Dynamics of wetting: effects of surface roughness - American

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J. Phys. Chem. 1986, 90, 5845-5849 presence of cosurfactant than without c o ~ u r f a c t a n t . ~ ~ Likewise, and by contrast, addition of a single-chained water-soluble ionic surfactant like dodecyltrimethylammonium bromide (DTAB) for the ternary system will induce phenomena easily comprehensible. Here head-group areas of surfactant and cosurfactant and chain length are the same. The curvature as measured by v/(al) for the surfactant-cosurfactant mixtures in water is now reduced, with

v a1

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( X D / ( ~ ) D D+A(BX V / ( ~ ) D T A B XDDAB + XDTAB

whereXare mole fractions and v/(al)DDAB i= 1, v/(al)DTAB = 1/3 (since the cosurfactant forms micelles in water). Hence with oil the system forms an L2 phase a t a higher initial water content than without cosurfactant. Water will continue to be taken up in these systems. In the process the head-group area is increased because of decreased electrostatic screening of head-group repulsion until u / ( a l ) (eff) is reduced to unity. Beyond this point the curvature is normal, excess oil is squeezed out by strong repulsive double-layer interactions between aggregates, and the system phase separates into lamellar phase plus excess water and oil. It can be inferred that both low curvature and weak interaggregate interactions are necessary for the formation of substantial middle or L2 phase microemulsions. Consider next a soluble micelle-forming ionic surfactant like SDS. For the surfactant water system u/(al) = l/j, and very little oil can be solubilized. One role for a cosurfactant like pentanol or dodecanol is as before to increase v/(ar)to a value large enough to permit uptake. But this is not sufficient. Design of a microemulsion middle phase of normal curvature requires also weaker repulsive forces than those that exist between swollen ionic aggregates in water. And this is accomplished if on addition of a highly penetrating oil pentanol is expelled from the oil and simultaneously induces additional attraction. Already the work of Zemb and collaborators16 suggests that this dual role for cosurfactant is operative. Our force measurements confirm this and indicate besides that the phenomenon is not restricted to anionics. (24) Ninham, B. W.; Hashimoto, Sci. 1983, 95, 594.

S.;Thomas, J. K.J . Colloid Interface

5845

(It is worth noting that the formation of microemulsions from single-chained surfactants is most easily accomplished by more hydrophilic oils like xylene or toluene, which penetrate strongly into the surfactant tail region.) Double Layer and Hydration Forces. Concerning the second issue, the real nature of double layer and hydration forces, we remark that earlier measurements of the forces between these bilayers as a function of salt show dramatic differences between those forces with different monovalent counterions.1° With Br-, the forces are accurately described by the Poisson-Boltzmann equation assuming a “binding” constant which gives 90% Brbound to the interacting bilayers.l0 With the more strongly hydrated acetate counterion, the forces are well fitted to the Poisson-Boltzmann force law almost down to contact (0.5 nm) with no ion binding. From parallel work on micelles4 it is known that here no chemical binding of counterion is required to explain the phenomenological (measured) binding parameters. There is a clear conflict here because interactions between bilayers cannot invoke a “chemical” binding constant. What seems to be called into question is the validity of the Poisson-Boltzmann description itself. on the primitive model of electrolytes Recent theoretical shows that if the more refined hypernetted chain (HNC) equation (in agreement with Monte Carlo simulation) is used, then with small counterions like Br- the H N C force law with full dissociation is identical with the Poisson-Boltzmann prediction. But the fact that the Poisson-Boltzmann equation with no binding fits the measured force law is probably an artifact. The observed force may, in fact, be the sum of the HNC result plus an additional hydration repulsion. Adsorption of pentanol at the bilayer surface then breaks up water structure associated with the hydrated counterions and reduces this repulsion. Even so, it is clear that the measured forces between the same charged bilayers depend critically on the counterion. Further experiments and more extensive theoretical studies14 would be necessary to definitely confirm this thesis. If borne out, the implication is that all measured electrostatic force laws and interpretations of { potentials require reexamination.

Acknowledgment. W e thank J. Brady for supplying the surfactant and D. F. Evans for his interest and encouragement in this work. Registry No. DHDAA, 71326-37-9; pentanol, 71-41-0.

Dynamics of Wettlng: Effects of Surface Roughness A. M. Cazabat* and M. A. Cohen Stuartt CollPge de France, Physique de la MatiPre CondensCe, 75231 Paris Cedex 05, France (Received: February 28, 1986; In Final Form: May 21, 1986)

The rates of “dry” (nonvolatile) spreading on smooth and on rough surfaces are compared. For smooth surfaces, the experimental results appear to be well described by two simple, theoretically predicted, power laws, one for the initial, “capillarity” regime, well observable for small drops, and one for more spread-out drops, dominated by gravity effects. The transition, however, is not located at a well-defined value of the radius R of the wetted spot but involves time and the chemical nature of the solid surface. Rough surfaces give rise to a new and interesting regime of fast spreading along troughs offered by the surface roughness. The data seem consistent with another power law R t’, where r ranges between 0.25 and 0.40. A tentative explanation is forwarded in terms of spreading under an essentially constant capillary force.

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Introduction The dynamics of wetting is a subject that, in spite of its enormous practical interest, has received only little attention in fundamental H ~ a survey ~ of new~theoretical ~ insights ~ ‘On leave from the Department of Physical & Colloid Chemistry, Agricultural University Wageningen, The Netherlands.

appeared recently1 that provides a stimulating basis for experimental work. We explore here the kinetics of “dry” spreading (Le., spreading of nonvolatile liquids) in order to assess the validity ~and the, limitations of the relevant predictions. Also, we address the problem of spreading on rough surfaces, since this would seem (1) de Gennes, P.-G. Reu. Mod. P h p . 1985, 57, 827.

0022-3654/86/2090-5845$01.50/00 1986 American Chemical Society

5846 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986

important from a practical point of view. One expects, of course, some similarities with wetting of porous bodies.24 There are, generally, two forces that drive spreading: capillarity (nonzero dynamic contact angle 0,) and gravity (drop weight). Theoretical calculations for drops of completely wetting liquids on smooth, plane surfaces were carried out for both cases, namely for negligible gravity effects (small drops) by Tanner5 and for dominating gravity effects (large drops) by Lopez et a1.6 Both forces decrease considerably as a drop flattens out, whereas the opposing viscous force increases. For drops of volume Q,viscosity 7, density p , and surface tension y, the radius R of the wetted spot grows as

for small drops and as

for large drops. Both laws can be constructed by a very simple argument.’ For a drop of maximum height h, the viscous force is approximately proportional to qUR/h, where U = dR/dt is the velocity of the contact line. Balancing this against a capillary force, which is given by 702, we find U (y/7)[h/(RO2)].Since, for a spherical and f& h / R QR3, we cap of constant volume Q,h QR2 (y/7)Q3@, which leads to eq 1. If we balance the find U viscous force against the gravity force given by h2pg, we find eq 2. The remarkable feature of these laws is that they do not involve the value of the spreading parameter S (= yso - ysL- yLG);Le., there is no dependence on the (chemical) nature of the surface, provided that it is smooth and completely wetted (S > 0). The explanation of this result is that a tiny film of liquid always precedes the droplet. In this “precursor” film, which is for normal cases extremely thin and extends only very little from the nominal contact line, the free energy of spreading is presumably nearly entirely spent through viscous dissipation. Indeed, the calculations cited above assume complete balancing of S by friction in the film. For rough surfaces, the dynamic contact angle becomes a local variable, and the calculations do no longer apply. To our knowledge no prediction exists here, and we will therefore explore the effects of surface roughness experimentally. The literature on kinetics of spreading drops was recently reviewed by Marmur.s His article reveals that the number of experimental data is regrettably small. Only part of the data are relevant for the case of dry spreading and, of course, only part agree with the theory. We therefore felt that a systematic study of spreading on a smooth surface was necessary as a basis of the discussion of roughness effects. For all our experiments, we chose the glass/silicone oil system for the following reasons: (i) glass surfaces of increasing roughness can easily be prepared by means of a depolishing treatment; (ii) chemical treatments allow for a variation of the chemical nature of the surface; (iii) silicone oil wets glass well; (iv) silicone oil can be obtained in a large range of viscosities. at constant surface tension.

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Experimental Section Drops in the initial stages of spreading were visualized by a simple projection arrangement, the size of the enlarged image (2) Washburn, E. D. Phys. Rev.1921,17, 374.

( 3 ) Good,R.J. J . Colloid Interface Sci. 1973,42,413.

(4) Lenormand, R.; Zarcone, C. 59th Annual. Technical Conference and Exhibition Society of Petroleum Engineering, Houston, TX, 1984. (5) Tanner, L. H. J . Phys. D 1979, 12, 1473. (6) Lopez,J.; Miller, C. A.; Ruckenstein, E. J . Colloid Interface Sci.1976, 56, 460. (7) Joanny, J. F. Ph.D. Thesis, University P. and M. Curie, Paris, France, 1985. (8) Marmur, A. Adv. Colloid Interface Sci.1983, 19, 75.

Cazabat and Cohen Stuart TABLE I: Correlation between Surface Roughness and Spread% Rate: yo Maximal Vertical Variation, ( A Y ~ ) ’ /Quadratic ~ Variation, and qD ( X 10” N) sample yo, bm ( A J J ~ ) ’rm /~, 1 0 ” ~ DN , I 50 12 111 29 6.5 89 V VI XIV XVI

XI1 IX

18 4.7 3.4 2.8 2.4 2

3.6 0.7 1 0.48 0.49 0.37 0.33

40 8 4.2 1.65 1.1 0.5

being measured as a function of time. When the wetted spot became large and the spreading rate low (as was the case with rough surfaces a t long times) the size of the spot was measured directly. For smooth surfaces, microscope glass slides (25 X 76 mm) were used. Rough surfaces were obtained either by depolishing glass slides (of minimally 50 X 50 mm) by means of various grades of abrasive powder or by sand blasting (for very rough surfaces). The roughness was characterized by scanning surface profiles on a Talysurf 5-10 (Taylor-Hobson, Rank Corp.). These data are summarized in Table I. Hydrophilic surfaces were cleaned prior to use by means of sulfochromic acid (Merck), rinsed with triply distilled water and alcohol, and dried in a stream of carefully filtered air. Contamination by dust was avoided. Smooth, hydrophobic surfaces were obtained by reaction with hexadecanol in the vapor phase. These surfaces were cleaned by mild heating in vacuo to remove excess reagent, rinsed with toluene and alcohol, and dried. Three silicone oils (poly(dimethylsiloxane),methyl terminated, type R47, Rh6ne-Poulenc) of viscosities of 0.02, 0.1, and 1 Pa-s, respectively, were used. The molecular weights of these products are sufficiently small to avoid special “polymer effects” in the spreading kinetics.l Results and Discussion Smooth Surfaces. Figure 1 gives the size of the drops as a function of time, R(t), for smooth, hydrophilic glass and for viscosities of 0.02 and 1 Paes, respectively. Drop weights ranged from 0.35 to 38 mg. All data can be well described by a combination of two straight lines, one with a slope of and one with a slope of This would correspond nicely to theoretically predicted exponents; see eq 1 and 2. The transition was tentatively located, as indicated by a dashed line in the figure. Figure 2 summarizes dependences on drop volume Q at fixed time. Dashed lines refer to the short-time behavior (1 min), i.e., the “capillarity” regime, and solid lines correspond to the “gravity” regime (7 min). Also here, we find very good agreement with the theoretical slopes (3/,0 and 3/s, respectively). Moreover, the distance on the ordinate between pairs of lines, corresponding to the viscosity effect, equals the theoretical value within limits of precision. Note that, for small drops, the gravity effect is not yet fully realized. At 7 min it is still in a transition zone, so that we find a point slightly off the straight line. So far, there seems to be good agreement. However, there is also a contradiction. Simple reasoning in terms of driving forces would imply that the transition between the “capillarity” and the “gravity” regimes would be controlled by the condition R N K-I = (y/pg)L/2.Here K-’ is the capillary length, which, for the liquids in this study, equals 1.49 mm. Evidently, the behavior is more complex and involves time. As is clear from Figure 1, the transition is, for both oils, located close to the same line, with a slope between 0.5 and 0.8. Indeed, we find all transition points around a single line for all viscosities and drop weights; this line corresponds to R(dR/dt)-2/3 = constant. We tend to ascribe this to the dynamic conditions close to the edge. As pointed out in the introduction, theoretical calculations are based on the assumption that the free energy of spreading is entirely dissipated in the film. If this is not the case, variations in S would be visible in the experimental data, although it is not immediately clear what effects should be expected. In order to

The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5847

Dynamics of Wetting: Effects of Surface Roughness

7

Rmn

Silicone o n hydrophilic smooth g l o s s

I

71.0.02 Pa. s

1

10

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Caplllorlty R - t M Gravity R-t’h

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30 b

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60

300

600

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60

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10

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Figure 2. The effect of drop volume, ! I on ,the rate of spreading on smooth surfaces: solid lines and crosses, drop size at 1 min (capillarity regime, slope dashed lines and diamonds, drop size at 7 min (gravity regime, slope 3/g). Silicone on hydrophobic m o o l h #lass

R(”?

st

I

2.5

3.5

-

2.5

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15.

I I

300

I

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Figure 1. Spreading kinetics of silicone oil on smooth hydrophilic glass surfaces (logarithmic plot). Solid lines are drawn according to theory (eq 1 and 2). The approximate location of the transition,is indicated by a circle. (a) q = 0.02 Pa-s; (b) q = 1 Pass. The dashed line separates the “cafillary” and “gravity” regimes.

check this, we repeated our experiments with drops on hydrophobic glass surfaces that have S smaller than for hydrophilic glass. The results are given in Figure 3. They do indeed show a systematic effect in the form of a shift of all transition points toward longer

looof b I Figure 3. Spreading kinetics of silicone oil on a smooth hydrophobic glass surface (logarithmic plot). Solid lines correspond to theory (eq 1 and 2). The transition is indicated by circles; the dashed line A separates the “capillary” and the “gravity” regimes; B idem for hydrophilic surfaces: (1) q = 0.02 Pass; (2) 7 = 0.1 Paas; (3) q = 1.0 Pavs. 25

50

100

200

400

times; the slopes themselves are hardly affected. We conclude that the spreading kinetics do indeed involve a small effect of the spreading parameter S. Rough Surfaces. The initial stages of the spreading process

5848 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986

Cazabat and Cohen Stuart

InR

s a m p l e III sample p 0 s a m p l e PI A s a m p l e XII

0

central droplet

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0.5

5

Figure 4. Schematic overview of regimes for spreading rates on rough

surfaces.

20

100

Figure 5. Plot of log D,where D is the “diffusion coefficient”in (AR)2 = D f , as a function of log q for five different rough surfaces and four

different silicone oils.

for rough surfaces are similar to those for smooth surfaces, at least in the limit of small roughness. Then, as the drop spreads, an important new regime appears, where part of the liquid spreads essentially in the roughness of the surface, while a spherical cap in the center remains that continues to follow the 1/8 power law. Eventually, all liquid is consumed by the troughs and holes on the surface. Finally, the rate of spreading slows down again. The behavior is schematically summarized in Figure 4. The initial part of the spreading curve can be characterized between the liquid by a macroscopic apparent contact angle e, surface and the average plane of the surface. Of course, the surface roughness gives rise to an angle that varies locally, Le., od,lm] = Od,app f 68d. For values of Od,a that are not too small, the average value of 6d,la91 may well foiow Od,app. The liquid, so to say, does not perceive the roughness and behaves as if the surface were smooth. In the limit of very small roughness, we would expect to return to the “capillary” regime. This seems, however, beyond the range of roughness studied here. As soon as odspp becomes small, however, the local variations, i.e., Od,lmal, start to have important consequences. A notable contribution comes, in fact, from the walls of the “canals” followed by the liquid. The average force is no longer given by the macroscopic value Od,app of :he contact angle but will depend only on the structure of the surface. Hence, an essentially constant capillary force pulls the liquid into the surface roughness. This gives rise to a distinctly visible rim of wetted, rough surface (see Figure 4) around the central droplet with its familiar spherical cap shape. The rate of spreading of this rim is much faster; after a rather broad transition zone we find a new (apparent) power law with exponents ranging from 0.25 to 0.40. A simple limiting case would be where the amount of liquid stored in the crevices of the rough surface is small with respect to the droplet volume. The central droplet then acts as a reservoir that feeds the flux of liquid in the porous spreading zone. This situation is very much analogous to penetration of liquid from a reservoir into a porous body or a capillary. Hence, we expect the rate of spreading in the porous zone, Le., AZ? = R(t) - R, ( t ) (where Rapis the radius of the spherical cap) to vary as (t7-$0.5. This result can be simply understood by realizing that the viscous force depends on the length, 1, of a path followed by the liquid and on a typical cross section along this path. Apart from a (constant) tortuosity factor, 1 AZ?, hence U = d(AZ?)/dt l/AZ?q, which leads to the expected power law (in ref 4 a simple model for a rough surface was used to arrive a t such a result). We checked the data for this dependence and found good ~ . ~ a diffusion coefficient agreement. Writing AZ? = ( D Z ) defines D that is expected to scale as 7-I. A logarithmic plot of D vs. 7 for various glass samples is given in Figure 5. Actually D 7-l and the product 7D is a characteristic of the glass roughness (see Table I).9 Figure 6 summarizes spreading curves on various rough

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sillcone q-0.02 Pa.$ depollrhed glass

I

50

!

10’

5.102

m3

5103 104

5.104 to5

5405

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Figure 6. Rate of spreading of silicone oil (q = 0.02 Pa.s) on depolished, hydrophilic glass of varying roughness (logarithmic plot). TABLE I 1 Drop Thickness li * at the Transition between “Smooth” and “Rough” Regimes glass viscosity drop sample of oil, P e s volume, p L h*, pm V 0.02 2.0 69 V 0.02 14.6 129 VI 0.02 1.4 46 VI 0.02 3.2 65 V 0.1 6.2 117 V 0.5 1.o a9 V 0.5 3.5 92 VI 0.5 2.4 82 VI 1.o 1.o 58 VI 1.o 4.1 120

surfaces, plotted as log R ( t ) vs. log t . As a result of the superposition of two spreading processes, we observe apparent power

J. Phys. Chem. 1986, 90, 5849-5853 laws with powers ranging from 0.25 to 0.40. The constancy of the driving force implies that we should find the transition from the smooth ("gravity") regime to the "porous regime" at about a constant value of the average thickness ( h ) , denoted by h*. We tabulate h*, calculated as for a spherical cap, ~ )Table , 11. Of course R* is not obtained i.e., h* = 2 f l / ( ~ R * in very accurately, so that h* is merely a rough indication of the transition rather than a precise criterion. Nevertheless, given that ( h ) varies, in this experiment, over 3 orders of magnitude, we might say that h* occurs, indeed, in a narrow range of values, thereby supporting our argument. (9) According to a model of flow along a rectangular duct (ref 4) and assuming that the scanning profiles of the various samples are homothetic (which seems actually to be the case), we would expect D yo, the maximal variation of profile. Clearly, the phenomena are more complicated, and two situations are observed (Table I). For yo k 5p, D yo indeed, but for smaller yo, D decreases much more rapidly. Thus the model is not immediately applicable in the present case.

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The final regime corresponds to the case where the liquid film at the edge becomes thinner than the characteristic length scale of the surface roughness. Then, the capillary force starts to decrease again and a corresponding slowing down is observed. We note in passing, that this characteristic thickness (and the corresponding transition) may vary, according to roughness between tens of microns and 0.2 pm, this lower bound being of the same order of magnitude as the famous macroscopic precursor film expected to appear when e,, becomes very small.'

Acknowledgment. We thank the Optical Workshop of the Ecole SupErieure d'Optique at Orsay for their kind help in preparing and characterizing some of the depolished surfaces for this study, M. A. Guedeau for providing us with smooth hydrophobic glass surfaces, and A. Bouillault for carrying out part of the experimental work. We also acknowledge F. Brochard, P.-G. de Gennes, J. P. H u h , A. Libchaber, M. May, and M. VeyssiE for kind interest and helpful discussions. This work was partly supported by Exxon Research and Engineering Co.

Size vs. Reactivity in "Organized Assemblies": Deacyiation and Dephosphorylation in Functionalized Assemblies Cirma Biresaw*' and Clifford A. Bunton* Department of Chemistry, University of California, Santa Barbara, California 93106 (Received: February 28, 1986; In Final Form: June 3, 1986)

Deacylation of p-nitrophenyl benzoate and dephosphorylation of p-nitrophenyl diphenyl phosphate were followed in 1:10 aggregates of tri-n-octyl(2-hydroxyiminoethy1)ammoniumchloride ( l b ) and tri-n-octylethylammonium mesylate ( l a ) and in micelles of cetyldimethyl(2-hydroxyiminoethyl)ammonium chloride (2b) or 1:lO comicelles of 2b and cetyltrimethylammonium chloride (2a). Analysis of the rate data shows that second-order rate constants in aggregates and micelles are similar and are independent of the size of the assembly. The second-order rate constant in the functional micelle is similar to that of reaction of the model compound trimethyl(2-hydroxyiminoethy1)ammoniumchloride (3) in water.

Introduction Amphiphiles, in solutions of three-dimensional, associated solvents, form organized assemblies of varying size,2 including single- and multilayer vesicles, micelles, and aggregates of tri1. Micelles and aggregates of n-octylalkylammonium (n-CBH17)3N+RX-

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0

0

n-C16H33N+(CH,)2RX-

II

RR'2NtCH2CH=NO-CPh

II

RR'2N)CH2CH=NOP-(OPh)2

+

t

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0 - c H~,No2

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3: R I R ' E C H 3 .

0 p N P B E P - N O ~ C B H ~ Op~NP PD ~ P; P 5 p-N02CsH40P(OPh)2

3

1 self-associate, but energy, e.g., from sanification, is often required for vesicle formation. Aggregates of 1, like micelles of the cor(1) Present address: Alcoa Technical Center, A h a Center, PA 15069. (2) Fendler, J. H. Membrane Mimetic Chemistry; Wiley-Interscience: New York, 1982. Romsted, L. S.In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1015. Bunton, C. A. In The Chemistry of Enzyme Action; Page, M.I., Ed.; Elsevier: New York, 1984; p 461. (3) Okahata, Y.; Ando, R.; Kunitake, T. J. Am. Chem. SOC.1977, 99, 3067. (4) (a) Bunton, C. A. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.;Plenum: New York, 1984; Vol. 2, p 1093. (b) Bunton, C. A.; Hong, Y. S.; Romsted, L. S.; Quan, C. J. Am. Chem. SOC.1981,103,5784,5788. (c) Bircsaw, G.; Bunton, C. A.; Quan, C.; Yang, Z.-Y. Ibid. 1984,106,7178. (d) Bunton, C. A.; Quan, C. J. Org. Chem. 1984,49, 5012. (e) Bunton, C. A.; Quan, C. Ibid. 1985, 50, 3230. (5) Kunitake, T.; Okahata, Y.; Ando, R.; Shinkai, S.;Hirakawa, S. J. Am. Chem. SOC.1980, 102, 7877.

responding cationic surfactants 2, bind reactants and can speed uni-"~~-~ and bimolecularM reactions. However, unlike surfactants, 1 do not have a critical micelle concentration, cmc, and cooperativity may be important in their aggregation. Also, unlike micelles,aggregates 1 are probably highly polydisperse, have lower aggregation numbers, and are poorer at binding hydrophilic counterions. These differences must be considered in analyzing reaction rates in these assemblies!v6 We use the terms aggregates and micelles to denote assemblies of 1 and surfactants, respectively. Oximes are deprotonated at high pH giving oximate anions (Scheme I), which are effective nucleophiles in deacylation, dephosphorylation and other bimolecular rea~tions.~-'O (6) Biresaw, G.; Bunton, C. A., this issue. (7) (a) Bunton, C. A.; Ihara, Y. J. Org. Chem. 1977,42,2865. (b) Bunton, C. A.; Hamed, F.; Romsted, L. S. J. Phys. Chem. 1982, 86, 2103.

0022-3654/86/2090-5849%01 .50/0 Q 1986 American Chemical Society I

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