Structural and Macroscopic Characterization of a Gel Phase of

Feb 17, 1999 - The structures present have been investigated by means of freeze-fracture electron microscopy and small-angle neutron scattering (SANS)...
0 downloads 6 Views 245KB Size
Download PDF
1416

J. Phys. Chem. B 1999, 103, 1416-1424

Structural and Macroscopic Characterization of a Gel Phase of Densely Packed Monodisperse, Unilamellar Vesicles M. Gradzielski,*,† M. Mu1 ller,† M. Bergmeier,† H. Hoffmann,† and E. Hoinkis‡ Lehrstuhl fu¨ r Physikalische Chemie I, UniVersita¨ t Bayreuth, D-95440 Bayreuth, Germany, and Hahn-Meitner-Institut, Glienicker Strasse 100, D-14109 Berlin, Germany ReceiVed: August 7, 1998; In Final Form: December 10, 1998

In the phase diagram of the surfactant system sodium oleate/octanol/water a very stiff gel phase has been found, which is usually not present in similar systems. The phases of this system have been characterized by electric conductivity and rheological measurements. The structures present have been investigated by means of freeze-fracture electron microscopy and small-angle neutron scattering (SANS). These experiments have shown that addition of octanol to the surfactant solution for concentrations higher than 130 mM Na oleate leads to the formation of small unilamellar vesicles. For sufficiently high octanol content these vesicles are so monodisperse that they are able to form a densely packed system with long-range order and with a shear modulus that is about 100 times higher than normally found for vesicle systems. Upon dilution with water the vesicles swell while keeping the packing fraction constant until a maximum diameter of about 450 Å is reached, beyond which no further growth of the vesicles can take place. This is the first system of such type that forms a cubic-phase-like arrangement of monodisperse vesicles.

I. Introduction Surfactant systems can exhibit a rich phase behavior by forming a variety of different micellar structures. Typically, this phase behavior becomes even richer when a cosurfactant is present as a third component,1,2 The surfactant aggregates can range from simple spherical micelles and rodlike micelles to flat bilayers, such as they are also present in biological membranes. These different structural entities are able to form a variety of phases with more or less ordered arrangements, i.e., by forming liquid crystalline phases (mesophases).1,3 A particular way of self-organization of surfactant molecules is the formation of vesicular structures. Such structures have attracted a large number of investigations since they can serve as good model systems for biological membranes.4,5 In these systems, the surfactant aggregation resembles that in flat bilayers, since typically these vesicles are fairly large, i.e., several hundred nanometers to a few micrometers, in comparison to the surfactant chain length. Therefore, the environment of a surfactant molecule in the bilayer looks at a local scale just like in a flat lamella. More recently, also the formation of relatively small and welldefined vesicles of diameters ranging from 15 to 40 nm has been reported.6,7 These vesicles have been found in the fairly dilute range of the phase diagram, but in these systems an increase of the total concentration at constant cosurfactant/ surfactant ratio leads to the formation of multilamellar vesicles (“onions”).6 Contrary to that we have recently found a relatively concentrated gel phase of small unilamellar vesicles, i.e., the first example of a densely packed and highly ordered system of monodisperse vesicles.8 In this paper we will give a much more detailed picture of this uncommon phase behavior. Because vesicle systems can be found for a large variety of different surfactants, we chose to study the phase behavior of a † ‡

Universita¨t Bayreuth. Hahn-Meitner-Institut.

classical carboxylate surfactant such as sodium oleate together with a medium chain alcohol as cosurfactant. It has been observed before that the addition of such a cosurfactant may induce the formation of classical lamellar phases or vesicles.9-15 An exemplary study of this effect has been done on surfactant mixtures of the zwitterionic surfactant tetradecyldimethylamine oxide (TDMAO) and the cationic tetradecyltrimethylammonium bromide (TTABr). Here it has been observed that the addition of the cosurfactant first leads to formation and growth of rodlike micelles. At higher cosurfactant content a transition to vesicles takes place, and at still higher cosurfactant content a classical lamellar phase is formed.13-15 In these surfactant mixtures formation of vesicles is the more preferred the higher the content of ionic surfactant and often one can induce formation of vesicles simply by adding an ionic surfactant to a lamellar phase made up from a nonionic surfactant.6,15,16 Such a stabilization of vesicular structures with respect to flat lamellae with increasing charge density of the bilayers is also expected on theoretical grounds.17-19 Accordingly, a fairly strong tendency for vesicle formation is to be expected upon addition of a medium chain alcohol as a cosurfactant, since sodium oleate is an ionic surfactant. In the following we have investigated the ternary system sodium oleate/1-octanol/water. In addition, experiments were performed on systems where the octanol was replaced by other alkyl alcohols ranging from pentanol to decanol. Variation of the alcohol was done in order to see how the structure of the cosurfactant influences the phase behavior of the corresponding systems. II. Materials and Methods II.1. Experimental Details. Sodium oleate was prepared by titration of oleic acid with sodium hydroxide in ethanol according to the method of Flockhart and Graham.20 1-Octanol, 1-pentanol, 1-hexanol, 1-heptanol, 1-nonanol, and 1-decanol

10.1021/jp9833303 CCC: $18.00 © 1999 American Chemical Society Published on Web 02/17/1999

Gel Phase of Unilamellar Vesicles

J. Phys. Chem. B, Vol. 103, No. 9, 1999 1417

were obtained from Fluka in p.A. quality. D2O (99.8% isotopic purity) was supplied by Euriso-top Groupe CEA, C. E. Saclay, Gif-sur-Yvette (France). For the determination of the phase diagram, samples of 2-5 g were weighed into glass tubes and homogenized by heating and vigorous shaking. Afterward, they were monitored for at least 4 weeks. Electrical conductivity data were obtained by means of a conductivity meter LF 2500 CON (WTW) that operates at a frequency of 4000 Hz. The rheological measurements were done with a Bohlin CS rheometer, which allows for oscillatory measurements at constant shear stress amplitude in the frequency range 0.001-10 Hz. For the freeze-fracture electron microscopy (FF-TEM) small amounts of the sample were placed on a 0.1 mm thick copper disk covered with a second copper disk. The sample was frozen by plunging this sandwich into liquid propane (cooled by liquid nitrogen). Fracturing and replication were carried out in a freezefracture apparatus (Balzers BAF 400, Germany) at a temperature of -140 °C. Pt/C was deposited at an angle of 45°, and the formed replicas were examined in a CEM 902 electron microscope (Zeiss, Germany). The small-angle neutron scattering (SANS) experiments were performed at the Hahn-Meitner Institute, Berlin (Germany), on the instrument V4.21 A wavelength of 6.0 Å was chosen, and sample to detector distances of 1, 4, and 15.85 m were employed. The data were recorded on a 64 × 64 twodimensional detector. They became afterward radially averaged and converted into absolute units, i.e., the differential crosssection, by comparison with the scattering of a H20 standard and proper correction for detector background and the scattering of the empty cell.22,23 However, the incoherent scattering was not subtracted from the intensity curves that are displayed in the following. II.2. Theoretical ConsiderationssModels for the SANS Data. The SANS intensity curves are indicative of the structure and size of the particles present. In particular, the higher q range is mainly sensitive to the scattering of the individual particles and less to their interactions. For the analysis of the scattering data we employed the following formulas that describe the scattering of flat lamellae of thickness d (eq 1) and that of rods of radius R and length L (eq 2)24:

I(q) ) I(q) )

∫0π/2

(

(

)

sin(qd/2) 2π Φ∆F2d 2 qd/2 q

2

(1)

)

sin[(qL/2) cos θ] 2J1(qR sin θ) 2 sin θ dθ (2) qR sin θ (qL/2) cos θ

Vesicular structures are, of course, spherical shells but for the case that the shell is relatively thin in comparison to their radius, their scattering pattern in the higher q range will be that of a flat lamellae, since on a local scale they look flat. For the further understanding of the SANS data, one has to keep in mind that the observed angular dependent scattering intensity is given by a product of the intraparticular interferences, described by the particle form factor P(q), and the interparticular interferences, as described by the structure factor S(q):

∫0∞dr f(r) P(q,r) S(q)

I(q) ) 1N

(3)

with r ) (Ri + Ra)/2, 1N the number density of the aggregates, and Ri and Ra the inner and outer radii of the vesicle. This formula already takes into account the aggregate polydispersity which is here described by a distribution function of the radii:

Figure 1. Particle form factor P(q) (- - -), structure factor S(q) (‚‚‚), and the corresponding intensity I(q) (s) as calculated for a vesicle system with the following parameters (with eqs 3-5): volume fraction Φ, 0.35; inner radius, 175 Å; outer radius, 200 Å; hard sphere diameter, 430 Å; polydispersity, 10%.

f (r). In the following we employ for f(r) a Schulz distribution as given by25

f(r) )

( ) t+1 Rm

(

)

rt t+1 r exp Rm Γ(t + 1)

t+1

(4)

with t + 1 ) 1/p2, which is directly related to the polydispersity index p of the vesicles. For a system made up from vesicles, the particle form factor P(q) is just that of a spherical shell (with inner radius Ri and outer radius Ra), as given by26

P(q) ) 16π2(FA - FS)2{Ra3f0(qRa) - Ri3f0(qRi)}2

(5)

with f0(x) ) (sin x - x cos x)/x3, q ) (4π/λ) sin(θ/2), and A ) (FA - FC)/(FA - FS), (FC and FS are the scattering length densities of vesicle shell and solvent). The structure factor S(q) may be described by that of a hard sphere system. Of course, our vesicle system is charged and will interact via Coulombic repulsion forces. However, since we are mainly concerned with densely packed vesicles, the main effect of the repulsive interaction will arise from the steric repulsion. S(q) for a hard sphere system is given in an analytical form in the Percus-Yevick approximation.27 For a system of densely packed vesicles the combination of eqs 2 and 3 will lead to an interesting scattering pattern. For shell-like particles of mean radius Rm, P(q) will have a minimum at π/Rm. At the same time S(q) will exhibit a correlation peak at 2π/d, where d is the mean intervesicle spacing. However, for a densely packed system the spacing d will only be slightly larger than 2Rm, which means that exactly at the point where S(q) has its maximum, P(q) will have its minimum. This will lead to the interesting effect that the scattered intensity I(q), as calculated according to eq 3, will not exhibit the typical correlation peak, but the minimum of P(q) will split this peak into two halves. This effect is demonstrated in Figure 1 where we have calculated P(q), S(q), and I(q) for parameters that are similar to the ones encountered in our system. This shows that for a system of densely packed vesicles one has to expect a fairly uncommon scattering behavior. III. Results and Discussion III.1. Phase Behavior. The phase behavior of the ternary system at 25 °C was investigated in a fairly large range of sodium oleate and octanol concentration. The obtained phase

1418 J. Phys. Chem. B, Vol. 103, No. 9, 1999

Gradzielski et al.

Figure 4. Zero-shear viscosity η0 as a function of the octanol concentration for systems of 200 mM Na oleate (at 25 °C). Figure 2. Phase diagram of the system Na oleate/1-octanol/water at 25 °C. Key: L1, micellar phase; LRι, vesicle phase; LRι-h, two-phase region of vesicles and lamellae; LRh, lamellar phase.

Figure 3. Texture of a sample in the LRh phase (composition: 258 mM Na oleate/900 mM 1-octanol).

diagram is given in Figure 2 as a function of the oleate and the octanol concentration. It shows that, at sufficiently high surfactant concentration, with increasing amount of octanol present one goes from an isotropic L1 phase via a two-phase region (which separates relatively fast into a main part consisting of a somewhat turbid, isotropic bottom phase and a highly turbid phase that swims atop) into a region that is denoted here as LRι. This phase is isotropic (deformations lead to birefringence under strain) and highly viscous. Upon an increase of the octanol content the viscosity rises and for sufficiently high octanol content a stiff gel phase is formed, which possesses a yield stress, i.e., no longer flows under its own weight. It should be stressed here that this stiff gel is still an isotropic phase and it exhibits the “ringing phenomenon” as has been typically observed for cubic phases.28-32 This stiff gel region (as all of the LRι phases) is made up from vesicles, as will be shown later on. A further increase then leads to a birefringent two-phase region (LRι-h) which does not separate macroscopically, due to the high viscosity of the gel phase, but microscopically. Finally, at still higher octanol concentration the phase becomes highly viscous but fluid again and monophasic. This LRh phase is strongly birefringent and shows the texture of a typical, conventional lamellar phase, as shown in Figure 3. The following investigations have mainly been done along two lines, which are also indicated in Figure 2. On one line the Na oleate concentration was kept constant at 200 mM, and on

the other line the molar ratio of octanol to Na oleate was kept constant at 3.1:1. III.2. Structural Transitions Induced by Increasing Alcohol Content. III.2.1. Transition from the L1 to the Lrι Phase. In the following we study the structural transitions that take place along a line of constant Na oleate concentration of 200 mM as a function of increasing octanol concentration (see the line in Figure 2). The viscosity of the L1 phase increases with increasing octanol concentration, as shown in Figure 4. The increase is particularly pronounced upon approaching the two-phase boundary. This can be explained by the fact that at low octanol concentration spherical micelles are present, which at higher octanol concentration grow anisometrically to form rodlike micelles, and their viscosity is significantly higher.14,33-36 A straightforward way to detect structural changes is given by SANS experiments. For that purpose measurements were performed on samples that contained 38, 68, and 115 mM octanol. The obtained scattering curves are given in Figure 5a. They show a correlation peak around 0.045 1/Å, for the two samples of lower octanol content (corresponding to a mean spacing of 140 Å between the aggregates) and a much different curve for 115 mM octanol (this sample is already located in the LRι phase). Here a first peak around 0.015 1/Å is followed by a second peak (similar to the scattering curves discussed later for the LRι phase at higher octanol content) and a different shape of the curve at higher q. The scattering curves were fitted with the form factors of rods and lamellae (eqs 1 and 2). The fitted curves are included in Figure 5b (which is another presentation of the data of Figure 5a, which shows much more sensitively the quality of the fitted curves) and the obtained fit parameters are given in Table 1. From looking at the data it is clear that the model of rods fits much better at lower octanol content, whereas for the sample in the LRι phase (115 mM octanol) the fit of lamellae is clearly superior. This means that within the L1 phase rodlike micelles are present, whereas beyond the phase boundary to the twophase region locally flat structures are formed. In Figure 6 the result of a conductivity measurement of a 200 mM Na oleate solution is given as a function of the octanol content. A relatively high conductivity is observed for the L1 phase, which drops drastically as soon as the two-phase boundary is reached (it should be noted here that all measurements were done on the mixed systems, i.e., before macroscopic phase separation took place). Such a marked drop of conductivity can often be explained by the fact that here vesicular structures are formed, which entrap a large amount of the

Gel Phase of Unilamellar Vesicles

J. Phys. Chem. B, Vol. 103, No. 9, 1999 1419

Figure 6. Electric conductivity κ for solutions of constant Na oleate concentration of 200 mM as a function of the octanol content at 25 °C.

Figure 5. SANS intensity curves for samples of 200 mM Na oleate with 38 (0), 68 (O), and 115 (×) mM of added 1-octanol: (a) I(q) vs q; (b) I(q) q2 vs q. Fitted curves for lamellae (s) and for rods (-‚-). Absolute scaling is valid for the sample with 38 mM octanol, and subsequent curves are each shifted upward by a value of 2 × 106 Å-3 for better lucidity.

TABLE 1: Fitted Parameters for Samples of 200 mM Na Oleate and Various Amounts of Added 1-Octanola c (octanol), mM

38

68

115

R, Å L, Å dev, % d, Å dev, %

19.2 85 ( 50 9.3 27.2 12.0

19.0 85 ( 50 9.0 26.8 10.7

18.3 110 ( 60 20.1 24.4 4.0

a Given are the radius R and length L of the rod model (eq 1) and the thickness d of the lamellae model (eq 2). In addition, the mean deviation of the fitted curve per data point (dev, %) is given for the individual models. The curves were fitted in the q range 0.07-0.35 1/Å for the samples with 38 and 68 mM octanol and in the range 0.040.35 1/Å for the sample with 115 mM octanol.

counterions.14,37 The value remains constant as the LRι phase is reached, which indicates that here the structures present remain the same. Within the LRι phase a slight increase in conductivity with increasing octanol content is observed. This may be explained by the fact that the octanol in the amphiphilic bilayer interacts with the ionic carboxyl group and will form H bonding. This gives rise to a decrease of the surface charge density and thereby leads to an increased degree of dissociation of the counterions. III.2.2. Transition from the Viscous Lrι Phase to the Stiff Gel Lrι Phase. The macroscopic properties of the LRι phase can be characterized by rheological measurements. For this purpose oscillatory shear experiments were performed. The shear modulus G0 and the yield stress σ0 are given in Figure 7 as a function of the octanol content of the samples, while the zeroshear viscosity η0 is given in Figure 4. It is found that η0

Figure 7. Shear modulus G0 (1) and yield stress σ0 (Ο) measured at 25 °C for samples containing 200 mM Na oleate as a function of the octanol content.

increases sharply for an octanol content of more than 400 mM. Samples with higher octanol content possess a yield stress and shear moduli G0 in the range of 1000 Pa and higher, whereas samples at lower octanol content possess no detectable elastic properties and no yield stress. This means that there exists a relatively well-defined transition point below which the viscous LRι phase is present and beyond which the “stiffness” of the system increases sharply; i.e., here an elastic gel phase is present. Beyond this transition to the gel phase, i.e., in the range of the stiff gel phase (see also Figure 2), the samples are solidlike, transparent, and isotropic and do not flow under their own weight. In addition, they possess elastic properties and exhibit the “ringing phenomenon”, as is frequently encountered for cubic phases.28-32 These interesting rheological properties can be characterized by an oscillatory shear experiment, and the rheogram for a sample of 200 mM Na oleate/630 mM octanol is given in Figure 8. It can be seen that the storage modulus G′ remains more or less constant over the whole frequency range investigated and has a value of about 8000 Pa, which is much higher (by a factor of 100-1000) than typically observed for vesicle systems.38-40 The loss modulus G′′ (viscous component) decreases somewhat with increasing frequency and is about 10-100 times smaller than G′; i.e., the difference between G′ and G′′ is larger than encountered for other systems of densely packed vesicles.38-40 This means that in this system the elastic properties dominate and it shows the behavior of a Bingham fluid. In Figure 9 the applied shear stress σ is given as a function of the observed shear gradient γ˘ . From this experiment one finds for this sample a yield stress of about 200 Pa.

1420 J. Phys. Chem. B, Vol. 103, No. 9, 1999

Gradzielski et al.

Figure 8. Rheogram of an oscillatory shear experiment for a sample of composition 200 mM Na oleate/630 mM octanol at 25 °C. Given are the storage modulus G′ (b), the-loss modulus G′′ (2), and the magnitude of the complex viscosity η* (9).

Figure 9. Applied shear stress σ as a function of the observed shear gradient γ˘ for a sample of composition 200 mM Na oleate/630 mM octanol at 25 °C.

After having characterized the macroscopic properties of the system, it is now interesting to investigate in some more detail the structures that are present at the various locations of the phase diagram. A very nicely suited method for this is freezefracture electron microscopy. In Figure 10a,b we see two electron micrographs from samples in the region of the stiff gel phase. One observes fairly monodisperse, small, unilamellar vesicles. Some larger vesicles are still present, but their quantity is relatively small. The diameter of the small unilamellar vesicles is about 300-350 Å. Basically, no cross-fracture is observed but the samples are always fractured around the shell. The small vesicles are densely packed and highly correlated. This dense packing is well visible, as indicated by the hexagons in Figure 10a. The vesicles are packed in a cubic array, as is known from the structure of metals; i.e., here one has a cubic phase of vesicles present. In addition, we used SANS experiments within the LRι phase to investigate the structural changes that take place upon increasing the octanol content. The scattering curves for octanol contents of 5, 6, and 7 wt % octanol (corresponds to 379, 454, and 530 mM) are given in Figure 11. All scattering curves show a very broad, but not very well-defined, peak between 0.015 and 0.04 1/Å. This peak then is followed by a second peak around 0.08 1/Å that is the more pronounced the higher the octanol content. In general, the scattering pattern looks like that described in section II.2 for densely packed vesicle systems. What is evident from looking at the SANS curves is that the position of the peak does not change, which means that the structural size of the system does not change; i.e., the vesicles remain constant in size. However, the features of the scattering

Figure 10. Freeze-fracture electron micrograph of samples of composition 200 mMNa oleate/505 mM (6 wt %) 1-octanol, the bar represents 100 nm (a); 200 mM Na oleate/630 mM (7.5 wt %) 1-octanol, the bar represents 100 nm (b); 200 mM Na oleate/756 mM (9 wt %) octanol (c). (All samples in 20 wt % glycerol.)

Figure 11. SANS scattering curves for samples containing 200 mM Na oleate and various amounts of added 1-octanol: (0) 375 mM; (9) 450 mM; (4) 525 mM. (Absolute units are valid for the 375 mM sample; subsequent curves are each multiplied by a factor 3 for better lucidity.)

curves (e.g., the second peak) become more pronounced with increasing octanol content, which is an indication of a lower degree of polydispersity and a higher degree of ordering in the system.

Gel Phase of Unilamellar Vesicles

Figure 12. SANS scattering curves for samples containing 300 mM Na oleate and various amounts of added 1-octanol: (0) 525 mM; (b) 630 mM; (+) 970 mM; (×) 1010 mM. (Absolute units are valid for the 1010 mM sample; subsequent curves are each multiplied by a factor 3 for better lucidity.)

Finally, from the high q range the thickness d of the bilayers can be determined (eq 2) and shows that d decreases from 22.4 Å (375 mM octanol) to 21.8 Å (525 mM octanol) with increasing octanol content. This is to be expected since increasing the presence of the shorter chain octanol (instead of the C18 surfactant) should render the bilayer thinner. II.2.3. Transition from the Lrι Phase to the Lrι Phase. Finally, we also investigated the transition from the LRι phase to the LRι phase that takes place at higher surfactant concentrations and higher cosurfactant concentrations. In Figure 10c an electron micrograph for a sample containing 756 mM of octanol is shown. This sample is now already beyond and the monophasic gel phase and in the two-phase region LRι/LRh. Upon an increase of octanol content the vesicles become not only bigger but also much more polydisperse, with diameters ranging from 30 to 200 nm. In addition, some lamellar fragments are visible, which shows the biphasic nature of this sample but which, due to its high yield stress, does not phase separate macroscopically. This shows that, due to the increasing concentration of octanol, some of the vesicles are transformed into planar bilayers. In order to investigate this transition in some more detail, some samples were measured by SANS that contained 300 mM Na oleate and 525, 630, 970, and 1010 mM 1-octanol in D2O, where the first two are located in the LRι phase and the last two in the LRh phase (see Figure 2). The scattering curves are given in Figure 12 and a striking difference between the samples in the different phases observed. For the samples in the LRι phase the typical scattering pattern as described in III.2.2 is found, whereas for the samples in the LRh phase a much more pronounced scattering peak can be seen. This peak is followed by a second peak at twice the q value of the first peak and even from a third peak at a q value of 3 times the first maximum. This scattering pattern is typical for classical lamellar phases and demonstrates that a significant structural change has taken place upon going from the isotropic region LRι to the birefringent phase LRh. Furthermore, the pronouncedness of the peaks demonstrates that the LRh phase has to possess a high degree of order. From the location of the peak one can calculate the mean lamellar spacing d, which is 105.5 Å for the 970 mM octanol sample and 105.2 Å for the 1010 mM octanol sample. From this and the volume fraction of the amphiphilic film (as calculated from the composition) the bilayer thickness can be determined to be 21.8 and 22.1 Å, which is very similar to the thickness of the bilayer in the vesicles of the LRι phase. This

J. Phys. Chem. B, Vol. 103, No. 9, 1999 1421

Figure 13. Shear modulus G0 (O) and zero-shear viscosity η0 (9) (at 25 °C) for samples of constant molar ratio of octanol/Na oleate ) 3.1:1 as a function of the surfactant concentration.

means that the same type of bilayer is still present but the topology of the bilayer has changed from strongly curved vesicles to flat lamellae by the presence of increased amounts of octanol. III.3. Structural Changes along a Line of Constant Na Oleate/Octanol Ratio. The next series of investigations was along a line of constant molar ratio of octanol/sodium oleate of 3.1:1, i.e., along a line of dilution from the isotropic gel phase. As seen from Figure 2, one goes along this line from the stiff, isotropic gel phase to the viscous phase and upon further dilution finally into the two-phase region. In that context it was of much interest to us how the structural entities and the macroscopic properties change along this line. Of course, the macroscopic properties are again most directly characterized by a rheological experiment. In Figure 13 we have the shear modulus and the zero-shear viscosity for such samples as a function of the surfactant concentration. It is easily observed that beyond 130 mM a dramatic increase of viscosity and the appearance of elastic properties occurs; i.e., only beyond this point does G0 become measurable. Here again (as observed before for the line of constant Na oleate content, cf. Figure 7) a relatively well-defined transition from a viscous vesicle system to a gel state takes place. This means that this stiff gel phase seems to be a fairly well-defined state. For its formation a molar ratio of octanol/Na oleate higher than 2.2:1 and a minimum Na oleate concentration of 130 mM is necessary. Of course, complimentary structural information on these systems can be obtained from SANS experiments for which the corresponding samples had to be prepared in D2O instead of H2O. For samples in the stiff gel phase the scattering curves along the “dilution path” are given in Figure 14. As in Figure 11 in all cases a pronounced double peak is observed, as is expected for a system of shell-like particles where the mean repeat distance and the particle diameter are about the same. The minimum between the two peaks is due to the minimum of the form factor and indicates that the polydispersity of the vesicles has to be fairly low. One finds that with increasing dilution the peaks and the minimum move toward smaller q values, which corresponds to an increase of the vesicle size with increasing dilution. If we now look at samples beyond the gel phase f viscous phase transition, we find that still the same principal scattering pattern is observed (Figure 15); i.e., still fairly densely packed vesicles have to be present. However, one difference now is that with increasing dilution the first peak becomes more pronounced relative to the second peak, while the minimum remains at the same q value. This means that the particle

1422 J. Phys. Chem. B, Vol. 103, No. 9, 1999

Gradzielski et al.

Figure 14. SANS curves for samples of constant molar ratio of octanol/ Na oleate of 3.1:1 as a function of the scattering vector q. All samples were located in the gel phase and the volume fractions (of surfactant plus cosurfactant) are indicated in the plot. The absolute units are valid for the most concentrated sample; subsequent curves are each multiplied by a factor 3 for better lucidity.

Figure 15. SANS intensity curves for samples of constant molar ratio of octanol/Na oleate of 3.1:1 as a function of the scattering vector q. The most concentrated sample was located in the gel phase, and the others were in the viscous phase. The volume fractions (of surfactant plus cosurfactant) are indicated in the plot. The absolute units are valid for the most concentrated sample; subsequent curves are each multiplied by a factor 3 for better lucidity.

TABLE 2: Obtained Parameters from the SANS Curves at Constant Molar Ratio of Octanol/Na Oleate of 3.1:1a Φs

Rm, Å

d, Å

Φv

0.130 0.119 0.108 0.0979 0.0883 0.0756 0.0680 0.0659 0.0585 0.0528

145.6 151.6 169.6 193.1 205.6 207.9 219.7 223.1 226.0 227.8

21.8 21.6 21.8 21.6 21.8 21.6 21.7 21.8 21.6 22.0

0.404 0.384 0.378 0.385 0.364 0.317 0.298 0.291 0.259 0.236

a Given are the volume fractions of Na oleate plus octanol, Φ , vesicle s radius, R, bilayer thickness, d, and the calculated volume fraction of the vesicles, Φv. Samples with Φs larger than 0.081 are in the gel phase, and the others, in the viscous phase.

diameter remains constant while the mean distance becomes larger; i.e., the packing fraction of the system is reduced. The bilayer thickness d of the vesicles can be obtained by fitting eq 1 to the high q part of the scattering data. By doing so one obtains values for d of 21.6-22.0 Å (see Table 2); i.e., the thickness of the bilayer is not affected at all by the dilution process. If we now plot in Figure 16 the mean radius (as obtained from the intensity minimum and also given in Table 2) as a

Figure 16. Vesicle radius Rm as a function of the volume fraction of Na oleate plus 1-octanol.

function of the volume fraction of surfactant plus alcohol, we find a very different behavior for the region of the stiff gel phase and for the viscous phase. In the stiff gel phase a slope of -0.96 is found, which is very close to the value of -1, as is expected for vesicles that keep a constant packing fraction Φv (i.e., a constant volume fraction that is entrapped in the vesicles). Therefore, they have to grow in size with decreasing volume fraction Φs of the amphiphile. This fact is described by eq 6a for the case of an infinitely thin shell (where Vs and as are the volume of the surfactant and its head group area, respectively) and by eq 6b for a finite shell thickness d.

R ) (6Vs/as)(Φv/Φs)

(6a)

R ) 3d(Φv/Φs){0.5 + x0.25 - (Φs/3Φv)}

(6b)

This scaling of inverse proportionality between the concentration of amphiphile and vesicle radius is also consistent with the rheological data. In the double-logarithmic plot of Figure 13, one finds that in the gel phase G0 is proportional to c2.7. However, this is close to what one expects for a system of densely packed vesicles if one assumes that each vesicle acts as a network point in the gel (and stores an elastic energy of kT per vesiclessimilar to a network of connected springs). For such a system the shear modulus G0 should be given by41,42

G0 ∼ 1NkT

(7)

where 1N is the number density of the vesicles. Now, if the vesicle radius R is inversely proportional to the surfactant concentration Φs then 1N is proportional to Φs3 and the observed scaling for G0 is explained. Moreover, the absolute values are in good agreement with other rheological experiments where densely packed phospholipid unilamellar vesicles of 250 nm radius have been studied and here also a scaling as given by eq 7, i.e., a proportionality of G0 to R3, has been suggested.38 The shear moduli reported there where about 10 Pa. If we consider that our radius is about 15-25 nm, eq 7 explains nicely why our shear moduli have to be about a factor 1000 higher. However, it might be noted here that for our systems the proportionality factor in eq 7 would be around 30-50; i.e., an elastic energy of about 30-50 kT is stored per vesicle. This proportionality factor is presumably related to the packing fraction of the vesicles.38 So far, a solid theoretical explanation for the applicability of eq 7 (and especially for the proportionality factor) to vesicle systems is still lacking, but it is an empirical relationship that has been observed for a number of vesicle systems.38,39,42

Gel Phase of Unilamellar Vesicles

J. Phys. Chem. B, Vol. 103, No. 9, 1999 1423

Figure 17. Shear modulus G0 (9) and yield stress σ0 (O) at 25 °C for samples containing 200 mM Na oleate and 9.68 vol % alcohol as a function of the number of C atoms of the alkly chain of the 1-alcohol.

Finally, one can estimate the volume fraction Φv of the vesicles from simple geometry, since we know both their radius R and their thickness d, as well as the volume fraction of the amphiphiles, Φs. Assuming monodispersity (this should still be a good approximation for not too high polydispersity), one obtains Φv from

Φv ) Φs

(Rm + d/2)3 3Rm2d + d3/4

(8)

The obtained values are given in Table 2 and we find a roughly constant vesicle volume fraction of 0.36-0.4 in the gel phase that is rapidly reduced upon crossing into the viscous phase. Once the transition to the viscous phase is crossed, one observes that the vesicles do not grow any further but remain of constant diameter of 450 Å upon further dilution. This means that by diluting the system the vesicles grow until a maximum size is reached. Beyond this point the vesicles can not grow any more and further addition of water leads to a decrease of the packing fraction and therefore to a rapid decrease of the elastic properties of the gel (i.e., the system is “melting”). This clearly demonstrates that there exists an energetic preference to form small unilamellar vesicles. This is in nice agreement with recent theoretical work that predicts the formation of small monodisperse vesicles for surfactant mixtures of surfactants with large differences in chain length (as in our case), whereas large vesicles of high polydispersity would be stable for surfactants of similar chain length.43 III.4. Substitution of the Alcohol. Another very interesting point about the formation of this gel phase can be addressed by a further variation of the system. Up to now we always employed octanol as the cosurfactant but in principle one may expect that other medium chain alcohols will work similarly. In order to study that effect we substituted octanol by other alcohols, such as pentanol, hexanol, heptanol, nonanol, and decanol, in such a way as to keep the composition of the samples constant at 200 mM Na oleate and 9.68 vol % alcohol (which corresponds in the case of octanol to 7.5 wt %). In Figure 17 the shear modulus G0 and yield stress σ0 are given for the alcohols ranging from pentanol to decanol. It is very interesting to note that the highly elastic gel phase is similarly formed only for hexanol, heptanol, and octanol. For pentanol an isotropic viscous phase is observed and for the longer chain alcohols turbid, viscous systems are observed that exhibit streaming birefringence. Electron microscopy of such samples has shown the coexistence of small and very large vesicles.

Figure 18. Freeze-fracture electron micrograph of a sample of composition 200 mM Na oleate/7.5 wt % 1-nonanol (in an 20 wt % aqueous solution of glycerol).

This is shown in Figure 18 for 1-nonanol as cosurfactant (that with respect to its composition corresponds to the sample in Figure 10). Here still the small unilamellar vesicles typical for the gel phase are visible but mixed now with a large number of much bigger and multilamellar vesicles. This means that there exists an optimum range of the cosurfactant chain length that allows the formation of the gel phase. For alkyl chains of other lengths no such gel phase is formed, as has been confirmed by investigation of the phase behavior with these alcohols. All this means that if this ratio of cosurfactant chain length to surfactant chain length is not fulfilled, no such stiff gel can be formed. Finally, SANS measurements of the identically composed stiff gel phase were performed with octanol, heptanol, and hexanol as cosurfactant. They showed a very similar scattering pattern, which indicates that the structures present are identical. The thickness of the vesicle shell was determined from the high q range (eq 2) and decreases with decreasing chain length of the alcohol from 21.8 Å for octanol to 20.6 Å for heptanol, and then to 19.4 Å for hexanol. This shows that the thickness of the bilayer is largely determined by the cosurfactant, a fact which is not too surprising since the bilayer is to a large degree made up from that alcohol. IV. Conclusions We have studied the phase behavior of the ternary system sodium oleate/1-octanol/water. In this system one finds a highly elastic, isotropic, stiff gel phase at relatively moderate surfactant concentration and for a certain range of ratio of cosurfactant to surfactant. This gel phase possesses a very high shear modulus and a yield stress as they typcially are not observed in such systems. The addition of the octanol to the micellar L1 phase first leads to the formation of rodlike micelles that for higher octanol content are transformed into bilayer structures. Here first an isotropic viscous phase is formed and upon further increase of the octanol content a fairly sharp transition to the stiff gel phase is observed. Finally, at still higher octanol content a classical lamellar phase with a high degree of positional ordering is formed. Conductivity measurements and, in particular, electron microscopy demonstrate that small unilamellar vesicles of about 250-400 Å diameter are present in this gel phase. They are densely packed and form a cubic phase of vesicles, which explains their isotropic properties and their very high rheological moduli. These findings are confirmed by SANS measurements

1424 J. Phys. Chem. B, Vol. 103, No. 9, 1999 that show that for constant surfactant concentration the monodispersity of the system increases with increasing octanol content. In addition, SANS showed that dilution of the gel phase with water leads to an increase in vesicle size that occurs in such a way as to keep the packing fraction of the system constant. Beyond a certain size this particle growth is not any longer possible and the densely packed vesicles of the stiff gel phase become diluted, which leads to a phase that is viscous but not any longer gel-like. This means that we have studied a new type of gel phase made up from monodisperse unilamellar vesicles. For the formation of the monodisperse vesicles, and therefore also for the formation of the stiff gel phase, two necessary requirements have to be met. First a certain ratio of the amount of cosurfactant to surfactant is necessary. Secondly, also the ratio of the chain length of cosurfactant to surfactant has to be in a certain range; i.e., for alcohols that have longer alkyl chains than C8 or shorter chains than C6, no such small unilamellar vesicles are formed with our C18 surfactant. Finally, of course, also a certain concentration of the vesicles, i.e., of the total surfactant, must be present in order to form the stiff gel phase of densely packed vesicles. Acknowledgment. All the SANS measurements were performed at the Hahn-Meitner Institute (HMI), Berlin, Germany. In that context we also want to thank D. Gra¨bner and St. Haas for help with the SANS measurements. References and Notes (1) Laughlin, R.G. The Aqueous Phase BehaVior of Surfactants, Academic Press, London, 1994. (2) Chevalier, Y.; Zemb, T. Rep. Prog. Phys. 1990, 53, 279. (3) Friberg, S.; Larsson, K. In AdVances in Liquid Crystals; Brown, G. H., Ed., Academic Press: New York, 1976; Vol. 2, p 176. (4) Lipowsky, R., E. Sackmann, E., Eds. Handbook of Biological Physics; Elsevier: Amsterdam, 1995. (5) Rosoff, M., Ed. Vesicles; Surfactant Science Series 62; Marcel Dekker Inc.: New York, 1996. (6) Oberdisse, J.; Couve, C.; Appell, J.; Berret, J. F.; Ligoure, C.; Porte, G. Langmuir 1996, 12, 1212. (7) Oberdisse, J.; Porte, G. Phys. ReV. E 1997, 56, 1965. (8) Gradzielski, M.; Bergmeier, M.; Mu¨ller, M.; Hoffmann, H. J. Phys. Chem. B 1997, 101, 1719.

Gradzielski et al. (9) Ekwall, P.; Mandell, L.; Fontell, K. Mol. Cryst. Liq. Cryst. 1969, 8, 157. (10) Ekwall, P. In AdVances in Liquid Crystals; Brown, G. H., Ed.; Academic Press: New York, 1975. (11) Miller, C. A.; Gradzielski, M.; Hoffmann, H.; Kra¨mer, U.; Thunig, C. Prog. Colloid Polym. Sci. 1991, 84, 243. (12) Auguste, F.; Bellocq, A. M.; Roux, D.; Nallet, F.; Gulik-Krziwicki, T. Prog. Colloid Polym. Sci. 1995, 98, 276. (13) Hoffmann, H.; Thunig, C.; Valiente, M. Colloids Surf. 1992, 67, 223. (14) Valiente, M.; Thunig, C.; Munkert, U.; Lenz, U.; Hoffmann, H. J. Colloid Interface Sci. 1993, 160, 39. (15) Hoffmann, H.; Munkert, U.; Thunig, C.; Valiente, M. J. Colloid Interface Sci. 1994, 163, 217. (16) Schoma¨cker, R.; Strey, R. J. Phys. Chem. 1994, 98, 3908. (17) Winterhalter, M.; Helfrich, W. J. Phys. Chem. 1992, 96, 327. (18) Lekkerkerker, H. N. W. Physica A 1989, 159, 319. (19) Helfrich, W. J. Phys.: Condens. Mater. 1994, 6, A 79. (20) Flockhart, B.D.; Graham, H. J. Colloid Sci. 1953, 8, 105. (21) Keiderling, U.; Wiedenmann, A. Physica B 1995, 213 & 214, 895. (22) Chen, S. H.; Lin, T. L. Methods Exp. Phys. 1987, 23B, 489. (23) Keiderling, U. Physica B 1997, 234-236, 1111. (24) Porod, G. In Small Angle X-ray Scattering; Glatter, O., Kratky, O., Eds.; Academic Press: London, 1982. (25) Schulz, G. V. Z. Phys. Chem. B 1939, 43, 25. (26) Guinier, A.; Fournet, G. Small-angle Scattering of X-rays; Wiley: New York, 1955. (27) Ashcroft, N. W.; Lekner, J. Phys. ReV. 1966, 145, 83. (28) Lower, E. S.; Harding, W. H. Manuf. Chem. 1966, 37, 52. (29) Rosevear, F. B. J. Soc. Cosmetic Chemists 1968, 19, 581. (30) Nu¨rnberg, E.; Pohler, W. Prog. Colloid Polym. Sci. 1984, 69, 48. (31) Gradzielski, M.; Oetter, G.; Hoffmann, H. Colloid Polym. Sci. 1990, 268, 167. (32) Fontell, K. Colloid Polym. Sci. 1990, 268, 264. (33) Førland, G. M.; Samseth, J.; Høiland, H.; Mortensen, K. J. Colloid Interface Sci. 1994, 164, 163. (34) Hoffmann, H.; Hofmann, S.; Illner, J. C. Prog. Colloid Polym. Sci. 1994, 97, 103. (35) Staples, E. J.; Tiddy, G. T. J. Chem. Soc., Faraday Trans. 1 1978, 74, 2530. (36) Porte, G.; Marignan, J.; Bassereau, P.; May, R. J. Phys. 1988, 49, 511. (37) Herve´, P.; Roux, D.; Bellocq, A. M.; Nallet, F.; Gulik-Krzywicki, T. J. Phys. II 1993, 3, 1255. (38) de Haas, K. H.; Blom, C.; van den Ende, D.; Duits, M. H. G.; Haveman, B.; Mellema, J. Langmuir 1997, 13, 6658. (39) Hoffmann, H.; Thunig, C.; Schmiedel, P.; Munkert, U. Langmuir 1994, 10, 3972. (40) Panizza, P.; Roux, D.; Vuillaume, V.; Lu, C. Y. D.; Cates, M. E. Langmuir 1996, 12, 248. (41) Flory, P. J. J. Chem. Phys. 1950, 18, 108. (42) Hoffmann, H. Ber. Bunsen-Ges. Phys. Chem. 1994, 98, 1433. (43) Yuet, P. K.; Blankschtein, D. Langmuir 1996, 12, 3819.