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Surfactant Diffusion through Bicontinuous Micellar Networks: A Case Study of the C9G1/C10G1/H2O Mixed Surfactant System Christy Whiddon, Johan Reimer,* and Olle So¨derman Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden Received August 27, 2003. In Final Form: December 10, 2003 Self-diffusion coefficients were obtained by means of NMR diffusometry for differing ratios of n-decylβ-D-glucopyranoside (C10G1) and n-nonyl-β-D-glucopyranoside (C9G1) surfactant mixtures, along dilution lines through the micellar region of the ternary C9G1/C10G1/H2O phase diagram. Networks of bicontinuous micelles have been suggested to exist throughout the micellar regions of the phase diagram. A phase separation into two coexisting liquid solutions is observed in the dilute, C10G1-rich regions of the phase diagram. The fact that the dilution curves follow scaling relations pertaining to surfactant diffusion in a network for mixtures rich in C10G1 indicates that the phase separation is due to differences in the networks in different micellar regions of the phase diagram; networks remain largely intact despite dilution down to the phase separation in the C10G1-rich region, whereas networks with scissions are predicted to exist in the C9G1-rich regions of the micellar phase.
I. Introduction A continuing problem in determining the phase behavior of simple binary alkylglucoside/water systems has been the determination of the aggregate structure in the micellar region.1,2 There is a two-phase region in the phase diagram of n-decyl-β-D-glucopyranoside (C10G1), which spans from slightly above the critical micelle concentration (cmc) up to 15 wt % (in H2O), within experimentally accessible temperature limits.3 There is no observable phase separation within similar concentration and temperature regions for n-nonyl-β-D-glucopyranoside (C9G1); however, when one begins to combine the two surfactants, a phase separation in the lower-concentration micellar region is induced by lowering the fraction of C9G1 in the surfactant mixture below δ ) 0.24 (for a definition of δ, see eq 1).2 Different methods of investigation (cryotransmission electron microscopy and time-resolved fluorescence quenching), in addition to NMR diffusometry, have all indicated the presence of a network of interconnected rodlike micelles in the lower-concentration micellar regions surrounding the miscibility gap for the mixed C9G1/ C10G1 surfactant system (δ ) 0.22).1-3 However, the reason for the phase separation is still not entirely understood because bicontinuous networks are expected to exist in the C9G1/H2O system as well.3,4 To further elucidate the mechanism of the phase separation in the C10G1/H2O system, NMR diffusion measurements have been made at regularly spaced intervals along the dilution lines of four ratios of C9G1 within the ternary phase diagram (δ ) 0.75, 0.50, 0.25, and 0.125). (See Figure 1.) For comparison, diffusion coefficients for diffusion within the cubic bicontinuous phase were also obtained for some ratios. The resulting surfactant mixture NMR echo decays have been checked * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Nilsson, F.; So¨derman, O.; Reimer, J. Langmuir 1998, 14, 6396. (2) Whiddon, C.; So¨derman, O.; Hansson, P. Langmuir 2002, 18, 4610. (3) Nilsson, F.; So¨derman, O.; Hansson, P.; Johansson, I. Langmuir 1998, 14, 4050. (4) Nilsson, F. Ph.D. Thesis, Lund University, Lund, Sweden, 1998.
Figure 1. Ternary phase diagram of the C9G1/C10G1/H2O system. Inset shows the two-phase region in the C10G1-rich region of the diagram. L1 and L1′ are micellar solutions, I is a cubic liquid crystalline phase, and LR is a lamellar phase. Values of δ examined are (4) 0.75, (O) 0.50, (0) 0.25, and (]) 0.125. The symbol b denotes a sample in the two-phase micellar/cubic region. Please note that the extensions of the cubic and lamellar phases are approximate.
for the presence of biexponentiality, and the diffusion rates as a function of concentration (from here on referred to as the dilution curves) are evaluated according to scaling models pertaining to micelles with connections, that is, branched micelles.5,6 II. Experimental Section The surfactants, C10G1 (>99%) and C9G1 (>99%), were purchased from Anatrace (Maumee, OH) and used as received. Solutions were made using deionized water that was further purified with a Milli-Q Plus filtration system with a pore size of 22 µm (Millipore Corp., Bedford, MA). (5) Schmitt, V.; Lequeux, F. Langmuir 1998, 14, 283. (6) Anderson, D.; Wennerstro¨m, H.; Olsson, U. J. Phys. Chem. 1989, 93, 4243.
10.1021/la035588c CCC: $27.50 © 2004 American Chemical Society Published on Web 02/11/2004
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The surfactant mixtures were made by varying the ratio, δ, of C9G1 in the mixture according to
δ)
mC9G1
(1)
mC9G1 + mC10G1
Thus, an increase in δ correlates to an increase in C9G1 in the surfactant mixture. When wt % is used, this is defined as (mC9G1 + mC10G1)/(mC9G1 + mC10G1 + mH2O) × 100. The surfactants and water were weighed directly into 5-mm NMR tubes, which were then flame-sealed and centrifuged. All samples were allowed to equilibrate at room temperature for a minimum of 4 weeks. Self-diffusion coefficients were measured using pulsed field gradient spin-echo proton NMR, on a Bruker DMX-200 spectrometer fitted with a field gradient probe unit. All experiments were conducted at controlled probe temperatures (25 °C) in 5-mm NMR tubes. Stejskal-Tanner7 spin-echo was used, following procedures recommended in refs 8 and 9. The self-diffusion coefficient, D, was obtained by fitting eq 2 to the experimental data:
{
(
I ) I0 exp -γ2G2τ2 ∆ -
)}
τ D 3
(2)
where I is the observed echo intensity, I0 is the echo intensity in the absence of field gradient pulses, γ is the gyromagnetic ratio, G is the field gradient strength, τ is the duration of the gradient pulse, and ∆ is the time between the leading edges of the gradient pulses. In the experiments, τ was typically 2 ms and the value of G was varied between 0.1 and 8.8 T/m. At least two measurements were taken of each sample, with varying values of ∆ to check that the observed diffusion coefficient was not dependent on the time scale of the experiment, which would indicate non-Gaussian diffusion, or affected by convective flow within the instrument.10 Random samples were also measured after a longer time period had elapsed to make sure they had reached equilibrium before the first measurements were made. The error in the fit of eq 2 to the data is in general less than 1%. From repeated measurements, the reproducibility is in general within 5%. In the case of surfactant solutions, the observed diffusion coefficient (Dobs) is assumed to be a combination of the diffusion coefficients for both micellar-bound (Dmic) and free (Dfree) surfactant monomers, so that under fast exchange8,11,12
Dobs ) pDfree + (1 - p)Dmic
(3)
where p is the fraction of surfactant present as free monomers in solution (obtained from the cmc assuming ideal mixing of the two surfactants in the micelles). Although at higher concentrations the contribution of free monomers is negligible, all diffusion coefficients shown were adjusted from Dobs to Dmic to avoid any influence due to the free (nonmicellized) surfactants in solution. The Dmic value was calculated assuming Dfree(298 K) to be 3.4 × 10-10 m2 s-1, based upon the self-diffusion coefficient previously reported for aqueous C10G1 at concentrations below the cmc at 25 °C.4 The cmc used for the different mixtures was calculated assuming ideal mixing and is based on values reported previously [0.2 wt % (6.5 mM) and 0.07 wt % (2.2 mM) for C9G1 and C10G1, respectively].3 Before leaving this section, we point out that the term Dmic will be used to indicate the diffusion of surfactant in the micellized state, irrespective of whether the diffusion process is dominated by aggregate diffusion or by lateral diffusion along the contour of a micelle. (7) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (8) So¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445. (9) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1. (10) Hedin, N.; Yu, T. Y.; Furo, I. Langmuir 2000, 16, 7548. (11) Lindman, B.; So¨derman, O.; Wennerstro¨m, H. In Novel Techniques to Investigate Surfactant Solutions; Zana, R., Ed.; Dekker: New York, 1987; p 295. (12) Holmberg, K.; Jo¨nsson, B.; Kronberg, B.; Lindman, B. Surfactants and Polymers in Aqueous Solution, 2nd ed.; Wiley: Chichester, U.K., 2002.
Figure 2. Diffusion curves obtained at different volume fractions, φS, throughout the micellar region for the ratios (4) 0.75, (O) 0.50, (0) 0.25, and (]) 0.125. Closed symbols denote cubic samples. Equation 3 was used in obtaining the presented values of Dmic. The volume fraction of surfactant, φS, was calculated from the densities of glucose and hydrocarbon chains.13 The values of φS used thus correspond to the volume fraction of “dry” surfactant; no hydration water was included in φS.
III. Results A partial ternary phase diagram for the C9G1/C10G1/ water system at 25 °C is presented in Figure 1. Note the two-phase region in the water-rich region of the C10G1/ water edge. The phase separation in the aqueous C10G1 system occurs between approximately 0.1 and 15 wt %.1 The phase separation region diminishes as the fraction of G9G1 increases and disappears when δ ) 0.24.2 Measurements in the δ ) 0.125 sample were not disturbed by phase separation, however, because the lower consolute boundary of the two-phase region is above 30 °C at concentrations above 8 wt %.1 At 5 wt %, where the lower consolute boundary is near room temperature, a phase separation was observed, with the phase volume on top being very small. In the NMR experiments, the bottom phase was measured. On account of the phase separation, there is some uncertainty as to the concentration in the bottom phase. However, because we are close to the critical point, we may assume that the concentrations in the two phases are quite similar and, thus, the diffusion results should not be significantly affected by the presence of two phases. In any event, the value at 5 wt % is of minimal importance to the conclusions presented here. The micellar diffusion coefficients for the various samples are plotted versus φS in Figure 2. All values are for micellar diffusion, obtained by the application of eq 2 to the echo decays and subsequent correction by application of eq 3. Two representative diffusion decays (δ ) 0.5, 50 wt % and 70 wt %) are presented in Figure 3. Note that the 70 wt % sample was a two-phase sample in which a micellar phase was in equilibrium with a bicontinuous cubic phase (see Figure 1). No biexponential decay is evident (cf. Figure 3), and this holds for all the samples investigated. Clearly visible in Figure 2 is the difference in the dilution curve slopes for different ratios (see also Figure 4). There are two noticeable differences between the curves obtained for samples rich in C9G1 (δ g 0.50) versus those rich in C10G1 (δ e 0.25). First, the diffusion coefficients obtained in the dilute region of the δ ) 0.50 and 0.75 samples are much larger than in the δ ) 0.125 and 0.25 samples. However, the diffusion coefficients are similar for all of the samples past a volume fraction of φS ≈ 0.20. As a (13) Nilsson, F.; So¨derman, O.; Johansson, I. Langmuir 1996, 12, 902.
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Figure 3. Representative echo decays obtained from samples within the two-phase micellar/cubic region (b in Figure 1) with δ ) 0.50, 70 wt % (a) and the micellar phase with δ ) 0.50, 50 wt % (b). Residuals are plotted above the decays and reinforce the monoexponential nature of the decays. k is defined as γ2G2τ2(∆ - τ/3) (cf. eq 2).
Figure 4. Surfactant diffusion dilution curves. The line is for the sake of comparison with experimental data and shows the predicted surface diffusion of surfactant along a network of interconnected rods,23 Dmic ∝ φS0.25. (4 represents 0.75, ] represents 0.125, and closed symbols denote cubic samples.)
result, whereas there is only about a 30% difference in diffusion coefficients in the δ ) 0.125 sample for samples throughout the micellar region (investigated concentrations from 5 up to 75 wt %), in the δ ) 0.75 sample the decrease in the diffusion rate is 75%. The second clear difference is the behavior of the diffusion dilution curve past φS ) 0.2. For the C9G1-rich samples, the self-diffusion rates appear to level off and appear constant with increasing volume fraction. In contrast, for the C10G1-rich samples, there is a minimum in the diffusion rate close to φS ) 0.2, after which the diffusion rates begin to increase with increasing concentration. These effects are more clearly visible in the representation of Figure 4. IV. Discussion As was mentioned, single exponential decays were obtained for samples throughout the ternary phase diagram (cf. Figure 3). Biexponential decays might be expected in a bicontinuous network containing different molecular species due to the difference in size of the two surfactants; however, because lateral diffusion appears to be controlled by headgroup interactions in sugar surfactants,14 it is not surprising that no biexponential decays were observed. The kind of size-dependent differences detectable in a mixed-component bilayer system is uncertain. Some experimental results have shown large (14) Sottmann, T.; Kluge, K.; Strey, R.; Reimer, J.; So¨derman, O. Langmuir 2002, 18, 3058.
differences in diffusion coefficients for large differences in the hydrophobic chain length,15 whereas others have indicated that differences in the diffusion coefficients may depend only on the nature of the headgroups.16 In any mixed system, the diffusion coefficients of the components in the system usually become more similar than they would be if they were not mixed, which in fact significantly reduces the chance of observing biexponential decays. To observe biexponential decays, from echo decays with typical intensity signal-to-noise ratios, the two components must have lateral diffusion coefficients that differ by more than a factor of around 2; C9G1 and C10G1 are so similar that this is unlikely. In water, monomer diffusion coefficients of C9G1 and C10G1 differ by a factor of less than 10%, at 3.65 × 10-10 m2 s-1 and 3.39 × 10-10 m2 s-1, respectively.17 The fact that the 70 wt % sample is single-exponential requires a comment. As noted, this is a two-phase sample with a cubic phase and a micellar phase (cf. Figure 1). The fact that this sample shows single exponential decays (cf. Figure 3b) implies not only that there is no detectable difference in the diffusion coefficients of the two surfactants but also that the surfactant diffusion in the two phases are equal, within the experimental uncertainty. We note that the two-phase region between the micellar and the cubic phases is very narrow. The first result of note is the difference in the diffusion rates in the dilute region for C9G1-rich samples versus those for the C10G1-rich samples. Because all ratios have similar diffusion coefficients at concentrations from approximately φS ) 0.20 and these are similar in value to the diffusion coefficients within the cubic bicontinuous phase, it is rather safe to assume that bicontinuous micellar networks are present throughout the higherconcentration micellar regions of the phase diagram. When no obvious discontinuity in surfactant self-diffusion across a phase boundary is observed, this fact implies that the microstructures on either side of the phase boundary are similar in structure.18 This follows because the surfactant diffusion depends on the phase microstructure. The small differences between the diffusion coefficients at high and low concentrations in the C10G1-rich samples indicate that the micellar microstructure throughout the micellar region (15) Lindblom, G.; Wennerstro¨m, H. Biophys. Chem. 1977, 6, 167. (16) Balcom, B. J.; Petersen, N. O. Biophys. J. 1993, 65, 630. (17) Nilsson, F.; So¨derman, O.; Johansson, I. J. Colloid Interface Sci. 1998, 203, 131. (18) Monduzzi, M.; Olsson, U.; So¨derman, O. Langmuir 1993, 9, 2914.
Diffusion through Bicontinuous Micellar Networks
does not differ significantly with the change in concentration until at quite low concentrations.18 Significant increases in the diffusion rates do not occur until the dilution curves come quite close to the two-phase region. In contrast, in the C9G1-rich systems there are quite large differences in the diffusion rates between the concentrated and dilute regions of the micellar phase, indicating that there should be larger differences in the microstructure present in these systems than in those rich in C10G1. Taken together, the data imply that networks present in the C9G1 region of the phase diagram break down rather easily with dilution so that the networks become smaller and the concentration of discrete micelles increases simultaneously, resulting in the large observed increase in the diffusion coefficient with dilution. In comparison, dilution seems to have less of an effect upon the size or breakup of networks in the C10G1 region of the phase diagram. Perhaps most interesting is the different diffusion behaviors at concentrations above φS ) 0.20. Similar behavior has been observed in other aqueous surfactant systems, and the general conclusion drawn from a diffusion dilution curve that contains a minimum is that the initial decrease is due to growth of micelles and eventual formation of bicontinuous networks and the increase in the diffusion rate is due to a change in the dominating diffusion mechanism; lateral diffusion of surfactant monomers along the network now dominates over aggregate diffusion.18-22 For an infinitely dilute network, the observed diffusion coefficient is 1/3 of the lateral diffusion coefficient23 (in this context, the lateral diffusion is the curvilinear diffusion coefficient along the surfactant aggregate), provided that the distance between branch points is short compared to the root-mean-squared distance diffused by the surfactant. As the volume fraction of surfactant increases, the surfactant can take shortcuts over the junction zones, and this fact accounts for the mild increase in self-diffusion with increasing φS. Note that the length scale of the experiments is on the order of micrometers and that despite an increase in the diffusion rate, the viscosity of the system continues to increase with the concentration. However, previous work indicated that networks also exist in the C9G1/H2O-rich region of the phase diagram,1,3 yet a minimum in diffusion coefficient is not observed for these samples. There must then be some significant difference in the networks that results in phase separation upon dilution for one network and not for the other. To gain further insight into the type of networks present, scaling models for polymer diffusion, adjusted for surfactant diffusion as presented by Schmitt and Lequeux,5 has been applied to the dilution curves. For a connected system, the surfactant diffusion scales with the volume fraction as Dmic ∝ φS0.25. The result of Schmitt and Lequeux can be compared to the calculations of Anderson and Wennerstro¨m23 of surface diffusion in interconnected rod systems.24 The results of Anderson and Wennerstro¨m imply that the surfactant diffusion scales with the volume fraction according to the exponent above for rod volume (19) Nilsson, P. G.; Wennerstro¨m, H.; Lindman, B. J. Phys. Chem. 1983, 87, 1377. (20) Harwigsson, I.; So¨derman, O.; Regev, O. Langmuir 1994, 10, 4731. (21) Constantin, D.; Oswald, P.; Imperor-Clerc, M.; Davidson, P.; Sotta, P. J. Phys. Chem. B 2001, 105, 668. (22) Ambrosone, L.; Angelico, R.; Ceglie, A.; Olsson, U.; Palazzo, G. Langmuir 2001, 17, 6822. (23) Anderson, D. M.; Wennerstro¨m, H. J. Phys. Chem. 1990, 94, 8683. (24) Luzzati, V.; Tardieu, A.; Gulik-Krzywicki, T.; Rivas, E.; Reisshus, F. Nature 1968, 220, 485.
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fractions in excess of 0.25. Figure 4 compares the scaling predictions to the δ ) 0.125 and 0.75 dilution curves. Other lucid discussions of surfactant diffusion in three-dimensional infinitive networks can be found in refs 22 and 25. As can be seen, the scaling model reasonably predicts the trends in the data above φS ) 0.25 for the 0.125 ratio, which is the concentration at which discrete micelles should be completely replaced by networks. At higher concentrations, the model less accurately fits the data; this is not surprising because the model assumes that the lateral diffusion coefficients are concentration-independent. The slope of the model should decrease if the lateral diffusion coefficients are concentration-dependent, which is what we observe in this system of bicontinuous micelles. The model does not predict the dilution curves from the C9G1-rich region of the phase diagram. With the knowledge that networks are present in this region of the phase diagram also, there are two conceivable explanations for the difference in the slopes for the two regions: either the dependence of lateral diffusion on concentration accounts for the lack of increase or else the lateral diffusion may be decreasing with concentration as a result of scissions (i.e., formation of “dead” ends) of the network. Because it is reasonable that the lateral diffusion coefficient would show the same concentration dependence for all of the ratios, the former explanation can be ruled out. We can gain some support for the suggestion that scissions in the network account for the observed constancy in the slope of the diffusion dilution curves from scaling relations pertaining to the diffusion of monomers though a network of wormlike micelles. When scissions are introduced, the dependence of the self-diffusion on φS changes and the difference in the slopes for the networks with and without scissions is similar to what we observe for the networks rich in C9G1 and C10G1, respectively.5 A decrease in the diffusion rates due to scissions makes sense because micelled surfactants will encounter more ends due to the scissions and as a result have more limited movement through the network. If the models are assumed correct in describing the ability of the network branches to break apart (via scissions) and reform, then the mechanism of phase separation is rather easily formulated. Through scission mechanisms, the networks in the C9G1-rich region of the phase diagram, δ ) 0.75 and 0.5, are able to continuously break and reform; as a result, they are able to transform from a network to discrete aggregates in a continuous fashion by breaking off branches completely as needed, lowering the free energy of the system. In contrast, a bicontinuous network without the scission mechanism will remain intact as long as possible, until the free energy stress of dilution forces it for energetic reasons to break up, resulting in a two-phase system, with intact networks in one of the phases and discrete micelles in the other.3 Such behavior has been observed upon dilution of some microemulsion systems, as well as L3 sponge phases.6 Small-angle X-ray scattering experiments done on the δ ) 0.125 sample (75 wt %) indicate that the cubic phase of these C10G1-rich mixtures are of the Ia3d space group, which is the same space group observed within the n-octylβ-D-glucopyranoside cubic region.13 It is expected that the cubic regions in the C9G1 phase diagram and all cubic regions composed of mixtures of C9G1 and C10G1 are of a similar space group. The diffusion coefficients obtained for the cubic-phase samples of differing δ values (φS > 0.7) are presented in Table 1 (two of the values are also included (25) Halle, B.; Gustafsson, S. Phys. Rev. E 1997, 55, 680.
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Table 1. Diffusion within Different Composition Cubic-Phase Samples δ
wt %
D × 10-12, m2 s-1
0.125 0.25 0.50 0.625 0.75 pure C9G1
73.7 72.6 75.2 74.2 75.4 76.3
4.64 4.49 4.21 4.44 4.26 4.41
in Figure 4). Although the values are all close, there is still a significant bit of scatter observed. We attribute the variation in the diffusion rates to concentration differences in the samples (Table 1); when the individual concentration of the cubic-phase samples are examined, the samples follow the expected trend of decreasing diffusion with increasing concentration of surfactant. Differences in the diffusion rates due to small changes in concentration have been observed within cubic-phase samples for other surfactant systems.26 One final note concerns the properties of the lamellar phase in the C10G1-rich phases (below δ ≈ 0.1). As is clear from Figure 1, at decreasing values of δ the first liquid crystalline phase that precipitates out is a lamellar phase. If, as we argued previously, there is a bicontinuous micellar phase in the micellar region and there is some resemblance (26) So¨derman, O.; Olsson, U.; Wong, T. C. J. Phys. Chem. 1989, 93, 7474.
between the structures in the solution phase and the lamellar phase, this may indicate that the lamellar phase is holey. We are presently investigating this suggestion. V. Conclusions Different mechanisms of network breakdown are likely responsible for the phase separation observed in some regions of the C9G1/C10G1/H2O phase diagram. Modeling of NMR self-diffusion for different ratios of surfactant within the micellar region of the phase diagram indicate that, while networks are present throughout the micellar region of the phase diagram, networks rich in C9G1 are more likely to undergo scissions. The result is that upon dilution they break apart more easily, avoiding phase separation, whereas the networks rich in C10G1 are less likely to have scissions and, thus, deal with dilution stress by separation into two phases, one with intact networks and one with discrete micelles. Acknowledgment. This work has been supported by the Center of Competence for Surfactants from Natural Products (SNAP), which receives funding from the Swedish Agency for Innovation Systems (VINNOVA) and a number of companies active in the Center. We would like to thank Håkan Wennerstro¨m for helpful discussions regarding sponge phases and holey lamellar structures. LA035588C
