J. Phys. Chem. 1986,90, 5854-5858
5854
Appllcatbn of Stepwlse Self-Assoclatlon Models for the Analysls of Reaction Rates In Aggregates of Tri-n-octylalkylammonium Salts Girma Biresaw*l and Clifford A. Bunton* Department of Chemistry, University of California, Santa Barbara, California 931 06 (Received: February 28, 1986; In Final Form: June 3, 1986)
Tri-n-octylalkylammoniumsalts, 1, form small, polydisperse aggregates and do not have a critical micelle concentration. Rate enhancements of decarboxylationof dnitrobenzisomzoleboxylate ion in IC (alkyl = Et) and le (alkyl = 2-hydroxyethyl) and dephosphorylation of 2,4-dinitrophenyl phosphate were analyzed by using a one-parameter self-association scheme of aggregation. Reactions of 2,4-dinitrochlorobenzene,bis(2,4-dinitrophenyl) phosphate and p-nitrophenyl diphenyl phosphate with le at high pH were analyzed by using a similar model. Better fits of the data were obtained than with schemes based on a simple mass-action model.
Introduction In aqueous solution tri-n-octylalkylammonium salts 1 spontaneously associate to form aggregates that bind reactants and speed bimolecular reactions.24 Second-order rate constants in ag(wCSH I7)3N+RX-
la: lb: IC: Id: le:
R = Me; X
n-C16H33N+(Me)2RX-
= CI
R 3 Et; X Br R = Et; X p OMS R % CH2CH20H;X R 3 CH2CH20H;X
2a: R 2b: R E
E
= Me; X = Br 5
CH2CH20H;X
6-BIC
3
Br
Br OMS
gregates of 1 are similar to those in micelles of the corresponding hexadecyl surfactants Z3-'But unimolecular reactions are faster in aggregates of 1 than in micelles of 2 . " ~ ~ Unlike micelles, aggregates of 1 are poor at binding hydrophilic counterions3J but appear to be better at stabilizing transition states in unimolecular reactions.'~~ Aggregates of 1 are probably polydisperse and have lower aggregation numbers than micelles and la does not exhibit a critical micelle concentration (cmc). To this extent aggregation of 1 may be assisted by cooperative interaction with hydrophobic solutes, whereas micellization does not require such interactions. Unimolecular reactions are ideal for analyzing cooperativity in the aggregation of 1 because the rate constants are independent of concentration and few parameters are required to analyze the data. The rate of unimolecular decomposition of 6-nitrobenzisoxazole-3-carboxylate,6-NBIC, is highly dependent on the nature of the reaction medium.10," The rate is very low in water because of stabilization of the ground state due to hydrogen bonding and organic solvents increase the rate."
The rate is unaffected by anionic micelles but increases by 2-3 orders of magnitude in cationic micelles and vesicles, mainly because of stabilization of the transition state 3 by the cationic surface.*JI We have measured the rate of decomposition of 6-NBIC in aqueous solutions of tri-n-octylethylammonium mesylate," IC, and in solutions of the hydroxyethyl derivative l e in 2% (v/v) aqueous MeCN (H20:MeCN 98:2 V / V ) . ~A> simple ~ mass-action mode1,8v9similar to that used to analyze reaction rates in micelles,I3 is inadequate to describe our data in dilute nonmicellar aggregates of 1. A better fit is obtained if reaction is assumed to occur in aggregates formed via a stepwise self-associationprocess, consistent with the observation that 1 does not exhibit a cmc2 This model was also applied to published rate data in aggregates of le: viz., spontaneous decomposition of 2,4-dinitrophenyl phosphate (2,4DNPP),9J3b bimolecular reactions of bis(2,4-dinitrophenyl) phosphate (bi~-2,4-DNpP),~ 2,4-dinitrochlorobenzene(DNCB), and p-nitrophenyl diphenyl phosphate @-NPDPP) at high P H . ~ No7
(1) Present address: Alcoa Technical Center, Alcoa Center, PA 15069. (2) Okahata, Y.; Ando, R.; Kunitake, T. J. Am. Chem. SOC.1977,99, 3067. (3) Bunton, C.A.; Hong, Y. S.;Romsted, L. S.;Quan, C. J . Am. Chem. SOC.1981,103, 5788. (4) Bunton, C. A. In Surfactants in Solution;Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1093. (5) Biresaw, G.; Bunton, C. A.; Quan, C.; Yang, 2.-Y. J . Am. Chem. Soc. 1984,106, 7178. (6) Bunton, C. A.; Quan, C. J. Org. Chem. 1984,49,5012. (7) Bunton, C. A. In The Chemistry ofBnzyme Action; Page, M. I., Ed.; Elsevier: New York, 1984; pp 461-504. (8) Kunitake, T.; Okahata, Y.; Ando, R.; Shinkai, S.; Hirakawa, S. J. Am. Chem. SOC.1980,102, 7817. (9) Bunton, C. A.; Quan, C. J . Org. Chem. 1985,50,3230. (10) Kemp, D. S.; Paul, K. G. J. Am. Chem. SOC.1975,97,7305. (1 1) (a) Bunton, C. A.; Minch, M. J.; Hidalgo, J.; Sepulveda, L. J . Am. Chem. SOC.1973.95,3262. (b) Bunton, C. A.; Kamego, A. A.; Minch, M. J.; Wright, J. L. J . Org. Chem. 1975,40, 1321.
Ar
ArOPOl2,4-DNPP
N
O
2
ArO
bis-2A-DNPP
4
-
qNo 7'
NO2
DNCB
0
DNPDPP
(12) Kunitake et al. followed the decomposition of 3 only in very dilute [la]: and no quantitative conclusions could be drawn from such data. (13) (a) Menger, F. M.; Portnoy, C. E. J. Am. Chem. SOC.1967.89.4698. (b) Bunton, C.A.; Fendler, E. J.; Sepulveda, L.; Yang, K. U. Ibid. 1968.90, 5512.
0022-3654/86/2090-58S4$01 .50/0 0 1986 American Chemical Society
Aggregates of Tri-n-octylalkylammonium Salts
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5855 where
SCHEME I S,
+
Kb
Tq z== Sq
[Sql = Kqwwltq = 4KJSwItq
1
(5)
Thus L product 2
In all cases, good fits were obtained by using parameters consistent with the effect of added organic solvent and electrolyte on substrate binding and self-association. The simple mass-action model fits the dqta for all these reactions reasonably well at high [l], but it does not predict the observed inflections in dilute 1. The deviations are outside the expected spread of the rate constants of ca. 5% (Figures 1-4 and ref 3, 6, and 9) and were noted in the earlier discussions.
Experimental Section Materials. 6-Nitrobenzisoxazole3-carboxylicacid was obtained by heating 6-nitrocarbomethoxybenzisoxazole14 on a steam bath in 70% aqueous H2S04for 5 h and recrystallization from ethyl acetate/hexane; mp 179-180 OC (MI4 mp 167-169 OC (monohydrate); 189-190 OC (anhydrous)). Anal.15 Calcd. for C8H4N2O5:C, 46.17; H, 1.94; N , 13.46. Found: C, 45.88; H, 2.05; N , 13.28. The synthesis and purification of the tri-noctylalkylammonium salts is d e s ~ r i b e d . Solvents ~,~ were purified by standard methods. Kinetics. Stock solutions of substrate were prepared daily. Formation of 2-cyano-5-nitrophenoxideion was followed spectrophotometrically a t 410 nm on a Beckman spectrophotometer a t 25.0 OC,with ca. 2.5 X 10" M substrate. First-order rate constants, k+, are expressed in reciprocal seconds. Mesylate salts of 1 are more soluble than the halide salt^,^^^ and were used in all the work described here. Results and Discussion Analysis of Rate Constants in Aggregates Formed by Stepwise SelfAssociation. The distribution of substrate between water and the aggregate with q monomers, T,, for q 3 2, is given in Scheme I, where S,, S, are respectively the substrate in water and that bound to T,, K,' is the binding constant, and k,' and k,' are the first-order rate constants in water and T,, respectively. We made the simplifying, but unproven, assumptionsI6 that K,' is proportional to q and k,' is independent of q, i.e. K,' = qK,
(1)
k,' = kM'
(2)
where K, is the intrinsic substrate binding constant expressed per [monomer] and kM' is the intrinsic first-order rate constant, s-l, in any aggregate. For the sake of brevity, we use the following symbols [TI] = ti;
[T,] = t,;
[TI = t
m
rate = k p [ S ] = k,'[S,]
+ xk,'[S,] q=2
m
= k,'[S,]
+ kM'x[S,] q-2
(4) (14) Borsche, W. Ber. 1905, 42, 1310. (15) Elemental analysis was performed by Galbraith Laboratories of Knoxville, TN. (16) These assumptions agree with the condition that bigger aggregates bind substrates better but that rate constants are independent of the size of aggregates.p7J7 (17) Bunton, C. A.; de Buzzaccarini, F. J. Phys. Chem. 1981,85, 3139. (18) Bunton, C. A. Catal. Rev.Sci.-Eng. 1979,ZO.l. Romsted, L. S. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1015.
q-2
(9)
1
+ K,gqtq q=t
Following the general stepwise association mechanism depicted in Scheme 11, t, and t can be expressed in terms of the equilibrium SCHEME I1 K
K
2T1 2T2 + TI 3-1. T3
+ ... + T, + TI 2T,+ ...
t2 =
t3 =
K2tI2
K3tZtl = K2K3tI3
t, = K2K3...K,t1" tq
= pqt1q
where
p, = K2K3...Kq= h K i i=2
(12)
monomer concentration t1.19-22 For the simplest model (which we refer to as the model, henceforth) in which the self-association constant Ki remains ~ n c h a n g a d , for ~ , ~any i 2 2 Ki = K = constant (13)
p, = K9-I
(14)
qt, = q(KtdU/K
(15)
it can be shown that19,20*24JS
(3)
where [TI] and [T,] are equilibrium concentrations of monomer and q-mer, respectively, and [TI is the analytical concentration of the ammonium salt. If the pseudophase mode113J8is applied to Scheme I, the observed rate is the sum of the rates in the aqueous and aggregate pseudophases, i.e.
+ kM'Ks2 qt,
k,' kq =
(1
Kt1 =
+ 2Kt) - (1 + 4Kt)'I2
2Kt Substitution of (15) in (9) for qt, gives
(16)
(19) Rossotti, F. J. C.; Rossotti, H. J . Phys. Chem. 1961, 65, 926, 930, 1376. (20) Mukerjee, P. In Physical Chemistry: Enriching Topicsfrom Colloid and Surface Science; Olphen, H. von, Mysels, K. J., Eds.; Theorex: La Jolla, CA, 1975; p 135. (21) Mukerjee, P. Adu. Colloid Interface Sci. 1977, 1, 241. (22) Mukerjee, P. In Micellization, Solubilization and Microemulsion; Mittal, K. L., Ed.;Plenum: New York, 1977; Vol. 3, p 171. (23) Equally good fits were obtained for a model in which Ki gradually increased to a limiting value of K. (24) Tsb, P. 0.P, Melvin, I. S.;Olson, A. C. J . Am. Chem. Soc. 1963,85, 1289. (25) (a) Attwood, D.; Agarwal, S. P. J . Chem. SOC.,Faraday Trans. 1 1980, 76, 570. (b) Attwood, D.; Agarwal, S. P.; Waigh, R. D. Ibid. 1980, 76, 2187. (c) Attwood, D. Ibid. 1982, 78, 2011. (d) Attwocd, D.; Tolley, J. A. J . Pharmacol. 1980, 32, 761.
5856
The Journal of Physical Chemistry, Vo1. 90, No. 22, 1986
Biresaw and Bunton
where
0 02c
0
m
For bimolecular reactions, the first-order rate constants kw' and kM' must be expressed in terms of the corresponding second-order rate constants as5J8
. LI O. i C
+-
I
/
1
where i 0 3 [ i c ] ,M
[NM]and [N,] are, respectively, the total concentrations of the nucleophile in the aggregates and water; kM is the second-order rate constant in the aggregate expressed in reciprocal seconds, and k, is the second-order rate constant in water expressed in M-' s-l. Substitution of (19, 20) in (17) gives
In applying the model to analyze rates in aggregates of 1, we found that a better fit was obtained if the rates in the dimer and trimer were neglected.26 Also, the contribution to the rate of reactions in large aggregates whose aggregation number is 3Naggiax was insignificant, where Naggmax = 10-40 depending on the binding constant, K,, of the substrate to the aggregate. This assumption is reasonable because 1 should not form large aggregates. Thus, in all our analyses, the summation of eq 18 was carried from 4 up to Naggmax; i.e. q=4
We examined minor variants of the model but saw no improvement of the fit to the data and therefore we use this simple form. Analysis of Unimolecular Decomposition Reactions. Application of the model to unimolecular reactions in aggregates of 1 requires combination of eq 16, 17, and 23 and three parameters, namely the first-order rate constant in the aggregate, kM', and the intrinsic, association and binding constants, K, and K,. Of these, kM' is unambiguously obtained from the rate constant with fully bound substrate and is not an adjustable parameter. Unimolecular Decomposition of 6-Nitrobenzisoxazole-3Carboxylate, 6-NBIC. The rate constants of decomposition of 6-NBIC in IC at 25.0 OC in the presence of 0.002 M NaOH are shown in Figure 1. A simple mass-action model (eq 24) does not fit the data in dilute IC, but the continuous aggregation model k,' -k kM'Klt kq, = 1 + K l t (24) gives a good fit (Figure 1) with the parameters: K, = 5000 M-l, K = 2000 M-I, kM' = 0.027 s-'. The observation that K, > K accords with Coulombic factors favoring binding of the anionic 6-NBIC to the cationic aggregate over incorporation of a cationic monomer. Decomposition of 6-NBIC was also followed over a limited range of [le] in 2% aqueous MeCN and 2 X M NaOH. The data in Table I give kM' E 0.026 s-l. This value is similar to that in IC, in accord with earlier observations in the corresponding cationic micelles. Reaction is much faster in nonmicellar aggregates of 1 than in micelles, Table 11, and a hydroxyl group does not affect the reaction rate unless it is deprotonated. Effects of the amphiphiles are larger than those of the organic solvents. Nonmicellar aggregates of 1 are more effective than cationic micelles in speeding spontaneous decarboxylation (and dephosphorylation) because the aggregates interact with, and sta(26) Alternatively we could assume that rates in the dimers and trimers are not different from those in the water.
Figure 1. Spontaneous reaction of 6-NBIC in ICand 0.002 M NaOH. The line is predicted by using the model. TABLE I: Effect of l e on the Decomposition of 6-NBIC"
104[le], M
10S[6-NBIC], M
2 5 10 30
2.5 2.5 2.5 2.5 1.o 2.5
50
lO'k,,
s-I
2.16 24.0 24.2 25.4 25.7 24.0
"At 25.0 'C in 2% (v/v) MeCN and 2 X
M NaOH
TABLE 11: Relative Rate Constants for the Decarboxylation of 6-NBIC in Various Reaction Media
ku'lk,'
medium 1,2-ethanediol, 77.5% ( w / w ) ~ n-hexanol, 95% ( w / w ) ~ cetylpyridinium bromide' 2aC IC 2bb.d n-C,2H2sN+(Me)2CH2CO;
"
11 41 100
98 9000 110 (210) 200 200 8700
n-C12H2sN+(Me)2CH(CH,)C0,le'
"At 25.0 'C in water,'lb k,' = 3 X 10" s-I. bReference l l b . CReference 1 la. dValue in parentheses is in 0.9 M NaOH in which the hydroxyl group is deprotonated. 'In 2% (v/v) MeCN. TABLE I11 Best-Fit Parameters for the Analysis of Rates of Unimolecular Decomwsition Reactions"
substrate IO'[NaOH], (ammonium salt) M 6-NBIC (IC) 2 2,4-DNPP (le)b free 2,4-DNPP 0.1 2,4-DNPP 0.1 lutidinium salt 0.1 0.1 'In lc,e with Naggmai b 20.
MeCN, % (v/v)
5 5
10 20
&, M-' K , M-' 5000
2000
20000 4000 1500 300
1800
1800 1000 200
kM', s-' 0.027
7.2 X 9.3 X 2.5 X 2.1 x 10-4
le, ref 9.
bilize, the charge-dispersed transition states, but they do not strongly stabilize the hydrophilic high charge density, initial states. Micelles, on the other hand, interact with and stabilize both initial and transition states, although greater stabilization of the transition state leads to an overall rate increase. The best-fit parameters for analysis of the kinetic data are in Table 111. Unimolecular Decomposition of 2,4-Dinitrophenyl Phosphate, 2,4-DNPP. Decomposition of 2,4-DNPP is fastest in media of low polarity:' as with 6-NBIC,Io and decomposition of 2,4-DNPP (27) (a) Kirby, A. J.; Varvoglis, A. G. J . Am. Chem. SOC.19 7 89 415 (b) Bunton, C. A.; Fendler, E.J.; Fendler, J. H. Ibid. 1967, 8f i22i. (c) Bunton, C. A,; Diaz, S.; Hellyer, J. M.; Ihara, Y . ;Ionescu, L, G.J . Org. Chem. 1975, 40, 2313.
Aggregates of Tri-n-octylalkylammonium Salts
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5857
103[[le], M I
5
10
I
I
~
50
30 IA
V I
I
6 t
.,
io2[ le], M
Figure 3. Bimolecular reactions in l e and 0.01 M NaOH: 0,bis-2,4DNPP in 20% (v/v) MeCN; 0 , 2,4-DNCB in 20% (v/v) MeCN; 2,4-DNCB in 30% (v/v) MeCN. The lines are predicted by using the model. The insert gives rate data in dilute le.
le], M
Figure 2. Spontaneous reaction of 2,4-DNPP in l e and 0.1 mM NaOH:
the unimolecular rate constants increase in the order water C cationic micelle < aggregates of 1. Analysis of Bimolecular Reactions in the Hydroxyethyl Derivative, l e . At high pH, aggregates of l e are deprotonated and the resulting zwitterion is a good nucleophile in deacylation, dephosphorylation, and nucleophilic aromatic sub~titution.~” Analysis of bimolecular reactions using the model requires combination of eq 16,22, and 23 and six parameters: the second-order rate constants of cholinate, kwN,and hydroxylate, kwoH, ions in the aqueous pseudophase, KBaPP,kM,K,, and K . KBaPPis required to estimate mNsin eq 22, and monomeric l e and choline chloride should have similar reactivities. We assume that the aggregate does not bind hydrophilic counterions and competition of ions for the surface of the aggregate is neglected. Thus, mNSis obtained from KBaPPof le, initial [OH-,], and [le] as
0, free 2,4-DNPP and 5% (v/v) MeCN; 2,4-DNPP lutidinium salt; 0 , 5% (v/v) MeCN; m, 10% (v/v) MeCN; A, 20% (v/v) MeCN. The lines
are predicted by using the model.
TABLE I V Rate Constants for the Unimolecular Decomposition of 2,4-Dinitrophenyl Phosphate in Various Reaction Medium and 25.0 O C
reaction medium, conditions
IC, 1 mM KOHb 2a, pH 9 (borate buffer)‘ le, 5% (v/v) CH3CN, pH lob 2b, 0.14.01 M NaOHC
IO4kd, s-’
k,’/k,’”
3.2-4.5 1.86 9 2.3-3.3
39-54 22 108 28-40
“Reference 13b, in water, pH 9, k,’ = 8.3 X IOd cReference 27c.
s-l.
bReference 9
mNS= (0.5(-B - (B2 - 4C)1/2))/[le]
in lc,e is faster than in the corresponding cationic micelle^.^ Because of solubility problems, reactions in l e were followed in solutions containing 5-20% (v/v) MeCN, and analysis of the data in 0.1 mM NaOH using the model is shown in Figure 2. Again, good fits are obtained by using reasonable parameters, as summarized for both reactions in Table 111. Because of dilute [NaOH], the degree of deprotonation of l e is too low to affect self-association or the binding constant. On the other hand, added MeCN should reduce the association constant K by breaking the water structure. Thus, the value of K is lower than that used for ICin the absence of MeCN, and decreases with increasing MeCN content. The free substrate, being dianionic, should bind more strongly than 6-NBIC, as is observed. Also, the value of K, decreases with added lutidine and MeCN, probably because lutidine competes with 2,4-DNPP for sites on the aggregate or reduces its charge density, while added MeCN reduces binding by disrupting the aggregate. The observation that kM’values are reduced with high MeCN content implies slight dependence of kM’ on aggregate size because smaller aggregates should predominate at high [MeCN]. Table I11 compares the best-fit parameters for decomposition of 6-NBIC in ICto that of 2,4-DNPP in le. The value of K is consistent with the effect of added MeCN, while that of K, is consistent with charge of substrates. The reactivities of 2,4-DNPP in various reaction media are compared in Table IV and the trend is as for 6-NBIC; namely,
where B = -(KBaPP
+ [le] + [OH-,])
C = [le][OH-,]
In fitting the published data for bimolecular rate constants in le, eq 16,22,23, and 25 were combined by using a simple computer program. Of the six parameters, experimentally determined values of KwN,KwoH,and KBaPPwere used. The rate constant kMis not a free parameter but is given by the limiting value of kq at high [le] and the literature value of KBaPP;and only K, and K were variable parameters. The fits are shown in Figures 3 and 4, where the points are experimental and the lines are predicted by using the model and the indicated parameters (Table V). Analysis of the dephosphorylation of bis-2,4DNPP6 in l e and 0.01M NaOH is shown in Figure 3. The values of K , and K are consistent with the effect of added MeCN (20%, v/v) on water structure. Figures 3 also shows the fit for the reaction of 2,4DNCB in l e in the presence of 0.01 M NaOH and 20-30%, v/v MeCN.5 Again the fits are good and the parameters used are consistent with the effect of added organic solvent. Analysis of the dephosphorylation of pNPDPP in l e in solutions of 0.01-0.02 M NaOH and 10-30% (v/v) MeCN4 is shown in Figure 4. In general, good fits are obtained. The inhibition by added MeCN is also observed here. An interesting feature is that a larger value of K is required to fit the data with increasing
TABLE V Best-Fit Parameters for the Analysis of Rates of Bimolecular Reactions4 substrate bis-2,4-DNPP 2,4-DNCB pNPDPP
(25)
103[NaOH], M 10 10 1Ob 10 20‘
MeCN, % (v/v) 20 20 30 10 10
KBaPD,M 0.16 0.16 0.16 0.16 0.16
1o c 10
20 30
0.16
Ks, M-l 150 70 6 600 600 250 20
K, M-’ 200 200 180 1000 1500
kM, S-I 5.7 x 10-3 (4 x 10-3) 0.18 0.19 (0.07-0.12) 3.3 4.2
200 180
i(1.2-1.3)
A:$
3 20 unless otherwise indicated; values of kM in parentheses are earlier estimate^.^^^ bNaggmar 3 40.
