Langmuir 1995,11, 1537-1545
1537
Structures and Emulsification Failure in the Microemulsion Phase in the Didodecyldimethylammonium Sulfate/Hydrocarbon/Water System. A Self-DiffusionNMR Study Magnus Nyden and Olle Soderman" Physical Chemistry 1, Chemical Centre, Box 124 University of Lund, S-221 00 Lund, Sweden Received December 28, 1994. I n Final Form: February 17, 1995@ The microemulsionphase in the didodecyldimethylammonium sulfate (DDASYhydrocarbodwater system is investigated. This phase extends from the water corner in the ternary phase diagram. The extension of the phase for various oils is determined, and it is found that the phase is not formed for straight chain hydrocarbons having less than 10 carbons. Neither is it formed with benzene or toluene as oils. At higher oil contents the phase is in equilibrium with almost pure oil, and the boundary to this two-phase region is a straight line which connects the water apex and the oil-surfactant line. It is argued that this line is an emulsification failure boundary. As a consequence, the micellar aggregates are suggested to be spherical in shape and constant in size along this boundary. NMR diffusion studies along this line support this notion. At higher surfactanuoil ratios in the microemulsion the structure is different and there is a growth in the micellar size upon increasing the oil-surfactant concentration. It is pointed out that all the aggregates formed in the DDAShydrocarbodwater system have aggregate curvature toward the oil medium. This is contrary to what is observed in the corresponding systems with bromine as counterion. Possible reasons for this difference are discussed. 1. Introduction
The twin-tailed surfactants belonging to the class of didodecyldimethylammonium halides (DDAX)have been thoroughly investigated,l-15 and one of the first works performed was with didodecyldimethylammonium bromide (DDAB).la Subsequently, interest in the DDAX systems developed since there were large and unexpected differences in the binary DDMwater phase behavior when changing the counterions from bromine to other counterions.2 It was shown that the binary phase behavior changed dramatically when the counterion was changed from Brto Ac- and OH-.8 Both DDAOH and DDAAc are miscible in water (up to about 25 wt%) while DDAB has a low solubility in water.la This work was later expanded by Fontell et a1.,16 who determined ternary phase diagrams with oil, and it was shown that DDAB forms microemul~~
* Author to whom correspondence should be addressed.
Abstract Dublished in Advance A C S Abstracts. A ~ r i l l 5 . 1 9 9 5 . (1) Blum, F: D.; Pickup, S.; Ninham, B. W.; Chen; S.-J.; Evans, D. F.; J . Phys. Chem. 1985,89, 711-713. (2) Bradv. J. E.: Evans, D. F.; Warr. G. G.; Grieser, F.; Ninham, B. W. J . Phys: Chem. 1986, 90, 1853-1859. (3) Chen, S. J.; Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1984, 88. - - , 1631-1634 ~ - ~-~~ ~ (4) Chen, S. J.; Evans, D. F.; Ninham, B. W.; Mitchell, D. J.; Blum, F. D.; Pickup, S. J . Phys. Chem. 1986, 90, 842-847. ( 5 ) Chen, V.; Evans, D. F.; Ninham, B. W. J . Ph.ys. Chem. 1987,91, 1823- 1826. (6) Kang, C.; Kahn, A. J . Colloid Interface Sci. 1993,156,218-228. (7) Ninham, B. W.; Evans, D. F.; Wel, G. J. J . Phys. Chem. 1983,87, 5020-5025. ( 8 )Ninham, B. W.; Evans, D. F. Faraday Discuss. Chem. Soc. 1986, 81, 1-17. (9) Radlinska, E. Z.; Ninham, B. W.; Dalbiez, J. P.; Zemb, T. N. Colloids Surf. 1990, 46, 213-230. (10)Sjoblom, J.; Skurtveit, R.; Saeten, J. 0.;Gestblom, B. J . Colloid Interface Sci. 1990, 141, 329-337. (11) Skurtveit, R.; Olsson, U. J . Phys. Chem. 1992,96,8640-8646. (12) Warr, G. G.; Sen, R.; Evans, D. F.; Trend, J. E. J . Phys. Chem. 1988,92, 774-783. ( 13) Barnes, I. S.; Hyde, S. T.; Ninham, B. W.; Derian, P. J.;Drifford, M.; Zemb, T. N. J . Phys. Chem. 1988,92,2268-2293. (14) Zemb, T. N.; Hyde, S. T.; Derian, P. J.; Barnes, I. S.; Ninham, B. W. J . Phys. Chem. 1987,91, 3814-3820. (15) Reference deleted in press. (16) Fontell, K.; Ceglie, A.; Lindman, B.; Ninham, B. W. Acta Chem. Scand. 1986, A40,247-256. @
0743-746319512411-1537$09.00/0
sions with some hydrocarbons. Experiments were carried out with highly penetrating oils such as hexane and less penetrating long-chained hydrocarbons like dodecane. They all showed a large microemulsion area in the oil rich region of the phase diagram, and the phase boundary close to the binary oil-surfactant line showed a tendency to move away from that line as the oil length was increased (see Figure 1). This paper deals with didodecyldimethylammonium sulfate (DDAS) and water with three different oils: hexadecane, tetradecane, and dodecane. The reason for our interest in these systems is the difference in phase behavior between DDAS and DDAB as reported by Kang et CIZ.~ All phases in the DDAS ternary phase diagram, above the binary water-DDAS axis, have normal aggregate curvatures (bending toward the oil) while in the DDAB system the aggregate curvature is reversed (bending toward the water). With bromine as counterion a large microemulsion area appears in the oil rich corner while with sulfate as counterion a microemulsion is formed in the water rich corner (see Figure 2, where the phase diagrams for DDAS/dodecane/water, from ref 6, and DDAB/dodecane/water are shown). At first sight, taking only electrostatic effects into account, this would seem to contradict the common wisdom that sulfate would tend to interact more strongly with the charged surface on account of it being divalent. If this was the case, the area per surfactant head group would decrease when changing from bromine to sulfate. Thus the replacement of bromine with sulfate would in fact promote even smaller reversed curvatures of the aggregates. There are, however, other aspects that must be taken into account when predicting the strength and degree of counterion binding. Such important aspects are counterion hydration, image charge effects, and dispersion forces between the ions and the surfactant monolayer. For instance, sulfate has a higher hydration number than does bromine, and thus it is conceivable that sulfate cannot come as close to the aggregate surface as can bromine."J8 (17) Marra, J. J . Phys. Chem. 1986, 90, 2145-2150. (18) Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W.; Brady, J.; Evans, D. F. J . Phys. Chem. 1986,90, 1637-1642.
1995 American Chemical Society
Nyd6n and Soderman
1538 Langmuir, Vol. 11, No. 5, 1995
I
H20
DDAB
H20
DDAB
Figure 1. Partial ternary phase diagrams for hexane, octane, decane, and dodecane. Redrawn from ref 16. Note that the L1-phase boundary closest t o the binary surfactant-oil line is moving toward the binary water-oil line as the oil length is increasing.
It is interesting to note that the same trends can actually be found in the single chain quartenary ammonium surfactants. Thus in the binary hexadecyltrimethylammonium sulfate/water systems, the micelles that are formed appear to be smaller than those formed in the corresponding bromine system.19 In order to shed some light on the origins of these differences it is important to determine what structures are formed in the DDAS microemulsion and the driving force behind their formation. More specifically this work has been performed to increase our understanding of the structure in the DDAS microemulsion by means of the NMR self-diffusion technique. In addition, we will also discuss the effect of different hydrocarbons on the phase behavior in the system. 2. Experimental Section Materials. DDAB was purchased from Tokyo Kasei and was used without further purification. The DDAS was prepared by an ion exchange procedure6 (Dowex 1ionic form, hydroxide, dry mesh 20-50) from the corresponding bromine (DDAB). Before the procedure the ion-exchanger was stirred with 1M NaOH for 2 h and then rinsed carefully with deionized water until the pH in the batch reached 7. A 10 g sample of DDAB was added to a flask containing a 100 g batch of ion-exchanger and 150 mL of deionized water. The solution was stirred until there was no undissolved DDAB left. The filtrate was filtered into a new batch of 100 g of ion-exchanger and 150 mL of water and was stirred further for 2 h. The strongly basic solution was then rinsed with deionized water through a filter until the filtrate was neutral. 1 M sulfuric acid was added to the strongly basic filtrate until the pH was 6 and then the “milky” dispersion was lyophilized. The yield was better then 95%. Dodecane and tetradecane were obtained from BDH chemicals, and hexadecane was from Fluka. Heavy water (’99.8%) was purchased from Dr Glaser AG, Basel, Switzerland. Sample Preparation. Water and surfactant were weighed into glass tubes and titrated with oil. After each oil addition the suspension was carefully shaken and the procedure was repeated ~
~~~
(19)Maciejewska; Khan, A,; Lindman, B. Progr. Colloid Polym. Scz. 1987,73,174-179.
until the microemulsion phase appeared. For NMR self-diffision measurements, two standard microemulsion solutions for each oil was prepared, one of which was on the lower line, close to the binary water-surfactant line (cf. Figure 2) and one that was on the upper line. The samples on the upper line were overtitrated with oil to make sure that the upper line was reached. The isotropic lower phase was then removed from the upper oil phase with a syringe. This procedure gave rise t o anuncertainty in the sample composition. However, this error could be estimated to be less than 5%of the total amount of oil. Samples on the middle line (cf. Figure 2) was prepared by combining equal amounts of the two standard samples. The three standard samples were then diluted with water, and the volume fractions for surfactant plus oil for the system with Clz are summarized in Table 1. Table 2 shows the values of the weight ratios m ~ ~ d m c along lz the three lines. The densities for water, dodecane, and DDAS used in all the calculations in this work are shown in Table 3. The samples were equilibrated for at least 1 week prior to the performance of any measurements. Self-Diffusion Measurements. The self-diffision measurements were performed on a Surrey Medical Imaging Systems Inc. (England) NMR spectrometer interfaced to a JEOL FX 100 magnet equipped with an external 2H-lock. The gradient unit was of “in-house”design and construction. The temperature was controlled with a JEOL NM 5471variable-temperature controller unit. The air flow was always kept high t o minimize the temperature gradient over the sample. The temperature drift over the sample was always smaller than *0.3 “C. The probe temperature was 26.0 “C and was measured with a copperconstantan thermocouple. The method used to measure the diffusion was the regular spin-echo technique with two pulsed magnetic field gradients of duration A.36 For all samples, a single exponential decay was observed as deduced from plots of the intensity, Z, vs a2(A - (613))(cf. eq 1 below). Since theN-methyl peak was absent in all experiments
(due to rapid TZrelaxation), this indicates that the surfactant contribution t o the intensity of the main methylene peak was negligible. The diffusion coefficients were calculated by means of a nonlinear least square fitting procedure of eq 1to the raw NMR signal intensities. In eq 1,y is the magnetogyricratio andZo is the peak amplitude in the absence of gradient pulses. In a typical experiment, A was 70 ms and 6 was increased stepwise between 3 and 60 ms with 13 different values of 6 used. For oil diffusion, a gradient of 0.13 T/m was used, and for water diffusion, the strength (G,) gradient was 0.01 T/m. The signal to noise ratio was such that, with the exception of the most dilute samples for which four transients were accumulated, a single transient was enough in obtaining a satisfactory signal to noise level. SAXS. Small angle X-ray scattering experiments were performed at 25 “C. The camera was an adaption of a Kiessig setup20 and the sample to film distance was 0.2 m. Pinhole collimation and Cu Ka radiation was used in the experiments.
3. Results and Discussion Phase Diagram. In order to put our results in context, we first recall what is known for the DDAX/water/oil systems: With DDA13,3J3,16,21322 reverse curvature microemulsions form, with the curvature set by oil penetration into the surfactant tail region. With increasing alkane chain length16 and/or decreasing hydrophilicity of 0 i P 3 ~ ~ there is a systematic evolution of phase boundaries16 (cf. Figure 1) and microstructure1J3 that takes place at constant head group area per surfactant. When the alkane (20) Kiessig, J. Kolloid 2. 1942,98,213. (21) Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J . Phys. Chem. 1986.90. 2817-2825. (22) Tingey, J. M.; Fulton, J. L.; Matson, D. W.; Smith, R. D. J . Phys. Chem. 1991,95,1445-1448. (23) Ninham, B. W.; Chen, S. J.;Evans, D. F. J . Phys. Chem. 1984, 88,5855-5857.
A Self-Diffusion NMR Study of DDASloillHzO
Langmuir, Vol. 11, No. 5, 1995 1539 Dodecane
line
line
line
Figure 2. Ternary phase diagrams for DDAS and DDAB from ref 6. The various regions are labeled according to the following notation: D, D1, and D2 are lamellar phases. L1 and L2 are normal and reversed microemulsions,respectively. E and F are normal and reversed hexagonal phases, respectively. I is a cubic phase and Em is an emulsion region. Also given are the upper, middle, and lower lines in the DDAS microemulsion area along which diffusion measurements were carried out (see the text for details). Table 1. The Volume Fractions of Surfactant Plus Oil (@o+s) for the System with Dodecane
chain length is greater than that of the surfactant, there is little oil penetration and a quantitative change in phase behavior and in the solution microstructure. A summarizing discussion on these features can be found in ref 24. With DDAS, the situation is quite different. The phase diagram for DDAS/water/dodecane has been explored previously.6 Here the curvature is normal, with the
surfactant film enclosing the oil region and the microemulsion phase extends to the water corner, a situation which also occurs for double chained quartenary ammonium bromides of the type C&16DfiB12 when the oil used is hexadecane. Although exhibiting normal curvature, the DDAS system is reminiscent of the DDABIwaterl tetradecane or tetradecane systems, where there is little or no oil penetration and an incomplete understanding of the system. Here the LZphase does not reach the oil corner as it does for other oils and DDAB. With D D B I tetradecane, a small admixture of a penetrating oil, e.g. hexane, will however change the curvature dramati~ally.~ The DDAS system appears to be equally delicately poised. We have explored the influence of the oil type on the phase behavior with benzene, toluene, and saturated hydrocarbons from n-cg to n-Cl6. Experiments performed with benzene and toluene showed no tendency for microemulsion formation. The same result was noted for n-C6 to n-Cs. For n-Clo to n-C16 a one-phase microemulsion region formed. Partial phase diagrams showing the microemulsion area of Clz, C14, and are shown in Figure 3. The results showed that, as the chain length of the normal hydrocarbons approached that of the surfactant, the L1-area decreased in extension and with sufficiently few carbons in the chain it was no longer formed. Anticipating the discussion below, it would appear that hydrocarbons with shorter carbon chain length than the surfactant tail are penetrating the surfactant tails. Since there was no microemulsion formed with benzene and toluene we assume that these oils also have a pronounced penetration effect. The results are in agreement with earlier work pertaining to surfactant tail penetrati~n.~ The penetration makes it difficult for the system to form aggregates with curvature that is bending toward the oil. This can be understood from the surfactant parameter ulalZ5where u is the surfactant hydrocarbon volume, a is the polar head area, and 1 is the length of the surfactant tail. When the ratio vlal is larger than unity, the aggregate curvature will be toward the water. This corresponds to a situation where the oil is penetrating the surfactant tails andor the electrostatic repulsion between the charged head groups is low. When the ratio is less than unity we
(24) Evans, D. F.; Wennerstrom, H. The Colloidal Domain. Where physics, chemistry, biology and technology meet;VCH Publishers: New York, 1994.
(25) Israelachvili, J. N.; Mitchell, D. J.;Ninham, B. W. J.Chem. SOC. Faraday Trans. 2 1976,72, 1525-1568.
@o+sa nm
c:2
L, 12
CY2
0.365gb 0.3068 0.2680b 0.2173 0.1689 0.1345b 0.0994 0.0628 0.02436 0.01286
0.3688b 0.3080 0.2631b 0.2167 0.1729 0.1374b 0.0999 0.0635 O.027gb O.01Eb
0.3703b 0.3092 0.2670b 0.2199 0.1718 0.1377b 0.0996 0.0644 0.0246b 0.0123
a C& means the lower line, CE the middle line, and Cy2 the upper line in the dodecane microemulsion. Ten samples for each line in the microemulsion were made, ranging from 68 to 99 wt% water. The dilution series for tetra- and hexadecane are made in a similar way. Samples used in the water diffusion study.
Table 2.
m D D A S / m C l n for
the Lower, Middle, and Upper Lines in the Microemulsion Area lower line middle line upper line 2.34
2.03
1.71
Table 3. Densities (p) and Molecular Volumes Used When Calculating @o+s Qlg ~ m - ~ DDAS 0.8021
DzO 1.0968
ClZ
0.7485
molecular VO& DDA+
HzO
Cl2
so4
DDAS
777.16
30.0
378.28
60.6
1614.92
Nydin and Soderman
1540 Langmuir, Vol. 11, No. 5, 1995 OIL
R --31 O - :z(1+
2) 5 -
Equations 5 and 2 finally yield the following expression:
@o u
[(3$i
90
H20
(>
=
Dodecane
80
- Tetradecanp
DDAS
- Hexadecane
Figure 3. The figure shows microemulsions in the enlarged water corner in the water/DDAS/oil ternary phase diagram for the three oils, (212, (214, and (216. The hexagonal phase is to be found in the extensionof the microemulsion area. Please note that the microemulsion area is extendedtoward larger volume fractions of oil and surfactant when the hydrocarbon chain length is increased.
have a situation where the electrostaticrepulsion is large and/or the oil is not penetrating the surfactant tails. One interesting observation that can be made in the partial phase diagrams in Figure 3 is the fact that the position of the upper line is relatively unaffected when changing the oils, while the lower line is not. We suggest that the upper line is the result of a so-called emulsification failure.26 This implies that the system is adopting the structure that can solubilize the maximum amount of oil, which corresponds to a situation where the oil is confined to a spherical aggregate. If the oil concentration is increased, the system will form a two-phase region with an oil swollen micellar structure in equilibriumwith excess oil, which is also observed in the phase diagram. We are now in a position to actually compute a value for the surfactant parameter. Let us assume that there is no oil penetration and that the value of ulal is fixed. Let Ro be the radius of the oil core of the micelles (which are assumed to be spherical in shape) and 1 the surfactant chain length. The ratio of the volumes of surfactant, VS, and oil, VO, or equivalently, the ratio of the corresponding volume fractions, @S and @o,in each micelle may now be written:
-
34 +
=
We show in Figure 4 the dependence of the surfactant parameter upon the ratio of the surfactant volume to the oil volume. In Figure 4 is also indicated the value of @d @S along the emulsification boundary, where the aggregates indeed are spherical in shape. From Figure 4 a value of the surfactant parameter equal to 0.79 is obtained for DDAS. This is a value which is clearly reasonable. We expect it to be less than 1(since the curvature is toward oil)but larger than 0.5 since the aggregates are oil swollen. Finally we note that, if the surfactant parameter is to be constant,the aggregates have to change shape as the value of @O/@s is decreased from the value pertinent at the emulsification boundary. The fact that the lower line is affected when changing oil from C12 to and c16 shows that even though it seems as if there is no pronounced differences in penetration between the oils, the system adopts different structures. We suggest that small changes in the nature of the oil does not affect the upper emulsification failure. On the lower line, however, the system has a larger freedom to form slightly different structures and thus small changes in oil properties become significant. Another observation made was that the phase boundary between the microemulsion and the two-phase region between the microemulsion and the hexagonal phase, approached the water corner as the hydrocarbon chain length was decreased. Differences in densities alone cannot explain this behavior (see Table 3). X-ray Results. Earlier X-ray measurements of the DDAS hexagonal phase6 have shown that it has normal aggregate curvature. We have performed X-ray measurements on two samples with different concentrations in the hexagonal phase to investigate whether the area per polar head group was affected by the variation in sample composition. The sample compositions are indicated in Table 4. The positions of the Bragg peaks were used to calculate the radius of the hexagonal tube by use of the relation
+
dhk= y&( h 2 k2 - hk)-l"l
We also have the following for the micellar area and volume in terms of the number of surfactant molecules, Ns, and oil molecules, NO,per micelle:
(7)
where a is the dimension of the unit cell, dhk is the Bragg spacing, and h and k are the Miller indices for the planes. The raw data from these measurements are shown in Table 4. The experimental dEpis compared to calculated dElc (obtained from eq 7) and the difference (dEp d:") is minimized to obtain the best, in the least square sense, value of a . The radius rs of the tube is related to a through:
(4) Combining eqs 3 and 4 gives (26) Safran, S. In NATO ASI Proceedings; Kluwer Academic Publishers: Dordrecht, Netherlands, 1991; pp 1- 15.
+
were @O+S is the aggregate volume fraction (oil surfptant). The results wereoforsamples l(rs = 39.0 f 1.0 A) and 2(rs = 31.3 f 1.0 A).
A Self-Diffusion NMR Study of DDAS loil lH20
Langmuir, Vol. 11, No. 5, 1995 1541 1.o
' L
0.9
0.9
-.
0.8
J
8n
0.7
0.8
0.6
0.7 0,s
t 0.6
@O'@S
Figure 4. The surfactant parameter as a function of the ratio of the volume fractions of surfactant and oil for a spherical aggregate as predicted by eq 6. The dotted line corresponds to the ratio of the volume fractions alongthe upper emulsification failure boundary of the isotropic liquid solution phase (L1 in Figure 2). Table 4. SAXS Results from the Two Samples in the Hexagonal Phasea h ,k
alA
d;"/A
dEplA
Sample 1 1,o 2,1 2,o 3,1 3,3
77.1 44.4 38.6 29.4 25.2
LO
63.7 36.8 31.8 24.1
2s
2,O 3,1
76.9 44.4 38.5 29.1 25.6
88.8
64.3 36.7 32.5 21.4
73.5
Sample 2
a The results are calculated with the assumption that the system is forming a normal hexagonal phase. The upper part of the table is the result for the sample with composition38.9/31.9/29.2(sample 1)and the lower part is the result for the sample with composition 42.7136N20.5 (sample 2) wt% DDAS/HZO/C12. The calculated radius and the area per polar head group (A, ) are as follows: sample 1, A,, = 75.2 f 1A2 and R = 39.0 f 2 sample 2, A,, = 77.4 f 1 A2 and R = 31.3 k 2
A.
1,
These results made it possible to calculate the area per polar head group from the known sample compositions. The relation used was
where V is the volume of the surfactant. With the assumption that the system is forming aggregates of normal curvature and by using the densities in Tqble 3 the results were A,, = 75.2 f 1.0 and 77.4 f 1.0 A2 for samples 1 and 2, respectively. It should be noted that the head group areas refer to the hydrophilidhydrophobic interface, defined by assuming that the hydrophilic part is made up of water and counterions, while the oil and the surfactant cation make up the hydrophobic part. The results indicate that the area per polar head group remains fairly ynchanged when changing the composition. The value 76 A2 is to be compared with th? head group area for DDAB, which is reported to be 68 A2.11 The fact that the area per polar head group is unaffected by differences in composition is unexpected for an ionic surfactant where the curvature is set by the balance between the electrostatic repulsion and the tail volume. However a similar result has been reported for DDAB,
0
0.1
0.2
0.3
0.4
@O+S
Figure 5. The reduced water diffusion, DIDO, for the system with Clz along the three lines in the microemulsion. shows the experimental data for the lower line, 0 is for the middle line, and 0 is for the upper line in the microemulsion area. Also shown in the figure is the result of the fit of eq 13 to the data on the upper line (solid line).
+
where experiments performed in the dilute binary lamellar phase16gave the same head group area as the analysis of SAXS-data from the Lz-phase with various oils.l3 The fact that our results indicate that the area per polar head group is larger for DDAS than DDAB is in line with the differences in aggregate curvature between DDAS and DDAB. NMR Self-DiffusionMeasurements. To investigate the solution structure, a comprehensive self-diffusion study has been performed on samples along the three water dilution lines in the microemulsion region. Both the water and oil diffusion coefficients have been determined. We start by discussing the water diffusion results. Water Diffusion. To investigate the surfactant water hydration and whether water is a continuous phase or not, measurements were performed on samples along the three lines in the microemulsions (cf. Figure 2) for dodecane, tetradecane, and hexadecane. Four samples on each line, the concentration of which are indicated in Table 1, were measured. Here we have chosen to show the water diffusion for the dodecane system; the results are similar for the C14 and systems. In Figure 5, the reduced diffusion coefficients (the diffusion coefficient divided by the diffusion coefficient for pure water at 26 "C) are plotted against the volume fraction of DDA+ plus oil, @o+s. The densities usedin calculating @O+S are shown in Table 3. The decrease in the water diffusion rate when the water volume fraction is decreased can be ascribed to two factors. One is the obstruction effect due to the surfactant/oil aggregates, which hinders the diffusion path of the water molecules. The other effect is the solvation of the charged head groups and counterions. With the assumption that the aggregates are of normal curvature (Le. with water as a continuous phase) the water diffusion hindrance due to solvation can be deduced from
Here Dabsis the observed diffusion coefficient, p~ is the fraction of "bound" water, Dg is the diffusion of the aggregate to which the water is bound, and Dfreeis the diffusion of free water in the solution. With the assump-
Nyddn and Soderman
1542 Langmuir, Vol. 11, No. 5, 1995
tions that there are X number of water molecules bound per surfactant and that the aggregate diffusion can be assumed to be the same as the oil diffusion, eq 10 can be written as
3.5
‘v)
I
I
I
I
I
I
I
I
I
I
I
I
1
2.5
E
1.5
In eq 11, ~ D D Mare the number of DDAS molecules present, ng;, is the total number of water molecules, and Doilis the oil diffusion coefficient. The water diffusion hindrance due to the obstruction effect of spherical particles occupying a fraction of the total volume equal to @+,s is given byz7
(12) 1+-
2
where D&,,is the bulk diffusion coefficient of pure water at the appropriate temperature. If eqs 11 and 12 are combined, and if the aggregate diffusion is neglected (water diffuses with a factor lo2 faster than the oil), the total water diffusion hindrance can be expressed as
l+-
2
By using eq 13 it was found that the number of water molecules that best fitted the experimental data for the upper line (were the aggregates are presumably spherical in shape) was 25 for the case of n-Clz. The result of the fit is shown in Figure 5. Studies on lamellar phases of typical single-chain ionic surfactants have shown that no more than 5-6 water molecules are oriented along the aggregates.2s Furthermore, for a number of cases, the hydration number per surfactant has been found to be 5-12.29 The experimentally found number of “bound water molecules is quite high and may be the result of the strongly hydrated sulfate ions. The plots in Figure 5 show that the water diffusion rate decreases linearly with decreasing water concentration. The values of the diffusion coefficient indicate that water is the continuous phase throughout the microemulsion area. It also rules out the presence of disklike aggregates with large values of the axial ratios (in excess of around 20:1), for which the obstruction factor is close to z/3.27 As will be discussed below in the evaluation of the oil diffusion coefficients, the system is most likely changing its structure on the lower line when the oil surfactant volume fraction is increased. Thus, although it would appear that there is a change in aggregate structure, the water diffusion continues to decrease linearly. As a consequence it seems that the water diffusion rate is sensitive to the aggregate volume fraction and not so much to the aggregate structure. This is in agreement with a
+
(27)Jonsson, B.;Wennerstrom, H.; Nilsson, B.; Linse, P. Colloid Polymer Sci. 1986,264, 77-88. (28) Persson, N. 0.;Lindman, B. J. Phys. Chem. 1975,79, 14101418. (29)Wennerstrom, H.; Lindman, B. J . Phys. Chem. 1979,83,29312932.
0.5
b
1
0.1
0.2
I
0.3
0.4
(D O+S
Figure 6. The experimental oil diffusion coefficient values against QO+S for the case of Clz along the upper line (cf. Figure 2). Also given as a solid line are the predictions of eq 11. structure of spheres or prolates, as for these geometries the obstruction effect is quite low. Oil Diffusion. We now turn to the oil diffusion data and we start with samples along the upper line, the results of which are presented in Figure 6. As can be seen in Figure 6, the value of the oil diffusion coefficient decreases linearly with decreasing water content. From investigations ofthe partial phase diagram we suggested that this upper line in the microemulsion region was an emulsification failure boundary (cf. discussion above) which implies that the aggregate structure on the upper line is one of spherical aggregates. Indeed, the dependence of the oil diffusioncoefficients on the aggregate volume fraction as well as the value of the diffusion coefficient at low aggregate volume fraction indicate that the aggregates along the upper line in the microemulsion phase are spherical in shape. Upon increasing the aggregate volume fraction it is only the number of aggregates that changes. This statement can be rationalized in the following way. The Stokes-Einstein equation accounts for the diffusion coefficient of a sphere with hydrodynamic radius RH:
(14) where k is the Boltzmann constant, Tis the temperature, is the solvent viscosity, and RHis the hydrodynamic radius ofthe sphere. By extrapolating the upper straight line (cf. Figure 6) to infinite dilution, the sphere hydrodynamic radii were calculated an$ the results are for RH = 64 f 1, 63 f 1, and 61 f 1 A for C I Z ,(214, and C 1 6 , respectively. Let us compare this result with the radius which can be calculated for the case of spherical aggregates along the upper line. We cpnsider specifically the case of (212, and by assuming 76 A2 as the area per polar head group (the value that was found in the hexagonal phase), we can calculate the “bare” radius R of the surfactant aggregate from the known molar ratio of oil to surfactant aloFg the upper line (cf. Table 2). The result obtained is 55 A. The relation between R and RH is illustratgd in Figure 7. The difference between RHand R is thus 9 A. It is interesting to note that the radius of a sphere that encompasses a sulfate moleculeo plus 12 water of hydration is approximately 4.5 A. Thus the oil diffusion data long the upper line extrapolated to infinite dilution does not contradict the notion that the aggregates at the upper line in the microemulsions phase are spherical in shape, at least at high dilution. Moreover, it would also appear that the area per polar
A Self-Diffusion NMR Study of DDASloillH~O
Langmuir, Vol. 11,No. 5, 1995 1543 3.5
a
2.5
a
1.5
e a 0
0.5 0
0.2
0.1
0.3
0.4
@o+s
Figure 8. Oil diffusion coeficients for the system with against
@O+S
C12
for the middle line in the microemulsion.
8.0
Figure 7. Illustration of an oil swollen micelle in the microemulsion on the upper line. This attempt, to illustrate that the oil is not penetrating the tail of the surfactant and that the sulfate ions are strongly hydrated. This makes it harder for the counterions to come close to the charged surface.
head group of the surfactant remains rather invariant to alterations in surfactant concentrations. It remains to explain the dependence of Doil upon the volume fraction of surfactant plus oil, @o+s. To start, we note that any aggregate growth, such as the formation of threadlike micelles, would lead to a rather significant decrease in the oil diffusion. This is clearly not the case. For an oil swollen micellar system, with no micellar growth upon increasing the volume fraction of micelles, the dependenceof aggregate diffusion coefficient on @O+S is given (to first-order in aggregate volume fraction) by
h
c
'u)
-
N~
6.0
7
0 v
--
w
4.0
a
no 2.0 0.0
0
0.1
0.2
0.3
0.4
%+S
Figure 9. Oil diffusion coefficients for the system with against
@O+S
C12
for the lower line in the microemulsion.
Figures 8 and 9 show the results from the middle and lower lines in the microemulsion, respectively. In the dilute regime, the values of the self-diffusion coefficients are similar in magnitude to those of the upper line. However, as @O+S is increased, the values of the diffusion coefficients decay much more rapidly than for the case of the upper emulsification failure line. On both lines the where D: here is the diffusion coefficient at infinite diluvalue of Doil then pass through a minimum after which tion and is a constant ranging from 2 to 2.5, depending on the system studied. It has been found t h e ~ r e t i c a l l y ~ ~ the value of the oil diffusion coefficient starts to increase upon further increase in @o+s. These findings indicate that, if pairwise hydrodynamicinteractions are taken into that the aggregates on the middle and lower lines have account, k is approximately 2.1 for hard spheres. For a different sizelshape as compared to the aggregates on nonionic surfactant micellar systems, as for example in the upper emulsification failure line. We shall therefore the C,E, case,31this value of k is indeed experimentally consider the case of a transition from spherical to prolate determined. For an ionic system, one would expect a shape as the oil to surfactant ratio is lowered (justifications slightly higher value on account of the long range for this choice are that the system at lower water electrostatic interactions between the charged spheres. concentrations forms a hexagonal phase with normal From a linear fit of eq 15 to the diffusion coefficients for curvature and the fact that water self-diffusioncoefficients the samples along the upper lines for C12,C14,and CIS (see rule out the presence of large disklike aggregates). The Figure 6,where the results of such a fit are included for self-diffusion constant for prolates at infinite dilution is the case of C12)the following results were obtained: kclz given by = 2.2, kc14 = 2.3, kcls = 2.2. The results are in fair agreement with the theoretical predictions referred to above.30This indicates that, for the three oils investigated, the aggregate structure on the upper lines remains invariant to changes in the surfactant oil volume fraction. It would thus seem that also the concentration dependence of the oil diffusion coefficients along the upper where b is the length of the prolate minor axis and ar is lines are in agreement with the suggestion that the upper the length of the major axis divided by the length of the line is indeed an emulsification failure. minor axis. We will use this relation to estimate the axial ratio, assuming that the area per polar head group is the (30) Pusey In Liquids, freezing and glass transition; Hansen Zinnsame as in the hexagonal phase and along the upper line Justin, L., Ed.; North Holland, 1989; Vol. 2, pp 763-931. (31) Olsson, U.; Schurtenberger, P. Langmuir 1993,9,3389-3394. in the microemulsion area. The following relations are
+
N y d h and Soderman
1544 Langmuir, Vol. 11, No. 5, 1995
used for the area and the volume of a prolate:
&)
arccos(
4n volume = -b3L 3 ar Since there is an infinite number of combinations of axial ratios and minor axes that correspond to one particular diffusion coefficient, we h a y chosen to compute the axial ratio that corresponds to 76 A2in area per polar head group of the surfactant on the surface of the prolate. In order to account for the fact that the translational diffusion coefficient gives a hydrodynamic dimension, while the area per polar head group should be evaluated at the hydrophobichydrophilic interface, we have used the followingprotocol to estimate the aggregate axial ratio. First a value of the prolate minor axis is chosen. This yields, together with the observed diffusio9 coefficient, a value for the axial ratio. Subsequently, 9 A (which is the difference between R and RH for the spheres along the upper line) is subtracted from the initial guess of b and the axial ratio is corrected so that it corresponds to the value a t the hydrophobichydrophilic interface. An area per polar head group is then computed,A,,, and the process i,s repeated by varying the initial guess of b until A,, is 76 A2. In order to avoid problems connected with the particleparticle obstruction effects, calculations were carried out for the first two samples at high dilution on the lower line for the system with (312. Similar results were obtained for C14 and CIS. The diffusion coefficient for the most dilute sample (@o+s = 0.01277) is 3.13 x m2/s,which copesponds to an axial ratio of 2.2 and a minor axes of 45 A (all data refer to the hydrophobichydrophilic interface). A similar calculation performed on the results from the second most dilute sample (@o+s = 0.02426) with a m2/s shoowed that the diffusion coefficient of 1.40 x axial ratio was 11with a minor axis of 42 A. Within the assumptions of these calculations, the results show that as the volume fraction of surfactant plus oil is increased, the prolate grow roughly in one dimension. Before leaving this section, we note that a similar calculation where it is assumed that the aggregates are hemisphere-capped rods (using results in ref 32 to estimate the dependence on the diffusion coefficient on the aggregate axial ratios) gives very similar results. Explanation of the rather marked increase in the selfdiffusion coefficient that takes place both on the middle and lower lines upon increasing @O+S remains. As is clear from Figures 8 and 9, the values of the self-diffusion coefficients pass through a minimum a t around @O+S = 0.2 for samples on the middle and @O+S = 0.05 for samples on the lower line. It seems very unlikely that the aggregates would decrease in size at these points in the phase diagram. Thus we are forced to conclude that an additional diffusion process whereby the transport of oil is mediated starts to operate at these volume fractions. Such a transport process is constituted by diffusion of oil between droplets, either as droplets collide in the solution or through diffusion in “clustered” prolates. It is interesting to note that prolates of axial ratio 1 O : l start to overlap already at a volume fraction of 0.01. (32)Yoshizaki, T.;Yamakawa, H. J . Chem. Phys. 1980,72, 57.
W
Figure 10. This figure attempts to summarize probable structures on the upper and lower lines in the DDAS microemulsion area.
An alternative explanation would be that the microstructure changes into a truly bicontinuous one by the formation of a real network, as has been suggested to form in some cationic single-chain surfactant^.^^ However, for such a situation one would expect a reduced oil diffusion coefficient on the order Of 2/3 (see discussion in refs 33 and 34). For the highest concentrated samples, the value of the reduced diffusion coefficient is roughly 0.025 on the middle line and 0.1 for the lower line. 4. Concluding Remarks (1)For the ternary system with DDAB water and dodecane the phases above the binary water DDAB line are of reversed aggregate curvature, whereas all phases in the system with DDAS above the binary water DDAS line is of normal aggregate curvature. Measurements performed on different phases in the systeom with DDAB shows an area per polar head group of 68 A2.11 Although sulfate is divalent and bromine is monovalent, it appears as if bromine binds closer to the surface than does sulfate. A possible reason for this behavior can be found in the fact that sulfate is more strongly hydrated than bromine. Another possible reason is image charge effects. A third possibility can be found in the attractive dispersion forces between the ions and the bilayers, which are larger for bromine than for sulfate on account of the bromines having larger polarizability in comparison to the sulfate ion. To shed some more light on which mechanism that is actually a t hand here, ion competition experiments, in which, for example, sodium bromine is added to the microemulsions phase in the DDAS system, would be very useful. Such experiments are underway. (33)Monduzzi, M.;Olsson, U.; Soderman, 0. Langmuir 1993,9, 2914-2920. (34)Anderson,D.;Wennerstrom, W. J . Phys. Chem. 1990,94,86838694.
A Self-Diffusion NMR Study of DDASloillHzO (2) X-ray measurements show that even though there is a difference in concentration the area per polar head group in the hexagonal phase is approximately the same. Thus the area per polar head group seems to be an invariant quantity in this system. (3)We suggest that the upper line in the microemulsion region is the result of an emulsification failure and thus the aggregate structure on the upper line is one of monodisperse oil swollen droplets. With decreasing oil content the system forms prolates. In qualitative terms, this means that upon removing the oil, the system adopts a different geometry so as to keep the actual curvature as close to the spontaneous curvature as possible.36 The
Langmuir, Vol. 11, No. 5, 1995 1545 suggestions concerning the structures in the microemulsion phase of DDASIoiUwater are summarized in Figure
10.
Acknowledgment. Stimulating discussions with HBkan Hagslatt and Barry Ninham are gratefully acknowledged. In particular, we thank the later for suggesting the calculations underlying Figure 4. We thank Frank Blum for supplying us with some rather essential parts for the NMR spectrometer used in this work. Ingegerd Lind is acknowledged for technical assistance. This work was financially supported by the Swedish Natural Science Research Council. LA941040H
(35)Olsson, U.; Wennerstrom, H. Adu. Colloid Interface Sei. 1994, 49, 113-146.
(36)Stilbs, P.Prog. NMR 1987,19, 1-45.
