J. Phys. Chem. 1994, 98, 12708-12714
12708
Optical Contrast Variation Experiments in Water-in-Oil Microemulsions: Size Distribution and Structure of Protein-Free and Protein-Containing Microemulsions S. Christ and P. Schurtenberger' Institut fiir Pblymere,
ETH antrum, 8092 Zurich, Switzerland
Received: June 15, 1994; In Final Form: September 7, 1994@
We report on a study of protein-free and protein-containing AOT water-in-oil microemulsions with isooctane and decane as solvents by using static and dynamic light scattering measurements. In a first step, using a model of polydisperse layered spheres, we show that we can determine the size polydispersity y of the microemulsion droplets with very high precision because the variation of both the scattering intensity as well as the hydrodynamic radius with the water content are very sensitive to y in the vicinity of the optical match point of the microemulsion particles. In a second step, we then focus on the size and structural perturbations induced in the reverse micellar system upon solubilization of the enzyme a-chymotrypsin by using optical contrast variation techniques. In particular, we show that light scattering experiments close to the optical match point can be used as a very sensitive method in order to quantitatively test the currently existing theoretical models for protein solubilization in microemulsions.
1. Introduction Reverse micelles and water-in-oil (w/o) microemulsions can solubilize guest molecules such as ions,' enzymes, or synthetic polymers,2 which would otherwise have only limited or no solubility at all in the organic ~ o l v e n t . ~This , ~ property makes microemulsions very interesting model systems for both basic research5 as well as an increasing number of applications such as enzymatically catalyzed organic-phase synthesis,6chromatographic separation, or extraction of proteins through phasetransfer methods. The knowledge of the geometrical parameters of the microemulsion particles and their size distribution is very important to correctly interpret the observed phenomena and to develop good theoretical models of the driving forces responsible for both droplet formation and polymer and biopolymer solubilization in micro emulsion^.^-^^ In the last years these problems were often discussed and a number of experimental studies and theoretical models have been presented.12-19 However, no unambiguous solution to these problems has been found, and the situation still remains controversial. It is the aim of this study to show that we can use dynamic (DLS)and static (SLS)light scattering experiments close to the so-called optical match point as a very sensitive method20 to quantitatively test the currently existing theories for the formation of microemulsion droplets on the one hand and for the protein solubilization in microemulsions on the other hand. In this study we shall focus on two aspects of microemulsion formation. First we shall discuss the size and polydispersity of a three-component model microemulsion. The free energy of thermodynamically stable microemulsion droplets can be expressed in terms of the osmotic pressure difference between the inside and the outside of the droplets, the interfacial tension, and the bending energy of the interfa~e.*~-*~ The knowledge of this free energy allows calculation of the size distribution of the droplets and consequently their polydispersity. We can thus use these quantities, which are both more accessible experimentally than the osmotic pressure difference and the interfacial tension, to test the theoretical models. In particular we use the ls718
@Abstractpublished in Advance ACS Abstracts, October 15, 1994.
fact that the scattering data in the vicinity of the match point are very sensitive to the polydispersity. This allows us to measure the polydispersity very precisely. This will be illustrated with experiments using w/o microemulsions in isooctane and decane, and the results will be compared with the existing data on the size and polydispersity of AOT. In a second step, we shall then look at the size and structure changes accompanying the protein solubilization in the microemulsion. The size difference between the empty reverse micelles and the average size measured in the biopolymercontaining solution is often very small, so that the size distribution changes induced by the presence of biopolymers cannot be determined unambiguously by normal light scattering experiments. However, we can overcome this problem by suppressing the scattering contributions from the empty reverse micelles close to the optical match point of the microemulsion droplets. These experiments provide us with information over a relatively narrow range of water-to-surfactantmolar ratio ( W O ) only. However, we can shift the optical match point significantly using different solvents. We have thus chosen decane and isooctane as solvents in this study. For decane, we observe an optical match point at wo 17.5, i.e., in the range of WOvalues where most investigations dealing with enzymatically catalyzed reactions have been performed. For isooctane, the match point increases to w o 30, which allows us to monitor the variation of the micellar radius as a function of w o over a much larger range. As a first test, we have performed measurements on a-chymotrypsin containing AOT microemulsions and compared the experimental data with the predictions based on a model recently presented by Rahaman and Hatton.19 We show that this model predicts much higher effects on both the size and the scattering intensity of the reverse micelles after protein solubilization in the microemulsion than experimentally observed. 2. Experimental Section
Materials. Aerosol-OT (bis(2-ethylhexy1)sodiumsulfosuccinate) (99% purity) was obtained from Sigma and stored over self-indicating silica gel. Isooctane (UV spectrophotometric
0022-3654/94/2098-12708$04.50/0 0 1994 American Chemical Society
Optical Contrast Variation Experiments grade) and decane (98% purity) were obtained from Fluka. a-Chymotrypsin (EC.3.4.21.1) from bovine pancreas was obtained from Fluka (BioChemika, 60 U/mg activity). Tris(hydroxymethy1)aminomethaneof research grade was obtained from Serva and HCl (37%, puriss. p.a.) was from Fluka. The water used for the preparation of the buffers was purified with a MilliQ-setup (Millipore). All these compounds were used without further purification. The dialysis membrane (Spectra/ Por 3 with a molecular weight cutoff of 3500) was obtained from Spectrum and the "low binding" filters (Millex, pore size 0.45 pm and 0.1 pm, respectively) were obtained from Millipore. Methods. Preparation of the Protein Stock Solution. 50 mM and 200 mM Tris/HCl buffers, pH = 7, were prepared and filtered (pore size 0.1 pm). Five milliliters of a stock solution containing 80 mg/mL protein in 50 mM Tris/HCl buffer was prepared. Since this resulted in a pH drop to pH 3.4, this stock solution was then first dialyzed at 4 "C for approximatively 6 h against 2 L of 200 mM Tris/HCl buffer. In a second step the stock solution was then dialyzed about 12 h overnight against 5 L of 50 mM Tris/HCl buffer. After dialysis the protein solution was passed through a filter with pore size 0.45 pm and then continuously filtered in a closed-loop filtration setup with 0.1-pm pore size and 2.2 f 0.1-mL flow rate during about 1 h at room temperature. After filtration the pH of the solution was controlled (6.85 f 0.05) and the concentration was measured spectrophotometrically at d = 280 nm with a Beckman DU-68 spectrophotometer, using a molar extinction coefficient of 50 000 M-' cm-'. The dialyzed and filtered solution was stored at 4 "C prior to injection into the microemulsion, which occured within 1 h after filtration. The dielectric constants of the TRIS buffer and the protein were obtained from dnldc measurements, using a differential refractometerz4 at d = 633 nm. Preparation of the Microemulsions. First, 0.1 M AOT stock solutions in isooctane and decane were prepared. Buffer and protein stock solution were then added with an electronic pipette (edp-plus pipette from Rainin) in order to obtain microemulsions with various wo-values and constant protein water pool concentrations (0 and 7 mg/mL, respecti~ely),~~ where wo is the molar ratio of water to surfactant. After injection, the samples were vigorously vortex mixed for 2-3 s and then stored at 25 "C for at least 1 h prior to the light scattering measurements. All light scattering experiments were performed within a maximum of 20 h after the sample preparation. The wo-values were corrected for the water content of the "dry" AOT, which was measured by using IR spectroscopy (5 SXC FT-IR spectrometer from Nicolet). The molecular volume of AOT in isooctane and decane was calculated from density measurements with a density and sound analyzer (DSA 48 from AP Paar). Light Scattering Measurements. Static (SLS) and dynamic (DLS) light scattering measurements were performed with a Malvem 4700 PS/MW spectrometer equipped with an argonion laser (Coherent, Innova 200-10, d = 488 nm), a digital autocorrelator (Malvem 7032ES/136C), and a computer controlled and stepping motor driven variable angle detection system. Measurements were made at 25 f 0.1 OC. Approximatively 1 mL of micellar solution was transferred into a cylindrical cell, which was then centrifuged for 20 min at approximatively 5000g and 25 "C in order to remove dust particles from the scattering volume. DLS measurements were performed at a scattering angle of 45". At least three measurements of a duration of 1-10 min were performed for each sample. The individual correlation functions were analyzed by using a second-order cumulant fit?6 The measured polydis-
J. Phys. Chem., Vol. 98, No. 48, 1994 12709
persity, Y a , defined by
where pz is the second cumulant and (r)is the average line width, was for all samples smaller than 0.1. SLS measurements were performed at nine different angles (30" I0 I150"). For each sample, 50 individual short measurements were performed and averaged, resulting in average intensities (I(e)). For spherical particles in this size range (Rh 10 nm), the normalized scattering intensity is independent of the angle. Therefore we used the following procedure in order to obtain an average normalized intensity (I,). For each value of 8 the data were corrected for solvent scattering and normalized by using toluene as a reference standard
where (&(e)) is the average solvent intensity and (Z~,,l(e)) is the average intensity of toluene. Finally, the data from all angles were averaged and a mean normalized intensity (I,) was calculated. In this last averaging procedure, the standard deviations (J of the individual (I(@)) were used as a "dust discrimination criterion", and only measurements with (J 5 2% were used. Furthermore, all values of (I(@) which showed systematic deviations from the other angles were also eliminated.
3. Theoretical Background Optical Matching and Polydispersity in AOT Microemulsions. Geometrical Considerations. For water-in-oil microemulsions, the total amount of surfactant defines the total available area of the interface, Atot,whereas the water determines the total core volume, Vw,tot. At constant surfactant concentration, the water core radius, r, therefore increases monotonically with increasing water content, WO. In the absence of polydispersity, an approximate relation for the water core radius r(w0) can be written as (3) where vw and vs are the molecular volume of water (30 A3 27) and surfactant (645 A3 for AOT in isooctane and 655 A3 for AOT in decane) and A, is the curvature-dependent area per AOT molecule at the interface.' A, is given by
A,(w,) = 48 - (1 1 exp[-0.0963(wo - lo)])
(4)
Furthermore we obtain the hydrodynamic radius, Rh, using
R, = (r3
+ 36r2)"3
(5)
where 6 is given byzo
6 = VJA,
(6)
and corresponds to the thickness of the surfactant layer when r >> 6 only. Calculation of the Mean Scattering Zntensity ( I ) and the Hydrodynamic Radius (Rh) for Polydisperse Systems and Direrent Solvents. The total average intensity (0 for a polydisperse solution of microemulsion particles is given by (7)
Christ and Schurtenberger
12710 J. Phys. Chem., Vol. 98, No. 48, I994 WO
.-.
10
tS
r
-
r
d -10
n
EP
water core radius r [A] Figure 2. Water core radius dependence of the optical excess polarizability a(r) of a reverse micelle in the systems TRIS buffer/ AOT/isooctane and TRIS buffer/AOT/decane with (-) and without (- - -) a-chymotrypsin from eq 12 and the parameters given in the text. Ep
Figure 1. Shown are the profiles of the dielectric constant for (A) a protein-free and (B) a protein-containing reverse micelle modelled as layered dielectrical spheres (see text for details).
Olfilled
+- Eo
3
= 4nEO[ Ep 2E3
+
E,
+ 2E0 -E3, i-~ Eo ] E,
+
(12)
2E0
and
(a2) = Jflr)a2(r) dr
+
where 4 is the volume fraction of the dispersed phase (water surfactant), A is the wavelength in vacuo (488 nm) of the light beam, (V) is the average volume, (a2) is the mean square excess polarizability, and Ar) the explicitly chosen size distribution of the microemulsion particles. For our calculations we used a Schulz size distribution.28 Similarly, we can calculate the apparent z-average diffusion coefficient (DJZ measured in the DLS experiments using
Finally we obtain the corresponding z-average hydrodynamic droplet radius (&Jz using the Stokes law and
We can now use a layered sphere mode120 for the structure of the microemulsion droplets without and with solubilized enzymes in order to calculate a analytically as a function of r (see Figures 1 and 2), and we obtain Gmpty and afilled as a function of the dielectric constants EO, E,, E,, and cp, of the solvent, the water, the surfactant, and the protein (a-chymotrypsin), respectively, the radii rpand r, of the protein and water core, and 6 (see eq 4). The layered sphere model in a simple linear mixing approximation then leads to
where Vp, V,, and V, are the volume of the protein, the water core, and the surfactant layer, respectively, and
We can calculate Ctempty by setting Vp (and rp) to zero. For our calculations we used EO = 1.942 for isooctane29and EO = 2.008 for decane,29E, = 1.795, E~ = 2.205,20 and ep = 2.536, and rp = 21.7 A.30 In Figure 2 we see that the resulting excess polarizability goes through zero for a particular composition (radius), i.e., for this value of r the particles become "invisible" in a light scattering experiment. Figure 2 also shows that the location of this optical match point can be shifted by changing the solvent in the microemulsion because of the strong dependence of (a) on the dielectric constant E (low E value leads to a match point at high WO; see, for example, the work of Ricka et al.,*O where the match point of the ternary system H2OIAOThhexane (En-hexane = 1.87) is located at wo = 67). Figure 2 shows clearly that the insertion of an enzyme in the microemulsion droplet dramatically alters its polarizability (and thus its scattering cross section), particularly at low droplet radii. Thus it is possible to perform contrast variation experiments in which either empty or filled microemulsion particles dominate the scattering intensity quite similarly to neutron scattering measurement^,^ where large differences in the scattering cross section can be obtained by choosing a suitable distribution of hydrogen and deuterium atoms. While the resulting differences in droplet radii between the protein-containing and non-protein-containing reverse micelles are too small to be determined unambiguously with DLS measurements directly, we can use SLS and DLS measurements at wo-values close to the optical match point in order to considerably suppress the scattering contributionsfrom the empty micelles. Optical contrast variation experiments not only allow for a structural characterization of empty and filled reverse micelles, they also permit a precise determination of the polydispersity of droplet-like microemulsion particles.20 This is illustrated which Figure 3, where the normalized intensity (I,) is shown as a function of wo for polydisperse microemulsion droplets in decane and in isooctane. (I,) was calculated from eqs 7 and 8 by using a Schulz distribution and eq 3 for the mean radius as a function of W O . Several curves of (I,) vs wo are shown for different values of the polydispersity index y, where y is defined
J. Phys. Chem., Vol. 98, No. 48, 1994 12711
Optical Contrast Variation Experiments 120
t
I I
decane l
10
,
.
l
‘i i I
I , ,
,
,
,
I
30
20
,
\/ ,
1
,
,
,
I
,
,
I
,J
40
wo Figure 3. Calculated normalized intensity (Is)as a function of the water content wo for monodisperse (-) and polydisperse microemulsion droplets in decane and isooctane. The shape of the curves is completely given by the value of the polydispersity index y , where in decane (-) y = 0.01 and (- -) y = 0.02 and in isooctane (- -) y = 0.035 and (-) y = 0.07.
~
10
,
,
,
20
,
,
,
30
,
,
,
4. Results and Discussion
Protein-Free Microemulsions. Figure 5 shows the variation of the mean normalized intensity (Is) with wo obtained from SLS measurements for TRIS buffer/AOT/isooctane and TRIS
,
,
wo
,
,
50
Figure 4. Calculated hydrodynamic radius R h as a function of the water content wo for monodisperse (-) and polydisperse microemulsion droplets in the system TRIS buffer/AOT/isooctane. The shape of the curve depends on the value of the polydispersity index y only. Shown are the curves for y = 0.035 (- -) and y = 0.07 (-).
i
First, we recognize the different location of the match point in both solvents. Second, we see that at the match point (Is) disappears only for y = 0, Le., for monodisperse systems. As soon as the system exhibits some polydispersity ( y f 0), only part of the microemulsion droplets are completely matched and thus invisible. For polydisperse systems at the match point, the intensity curve shows a minimum, whose depth and position are extremely sensitive to y . We can thus precisely determine the polydispersity of AOT microemulsion particles for different solvents. A similar effect can be observed in the dependence of the hydrodynamic radius R h on wo as determined in a DLS experiment. The water core radius r increases linearly with W O . For monodisperse droplets, this leads to an almost linear dependence Of Rh on ~ 0 However, . ~ for ~ polydisperse solutions, the incomplete optical matching at the match point results in a sigmoidal shape of R h versus WO, which depends on the polydispersity parameter y only. This has already been recognized by Zulauf and Eicke?’ who attributed the discrepancy between the simple shell model and the experimental results to the polydispersity of the microemulsion droplets. More recently, Ricka et aLZ0 observed the same behavior for the system HzO/AOT/n-hexane, and they were able to quantitatively interpret this in the context of a polydisperse layered sphere model. The effect of the polydispersity on R h as a function of wo is shown in Figure 4. (&)z was calculated from eqs 8-10 by using a Schulz distribution and eqs 3-6 for the determination of the hydrodynamic radius. For y = 0 (monodisperse system) there is a linear dependence between Rh and W O . With increasing y , the slope of the sigmoidal curve in the vicinity of the match point increases strongly. As in the case of (Is)versus W O , the curve shape of (R& versus wo is extremely sensitive to y . Thus we can independently determine the polydispersity of AOT microemulsion droplets in different solvents from DLS measurements and compare the results with the values obtained from SLS measurements as a further test for the self-consistency of the data interpretation.
~
40
0
I
10
20
30
40
50
wo Figure 5. Experimental data points for the normalized intensity (Is) as a function of the water content w o for the systems TRIS buffer/ AOT/decane (A) and TRIS buffer/AOT/isooctane (0).Also shown are the best-fit curves corresponding to y = 0.01 for decane and y = 0.035 for isooctane.
buffer/AOT/decane microemulsions, where [TRIS] = 50 mM, pHms = 7, and [AOT] = 100 mM. Both systems exhibit a well-defined minimum of the intensity at values of wo = 30.0 f 0.5 for isooctane and w o = 17.5 =t 0.3 for decane, respectively. We can now try to analyze the experimental curves using the model of polydisperse layered spheres. Best agreement between data and theoretical curves is obtained for y = 0.035 for isooctane and y = 0.01 for decane, which leads to an intensity minimum at wo = 29.7 and wo = 17.6, respectively. The corresponding theoretical curves are also shown in Figure 5. We immediately note that the data-in particular the curve shape and the position of the match point-are very well fitted over almost 2 orders of magnitude. A further test of the thus obtained y-values can be made with the results from the dynamic light scattering measurements shown in Figure 6. Data for AOT in isooctane are shown only. As already illustrated in Figure 5, the polydispersity obtained from SLS measurements for AOT in decane is very low ( y = 0.01). Due to the small droplet size and the low polydispersity, the scattering intensity at the match point is very low, which leads to an unfavorable signal-to-noise ratio and therefore to unreliable DLS data. The theoretical curve on the basis of the layered sphere model with y = 0.035 (eq 10) is also shown in Figure 6, and excellent agreement between experimental data and theoretical values can be observed. The fact that we can obtain a self-consistent interpretation of the SLS and DLS data on the basis of the layered sphere model-both sets of data resulting from fundamentally different measurements-confirms
Christ and Schurtenberger
12712 J. Phys. Chem., Vol. 98, No. 48, 1994 120
hydrodynamic radius,
/
A&,, given by (14)
loo]
and 7
10
20
I
30
wo
40
50
Figure 6. Experimental data points (0)for the hydrodynamic radius as a function of the water content w o for the system TIUS buffer/
Rh
AOT/isooctane. Also shown is the best-fit curve corresponding to y = 0.035. 0.8-
U 0
d
-4 0
-0.2-
where “mix” and “e” stand for protein-containing and proteinfree microemulsion systems, respectively. These data can now be used to test currently existing models for the size distribution of protein-containing microemulsions. Rahaman and Hatton have recently developed a thermodynamic modelI9 for the prediction of the size of protein-containing and non-protein-containing reverse micelles as a function of system parameters such as ionic strength, protein net charge and size, protein concentration, and water content in the micellar phase. When applied to the case of a-chymotrypsin, an important result is the dominance of electrostatic proteinmicelle interactions for pH < PI, Le., positive net charge of the protein, and hence of the energetics of the filled micelles, in determining system behavior. Except at very low W O , the size of the filled micelles remains constant, while that of the empty micelles increases with increasing WO. We can now test this model using optical contrast variation. The theoretical predictions on the basis of the model by Rahaman and Hatton were calculated as follows: with the use of two assumptions, constant size (rfind % 40 8,) and single occupancy for protein-containing microemulsions, and eqs 7 and 8, the total scattered intensity of the mixture is given by
i 30
-0.4 20
40
wo
(16)
where K is a porportionality constant, and the mean value of R h , similarly obtained by using eq 10, is given by
J
-1.04
5
15
wo
25
Figure 7. Illustration of the effect of a-chymotrypsin solubilization on the hydrodynamic radius and the scattered intensity of the microemulsion droplets as a function of the water content in isooctane (A) and decane (B). Shown are the normalized differences in intensity AI (0)and in hydrodynamic radius AF& (0)between protein-containing and protein-free microemulsions. Also shown are the theoretical curves calculated on the basis of the model by Rahaman and Hatton19 with a water core radius for the filled micelles rfilled = 40 A.
the small polydispersity of the droplet radius in microemulsions as already found by Ricka et al. in their recent study of the ternary system water/AOT/n-hexane.20 As already pointed out by these authors, this is in contrast to the higher value of y obtained by several authors28,33-36 from small-angle neutron and X-ray experiments or dynamic light scattering using a secondorder cumulant analysis of the intensity autocorrelation function only. Protein-Containing Microemulsions. Parts A and B of Figure 7 show the effect of a-chymotrypsin solubilization on the size and the scattered intensity of the micelles as a function of the water content in isooctane and decane, respectively. Shown are the normalized differences in intensity, AZ, and in
where “mix,e” and “mixf’ stand for the empty and the filled reverse micelles in the protein-containing microemulsion, respectively. As expected, the A1 versus wo curve shows its maximum in the vicinity of the match point of the protein-free microemulsion for isooctane as well as for decane (see Figure 7A,B). The position of this maximum depends on the proportion of filled micelles in the mixture and on the relative position of the a(r) curves of protein-containing and protein-free microemulsion droplets (see Figure 2 ) . Figure 2 showed that the filled microemulsion droplets have a higher U-value than the proteinfree micelles and therefore dominate around the match point. Whereas AI versus wo exhibits a maximum in the vicinity of the match point, the shape of A&, versus wo is characterized by a minimum (see Figure 7A). This behavior results from a combination of two effects. First, we assume a value for the water core radius of the filled micelles (rfil1,d = 40 A) which is smaller than the radius of the empty micelles in the vicinity of the match point (see Figure 6, which leads to a variation of r from r 45 8, for wo = 25 to r 90 8, for w o = 35, using eq 5 ) . Due to the fact that in a DLS experiment the diffusion coefficients of the particles are weighted by their corresponding scattering intensities (see eqs 9 and 17), the contribution of the
Optical Contrast Variation Experiments filled micelles dominates in the vicinity of the match point, leading to a decrease of the average value of A&. Since the signal-to-noise ratio is the least favorable at the match point and the measured intensities are very low, we furthermore expect the biggest error bars in this region. For the same reasons that have already been explained above (see comments to Figure 6 ) , Figure 7B does not show the experimental h R h data for the system TRIS buffer/AOT/decane. In isooctane we see that incorporation of a-chymotrypsin has a weak effect on the measured A&, only, which is barely significant if we take into account the error bars. Although the agreement between the theoretical curve and measured points is somewhat better for h R h versus wo than for AZ versus wo (see Figure 7A), we cannot explain our measurements using the model of Rahaman and Hatton. A crucial assumption in our model calculation is the choice of a constant size of the filled droplets of rfilled = 40 A. We therefore performed a series of calculations, where we kept all the model assumptions and changed the (constant) value of the water core radius of the filled micelles only. The results of this procedure are shown in Figure 8, where r and AI versus wo are reported for isooctane and decane. Figure 8A shows that an increase of the size of the filled micelles, ?-filled, leads to a decrease of the size of the empty micelles, rempty, because of the constant interface surface and the constant total volume of the dispersed phase. However, we also see from Figure 8A that rempty is not very sensitive to the value of rfilld: an increase of 90% for rfiued results in a wo-dependent decrease for rempty of up to 20%.Figure 8B shows that for decane it is possible to fit the experimental data within the experimental uncertainties with a single parametrical curve; Le., our data at low values of wo are consistent with an approximately constant value for the size of the filled micelles, rfilled % 50 A. For lower and higher values of rfilld (rfilled = 41.3 8, and ?-filled = 53.2 A), the theoretically predicted values for AZ in the vicinity of the match point would be much too high. While for the low wo-values investigated in decane the data are consistent with a constant value of r f i e d , Figure 8C indicates that it is not possible to obtain good agreement between theoretical calculations and experimental data for a single value of rflled at the higher values of wo investigated in the isooctane samples. At wo x 25, the experimental data are consistent with rfilld % 65 A. However, Figure 8C shows that this choice of ?-filled clearly leads to an incorrect wo-dependence of AI at higher values of wo. The experimentally observed significant decrease of AI at wo 27.5 can only be achieved by assuming larger values of Ifilled. However, a choice of rfid = 75-80 A, which would be in agreement with the data at higher values of wo, leads to a very pronounced maximum around the match point, which is not consistent with the experimental data. We thus conclude that we have to allow for a wo-dependent growth of the size of the filled micelles at the higher values of wo investigated in isooctane.
J. Phys. Chem., Vol. 98, No. 48, I994 12713
Q3 20--
.'
5. Conclusion
Using static and dynamic light scattering techniques we investigated the wo-dependence of the size distribution of protein-free AOT w/o microemulsions for two different solvents. The data are quantitatively consistent with the predictions of a model of polydisperse layered spheres. Using this model, it is possible to determine the polydispersity of the microemulsion particles with very high precision because both (Is) versus wo (from SLS measurements) and Rh versus wo (from DLS measurements) depend on the polydispersity parameter y only and are very sensitive to y in the vicinity of the match point. For AOT microemulsions in isooctane and in decane, we found y = 0.035 and y = 0.01, respectively. These values are in
Figure 8. (A) Theoretical dependence of the water core radius rempq of the protein-free reverse micelles in the system TRIS buffer/AOT/ isooctane on the overall water content wg calculated on the basis of the model by Rahaman and Hattonlg using several (constant) values for the water core radius of the protein-containing reverse micelles where (- -) rf = 39.9 A, (-) rf = 65.4 A, and (-) rf = 76.1 A. (B, C) The normalized differences in intensity AI (0)are shown as a function of the water content w o for the systems TRIS buffer/AOT/ decane (B) and TRIS buffer/AOT/isooctane (C). Also shown are the predicted dependence of Al on wg calculated on the basis of the model by Rahaman and HattonI9 using several (constant) values for the water core radius of the protein reverse micelles, where in decane (B) (-) rf = 41.3 A, (-) rf = 49.8 A, and (- -) rf = 53.2 8, and in isooctane (C) (-) rf = 65 A, (- -) rf = 70 A, and (-) rf = 76 A.
12714 J. Phys. Chem., Vol. 98, No. 48, 1994
good agreement with the small value ( y = 0.014) found by Ricka et al.*O for AOT microemulsion in n-hexane. In a second step we then looked for the effect of protein addition to AOT microemulsions on the scattering intensity and the droplet size using optical contrast variation techniques. We have shown that experiments close to the optical match point allow for a very precise test of different models for the structural properties of filled and empty micelles. These experiments provide us with information over a relatively narrow range of wo-values only. However, we can shift the optical match point significantly using different solvents. For 10 5 wo 5 25 we used decane and for 20 I w o I 40 isooctane. Our light scattering experiments clearly indicate that a-chymotrypsin incorporation results in a small alteration of the micellar radius only, although the scattering intensity significantly changes due to the strong modification of the scattering profile of the reverse micelles. A first semiquantitative calculation on the basis of Figure 2 and the model by Rahaman and Hatton19 (using rfilled = 40 8, for all WO)would predict much higher effects on both the size and the scattering intensity of the reverse micelles after a-chymotrypsin uptake (see Figure 7A,B). Only for the low wo-values measured with decane was it possible to fit our (intensity) data with a constant rElled-value of rfilled x 50 A. For isooctane it was impossible to obtain a good fit with constant rfilled. Our calculations indicated a growth of &]led from rfiU.$d 5 65 A at wo 5 25 to rfilled 75-80 A at wo = 37.5. In this study the protein concentration in the water pool was kept constant (7 mg/mL). This corresponds to a wo-dependent overall concentration varying from 5 to 20 mM for wo increasing from 10 to 40. Simultaneously, the ratio of the empty to the filled micelles decreases from about 15 to 3 in isooctane (20 5 w o 5 40) and from about 100 to 10 in decane (10 Iwo I25). In a future publication we shall show the effect of an increase of the protein concentration on both the scattering intensity and the droplet size as a further important test for the self-consistency of the theoretical models. Our study shows that we can use light scattering experiments close to the optical match point as a very sensitive method in order to determine very precisely the size polydispersity of the microemulsion droplets and to quantitatively test the currently existing theoretical models for protein solubilization in microemulsions. Using the size distributions predicted by these models, we can calculate both the total scattering intensity and the z-average diffusion coefficient unambiguously from the known dielectric constants of the components.
Acknowledgment. We gratefully acknowledge fruitful discussions and continuous support from Prof. P. L. Luisi. This work was supported on part by the Swiss National Science Fundation. References and Notes (1) Leodidis,E. B.; Hatton, T. A. In Structure andReactivity of Reverse Micelles; Pileni, M. P., Ed.; Elsevier Science: Amsterdam, 1989; Vol. 65, pp 270-302.
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