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J. Phys. Chem. B 1997, 101, 732-739
X-ray Studies on the C12EO2/Water System Se´ rgio S. Funari* and Gert Rapp EMBL-Outstation at DESY, Notkestrasse 85, D-22603 Hamburg, Germany ReceiVed: September 23, 1996; In Final Form: NoVember 13, 1996X
Binary mixtures of the poly(oxyethylene) surfactant C12EO2 and water have been investigated using optical microscopy and time-resolved X-ray diffraction during temperature scans. At concentrations in the range from 48 to 70 wt % of surfactant a thermal sequence from lamellar LR to cubic Ia3d to cubic Pn3m to L2 was found upon heating. The geometrical parameters of the phases such as thickness of the hydrocarbon core of the lamellar phase and length and diameter of the rods forming the cubic structures were calculated for such conditions. In the lamellar LR phase the surface area per molecule and the thickness of the hydrocarbon core showed little sensitivity to concentration. The thickness of the ethoxy groups was estimated to 1 nm. At high concentrations and temperatures near the cloud point, equilibrium conditions are difficult to reach, leading to the formation of cubic phases with apparently the same structure but different thermal behavior. One is insensitive to temperature changes while the other shrinks upon heating. The transition between the Ia3d and Pn3m cubic phases has the characteristics of a Bonnet transformation.
1. Introduction Binary mixtures of nonionic surfactants of the type CnEOm and water display a rich variety of liquid crystalline phases, depending on concentration, temperature, and length of the alkyl and poly(oxyethylene) chains, allowing one to exploit the hydrophobic effect in an extensive range of conditions.1,2 Apart from many industrial applications they are particularly suitable as modifiers of the balance of interactions in the head group region of model membranes without introduction of electrical charges in the system.3 The most common phases reported for lyotropic liquid crystalline systems are lamellar, hexagonal, and cubic phases and micellar solutions. The lamellar phase is formed by layers of surfactant separated by water with one-dimensional positional order in the direction perpendicular to these layers. The hexagonal phase consists of surfactant molecules aggregated to form long rods which pack on a two-dimensional hexagonal lattice perpendicular to the rod axis. The molecules forming these rods have a hydrophobic core with the head groups at the water interface. The phase transition between these two phases reflects a change in the curvature of the aggregates as a result of intermolecular interactions arising from changes in concentration, temperature, or presence of additives in the system. Lyotropic cubic phases have been known for a long time, although only recently they have been extensively studied.4 Bicontinuous cubic phases, of which there are a number of possible structures (see Figure 1), normally occur between the lamellar and hexagonal phases and have been regarded as forming the intermediate structure by which the lamellar phase can undergo a morphological change to the hexagonal phase. Further to these phases, so-called intermediate ones have been reported in some systems, replacing the cubic phase.5-7 Both C16EO6 and C22EO6 aqueous systems form an intermediate phase between hexagonal HR and lamellar LR, and their structure has been described as disrupted lamellar.5,6 Concentrated samples of surfactant/water systems can also form the so-called inverted phases, where the rods forming the inverted hexagonal HII or inverted cubic phases have the head * Corresponding author. Tel/Fax: ++49 49 89 902 -(120/149). E-mail:
[email protected] X Abstract published in AdVance ACS Abstracts, January 1, 1997.
S1089-5647(96)02925-2 CCC: $14.00
Figure 1. Schematic view of the cubic phases Ia3d and Pn3m. Complex changes in morphology and structure are accompanied during a phase transition between them.
Figure 2. Redraw of the phase diagram of the C12EO2/2H2O system as proposed by Conroy et al.8 It shows the relative position of the phases and the corresponding range of temperatures where they can be found. (Reproduced with permission from ref 8. Copyright 1990 Springer.)
groups facing inward (negative mean curvature), while in the “normal” phases the head groups point outward (positive mean curvature).4 The phase diagram of the system C12EO2/2H2O (Figure 2) has been known for many years and shows interesting aspects, such as the absence of hexagonal phases8 and the two neighboring cubic phases which form at one temperature but at different concentrations. This is unusual since in most other systems © 1997 American Chemical Society
X-ray Studies on the C12EO2/Water System the interconversion of cubic phases is mainly temperature rather than concentration driven. The cubic phases in this system have been assigned to be bicontinuous V2(1) and V2(2); however, their structures have not been determined so far. In the phase diagram shown they are surrounded by a lamellar LR phase at lower temperatures and by an L3 phase at the higher temperature boundary. We observed changes between the cubic phases on a dynamic scan of temperatures, therefore being unwise to directly compare our results with the published phase diagram.8 The nature of our measurements follows kinetics changes while others have observed thermodynamics ones. These changes do not necessarily happen in the same time scale. The transition from lamellar to continuous cubic phase requires dramatic changes in the morphology of the mesogenic units, going from infinite lamellae to finite cylindrical rods organized in a three-dimensional continuous array, where each rod has both ends connected in the amphiphilic network, as shown in Figure 1. The transition between the two cubic phases is associated with a change in (i) the spatial distribution of the connecting rods and (ii) the number of rods present in the unit cell for each of the cubic structures. It is a property of amphiphiles and has been observed, e.g., in both binary and ternary lipid based systems. Recently, we reported the transition between Ia3d and Pn3m cubic phases in POPC/C12EO2/2H2O (POPC is 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine).9 A similar situation was found in monoacylglyceride, MAG, systems.10 Phase transitions in lipids induced by changes in pressure have also been studied and, among others, a cubic Pn3m to cubic Im3m transition was observed.11 In some cases these transitions follow an epitaxial relationship and resemble a Bonnet transformation between the phases.9,12,13 In the present study we aimed to determine the structure of the two cubic phases previously observed8 in the system C12EO2/2H2O and to obtain the geometrical parameters of the LR and cubic phases. We used time-resolved X-ray diffraction during continuous heating and cooling scans, thus at nonequilibrium conditions. We observed the changes in the system at temperatures between 15 and 60 °C and in the concentration range between 49 and 70% in weight of surfactant. This corresponds to the part of the phase diagram where the cubic phases have been reported.8 Two cubic structures, i.e., Ia3d and Pn3m, were identified and their geometrical parameters determined. The Ia3d structure always appears at lower temperatures and transforms into Pn3m upon heating. Intuitively we can relate the Ia3d structure with the V2(1) and the Pn3m with the V2(2) cubic phases, noting that in the original phase diagram the V2(1) appears at higher temperatures than V2(2) (see Figure 2). 2. Materials and Methods The surfactant diethylene oxide monododecyl ether (C12EO2) was purchased from Aldrich and Nikko Chemicals with purity higher than 97% and was used without further treatment. Water was taken from a batch mixture of 86% H2O and 14% 2H2O. Samples were prepared by weighing the desired amount of each component directly into a tube and sealed. For mixing they were vortexed at different temperatures after which they were kept at room temperature overnight. From these samples Lindeman capillaries of 1 mm diameter were filled and flame sealed. These capillaries were stored at 4 °C until before the measurements when they were brought to room temperature. Other samples were put in flat sample holders with 0.75 or 1 mm path length. The temperature was controlled by a circulat-
J. Phys. Chem. B, Vol. 101, No. 5, 1997 733 TABLE 1: Composition of the Samples (wt %), the Structures, and the Corresponding Temperature Ranges Where They Have Been Observeda composn (wt %)
LR
49 55 58 60 67 70
- 24.6 -24.5 - 25.0 - 24.3 - 27.1 - 27.8
temp range for given structure LR + Ia3d Ia3d Ia3d + Pn3m 24.6-25.8 24.5-27.5 25.0-26.7 24.3-27.0 27.1-28.3 27.8-29.4
25.8->29 27.5-29.4 26.7-29.3 27.0-30.5 28.3-34.6 29.4-33.8
29.4-31.0 29.3-31.0 30.5-30.5 34.6-35.0 33.8-35.2
Pn3m 31.0-33.3 31.0-33.3 30.5-34.1 35.0-36.0 >35.2
a Note that these data were collected in time-resolved measurements during heating and cooling scans, and therefore the temperatures should not be taken as the temperature of phase transition but instead as the temperature range where they have been observed under our experimental conditions.
ing water bath with heating and cooling rates typically between 0.2 and 1 °C/min. X-ray diffraction data were collected on the beam line X13 of the EMBL Outstation at DESY operating at a wavelength of 0.15 nm (for details, see Rapp14). One-dimensional diffraction patterns were taken with a sealed linear detector15 as part of the standard data acquisition system,16 which is PC controlled. Two-dimensional patterns were recorded on an image plate and processed with a Fuji Bas 2000 scanner. Data were analyzed using the in-house software SCACO for the 2D patterns or the interactive data evaluation program OTOKO17 for 1D data. The interplanar distances d were calculated from the reciprocal spacing s ) 1/d ) (2/λ) sin θ (2θ, scattering angle; λ, wavelength). The instrument was calibrated using dry collagen from a rat tail tendon which has a repeat distance of 65.0 nm. In some cases the samples contained in sealed capillaries were spun at about 1000 rpm to eliminate partial orientation effects in the diffraction pattern. During heating and cooling scans the samples were typically exposed for 10 s followed by a 20 s period where they were protected from irradiation by a solenoid driven shutter close to the sample to minimize the possibility of radiation damage. 3. Results and Discussion Prior to the X-ray measurements, polarizing optical microscopy (POM) was performed during temperature scans. All samples changed from birefringent to isotropic at about 26 °C, which is indicative of a phase transition from a lamellar LR to a cubic phase. At about 32-35 °C, depending on concentration, the samples apparently ”boil”. This apparent boiling effect is the visualization of the lower consolute boundary, where demixing starts. It corresponds to the temperature where the interactions which hold the different components of the system together are broken and molecules of the same type associate.7 From the time-resolved X-ray diffraction data, we identified the structures and estimated the respective phase transition temperature range for each composition (Table 1). Although these samples are usually weak scatterers, in all cases several Bragg reflections were observed which allowed determination of the structure. The phase assignment from polarizing optical microscopy was compatible with the results from X-ray diffraction. For each phase observed we describe the results of individual samples followed by an overall interpretation of them. Lamellar Phase. To begin with, for a sample containing 49% in weight of surfactant the X-ray diffraction pattern displays two reflections with a 2:1 ratio of the corresponding distances, which is typical for one-dimensional lamellar phases. A series of diffraction patterns collected during a heating scan at 0.5 °C/min is shown in Figure 3. At 17.4 °C the lamellar repeat distance is 5.34 nm and remains constant until 22.0 °C when it
734 J. Phys. Chem. B, Vol. 101, No. 5, 1997
Funari and Rapp
Figure 3. Series of diffraction patterns during a temperature scan at 0.5 °C/min for a sample of 49 wt % of surfactant. The phase transitions can easily be seen as well as the evolution of the peaks’ intensity and position during the transitions. The scattering patterns do not give evidence of pretransition or intermediate structures between LR and Ia3d structures.
gradually starts to decrease with increasing temperature, reaching 4.82 nm at 24.8 °C. At this temperature, the intensity of the reflection associated with the lamellar structure drastically decreases and a new phase is observable which has much weaker reflections at smaller s values, i.e., larger interplanar distances (see Figure 3). It is attributed to an inverted bicontinuous cubic Ia3d structure (see below). With an increase in the concentration to 52 wt % the same behavior is seen. The interplanar distance is constant at 5.11 nm until 23.8 °C, i.e., 1.8 °C higher than at the lower concentration. The repeat distance also decreases to 4.77 nm, and at ∼26 °C the lamellar phase transforms into cubic Ia3d. At 55 wt % again the repeat distance is constant at 5.20 nm up to 24.3 °C. It continuously decreases to 4.76 nm at 27.0 °C. The same behavior, and similar parameters, are observed for samples containing 58 and 60 wt % surfactant. Note that although these samples have slightly different lamellar spacings at low temperatures, the repeat distance decreases on heating, to reach a limit of 4.8 nm, where samples at surfactant concentrations of 60 wt % and below transform from the LR + Ia3d two-phase region into a single cubic phase. Samples containing 67 and 70 wt % of surfactant also show a lamellar phase with similar behavior, but with a smaller interplanar distance before entering the two-phase region, indicative of possible partial hydration. This is supported by the observation that samples in this region of the phase diagram show decreasing repeat distances with decreasing amounts of water in the lamellar phase. At 67 wt % surfactant and 26 °C the repeat distance is d ) 4.73 nm, while at 70 wt % and the same temperature it is d ) 4.57 nm. It must also be noted that in these two samples the lamellar phase is present as a single phase up to 27 °C. The differences in the behavior of samples containing 60 wt % of surfactant or less and 67 wt % or more is illustrated in Figure 4. The thermal width of the LR - Ia3d two-phase region is broader at higher water content, and the onset of the transition occurs at lower temperatures. One can also see significant differences in the thermal range of stability of the cubic phases. No reflections were observed in the wide-angle regime of the diffraction patterns (WAXS), which is evidence that the
Figure 4. Interplanar distance changes with temperature during heating scans for samples containing 60 and 67 wt % surfactant. They correspond to the (001) for the LR, (110) for the Ia3d, and (211) for the Pn3m structures. Both graphs have been plotted using the same scale for direct comparison of the dimensions of corresponding structures at different conditions. Vertical lines indicate phase boundaries.
decrease in the repeat distance does not arise from interdigitation of the alkyl chains in the lamellar phase. In all samples the repeat distance in the lamellar phase is constant until a certain temperature, which is concentration dependent, when it starts to decrease. This marks the onset of the phase transition to the cubic phase. At this stage the position of the peak associated with the lamellar phase and its intensity change gradually. As the temperature raises and the phase transformation proceeds, a peak associated with the cubic phase becomes observable. As shown in Figure 3, during this process some of the scattering patterns clearly show the presence of lamellar and cubic phases simultaneously. Finally only reflections of the cubic phase are seen, and they show no thermal sensitivity. These results are evidence of the slow kinetics of the phase transition, enabling us to measure the behavior of such a system in a two-phase region using time-resolved X-ray diffraction, even though at the onset of the transition only one phase could be identified. From the data obtained for the lamellar phase we used the model described by Luzzati18 and a modification of it to calculate its geometrical parameters. The surface area per molecule S and the thicknesses of the water and hydrocarbon chain layers are summarized in Table 2 for the different concentrations at 23.5 °C. In the Luzzati formulas it is assumed that the volumes of the molecules are additive. We introduced a modification in which the EO2 groups are considered to be in the water moiety, and for that we calculated the volume fraction of the hydrocarbon core Φhc according to
[
Φhc ) 1/ 1 +
Meo Fhc Fhc mw MS + Mhc Feo Fw mS Mhc
]
(1)
where MS, Mhc, and Meo are molecular weights of surfactant and alkyl and ethoxy chains. Feo ) 1150, FS ) 900, Fhc ) 832,
X-ray Studies on the C12EO2/Water System
J. Phys. Chem. B, Vol. 101, No. 5, 1997 735
TABLE 2: Compositions of Samples and Geometric Parameters of the Lamellar Lr Phase at 23.5 °Ca composn wt %
Rw/s
ΦS
Φhc
d (nm)
55 58 60 67 70
12.3 10.9 10.0 7.4 6.4
0.58 0.61 0.63 0.70 0.72
0.39 0.41 0.43 0.48 0.50
5.19 5.21 5.19 4.73 4.57
dw+eo dhc deo (nm) (nm) S (nm2) (nm) 3.14 3.05 2.97 2.48 2.31
2.04 2.16 2.22 2.25 2.26
0.33 0.31 0.30 0.30 0.30
0.95 1.02 1.03 1.04 1.04
a Rw/s is the molar ratio between water and surfactant, ΦS and Φhc are the volume fractions of surfactant and alkyl chains, respectively. d is the measured lamellar repeat distance. The thickness of the water plus ethoxy groups layer is dw+eo, while dhc refers to the hydrocarbon core. S is the surface area per molecule. deo is the thickness of the ethoxy group layer estimated using eqs 1-4.
and Fw ) 1010 kg m-3 are the densities of the ethoxy chain, surfactant, alkyl chain, and water,5 mw and mS are the masses of water and surfactant present in a sample, respectively. Additionally, using a very simple model of three layers (water, head groups, and hydrocarbon chains), we can estimate the thickness of the head group region, deo, if we assume that there is a homogeneous layer of ethoxy head groups only between the hydrophobic core and water. This assumption is certainly too simple to provide precise quantitative parameters. However, it can be useful in a qualitative description of this region of the lamellar phase. To estimate the thickness of the EO head group region deo, we related the water thickness dw calculated in two ways: (i) using Luzzati’s definition of the volume fraction ΦS of the surfactant directly and (ii) using the above modified equation for the volume fraction of the hydrophobic core. The molecular weight and the density of water were calculated by considering the composition of the H2O and 2H2O mixture. Taking the lamellar spacing d
d ) dhc + deo + dw
and
dS ) deo + dhc
(2)
we get
dS ) d - dw
with dw ) d(1 - ΦS) (Luzzati formalism) (3)
dhc ) dΦhc (Φhc from eq 1, modification of Luzzati formalism) (4) The results are shown in Table 2, where it can also be seen that the parameters calculated for the LR phase, such as the thickness of the hydrophobic core dhc and surface area per molecule S, are only slightly dependent on concentration. However, the thickness of the aqueous moiety (dw+eo) increases linearly with the molar ratio between water and surfactant, Rw/S. The linearity is a consequence of the assumption made that the ethoxy groups are part of the aqueous moiety and thus not distinguishable from water. In this case one must neglect that there are two regimes for water addition to the surfactant, initially hydration of the head groups followed by swelling of the lamellae. Lamellar and Nonlamellar Phases. The phase transition from the LR to cubic phases requires large changes in the topology of the mesogenic units forming the respective phases, going from flat lamellae to cylindrical surfaces. A similar change in topology is observed in lamellar to hexagonal phase transitions, with the difference that in the hexagonal phase we have individual “infinite” cylinders, while the cubic Ia3d formed upon heating the LR phase consists of a three-dimensional network of connected finite cylinders.
Transitions to nonlamellar structures have been reviewed recently.19 Time-resolved T-jump experiments on phosphoethanolamines under non-equilibrium conditions showed the existence of a short-lived intermediate thin LR structure containing the nucleation sites for the budding-off of the cylindrical aggregates.20 These topological changes can also be explained by assuming the formation of intermediate structures such as uncorrelated disruptions in the lamellae, as it happens in nonionic surfactants such as C16EO6 and C22EO65,6 or as broken lamellar bilayers, as suggested by Ranc¸ on and Charvolin12 studying the C12EO6 system. They proposed the formation of an intermediate structure between lamellar and cubic phases formed by cylinders arranged in an interplanar two-dimensional hexagonal lattice. The C12EO2 system studied here did not give evidence for the formation of intermediate structures, as can be seen in Figure 3. Our explanation for the LR to Ia3d phase transition observed in this system is to consider that the head groups dehydrate with heating, weakening the repulsion between the EO groups. This should happen in parallel with an increase of the alkyl chain flexibility. Both effects favor the formation of highly curved interfaces of the inverted type, necessary for building the cubic network. This also explains the fact that in the C12EO2 system the cubic phases occur at higher temperatures than in the lamellar phase, in contrast to C12EO6 which has a much larger head group and forms a “normal” cubic phase.12 The relative position of the lamellar phase in relation to these curved phases is determined by the ratio between the length of the alkyl chain and the head group. Shorter heads, with a small number of EO groups, favor curved phases of the inverted type which occur at higher temperatures than the lamellar phase, while longer ones form normal curved phases at lower temperatures. Heating the Ia3d cubic phase induces the transition to the Pn3m cubic phase, where the curvature at the nodes (junction of rods) is even higher than in the Ia3d phase. Note that the mean curvature in both cubic phases is zero. The transition from Pn3m to the L2 phase upon heating can be explained by strong dehydration of the head groups because it coincides with the lower consolute boundary. At this temperature the interactions between the head groups disfavors the formation of an inverted hexagonal phase at high temperatures, as one would expect when considering a gradual increase in curvature due to heating. Cubic Phases. In all samples studied we observed two cubic phases, one at lower temperature which transforms to another as the temperature is raised. Both phases are separated by a small two-phase region. The coexistence of bicontinuous cubic phases over a wide range of temperatures has been reported mostly in studies involving lipids.4,11,21 Among the different structures formed by the C12EO2 system, the cubic structures were identified by polarizing optical microscopy and X-ray diffraction. A sector integration of two-dimensional diffraction patterns of a sample containing 58 wt % at 29 and 33 °C, respectively, is shown in Figure 5. The experimental data of the low-temperature cubic phase could be fitted to a cubic Ia3d structure, which is among the most commonly observed ones. This structure was initially described by Luzzati and Spegt22 and belongs to a body centered space group of rods connected three by three to form two interwoven but independent threedimensional networks. The rods are essentially a surfactant bilayer with a circular cross-section. Following the same procedure, the higher temperature cubic phase has been assigned as Pn3m, also an inverted bicontinuous phase with a primitive
736 J. Phys. Chem. B, Vol. 101, No. 5, 1997
Figure 5. Scattering patterns from a sample containing 58 wt % surfactant at 29 (bottom) and 33 °C (top) collected at constant temperature (static; see text). These patterns were obtained by sector integration of 2D data. The reflections can be indexed on a cubic Ia3d space group at 29 °C and a Pn3m space group at 33 °C.
cubic lattice formed by rods connected four by four at tetrahedral angles, generating two unconnected but interwoven diamond lattices. These structures can also be described by an infinite periodical minimal surface, IPMS. In these surfaces the mean curvature is zero, i.e., positive and negative curvatures of the bilayers forming the “rods” balance each other in every point. The centers of these rods lie on the IPMS. The Ia3d phase corresponds to IPMS of the gyroid type, while Pn3m is of the (double) diamond type.23 The dimensions of these rods, i.e., their length l and radius r, were calculated on the basis of purely geometrical grounds, as described recently.9
Ia3d:
l ) a/x8; r ) a(x8/24π)1/2
Pn3m:
l ) ax3/2; r ) a(1/2πx3)1/2
In the above equations a is the unit cell dimension of the respective cubic structure. Low-Temperature Cubic Phase. The sample containing 55 wt % shows a single Ia3d cubic phase between 27.5 and 29.4 °C with a constant lattice parameter. The ratio between the interplanar distances corresponding to the first and second reflections is d2/d1 ) 0.86, which is typical for the Ia3d structure. From these data we estimated the lattice parameter a ) 14.24 nm, the length of the rods l ) 5.03 nm, and the radius r ) 2.76 nm. According to Fontell24 the aggregates forming the two interwoven networks have almost the same length and diameter. The agreement of our data with this observation is further evidence of the right assignment of the cubic structure. From the sequence of reflections in the diffraction patterns we can see that the (001) plane of the lamellar phase transforms into the (220) plane of the Ia3d cubic phase. In the C12EO6/ water system25 it has been shown that an epitaxial relation exists between the hexagonal, cubic, and lamellar phases. Upon
Funari and Rapp heating the cubic phase, a lamellar mesophase develops with the lamellar planes perpendicular to the [211] direction of the cubic phase. Increasing the surfactant concentration to 58 wt % decreases the temperature onset of the Ia3d phase to 25.0 °C, and it exists as a single phase until 29.4 °C. The geometrical parameters are very similar, i.e., the lattice a ) 14.49 nm, the rod length l ) 5.12 nm, and r ) 2.81 nm. At 60 wt % the cubic phase has the same geometrical parameters, however, it exists over a larger temperature range from 27.0 to 30.5 °C. The sample containing 67 wt % surfactant (see Figure 4) shows significant changes in the Ia3d phase, parallel to what has been seen in the lamellar phase. The range of temperatures where it exists as a single phase is much larger (28.5-34.5 °C), while the geometrical parameters are smaller (a ) 12.85 nm, l ) 4.54 nm, and r ) 2.49 nm) but remain practically constant over the entire range of temperatures. This is evidence for the fact thatswithin limitssthis Ia3d phase is favored at lower hydration of the surfactant molecules. Similar behavior has been observed in ternary systems containing lipids.4 It implies that the head groups play a significant role in the stability of this phase. The hydration force acting on them is weak enough to keep the EO groups together, forming the rod units of the networks. Therefore, addition of water strengthens the hydration force, increases the total volume of EO groups and bound water, and decreases the stability of the Ia3d cubic phase. This view is supported by the observation that the range of temperatures where the cubic Ia3d phase exists as a single phase depends on the amount of water present and decreases with increasing water content. In order to unambiguously confirm the assignment of these cubic phases, we recorded 2D diffraction patterns on an image plate at a constant temperature. In these measurements we used exposure times up to 3 min and obtained diffraction patterns with a larger number of reflections. The sample containing 58 wt % surfactant at 29 °C showed six peaks corresponding to a/ x6:x8:x14:x16:x20:x22, which are associated with the (211), (220), (321), (400), (420), and (332) planes, respectively, see Figure 5. The lattice parameter was calculated to a ) 12.17 nm, the rod length l ) 4.30 nm, and radius of the rod r ) 2.36 nm. A plot of the reciprocal spacings vs (h2 + k2 + l2)1/2 is shown in Figure 6 and proves that the assignment is correct. The parameters have smaller values than those obtained during the heating scan using the 1D detector. This difference can be attributed to dehydration during the first scan, where the sample was heated to reach the L2 phase, cooled, and reheated to 29 °C when the 2D pattern was collected. The sample containing 70 wt % of surfactant clearly shows a complex behavior after the LR to Ia3d phase transition started. The temperature scan of this sample (Figure 7) shows a lamellar LR phase up to 27.8 °C, transforming into an LR + Ia3d twophase region until 29.4 °C. Up to about 34 °C there are apparently three phases coexisting, i.e., two Ia3d cubic ones and an unidentified phase. The latter shows only one reflection which makes its assignment impossible. Such unusual behavior should be taken with care because it could also be observed in a sample not properly mixed. Moreover, our measurements were done in non-equilibrium conditions. It is interesting to note from these two cubic phases showing the same structure that one has a significant thermal dependence of its lattice parameters and the other has not. For the assignment of these phases the ratios of the corresponding interplanar distances for the two most intense reflections (see Figure 7) of each of them were calculated. In both cases the ratio between the second
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J. Phys. Chem. B, Vol. 101, No. 5, 1997 737
Figure 6. Reciprocal spacing of the two cubic lattices observed for a sample containing 63 wt % vs (h2 + k2 + l2). The straight lines are linear regressions. The lattice parameters obtained from the slope are a ) 12.2 nm for the Ia3d and a ) 9.8 nm for Pn3m structures.
and first reflections d2/d1 was 0.87 which is strong evidence for the cubic Ia3d structure. It is striking that under these conditions two cubic phases form having a different behavior with temperature. One has a linearly increasing lattice parameter from a ) 12.55 nm at 30.0 °C to a ) 13.02 nm at 33.0 °C. This phase disappears at higher temperatures. The other cubic phase shows behavior similar to the samples described before. It has a lattice parameter a ) 12.43 nm which remains constant. At temperatures above 33.5 °C, where a phase transition to a cubic Pn3m takes place, the lattice parameter of this Ia3d increases within the two-phase (Ia3d + Pn3m) region (see Figure 7). High-Temperature Cubic Phase. The second cubic phase which forms upon heating the Ia3d appears in all samples measured. It should be noted that this transition occurs near the cloud point. Results from polarizing optical microscopy and a systematic study of the thermal behavior of this phase showed the need to choose very low heating rates because the thermal width of the Pn3m phase is very small. One could reach the cloud point where strong dehydration of the surfactant head groups starts, while the cubic network would still be present in some domains of the sample, creating the impression of a multiphase system. The sample containing 58 wt % surfactant was heated at 0.2 °C/min up to 33 °C and another 2D diffraction pattern was recorded on an image plate. It showed four peaks with corresponding spacing ratios of a/x2:x3:x4:x6, which are related to the (110), (111), (200), and (211) planes typical for the cubic Pn3m structure. As shown in Figure 5, the first two peaks have very high intensity while the last two are very weak. The lattice parameter was calculated to a ) 8.03 nm, the rod length l ) 6.95 nm, and radius r ) 2.43 nm. The rod dimensions in the Ia3d and Pn3m cubic phases differ only in length (4.30 nm vs 6.95 nm), whereas the radius remains unchanged. The diameter of the rods in both cubic phases (2r ) 4.86 nm) has a value similar to the bilayer thickness of the lamellar LR phase at the onset of the transition to cubic. Note that here we refer to the diameter of the rods, comprising both
Figure 7. Time-resolved diffraction patterns of a 70 wt % C12EO2/ water sample during a heating scan. At low temperatures two sets of reflections compatible with the cubic Ia3d space group (dashed lines) can be observed showing two reflections for each of them. Diffraction patterns at low temperatures have a reflection of an unidentified phase (solid line) corresponding to d ) 5.0 nm as indicated by the arrow. At higher temperatures reflections of another cubic phase attributed to the Pn3m space group can be seen.
hydrophobic and hydrophilic moieties, and not only the diameter of the central core of them. It suggests, but does not prove, an epitaxial relationship between these phases. Further, during the cubic-cubic transition from Ia3d to Pn3m the reorganization of the rods leaves the “rod density” in the unit cell almost unchanged. E.g., with the 58 wt % sample we obtain 24/a3 ) 7.9 × 10-3 rod/nm3 for the Ia3d structure, while for the Pn3m one we obtain 4/a3 ) 7.7 × 10-3 rod/nm3. The metric relation between the lattice parameters of both phases, at this concentration, i.e., aIa3d/aPn3m ) 12.17 nm/8.03 nm ) 1.52, is close to the expected value of 1.11x2 ) 1.57 when such transition occurs via a Bonnet transformation.9 In such transformations a reorganization of the rod units occurs without a change in the mean curvature. It is entropically driven only and does not involve an enthalpy change, therefore, ∆H ) 0. Further support for this view was obtained from structural studies on ternary mixtures of this system containing 8 wt % phospholipid (POPC). There the phase sequence on heating was from lamellar to Ia3d to Pn3m, and the Bonnet transformation was unambiguously identified.9 For most of the other samples only 1D patterns were collected. They showed two reflections with the ratio between the corresponding distances d2/d1 ) 0.82, which, together with the above 2D data, is indicative of the Pn3m phase. In the samples containing 55, 58, and 60 wt % the lattice parameter a of the cubic Pn3m phase is basically constant in the range of the temperatures where it could be seen as a single phase, i.e.,
738 J. Phys. Chem. B, Vol. 101, No. 5, 1997 typically between 31 and 34 °C where a ) 8.96, 9.01, and 8.81 nm, respectively. The transition to the isotropic L2 phase, as the temperature is raised, is accompanied by a steep decrease of the lattice parameter, while the second reflection disappears. Like those of the lamellar and the cubic Ia3d phases, the samples containing 67 and 70 wt % surfactant also show a significant difference in the existence range of the cubic Pn3m phase as compared to samples at lower surfactant concentration. In both samples with high concentration the lattice parameter increases with increasing temperature from 8.1 nm at 35.0 °C to 8.4 nm at 36.0 °C, whereas at the less concentrated samples the lattice parameter remains almost constant until the Pn3m phase vanishes (see Figure 4). The diameter of the rods in the Pn3m phase is 4.9 nm for a lattice parameter a ) 8.1 nm at 35.0 °C and 5.1 nm for a ) 8.4 nm at 36.0 °C, while the length of the rods increases only from 7.0 to 7.3 nm. The difference in the circumference of these rods is 0.6 nm. Taking the value 0.30 nm2 for the surface area per surfactant molecule from Table 2 and assuming that this parameter is the same in both phases,5-7 we calculate the diameter of one surfactant molecule to be also 0.6 nm. Thus, the increase in lattice constant most likely arises from incorporation of one surfactant molecule per rod crosssection and reflects the dynamics of the Pn3m unit cell formation which does not fully develop during the temperature scan at this high surfactant concentration. From the data for the lamellar and cubic phases we could observe two regimes for the samples’ behavior, depending on their concentration. At amounts of surfactant below approximately 60 wt %, i.e., molar ratios Rw/s > 10, Table 2, the samples are fully hydrated. We support this argument with the observation that the repeat distance of the lamellar phase in the two-phase region decreases continuously with increasing temperature (dehydration), reaching a “critical” value of 4.8 nm which is slightly larger than twice the estimated all trans length of a C12EO2 molecule (l ∼ 2.2 nm), where the transition to a single cubic phase occurs. At concentrations higher than 60 wt % the lamellar repeat distance in the single phase is smaller than 4.8 nm. This suggests that the interactions between the head groups play a larger role in the stability of this phase than in the fully hydrated regime. This can be explained by assuming dipolar interactions and hydrogen bonds among adjacent head groups contributing to the stability of the lamellar phase. Upon heating, the increasing flexibility of the alkyl chains would induce the transition to the inverted cubic Ia3d phase. The hydration and structural properties of a homologous series of C12EOn (n ) 1-7) has been shown recently;26 however, one should be careful with comparisons because hydration of the samples in both studies have been obtained in different ways, and most important, in our case the system was investigated during scan conditions, i.e., not in equilibrium. L2 Phase. According to the phase diagram8 (Figure 2) an L2 phase forms at high temperatures or high concentrations. It has been described as a concentrated surfactant liquid. Our temperature scans under the polarizing microscope have shown that at about 32-35 °C the system passes the cloud point and one ends with a water rich and a surfactant rich two-phase system. Dehydration of the surfactant due to an increase in temperature induces aggregation into small units where the polar head groups face the inner core. This phase has been identified in scattering patterns as a broad peak occurring at high temperatures. It appears in all of the concentrations measured, and the width of the peak reflects a wide range of distances. The maximum position corresponds to the average distance in the system under the experimental conditions with an estimated value of 4.3 nm. The transition
Funari and Rapp from cubic to L2 phase can be seen by a sharp decrease of the peak intensities corresponding to the cubic phase accompanied by a strong decrease of the associated interplanar distance. L3 Phase. In the reported phase diagram (Figure 2) this phase should appear in a narrow regime between the cubic and the L2 phase. It has been described by Anderson et al.27 as having its basic structural unit formed by surfactant bilayers. It is a rather viscous isotropic solution showing flow birefringence and strong light scattering arising from extended surfactant aggregates. Using POM and X-ray diffraction, we were not able to unequivocally identify or characterize it. Such investigations would require experimental conditions not available to us at present. An elegant description of the L3 phase is presented by Strey et al.28 based on the C12EO5/water system which is a surfactant similar to that in the present samples. Conclusions Using time-resolved X-ray diffraction on binary mixtures of C12EO2/water, the thermal phase sequence from lamellar LR to cubic Ia3d to cubic Pn3m was established. The dependence on temperature and concentration of the geometrical parameters and the stability of the phases observed were established. Assuming a three-layer model of alkyl chains, head groups, and water, we estimated the thickness of the polar head group layer (deo) and found that it is basically independent of the sample concentration. We observed a temperature driven phase transition between two cubic phases which was not reported in earlier studies.8 At high concentrations of surfactant the system apparently forms two cubic phases with the same symmetry (Ia3d) but with different thermal behavior. This has been attributed to a kinetic effect in a non-equilibrium situation. The thermal behavior of the geometrical parameters of the Pn3m cubic phase at high concentrations could be explained assuming that during the heating scan surfactant molecules are incorporated into the rods forming the unit cell. They change the rod diameter but have little effect on the rod length. The transitions involving the LR and the two cubic phases (Ia3d and Pn3m) followed a similar trend observed for the mixture of this surfactant with POPC. There it has been argued9 that they are connected by an epitaxial relationship and the cubic to cubic transition follows a Bonnet transformation. In the system described here we did not have enough evidence of the epitaxial relationship between the phases. However, the transition between these cubic phases has characteristics of a Bonnet transformation. Acknowledgment. We gratefully acknowledge Prof. G. J. T. Tiddy and Drs. M. S. Leaver and J. Burgoyne for critical reading of the manuscript. We thank Dr. W. Bennet and Prof. A. Yonath for making the image plate scanner available to us and Dr. B. Ma¨dler for technical support. References and Notes (1) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975. (2) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; John Wiley & Sons, Inc.: New York, 1973. (3) Funari, S. S.; Klose, G. Chem. Phys. Lipids 1995, 75, 145. (4) Seddon, J. M.; Templer, R. H. Philos. Trans. R. Soc. London A 1993, 344, 377. (5) Funari, S. S.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1994, 98, 3015. (6) Funari, S. S.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1992, 96, 11029. (7) Burgoyne, J.; Holmes, M. C.; Tiddy, G. G. T. J. Phys Chem. 1995, 99, 6054.
X-ray Studies on the C12EO2/Water System (8) Conroy, J. P.; Hall, C.; Lang, C. A.; Rendall, K.; Tiddy, G. J. T.; Walsh, J.; Lindblom, G. Prog. Colloid. Polym. Sci. 1990, 82, 253. (9) Funari, S. S.; Ma¨dler, B.; Rapp, G. Eur. Biophys. J. 1996, 24 (5), 293. (10) Caffrey, M. Biochemistry 1987, 26, 6349. (11) Czeslik, C.; Winter, R.; Rapp, G.; Bartels, K. Biophys. J. 1995, 68, 1423. (12) Ranc¸ on, Y.; Charvolin, J. J. Phys. Chem. 1988, 92, 2646. (13) Hyde, S. T.; Anderson, S.; Ericsson, B.; Larsson, K. Z. Kristallogr. 1984, 168, 213. (14) Rapp, G. Acta Phys. Pol. 1992, A82, 103. (15) Gabriel, A. ReV. Sci. Instrum. 1977, 48, 1303. (16) Boulin, C.; Kempf, R.; Gabriel, A.; Koch, M. H. J. Nucl. Instrum. Methods 1988, A269, 312. (17) Boulin, C.; Kempf, R.; Koch, M. H. J.; McLaughlin, S. M. Nucl. Instrum. Methods 1986, A249, 399. (18) Luzzati, V. In Biological Membranes; Chapman, D., Ed.; Academic Press: London, 1968; p 71.
J. Phys. Chem. B, Vol. 101, No. 5, 1997 739 (19) Seddon, J. Biochim. Biophys. Acta 1990, 1031, 1. (20) Laggner, P.; Kriechbaum, M.; Rapp, G. J. Appl. Crystallogr. 1991, 24, 836. (21) Larsson, K. J. Colloid Interface Sci. 1986, 113, 299. (22) Luzzati, V.; Spegt, P. A. Nature 1967, 215, 701. (23) Fontell, K. Colloid Polym. Sci. 1990, 268, 264. (24) Fontell, K. AdV. Colloid Interface Sci. 1992, 41, 127. (25) Clerc, M.; Levelut, A. M.; Sadoc, J. F. J. Phys. 2 Fr. 1991, 1, 1263. (26) Klose, G.; Eisenba¨tter, St.; Galle, J.; Islamov, A.; Dietrich, U. Langmuir 1995, 11, 2889. (27) Anderson, D.; Wennerstro¨m, H.; Olsson, U. J. Phys. Chem. 1989, 93, 4243. (28) Strey, R.; Schoma¨cker, R.; Roux, D.; Nallet, F.; Olsson, U. J. Chem. Soc., Faraday Trans. 1990, 86 (12), 2253.
