J . Phys. Chem. 1990, 94, 1224-1232
7224
of the cmc and of the aggregation number is consistent with the change in the environment of the polar head. In the case of Clo(H),with respect to DTAB, the presence of the alcohol group - C H 2 0 H should render the polar head more hydrophilic, reinforce the inhibition of micellization, and thus increase the cmc and decrease the aggregation number. In C10(C2HS) the increase of hydrophilicity due to the alcohol function is compensated by the hydrophobicity of the alcohol length C2H5, which may explain the observed decrease in the cmc and increase in the aggregation number. A similar behavior (the decrease in the cmc and the change in the aggregation number) was observed in the case of the direct addition of alcohols in surfactant solutions to form mixed mic e l l e ~ . ' ~Because ,'~ there is a possibility that alcohol molecules are partitioned between the solvent and the hydrocarbon core in this procedure of alcohol addition, the explanation of these properties could not be determinate. In the present case, the incorporation of alcohol in the surfactant molecules removes this ambiguity, so that the observed behaviors can be assigned to the effect of alcohol in the polar head on the balance of hydrophil-
icity-hydrophobicity as well as on the steric hindrance.
Conclusion In this work, the micellar properties of two heteropolar surfactants, 2-(decyldimethylammonio)ethanol bromide and 24decyldimethylammonio)butanol bromide, in aqueous solutions were studied to investigate the effect of the polar head and the contribution of the alcohol functional groups to the micellization. The micelles formed have been characterized for the first time by the determination of their mass, their aggregation number, and their size. The comparison with the case of decyltrimethylammonium bromide shows that the presence of the alcohol groups in the polar head affects the cmc and the aggregation number. This is consistent with the change in the hydrophilicity-hydrophobicity balance induced by the presence of alcohol. On the other hand, the comparison between the cases where the polar heads contain ethanol or butanol clearly shows a steric effect on the micelle shape. For the same hydrocarbon chain length Clo,to a smaller polar head correspond a decrease in the aggregation number and an elongation of the micelles.
Reverse Micelles in Supercritical Fluids. 2. Fluorescence and Absorption Spectral Probes of Adjustable Aggregation in the Two-Phase Region Parvin Yazdi,t Gregory J. McFann,t Marye Anne Fox,*.t and Keith P. Johnston*-+ Departments of Chemical Engineering and Chemistry, The University of Texas, Austin, Texas 7871 2 (Received: November 9, 1989; In Final Form: April 12, 1990)
The properties of bis(2-ethylhexyl) sodium sulfosuccinate (AOT) reverse micelles and microemulsions in supercritical fluid (SCF) ethane, liquid propane, and other alkanes are reported. The microscopic environment inside the reverse micelles was investigated with the absorption probe pyridine N-oxide and the fluorescence probe 8-anilino-1-naphthalenesulfonic acid (ANS). The microscopic behavior is related directly to a macroscopic property, the water-to-surfactant ratio W,. In the one-phase region, a reverse micelle in a SCF is much like that in a liquid solvent. However, in the two-phase region, both the microscopic and macroscopic properties may be adjusted with pressure in ethane and propane, because of changes in the partitioning of the components between the phases. The large effect of pressure on W, at saturation, West, and likewise on the micelle radius, is described in terms of the repulsive solvent penetration of the surfactant tails and the attractive tailsolvent interactions.
Introduction I n a near-critical or supercritical fluid (SCF), the density and the solvent strength may be adjusted over a continuum without the need to change the solvent's molecular structure. This affords an opportunity to achieve a richer understanding of solvent effects on reverse micelles than is possible with conventional liquid solvents. The adjustable solvent strength has been used to manipulate phase behavior and ~eparations,I-~ to control reaction rate and equilibrium constants? and as a technique to study reaction mechanisms.2*5 Recently, the structure and solvent strength of pure and blended supercritical fluids have been studied with absorbance and fluorescence probes,&*as a test of Kirkwood-Buff solution t h e ~ r y . ~ , ~The , ' ~ dipolarity/polarizability (solvent strength) of fluids such as C 0 2 and ethane are low, so they are The appropriate solvents primarily for lipophilic solvent strength may be raised significantly by the addition of small amounts of liquid cosolvents (such as ethanol) in order to increase the solubilities of moderately polar substances selectively, sometimes by several hundred p e r ~ e n t . ~ . ~Even ~ . ' greater ~ increases have been obtained with complexing agents such as tri-n-butyl ph0~phate.I~The cosolvent concentration is enhanced in the local 'Department of Chemical Engineering. f Department of Chemistry.
0022-3654/90/2094-1224$02.50/0
environment of the solute, particularly in the highly compressible near-supercritical fluid region, as described both theoretically and spectros~opicaIIy.~*~J~ Semiquantitative equation of state models have been developed to predict the effect of cosolvents on solubilities.'' ( I ) Johnston, K. P., Penninger, J. M. L., Eds. Supercritical Fluid Science and Technology; ACS Symposium Series 406; Amercian Chemical Society: Washington, DC, 1989. (2) McHugh, M. A.; Krukonis, V. J. Supercritical Fluid Extraction: Principles and Practice; Butterworths: London, 1986. (3) Brennecke, J. F.; Eckert, C. A. AIChE J . 1989, 35, 1409. (4) Johnston, K. P. In ref I , p 1. ( 5 ) H r j e z , B. J.; Mehta, A. J.; Fox, M. A,; Johnston, K. P. J . Am. Chem. Soc. 1989, 11 1 , 2662. ( 6 ) Johnston, K. P.; Kim, S.; Combes, J. In ref 1, p 52. (7) Kim, S.; Johnston, K. P. AIChE J . 1988, 33, 1603. (8) Brennecke, J. F.; Eckert, C. A. In ref I , p 14. (9) Debenedetti, P. G. Chem. Engl. Sci. 1987, 42, 2203. (IO) Cochran, H. D.; Lee, L. L.; Pfund, D. M. Fluid Phase Equilib. 1987, 34, 219. ( 1 1) Johnston, K. P.; Peck, D. G.; Kim, S. Ind. Eng. Chem. Res. 1989, 28, 1115. (12) van Alsten, J. G.Ph.D. Dissertation, University of Illinois, Urbana, 1986. Dobbs, J . M.; Johnston, K. P. Ind. Eng. Chem. Res. 1987, 26, 1476. (13) Johnston, K. P.; McFann, G.J.; Peck, D. G.;Lemert, R. M. Fluid Phase Equilib. 1989, 52, 337. (14) Yonker, C . R.; Smith, R. D. J . Phys. Chem. 1988, 92. 2374.
0 1990 American Chemical Society
Reverse Micelles in Supercritical Fluids The present work examines the surfactant bis(2-ethylhexyl) sodium sulfosuccinate (AOT), which is considerably more surface active than a cosolvent such as an alcohol. In nonaqueous solvents, AOT forms thermodynamically stable reverse micelles and microemulsions in which the hydrophilic heads form a core and the lipophilic tails extend into the oil continuous phase. Reverse micelles may be formed in supercritical and compressed fluids, as discussed in a recent symposium.' For example, cytochrome c dissolves in AOT reverse micelles in ethane based on visual ob~ervation.'~The formation of small aggregates of spin-labeled cholesterol in C 0 2was discovered to be highly pressure dependent as determined with EPRI6*I7spectroscopy. Quantitative solubilities were reported for the first time that demonstrate that AOT in SCF ethane can dissolve significant amounts of hydrophilic substances such as tryptophan18 and proteins.19 There are two fundamentally different ways to investigate the properties of reverse micelles.20 In the one-phase method (also called the injection method), a known amount of aqueous solution is injected into an organic phase containing a surfactant, such that only a single phase is present. In the two-phase method (also called the interphase transfer method), an organic and an aqueous phase are equilibrated, and the compositions and the structure of one or both phases are analyzed either in situ spectroscopicallyor by sampling. This method is important for understanding the thermodynamics of partitioning, which is relevant for separation processes. With either technique, the micropolarity and microviscosity inside the reverse micelle, the micelle radius, and the solute binding may be investigated with a variety of UV-visible21 or fluorescent22probes, by NMR,23 ESRI6, and FTIRI9 spectroscopies, by conductivity and dielectric measurement^,^^ and by light-scattering measurement^.^^ Most studies of AOT reverse micelles in near-critical and supercritical fluids have focused on the one-phase technique, because the phase composition is known exactly. Dynamic light-scattering measurements were used to determine the apparent hydrodynamic diameter in ethane at high pressures, at least 5P,.26 The micropolarity in the interior of AOT reverse micelles was characterized by measuring shifts in the absorbance wavelength of thymol blue from 250 to 1300 bar26and pyridine N-oxide from 148 to 345 bar.18 By using FTIR spectroscopy, the interactions of water with other molecules in the interior of reverse micelles were studied in liquid propane at 25 "C ( T , = 96.7 " C ) from 1 to 400 bar.I9 These studies provide an important characterization of reverse micelles; however, they indicate that pressure has a small effect on micellar properties in the one-phase region at a given waterto-surfactant ratio ( W,,). In the two-phase region, a pressure variation causes large effects on the properties of AOT and also poly(ethy1ene glycol ether) reverse micelles in SCF ethane at pressures from 50 to 250 bar.18 The micropolarity inside premicellar aggregates and reverse micelles is a strong function of pressure, as judged by shifts in the observed A,, for the solvatochromic probe pyridine N-oxide. As a result, the solubility of solid tryptophan increases in this pressure regime by an order of magnitude from 120 to 200 bar. (1 5) Gale, R. S.; Fulton, J. L.; Smith, R. D. J. Am. Chem. Soc. 1987,109, 920. (16) Randolph, T. W.; Clark, D. S.; Blanch, H. W.; Prausnitz, J. M. AIChE National Meeting. Washington, DC, 1988. (17) Prausnitz, J. M.; Randolph, T. W.; Clark, D. S.; Blanch, H. W. Science 1988, 238, 387. (18) Johnston, K. P.; McFann, G. J.; Lemert, R. M. In ref 1, p 140. (19) Smith, R. D.; Fulton, J. L.; Blitz, J. P.; Tingey, J. M. J. Phys. Chem. 1990, 94, 78 1. (20) Leodidis, E. B.; Hatton, T. A. J. Phys. Chem., in press. (21) Vos, K.; Laane, C.; Visser, A. J. W. G. Photochem. Photobiol. 1987, 45, 863. ( 2 2 ) Wong, M.; Thomas, J. K.; Graetzel, M. J. Am. Chem. Soc. 1976,98, 2391. (23) Wong, M.; Thomas, J. K.; Nowak, T. J. Am. Chem. SOC.1977,99, 4730. (24) Middleton, M. A.; Schechter, R. S.; Johnston, K. P. Lungmuir 1990, 6, 920. (25) Zulauf, M.; Eicke, H. F. J. Phys. Chem. 1979, 83, 480. (26) Fulton. J. L.; Blitz, J. P.; Tingey, J. M.; Smith, R. D. J. Phys. Chem. 1989, 93,4198.
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 7225
S I
'
I
EXCITATION BEAM
SPECTROFLUOROMETEFI
CoMFWlER
Figure 1. Apparatus for fluorescence studies at elevated pressures up to 350 bar.
The present objective is to explore further the concept of manipulating the properties of reverse micelles by adjusting the pressure in the two-phase region. The Results and Discussion sections are designed to delineate clearly the differences in the micellar properties in the one-phase versus two-phase regions. We compare in a fundamental manner the properties of micelles in supercritical fluids versus conventional liquid solvents. The fluorescent solute 8-anilino- 1-naphthalenesulfonic acid (ANS) probes the degree of motion of water in the reverse micelle (which is related to the microviscosity and micropolarity),as well as W,.22 It does not fluoresce in hydrocarbons, so the presence of emission is unequivocal evidence that ANS is in a micellar environment. The micropolarity is also described by new solvatochromic shift data for the UV-visible absorbance probe pyridine N-oxide, which supplement previous data.18 These spectroscopic probes provide a useful description of the microscopic environments that would be encountered by a hydrophilic solute such as a protein. The effect of pressure on the microscopic environment and on WTt will be compared. This study of the pressure efects on reverse micelles provides a basis for part 3 of this series, which considers the partitioning of amino acids between AOT reverse micelles in propane and a bulk aqueous phase.27 This complements previous studies, as the AOT concentration is reported in both phases. In regions where is variable, it is possible to solubilize hydrophiles selectively into reverse micelles and then to recover solvent-free product simply by manipulating the pressure. This influences protein conformation and partitioning, which is relevant for separation processes28and for enzymatic reactions29 in reverse micelles.
Wzt
Experimental Section AOT was obtained from Fluka (98%) and was purified according to a well-accepted technique.30 It was dried under vacuum (27) Lemert, R. M.; Fuller, R. A.; Johnston, K. P. J. Phys. Chem., 1990, 94, 6021. (28) Goeklin, K. E.; Hatton, T. A. Sep. Sci. Technol. 1987, 22, 831. (29) Luisi, P. L. Angew. Chem., Int. Ed. Engl. 1985, 24, 439. (30) Kotlarchyk, M.; Chen, S. W.; Huang, J. S.; Kim, M. W. Phys. Reu. A 1984, 29, 2054.
1226
Yazdi et al.
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990
at 40 OC for 15 h and stored in a desiccator. Even though it is likely that one water molecule is still bound to each AOT molecule after purification, we will refer to this condition as W, = 0. ANS (Aldrich, 97%) was used as received. Deionized water was obtained from a Millipore Milli-Q reagent-water system. The ethane (Big 3,99%) and propane (Liquid Carbonic, 99.5%) were purified with activated carbon. The fluorescence of the pure fluids was negligible. The high-pressure fluorescence experiments were conducted in a 3-in. cubic stainless steel cell mounted on an adjustable stage, which provided for precise alignment and reproducible spectra (see Figure I ) . A 5/,-in. (diameter) by i/lo-in.(thick) sapphire window was inserted into each of the four 5/i6-in. channels, and a seal was made with a Teflon O-ring. Two 1/4-in. cartridge heaters, a platinum resistance thermometer, and an Omega RTD temperature controller were used to maintain the cell temperature to within f 0 . I OC. Solutions of AOT and A N S in a volatile solvent were loaded into the cell. The solvents were evaporated, and the cell was evacuated for 1 h to remove trace residues. The cell was filled with argon, then a known amount of water was introduced quickly, and the closure was sealed to avoid oxygen contamination. The S C F was added to the cell with a 60-mL syringe pump (High Pressure Equipment Co.), and the pressure was measured to f0.2 bar with a digital pressure gauge (Heise). Experiments were always performed in the order of increasing pressure so that the molar concentration of the solutes was constant, and the valve between the pump and the cell was closed after setting each pressure. The solution was agitated with a 2-mm (diameter) by 7-mm (long) stir bar that was moved outside of the light path during excitation. After mixing, 15 min was allowed for the two phases, if present, to separate. I n control experiments, spectra did not change after 15 min in either the one-phase region or the two-phase region. The emission spectra were measured on an SLM-AMINCO SPF-500 C spectrofluorometer equipped with a Packard-Bell computer interface. No additional filters were used. For experiments in the two-phase region, the excitation beam passed through the fluid phase alone and did not contact the small amount of surfactant-rich phase on the bottom of the cell. The excitation wavelength was 380 nm, and the excitation and emission bandwidths were 2 and 1 nm, respectively. The bandwidths were doubled for the series of propane spectra in the two-phase region due to the large degree of quenching. The spectra were smoothed with 99 smoothing passes. A Savitzky-Golay algorithm3' was used to differentiate the smoothed data in order to determine the fluorescence maximum. The reproducibility was f 1 nm. The solvatochromic shifts for pyridine N-oxide were determined in a 2-mL high-pressure UV cell with a Cary (Varian) 2290 spectrophotometer as described previously.I8 The cell was removed periodically and examined to ensure that there was no cloudiness in the SCF phase or deposits on the windows. The typical uncertainty in A,, was f0.2 nm. For absorbances less than 0.75 au, the uncertainty was f I nm due to the influence of the baseline. Was' was determined by the synthetic method in a variable-volume W:,, is defined as the maximum W, at a phase view boundary, which is an end point on a tie line (or tie triangle for three-phase equilibria). At a given temperature and composition, the pressure was lowered until the solution turned cloudy and the liquid precipitated at the retrograde dew point. The reported pressure is the average between the dew point and the point where the last drop of liquid solution dissolves upon pressurization. These pressures differed by less than 2 bar. Results Nature of Reoerse Micelles in the One-Phase Region. The degree of aggregation of AOT may be determined with the solvatochromic probe pyridine N-oxide, a blue-shift indicator. A, is shown as a function of AOT concentration for the solvents (31) Savitzky, A.; Golay, M. J . E. Anal. Chem. 1964, 36, 1627. (32) Fulton. J . L.; Smith, R. D.J . Phys. Chem. 1988, 92, 2903.
1
t
x 0
.
0
mm
m
P-345bar wO-o
~m
A
I
0
""yo
1
10
10
10'
[AOT] (moleiL)
Figure 2. Aggregation of AOT in ethane and cyclohexane without added water as indicated by A, of pyridine N-oxide at 345 bar in the one-phase region. So -S
1.np
I
i
h V F np
__ S I.ct-So
c _
I
hvF
a
Figure 3. Photophysics of 8-anilino-l -naphthalenesulfonicacid.
cyclohexane and supercritical ethane in the one-phase region without added water in Figure 2.18 For an AOT concentration (polarity) indicates that the probe is in a below 0.5 mM, A, nonpolar alkane-rich environment. Aggregation becomes prevalent at a concentration of about 0.002 M AOT and is essentially fully developed at 0.01 M. The values of A,, are equivalent for the liquid and supercritical fluid solvent in this one-phase region. On the basis of these results, the fluorescence experiments were performed at an AOT concentration of 0.01 M, where aggregation is prevalent. The photophysics of (pheny1amino)naphthalenesulfonates (such as ANS) has been studied e x t e n ~ i v e l y . The ~ ~ nonpolar ground state is excited to which undergoes intramolecular electron transfer to a charge-transfer state, SI,ctras shown in Figure 3. These states were assigned from the well-known observation that solvent polarity and substituent effects are small for Si,np and large for Si,c,. The electron transfer to Si,ctis favored by an increase for emission to in solvent dielectric relaxation, which causes A, undergo a shift to longer wavelengths (red shift). The dielectric relaxation is correlated with the polarity of the solvent.33 Emission from the state is quenched by nonradiative electron transfer; thus the quantum yield decreases with a decrease in the viscosity of the media. Since both the electron-transfer reactions, to to So,np,are accelerated by an increase in solvent and relaxation (polarity), the quantum yield becomes very small and the red shift very large in pure water. ANS has been used to study the water core of reverse micelles.22 I t is a very sensitive probe of the rotational relaxation and concentration of water in reverse micelles, both in terms of the emission intensity and the wavelength. For a given W,, the intensity increases as the temperature decreases from 53 to -31 "C, which is consistent with the decrease in the rotational motion of water as icelike structures are formed. Although the probe itself can have a small influence on aggregation, this decreases as W, increases. In order to calibrate A N S as a probe over the desired range in W, and AOT concentrations, a series of spectra were obtained in n-hexane in a standard 1-cm cuvette as shown in Figure 4. These experiments were performed in the one-phase region. The increase in the red shift with W, is in quantitative agreement with the results of Wong et a1.22 The first few added water molecules are tightly bound by the ionic headgroups. As W, increases, the water molecules rotate more freely and contribute more effectively charge transfer and to the radiationless to the Si,np to deactivation of S,,c,. The increase in the accessibility of water (33) Kosower, E. M.; Kanety, H.; Dodiuk, H.; Striker, G.; Jovin, T.; Boni, H.;Huppert, D.J . A m . Chem. SOC.1983.87, 2419.
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 1227
Reverse Micelles in Supercritical Fluids
500
1
r-----l
.I
propane, 07M AOT 2 5 ~
- I
0
:0
Z 40
0
0
(AOT]=0005 M [AOT]-O01 M
W
460
440
A
'
0
(AOT]=O068M
I 10
20
30
wo
Figure 4. Emission maximum of A N S (4 X lo4 M) for A O T reverse micelles in n-hexane at 25 OC and 1 bar for an excitation wavelength of 380 nm.
P = 278 bar
WO.0
T
3.0-
25%
3
C
.-fn0 .-fn
E'
W
400
500
Emission Wavelength
400
600
500
Emission Wavelength
(nm)
Figure 5. Emission spectra of ANS in AOT'reverse micelles in ethane without added water (the system becomes one phase for P > 148 bar).
to these two electron-transfer processes may be thought of as an increase in the micropolarity and a decrease in the microviscosity. As a result, the fluorescence maximum undergoes a red shift, and the fluorescence quantum yield is greatly reduced. The probe is extremely sensitive to W, for W, I6 and becomes less sensitive at higher values where the water is more weakly bound, in accordance with studies of AOT that used other techn i q u e ~ . ' ~Another ~ ~ ~ *important ~ ~ ~ ~observation ~ is that even at a W, of 30, the water does not appear to become totally free as the fluorescence maximum is 510 nm in pure water.22 However, some of the A N S molecules could be near the palisade region where water is bound to the surfactant headgroups. Not only is the probe sensitive to W, but the fluorescence maximum is independent of AOT concentration. This is very useful for experiments in the two-phase region, as the AOT concentrations in the individual phases may be unknown. A series of ANS fluorescence spectra were measured for AOT at 0.01 M in liquid propane ( T , = 96.7 O C , P, = 42.4 bar) at 25 OC without any added water from 16 to 278 bar. Even at the lowest pressure, all of the AOT is a soluble at 0.01 M, based on an independent measurement in the variable-volume view cell and on previous results.35 Because water was not added, the conversion to SI.,,is relatively small, and thus the red shift is small (fluorescence maximum = 450 nm) and essentially constant over the entire pressure range. There is a small but measurable increase in the emission intensity with pressure. A possible explanation is that the propane penetrates the polar core to a greater degree as the pressure increases. This would lower the polarity of the (34) Eicke, H. F.; Kvita, P. In Reuerse Micelles; Luisi, P. L., Straub, B. E., Eds.; Plenum: New York, 1984. (35) Smith, R.D.; Fulton, J. L.; Jones, H. K.; Gale, R. W.; Wright, B. W. J. Chromarogr. Sci. 1989, 27, 309.
600
(nm)
Figure 7. Emission spectra of ANS in AOT reverse micelles in propane at 25 "C in the one-phase region a t 278 bar and various W,.
medium slightly in the vicinity of ANS, which would increase the intensity. It would also shift the fluorescence maximum but to a degree that is too small to be observed. This intensity changed about the same amount with pressure for AOT in propane with added water for W, = 2 and IO in the one-phase region. In Figure 5, spectra are presented as a function of pressure for the same AOT and A N S concentrations in supercritical ethane at 37 OC ( T , = 32.3 OC, P, = 48.8 bar), again for W, = 0. The situation is more complex than for propane since AOT is less soluble. According to measurements with the variable-volume view cell, the system contains only one phase at pressures above 150 bar. In the one-phase region, the fluorescence maximum is 452 nm, which is indicative of a micellar environment without added water. The intensity increases slightly from 166 to 276 bar, which again may be due to increased solvent penetration of the aggregates. The size of reverse micellar aggregates grows considerably with the addition of water.34 In order to understand this observation, we analyze both phase behavior and spectroscopic data. In Figure 6, Womtis plotted versus pressure for 0.01 M AOT in supercritical ethane at 37 OC and 0.07 M AOT in liquid propane at 25 "C. is the ratio of water to surfactant at the For each pressure, WOmt phase boundary. The results are very similar to previous ones.35 As the density of the fluid increases, WOa1always increases over this range. The much larger values of W,Sat in propane versus ethane are striking and cannot be explained by the temperature difference alone, as will be explained in the Discussion section. The effect of water on ANS fluorescence in reverse micelles of AOT in liquid propane is presented in Figure 7 at 278 bar and 25 OC. All of these propane data are in the one-phase region. Analogous spectra were also obtained in S C F ethane at 37 OC. At this pressure, the ethane data were in the one-phase region based on Figure 6 only up to W, = 4, which is near the phase boundary. In both solvents, the red shift increases and the intensity decreases with Wo. Because these spectra are well-behaved, it is useful to examine the spectral shifts and the integrated intensities in greater detail.
7228 The Journal of Physical Chemistry, Vol. 94, No. 18, I990
Yazdi et al.
i P
.-2 ,"
x
1 I
!'ooob I
'-
500
E
Propane
1
E'hane
0)
m C
;
1
s
zL00
10
20
30
40
50
Figure 8. Degree of water motion about A N S as described by emission intensity in reverse micelles of AOT (0.01 M) in liquid propane at 25 O C and SCF ethane a t 37 O C , both at 278 bar in the one-phase region.
i
480
Ethane
10
'
2'0
,
~,
,
,
,
b
H
WO.0
-:
WO-4
1 0 0 2 0 0 3 0 0 400 Pressure(bar)
500
E c C
c Y)
'
,
5
s
440d
2600
,
,
ai
wo
2
2701
265
A
Propane
0
Hexane
3'0
4'0
.
'
wo Figure 9. Degree of water motion about A N S as described by the emission maximum in reverse micelles of AOT (0.01 M) in propane at 25 OC. 278 bar, S C F ethane at 37 "C, 278 bar, and hexane at 25 OC, I bar. All data are in the one-phase region.
The emission intensities for ANS in ethane and propane were integrated from 392 to 650 nm and are plotted in Figure 8. At a given W,, the results are similar, which suggests that the continuous phase does not influence the degree of motion of water (microviscosity or polarity) significantly, as might be expected, since the water pool is shielded from the solvent by the surfactant interface. There is an enormous change in the intensities at low values of W,, which becomes progressively smaller as the water becomes less strongly bound, as was also observed for n-hexane. The probe is highly useful in that it is sensitive to each increment of water at low values of W,, yet it can also be used to measure changes at high Wo's. A summary of the results for the fluorescence maximum in the one-phase region is presented in Figure 9. The important conclusion is that for a given W, there are no significant differences in the water environment surrounding A N S in AOT reverse micelles for the continuous phases liquid hexane at 1 bar and liquid propane and S C F ethane at 278 bar. For W, below 6, the values of the fluorescence maximum indicate that the water is tightly bound but rotates much more freely at higher W,. Even at a W, of 40, the water is not totally free, as the fluorescence maximum is 510 nm in pure water. The same trends are observed as a function of W, for the integrated intensities, as both properties are influenced by the degree of water motion in accordance with the mechanism in Figure 3. The fluorescence maximum for ANS is influenced very little by pressure, AOT concentration, and the nature of the hydrocarbon in the one-phase region. However, the fluorescence maximum varies significantly as a function of W, over a wide range, particularly for small values of W,. Therefore, ANS will be a very useful probe for measuring W, in situ in the two-phase region. Adjustability of Aggregation of Reverse Micelles in the Two-Phase Region. I n this section, we explore both the macro-
2651,
,
;F,:D
-,
,".
,=, , ,
WO.8
260 0
200 300 400 Pressure (bar)
100
j; 500
Figure 10. A, of pyridine N-oxide in supercritical ethane at 37 OC. A one-phase solution is obtained for pressures above 148, 183, and 255 bar for W, = 0, 2, and 4, respectively. Two phases are present at all pressures for W, = 8.
scopic and microscopic properties of reverse micelles in the two-phase region. The combination of intensity and solvatochromic shift data for the probes ANS and pyridine N-oxide, along with phase behavior measurements, will be used to achieve a better fundamental understanding of micellization in supercritical fluids. In the two-phase region, the components partition between the liquid phase, which is often aqueous, and the fluid phase. Data from the well-defined one-phase region will provide an important basis for calibrating and interpreting the data in the two-phase region. We begin by considering AOT in systems without added water. As shown in Figure 5, the emission intensity of A N S in AOT reverse micelles in ethane increases rapidly with pressure from 103 to 148 bar, where the system becomes one phase. This reflects the increasing solubilization of AOT into the fluid phase, which provides an environment for ANS to dissolve and fluoresce. Above 167 bar, there is only a small change in intensity because the system is in the one-phase region. The change in the fluorescence maximum is less than 1 nm over the entire pressure range, since no water was added. Similar conditions were studied with the UV-visible solvatochromic probe pyridine N-oxide as shown for W, = 0 in Figure 10. From 61 to 103 bar, , , A is shifted relatively little compared to its value of 281 nm in pure ethane, and the absorption intensity is low. This suggests that the fluid phase is composed only of "premicellar aggregates" such as are seen in liquid solvents at low surfactant level^.^^.^^ Above 103 bar,, , ,A changes significantly, until 148 bar where the system becomes one phase (see Figure 6). In this region, the concentration of AOT in the fluid phase is sufficient for micelles to form. Absorbance increases rapidly above this concentration, as pyridine N-oxide partitions into the micelles. The same result was observed for the ANS emission becomes relatively intensity in Figure 5. At higher pressures, ,A, constant, which again is consistent with the plateau in A N S emission intensity. The change in intensity in the two-phase region, which is due to partitioning of AOT, is much larger than the slight change in the one-phase region. Shifts in, , ,A are measurable for pyridine N-oxide but not in the fluorescence maximum for A N S in AOT in the two-phase region without added water. Pyridine N-oxide is highly basic, and A, can be influenced significantly by interactions with the (36) Eicke, H. F.; Hopman, R. F. W.; Christen, H. Eer. Eunsenges. Phys. Chem. 1975, 79, 667. ( 3 7 ) Ruckenstein, E.; Nagarajan, R. J . Phys. Chem. 1980, 84, 1349.
T e 3fC
W0.40
0
-+
t
.-E Y
-
i
W0.lO
0
173 145 135
Emission Wavelength
(nm)
Figure 11. Emission spectra of ANS in AOT reverse micelles in ethane at 37 OC in the two-phase region for an overall loading of W, = 3. 478'".'
" " " ,
'
0
476
0
--E 1
:I
7
.
w0.3
=I
474
f i r 3 4 6
bar
=
1 .66 5
5 2
2 472
a
0
P)
c
E
g
e P -.33 8
91 0
5 bar
I
4661 46fd0 ' 1 5 0 ' ' 2 0 0 ' ' 2 5 0 ' ' 3 0 0
3O :
Pressure (bar)
Figure 12. Degree of water motion about ANS as described by the emission maximum for AOT (0.01 M) reverse micelles in ethane at 37 "C in the two-phase region for an overall loading of W, = 3.
ionic headgroups in AOT. The strength of these interactions could be affected strongly by changes in the aggregation number, which influence the rigidity and curvature of the interface and the orientation of the pyridine N-oxide molecules. In micelles with added water, pyridine N-oxide is affected less by interactions with the interface, since it is highly hydrophilic and tends to partition toward the water pool.'* The mechanisms are very different for the shifts in spectroscopic properties for pyridine N-oxide and ANS. While ANS provides a quantitative in situ measure of W, as demonstrated above, pyridine N-oxide does not. The emission of A N S is affected much more by water than by surfactant headgroups, while the absorbance of pyridine N-oxide is influenced to a large degree by both. The addition of water to the AOT solutions provides a means to achieve much more polar micellar environments and thus larger adjustability with pressure, as shown in Figure 1 1 . The fluorescence cell was loaded with 0.01 M AOT and a W, of 3 at atmospheric pressure, and ethane was added in increments to achieve various pressures. According to the phase behavior measurements in Figure 6, only part of the water dissolves at the lower pressures and all of it is soluble at 214 bar. It is clear from the emission intensity in Figure 1 1 that the ANS concentration increases rapidly with pressure, particularly above 173 bar. The AOT partitions between the small volume of aqueous phase and the SCF phase, such that its concentration in the S C F phase increases with pressure. This increases the A N S concentration and the emission intensity, which eventually reaches an asymptote at about 220 bar, the point where all of the aqueous phase is solubilized. The quenching of the emission by the water is small compared to the large increase in emission due to A N S solubilization. The fluorescence maximum is sensitive to pressure as shown in Figure 12. As pressure increases from 124 to 280 bar, the red shift and thus the degree of water motion increases as W, increases. This means that the micropolarity increases and the
1 0 $40
260
280
300
320
Wavelength (nm)
Figure 14. Absorption spectra of pyridine N-oxide for AOT (0.01 M) reverse micelles in ethane at 37 O C in the one- and two-phase regions ( W, = 4).
microviscosity decreases as the water pool grows. For reference, W, is indicated for two values of the fluorescence maximum based on the calibration in the one-phase region, which is given in Figure 9. At the highest pressure where only one phase is present it is known that W, = 3 based on the initial concentrations loaded into the cell. This is in agreement with the calibrated value. At lower pressures, the fluorescence maximum provides an in situ measure of W, in the fluid phase, even though the AOT concentration changes. Recall that the fluorescence maximum was shown to be independent of AOT concentration in Figure 4. In the region where water is tightly bound, ANS is able to sense the change in the water motion, even for very small changes in W,. Between 466 and 476 nm, the values of the fluorescence maximum correspond to noninteger values of W,. For liquid propane at 25 OC, there is an enormous pressure effect on the fluorescence maximum of ANS in reverse micelles of AOT as shown in Figure 13. A W, of 40 was loaded into the cell, and the water was fully dissolved at 200 bar. Reference values of W, are listed based on the calibration in Figure 9. At 15 bar, the fluorescence maximum indicates that W, in the fluid phase is only 10 and changes very rapidly with pressure. Here the fluorescence intensity is sufficiently large that there is still a significant concentration of AQT in the fluid phase. These microscopic measurements indicate that the degree of water motion (micropolarity and microviscosity) varies over a wide range in propane, which is consistent with the large variation in W,. The differences in the one-phase and two-phase regions are also very clear in the solvatochromic data for pyridine N-oxide as shown in Figure 14 for a W, of 4. At low pressures, only a small amount of the probe partitions into the fluid phase and the absorbance is low. The difference in the spectra at 85 and 92 bar is within experimental error given the very low absorbance on the order of 0.1 au. The peaks are relatively broad, which is consistent with the large polydispersity that is expected for premicellar aggre-
7230 The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 TABLE I: Pressure Effects in the One-Phase and Two-Phase Regions for Various Macroscopic and Microscopic Properties of AOT Reverse Micelles in Near-Critical and Supercritical Fluids pressure effect onetwophase phase property fluid T, 'C region region ref WOW' ethane 37 na" large 32, this work propane 25 na large 19, this work ethane 37 small see text 45 app hydropropane 25 small see text 45 dynamic radius ethane 37 small large 18, this work A,, of pyridine N-oxide solubility of ethane 37 small large 18 tryptophan propane 25 small not FTlR spectra of 19 water studied A,, of thymol blue ethane 25, 37 small not 26 studied emission max of ethane 37 small large this work ANS propane 25 small large this work 37 small large this work emission intensity of ethane small large this work ANS propane 25 "Not applicable.
gates.38 The broad distribution of aggregate sizes provides a wide variety of environments for the probe, including the continuous solvent, which is indicated by the large peak width. The interaction between the probe and various environments in the fluid phase may be described by a multiple-equilibria mechanism. As pressure increases from 102 to 150 bar, the surfactant becomes more soluble and forms micelles, as is evident from the large increase in the absorbance. This influence of pressure on the partitioning of AOT was also evident in the emission spectra of ANS based on the above discussion of Figures 5 and 1 I . This observation of a pressure effect on the distribution of AOT as well as water is extremely important. For example, this pressure effect may be used to manipulate the solubilization of amino acids in reverse micelles.27 In Figure 14, the peak width to peak height ratio decreases with pressure, which suggests that the polydispersity decreases as the reverse micelles become more fully developed, decreases sharply in accordance with theory.38 In this region, ,A, as water solubilization increases and more polar environments become available to the probe. Because pyridine N-oxide is a very small and hydrophilic probe, it is attracted preferentially toward the most polar environments. At higher pressures, the system reaches the one-phase region based on the asymptote in the absorbance as well as the independently measured value of WoWt(see Figure 6 ) . In the one-phase region, pressure effects are small, as is also the case for the probe ANS.
Discussion Pressure and Solvent Effects in the One-Phase Region. The formation of reverse micelles is favored by polar and ionic headgroup interactions and opposed by repulsion between the tail^.^^,^^ AOT is particularly well suited for forming reverse micelles because its twin tails and short side chains allows it to assume the shape of a truncated cone.34J9 This gives it an extremely favorable "packing ratio".40 For AOT without added, water, the aggregation number is relatively small: for example, it is 22 f 2 in decane and does not change much from one solvent to a n ~ t h e r . ~In~systems ~ ~ ' ~with ~ ~ added water, the micelle radius R is related directly to W, by the expression W, = Z R / ( 3 v W )- v , / v , where Z: is the external interfacial area per surfactant molecule
Yazdi et al.
60
I
c7
A C8
i
i
Solvent Density (gicc) Figure 15. Woa' versus solution density in various supercritical fluid and liquid solvents a s 25 OC ((m) this work; (0)ref 48; (A)ref 44).
and us and u, are the surfactant and water molecular volumes. It has been observed43 for a variety of solvents that R, = 1.75W0 15 (2) where Rh is the hydrodynamic radius in angstroms. The measurement of W, is a convenient method to determine the micelle size. Since Woa' is solvent" and pressure dependent, the micelle size is likewise adjustable with these variables. A summary of the pressure effects on the properties of reverse micelles of AOT in liquid propane and supercritical fluid ethane is presented in Table I. The table shows clear differences in pressure effects for the one- and two-phase regions. Obviously W, is fixed in a one-phase system, so it is not possible to have a pressure effect on W,. For the other seven techniques, the effect of pressure is small for a given W, in the one-phase region. This result was already known from previous studies and is confirmed with the new ANS and pyridine N-oxide data. According to these spectroscopic studies, there is little change in the micellar environments for the solvents SCF ethane, liquid propane, and other liquid alkanes. Specifically, there are no significant differences in the polarities inside the reverse micelles, the water environment, micellar size, and the degree of water motion, again for a given W,. These results are consistent with eq 2, since W, fixes the micelle radius. A property that is solvent dependent is the diffusion coefficient of AOT reverse micelles, as measured by dynamic light scattering.45 It is 10 times greater for AOT micelles in dense ethane than in isooctane, which could allow much shorter contacting times and faster settling rates in supercritical separations. The diffusion coefficient provides insight into the changes that occur in the transition between the one-phase and two-phase regions. In the one-phase region well away from the phase boundary, the Stokes-Einstein relationship may be used to determine the hydrodynamic radius for spherical micelles from the diffusion coefficient. As pressure decreases toward the phase boundary, the diffusion coefficient decreases. This is due to interactions between the micelles46and to fluctuations in the curvature of the interface.47 In this region, the apparent hydrodynamic radius, which is calculated from the Stokes-Einstein equation by assuming noninteracting spheres, is difficult to interpret. Because of these complications, it is helpful to use a variety of techniques in order to interpret pressure effects on micellar properties, particularly in the two-phase region. Pressure and Solvent Effects i n the Two-Phase Region. As shown in Table I , the pressure effects are large in the two-phase
+
(38) Borkovec, M.; Eicke, H. F.; Ricka, J. J . Colloid Interface Sci. 1989, 131. 366.
(39) Maitra, A. M.; Patanjali, P. K. In Surfactanfs in Solution; Mittal, K. L., Bothorel, P.. Eds.; Plenum: New York, 1986; Vol. 5, p 581. (40) Mitchell. D. J.; Ninham, B. W. J . Cbem. SOC.,Faraday Trans. 2 1981. 77, 601.
(41) Peri, J . B. J . Colloid InterfaceSci. 1969, 29. 6. (42) Kotlarchyk, M.; Huang. J. S. J . Pbys. Cbem. 1985, 89, 4382.
(43) Fletcher, P. D. 1. J . Cbem. SOC.,Faraday Trans. I 1986, 82, 2651. (44) Hou, D. J.; Shah, D. 0. Langmuir 1987, 3, 1086. (45) Smith, R.D.; Blitz, J . P.; Fulton, J . L. In ref 1, p 165. (46) Roux, D.; Belloq, A. M.; Bothorel, In Surfactants in Solution Mittal, K. L., Lindmann, B., Eds.; Plenum: New York, 1984; Vol. 3, p 1843. (47) Bourrel, M.; Schechter, R.S. Microemulsions and Related Systems; Surfactant Science Series 30; Marcel Dekker: New York,1988.
Reverse Micelles in Supercritical Fluids
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 7231
region in contrast with the small effect observed in previous studies in the one-phase region. The large pressure effects on the spectral properties of pyridine N-oxide and A N S indicate large changes in polarity inside the AOT reverse micelles and in the degree of water motion. This adjustability occurs only in the two-phase liquid-fluid region where there are changes in the partitioning of water and surfactant with pressure. The adjustability in the microscopic properties is a direct consequence of the adjustability of W T l , which again is a measure of the drop size. In Figure 15, the maximum water-to-surfactant ratio W,Sal is plotted versus solvent density for various alkanes. For pentane through decane, experiments were conducted only at atmospheric pressure. In previous studies, a maximum in WOmtwas observed in heptaneMand octane24for AOT concentrations of approximately 0.42 and 0.17 M, respectively. This local maximum is also found in the present study. For ethane and propane, pressure has a large effect on W,Sat. It was found that there is an increase in WTt as the solvent is changed from pentane at atmospheric pressure to propane at high pressure. This suggests that a second maximum is present in the density plot, which has not been reported previously. In the experiments at atmospheric pressure, 24 h or more was required for the lower phase to appear in some cases, e&, for hexane. Otherwise, it may appear that a given amount of water is soluble, when the system is actually in the two phase region. This is a possibility for the ethane and propane data since the equilibration time was typically about 30 min. The conductivity of the lower phase is much lower than that of water, and it has been suggested that it may be oil continuowa This could explain the slow kinetics for formation of the lower phase. The effect of the molar volume of the oil (solvent) on Woml has been described for AOT reverse micelles in a series of liquid alkanes at atmospheric pressuresu For the alkanes from pentane to heptane, W T t increases with u, as the oil penetrates the tails less effectively. A decrease in solvent penetration of the tails causes a decrease in interfacial curvature and thus an increase in W,Sat. We call this effect "repulsive penetration" of the tails, as this repulsive force bends the interface around water. Evidence for this concept is that a relatively large solvent such as decane only penetrates the AOT tails to a distance of 2.4 A, compared with a tail length of 8 A.42 For propane, we have shown that WOwt increases with an increase in pressure, or a decrease in u,. This effect of u, is opposite of that which is observed for the above alkane solvents. This suggests that other types of solvent effects must be present for propane, in addition to the repulsive penetration effect. Another property that influences W,Sat is intermicellar interactions. For higher molecular weight alkanes such as decane, the solvent is sufficiently large that it penetrates the tails poorly and For very is not effective in shielding intermicellar small alkanes such as ethane and propane, it is likely that W p t may also be influenced by intermicellar interaction^.^^ We propose that a third factor influences W,Sa' in addition to repulsive penetration of the tails and intermicellar interactions. It is the attractive interaction between the oil and the tails of the surfactant, which may be described qualitatively by regular solution theory. The free energy of mixing the oil and surfactant tails is related to the square of the difference of their solubility parameters. When their solubility parameters are the same, solvation of the tails is most favorable. I n Figure 16, W T t is plotted versus 6o for AOT in a series of supercritical fluid and liquid solvents. The cohesive energy density of propane is lower than that of an ethylhexyl AOT tail, especially at the lower pressures. Therefore, as the pressure is increased, the attractive interaction between the tails and the propane becomes more favorable, which would stabilize the reverse micelles and increase WOmt.As 6,, becomes closest to that of the tails, the attractive solvent-tail interaction is optimized. On the other side of the maximum where h0 is too large (for octane through decane), (48) Tingey, J. M.; Fulton, J. L.; Smith, R. D. J . Phys. Chem. 1990, 94, 1991,
c7
A C8
60.
."9
1
01 r 9 m 11 12
e "
SOL
" " " " " "
13
14
Parameter
15
16
17
(~/cc)"'
Figure 16. Effect of solvent-surfactant tail attractive forces on Woa' at 25 OC ((m) this work; (0)ref 48;(A) ref 44; solubility parameters for C2-C4, ref SO, for C5-CIo,ref SI).
Womtdecreases with bo. The interesting feature of a supercritical fluid is that h0 may be adjusted with pressure to manipulate the interactions between the tail and solvent. Again, the other contributions, repulsive penetration of the tails and intermicellar interactions, also influence W,Sa', given the somewhat complex shape of the solubility parameter plot. This analysis may be used to suggest reasons for the difficulty in forming AOT reverse micelles in C02.49 The solubility parameter of supercritical CO, can be adjusted with pressure to cover the entire range of Figure 16." Consequently, the attractive interactions between C 0 2and the tails should be sufficiently strong to stabilize reverse micelles. The large quadrupole moment and acidity of C 0 2may lower the activity of AOT in the liquid phase, thus limiting its solubility. Another possibility is that C 0 2 ,which is small and linear, can penetrate the surfactant tails and curve the interface to the point where micelles are not formed. Conclusions
In the one-phase region, there is no significant difference in the polarity and degree of water motion in AOT reverse micelles in liquid versus supercritical fluid solvents at a given W,. Here the polarities inside the reverse micelle and the micelle radius are relatively pressure independent as seen previously. Not only does the probe A N S provide a means to explore the motion of water inside the reverse micelle but it also provides an in situ measurement of W,. The degree of water motion (micropolarity) increases directly as a function of W,, particularly for small values of W, (below 6) where water hydrates the cations. In the twomay phase region, the polarity, degree of water motion, and WOa1 be adjusted over a wide range with pressure because of the changes in partitioning of surfactant and water. This adjustability is prevalent for ethane and propane but becomes small for dense liquids such as octane. The effect of pressure and solvent on WOmtis due to repulsive solvent penetration of the tails, intermicellar interactions, and solvent-tail attractive interactions. For ethane and propane up to 300 bar, the increase in the solubility parameter with pressure strengthens the solvent-tail attractive interactions, which contributes to the increase in micelle radius. This solvation of the tails influences the solubility of the surfactant, the curvature of the micellar interface, and the intermicellar interactions. TO further understand these effects, the next paper in this series explores in detail the partitioning of surfactant and water between the fluid and aqueous phases2' It is likely that studies with compressed and supercritical fluids will continue to aid the understanding of solvent effects on reverse micelles, since it is possible (49) Oates, J. Ph.D. Dissertation, The University of Texas, Austin, 1988. (50) Younglove, B. A.; Ely, J. F. J . Phys. Chem. ReJ Dara 1987, 16, 77. ( 5 1 ) Barton, A. F. M . Handbook of Solubility Parameters and Other Cohesion Parameters; CRC Press: Boca Raton, FL, 1983.
J . Phys. Chem. 1990, 94, 1232-1239
7232
to change the solvent's cohesive energy density without changing its molecular structure. Acknowledgment. This material is based on work supported by the National Science Foundation under Grants CTS-8900819 and CHE-85093 14. Any opinions, findings, and conclusions or recommendations expressed in this publication do not necessarily reflect the views of the National Science Foundation. Ac-
knowledgment is made to the State of Texas Energy Research in Applications Program, the Texas Advanced Research Program, the Camille and Henry Dreyfus Foundation for a Teacher-Scholar Grant (to K.P.J.), and the Separations Research Program at the University of Texas. We thank Bob Schechter for many helpful discussions, Caron Arnold for assistance in the laboratory, and Alan Hatton and Richard Smith for providing manuscripts prior to publication.
Coalescence and SolubNizate Exchange in a Cationic Four-Component Reversed Micellar System Andreas S. Bommarius,+Josef F. Holzwarth,t Daniel I. C. Wang,+ and T. Alan Hatton*,+ Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, and Fritz Haber-lnstitut der Max-Planck Gesellschafi, Faradayweg 4-6. 1000 Berlin 33, West Germany (Received: November IO, 1989; In Final Form: March 12, 1990)
Molecules solubilized in the water pools of reversed micelles are redistributed over the micelles when they coalesce to form temporary dimers before breaking apart again. The rates of this solubilizate exchange have been determined for the four-component system dodecyltrimethylammonium chloride (DTAC)/ hexanolln-heptanelwater by following suitable electron transfer indicator reactions using the continuous flow method with integrating observation (CFMIO). A population balance analysis incorporating distribution effects of probe molecules across micellar aggregates yielded solubilizate exchange rate constants of 106-107(Mas)-', 2-3 orders of magnitude lower than for molecular diffusion. The results are consistent with opening of the surfactant layer upon coalescence as the rate-determining step, random solubilization of the probe molecules, and proportional increase of rate constant with reversed micellar size.
Introduction
Reversed micelles are nanometer-sized water droplets stabilized by a surfactant layer in a water-immiscible organic medium. Because of their size (in the I-IO-nm range), these aggregates are subject to Brownian motion, colliding continually and sometimes coalescing to form short-lived dimers that redisperse again to form new micelles. As a result of the coalescence and decoalescence sequence, probe molecules solubilized in the water pools are redistributed over the micelle population at a rate that can be characterized in terms of a second-order rate constant kex. An understanding of this coalescence and solubilizate exchange phenomenon, and of dynamic processes in reversed micellar and water-in-oil microemulsions in general, can lead to better mechanistic descriptions of such diverse phenomena as phase transitions, emulsion stability, transport in cells and membrane-mimetic media, and drug delivery systems. Moreover, the effects of transport limitations on the chemical and biochemical synthesis of pharmaceutical products, semiconductor particles, and ceramics in these microheterogeneous systems can also be assessed once these fundamental interaction phenomena have been enumerated. There is clearly an incentive to explore the intermicelle exchange phenomena and, in particular, the manner in which they are affected by such factors as interfacial structure and solubilizate location within the micelle. A reversed micellar system cannot be observed directly during collisions or in the state of the transient dimer, and therefore indicator reactions between probe molecules must be used to obtain information about the coalescence process. To investigate solubilizate exchange between micellar cores, it is desirable that the probe molecules partition exclusively to the water pools; otherwise other, e.g.. interfacial transport, processes may dominate the exchange. The intermicelle exchange of noninterfacilly active
reagents and their subsequent reaction can then only occur once two reversed micelles have collided and coalesced. There are five sequential elementary steps associated with these coalescence and reaction processes, as illustrated schematically in Figure 1: (i) diffusional approach of the micellar aggregates, (ii) opening of the micellar walls, (iii) diffusion of the indicator ions in the temporary dimeric aggregate, (iv) chemical reaction of the indicator ions, and (v) decoalescence of the temporary dimeric aggregate. The observed overall time constant for the reaction can be expressed in terms of the individual time constants for each of the independent steps in this sequence by using the equation] 1 1 -=---.--kobs
kdiW.agg
+-+-1 kopening
1 kdiff,ions
+ - +1 kreac
Fritz Haber-lnstitut.
(1)
The time constants of all elementary steps except (ii) and (v) are either known or can be estimated with a reasonably high degree of precision. Collision between micellar aggregates is governed by diffusion, which is the fastest process by which two species can approach and encounter each other. The rate constant for the diffusional encounter of aggregates, kdiNagg, is thus an important upper bound for second-order processes such as reversed micellar coalescence. I t can be calculated from the simple Smoluchowski equation2 if there are no interactions between the diffusing species. DA and DBare the diffusion coefficients of species A and B respectively, rA and rB are their respective radii, and N A is the molar concentration of diffusing species A, all in cgs units. The diffusion rate constant kdiffin aqueous solution at 25 OC for equally sized diffusing species with no interaction potential has been determined to be 3.2 X IO9 (Mas)-' by H o l ~ w a r t hand , ~ later by Sutin and
* Author to whom all correspondence should be addressed.
' Massachusetts Institute of Technology.
1 kdccoal
(1) Noyes, R. M. frog. Reacf. Kin. 1961, I, 129. ( 2 ) Smoluchowski, M . v. Z. Phys. Chem. 1917, 92, 129.
0022-3654/90/2094-1232%02.50/0 0 1990 American Chemical Society
