesammelte matematische Abhandlung, SpringerVerlag: Berlin, 1890; Vol. 1. (22) Neovius, E. Bestimmung Zweier Speciellen Periodischen Minimalfiischen; J. C. Frenckell and Sons: Helsingfors, 1883. (23) Stessman, B. Math. Zeit. 1934, 33, 417. (24) Schoen, A. H. Infinite Periodic Minimal Surfaces without Self Intersections;NASA Tech. Note, TD-5541; National Technical Information Service Document N70-29782: Springfield, 1970. (25) Nitsche, J. C. C. Vorlesungen iiber MinimalfliSchen; SpringerVerlag: Berlin, 1975. (26) Osserman, R. A Survey of Minimal Surfaces; Dover: New York, 1986. (27) Karcher, H. Manuscr. Math. 1989, 64, 291. (28) The continuity of a cubic phase refers to the number of continuously separated subspaces or regions and will thus depend on the type of the cubic phase. Two types of monolayer cubic phases (normal, type I curvature) have been discussed in the literature. Single monolayer cubic phases exhibits two continuous spaces, the apolar and the polar region, and is hence bicontinuous. Intertwined double monolayer cubic phases exhibit three continuous spaces (tricontinuous) consistent of two apolar intertwined regions and one polar region. The apolar/polar interface(s) of these two types of monolayer cubic phases aredescribed by oneand two periodicconstant (nonzero)meancurvature surface, respectively. The bilayer cubic phases (reversed, type I1 curvature), whose midbilayer region is described by a PMS and whose two apolar/polar interfaces are described by two periodic constant mean curvature surfaces having the same magnitude, but different signs of the mean curvature, are in a sense tricontinuous. There are two independent intertwined continuous polar spaces, separated by the continuous bilayer, whose apolar part constitutes the third region. However, for historical reasons the term bicontinuous is used for both monolayer (single and double) and bilayer phases, which makes it important to identify the type (reversed or normal), as well as the topology, of the cubic phase that is studied. Tricontinuous cubic phases having the same symmetry and topology but with opposite curvature are known to exists for space group Ia3d (phases Q1230and Q11230). (29) Larsson, K. Nature 1983, 304, 664. (30) Luzzati, V.; Mariani, P.; Gulik-Krzywicki, T. In Physics of Amphiphilic Luyers; Meunier, J., Langevin, D., Boccara, N., Eds.; SpringerVerlag: Berlin, 1987; p 131. (311 Buchheim. W.: Larsson. K. J . Colloid InterfaceSci. 1987.117.582. , , (32j Caffrey, hi. Biochemisrry 1987, 26, 6349.(33) Caffrey, M. Biophys. J. 1989, 55, 47. (34) Caffrey, M. Annu. Rev. Biophys. Biophys. Chem. 1989, 18, 159. (35) Gulik, A.; Luzzati, V.; De Rosa, M.; Gambacorta, A. J . Mol. Biol. 1985, 182, 131.

The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 8467 (36) Mitchell, D. J.;Tiddy, G. J. T.; Waring, L.; Bostock,T.; McDonald, M. P. J. Chem. SOC.,Faraday Trans. I 1983, 79,975. (37) Jahns, E.; Finkelmann, H. Colloid Polym. Sci. 1990, 265, 304. (38) Barois, P.; Hyde, S.; Ninham, B.; Dowling, T. Lungmuir 1990, 6, 1136. (39) Radiman, S.; Toprakcioglu, C.; Faruqi, A. R. J . Phys. Fr. 1990,51, 1501. (40) Seddon, J. M.; Hogan, J. L.; Warrender, N. A.; Pebay-Peyroula, E. Prog. Colloid Polym. Sei. 1990, 81, 189. (41) StrGm, P.; Anderson, D. M. Lungmuir 1992, 8, 691. (42) Lutton, E. S.J. Am. Chem. SOC.1965, 42, 1068. (43) Krog, N.; Larsson, K. Chem. Phys. Lipids 1968, 2, 129. (44) Ericsson, B. Ph.D. Thesis, Lund University, Lund, Sweden, 1986. (45) Pader, M. In Surfactants in Cosmetics; Rieger, M. M., Ed.; Marcel Dekker: New York, 1985; p 293. Thau, P. In Surfactants in Cosmetics; Rieger, M. M., Ed.; Marcel Dekker: New York, 1985; p 349. (46) Lundsted,L. G.; Schmolka, I. R.In Blockandgaff copolymerization; Ceresa, R. J., Ed.; Wiley: London, 1976; Chapters 1 and 2. (47) Goddard, E. D. Colloids Surf. 1986, 19, 255. (48) Goddard, E. D. Colloids Surf. 1986, 19, 301. (49) Lindman, B.; KarlstrBm, G. In The Structure, Dynamics and Equilibrium Properties of Colloidal Systems; Bloor, D. M., Wyn-Jones, E., Eds.; Kluwer Academic Publishers: Netherlands, 1990; p 131. (50) Gennes de, P. G. J. Phys. Chem. 1990, 94, 8407. (51) Kekicheff, P.; Cabane, B.; Rawiso, M. J . Colloid InterfaceSci. 1984, 102,51. Singh, M.; Ober, R.; Kleman, M.; J . Phys. Chem. 1993,97, 11108. (52) Tiddy, G. J. T. Phys. Rep. 1980, 57, 1. (53) Luzzati, V.; Mustacchi,H.; Skoulios,A.; Husson, F. Acta Crysfallogr. 1960,13,660. Luzzati, V.; Baro, R.J . Phys. Rad. Phys. Appl. 1961 (Suppl. l l ) , 186 A. (54) Stenhagen, E. Acta Chem. Scand. 1951, 5, 805. (55) Hernqvist, L. Ph.D. Thesis, Lund University, Lund, Sweden, 1984. (56) (a) International Tables for Crystallography; Reidel, D., Ed.; Dordrecht: Holland, 1952; Vol. I. (b) International Tables for Crystallography; Reidel, D., Ed.; Dordrecht: Holland, 1952; Vol. 11, p 147. (57) Klug, H. P.; Alexander, L. E. X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials; Wiley: New York, 1974, p 618. (58) Benton, W. J.; Miller, C. A. J . Chem. Phys. 1983, 73, 4981. (59) Cosgrove, T. J . Chem. SOC.,Faraday Trans. 1990.86, 1323. (60) Wanka, G.; Hoffmann, H.; Ulbricht, W. Colloid Polym. Sei. 1990, 268, 101. (61) Malmsten, M.; Lindman, B.; GBransson, C. Macromolecules, submitted for publication. (62) Fontell, K.; Hernqvist, L.; Larsson, K.; Sjablom, J. J . Colloidlnterface Sci. 1983, 93, 453. (63) Porte, G.; Marignan, J.; Bassereau, P.; May, R. J . Phys. Fr. 1988, 49, 511. (64) Gazeau, D.; Bellocq, A. M.; Roux, D.; Zemb, T. Europhys. Lett. 1989, 9, 447. (65) Anderson, D.; Wennerstrbm, H.; Olsson, U. J . Phys. Chem. 1989, 93, 4243. (66) Strey, R.; Jahn, W.; Porte, G.; Bassereau,P. Langmuir 1990,6,1635. (67) Strey, R.; Schomlcker, R.; Roux, D.; Nallet, F.; Olsson, U. J . Chem. SOC.,Faraday Trans. 1990,86, 2253. (68) Milner, S. T.; Cates, M. E.; Roux, D. J . Phys. Fr. 1990, 51, 2629. (69) Landh, T. Manuscript in preparation. (70) Lindblom, G.; Larsson, K.; Johansson, L.; Fontell, K.; Forsbn, S. J . Am. Chem. SOC.1979, 101, 5465. (71) Kbkicheff, P.; Cabane, B. J . Phys. Fr. 1987,48, 1571. (72) Magalhaes, N. S. S.; Benita, S.; Baszkin, A. Colloids Surf. 1991,52, 195. (73) Jamshaid, M.; Farr,S. J.; Kearney, P.;Kellaway, I. W. Int. J.Pharm. 1988, 48, 125. (74) Technisches Merkblatt, LutrolFl27; Register 7, BASFCorp. Chem. Div.: Ludwigshafen, Germany 1989. P h o n i c F127; Material Safety Data Sheet no. 583106, BASF Parsippany, 1986. (75) Charvolin, J.; Sadoc, J. F. J . Phys. Fr. 1987, 87, 1559. (76) Schoen, A. H. Not. Am. Math. SOC.1969, 16, 519. (77) Lidin, S.; Hyde, S. T.; Ninham, B. W. J. Phys. Fr. 1990, 51, 801.

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