J . Phys. Chem. 1990, 94, 3695-3701
3695
Structural and Dynamic Properties of Polymer-like Reverse Micelles Peter Schurtenberger,*t+Roger Scartazzini,+ Linda J. Magid,$ Martin E. Leser,t and Pier Luigi Luis$ Institut fur Polymere, ETH Zentrum, CH-8092 Zurich, Switzerland, and Department of Chemistry, University of Tennessee, Knoxville. Tennessee 37996- 1600 (Received: June 1 , 1989; In Final Form: January 2, 1990)
A dramatic increase in the viscosity of reverse micellar solutions of lecithin in isooctane by up to a factor of lo6 upon the addition of a small amount of water can be observed. Evidence is presented that the formation of viscoelastic solutions in the system lecithin/isooctane/wateris due to the water-induced aggregation of lecithin molecules into flexible cylindrical reverse micelles and the subsequent formation of a transient network of entangled micelles. The existence of cylindrical aggregates in these solutions is in agreement with the results from systematic small-angle neutron scattering (SANS) measurements at different water to lecithin molar ratios and different lecithin volume fractions (a). The viscoelastic behavior of these solutions and the static and dynamic properties of the transient network formed at lecithin concentrations above the overlap concentration a* are then characterized by using a combination of dynamic light scattering, SANS, and rheological measurements.
1. Introduction We have recently described the formation of highly viscous, gellike and completely transparent solutions in the system lecithin/organic solvent/water.I We found a dramatic increase of the viscosity of reverse micellar solutions of lecithin to values as high as lo4 P upon the addition of a very small amount of water. This phenomenon could be observed in a large variety of different organic solvents. Preliminary investigations by means of polarizing microscopy and N M R indicated that these so-called "microemulsion gels" are completely isotropic, with no detectable anisotropic liquid crystalline order. However, at the time of the discovery we were not able to provide a model for the macroscopic structure of these solutions that could explain their interesting and novel properties. Several reports have been published recently that describe viscoelastic behavior of aqueous micellar solutions of ionic surfactants.2-8 It is generally believed that micelles present in aqueous solutions at high ionic strength tend to grow with increasing surfactant concentration into long, flexible, and cylindrical aggregates. It was thus concluded that the viscoelastic behavior observed in aqueous surfactant solutions is due to the formation of a transient network from overlapping elongated micelle^.^ Candau et al. were subsequently able to show that the results from static and dynamic light scattering and rheological measurements performed on viscoelastic surfactant solutions could be successfully interpreted in terms of theories used to describe the behavior of semidilute polymer s o l ~ t i o n s . ~ * ~ Recent theoretical work for microemulsion systems by Safran et al. predicts the existence of polymer-like phases, associated with the formation of long and flexible cylindrical microemulsions.I0 In this article we show that the formation of highly viscous solutions of lecithin in organic solvent is indeed consistent with a water-induced aggregation of lecithin molecules into flexible cylindrical reverse micelles and the subsequent formation of a transient network of entangled micelles. We first present an investigation of the phase behavior of the system soybean lecithin/isooctane/waterby means of polarizing microscopy, 2Hand 31PNMR, and small-angle neutron scattering (SANS). We then present evidence for the existence of cylindrical aggregates in these solutions based on SANS measurements at different lecithin volume fractions 9 and water to lecithin molar ratios wo. The viscoelastic behavior and the static and dynamic properties of the transient network are then characterized by using a combination of dynamic light scattering (QLS), SANS, and rheological measurements. This combination of different experimental techniques permits us to obtain complementary information on different dynamic and static properties of the entanglement network: ETH Zentrum. of Tennessee.
8 University
First we can study properties that depend primarily on the correlation length l , i.e., the "mesh size" of the network formed by the overlapping cylindrical micelles. This can be achieved by measuring the cooperative diffusion coefficient D,, associated with collective modes of the network, by using QLS. In addition, we can measure the high-frequency elastic modulus G (Le., measured at a time scale much shorter than the lifetime of the network) by means of dynamic shear viscosity experiments. Finally, we can determine the static correlation length [, using SANS. Additional and complementary information can be obtained from measurements of the rheological properties of the solutions at low frequencies. At these low frequencies one primarily probes the disentanglement or reptation process by which entire chains slither through the entangled mass of polymers (or micelles). The zero shear viscosity 7, is expected to depend strongly upon the micellar contour length L and the surfactant volume fraction 9. In addition, if the average micellar lifetime is comparable to or shorter than the longest viscoelastic relaxation time TR,we may encounter a situation analogous to "living polymers", with a significantly altered concentration dependence of 7, and stress relaxation time T.
2. Experimental Section 2.1. Materials. Soybean lecithin was obtained from Lucas Meyer (Epikuron 200) and used without further purification. Isooctane (2,2,4-trimethylpentane) was purchased from Fluka (spectroscopic grade), and fully deuterated isooctane-d18was from Cambridge Isotope Laboratories (98% purity). The water used was purified with a Super-Q water purification system from Millipore. Samples for phase diagram studies were prepared with D 2 0 (Fluka, >99.8% isotopic purity) instead of HzO. Solutions were prepared as followed: First the lecithin is dissolved in isooctane by use of a magnetic stirrer for approximately 2-3 h. The appropriate amount of HzO or D 2 0 is then added with either a microliter syringe (Hamilton) or pipet (Gilson Pipetman) under gentle stirring. A dispersion of the water can be achieved by subsequent vigorous stirring of the solution for a few minutes. During this process a steep increase of the viscosity (1) Scartazzini, R.; Luisi, P. L. J . Phys. Chem. 1988, 92, 829. (2)Gravsholt, S.J. J. Colloid Inrerface Sci. 1976,57, 575. (3)Hoffmann, H.;Rehage, H. Surf. Sci. Ser. 1987,22, 209. (4)Rehage, H.;Hoffmann, H. Furaday Discuss. Chem. Soc. 1983,76, 363. (5)Candau, S. J.; Hirsch, E.;Zana, R. J. Colloid Inferfoce Sci. 1985,105, 521. (6)Candau, S.J.; Hirsch, E.; Zana, R.; Adam, M. J . Colloid Inrerface Sci. 1988,122, 430. (7) Appell, J.; Porte, G. J . Phys. Left. 1983,44, L-689. (8)Olsson,U.; Siderman, 0.; Guering, P. J . Phys. Chem. 1986,90,5223. (9)Candau, S.J.; Hirsch, E.; Zana, R. J. Phys. (Paris) 1984,45, 1263. (10)Safran, S.;Turkevitch, L.A,; Pincus, P. J . Phys. Lei?. 1984,45, L-69.
0022-3654/90/2094-3695$02.50/0 0 1990 American Chemical Societv
3696 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 can be observed. Complete mixing is finally obtained by either slow stirring overnight or multiple and vigorous vortex mixing (for samples with very high viscosity). 2.2. Methods. N M R . 2H and 31PNMR spectra were recorded at 46.07 and 121.49 MHz, respectively, with a Bruker 300-MHz spectrometer (AM 300 WB). For the 2H N M R measurements the isooctane signal was used as an internal reference. The ,IP spectra were recorded with trimethyl phosphate in a capillary as an external standard. Rheological Measurements. Dynamic shear viscosity measurements of the complex viscosity ?*(a)and the storage and loss moduli G'(w) and G"(w), respectively, were performed with a Rheometrics instrument (RDS-7700) using a disk and plate measurement system. The temperature was controlled with an accuracy of f0.5 "C. Special care was taken in order to restrict solvent evaporation to a minimum during measurements. This was achieved by tightly enclosing the measurement system with a container and saturating the air in the system with isooctane. We have subsequently tested these modifications with repetitive measurements performed on the same sample. In general we have observed an increase of the values of v * ( w ) , G'(w), and G"(w) of less than 10% for consecutive experiments. However, if these precautions are omitted, large errors and nonreproducible results will be obtained especially at low frequencies. This will consequently lead to a particularly large overestimation of the zero shear viscosity vs. whereas the shear modulus G deduced from the high-frequency plateau of G'(w) will be less affected by solvent evaporation. We also carefully verified that measurements were performed in the linear viscoelastic regime. Samples at low H20/lecithin molar ratio wo (and thus low viscosity) were measured with a Haake CV 20 N or a Haake CV 100 instrument and ME 30 or ME 46 cylinder-cone measurement systems at a temperature of 20.0 f 0.2 "C. These measurement systems were modified with an aluminum cover to limit solvent evaporation. Quasielastic Light Scattering. Our light scattering apparatus consists of an argon ion laser (Spectra Physics, Model 166, Xo = 514.5 nm), a digital autocorrelator (Brookhaven BI 2030 multibit, 128 channels), a temperature-controlled scattering cell holder, and a variable-angle light detection system (EM1 9893A/100 photomultiplier tube, imaging optics as described in ref 11). Measurements were usually performed at a temperature of 25.0 f 0.1 "C and a scattering angle 0 of 90". Approximately 1 mL of solution was transferred into the cylindrical scattering cell (IO-mm inner diameter). The very high viscosity of some of the samples required a gentle warming of the sample and the pipet to approximately 35 "C, which causes a subsequent strong decrease of the v i s c ~ s i t y . ~ The ~ ? ~scattering ~ cell was then sealed and centrifuged for 90-180 min at approximately 5000g and 25 "C in order to remove dust particles from the scattering volume. A cooperative diffusion coefficient D, = TI/@, where TIis the initial decay rate and Q = (4m/Xo) sin (0/2) is the scattering vector, was obtained by means of a cumulant analysis of the intensity autocorrelation function G2(7).13 This data anlysis procedure was routinely tested with a modified version of the Laplace inversion method.14J5 From D, a hydrodynamic correlation length &, was calculated by using Fh = keT/(67rvoD,) (1) where 'tois the viscosity of the solvent. Small-Angle Neutron Scattering. SANS measurements were made on the high-resolution spectrometer at the High Flux Beam Reactor of Brookhaven National Laboratory. Two scattering geometries were employed, yielding usable Q ranges of 0.025 A-i < Q < 0.32 A-i and 0.0085 A-' < Q C 0.15 A-' (0.0085 A-l is ( 1 1 ) Haller, H. R. J . Phys. E : Sci. Insrrum. 1981, 14, 1137. ( I 2) The viscosity q depends strongly upon temperature. However, temperature-induced changes of q are completely reversible as verified from a
number of dynamic shear viscosity experiments at different temperatures (data not shown). ( 13) Koppel, D. E. J . Chem. Phys. 1972, 57.48 17. (14) Ostrowsky, N.; Sornette, D.; Parker, P.; Pike, R. Opt. Acta 1981.28, 1059. ( I 5 ) Schurtenberger, P.; Angehrn, S. Manuscript in preparation
Schurtenberger et al.
/
.01 0
-_
1
2
3
4
5
6
[H,O] / [lecithin] (= wo)
Figure 1. Zero shear viscosity qs versus added water to lecithin molar ratio wo for a 200 m M solution of soybean lecithin in isooctane a t a temperature of 20.0 "C. Also shown as a dashed line is the phase boundary wo,2mfor phase separation into two macroscopically separated and optically clear phases (see text for details).
the minimum Q value accessible on the Brookhaven spectrometer). The SANS data presented in this article were obtained at the latter geometry, with an incident neutron wavelength selected from the cold source of 1.4 A and a wavelength spread of AX/A = 0.08. The two-dimensional multidetector (1 28 X 128 pixels) was positioned at a sample-to-detector distance of 180 cm. The samples were placed in cylindrical cells having path lengths of 1 or 2 mm, mounted on a rotating sample wheel and thermostated at 25.0 f 0.1 "C. Samples were prepared with H 2 0 and perdeuterated isooctane. One series at w o = 3.0 was also prepared with D20 and protiated isooctane. Each two-dimensional set of raw scattering data was corrected for detector background and sensitivity and for empty cell scattering and radially averaged. The one-dimensional data (intensity versus Q)were further corrected by the sample thickness and transmission. The [(Q) values corrected in this fashion were converted to absolute intensities (in cm-I) using H 2 0 as a standard isotropic scatterer of known scattering cross section. 3. Results and Discussion 3.1. Phase Behauior. Soybean lecithin in isooctane forms clear and optically isotropic reverse micellar solutions.16 These solutions can be transformed into transparent and highly viscous gellike systems by adding very small quantities of water. Figure I shows a representative example of the dependence of the zero shear viscosity vs of a 200 mM lecithin solution upon the molar ratio of (added) water to lecithin, wo, at a temperature of 20.0 "C. The viscosity increases dramatically with increasing water concentration and reaches a distinct maximum of (8.3 f 0.8) X lo3 P at wo = 3.0. Upon further addition of water vsdecreases sharply, and phase separation into two macroscopically separated and optically clear phases can be observed for w o > 5.0. A simple addition of three molecules of water per molecule of lecithin to a liquidlike lecithin/isooctane solution thus causes the viscosity of the solution to increase by more than a factor of lo6. We then made an attempt to further characterize the stability and phase behavior of lecithin/isooctane solutions at low water content and examine the presence and location of phase boundaries in the vicinity of the oil-rich corner of the ternary phase diagram. We have prepared a total of 97 samples with different compositions, covering a range of concentrations (in wt %) of 0 < [lecithin] < 25, 0 < [D20] < 3.5, and 72.5 < [isooctane] C 100, respectively. These samples were then investigated during a period of more than 9 months by means of a combination of ocular inspection, polarizing microscopy, and 2H and 31P NMR. The ~
(16) It is important to point out that the lecithin used in this study contains approximately 0.9 mol of H20/mol of lecithin as seen from 'H NMR and FTIR investigations.
Properties of Polymer-like Reverse Micelles isooctane
A 0.15
::
cP* we expect to find experimental evidence for a transient network with a concentration-dependent correlation length (the “mesh size” of the transient network) and concentration-dependent rheological properties6 As pointed out by De Gennes, transient networks formed by entangled flexible chains have certain properties that exhibit a characteristic and universal concentration dependence irrespective of the exact chemical nature and the microscopic structure of the individual chains.24 According to the scaling theory for semidilute polymer solutions, t is related to the polymer volume fraction cP according to (4) and independent of N.24325SANS permits deduction of the static correlation length F , which corresponds to a screening length for excluded-volume interactions, from the low-Q portion of the scattering curves. The validity of relation 4 for E, has been tested for a number of semidilute polymer solutions by means of SANS26i3’and classical light scattering experiments.27 In general a value of about -0.70 was found for the exponent of the power law. For semidilute polymer solutions, QLS permits a measurement of a cooperative diffusion coefficient D,which is independent of scattering vector Q and associated with the collective modes of many chains in the transient network. A hydrodynamic correlation length (h can be obtained from Dcbyusing (1). &, corresponds to a screening length for hydrodynamic interactions. The same power law (4) as for E, should apply for E,,, and numerous experimental investigations have indeed established a value of approximately -0.67 for the e ~ p o n e n t . ~ ~However, , ~ ~ , ~ ’ it is important to realize that F, and t h are two different screening lengths with different physical origins as pointed out by Muthukumar and Edwards.30 These authors predict a ratio t h / t s = 32/9 for semidilute solutions in good solvents. Values of 2.2 and 1.8 were found experimentally for polystyrene in methylene chloride and tetrahydrofuran, respectively, from QLS and SANS experiments by Brown and Morten~en.~‘ Dynamic shear viscosity experiments permit a frequency dependent measurement of the storage modulus C’(w) and the loss modulus G”(w). In semidilute polymer solutions these quantities exhibit certain typical features. At high frequencies the storage modulus approaches a constant limiting value, the elastic shear modulus G. At these high frequencies the solution behaves like an elastic body, and this region is thus usually called the “rubber plateau”. At low frequencies, C’(w) becomes proportional to u2 and G”(w) becomes proportional to w ; Le., the solution behaves like a liquid. For entanglement networks, the elastic shear modulus G is insensitive to the overall length of the individual chains and depends mainly upon the correlation length t (or the number density of entanglements G is proportional to F3(or proportional to v ) , which leads together with (4) to the following relation for the concentration dependence of G: [
N
(p-077
(24) De Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY. 1979. (25) Des Cloizeaux, J. J. Phys. (Paris) 1975, 36, 281. (26) Daoud, M.; Cotton, J . P.; Farnoux, 8.;Jannink, G.; Sarma, G.; Benoit, H.;Duplessix, R.; Picot, C.: de Gennes, P. G. Macromolecules 1975, 8, 804. (27) Wiltzius, P.; Haller, H. R.; Cannell, D. S.;Schaefer, D. W. Phys. Reo. Letr. 1983, 51, 1183. (28) Adam, M.; Delsanti, M. Macromolecules 1977, I O , 1229. (29) Wiltzius, P.; Haller, H . R.; Cannell, D. S.;Schaefer, D. W. Phys. Reu. Leu. 1984, 53, 834. (30) Muthukumar, M . ; Edwards, S. F. Polymer 1982, 23, 345. (31) Brown, W.; Mortensen, K. Macromolecules 1988, 21, 420. (32) Ferry, J . D. Viscoelasric Properties of Polymers; Wiley: New York, 1980.
Schurtenberger et al. In addition, G should be almost independent of N and T. It has been shown by Candau et al. that viscoelastic aqueous micellar solutions indeed have network properties very similar to classical semidilute polymer solutions and that the scaling relations 4 and 5 are also valid in these ~ y s t e m s .However, ~ the situation is more complicated in the case of the viscoelastic properties at low frequencies, in particular for the zero shear viscosity qs and the viscoelastic relaxation time T . For semidilute polymer solutions in good solvents, the reptation theory by De Gennes predicts the following scaling law for q,:33 qs
-
~3a.3.92
(6)
However, the micellar aggregation number can be a function of both cP and T . Therefore, we can expect to find a much stronger dependence of qs upon cP and Tin micellar solutions as compared to polymer solutions. An additional difficulty for quantitatively predicting the rheological properties in micellar solutions arises from the fact that micelles are dynamic entities, Le., that they can break up and recombine and thus offer an additional relaxation mechanism for stress relaxation. This creates a situation analogous to the case of “living polymers”, for which Cates has recently proposed a theoretical approach.34 A detailed reevaluation of this analogy and its application to viscoelastic reverse micelles has recently appeared.40 Here we only summarize some results that are relevant for this study. If the longest viscoelastic relaxation time TRis much longer than the average lifetime T~ of a micelle (i.e., the time for an aggregate to break into two pieces), stress relaxation should be characterized by a new intermediate time scale ( TRrB)Il2. The micellar aggregation has been proposed to increase with the square root of the surfactant c o n ~ e n t r a t i o n . ~ J If~ ~we ~~ incorporate a @ ‘ I 2dependence of N into the scaling relation for qs, we obtain the following two limiting cases for micellar systems:
TR >> T g :
7s
TR
R , where R is the crosssectional radius, the scattering intensity distribution I ( Q ) should have an asymptotic l / Q dependence in the intermediate Q region (1/L C Q C l / R ) . In this Q region we can use the following approximation for I(Q):36
where C is the surfactant concentration, b, is the sum of the coherent neutron scattering lengths of one monomer, ps is the coherent neutron scattering length density of the solvent, V, is the volume of the surfactant monomer, and RGicis the radius of gyration of the cross-sectional area of the micelle. Equation 8 is valid for polydisperse systems as long as all micelles have similar (33) De Gennes, P. G. Macromolecules 1976, 9, 587. (34) Cates, M . E. Macromolecules 1987, 20, 2289. (35) Blankshtein, D.; Thurston, G.; Benedek, G. B. J. Chem. Phys. 1986, 85, 7268. (36) Lin, T.-L.; Chen, S.-H.;Gabriel, N. E.; Roberts, M. F. J. Phys. Chem. 1987, 91, 406.
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3699
Properties of Polymer-like Reverse Micelles
l
o
0
T
-
-
5
I
ft
.a01
0.0
0.1
scattering vector Q [A']
0.2
I
301
L 0.1 0.2
00.0
volume fraction Figure 4. Plot of the cross-sectional radius of gyration versus lecithin volume fraction 3 for three different water to lecithin molar ratios wo: (0) wo = 1.0; (A) wo = 2.0; (0)w, = 3.0. Also shown is the average value of 21.3 A as a dashed line.
gregates in these solutions. The corresponding values of R are shown in Figure 4. R G i c was found to be 21.3 f 0.6 r a n d essentially independent of lecithin concentration and wo,implying that the lecithin reverse micelles have a rodlike structure with a constant cross-sectional area and grow only in length with increasing woor @. For a uniform cylindrical particle, Re. is given by R/2Il2. Therefore, we can estimate the cross-sectional radius of the reverse micelles from RGic. This leads to a value of 30.1 f 0.9 A for R. For the samples prepared with protiated isooctane at w,, = 3.0, we obtain values for RGicof approximately 14-15 A, which leads to a radius of 21 A. For these samples the radii observed correspond to the rodlike water-headgroup channels present in the core of the reverse micelles. A t pica1 soybean lecithin molecule has an extended length of 30 of which approximately 18 A is hydrocarbon tails. The observed values for -a 0.00 0.01 ( 0.02 j 0.03 U the radii of 30 and 21 A, respectively, suggest that the water is distributed radially throughout a very extended headgroup region. 3.4. Network Properties. Quasielastic Light Scattering. Figure Q 2 [A'] 5A shows the dependence of the hydrodynamic correlation length l h upon the lecithin volume fraction @ at two different values of wo. The open squares correspond to wo = 3.0, i.e., the H 2 0 to lecithin molar ratio at which the viscosity reaches a maximum (see Figure I). The first reduced cumulant rI/Q2 was found to be independent of Q in the entire range of volume fractions investigated, providing thus a measurement of the cooperative diffusion coefficient D, or the hydrodynamic correlation length ththrough (1). The dependence of &, upon is well represented by a power law (relation 4) for 0.014 I@ I0.145, with an exponent of -0.65 f 0.05. The open triangles correspond to w o = 2.0. At this H 2 0 to lecithin molar ratio we find two distinct regimes for the concentration dependence of rI/Q2or &,. At volume fractions @ I0.05, t h depends only weakly upon the lecithin concentration. However, at 9 > 0.05 the dependence of [h upon @ is again well represented by a power law (relation 4), I 0.02 with an exponent of -0.65 f 0.07. The absolute value of f h ( @ ) 0.00002 0.00004 agree to within the experimental uncertainty with those measured Q 2 [A'] for wo = 3.0; Le., &, depends only upon @ and is independent of wo in this regime. Such behavior is in good agreement with the Figure 3. Representative examples of results from small-angle neutron scattering experiments on solutions of soybean lecithin in isooctane at wo predictions 2 and 3 made on the basis of our structural model. = 2.0 and different lecithin volume fractions: ( A ) 3 = 0.0137; ( 0 )+ The power law dependence of [h upon 9 (which is independent = 0.0389;(0)3 = 0.071 I ; (+) 3 = 0.108; (0)+ = 0.184. (a) Deof wo) is a clear indication for the presence of a transient network. pendence of the scattered intensity on scattering vector Q. (B) Plot of The value of the scaling exponent is in quantitative agreement log (Q/(Q))versus @. Also shown are linear least-squares fit to the data with the values found in semidilute polymer solutions in good used for the deduction of the cross-sectional radius of gyration RG;E.(C) solvents. The fact that a crossover to a power law dependence Plot of I(Q)-l versus @. Also shown are linear least-squares fit to the for &, can only be observed for wo = 2.0 indicates that the crossover data used for a deduction of the static correlation length &. concentration 9*is indeed decreasing with increasing wo. radial structure. We can use ( 8 ) to determine RGic from the Small-Angle Neutron Scattering. For semidilute polymer experimental data by plotting In (QZ(Q)) versus Q2 for each solutions, the scattering intensity Z(Q) follows a Lorentzian micellar solution. RGiccan then be. calculated from the slope of scattering law3' the data at high Q. Figure 3B shows the corresponding plots Z(Q) (1 + Q2FS2)-' (9) together with the fitted straight lines for the experimental data presented in Figure 3A. The neutron scattering curves obtained for Qt,< 1. The static correlation length t, can thus be determined for every value of lecithin volume fraction 9 and wo investigated are well represented at higher Q values by (8). This provides (37) Edwards, S . F. Proc. Phys. SOC.,London 1966,88, 265. strong evidence for the presence of rodlike reverse micellar ag-
I\
1,
-
~~~
3700 The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 1000
T - - ~
Schurtenberger et al.
-
”E
10000! ‘
A
i A
-. - o.i
.2.
1.1
1
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frequency [radisec] I-----oL.l-
.001
.01
.1
1
volume fraction
.-
I e
lo/
I 11
.1
1
10
100
1000
frequency [ractsec] Figure 6. Frequency dependence of the magnitude of the complex viscosity q* ( O ) , the storage modulus C ‘ ( O ) ,and the loss modulus G”(A) for soybean lecithin in isooctane at a temperature of 22.0 OC. (A) = 0.036;WO = 3.0. (B) Q = 0.145; WO = 3.0.
t, is well represented by a power law, with an exponent of 0.7 f
6
104 .001
I
.01
.1
1
volume fraction Figure 5. (A) Plot of the hydrodynamic correlation length (,, versus the lecithin volume fraction 9 for two different values of wo obtained from QLS: (0)wo = 3.0;(A) wo = 2.0. Also shown as a solid line is the fit of relation 4 to the data used for a deduction of the scaling exponent. (B) Plot of the static correlation length [,versus the lecithin volume fraction for three different values of wo obtained from SANS: (0) wo = 3.0; (A) wo = 2.0; (0)wo = 1.0. Also shown as a solid line is the fit of relation 4 to the SANS data for 0.03 < 9 < 0.1. In order to facilitate a comparison between 5, and &, we have included the solid line in (A), renormalized according to the experimental and theoretical findings from classical polymer solutions in good solvents: &/2.2 (dashed line) and Eh/(32/9) (dotted line) (see text for details).
from a plot I(Q)-l versus Q2,which yields 52 from the slope-tointercept ratio. Figure 3C shows plots of I(Q)-l versus @ for the same samples at wo = 2.0 already presented in Figure 3A. The scattering intensities clearly follow a Lorentzian scattering law at low Q values as predicted by (9) for a transient network. Figure 5B summarizes the static correlation lengths deduced from a linear fit of the f(Q)-’values obtained for the different volume fractions at the three w o values studied. At the lowest volume fractions (Le., largest 5, values) only the first few data points (0.0085 A-‘ < Q C 0.016 A-1) could be used. At these low concentrations the accuracy of the values of t, so obtained is thus limited, and an extension of the accessible Q range toward lower values would be preferable. This experimental limitation makes it difficult to unambiguously determine a* for the different values of wo. Additional difficulties arise at high lecithin volume fractions due to the relatively large cross section of the cylindrical micelles as compared to polymer chains. At these concentrations the correlation length becomes comparable in size with RGic. Therefore, network properties and micellar structure are probed in the same intermediate Q range and a deconvolution of the contributions to I( Q ) from the network and the individual chains (micelles) is required. However, we do not have an appropriate theoretical expression for this task at the present, which leads to a rather large uncertainty for t, at 9 L 0.1. At 0.03 C 9 < 0.1,
0.05. A comparison with the hydrodynamic correlation length th yields the relationship f h / & = 2.3, which is similar to the relationship found for polystyrene in good solvents” but lower than the theoretical value of 32/9.30 Rheological Measurements. Parts A and B of Figure 6 show two representative examples for the frequency dependence of the magnitude of the complex viscosity q*, the storage modulus G’, and the loss modulus G”at two different lecithin volume fractions of 0.036 and 0.145, respectively. The dynamic behavior of these solutions exhibits all the typical features found in systems that form transient networks. At high frequencies the storage modulus does approach a constant value and yields the elastic shear modulus G. At low frequencies, G’and G” intersect and decrease proportional to u2 and w , respectively, with decreasing frequency. At very low frequencies q* becomes independent of frequency and permits a measurement of the zero shear viscosity 7,. It is now interesting to investigate the concentration dependence of the quantities qs and G at different values of wo and compare it with the theoretical predictions in (5), (7a), and (7b). Figure 7 summarizes the results from dynamic shear viscosity measurements at two values of wo and different lecithin volume fractions. The concentration dependence of G is well represented by a power law (relation 5) with an exponent of 2.0 f 0.1. An exponent of 2.0 is quite comparable with the values found in viscoelastic micellar solutions or semidilute polymer solutions. G depends only weakly on wo,with an average ratio G(WO=~.O)/G(w0=2.5) = 1.3 f 0.3. Such a weak dependence of G upon wo IS qualitatively consistent with our simple structural model. In solutions with transient networks G is related to v, the number density of entanglements. Therefore, at concentrations above O*, G should primarily depend on 5 and be fairly independent of chain contour length L. In our model we postulate that w o is mainly controlling the micellar length L but has only a negligible effect on [ as already seen from QLS and SANS (see Figure 5 ) . We therefore expect to find only a weak dependence of C upon w0. but a much more pronounced dependence of the zero shear viscosity 7, upon wo. This is in agreement with our experimental results presented in Figure 7B, where we find an average ratio o,(w0=3.0)/~,(~0=2.5)= 2.0 f 0.4. The dependence of qs and 9 can also be described by a power law, with an exponent of 1.9
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3701
Properties of Polymer-like Reverse Micelles
4. Conclusions
1°0A
.I
1
volume fraction
100 .01
.1
1
volume fraction
Figure 7. (A) Plot of the elastic shear modulus G versus the lecithin volume fraction @ for lecithin/isooctane solutions at T = 22 OC and two wo = 3.0 (A)wo = 2.5. Also shown as solid different values of wo: (0) lines are fits of relation 5 to the data. (B) Plot of the zero shear viscosity 7, versus the lecithin volume fraction @ for lecithin/isooctane solutions at T = 22 OC and two different values of wo: (0)wo = 3.0;(A)w, = 2.5. Also shown as solid lines are fits of relation 7 to the data.
f 0.1. This value is in clear disagreement with both the exper-
rimental results from polymer solutions and aqueous viscoelastic micellar solutions and the theoretical predictions for classical polymer solutions (Le., reptation theory) or living polymers.6 These findings indicate fundamental differences between the dynamic properties of lecithin reverse micelles at low frequencies and those of synthetic polymers and ionic micelles.40 (38) Messager, R.; Ott, A,; Chatenay, D.; Urbach, W.; Langevin, D. Phys. Rev. Lett. 1988, 60, 1410.
The results presented in this article provide compelling evidence for the existence of long, cylindrical reverse micelles and the formation of an entanglement network at volume fractions larger than the overlap threshold a* in the system soybean lecithin/ isooctane/water. Dynamic light scattering, small-angle neutron scattering, and rheological measurements are in agreement with a simple structural model in which the addition of small amounts of water to lecithin/isooctane solutions induces one-dimensional growth of the lecithin molecules into cylindrical aggregates. Analogies to semidilute polymer solutions can be made at 0 > a*, and a power law dependence of the static and hydrodynamic correlation length and the elastic shear modulus upon concentration was found in agreement with scaling theory for polymers. However, the concentration dependence of the zero shear viscosity is in clear disagreement with polymer theory and the previous experimental findings for ionic micellar solutions.6 These novel results may be explained by the fact that micelles are dynamic aggregates which can break up and reform on time scales comparable to or faster than the experimental time scale. Additional and systematic relaxation time experiments as a function of lecithin volume fraction, water to lecithin molar ratio, and temperature will be needed in order to fully understand the dynamic properties of this system. We believe that reverse micellar solutions of lecithin may serve as good model systems for an experimental investigation of the dynamic properties of entanglement networks formed by nonpermanent objects and the application of theories developed for "living polymers". Previously, attempts were made in order to use giant cylindrical micelles formed in ionic surfactant solutions at high concentrations of added salt as an experimental model system for living polymer^.^,^*,^^ However, the interpretation of the results from these studies was critically affected by the presence of strong salt effects. It is thus most interesting to study solutions of polymer-like reverse micelles in oil, where these additional complications would be absent. Acknowledgment. This work was supported by the Swiss National Science Foundation (NF-19) and by the US.National Science Foundation (NSF-INT 8314066 and NSF-CHEM 861 1586). We thank Dr. H. Kramer at the EMPA for performing the majority of the dynamic shear viscosity measurements. We gratefully acknowledge the support by Haake, which offered us access to their CV 20 N and CV 100 rheometers. We thank Mr. F. Bangerter, who kindly performed the N M R measurements. We also thank Prof. J. Candau for extremely helpful suggestions and discussions. Registry No. Isooctane, 540-84- 1. (39) Cates, M. E. J . Phys. Fr. 1988, 49, 1593.
(40) Schurtenberger, P.; Scartazzini, R.; Luisi, P. L. Rheol. Acta 1989, 28, 312.
