Structural Polymorphism of Amphiphilic Copolymers: Six Lyotropic

Langmuir 1997, 13, 23-34

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Structural Polymorphism of Amphiphilic Copolymers: Six Lyotropic Liquid Crystalline and Two Solution Phases in a Poly(oxybutylene)-b-poly(oxyethylene)-Water-Xylene System Paschalis Alexandridis,* Ulf Olsson, and Bjo¨rn Lindman Physical Chemistry 1, Center for Chemistry and Chemical Engineering, University of Lund, P.O. Box 124, Lund S 22100, Sweden Received July 24, 1996. In Final Form: October 9, 1996X Six lyotropic liquid crystalline and two solution (equilibrium) phases can be formed (at 25 °C) by an amphiphilic diblock copolymer composed of poly(ethylene oxide) and poly(butylene oxide) in the presence of water (selective solvent for PEO) and “oil” (p-xylene, a selective solvent for PBO). Oil-in-water (“normal”) micellar solution (L1), micellar cubic liquid crystals (I1), hexagonal liquid crystals (H1), and a lamellar structure (LR) are formed with an increase of the copolymer concentration along the oil-lean side of the ternary phase diagram. A micellar solution (L2), micellar cubic liquid crystals (I2), hexagonal liquid crystals (H2), and bicontinuous cubic liquid crystals (V2), all of the water-in-oil (“reverse”) morphology, are formed in the water-lean part of the phase diagram with increasing copolymer concentration and in the presence of some water. The oil-in-water [water-in-oil] structures can accommodate up to 0.33 [0.40] g of oil [water]/ g of copolymer. The formation of a reverse micellar cubic phase (I2), indexed to the crystallographic space group Fd3m (face-centered), is an important feature of this phase diagram as it is one of the first times that such a structure has been identified. The normal micellar cubic structure (I1) is body-centered (Im3m). The microstructure in the bicontinuous cubic region (V2) can be described in terms of a multiply-connected amphiphile bilayer consistent with the Gyroid minimal surface (Ia3d). The absence of a “preferred curvature” in the self-assembly of this macromolecular amphiphile distinguishes it from typical low-molecular weight surfactants and bestows this remarkable structural polymorphism.

Introduction Amphiphilic molecules play a fundamental role in biology and find widespread technological applications because of their unique ability to self-organize at interfaces and in solution and thus modify interfacial properties and enhance compatibility or partition.1 The self-organization of surfactants and lipids into thermodynamically stable supramolecular assemblies such as micelles (in aqueous solutions), microemulsions (in multicomponent systems with water, oil, and, often, cosurfactant), and lyotropic liquid crystals, as well as kinetically stabilized vesicles and emulsions, has been the subject of intense investigation over the last 3 decades.2-5 Nevertheless, the structure of many so-called “intermediate” phases remains unresolved. The microstructural study of block copolymers in the absence of solvent (in the bulk) is more recent; solventfree block copolymers can attain a number of morphologies, such as spheres, cylinders, and lamellae, similarly to surfactants in solution.6,7 The phase behavior of block copolymers is becoming prominent nowadays with the emerging need to blend polymers, in order to achieve superior material properties and in order to recycle and reuse mixtures of polymers.8 * To whom correspondence should be addressed. Fax: +46-462224413. X Abstract published in Advance ACS Abstracts, December 15, 1996. (1) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain: Where Physics, Chemistry, Biology, and Technology Meet; VCH Publishers: New York, 1994. (2) Lindman, B.; Wennerstro¨m, H. Top. Curr. Chem. 1980, 87, 1. (3) Lindblom, G.; Rilfors, L. Biochim. Biophys. Acta 1989, 988, 221. (4) Fontell, K. Colloid Polym. Sci. 1990, 268, 264. (5) Laughlin, R. G. The Aqueous Phase Behavior of Surfactants; Academic Press: London, 1994. (6) Bates, F. S. Science 1991, 251, 898. (7) Bates, F. S.; Schulz, M. F.; Khandpur, A. K.; Fo¨rster, S.; Rosedale, J. H.; Almdal. K.; Mortensen, K. Faraday Discuss. 1994, 98, 7. (8) Tirrell, M. Chem. Eng. Sci. 1995, 50, 4123.

S0743-7463(96)00733-0 CCC: $14.00

In addition to the microstructures attained in the bulk state, di- and triblock copolymers are known to associate into micelles when dissolved in a selective solvent.9,10 One such example is amphiphilic copolymers composed of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) or poly(butylene oxide) (PBO) which form micelles in water, a selective solvent for the PEO block.11-16 However, the rich phase behavior afforded by these amphiphilic copolymers has only recently been recognized;17-23 PEO/ PPO copolymers can self-assemble (in the presence of water17-20 or in ternary systems with water and oil21-23) into lyotropic liquid crystalline structures, having one-, two-, or three-dimensional order. Besides its important ramifications in practical applications, the study of the structural polymorphism exhibited by amphiphilic block copolymers in solution would lead to an improved un(9) Tuzar, Z.; Kratochvil, P. In Surface and Colloid Science, Matijevic, E., Ed.; Plenum Press: New York, 1993; Vol. 15. (10) Alexandridis, P.; Hatton, T. A. In The Polymeric Materials Encyclopedia; Salamone, J. C., Ed.; CRC Press: Boca Raton, FL, 1996. (11) Almgren, M.; Brown, W.; Hvidt, S. Colloid Polym. Sci. 1995, 273, 2. (12) Alexandridis, P.; Hatton, T. A. Colloids Surf. A 1995, 96, 1. (13) Chu, B.; Zhou, Z. Surfactant Sci. Ser. 1996, 60, 67. (14) Alexandridis, P.; Hatton, T. A. In Dynamic Properties of Interfaces and Association Structures; Pillai, V. K., Shah, D. O., Eds.; AOCS Press: Champaign, IL, 1996. (15) Yang Y.-W.; Deng, N.-J.; Yu, G.-E.; Zhou, Z.-K.; Attwood, D.; Booth, C. Langmuir 1995, 11, 4703. (16) Yang, Y.-W.; Yang, Z.; Zhou, Z.-K.; Attwood, D.; Booth, C. Macromolecules 1996, 29, 670. (17) Mortensen, K.; Brown, W.; Norden, B. Phys. Rev. Lett. 1992, 68, 2340. (18) Mortensen, K. J. Phys.: Condens. Matter 1996, 8, A103. (19) Wanka, G.; Hoffmann, H.; Ulbricht, W. Macromolecules 1994, 27, 4145. (20) Alexandridis, P.; Zhou, D.; Khan, A. Langmuir 1996, 12, 2690. (21) Alexandridis, P.; Olsson, U.; Lindman, B. Macromolecules 1995, 28, 7700. (22) Alexandridis, P.; Olsson, U.; Lindman, B. J. Phys. Chem. 1996, 100, 280. (23) Alexandridis, P. Curr. Opin. Colloid Interface Sci. 1996, 1, 490.

© 1997 American Chemical Society

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Langmuir, Vol. 13, No. 1, 1997

derstanding of the phase behavior of solvent-free block copolymers as well as to a formal connection of the latter to the phase behavior of low-molecular weight surfactants.23 In the context of an ongoing investigation on the selforganization of amphiphilic copolymers, we explored the phase behavior of a diblock copolymer with the structure BO10EO17 (where BO denotes butylene oxide and EO ethylene oxide) in the presence of water and xylene, selective solvents for the PEO and PBO blocks, respectively. We recently identified in this ternary system a novel cubic structure consisting of “reverse” (water-inoil) micelles crystallized in a face-centered close-packed lattice.24 It turned out that this unique structure is only one facet of the structural polymorphism afforded by the BO10EO17 amphiphilic block copolymer. The complete phase diagram of the ternary BO10EO17-water-xylene system is presented here, revealing three different regions of cubic structure (of both discrete and bicontinuous topology), two regions of hexagonally packed cylinders (denoted here as “hexagonal” phases), a lamellar (smectic) region, as well as “normal” (oil-in-water) and “reverse” micellar solution regions, a total of eight different phases stable at the same temperature (25 °C). The boundaries of the various one-phase regions were identified using inspection under polarized light and 2H-NMR of heavy water (2H2O). Small-angle X-ray scattering (SAXS) was the main tool employed in the structural characterization of the lyotropic liquid crystalline phases. The presentation of our findings commences with an overview of the phase behavior and the factors influencing the self-assembly of amphiphilic copolymers. The structure in the onedimensional lamellar and two-dimensional hexagonal liquid crystalline regions is discussed then, followed by a crystallographic analysis of the cubic phases, which have a more complex, three-dimensional symmetry. Materials and Methods Materials. The Polyglycol BL50-1500 poly(butylene oxide)b-poly(ethylene oxide) copolymer (Lot GH07016107) was obtained as a gift from the Dow Chemical Co., Midland, MI, and used as received. BL50-1500 has a nominal molecular weight of 1500 and ≈50 wt % PEO and can thus be represented by the formula BO10EO17. According to the manufacturer, the BL50-1500 diblock copolymer has only one terminal primary hydroxyl group; the PBO block is terminated with monobutyl ether. p-Xylene (1,4dimethylbenzene) of purity >99.0% was obtained from Fluka Chemie AG, Switzerland, while 2H2O (99.80 atom % 2H) was purchased from Dr. Glaser AG, Switzerland. Heavy water (2H2O) was used instead of ordinary H2O in order to allow for 2H-NMR measurements in the investigation of phase equilibria;20 2H2O is slightly less polar than 1H2O (the dielectric constant of 2H2O at 25 °C, 77.94, is 0.76% lower than that of 1H2O, 78.54) and thus it is not expected to affect the features of the phase diagram that we present in this paper.21,25 Samples were prepared individually by weighing appropriate amounts of copolymer, water, and oil into 8 mm (i.d.) glass tubes which were flame-sealed immediately. The samples were centrifuged repeatedly in both directions during the course of several days to facilitate mixing and then in one direction to speed up phase separation (if not singlephase).21 They were kept at a temperature-controlled room which was maintained at 25 ( 0.5 °C. Adequate time (on the order of weeks) was allowed to ensure thermodynamic equilibrium. The attainment of equilibrium was confirmed by repeated 2H-NMR measurements (see below). Determination of the Phase Boundaries. The samples were first examined by ocular inspection of scattered light and between crossed polaroids to check for sample homogeneity and (24) Alexandridis, P.; Olsson, U.; Lindman, B. Langmuir 1996, 12, 1419. (25) Nivaggioli, T.; Alexandridis, P.; Hatton, T. A.; Yekta, A.; Winnik, M. A. Langmuir 1995, 11, 730.

Alexandridis et al. birefringence. This provided a quick indication of the boundaries between isotropic and anisotropic phases, as well as between one- and two-phase regions. Lamellar and hexagonal (anisotropic) phases are optically birefringent, while isotropic cubic liquid crystals and micellar solutions are not.19-22 From the general appearance of the 2H-NMR spectra (recorded at a resonance frequency of 15.371 MHz (2.3 T) on a Bruker DMX100 spectrometer) it was established whether a certain sample consisted of a single homogeneous phase or of two or three phases.20 The presence of an isotropic phase is directly noted from a sharp singlet and that of an anisotropic phase from a doublet of broad peaks (a theoretical treatment of 2H quadrupole splitting in lyotropic liquid crystalline phases can be found elsewhere26 ). Finally, the crystallographic structure of the various lyotropic liquid crystalline phases was established from an analysis of the SAXS diffraction patterns (see below), while the normal or reverse topology was inferred from the composition range occupied by a given phase in the ternary phase diagram and the structure of the adjacent phases. It was thus possible from a systematic variation of the composition, and from the use of both NMR and SAXS techniques, to determine with good precision ((0.5 wt %) the complete phase diagram. Small-Angle X-ray Scattering (SAXS). SAXS measurements were performed on a Kratky compact small-angle system equipped with a position sensitive detector (OED 50M from MBraun, Austria) containing 1024 channels of width 51.3 µm. Cu KR radiation of wavelength 1.542 Å was provided by a Seifert ID-300 X-ray generator, operating at 50 kV and 40 mA. A 10 µm thick nickel filter was used to remove the Kβ radiation, and a 1.5 mm tungsten filter was used to protect the detector from the primary beam. The obtained Bragg peaks are relatively sharp in which case the peak position can be evaluated from the slitsmeared SAXS data.20,21 The sample-to-detector distance was 277 mm. The volume between the sample and the detector was under vacuum during the measurements in order to minimize scattering from the air. The samples for SAXS measurements were filled into a quartz capillary using a syringe. Temperature control within 0.1 °C was achieved by using a Peltier element. Definition of “Polar” and “Apolar” Domains. The BO10EO17 molecule consists of a PBO and a PEO block; the former is less polar than the latter and thus assemblies are formed with domains which are rich in PBO and oil (denoted here as “apolar”) and domains which are rich in PEO and water (denoted as “polar”). The polarity difference (and degree of segregation) between the “hydrophilic” PEO block and the “hydrophobic” PBO block is smaller than that between “headgroup” (often charged) and “tail” (usually aliphatic) in typical, low-molecular weight, surfactants (still, the polarity difference between PEO and PBO is greater than that between PEO and PPO in the widely studied poloxamers27 ). Consequently, the interface between the polar and apolar domains is expected to be less sharp in the ternary copolymer-water-oil system,28,29 and the PBO-rich and PEOrich domains may still contain a certain amount of water and oil, respectively. To a first approximation, however, we consider the system as strongly segregated and define an apolar volume fraction, f, containing oil and PBO and the remaining polar volume fraction (1 - f) containing water and PEO

f ) Φo + 0.515Φp 1 - f ) Φw + 0.485Φp

(1)

where Φp, Φo, and Φw are the copolymer, oil, and water volume fractions, respectively (the PBO block, which is the 50% of the copolymer weight, makes up approximately 51.5% of the copolymer volume). In our calculations we have used the (bulk) density values of 1.05, 1.104, and 0.861 g/mL for the copolymer, heavy water, and p-xylene, respectively. We note that the density of the copolymer in solution and in the various assemblies can (26) Wennerstro¨m, H.; Lindman, B.; Lindblom, G. Chem. Scr. 1974, 6, 97. (27) Nace, V. M.; Knoell, J. C. J. Am. Oil Chem. Soc. 1995, 72, 89. (28) Hurter, P. N.; Alexandridis, P.; Hatton, T. A. Surfactant Sci. Ser. 1995, 55, 191. (29) Noolandi, J.; Shi, A.-C.; Linse, P. Macromolecules 1996, 29, 5907.

Structural Polymorphism of Amphiphilic Copolymers

Langmuir, Vol. 13, No. 1, 1997 25

be different than the bulk value.30 However, the copolymer concentration in the samples of interest is large (>30%), and thus the use of the bulk density appears justified. SAXS Analysis of the Lamellar Structure. The periodicity (spacing), d, of the lamellar stack (smectic liquid crystalline arrangement of the block copolymer molecules, see Figure 2d) is determined from the inverse bilayer area (Ab) per volume (V) ratio

d ) (Ab/V)-1

(2)

The effective area of the copolymer molecules at the interface between polar and apolar domains can thus be calculated from the SAXS data without any assumptions concerning the degree of segregation or the local structure of the copolymer film (other than the fact that all and only the amphiphilic copolymer participates in the lamellae21). Ab/V is equal to 1/2 of the polar/ apolar interfacial area-to-volume ratio ΦpRp/υp, where υp is the volume of one copolymer molecule (2380 Å3) and Rp is the average interfacial area per copolymer molecule. For a lamellar structure the position of the first-order Bragg peak corresponds to (q is the scattering vector)

q1 )

2π πΦpRp ) d vp

(3)

Assuming a sharp interface between the polar and apolar domains, we can also calculate the thickness, δ, of the apolar domain of the lamellae according to δ ) fd. The corresponding thickness of the polar domains is then given by d - δ. SAXS Analysis of the Hexagonal Structures. In the “hexagonal” liquid crystalline regions (where the structural elements are cylindrical assemblies arranged in a hexagonal packing, Figure 2c) the Bragg reflections correspond to

qhk )

4πxh2 + k2 + hk ax3

(

)

x3 Φ 2π cyl

(

)

)

h2 + k2 + hk x3 (1 - f) 2π

2(1 - f)υp ΦpRp

(8)

ΦpRp υp

(9)

1/2

SAXS Analysis of the Cubic Structures. Scattering data from lyotropic cubic phases generally contain only a small number of reflections which makes a proper crystallographic indexation and space group determination very difficult. There are three main families of cubic structures:31 primitive (P...), body-centered (I...), and face-centered (F...); within each family there are many crystallographic space groups with different symmetries. While it is difficult to check the experimental SAXS diffraction patterns against all possible structures, one can rule out certain families based on the relative position of the first few SAXS Bragg peaks (reflections) and certain space groups within the families based on the presence (or absence) of certain peaks or on the relative intensity of the peaks.32 The indexing of the SAXS peaks can be assessed by plotting the reciprocal spacings (1/dhkl) of the various reflections versus m ) (h2 + k2 + l2)1/2 (where h, k, and l are the Miller indices). For a given cubic structure, such a plot should pass through the origin and be linear with a slope of 1/a, where a is the cubic cell lattice parameter. The cell lattice parameter in a micellar cubic structure can be related to the molecular characteristics (υp, Rp) of the amphiphilic copolymer and the volume fraction of the copolymer, water, and oil components (Φp, f) through simple geometrical arguments for the volume occupied by the (spherical) micelles which make up the unit cell. From the volume/area ratio of oil-in-water (“normal”) spheres (Φsph ) f) we have (the polar-apolar interface is set at that separating the PBO and PEO blocks)

Rsph )

3fυp ΦpRp

(10)

The number, N, of the micelles in a cubic unit cell depends on the crystallographic space group. The volume fraction of the N normal micelles in a unit cell, N(4πR3sph/3)/a3, equals f. Substituting this into eq 10 we obtain

a ) (36πN f2)1/3

2fυp ΦpRp

(6)

)

h2 + k2 + hk x3 f 2π

(

1/2

(5)

This corresponds to defining the polar-apolar interface at the interface separating the PEO and PBO blocks. Substituting eqs 5 and 6 into eq 4 we then obtain

qhk )

qhk )

)

x3 (1 - f) 2π

1/2

Assuming a hexagonal arrangement of oil-in-water (“normal”) cylinders and assigning the PBO blocks to the apolar domain of the cylinders (Φcyl ) f) we have

Rcyl )

(

Rcyl ) a

(4)

where a is the lattice parameter (nearest neighbor distance). The first five reflections correspond to (h,k) ) (1,0), (1,1), (2,0), (2,1), and (3,0) and give the characteristic pattern 1:x3:2:x7:3. In the case of infinite cylinders of cross section radius Rcyl and volume fraction Φcyl we have the relation

Rcyl ) a

analogy with eqs 5-7 we have for the reverse hexagonal phase

1/2

ΦpRp υp

(7)

The area per copolymer molecule can thus be derived from eq 7 and substituted to eq 6 to obtain the cylinder radius and the distance between the centers of two adjacent cylinders. In the case of a water-in-oil (“reverse”) hexagonal structure (depicted in Figure 2e), the effective copolymer area and cylinder radius values can be calculated from the SAXS repeat distance in a similar manner to that of the normal hexagonal structure. In (30) Alexandridis, P.; Nivaggioli, T.; Hatton, T. A. Langmuir 1995, 11, 1468.

υp ΦpRp

(11)

For a reverse (water-in-oil) micellar cubic structure (I2 cubic phase), the volume fraction of the micelle cores (Φsph) is equal to 1 - f and eqs 10 and 11 are modified accordingly. For a given N and the lattice parameter, a, estimated from the 1/dhkl vs m ) (h2 + k2 + l2)1/2 plot, eq 11 can be solved for the area per copolymer molecule, Rp, and the Rp value then compared to that obtained in the hexagonal phase, adjacent to the micellar cubic region. Agreement between the Rp values is indicative of the use of a correct N and crystallographic space group. In the case of bicontinuous3,4 cubic structures, the identification of the crystallographic group from the SAXS peak assignment can be aided/confirmed by an appropriate analysis of the polar/ apolar interfacial area. The structure is composed of a multiply connected bilayer where the bilayer midplane can be modeled as a minimal surface,33 and the polar/apolar interface can be described as two parallel surfaces displayed on opposite sides of a minimal surface, each at a distance L.34 The total interfacial area per unit volume (A/V) is given by22 (31) Hahn, T., Ed. International Tables for Crystallography; Kluwer Academic Publishers: Dortrecht, The Netherlands, 1989. (32) Mariani, P.; Luzzati, V.; Delacroix, H. J. Mol. Biol. 1988, 204, 165. (33) Andersson, S.; Hyde, S. T.; Larsson, K.; Lidin, S. Chem. Rev. 1988, 88, 221.

26


(

Alexandridis et al.

( ))

2πχu L A 2ç ) 1+ V a ç a

2

(12)

where a is the cubic cell lattice parameter, ç is a dimensionless area constant, and χu is the Euler characteristic per unit cell of the minimal surface.22,34 A similar relationship holds for the volume fraction enclosed between the two interfaces. For a reverse bicontinuous structure (V2 cubic phase), this volume fraction is f and we can write

f)

(

2ç L a

1+

( ))

2πχu L 3ç

2

a

(13)

For a normal (oil-in-water) bicontinuous structure (V1 cubic phase), the volume fraction enclosed between the two interfaces is equal to 1 - f and eq 13 is modified accordingly. For a given minimal surface, χu and ç are known quantities.34 Equation 13 can thus be solved for L, and the area per molecule, Rp, calculated from eq 12. The area per molecule values are then compared to the ones obtained in the lamellar and hexagonal phases, adjacent to the bicontinuous region. Agreement between the area values at the different liquid crystalline regions is indicative of the use of a correct minimal surface/crystallographic assignment in eqs 12 and 13.

Phase Behavior Overview of the Ternary Phase Behavior. The isothermal phase diagram obtained at 25 °C for the ternary system BO10EO17-water-p-xylene is presented in Figure 1. Six different lyotropic liquid crystalline phases have been identified, a lamellar (LR), normal (H1) and reverse hexagonal (H2), a reverse bicontinuous cubic (V2), and normal (I1) and reverse micellar cubic (I2), as well as two isotropic solution phases, one rich in water (L1) and one with high xylene-to-water ratio (L2). The phase boundaries of the one-phase regions are drawn in Figure 1 with solid lines. The samples whose compositions fall outside the one-phase regions are dispersions of two or three (depending on the location in the phase diagram) different phases.21,22 Different modes of self-organization of the amphiphilic diblock copolymers in the presence of water and oil are illustrated in Figure 2. In the oil-lean part of the phase diagram (along the copolymer-water binary axis) the BO10EO17 amphiphilic copolymer self-assembles upon increase of its concentration into an isotropic normal micellar solution (L1), a micellar cubic array (I1), a hexagonal liquid crystalline structure (H1), a lamellar structure (LR), and finally a copolymer-rich pastelike phase. The same sequence of structures (sphere f cylinder f plane), but of the reverse (water-in-oil) morphology, is observed in the water-lean part of the phase diagram with increasing copolymer concentration at a (constant) water-copolymer weight ratio of 1/4 (which corresponds to approximately 1.3 water molecules per EO segment). The sequences of phases on the copolymer-water (oil-lean) and the copolymer-oil (water-lean) side of the ternary phase diagram are also shown in parts a and b of Figure 3, respectively, where the degree of swelling with oil and water is plotted as a function of the copolymer weight fraction in water and oil, respectively. The “reduced” coordinates of Figure 3 reveal that the maximum swelling of the oil-in-water and the water-in-oil structures is ≈25% and ≈30%, respectively. A detailed description of the different lyotropic liquid crystalline phases and their respective structures is presented in the structural characterization section. Isotropic Water-Rich (L1) and Water-Lean (L2) Solution Regions. The BO10EO17 copolymer dissolves (34) Anderson, D.; Wennerstro¨m, H.; Olsson, U. J. Phys. Chem. 1989, 93, 4243.

in heavy water up to approximately 22 wt % copolymer to form an isotropic solution. The BO10EO17 molecules are present in water at 25 °C as individual polymer chains (unimers) up to copolymer concentrations of ≈0.01 wt % (inferred from data on similar polymers summarized in ref 15). At higher concentrations, the copolymer molecules self-assemble into spherical micelles (of association number ≈50) with a hydrophobic core consisting mainly of BO segments and a corona composed of highly hydrated EO segments.15 The aqueous micellar solution has the capability of solubilizing p-xylene at most up to about 33% of the copolymer weight (as seen in Figure 3b). BO10EO17 is miscible with p-xylene only up to ≈40 wt %; the presence of some water (1-2 wt %) increases the copolymer solubility in xylene and allows the L2 phase to extend up to 75 wt % copolymer (see Figure 1). BO10EO17 is unable to accommodate significant amounts of water at copolymer concentrations less that ≈3 wt % (Figures 1 and 3b and ref 35), an indication that it does not form polymolecular micelles at these concentrations. Reverse micelles with a hydrated PEO core and a PBO corona are apparently formed by BO10EO17 in p-xylene at higher copolymer concentrations, judging from the capacity of the copolymer-oil mixture to solubilize significant amounts of water. It has been reported that up to ≈0.15 water molecules per EO segment are required for EO13PO30EO13 to form micelles in o-xylene;36 similar values have been recently measured for the micellization of a large number of polyoxyalkylene block copolymers in p-xylene.35 The presence of water is also a prerequisite for the formation of reverse micelles by nonionic alkyl oligooxyethylene surfactants37,38 and for the micellization of poly(oxyethylene)-polystyrene diblock copolymers dissolved in cyclopentane.39 It appears that PEO needs some water in order to become sufficiently polar and segregated from the hydrophobic block. We note that the maximum amount of water taken up by the reverse micelles is approximately 40% of the copolymer weight (as shown in Figure 3b) which corresponds to about two water molecules per EO segment. Sequence of Phases. The presence in the BO10EO17water-p-xylene ternary system of eight distinct phases, including three different cubic ones, at the same temperature is unique. In fact, this is the richest phase behavior reported to date in an amphiphile-containing system.5 There are four different types of cubic phases that can be formed by amphiphiles.3,4 Their structure may either consist of close-packed micelles or be bicontinuous, and the mean curvature of the polar/apolar interface can be either toward oil (normal) or toward water (reverse). Consistent with a monotonic variation of the interfacial mean curvature, the various cubic phases have different relative locations in the phase diagram, following the sequence:4,5

L1 f I1 f H1 f V1 f LR f V2 f H2 f I2 f L2 (12) which is symmetric around the lamellar phase. This structural sequence corresponds to a decreasing mean curvature (Η) from the left (Η > 0) to right (Η < 0), where Η ) 0 in the lamellar phase. The transition from a spherical to a cylindrical and then to a lamellar arrangement upon increase of the copolymer concentration is a consequence of a balance between interfacial energy and (35) Alexandridis, P.; Andersson, K. Submitted for publication. (36) Wu, G.; Zhou, Z.; Chu, B. Macromolecules 1993, 26, 2117. (37) Kahlweit, M.; Strey, R.; Busse, G. J. Phys. Chem. 1990, 94, 3881. (38) Olsson, U.; Jonstro¨mer, M.; Nagai, K.; So¨derman, O.; Wennerstro¨m, H.; Klose, G. Prog. Colloid Polym. Sci. 1988, 76, 75. (39) Gast, A. Langmuir 1996, 12, 4060.


Langmuir, Vol. 13, No. 1, 1997 27

Figure 1. The phase diagram of the BO10EO17-2H2O (“water”)-p-xylene (“oil”) ternary system at 25 °C. The phase boundaries of the one-phase regions are drawn with solid lines. I1, H1, LR, V2, H2, and I2, denote normal (oil-in-water) micellar cubic, normal hexagonal, lamellar, reverse (water-in-oil) bicontinuous cubic, reverse hexagonal, and reverse micellar cubic lyotropic liquid crystalline phases, respectively, while L1 and L2 denote water-rich (normal micellar) and water-lean/oil-rich (reverse micellar) solutions. The concentrations are expressed in wt %. The samples whose compositions fall outside the one-phase regions are dispersions of two or three (depending on the location in the phase diagram) different phases.

elastic (stretching) energy per polymer chain in the microstructure. When the apparent (modulated by the solvent) volume fraction of the “soluble” blocks is much larger than that of the “insoluble” blocks, spherical or cylindrical structures are favored.20 All of the above mentioned phases (eq 12) are commonly formed by amphiphiles in the presence of water and organic solvents (and most of them have also been observed in systems containing amphiphilic copolymers of the PEO-PPO-PEO family17-23), except for the reverse micellar cubic phase I2. This structure has previously been identified40,41 only in some particular surfactant/ cosurfactant/water systems, where the cosurfactant acts partly as the continuous apolar solvent, and it has never been observed in a ternary amphiphile/water/oil system. High volume fractions of reverse micelles (corresponding to high amphiphile concentrations) would be required in order to make a crystalline packing possible, because of weak intermicellar interactions. In the case of typical surfactants, it is more likely that the reverse micelles (L2) elongate upon an increase of the amphiphile concentration and then crystallize into a hexagonal array (H2) without going through a cubic ordering. For the macromolecular amphiphile studied here, the micellar size and volume fraction and the interactions between reverse micelles are all sufficiently large to facilitate their crystallization into a cubic array. The difficulty of forming reverse micellar cubic crystals is still reflected in the pronounced difference between the (40) Seddon, J. M. Biochemistry 1990, 29, 7997. (41) Ora¨dd, G.; Lindblom, G.; Fontell, K.; Ljusberg-Wahren, H. Biophys. J. 1995, 68, 1856.

copolymer-water and copolymer-oil axes of the ternary phase diagram as depicted in Figure 3. Along the copolymer-water axis (Figure 3a), the copolymer content is the main determinant of the structures formed, while along the copolymer-oil axis (Figure 3b) the relative amount of water is important in addition to the copolymer content. The normal micellar cubic phase is stable at 23-27 wt % copolymer content while the reverse one is formed at 47-62 wt % copolymer (twice that needed for I1) and requires additionally the presence of about 10 wt % water. Comparison with Other Self-Assembled Systems. The phase behavior of the ternary copolymer-water-oil systems resembles, in some respect, that of surfactantwater-oil systems. However, the “polymeric chain” nature of the BO10EO17 amphiphilic block copolymer allows for fine-tuning of the copolymer “packing” parameter (by the varying degree of swelling of the PBO and PEO blocks by xylene and water molecules, respectively) and thus leads to the progression (eq 12) of oil-in-water and waterin-oil lyotropic liquid crystalline structures upon increase of the oil/water ratio at the same temperature. Such a structural polymorphism as exhibited by BO10EO17 is not possible in, e.g., ternary systems formulated by typical surfactants; nonionic alkyl oligooxyethylene surfactants attain structures with curvature toward oil at lower temperatures, but higher temperatures are needed for the curvature to be toward water.42,43 The effective (42) Olsson, U.; Wennerstro¨m, H. Adv. Colloid Interface Sci. 1994, 49, 113. (43) Schubert, K.-V.; Kaler, E. W. Ber. Bunsenges. Phys. Chem. 1996, 100, 190.

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(d)

(c)

(e)

(b)

(f)

(a)

(g)

Figure 2. Schematic of different modes of self-organization of the amphiphilic diblock copolymers in the presence of solvents (“water” and “oil”) selective for the two blocks. Clockwise from bottom left: (a) normal micellar solution, (b) normal micellar cubic lyotropic liquid crystal (LLC), (c) normal hexagonal LLC, (d) lamellar LLC, (e) reverse hexagonal LLC, (f) reverse micellar cubic LLC, and (g) reverse micellar solution. The amphiphiles are localized at the interfaces between the water and oil domains. For reasons of clarity, only the copolymer molecules at the cross section of the (spherical, cylindical, and planar) assemblies are depicted, and only sections of the LLC structures are shown.

persistence length of the hydrocarbon chain in typical surfactants is of the order of the assembly characteristic dimension. In the system under consideration here, the persistence length of the copolymer is expected to be much smaller than the characteristic dimension of the domain, which, in turn, is much smaller than the stretched polymer length. The sequence of microstructures formed by BO10EO17 in water-oil mixtures is similar to that encountered in solvent-free A-B block copolymers at temperatures below the order-disorder transition (ODT).6,7 However, copolymers of different relative block composition are needed to attain the different structures in the solvent-free case.7 In the BO10EO17 case, the same molecule can form different structures depending on the type and amount of solvent present (which modulates the apolar volume fraction, f). The structural polymorphism in the amphiphilic copolymer-water-oil systems appears to be governed by similar mechanisms (mean-field effects) as in solvent-free block copolymers.29,44 It is important to note that BO10EO17, despite its relatively low molecular weight (≈1500), forms a large variety of ordered (liquid crystalline) structures over the whole (ternary) composition range, even at copolymer concentrations as low as 23 wt %. The EO13PO30EO13 (44) Matsen, M. W.; Bates, F. S. Macromolecules 1996, 29, 1091.

Figure 3. (a) Boundaries of the various phases along the copolymer-water side of the ternary phase diagram plotted in the “reduced” coordinates X, copolymer weight fraction in its mixture with water, and Y, oil weight fraction in its mixture with copolymer. (b) Boundaries of the various phases along the copolymer-oil side of the ternary phase diagram plotted in the “reduced” coordinates X, copolymer weight fraction in its mixture with oil, and Y, water weight fraction in its mixture with copolymer.

copolymer (of molecular weight ≈2900 and 40 wt % PEO) forms liquid crystalline phases at concentrations greater than 40 wt % (at 25 °C) and does not exhibit any micellar cubic phases,21 while PEO-PPO-PEO copolymers of molecular weight ≈4500 are able to form such structures at 27 wt %.17-20,45,46 There are two effects contributing to the remarkable structural polymorphism of BO10EO17: (i) the PBO block is more hydrophobic than the PPO block,15,27 resulting in stronger segregation between this and the PEO blocks and higher tendency for ordering; (ii) the copolymer is diblock, and there are indications47 that A-B diblock copolymers form domains of the same size (and presumably at a similar composition range) as A-B-B-A triblocks (of the same A/B composition but of double the A-B molecular weight). Nevertheless, the relatively low molecular weight of the BO10EO17 copolymer still influences the phase behavior, as reflected in the rather limited swelling of the lamellar phase compared to that of the EO13PO30EO13 system. Structural Characterization Lamellar Liquid Crystalline Phase (Lr). The LR phase is formed on the binary water-BO10EO17 axis at copolymer concentrations greater than 62 wt % and continues up to about 84% copolymer (Figure 1). LR is the most extensive of the liquid crystalline phases, it can accommodate up to 16 wt % xylene and allows a higher degree of swelling with oil than the L1, I1, and H1 phases (Figure 3a). The samples in this region are transparent and birefringent and exhibit a splitting in the 2H-NMR spectra. The one-dimensional lamellar (smectic) structure (shown schematically in Figure 2d) was established by (45) Holmqvist, P.; Alexandridis, P.; Lindman, B. Langmuir, in press. (46) Alexandridis, P.; Lindman, B., Eds. Amphiphilic Block Copolymers: Self-Assembly and Applications; Elsevier Science B. V.: The Netherlands, 1997. (47) Helfand, E.; Wasserman, Z. R. Macromolecules 1976, 9, 879.


Figure 4. Slit-smeared SAXS diffraction pattern obtained from a lamellar (LR) liquid crystalline sample of 60.0/30.0/10.0 copolymer/water/oil weight % composition at 25 °C. The scattering curve is also shown on an expanded intensity scale (right-hand side) to expose the higher order Bragg peaks (marked with the arrows). The positions of the higher order reflections with respect to that of the first (and most intense) peak, q*, are indicated on the upper X-axis.

Figure 5. Characteristic structural parameters (lattice parameter/lamellar spacing, apolar film thickness, and interfacial area) in the lamellar liquid crystalline region, plotted as a function of the copolymer volume fraction at (a) constant (zero) oil content, and (b) constant (35 wt. %) water content.

SAXS measurements. A second- and even a third-order peak can be observed in the SAXS diffraction pattern of Figure 4 (from a LR sample with 60.0/30.0/10.0 copolymer/ water/oil wt % composition) and the 1:2:3 relationship of the peak positions relative to that of the most intense peak (see the upper X-axis of Figure 4) confirms the lamellar structure. Values for the lattice parameter (lamellar spacing), d, the apolar (PBO + xylene) thickness, δ, and the interfacial area per copolymer molecule, Rp, are plotted in Figure 5 as a function of the copolymer volume fraction for constant oil content and for constant water content. The d values decreased (albeit by less than 10%) with increasing

Langmuir, Vol. 13, No. 1, 1997 29

Figure 6. Slit-smeared SAXS diffraction pattern obtained from the normal hexagonal H1 liquid crystalline phase at a 50.0/ 50.0/0 wt % copolymer/water/oil composition at 25 °C. The scattering curve is also shown on an expanded intensity scale (right-hand side) to reveal the higher order x3, 2, x7, and 3 Bragg peaks. Their positions with respect to that of the first (and most intense) peak, q*, are indicated on the upper X-axis.

copolymer volume fraction at both constant (zero) oil (Figure 5a) and constant (35 wt %) water content (Figure 5b). As the copolymer concentration increases, the amount of interface increases and thus the spacing between the lamellae decreases. The apolar thickness increased with increasing copolymer (and PBO) concentration at constant oil content (Figure 5a) and decreased with increasing copolymer concentration at constant water content (Figure 5b); in this case the increase in PBO content is not big enough to compensate for the corresponding decrease in the oil content. The δ values are in the range 35-50 Å. The interfacial area per copolymer is approximately 75 Å2 throughout the LR region, and decreases slightly with increasing copolymer concentration at constant oil content. The lamellar spacing values in the BO10EO17-waterxylene system fall in the range 80-120 Å, comparable to that of the lamellae formed21,22 in water + xylene by the triblock copolymers EO13PO30EO13 and PO19EO33PO19 (of approximately twice the BO10EO17 molecular weight and comparable hydrophile/hydrophobe content), in agreement with the prediction of ref 47. At constant copolymer content (60 wt %), the lamellar spacing increased from 101 to 105 Å when the oil concentration increased from 5 to 10%; similar variation has been observed in the PO19EO33PO19 lamellae (spacing ) 72 Å at 65.0/35.0/0.0 copolymer/water/oil wt % vs 81 Å at 65.0/25.0/10.0 wt %)22 but not in the EO13PO30EO13 lamellae (spacing ) 75 Å at both 75.0/25.0/0.0 and 75.0/ 20.0/5.0 copolymer/water/oil wt %).21 This observation can be also viewed as a (small) decrease in the interfacial area per molecule upon a decrease in the water concentration at constant copolymer content. While this can be attributed to a change in the hydration state of the PEO blocks, it is not clear at this time why copolymers of different block architecture behave in a different manner. Normal Hexagonal Liquid Crystalline Phase (H1). The H1 region is stable in the 42-54 wt % copolymer range along the binary water-BO10EO17 axis and swells with up to 6 wt % xylene (Figure 1). The samples in this region are stiff, transparent, and birefringent and exhibit a splitting in the 2H-NMR spectrum. The two-dimensional hexagonal structure (shown schematically in Figure 2c) was established by SAXS experiments, while the normal (oil-in-water) morphology was ascertained from the location of the H1 region in the ternary phase diagram. Figure 6 shows the slit-smeared SAXS diffraction pattern obtained for an H1 sample with a copolymer/water/oil wt %

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Figure 7. Slit-smeared SAXS diffraction pattern obtained from the reverse hexagonal H2 liquid crystalline phase at a 60.0/ 15.0/25.0 wt % copolymer/water/oil composition at 25 °C. The scattering curve is also shown on an expanded intensity scale (right-hand side) to reveal the higher order x3, 2, and x7 Bragg peaks. Their positions with respect to that of the first (and most intense) peak, q*, are indicated on the upper X-axis.

composition of 50.0/50.0/0.0. The relative positions of the five peaks resolved in the diffraction pattern of Figure 6 correspond to the 1:x3:2x7:3 relationship (see the upper X-axis), a confirmation of the hexagonal structure. The nearest neighbor (cylinder) distance decreased with increasing copolymer content from 127 Å at 45.0/55.0/0 wt % to 122 Å at 50.0/50.0/0 wt % copolymer/water/oil, consistent with a denser packing of the cylinders as their number increased. The interfacial area per copolymer molecule (obtained from eq 7) was 75 Å2, similar to that in the lamellar phase. Reverse Hexagonal Liquid Crystalline Phase (H2). The H2 region extends in the 45-84 wt % copolymer range and 8-18 wt % water range. The samples in this region are stiff, transparent, and birefringent and exhibit a splitting in the 2H-NMR spectrum. A SAXS diffraction pattern, typical of samples in the H2 region, is presented in Figure 7 (for a sample with copolymer/water/oil wt % composition of 60.0/15.0/25.0). The 1:x3:2:x7 relative position of the Bragg peaks (with respect to that of the first and most intense peak) confirms the two-dimensional hexagonal structure (i.e., hexagonal arrangement of cylindrical assemblies of amphiphiles as shown schematically in Figure 2e). The reverse (water-in-oil) morphology was ascertained from the location of the H2 region in the ternary phase diagram, between the LR and L2 phases. Characteristic structural parameters for samples in the reverse hexagonal region are plotted in Figure 8 as a function of the copolymer volume fraction at constant (15 wt %) water content. The distance between the centers of two adjacent cylindrical block copolymer assemblies (lattice parameter) decreased (from 135 to 100 Å) with increasing copolymer volume fraction (from 0.46 to 0.74). The polar (PEO + water) cylinder radius, R, remained indifferent to the increasing copolymer content. The dependence on copolymer concentration of two other lengths, b and c, characteristic to the hexagonal structure is shown in Figure 8b. b ) a - 2R, is the shortest distance between nearest-neighbor polar/apolar interfaces and corresponds to the smallest thickness of two overlapping (and interacting) PBO layers, while c ) b + R(2/x3 - 1) is the normal distance from the polar/apolar interface to the center of the triangular interstice (the various lengths are illustrated in the inset of Figure 8b). Both b and c decrease significantly (from ≈50 to ≈30 Å) with increasing copolymer volume fraction (from 0.46 to 0.74), indicating that the packing of the PBO chains in the domains between

Figure 8. (a) Characteristic structural parameters (lattice parameter/nearest neighbor distance, polar cylinder radius, and interfacial area) in the reverse hexagonal region, plotted as a function of the copolymer volume fraction (lower X-axis) and the oil volume fraction (upper X-axis) at constant (15 wt %) water content. (b) The shortest distance between nearestneighbor polar/apolar interfaces, b, and the normal distance from the polar/apolar interface to the center of the triangular interstice, c, plotted together with the cylinder radius, R, as a function of the copolymer volume fraction. A triangular section of the hexagonal structure is included in Figure 8b to illustrate the various chacteristic lengths.

the cylinders becomes denser. We note that the lowest value of b found (at high copolymer and low oil contents) in the H2 region is comparable to the apolar thickness, δ, values in the LR region in the absence of oil (see Figure 5a). At constant copolymer content (75 wt %), the lattice parameter decreased from 103 to 94 Å (and the interfacial area increased slightly from 85 to 88 Å2) when the oil concentration increased from 10 to 15 wt %. Rp was found to be fairly constant, 85-88 Å2, throughout the H2 region. The value of Rp in the H2 region (obtained from eq 9) is ≈10% higher than that in the LR region. The interfacial area per molecule for nonionic alkyl oligooxyethylene surfactants has been found constant regardless of the structure.42 If this were also the case for BO10EO17, then this 10% discrepancy between the interfacial areas in the lamellar and reverse hexagonal regions would probably have resulted from the definition of polar and apolar domains (eq 1), which may have overestimated the polar (PEO + water) content residing in the interior of the cylinders (there are no such assumptions involved in deriving Rp in LR). Reverse Bicontinuous Cubic Liquid Crystalline Phase (V2). The narrow V2 region occurs between the LR and H2 phases at high (≈80%) copolymer concentration. The samples in the V2 region are very stiff and isotropic (nonbirefringent) and exhibit a sharp singlet in their 2HNMR spectra, characteristics of cubic structure. The relative position of this cubic phase in the phase diagram (between the LR and H2 phases) indicates that its structure


Figure 9. Slit-smeared SAXS diffraction pattern obtained from the reverse bicontinuous cubic V2 liquid crystalline phase at a 80.0/15.0/5.0 wt % copolymer/water/oil composition at 25 °C. The scattering curve is also shown on an expanded intensity scale (right-hand side) to reveal the higher order Bragg peaks. The arrows mark the positions of the reflections afforded by the Ia3d crystallographic space group. Filled arrows indicate observed reflections, while hollow arrows indicate reflections that are anticipated but are not clearly observed in the SAXS diffraction pattern.

is bicontinuous with the curvature of the polar/apolar interface toward water.3,4 Two complementary descriptions are often used for bicontinuous cubic phases in surfactant systems, that of a multiply connected bilayer (described in terms of minimal surfaces of cubic symmetry) separating two distinguishable and continuous domains of the same solvent and that of two infinite channel networks of interconnected cylinders (associated with the skeletal graphs of the two interwoven subvolumes separated by the minimal dividing surface of the bilayer description).3,4,33,34 From the expected curvature of the polar/apolar interface, we anticipate the molecular arrangement in the V2 region to be that of an apolar film consisting of PBO and oil which forms a dividing bilayer between two polar domains containing PEO and water (as seen in Figure 10a). A SAXS diffraction pattern obtained from a sample with the 80.0/15.0/5.0 copolymer/water/oil wt % composition is shown in Figure 9. The scattering function is dominated by a strong correlation peak at q ) 0.070 Å-1, while another reflection is observed at q ) 0.082 Å-1. The most commonly observed space group of bicontinuous cubic phases in surfactant and lipid systems is Ia3d (Q230),3,4 where the bilayer/channel structure can be associated with the socalled Gyroid (G) minimal surface. This space group allows the Bragg reflections hkl ) 211, 220, 321, 400, 420, 332, 422, ..., which give peaks in the relative (scattering vector) positions x3, x4, x7, x8, x10, x11, x12, .... Recent structure factor calculations48 have shown the first reflection, corresponding to hkl ) 211, to be the most intense. The two first (intense) reflections in the present cubic phase follow the sequence x3 and x4 and are hence consistent with the first two (211 and 220) reflections of the Ia3d space group; three other (weak) peaks, marked in the SAXS diffraction pattern of Figure 9 with filled arrows, can be identified as the 420, 332, and 422 reflections of the Ia3d structure. Although less common, bicontinuous cubic phases have also been found which index to the space groups Pn3m (Q223) and Im3m (Q229) and correspond to the Diamond (D) and Schwarz-P (P) minimal surfaces, respectively.3,4 For Pn3m the sequence of allowed reflections is hkl ) 110, 111, 200, 211, 220, 221/300, 310, ... (relative peak (48) Clerc, M.; Dubois-Violette, E. J. Phys. II 1994, 4, 275.

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positions: x2, x3, x4, x6, x8, x9, x10, ...) and for Im3m hkl ) 110, 200, 211, 220, 310, 222, 321, ... (relative peak positions: x2, x4, x6, x8, x10, x12, x14, ...). The reflections identified in Figure 9 could correspond to the second (111) and third (200) reflections of the Pn3m structure or the third (211) and fourth (220) reflection of the Im3m structure. However, these possibilities are less likely since experiments have shown that, for both the Pn3m and Im3m bicontinuous structures, the first reflection in the series is the most intense.49 The Ia3d structure thus emerges as the best match to the diffraction data of Figure 9. From the positions of the peaks (1/dhkl vs m ) (h2 + k2 + l2)1/2 plot) marked in Figure 9, we obtain a lattice parameter of a ) 217 Å. This identification of the Ia3d/Gyroid structure in the V2 region of the BO10EO17-water-oil phase diagram receives further support when we calculate the area of the polar/apolar interface using the parallel surface model.34 For the Gyroid surface χu ) -8 and ç ) 3.091.22 With these values we obtain with eq 12 and 13 an area per copolymer molecule of Rp ) 73 Å2, a value very similar to that found in the LR phase adjacent to the V2 phase. We note that bicontinuous cubic phases of the Ia3d/Gyroid structure have been recently observed in ternary amphiphilic block copolymer-water-oil systems21,22,45,46 and in solvent-free block copolymers.50 The multiply connected (apolar) bilayer and (polar) channel representations of the morphology in the V2 phase, based on the Ia3d/Gyroid structure, are shown schematically in Figure 10. Normal Micellar Cubic Liquid Crystalline Phase (I1). An isotropic (nonbirefringent) liquid crystalline region is observed along the binary water-BO10EO17 axis (between the normal micellar solution and the normal hexagonal phase) in the 23-37 wt % copolymer concentration range (see Figures 1 and 3a). The samples in this region are stiff and exhibit a sharp singlet in the 2H-NMR spectrum, characteristics of a cubic structure. The location of this cubic phase in the ternary phase diagram suggests4,5 that it is composed of normal micelles which have crystallized into a cubic lattice (shown schematically in Figure 2b). Normal micellar cubic regions have recently been observed in PEO-PPO-PEO/water systems11-13 and their structure has been characterized with SANS17,18 and SAXS;20,45,46,51 the latter usually allows much better resolution of the numerous reflections originating from the cubic structure. The formation of “gels” (of presumably micellar cubic morphology) has also been reported52,53 for PBO-PEO and PEO-PBO-PEO block copolymers in water but no information regarding their structure has been published. A SAXS diffraction pattern obtained from the normal micellar cubic liquid crystalline phase at a 30.0/70.0/0.0 copolymer/water/oil wt % is presented in Figure 11a. On the basis of the relative positions of the first few SAXS peaks we have ruled out the face-centered (F...) cubic structures from consideration since the peaks in the SAXS diffraction pattern of Figure 11a do not follow the relative positions expected for the F... symmetry. Selecting between the I... and P.. structures is more difficult because the reflections afforded by the P... structure include as a subset the ones from the (higher symmetry) I... structure. While we cannot exclude the possibility of a P... structure, (49) Maddaford, P. J.; Toprakcioglu, C. Langmuir 1993, 9, 2868. (50) Hajduk, D. A.; Harper, P. E.; Gruner, S. M.; Honeker, C. C.; Kim, G.; Thomas, E. L.; Fetters, L. J. Macromolecules 1994, 27, 4063. (51) Zhou, D.; Alexandridis, P.; Khan, A. J. Colloid Interface Sci. 1996, 183, 339. (52) Nicholas, C. V.; Luo, Y.-Z.; Deng, N.-J.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C. Polymer 1993, 34, 138. (53) Yang, Z.; Pickard, S.; Deng, N.-J.; Barlow, R. J.; Attwood, D.; Booth, C. Macromolecules 1994, 27, 2371.

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Figure 11. (a) Slit-smeared SAXS diffraction pattern obtained from the normal micellar cubic liquid crystalline phase at a 30.0/70.0/0.0 wt % copolymer/water/oil composition at 25 °C. The scattering curve is also shown on an expanded intensity scale (right-hand side) to reveal the higher order Bragg peaks. The arrows mark the positions of the reflections afforded by the Im3m crystallographic space group. Filled arrows indicate observed reflections, while hollow arrows indicate reflections that are anticipated but are not clearly observed in the SAXS diffraction pattern. (b) Plot of the reciprocal d spacings (1/dhkl) of the reflections marked in the SAXS diffraction pattern of Figure 11a plotted versus m ) (h2 + k2 + l2)1/2. Figure 10. (a, top) A constant thickness structure based on the Ia3d/Gyroid minimal surface which is proposed as a representation of the microstructure in the V2 phase. For the BO10EO17-water-oil system investigated here, the molecular arrangement is such that an apolar film containing PBO and oil forms a dividing bilayer between two polar domains containing PEO and water. The figure has been drawn for a minority component (in our case, PEO + water) volume fraction of 0.33 and has been adapted from ref 50, where the reader is referred for more details. (b, bottom) The channel morphology (polar domains) for the constant thickness model of the Ia3d/ Gyroid structure. The figure been adapted from Harper, P. E. PhD Thesis, Princeton University: Princeton, NJ, 1996. Courtesy of S. M. Gruner.

we indexed the peaks of the diffraction pattern shown in Figure 11a to a body-centered structure. A total of seven Bragg peaks are identified (marked in Figure 11a with the filled arrows), which can be indexed as the hkl ) 110, 200, 211, 220, 222, 321, and 411 reflections of a bodycentered (I...) close-packed cubic structure, characterized by Bragg reflections whose reciprocal d spacings follow the relationship x2:x4:x6:x8:x12:x14:x18 .... The relative intensity of the observed peaks, as well as the very low intensity of the 310 and 400 reflections (indicated in Figure 10 with the hollow arrows) and those higher than 411, follow the trend expected from structures of cubic aspect 8 and, more specifically, from the centrosymmetric Im3m (Q229) space group.32

The straight line passing through the origin of the 1/dhkl versus m ) (h2 + k2 + l2)1/2 plot shown in Figure 11b indicates the good fit of the data to the I... structure. The value of the cubic cell lattice parameter, a, was estimated at 190 Å from the data of Figure 11. A lattice parameter of 180 Å was obtained using simple geometrical arguments (eq 11) for the volume occupied by the (N)) 2 normal micelles (assumed spherical) which make up the unit cell of the I... structure, and taking into account f for the 30.0/ 70.0/0.0 copolymer/water/oil wt % sample composition and the interfacial area per copolymer molecule (assumed to be 75 Å2 as in the neighboring H1 sample of 45.0/55.0/0 copolymer/water/oil wt %). The consistency of this predicted lattice parameter value with the experimentally determined one provides further evidence in support of the characterization of the normal micellar cubic structure as body-centered. Reverse Micellar Cubic Liquid Crystalline Phase (I2). An isotropic phase is formed between the L2 and H2 regions at copolymer concentrations 47-62 wt %, as seen in Figures 1 and 3b. The organization in this region has been determined as reverse micellar cubic (shown schematically in Figure 2f) and its characterization is described in detail in ref 24. Some structural information on I2 is provided here in order to facilitate its comparison with the I1 and V2 cubic structures discussed above.


Figure 12. Slit-smeared SAXS diffraction pattern obtained from the reverse micellar cubic liquid crystalline phase at a 50.0/10.0/40.0 wt % copolymer/water/oil composition at 25 °C. The scattering curve is also shown on an expanded intensity scale (right-hand side) to reveal the higher order Bragg peaks. The arrows mark the positions of the reflections afforded by the Fd3m crystallographic space group. Filled arrows indicate observed reflections while hollow arrows indicate reflections that are anticipated but not clearly observed in the SAXS diffraction pattern.

A SAXS diffraction pattern obtained from the I2 phase at a copolymer/water/oil composition of 50.0/10.0/40.0 wt % is plotted in Figure 12 (on the same scattering vector scale used for the I1 and V2 SAXS diffraction patterns). A total of 12 Bragg peaks were resolved (marked in Figure 12 with filled arrows), which can be indexed as the 111, 220, 311, 400, 331, 422, 440, 442, 533, 622, 551/711, and 642 reflections of the cubic space group Fd3m (Q227).24 A structural model for the Fd3m cubic phases has been proposed54 which involves a total of 24 spherical micelles per unit cell, with a bimodal size distribution composed of 8 larger and 16 smaller micelles. A lattice parameter of a ) 425 Å was obtained24 from plotting the reciprocal d spacings (1/dhkl) of the 12 observed reflections versus m ) (h2 + k2 + l2)1/2. From a calculation of the volume occupied by the (N)) 24 reverse micelles which participate in a face-centered cubic unit cell, a lattice parameter of 405 Å was obtained (for the 50.0/10.0/40.0 wt % copolymer/ water/oil composition), consistent with the lattice parameter determined from the SAXS data. We would have expected (for symmetry reasons with respect to the position of these phases in the phase diagram) the reverse and the normal micellar cubic phases to be of the same structure. However, the structure of the normal micellar cubic phase discussed above is bodycentered. The observed difference in the structure between I1 and I2 can be attributed to the different interactions between the normal and reverse micelles in the cubic lattice. Particles interacting through short range (hard-sphere-like) interactions crystallize in face-centered crystals, while long range (Coulomb-like) interactions favor body-centered crystals.55,56 The repulsion57 between the hydrated PEO blocks would result in long range intermicellar interactions in the normal micellar cubic structure; the interactions are short range in the reverse micellar cubic structure and thus allow the reverse micelles to pack more densely into a face-centered lattice. (54) Luzzati, V.; Vargas, R.; Gulik, A.; Mariani, P.; Seddon, J. M.; Rivas, E. Biochemistry 1992, 31, 279. (55) Robbins, M. O.; Kremer, K.; Grest, G. S. J. Chem. Phys. 1988, 88, 3286. (56) Agrawal, R.; Kofke, D. A. Mol. Phys. 1995, 85, 23. (57) Israelachvili, J.; Wennerstro¨m, H. Nature 1996, 379, 219.

Langmuir, Vol. 13, No. 1, 1997 33

Conclusions A wide spectrum of self-assembled structures can be formed by an amphiphilic diblock copolymer composed of poly(ethylene oxide) and poly(butylene oxide) in the presence of water (selective solvent for PEO) and “oil” (xylene, a selective solvent for PBO), rendering this the richest phase diagram reported to date. Six distinct lyotropic liquid crystalline phases and two solution phases (all are equilibrium states) have been identified (at 25 °C), whose relative location in the phase diagram (from the water corner to the polymer corner and to the oil corner) follows the sequence L1 f I1 f H1 f LR f V2 f H2 f I2 f L2. The oil-in-water (normal) morphology micellar solution (L1), micellar cubic liquid crystals (I1), and hexagonal liquid crystals (H1) and the lamellar structure (LR) are formed with an increase of the copolymer concentration along the oil-lean side of the ternary phase diagram. The micellar solution (L2), micellar cubic liquid crystals (I2), hexagonal liquid crystals (H2), and bicontinuous cubic liquid crystals (V2), all of the water-in-oil (reverse) morphology, are formed in the water-lean part of the phase diagram with increasing copolymer concentration and in the presence of water (≈1.3 water molecules per EO segment). The large variety of liquid crystalline structures observed over the whole composition range (even at copolymer concentrations as low as 23 wt %) is despite the relatively low molecular weight (≈1500) and the nonionic character (i.e., no long-range interactions) of BO10EO17 and can be attributed to its macromolecular nature and the high degree of segregation between the PBO and PEO blocks. The oil-in-water [water-in-oil] structures can accommodate up to 33 [40] wt % oil [water] with respect to the amount of copolymer. The interfacial area per copolymer molecule is approximately 75 Å2 throughout the LR region. The lamellar spacing values in the BO10EO17-water-xylene system fall in the range 80120 Å, comparable to that of the lamellae formed in water + xylene by the triblock copolymers EO13PO30EO13 and PO19EO33PO19 (of twice the BO10EO17 molecular weight and similar hydrophile/hydrophobe content). The presence of a reverse micellar cubic structure (I2) is an important feature of this phase diagram; its stability is attributed to the large size and volume fraction occupied by the BO10EO17 reverse micelles. It is one the first times such a structure has been observed in a ternary amphiphile-water-oil system. The reverse micelles crystallize in a structure of cubic aspect 15 and, more specifically, the Fd3m (Q227) space group. A micellar cubic structure (I1) is also formed along the water-copolymer axis. PBO-PEO and PEO-PBO-PEO block copolymers have been known to form “gels” in water, but ours is the first structural characterization of such a “gel”. SAXS diffraction patterns from the normal micellar cubic structure match the body-centered cubic aspect 8, and, most likely, the Im3m (Q229) space group. The difference in the preferred cubic organization between the normal and the reverse micelles (body-centered vs face-centered) can be attributed to the longer range intermicellar interactions in water (compared to that in the organic solvent). The microstructure in the bicontinuous cubic region (V2) can be described in terms of a multiplyconnected amphiphile bilayer separating two distinguishable and continuous domains of the same solvent (water); the global arrangement of the bilayer is consistent with the Gyroid minimal surface of body-centered Ia3d (Q230) cubic symmetry. The progression of oil-in-water and water-in-oil lyotropic liquid crystalline structures upon increase of the oil/water ratio at the same temperature is a novel feature of the

34


PBO-PEO (and also PEO-PPO-PEO) block copolymers and distinguishes them from, e.g., the nonionic alkyl oligooxyethylene surfactants which exhibit a temperaturedependent preferred curvature in their self-assembly. The structural polymorphism in the amphiphilic copolymerwater-oil systems appears to be governed by similar mechanisms as in solvent-free block copolymers.

Alexandridis et al.

Acknowledgment. P.A. is the recipient of a postdoctoral fellowship from the Swedish Natural Science Research Council (NFR). The acquisition of the SAXS apparatus was funded by the Swedish Council for Planning and Coordination of Research (FRN). LA960733Q

Structural Polymorphism of Amphiphilic Copolymers: Six Lyotropic

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