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Temporal Evolution of Microstructures in Aqueous CTAB/ SOS and CTAB/HDBS Solutions Yashen Xia,† Isabella Goldmints,‡ Paul W. Johnson,§ T. Alan Hatton,‡ and Arijit Bose*,† Department of Chemical Engineering and Electron Microscope and Imaging Facility, University of Rhode Island, Kingston, Rhode Island 02881, and Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received November 12, 2001. In Final Form: February 4, 2002 Vesicles are formed spontaneously when aqueous solutions of cetyl trimethylammonium bromide (CTAB) and sodium octyl sulfate (SOS), as well as CTAB and dodecyl benzene sulfonic acid (HDBS), are mixed in well-defined ratios. Microstructures in the starting solutions are composition-dependent and, in these experiments, include spherical and rodlike micelles as well as monomers. Starting from these initial morphologies, relaxation to the equilibrium vesicle state can take several hours to months in the CTAB/ SOS system, but the transition occurs within minutes in the CTAB/HDBS system at the concentrations studied. In this paper, the temporal evolution of aggregate microstructures from a range of initial states was monitored using time-resolved turbidity, dynamic light scattering, and cryogenic transmission electron microscopy (cryo-TEM). For the CTAB/SOS system, the turbidity changes slowly over a period of 2 h. The rate of growth of the aggregates, measured by dynamic light scattering, was found to be independent of the specific morphology of the initial aggregates and of the added NaBr concentration. The morphologies of intermediate-state aggregates were directly identified by cryo-TEM observations of solutions quenched at different times after mixing and confirmed to be wormlike micelles, disks, and vesicles. The model that emerged for the transitions is that the micelles grow to floppy, undulating disks. The competition between the edge and bending energies drives the transition to small vesicles at a critical disk size. These vesicles then grow to the final size distribution. Varying proportions of each of these aggregates exist at all time points. In contrast to the CTAB/SOS results, both turbidity and dynamic light scattering reveal that the transition to the final size is rapid in the CTAB/HDBS system. Within the time resolution of the cryo-TEM measurements, only vesicles, and no disks are observed. These observations indicate that the bilayer bending energy dominates in this system. The solubility difference between SOS and HDBS could also play a role in the observed difference in kinetics.
1. Introduction Aqueous mixtures of cationic and anionic surfactants form a rich variety of composition-dependent microstructures in solution,1 including spherical micelles, wormlike mixed micelles, vesicles, and a variety of lamellar phases. Vesicles are of particular interest because of the large number of potential applications. Although these systems are not biologically compatible, they can serve as models for biological membranes and encapsulation devices for drug, flavor, or fragrance delivery and release. Vesicles can also be used as microreactors for the formation of nanoparticles.2 Although these catanionic vesicles are formed spontaneously (that is, they require no external energy input), the process of formation and the evolution to the final size distribution can sometimes take hours to months.1,3 An understanding of the mechanism of formation and growth of vesicles and knowledge of the time scales of such processes and of the characteristics of the intermediate * To whom correspondence should be addressed. Tel.: 401-8742804. Fax: 401-874-4689. E-mail:
[email protected]. † Department of Chemical Engineering, University of Rhode Island. ‡ Massachusetts Institute of Technology. § Electron Microscope and Imaging Facility, University of Rhode Island. (1) Yatcilla, M. T.; Herrington, K. L.; Brasher, L. L.; Kaler, E. W.; Chiruvolu, S.; Zasadzinski, J. A. J. Phys. Chem. 1996, 100, 5874. (2) Yaacob, I.; Nunes, A. C.; Bose, A. J. Colloid Interface Sci. 1995, 171, 73. (3) O’Connor, A. J.; Hatton, T. A.; Bose, A. Langmuir 1997, 13, 6931.
aggregates are important for a fundamental understanding of self-assembly dynamics, as well as from the perspective of applications where the kinetics of encapsulation and breakup are of interest. In addition, these studies can lead to the identification of new, nonequilibrium aggregate microstructures that have sufficient lifetimes to be useful in certain applications. Kinetic studies of vesicle formation and growth are still rare. Cholesterol-lecithin vesicle growth has been studied using turbidity and light scattering measurements and fluorescence probe encapsulation.4 Vesicles grow by the transfer of lecithin and cholesterol via diffusion in the aqueous medium. A stopped-flow study of vesicle formation in sodium xylenesulfonate/Laureth 4 aqueous solutions shows that vesicles are formed by unimer addition.5 Smallangle neutron scattering (SANS) and dynamic light scattering studies of the bile salt-lecithin system have shown that the process of vesicle formation and growth takes hours and proceeds through a series of intermediate states,6-8 beginning with the formation of elongated micelles. These micelles grow into long, polymer-like aggregates and form metastable disks and nonequilibrium vesicles. These vesicles then grow to their equilibrium size. At each step, a combination of these structures rather than only one type of aggregate is present. (4) Luk, A. S.; Kaler, E. W.; Lee, S. P. Biochemistry 1997, 36, 5633. (5) Campbell, S. E.; Yang, H.; Patel, R.; Friberg, S. E.; Aikens, P. A. Colloid Polym. Sci. 1997, 275, 303. (6) Egelhaaf, S. U.; Schurtenberger, P. Phys. Rev. Lett. 1999, 82, 2804. (7) Egelhaaf, S. U.; Schurtenberger, P. J. Phys. Chem. 1995, 99, 1299. (8) Egelhaaf, S. U.; Schurtenberger, P. Physica B 1997, 234, 276.
10.1021/la0156762 CCC: $22.00 © 2002 American Chemical Society Published on Web 04/11/2002
Microstructures in CTAB/SOS and CTAB/HDBS Solutions
A systematic study of vesicle formation is greatly aided by the availability of a phase diagram over the expected composition range, as the start and end points of any transition are then well-defined. One of the surfactant pairs used in this study is sodium octyl sulfate (SOS) and cetyl trimethylammonium bromide (CTAB), for which the phase diagram in the dilute aqueous region is available.1 The electrostatic effects on the phase behavior of this mixture have been studied, and phase diagrams of CTAB/ SOS mixtures have been mapped for different concentrations of added salt (sodium bromide).9 The structure and composition of the equilibrium vesicles have been probed by SANS and analyzed using a thermodynamic cell model.10 The vesicles formed in the solution with a total surfactant concentration of 2% and a 3/7 weight ratio of CTAB/SOS (21/79 molar ratio) were composed of 45 mol % CTAB. The bilayer thickness was 22 Å. The theoretical predictions are in good agreement with experimental measurements. Additional experiments have been performed using dodecyl benzene sulfonic acid (HDBS) as the anionic surfactant. Here, a detailed phase diagram is not available, but the aggregate microstructures at the initial and end points are well-known for the concentrations used in this study.11 The dynamics of the micelle-to-vesicle transition in the CTAB/SOS system have been explored using time-resolved static (at a fixed scattering angle of 90°) and dynamic light scattering.3 Vesicles were formed by mixing two single-surfactant solutions containing micelles of SOS and CTAB. Three characteristic time scales, on the order of 10, 100, and 2000 s, were identified. The intensity of the scattered light during the slowest of these three processes is proportional to the square of the aggregate diameter, indicating that the growth during this time period is twodimensional. The proposed mechanism for the transition to vesicles is the formation of mixed micelles and their growth to disks, followed by the formation of small nonequilibrium vesicles and the growth of these vesicles to their equilibrium size. In this paper, the transition from the initial aggregates to the final equilibrium structures in the CTAB/SOS/water and CTAB/HDBS/water systems is monitored using timeresolved turbidity, dynamic light scattering, and cryogenic transmission electron microscopy (cryo-TEM). Observations and data from each of these methods are exploited to develop a consistent model for the formation of vesicles from a range of initial states during the stages of the transformation from the first few minutes to approximately 2 h after mixing. 2. Experimental Details 2.1. Materials. Sodium octyl sulfate (SOS, 99%) was obtained from Lancaster Synthesis, Inc. (Windham, NH), dodecyl benzene sulfonic acid (HDBS) from Stephan Company (Chicago, IL), cetyl trimethylammonium bromide (CTAB, >99%) from Sigma Chemical Co. (St. Louis, MO), and sodium bromide (NaBr, 99.5%) from Acros (Morris Plains, NJ). All chemicals were used as received without further purification, on the basis of previous results that showed that the purified surfactant displayed kinetics that were indistinguishable from those of the unpurified surfactant.3 All surfactant solutions were prepared in Milli-Q water at room temperature and then stored at 25 °C until used. 2.2. Experimental Techniques. 2.2.1 Turbidity. Solutions of each surfactant were drawn into syringes from vials stored in a constant-temperature bath and mixed into a sample vial (also in the constant-temperature bath). Sample turbidity was ob(9) Brasher, L. L.; Kaler, E. W. Langmuir 1996, 12, 6270. (10) Brasher, L. L.; Herrington, K. L.; Kaler, E. W. Langmuir 1995, 11, 4267. (11) Yaacob, I.; Bose, A. J. Colloid Interface Sci. 1996, 178, 378.
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Figure 1. Ternary phase diagram in the dilute regime for CTAB/SOS/water. The pairs B, C and D, E represent surfactant compositions in the starting solutions. These solutions are mixed in mass ratios such that the final composition is represented by point A.
Figure 2. Mean hydrodynamic diameter of the aggregates formed in the solution after the mixing of equal amounts of 1.5% CTAB (point B) and 3.4% SOS (point C) at 25 °C. The final total concentration of the surfactant is 2.45%, and the weight ratio of CTAB/SOS is 7/3. The characteristic error bars are shown in the figure. served qualitatively by placing a vial containing the mixture into a plexiglass box where the temperature was maintained at 25 °C. A digital camera was used to capture images of the sample against a ruled- paper background at various times after mixing. 2.2.2. Dynamic Light Scattering. Dynamic light scattering measurements for the estimation of particle diffusion coefficients, and thus hydrodynamic radii, were performed on a Brookhaven model BI-200SM laser light scattering system (Brookhaven Instrument Corp.) at a scattering angle of 90° and wavelength of 514 nm. The solution temperature was maintained at 25 ( 0.1 °C. Intensity autocorrelation functions were gathered over durations of 1 min at preset intervals after the two thermally equilibrated starting solutions were mixed inside a vial located in the light scattering apparatus. Hydrodynamic radii were obtained using cumulant analysis. The autocorrelation functions were also processed using nonnegatively constrained leastsquares fits (NNLS); these fits gave results that agreed well with the simpler cumulant fits, so that only the cumulant data are reported here.
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Figure 3. Cryo-TEM images of aggregate solutions vitrified at various times after the mixing of solutions B and C to make vesicles of composition A. Scale bar ) 100 nm. 2.2.3. Cryogenic Transmission Electron Microscopy. Predetermined volumes of the two feed solutions, stored at 25 °C in a controlled environment vitrification system (CEVS, University of Minnesota; the temperature within the CEVS box is precisely controlled, and the relative humidity is kept at >90%) were added into a vial and vortex-mixed for 15 s. Approximately 15 mL of the mixed solution was formed. A few (2-3) microliters of the sample solution were withdrawn periodically over 1-2 h from the same mixed solution, allowing us to observe the evolution of microstructures at different time points after mixing. The sample was deposited on a specially prepared lacey carbon electron microscope grid and blotted to remove excess liquid. All of this processing took place within the CEVS unit, preventing water evaporation and temperature changes in the sample. The grid bearing the sample was then plunged into a liquid ethane reservoir, which was cooled by liquid nitrogen to a temperature close to its freezing point. The rapid heat transfer away from the grid vitrified the sample. The time elapsed between the mixing of the two solutions and sample vitrification was noted. The specimen was transferred under liquid nitrogen to the cooled tip of a cryotransfer stage (CT3500J; Oxford Instruments). The stage was then inserted under positive dry nitrogen pressure into the JEOL 1200 TEM and imaged at slight underfocus (1-3 µm). The sample temperature was maintained at -165 °C at all times during imaging to prevent the amorphous-to-crystalline phase transformation in ice.
3. Results The phase diagram for CTAB/SOS aqueous mixtures is shown in Figure 1. Either equal weights of two single-
surfactant solutions (points B and C) were mixed with the resulting composition and total concentration of the surfactants corresponding to point A in the vesicle region, or mixed surfactant solutions (points D and E) were added together to reach the same final point A on the phase diagram. Although the complete phase diagram for the CTAB/HDBS system is not available, the beginning and end states, consisting of micelles and vesicles, respectively, are known.11 3.1. Growth and Evolution of the Aggregates. 3.1.1. Mixing of Single-Component SOS and CTAB Solutions. Whereas micelles of SOS or CTAB are small, the aggregates formed after mixing of the two single-component solutions are relatively large and grow with time. Thus, the sample turbidity gives a qualitative idea of the transition kinetics. The turbidity of the sample at 120 min is only slightly larger than that of the initial micellar solutions, indicating a slow formation of aggregates. This qualitative observation is confirmed by dynamic light scattering. The increase of the apparent mean hydrodynamic diameter of the aggregates with time after mixing equal weights of 1.5% CTAB and 3.4% SOS (points B and C) is shown in Figure 2. The aggregate sizes grow from ∼15 nm right after mixing to ∼35 nm at the end of 120 min . Analysis of the size distributions at the various times shows only a small relative variance, 0.08 ( 0.02, in the aggregate size, indicating fairly monodisperse aggregates.
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Figure 5. Mean hydrodynamic diameter of the aggregates formed in the solution after the mixing of a solution of 0.17% SOS and 1.43% CTAB (point D) with a solution of 0.3% CTAB and 2.7% SOS (point E) in the proportion of 2/3 at 25 °C. The final total concentration of the surfactant is 2.45%, and the weight ratio of CTAB/SOS is 7/3. The characteristic error bars are shown in the figure.
Figure 4. Cryo-TEM images of aggregates observed by stage tilting. (a) Stage normal to the electron beam. (b) Stage tilted by 30° around the axis marked by the dashed line. Disk-shaped objects with their axes parallel to the tilt axis retain their rodlike projection (1). Those that have their axes normal to the tilt axis change appearance from rods to flat objects of very low contrast (2) or from flat low-contrast objects to rods (3). Vesicles always appear as dark circles with a gray level in the interior that is greater than that of the vitrified water (4). Scale bar ) 100 nm.
The establishment of the eventual size distribution for the aggregates is a slow process, as growth continues well after 2 h to a final mean diameter of ∼70 nm. Images from time-resolved cryo-TEM experiments for the same solutions (the mixing of equal weights of solutions at B and C) are shown in Figure 3. At 8 min after mixing, small vesicles are visible. Vesicles are observed at 12 min , along with rod-shaped objects. At 47 min after mixing, the vesicles have grown. The rod-shaped objects are not observed in this region of the grid, but they can be seen in other regions. This vesicle growth continues over the remainder of the observed time period (up to ∼2 h). The rod-shaped objects are also visible in the image at ∼2 h. Cryo-TEM images represent two-dimensional projec-
tions of three-dimensional objects. Stage-tilting experiments were performed to establish correctly the morphology of the rod-shaped objects seen in several of these images, and the results are shown in Figure 4. Disks with their axes parallel to the tilt axis should retain their rodlike projections (box 1). Those that have their axes normal to the tilt axis should change appearance from rods to flat objects of very low contrast (box 2) or from flat low-contrast objects to rods (box 3). Indeed, the contrast provided by the disks when placed normal to the electron beam is often so low that they cannot be observed. All three types of projections are visible. Vesicles, on the other hand, always appear as dark circles with a gray level in the interior that is greater than that produced by the surfactant-free vitrified region (box 4). Thus, the stage-tilting experiments performed here confirm the presence of disks within the mixed solutions during the transition to vesicles. 3.1.2. Starting from Mixed Micelles. To investigate whether the formation and growth of mixed micelles limits the first stage of the growth and whether transition state microstructures are initial-state-dependent, we performed an experiment in which we started with mixed micellar systems. A solution containing 0.3% CTAB and 2.7% SOS (point E) was added to one containing 0.17% SOS and 1.43% CTAB (point D) in a proportion required to reach point A on the phase diagram. Dynamic light scattering measurements showed that small aggregates existed in the original mixtures. It was difficult to determine the exact hydrodynamic diameters of these aggregates because of the effects of electrostatic interactions on the apparent diffusion coefficients, but the apparent micelle hydrodynamic diameter in the SOS rich solution was about 5 nm, and the CTAB-rich solution exhibits a bimodal distribution of the apparent hydrodynamic diameters (3 and 19 nm), which might indicate that these mixed micelles are rods. The apparent hydrodynamic diameters do not account for the electrostatic interactions and can only be used to estimate the order of magnitude of the micellar size. The growth of the aggregates formed from the mixing of these solutions is shown in Figure 5. No difference can be seen between the results for mixing pure surfactant solutions and solutions with preassembled mixed micelles. Thus, the formation of mixed micelles does not significantly limit the vesicle growth kinetics.
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Figure 6. Cryo-TEM images of aggregate solutions vitrified at various times after the mixing of solutions D and E to make vesicles of composition A. Scale bar ) 100 nm.
Cryo-TEM images from parallel experiments done with solutions D and E are shown in Figure 6. Although the dynamic light scattering measurements show no significant difference in transient hydrodynamic radii between the mixing of solutions B and C and the mixing of solutions D and E, the aggregate morphologies are quite different. At 9 min after mixing, branched threadlike micelles are observed. Disks and vesicles are observed at 27 min and persist even in the sample aged to 114 min . 3.1.3. Effect of Added Salt. The change in the mean hydrodynamic diameter upon the mixing of equal amounts of 3.4% SOS solution and 1.5% CTAB solution with varying NaBr concentrations is shown in Figure 7. The size of the aggregates is independent of the salt concentration within the experimental error. If all of the surfactants are fully ionized, the total counterion concentration in the solution is ∼0.2 M. The role of small amounts of additional salt is therefore expectedly minor. 3.1.4. CTAB/HDBS System. The sample turbidity increases immediately after the mixing of 0.866% (24 mM) CTAB and 0.778% (24 mM HDBS) in a 7/3 volumetric ratio (shown previously to form vesicles11) and remains unchanged over 2 h. The apparent hydrodynamic diameter also does not change over the time period of the experiment, as shown in Figure 8. In contrast to the CTAB/SOS
solution, the CTAB/HDBS system is one that achieves its final equilibrium state within the time resolution of our experimental measurements. Time-resolved cryo-TEM images for the same solutions are shown in Figure 9. At 7 min after mixing, vesicles are visible, but there are no disks. At 11 min, relatively monodisperse unilamellar vesicles are observed, along with some multilamellar vesicles. These aggregates persist without change in size for 120 min . 4. Discussion Although overall two-dimensional growth on the time span of these experiments has been predicted before,3 these experiments provide the first direct evidence of the microstructures that exist in solution during the transition process. The disk-shaped aggregate seen in these experiments is a metastable intermediate state that does not appear in the published equilibrium phase diagram for the CTAB/SOS/water system. In this case, the pathway from the initial states containing micelles to the final vesicle state cannot be completely tracked by structures that appear on the phase diagram. Whereas these results are specific to the CTAB/SOS/water solution, the presence of nonequilibrium structures that have sufficient stability
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small nonequilibrium vesicles at short times after mixing for the CTAB/SOS system can be understood by considering the transition from undulating bilayer disks to vesicles. If the disks are treated as membranes (portions of spheres) with a bending modulus κ, an edge energy/length λ, and an area πL2, the total energy E is the sum of the bending and edge energies,12-14 that is
E ) Ebending + Eedge ) 2πκ[LC - LCsp]2 + 2πλL[1 - (LC/2)2]1/2 (1) where C is the membrane curvature and Csp is the spontaneous curvature. In dimensionless form, the total energy E′ is given by
E′ ) E/(2πκ) ) [LC - LCsp]2 + L/ξ[1 - (LC/2)2]1/2 (2) Figure 7. Mean hydrodynamic diameter of the aggregates formed in solution after the mixing of equal amounts of 3.4% SOS and 1.5% CTAB at 25 °C for different concentrations of NaBr. The final total concentration of the surfactant is 2.45%, and the weight ratio of CTAB/SOS is 7/3. The NaBr concentrations shown in the figure are the concentrations in the final mixture. The characteristic error bars are shown in the figure.
where ξ ) κ/λ. The transition from disks to vesicles will occur spontaneously at a critical membrane area when the energy barrier for vesicle formation disappears12-14 (only the lowest-frequency eigenmode for bending needs to be considered). Thus, at the critical condition
dE′/d(LC)|L/ξ)constant ) d2E′/d(LC)2|L/ξ)constant ) 0 (3a,b) For a finite ξ, conditions 3a and 3b imply that this transition occurs at a critical membrane area πLcr2, where
Lcr ) 8ξ/[1 + (4Cspξ)2/3]3/2
(4)
Shioi and Hatton12 equated Lcr to the diameter of the embryonic vesicles that form by membrane closure, D0, and used the final vesicle diameter Deq ) 2/Csp to rearrange eq 14, giving
D0-2/3 ) Deq-2/3 + (8ξ)-2/3 Figure 8. Mean hydrodynamic diameter of the aggregates formed in the solution after the mixing of 0.866% CTAB (24 mM) and 0.778% (24 mM) HDBS in a 7/3 ratio at 25 °C. The diameter remains unchanged over the course of the experiment. The symbols represent different experimental runs.
to be observed by these probing techniques is likely to be a general phenomenon for many self-assembling colloidal systems. The addition of anionic surfactant, SOS, into the cationic micellar solution changes the area occupied per headgroup because of charge screening and induces a transition from micelles to disks. These disks are too small to be observed by cryo-TEM at 8 min when solution B and C are mixed, but they are visible at 12 min after having undergone two-dimensional growth. When starting with solutions D and E, the initial transition is to wormlike micelles, caused by the growth of rodlike mixed micelles present in the starting solutions. The wormlike micelles eventually grow to disks as more anionic surfactant becomes incorporated. Although aggregate morphologies present at short times are dependent on the initial compositions of the starting solutions, these differences are eliminated over time, pointing to the fact that these vesicles are indeed equilibrium structures. In their experiments and analysis of the dynamics of catanionic vesicle formation, Shioi and Hatton,12 drawing on the earlier work of Fromherz13 and Lipowsky,14 recognized that the presence of the large proportion of
(5)
Thus, the initial vesicle size will always be smaller than the final equilibrium size, the difference depending upon the ratio of the bending modulus to the edge energy/length, ψ. Shioi and Hatton12 used both published data1 and their own results to show that this relationship holds for these systems, with a value of ψ ) 6.9 nm. Growth of these vesicles to the final size distribution then proceeds by coalescence or by monomer addition from the bulk. The absence of disks in the CTAB/HDBS system, as well as the rapid transition to the final vesicle size distribution implies, that the bending modulus for these vesicles is high (large ξ). Further corroboration of this conclusion is the narrow size distribution of vesicles in this system.15 The lower solubility of HDBS compared to SOS is another potential factor affecting the variation in the kinetics. 5. Conclusions Starting with different initial states of CTAB/SOS solutions and a CTAB/HDBS solution the evolution of aggregate microstructures during the formation of vesicles has been monitored using time-resolved turbidity measurements, dynamic light scattering, and cryogenic transmission electron microscopy. For the CTAB/SOS system, the turbidity changes slowly over the time span of the (12) Shioi, A.; Hatton, T. A., submitted to Langmuir, March 2002. (13) Fromherz, P. Chem. Phys. Lett. 1983, 94, 259. (14) Lipowsky, R. J. Phys. II Fr. 1992, 2, 1825. (15) Xia, Y. Ph.D. Thesis, University of Rhode Island, Kingston, RI, 2001.
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Figure 9. Cryo-TEM images of aggregate solutions vitrified at various times after the mixing of 0.866% (24mM) CTAB and 0.778% (24mM) HDBS in a 7/3 ratio at 25 °C. Note that no disks are observed and that the vesicle diameters appear to remain unchanged over time. Scale bar ) 100 nm.
experiments, indicating a slow transition to vesicles. Dynamic light scattering shows a growth of aggregate sizes that is independent of initial state as well as salt concentration. Cryogenic transmission electron microscopy reveals the presence of small nonequilibrium vesicles and disks at short times, consistent with the idea of twodimensional growth. The disks form small vesicles, which then grow by coalescence or by monomer addition from the bulk solution. The short-time (several-minute) evolution of microstructures appears to be initial-state-dependent in these systems, although the differences are eliminated as time proceeds. Dynamic light scattering shows that the mean hydrodynamic diameters are composition-independent. Both of these results are indicative of the equilibrium nature of these vesicles. A qualitatively
different result is observed for the CTAB/HDBS system. The turbidity changes rapidly and stays level for several hours. The aggregate size also stays constant, and cryoTEM shows only vesicles and no disks over the course of an hour. These results point to the bending modulus dominating the membrane-to-vesicle transition in the CTAB/HDBS system. The lower solubility of HDBS compared to SOS could be an additional factor affecting the kinetics. Acknowledgment. This work was supported by NSF grants to T.A.H and A.B. (CTS 9809286, 0079332). A.B. thanks Angelo Lucia for several useful discussions. LA0156762
