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Effect of aggregation on the reactivity of dodecylammonium propionate in organic solvents
Effect of Aggregation on the Reactivity of Dodecylammonium Propionate in Organic Solvents 1. Kinetic Models for Esterolysis Reactions BERNARD
V A L E U R , 1 AND E R I C M O N N I E R
Laboratoire de Chimie G~n~rale (CNRS URA 1103), Conservatoire National des Arts et M~tiers, 292 rue Saint-Martin, 75003 Paris, France
Received April 30, 1991; accepted September 30, 1991 Dodecylammonium propionate (DAP) is a surfactant that undergoes sequential self-association in organic solvents. Its reactivity as a nucleophilic agent depends on the aggregation state. The kinetics of esterolysis of three allophanic esters and p-nitrophenylacetate were studied in benzene and 1,2-dichloroethane as a function of surfactant concentration. After demonstrating by FTIR experiments that the monomeric form of DAP consists of dodecylamine and propionic acid, various kinetics models were developed. Excellent agreement of the experimental data was found with a model in which two rate constants, k~ (for the monomeric form) and k~ (for a surfactant molecule in an aggregate, whatever the size of the aggregate), are considered. Analysis of the data also provides the equilibrium constant K of self-association. The validity of the kinetic model is further supported by the fact that the value found for K in benzene is the same for the four esters and in agreement with the value reported in the literature (determined by vapor pressure osmometry ). Furthermore, this agreement means that the self-association ofa surfactant like DAP can be studied by chemical kinetics. © 1992AcademicPress,Inc. INTRODUCTION C h e m i c a l reactions in organized m e d i a , especially in a q u e o u s micelles or reverse micelles, have b e e n the object o f n u m e r o u s studies b e c a u s e o f t h e v a r i o u s specific effects t h a t can be observed ( 1 ). T h e catalytic effect, which is o f p a r a m o u n t interest, a p p e a r s to be m o r e p r o n o u n c e d in reverse micelles ( f o r m e d in a p o l a r solvents) t h a n in a q u e o u s m i c e l l a r solutions. In reverse micelles, the substrates are i n d e e d c o n f i n e d in the i n t e r i o r o f the aggregates a n d the i n t e r a c t i o n s with the p o l a r h e a d groups o f the surfactant ( a n d possibly solubilized water m o l e c u l e s ) are thus stronger. F o r instance, a n increase in rate c o n s t a n t b y a fact o r o f m o r e t h a n 5 X 10 6 has b e e n o b s e r v e d in m i c e l l a r aggregates o f a l k y l a m m o n i u m carboxylates in benzene solutions ( 1-3 ). It should To whom correspondence should be addressed.
be n o t e d that the n a t u r e o f the solvent also plays a role ( 4 ) . It is the a i m o f the present w o r k to investigate the s t r u c t u r e - r e a c t i v i t y relationship in d o d e c y l a m m o n i u m p r o p i o n a t e ( D A P ) reversed m i c e l l a r aggregates in organic solvents such as benzene a n d 1,2-dichloroethane. These aggregates are c o m p o s e d o f ion pairs, b u t owing to the a m p h o t e r i c n a t u r e o f D A P , d o d e c y l a m i n e can be formed. Therefore, the surfactant itself acts as a n u c l e o p h i l i c agent, a n d thus it plays n o t only a structural role b u t also a r e a c t a n t role. T h e c h e m i c a l reaction investigated in the present w o r k involves three all o p h a n i c esters as m o d e l s for c a r b o x y b i o t i n a n d p - n i t r o p h e n y l a c e t a t e ( P N P A ) . Several a u t h o r s ( 5 - 8 ) have a l r e a d y r e p o r t e d that despite the u n a v o i d a b l e traces o f water in the solvent, the r e a c t i o n o f P N P A with D A P is n o t a hydrolysis b u t a direct aminolysis, the
473 0021-9797/92 $3.00 Jourmt/:ff('olh#d and lnledace &kiem'e. Vol. 150, No. 2. May 1992
Copyright ~? 1992 by Academic Press, [nc. All rights of reproduction in any form reserved.
474
VALEUR
AND
MONNIER
nucleophilic agent being dodecylamine. The reaction is thus of the type RCOOR' + CH3-(CH2)I:NH2 -~
AE-H
O
O2N~O/~
AE-CH3 AE- (I~
CH3-(CH2)I:NH-COR + R'OH. It is shown in this paper that dodecylamine is also the nucleophilic agent in the case of allophanic esters. Various esterolysis reactions in reverse micellar aggregates of alkylammonium carboxylate surfactants have been studied by several authors (5, 7-11 ), but none of these studies relied on a thorough analysis of the data in terms of kinetic models involving the aggregation state of the surfactant. For a correct interpretation of the kinetic data, the aggregation process of DAP should indeed be taken into account. The question of the best model describing this aggregation process has been the object of many papers (12-22) and is not completely settled. Nevertheless, from a critical analysis of all the relevant papers, it seems that multiple equilibrium models are more appropriate that the pseudo-phase model. In particular, Adams and co-workers (16) tested several models and a sequential indefinite selfassociation process was found to best describe their data obtained by vapor pressure osmometry. Therefore, this model will be used in the analysis of our kinetic data. It will be shown that the equilibrium constant for self association of DAP can be derived from this analysis and that the value obtained in benzene is very close to that determined by those authors, which thus justifies a posteriori the use of the sequential indefinite self-association model. EXPERIMENTAL
PROCEDURE
Materials The syntheses of the allophanic esters, Np - nitrophenoxycarbonyl- 2-imidazolidinone ( A E - H ) , 1N-p-nitrophenoxycarbonyl-3Nmethyl-2-imidazolidinone (AE-CH3), and 1Np -nitrophenoxycarbonyl- 3N-phenyl- 2-imidazolidinone (AE-~) (see scheme 1 ) have been reported elsewhere (23, 24). p-NitrophenyJournal tfColloid and lnte([~t~z, Science, Vol. 150, No. 2, May 1992
-
CH~ PNPA
SCHEME 1
lacerate was purchased from Fluka (puriss. grade) and further purified by recrystaUization. DAP was prepared by Kitahara's method (25) from dodecylamine and a slight excess ofpropionic acid; these two compounds were from Janssen and were distilled prior to use. DAP was purified by three successive recrystallizations in the solvent to be used in the kinetic study and then dried under vacuum over P205. Spectroscopic grade solvents (Merck) were used. Benzene was distilled and dried on sodium, and 1,2-dichloroethane was dried on molecular sieves (4 A).
Instruments and Methods The esterolysis reactions were monitored by following the increase in the absorbance of the liberated p-nitrophenol. These measurements were made on a Uvikon 820 spectrophotometer. The wavelength was selected to be 330 nm where all the other compounds present in the solution do not absorb. The cell compartment was maintained at 26 _+ 0.1 °C in all the experiments by means of a Haake FE2 water circulator. The absorbance was recorded against time for about six half-lives (98% completion). The amounts of DAP (or dodecylamine) with respect to ester (about 10 -4 M ) correspond to at least a 20-fold excess. We checked that the reactions were first-order in ester. The pseudofirst-order rates were calculated from the kinetic data by means of Guggenheim's method (26), which offers the advantage that the knowledge of the absorbance at infinite time is not required. The correlation coefficients were typically greater than 0.999.
EFFECT OF AGGREGATION ON REACTIVITY Stock solutions (0.2 M ) of DAP were prepared less than 24 h prior to use and solutions of DAP at various concentrations were prepared by appropriate dilutions. Fourier-transform infrared ( F T I R ) spectra were recorded on a Nicolet 7199 spectrometer at 23°C in NaC1 cells.
475
1 0 3 kob " .IDAP]- I
150
li
EXPERIMENTAL RESULTS 100
The reaction ofallophanic esters and PNPA with DAP was studied at 26 °C in benzene and 1,2-dichloroethane. In all cases, the observed rate constant increases as the concentration in DAP increases. However, it should be emphasized that the kobs/[DAP] ratio decreases with increased DAP concentration, as shown in Figs. 1 to 3. These results show that the reactivity of DAP decreases as it becomes more and more self-associated. This inhibitory effect of aggregation should be examined in light of the sequential self-association model, according to this model, the fraction of DAP that exists in the monomeric form decreases with surfactant concentration (vide infra). There-
10: kobs.[DAP] -I (S-I M-I)
©
AE-$
50
AE-H
A E-CH 3
o.'1
o'.2
[o A p]
FIG. 2. Variations of the ratio ko~/[DAP] as a function of DAP concentration for allophanic esters in 1,2-dichloroethane at 26°C.
fore, DAP appears to be more reactive in its monomeric form than in the aggregated form. This prompted us to examine the nature of the monomeric form of DAP in benzene and dichloroethane. 10 3 kobs. IDA P]-I ( s -1M -1)
60c
15C
100
©
40
50
20 ~ (I AE $ PNPA 0
0.1
0.2
0
0
N
[OAP]
FIG. 1. Variationsof the ratio kobd[DAP]as a function of DAP concentration for the allophanicesters in benzene at 26°C.
0,1
0.2
0-3
[DAP]
FIG. 3. Variations of the ratio ko~/[DAP ] as a function of D A P concentration for PNPA in benzene at 26°C. Journal ¢~/Colloid and Interlace Science
Vol.150,No.2, May1992
476
VALEUR AND MONNIER
The basic question arises as to whether the monomeric form of DAP is an ion pair or consists of propionic acid and dodecylamine. Previous investigations on DAP by ~H N M R (12, 13, 15, 27-29), mainly based on the chemical shift of the protons of the carboxylate and a m m o n i u m moieties, led to the conclusion that DAP in solvents of low polarity such as benzene is in the form of solvated ion pairs even at concentrations lower than the concentration at which aggregates begin to appear (i.e., 3-7 × 10 -3 M a t 26-30°C). These findings are surprising considering the phenomena responsible for ion solvation. In fact, the solvating power of an aprotic solvent is closely related to its ability to donate electrons to cations (cation solvation) or accept electrons from anions (anion solvation), whereas the dielectric constant plays a minor role (30, 31 ). The donor character (which can be expressed by the " d o n o r number" easily determined by experiment (32)) is very weak for benzene and dichloroethane. Therefore, ion pairs are not expected to exist predominantly in these solvents. In order to clarify this important point, we performed Fourier-transform infrared spec-
troscopy experiments on DAP solutions in benzene and dichloroethane at low concentrations and on solutions of propionic acid for comparison. The infrared spectra were recorded from 1500 to 1800 cm -I in order to observe the C - O vibrational bands of propionate ( 1575 cm -~ ) and propionic acid in the monomeric form ( 1755 cm -I ) and the dimeric form (1715 cm-1). The 3500-3700 cm -1 region is also of interest for the detection of the N - H vibrational bands of a primary amine (dodecylamine). It was not possible to see the a m m o n i u m bands because of the high absorption of the solvents in the relevant region of the spectrum. Figures 4 and 5 clearly show that at concentrations lower than 2 × 10 -3 M, the spectra of DAP (in the 1500-1800 cm -~ region) closely resembles that ofpropionic acid in both solvents. Moreover, the characteristic N - H bands of a primary amine are easily detected in dichloroethane. Upon gradual addition of DAP, the C - O bands of propionic acid decrease and those of propionate appear. The concentration in DAP at which the propionate bands appear is in agreement with the operational CMC reported in the literature (13, 25). These findings provide compelling
DAP
~
o
o o
_
1
2.10-3M
0.3
2"10-3M
~
I ~l ~
0"1 A~ o . 0 4 p, /
o ~
0.02
} v~ 10"3M
IA~ ~10-2M
oo,
A
--
.,,,
I
a
0,041.. `
I
0.02 I
,
~
I
I
18o0 1700 1600 1500 180o 1700 1600
FIG. 4. FTIR spectra of DAP and propionic acid in 1,2-dichloroethane. Journal o[Colloid and lnter[~tce Science, VoL 150, No. 2, May 1992
DAP
t/
o J L. ~.~o-'.
" 18o0 17o0
-2 M
0.1
/DA~ 0"01
3700 3600
"~
0-04~- M ~-
i
_
~(©m-1)
477
EFFECT OF AGGREGATION ON REACTIVITY ABSORBANCE
C2HsCOzH
I AA
2.10-3M
0-3
0.1 -2 M
5.10-3M
0.06
OOo31 I
1800
o''
esters by dodecylamine is always higher than by DAP at the same concentration, and the ratio kobs(DA)/kobs(DAP) approaches 1 at very low identical concentrations of DA and DAP. This means that dodecylamine is most likely to be the nucleophilic agent, as in the case of PNPA. This is further supported by the following observations: solutions of dodecylammonium chloride or sodium propionate in benzene at a concentration of 5 × 10-z M at 60°C have no effect on the esters under study. From the experimental results, it can be concluded that (i) the monomeric form of DAP consists of dodecylamine and propionic acid; (ii) at very low concentrations where DAP is in the monomeric form, the esterolytic efficiency of DAP is close to that of dodecylamine; and (iii) as the concentration of DAP increases, its esterolytic efficiency decreases together with the fraction of DAP monomers. The following questions now arise:
2.10 .3 M i
I
1700
i
i
1600
.=
~( crn-1)
FIG. 5. FTIR spectra of DAP and propionic acid in benzene.
evidence of the fact that DAP is in the form of dodecylamine + propionic acid at low concentrations ( < 2 × 10 -3 M ) at which only the monomeric form exists. At higher concentrations, aggregation of DAP occurs in the form of dodecylammonium propionate, with coexistence ofdodecylamine and propionic acid: the fraction of these species should be in accordance with the fraction of monomer predicted by the sequential self-association model C12H25NH3G, ®O2C-C2H5 ~--
aggregated form
(i) Is the reactivity of DAP due only to the monomeric form or is there a contribution of the aggregates? (ii) If there is a contribution of the aggregates, do they act as a whole as kinetic species or should the surfactant molecules in the aggregates (ion pairs) be considered individually? (iii) Is it possible to determine the rate constants relevant to the monomers and that (or those) relevant to the aggregates? To answer these questions, kinetic models should be developed. KINETIC MODELS
Basic Relations for Sequential Indefinite Self-Association with All Molar Equilibrium Constants Equal This multiple-equilibrium model of aggregation can be described as
C,2HzsNH2 + C2HsCO/H monomeric form These results led us to examine the reactivity of dodecylamine alone as compared to that of DAP. The rate of aminolysis of the allophanic
S] + Sl ~ 52
KI2
52 -1- S| ~-- S 3
K23
Sn-l+Sl ~S, with Kl2
=
K23
. . . . .
K,-ln, gn-I
Journal o[ Colloid and lnteff?lce &'ience, Vol.
n = g.
[1]
150, No. 2, May 1992
478
VALEUR AND MONNIER
Let [Si] be the concentration in aggregates containing i surfactant molecules. The total concentration in surfactant is then given by [S]o = [SI] + 2[S2] + 3[$3]
+---
+
0.8 0.6
+n[S.]+...
= IS1] --~2K[$1] 2 +
2
i
0.4-
3K2[S1] 3
• • • + nKn-l[s1]n
f'lt
+
• • • .
0.2-
[2]
0
i 0.05
0.~1
i 0.15
0.~2
i 0.25
0.'3
~' [S]o
Summation of the series leads to
[Sl] [S]o - (1
__ K [ S 1 1 2 )
.
[3]
The fraction of monomer is defined as
FIG. 6. Variations in the fraction of monomer as a functionof the total concentrationofsurfactantfor various values of the equilibrium constant K (expressedin M-l): 10 (1), 20 (2), 30 (3), 50 (4), 90 (5), 150 (6), 230 (7), 350(8/.
[S~]
fl = -
[S]0
"
Then, from Eq. [3] we obtain K[S]0 -
1 - - f l 1/2
[4]
fl
This equation was previously derived by Lo e t a l . (16). fl can then be expressed as a function of K and [ S ]o: f =
1 + 2K[S]o - (1 + 4K[S]o) 1/2 2K2[S]02
[5]
The fraction ofdimer, trimer . . . . . n-mer can be expressed as a function of the fraction of monomer f : dimer:
j ~ _ [$2___]-fl(1
n-mer:
f~-
[S]o
-fl
1/2)
[s,__j]-fl(1--fll/2) "-1.
[S]o
[6]
[7]
The fraction of surfactant in the aggregated form can be written as [ag]
fag-- [S]o-
E ~ 2 [Si]
[S]o =fll/2(l-fli/2).
[8]
The fraction of monomer as a function of [S]o for various values of K (Eq. 5 ) is shown Journal qfCblloid and lnte(/bce Science.
Vol.150,No.2,May1992
in Fig. 6. From the examination of this figure together with Figs. 1, 2, and 3, it can be guessed that a satisfactory agreement will never be obtained by considering that only the monomers are the kinetic species. The slow decrease in the kobs/[DAP] ratio at high DAP concentrations is in favor of the participation of other kinetic species, i.e., the aggregates. Several assumptions can be made, leading to different models. Model I n . The assumptions pertaining to this model are the following: (i) A surfactant molecule acts individually as a kinetic species either in the monomeric form or in an aggregate with pseudo-first-order kinetics; the rate constant is kl for a surfactant molecule in the monomeric form and ka within an aggregate. (ii) ka is assumed to be independent of the size of the aggregate. (iii) The aggregation process is assumed to be a sequential indefinite self-association with all equilibrium constants equal. It should be noted that assumptions (i) and (ii) are usually made in treating kinetic data in aqueous micellar solutions with different reactivities in the bulk and in aggregates. From the above assumptions, the following relations can be easily derived:
479
EFFECT OF AGGREGATION ON REACTIVITY
kob~ = kl[Sl]
kobs = kl[Sl] + k,(2152]
+ kag([52] 31- [53] + [54] -1- • " ")
+ 3[$31 + 4 1 5 4 1 + " • ") or
= k~[Sl] + k , ( [ S ] 0 - [S~]) kob~ = k l f l [ S ] o + k a ( 1 - f l ) [ S ] 0 .
[9]
]gobs
[S]o
- (k, - ka)fl + ka.
[S]o
[101
According to assumption (iii), f~ is given by Eq. [5]. M o d e l Ib. The assumptions are the same as in model Ia but the rate constant for the dimer (k2) is different from that of the other aggregates:
+ k a g ( [ 5 3 ] --[- [ 5 4 ] +
• • .)
= kl[S~] + k2152]
kobs = kl[Sl] + 2k2152]
+ kag([ag] - [$2]).
[17l
Hence
+ k . ( [ S ] 0 - [Sl] - 2[S2]).
[11] kobs
By using Eq. [6], we obtain
[S]0
- ( k l + k2 - 2 k a g ) f
+ kagfl 1/2 + (kag - k2)fl 3/2. - [kl + 2k2 - 3ka]f~ + 2(k~ - k 2 ) f l 3/2 + ka.
[12]
M o d e l Ic. This model is identical to model Ia but the rate constant for the monomer is kl[S~] + k~ [S~ ]2, as in the case of esterolysis in homogeneous solutions (33-37): kobs = k l [ S l ]
[16]
kobs = k~[S~] + k2[$2]
+ k,(3[S3l + 4 1 5 4 1 + " " ")
[S]0
- (kl - kag)f + kagfl 1/2.
M o d e l lib. This model is identical to model IIa but the rate constant for the dimer (k2) is different from that of the other aggregates:
kobs = kt[S~] + 2k21521
kobs
[15]
By using Eq. [8 ], we obtain
Hence, kob~
kobs = k~[S~] + kag[ag].
+ k] [Sl] 2
+k~([Slo-[Sl])
[13]
,o,s k'l f l3/2 + k a.
[14]
K M o d e l IIa. In contrast to model Ia, each aggregate acts as a kinetic species with pseudofirst-order kinetics. The rate constant is kl for the m o n o m e r and k~g for the aggregates, whatever their size:
[18]
These models were checked with the experimental data obtained for the three allophanic esters in benzene and in dichloroethane and for PNPA in benzene. The following procedure was employed: for a given value of K, the fraction of monomer j] is calculated by using Eq. [ 5 ] at each concentration of DAP; then curve fitting of the plot ofkob~/[So] versus J~ by a nonlinear least-squares method is attempted by using Eqs. [10], [12], [14], [16], or [18], the criterion being the reduced X 2. Various values of K are successively tried until the minimum of the X 2 is reached. Model Ia gives excellent agreement, as shown in Figs. 7, 8, and 9 and in Table I. No significant improvement of the quality of the fit is obtained by considering the rate constant for the dimer (k2) to be different from that of the other aggregates (model Ib). Analysis of the kinetic data by means of Eq. [14 ] relevant to model Ic failed to give a value JournalolColloidand lnteffhceScience, Vol. 150, No. 2, May 1992
480
VALEUR AND MONNIER
103
kobs (s'1) ].1
Ar--
©
A E--CH,
/ 0.'01
0~005
AE-H
2.
0:02
o
,,-t
I, I
I
0:04
0:06
0.1' [DAP]
At-~
I J
i i
0:08
I
A E--CH t
1
AE--H I =
1
i£1 E,
FIG. 7. Kinetic data obtained for the allophanic esters in benzene at 26°C and best fit (solid lines) with model la. The parameters corresponding to the best fit are given in Table I.
of k'~ with an acceptable error, and no improvement of the reduced X 2 was obtained with respect to model Ia. With regard to models IIa and lib pertaining to cases where the aggregates are considered as kinetic species, it was not possible to get a satisfactory fit of the data with the relevant equations. Jo trnal ~[ Colloid and Interlace Science,
Vol. 150,No. 2, May 1992
DISCUSSION
The tests of the various kinetic models show that the kinetic data are very well described by model Ia. There is definitely a contribution of the aggregates to the aminolysis of the esters, and each surfactant molecule in the aggregate, not the aggregate as a whole, acts as a kinetic
EFFECT OF AGGREGATION ON REACTIVITY 10 3 kob L2 (s-l)
481
•
CJ~CJ
AE
~)
6.
i,
4,
6.02 o
.1[
0:04
o'.o6
o:oa
o.~' loOP]
I l
I
i
l
J
J
I
AE--CH
3
r't tl,I a"
I
J
,
t
AE--H
I
'
FIG. 8. Kinetic data obtained for the allophanic esters in 1,2-dichloroethane at 26°C and best fit (solid lines) with model Ia. The parameters corresponding to the best fit are given in Table I.
species. This is in contradiction with the conclusions o f O ' C o n n o r and co-workers who stated that each aggregate has its own kinetic identity, i.e., acts as a kinetic species (5, 10). It should be noted that no curve fitting evidenced their statement. T h e fact that model Ic, involving a secondorder dependence on the m o n o m e r concen-
tration, does not provide a better description of the kinetic data than model Ia deserves further attention. At first sight, this is surprising because it is well established that esterolysis in aprotic solvents show first- and higher-order dependence on the a m i n e concentration ( 3 3 37). N o i m p r o v e m e n t in the quality of the fit after adding the term k'~ [S~ ]2 does not m e a n Journal (~]('otloid and Interlace Science, Vol. 150. No. 2, May 1992
482
VALEUR AND MONNIER 10 3 kobs (s-~)
© O.
PNPA
0.~ i
i
0-6
OA
0.2.
olo= I
olo,
0:06
o'.oa
o!1 C~"]
i
-2Y.. ¸
FIG. 9. Kinetic data obtained for PNPA in benzene at 26°C and best fit (solid lines) with model Ia. The parameters corresponding to the best fit are given in Table I.
that this term does not exist, but it m a y be so small with respect to the other terms that it cannot be detected. In fact, it will be shown in the next paper of this series (38) that for the reaction of allophanic esters with dodecylamine in benzene, the second-order term has a much smaller contribution than the fLrstorder one. In contrast, for the reaction of PNPA with dodecylamine in benzene, previous works have shown that the contribution of the general base-catalyzed pathway (resultJournal of Colloid and lnterJace Science, Vol. 150, No. 2, May 1992
ing in second-order dependence on dodecylamine concentration) is m u c h larger than that of the uncatalyzed pathway. However, the mechanism of the reaction of PNPA with DAP is different despite the fact that dodecylamine is still the nucleophilic agent. The variations in ko~ versus DAP or dodecylamine concentration are completely different because, in the reaction with DAP, the d o d e c y l a m m o n i u m ion plays an important role which will be discussed in detail in a forthcoming paper (38).
EFFECT OF AGGREGATION
483
ON REACTIVITY
TABLE I Results of C u r v e Fitting o f the Kinetic D a t a O b t a i n e d for the A l l o p h a n i c Esters a n d P N P A in Benzene a n d 1,2-Dichloroethane at 2 6 ° C K (M-I ) Solvent: benzene AE-H AE-CH3 AE- ql, PNPA Solvent: 1,2-dichloroethane AE-H AE-CH3 AE-~
235 240 225 215
+ 35 + 30 -+ 25 + 25
120 _ 30 195 + 55 175 -+ 35
l0s kl (s-I M -~)
308 277 311 105
l0s ku (s-1M -l)
+ 24 __ 17 + 16 -+ 6
248 + 25 274 - 37 579 -+ 53
X~
(Estimated errors)
14.9 23.7 36.4 5.45
__+0.9 __+0.7 -+0.8 __ 0.25
0.92 0.98 1.26 0.85
(2%) (1%) (3%) (2%)
24.3 25.8 58.9
- 3.0 + 2.4 -+ 3.7
1.40 0.75 0.66
(3%) (3%) (3%)
N o t e . x 2 is the reduced x 2 whose value s h o u l d be close to 1 for a satisfactory fit.
The results of the kinetic analysis by means of model Ia (Table l ) show that the rate constant for the surfactant molecules in the aggregated form (ion pairs) is always much lower than in the monomeric form (dodecylamine + propionic acid) by a factor of nine or more. It is also worth pointing out that the kinetic model provides the equilibrium constant of the self-association process and that its value does not significantly depend on the nature of the ester under study. It is remarkable that the average value of K in benzene (230 _+40 M - t at 26°C) is in excellent agreement with the value of 230 M -1 calculated from vapor pressure osmometry experiments (16 ) (this value is extrapolated from the values of 207 M-~ at 27°C and 70.4 M -I at 37°C by using Van't Hoff's equation). This excellent accordance further confirms the validity of the kinetic model and justifies a posteriori the use of the aggregation model based on sequential indefinite self-association with all molar equilibrium constants equal. It can be also concluded that the substrates at a concentration of 10-4 M do not alter significantly the aggregation process. The values of K obtained in dichloroethane are more scattered, but the average value (around 150 M -1 ) is significantly lower than that in benzene. The difference in polarity of these two solvents may account for the ob-
served difference in the efficiency of self-association. The value of this equilibrium constant in dichloroethane obtained in this work was not reported previously. The values in other organic solvents could be easily determined. The validity of this method of determination of K is supported by the excellent agreement found for K in benzene by the physical and the chemical methods. Such an approach of structural features by chemical kinetics is of great interest. Generalization to other systems is possible, but the reliability of the method may be affected by possible perturbation of the aggregation process by the substrate. A control by a physical method is a prerequisite. Interestingly, Figs. 7 to 9 show that at high concentration in surfactant the variation in kob s tends to be linear. From Eqs. [ 9 ] and [ 5 ], it is indeed easy to show that the asymptotic behavior of kobs is expressed by kobs ~
ka[S]0 +
kl - ka K for
K[S]0>> 1.
[19]
Therefore, it is of interest to note that the slope of the asymptote represents the rate constant ka for the aggregated surfactant and the intercept is (k~ - k a ) / K (Fig. 10). This provides Journal t~l'Colloid and Interlace Science, Vol. 150, No. 2, May 1992
484
VALEUR AND MONNIER available to us. Thanks are also due to Dr. B. Jasse, ESPCI, Paris, for his help in FTIR experiments.
k°bs I Slope: k a
REFERENCES
k1-
ka
...-.............., J ' J
[Sl0 FIG. 10. Illustration of the variations in ko~ versus surfactant concentration showing the asymptotic behavior and involved parameters. an easy w a y to d e t e r m i n e ka p r o v i d e d that the linear part o f the p l o t at high c o n c e n t r a t i o n s is well enough defined. Satisfactory agreement between the values o f ka d e t e r m i n e d b y this m e t h o d a n d those o b t a i n e d b y the general p r o c e d u r e was f o u n d in m o s t cases. F o r instance, in the case AE-cI, in benzene, the range o f c o n c e n t r a t i o n was e x t e n d e d to 0.2 M ; b y t a k i n g the e x p e r i m e n t a l values o f kobs for conc e n t r a t i o n s ranging from 0.06 to 0.2 M, a linear regression in this range yields the slope, i.e., ka, equal to 35.9 × 10 -3 s - l M - l , a value close to that o b t a i n e d by the general p r o c e d u r e (36.4 × 10 -3 s -1 M - l ) . In principle, the rate c o n s t a n t kl c a n be t h e n d e t e r m i n e d from the intercept p r o v i d e d that the e q u i l i b r i u m constant is k n o w n . H o w e v e r , the value o f the intercept was found, in s o m e cases, n o t accurate e n o u g h to p r o v i d e a value o f k l in g o o d agreem e n t with t h a t o b t a i n e d b y the general p r o cedure. It s h o u l d be e m p h a s i z e d that the rate constants for the a l l o p h a n i c esters are higher t h a n those o f P N P A . A d e t a i l e d study o f the m e c h a n i s m s will be r e p o r t e d elsewhere ( 3 8 ) . Alt h o u g h a m i n o l y s i s b y d o d e c y l a m i n e is the c o m m o n feature o f the reaction o f P N P A a n d a l l o p h a n i c esters with D A P , the m e c h a n i s m o f a m i n o l y s i s is different. ACKNOWLEDGMENTS The authors thank Professors J. Prri6 and A. Klarbr, University of Toulouse, for making the allophanic esters Journalq/Colloidand lnterJace&'ience,Vol.150,No.2, May1992
1. Fendler, J. H., and Fendler, E. J., "Catalysis in Micellar and Macromolecular Systems," p. 340. Academic Press, New York, 1975. 2. O'Connor, C. J., Fendler, E. J., and Fendler, J. H., J. Am. Chem. Soc. 95, 3273 (1973). 3. O'Connor, C. J., Fendler, E. J., and Fendler, J. H., J. Chem. Soc. Dalton Trans. 625 (1974). 4. Fendler, J. H., Fendler, E. J., Medary, R. T., and Woods, V. A., J. Am. Chem. Soc. 94, 7288 (1972). 5. O'Connor, C. J., Lomax, T. D., and Ramage, R. E., Adv. Colloid Interface Sci. 20, 21 (1984), and references cited therein. 6. O'Connor, C. J., and Lomax, T. D., Aust. J. Chem. 36, 895 (1983). 7. Farah, J. P. S., El Seoud, M. I., and El Seoud, O. A., J. Org. Chem. 49, 4063 (1984). 8. El Seoud, O. A., Vieira, R. C., and Novaki, L. P., Bull. Chem. Soc. Jpn. 60, 1163 (1987). 9. El Seoud, M. I., Vieira, R. C., and E1 Seoud, O. A., J. Org. Chem. 47, 5137 (1982). 10. O'Connor, C. J., and Lomax, T. D., J. Colloidlnterface Sci. 95, 204 (1983). 11. Sunamoto, J., in "Solution Behavior of Surfactants" (K. L. Mittal and E. J. Fendler, Eds.), p. 767. Plenum, New York, 1982. 12. Fendler, J. H., Fendler, E. J., Medary, R. T., and E1 Seoud, 0. A., J. Chem. Soc. Faraday Trans. 1 69, 280 (1973). 13. Fendler, J. H., Fendler, E. J., Medary, R. T., and E1 Seoud, 0. A., J. Phys. Chem. 77, 1432 (1973). 14. E1 Seoud, O. A., and Ribeiro, F. P., J. Org. Chem. 41, 1365 (1976). 15. El Seoud, O. A., Fendler, E. J., Fendler, J. H., and Medary, R. T., J. Phys. Chem. 77, 1876 (1973). 16. Lo, F. Y. F., Escort, B. M., Fendler, E. J., Adams, E. T., Larsen, R. D., and Smith, P. W., J. Phys. Chem. 79, 2609 (1975). 17. Herrmann, U., and Schelly, Z. A., J. Am. Chem. Soc. 101, 2665 (1979). 18. Muller, N., J. Phys. Chem. 79, 287 (1975). 19. Verbeeck, A., Gelade, E., and De Schryver, F. C., Langmuir 2, 448 (1986). 20. Eicke, H. F., and Denss, A., J. Colloid Interface Sci. 64, 386 (1978). 21. Correll, G. D., Cheser, R. N., Nome, F., and Fendler, J. H., J. Am. Chem. Soc. 100, 1254 (1978). 22. Jean, Y.-C., and Ache, H. J., J. Am. Chem. Soc. 100, 6320 (1978). 23. Monnier, E., Klaebe, A., and Prrir, J., Tetrahedron 41, 3269 (1985).
EFFECT OF AGGREGATION ON REACTIVITY 24. Monnier, E., Botella, J. M., Murillo, A., Klaebe, A., and P6ri6, J., Tetrahedron 42, 1315 (1986). 25. Kitahara, A., Bull. Chem. Soc. Jpn. 28, 234 (1955). 26. Guggenheim, E. A., Philos. Mag. 2, 538 (1926). 27. E1 Seoud, O. A., Fendler, E. J., and Fendler, J. H., Z Chem. Soc. Faraday Trans. 1 70, 450 (1974). 28. El Seoud, O. A., Fendler, E. J., and Fendler, J. H., J. Chem. Soc. Faraday Trans. 1 70, 459 (1974). 29. O'Connor, C. J., and Lomax, T. D., Aust. J. Chem. 36, 917 (1983). 30. Gutmann, V., "Coordination Chemistry in NonAqueous Solutions." Springer-Verlag, New York, 1969. 31. Szwarc, M., in "Ions and Ion Pairs in Organic Reactions" (M. Szwarc, Ed.), p. 1. Wiley-lnterscience, New York, 1972.
485
32. Gutmann, V., and Wychera, E., lnorg. Nucl. Chem. Lett. 2, 257 (1966). 33. Menger, F. M., and Smith, J. H., Z Am. Chem. Soc. 94, 3824 (1972). 34. Menger, F. M., and Vitale, A. C., J. Am. Chem. Soc. 95, 4931 (1973). 35. El Seoud, O. A., Martins, A., Barbur, L. P., da Silva, M. J., and Aldrigue, V., J. Chem. Soc. Perkin Trans. 2 1674 (1977). 36. E1 Seoud, O. A., Pivetta, F., E1 Seoud, M. I., Farah, J. P. S., and Martins, A., J. Org. Chem. 44, 4832 (1979). 37. Neuvoven, H., J. Chem. Soc. Perkin Trans. 2 159 (1987). 38. Monnier, E., Peri6, J., KlaOb6, A., and Valeur, B., to be published.
Journal ~!/C~*ltoidand lnleiJace Sciem'e, Vol. 150. No, 2, May 1992
V A L E U R , 1 AND E R I C M O N N I E R
Laboratoire de Chimie G~n~rale (CNRS URA 1103), Conservatoire National des Arts et M~tiers, 292 rue Saint-Martin, 75003 Paris, France
Received April 30, 1991; accepted September 30, 1991 Dodecylammonium propionate (DAP) is a surfactant that undergoes sequential self-association in organic solvents. Its reactivity as a nucleophilic agent depends on the aggregation state. The kinetics of esterolysis of three allophanic esters and p-nitrophenylacetate were studied in benzene and 1,2-dichloroethane as a function of surfactant concentration. After demonstrating by FTIR experiments that the monomeric form of DAP consists of dodecylamine and propionic acid, various kinetics models were developed. Excellent agreement of the experimental data was found with a model in which two rate constants, k~ (for the monomeric form) and k~ (for a surfactant molecule in an aggregate, whatever the size of the aggregate), are considered. Analysis of the data also provides the equilibrium constant K of self-association. The validity of the kinetic model is further supported by the fact that the value found for K in benzene is the same for the four esters and in agreement with the value reported in the literature (determined by vapor pressure osmometry ). Furthermore, this agreement means that the self-association ofa surfactant like DAP can be studied by chemical kinetics. © 1992AcademicPress,Inc. INTRODUCTION C h e m i c a l reactions in organized m e d i a , especially in a q u e o u s micelles or reverse micelles, have b e e n the object o f n u m e r o u s studies b e c a u s e o f t h e v a r i o u s specific effects t h a t can be observed ( 1 ). T h e catalytic effect, which is o f p a r a m o u n t interest, a p p e a r s to be m o r e p r o n o u n c e d in reverse micelles ( f o r m e d in a p o l a r solvents) t h a n in a q u e o u s m i c e l l a r solutions. In reverse micelles, the substrates are i n d e e d c o n f i n e d in the i n t e r i o r o f the aggregates a n d the i n t e r a c t i o n s with the p o l a r h e a d groups o f the surfactant ( a n d possibly solubilized water m o l e c u l e s ) are thus stronger. F o r instance, a n increase in rate c o n s t a n t b y a fact o r o f m o r e t h a n 5 X 10 6 has b e e n o b s e r v e d in m i c e l l a r aggregates o f a l k y l a m m o n i u m carboxylates in benzene solutions ( 1-3 ). It should To whom correspondence should be addressed.
be n o t e d that the n a t u r e o f the solvent also plays a role ( 4 ) . It is the a i m o f the present w o r k to investigate the s t r u c t u r e - r e a c t i v i t y relationship in d o d e c y l a m m o n i u m p r o p i o n a t e ( D A P ) reversed m i c e l l a r aggregates in organic solvents such as benzene a n d 1,2-dichloroethane. These aggregates are c o m p o s e d o f ion pairs, b u t owing to the a m p h o t e r i c n a t u r e o f D A P , d o d e c y l a m i n e can be formed. Therefore, the surfactant itself acts as a n u c l e o p h i l i c agent, a n d thus it plays n o t only a structural role b u t also a r e a c t a n t role. T h e c h e m i c a l reaction investigated in the present w o r k involves three all o p h a n i c esters as m o d e l s for c a r b o x y b i o t i n a n d p - n i t r o p h e n y l a c e t a t e ( P N P A ) . Several a u t h o r s ( 5 - 8 ) have a l r e a d y r e p o r t e d that despite the u n a v o i d a b l e traces o f water in the solvent, the r e a c t i o n o f P N P A with D A P is n o t a hydrolysis b u t a direct aminolysis, the
473 0021-9797/92 $3.00 Jourmt/:ff('olh#d and lnledace &kiem'e. Vol. 150, No. 2. May 1992
Copyright ~? 1992 by Academic Press, [nc. All rights of reproduction in any form reserved.
474
VALEUR
AND
MONNIER
nucleophilic agent being dodecylamine. The reaction is thus of the type RCOOR' + CH3-(CH2)I:NH2 -~
AE-H
O
O2N~O/~
AE-CH3 AE- (I~
CH3-(CH2)I:NH-COR + R'OH. It is shown in this paper that dodecylamine is also the nucleophilic agent in the case of allophanic esters. Various esterolysis reactions in reverse micellar aggregates of alkylammonium carboxylate surfactants have been studied by several authors (5, 7-11 ), but none of these studies relied on a thorough analysis of the data in terms of kinetic models involving the aggregation state of the surfactant. For a correct interpretation of the kinetic data, the aggregation process of DAP should indeed be taken into account. The question of the best model describing this aggregation process has been the object of many papers (12-22) and is not completely settled. Nevertheless, from a critical analysis of all the relevant papers, it seems that multiple equilibrium models are more appropriate that the pseudo-phase model. In particular, Adams and co-workers (16) tested several models and a sequential indefinite selfassociation process was found to best describe their data obtained by vapor pressure osmometry. Therefore, this model will be used in the analysis of our kinetic data. It will be shown that the equilibrium constant for self association of DAP can be derived from this analysis and that the value obtained in benzene is very close to that determined by those authors, which thus justifies a posteriori the use of the sequential indefinite self-association model. EXPERIMENTAL
PROCEDURE
Materials The syntheses of the allophanic esters, Np - nitrophenoxycarbonyl- 2-imidazolidinone ( A E - H ) , 1N-p-nitrophenoxycarbonyl-3Nmethyl-2-imidazolidinone (AE-CH3), and 1Np -nitrophenoxycarbonyl- 3N-phenyl- 2-imidazolidinone (AE-~) (see scheme 1 ) have been reported elsewhere (23, 24). p-NitrophenyJournal tfColloid and lnte([~t~z, Science, Vol. 150, No. 2, May 1992
-
CH~ PNPA
SCHEME 1
lacerate was purchased from Fluka (puriss. grade) and further purified by recrystaUization. DAP was prepared by Kitahara's method (25) from dodecylamine and a slight excess ofpropionic acid; these two compounds were from Janssen and were distilled prior to use. DAP was purified by three successive recrystallizations in the solvent to be used in the kinetic study and then dried under vacuum over P205. Spectroscopic grade solvents (Merck) were used. Benzene was distilled and dried on sodium, and 1,2-dichloroethane was dried on molecular sieves (4 A).
Instruments and Methods The esterolysis reactions were monitored by following the increase in the absorbance of the liberated p-nitrophenol. These measurements were made on a Uvikon 820 spectrophotometer. The wavelength was selected to be 330 nm where all the other compounds present in the solution do not absorb. The cell compartment was maintained at 26 _+ 0.1 °C in all the experiments by means of a Haake FE2 water circulator. The absorbance was recorded against time for about six half-lives (98% completion). The amounts of DAP (or dodecylamine) with respect to ester (about 10 -4 M ) correspond to at least a 20-fold excess. We checked that the reactions were first-order in ester. The pseudofirst-order rates were calculated from the kinetic data by means of Guggenheim's method (26), which offers the advantage that the knowledge of the absorbance at infinite time is not required. The correlation coefficients were typically greater than 0.999.
EFFECT OF AGGREGATION ON REACTIVITY Stock solutions (0.2 M ) of DAP were prepared less than 24 h prior to use and solutions of DAP at various concentrations were prepared by appropriate dilutions. Fourier-transform infrared ( F T I R ) spectra were recorded on a Nicolet 7199 spectrometer at 23°C in NaC1 cells.
475
1 0 3 kob " .IDAP]- I
150
li
EXPERIMENTAL RESULTS 100
The reaction ofallophanic esters and PNPA with DAP was studied at 26 °C in benzene and 1,2-dichloroethane. In all cases, the observed rate constant increases as the concentration in DAP increases. However, it should be emphasized that the kobs/[DAP] ratio decreases with increased DAP concentration, as shown in Figs. 1 to 3. These results show that the reactivity of DAP decreases as it becomes more and more self-associated. This inhibitory effect of aggregation should be examined in light of the sequential self-association model, according to this model, the fraction of DAP that exists in the monomeric form decreases with surfactant concentration (vide infra). There-
10: kobs.[DAP] -I (S-I M-I)
©
AE-$
50
AE-H
A E-CH 3
o.'1
o'.2
[o A p]
FIG. 2. Variations of the ratio ko~/[DAP] as a function of DAP concentration for allophanic esters in 1,2-dichloroethane at 26°C.
fore, DAP appears to be more reactive in its monomeric form than in the aggregated form. This prompted us to examine the nature of the monomeric form of DAP in benzene and dichloroethane. 10 3 kobs. IDA P]-I ( s -1M -1)
60c
15C
100
©
40
50
20 ~ (I AE $ PNPA 0
0.1
0.2
0
0
N
[OAP]
FIG. 1. Variationsof the ratio kobd[DAP]as a function of DAP concentration for the allophanicesters in benzene at 26°C.
0,1
0.2
0-3
[DAP]
FIG. 3. Variations of the ratio ko~/[DAP ] as a function of D A P concentration for PNPA in benzene at 26°C. Journal ¢~/Colloid and Interlace Science
Vol.150,No.2, May1992
476
VALEUR AND MONNIER
The basic question arises as to whether the monomeric form of DAP is an ion pair or consists of propionic acid and dodecylamine. Previous investigations on DAP by ~H N M R (12, 13, 15, 27-29), mainly based on the chemical shift of the protons of the carboxylate and a m m o n i u m moieties, led to the conclusion that DAP in solvents of low polarity such as benzene is in the form of solvated ion pairs even at concentrations lower than the concentration at which aggregates begin to appear (i.e., 3-7 × 10 -3 M a t 26-30°C). These findings are surprising considering the phenomena responsible for ion solvation. In fact, the solvating power of an aprotic solvent is closely related to its ability to donate electrons to cations (cation solvation) or accept electrons from anions (anion solvation), whereas the dielectric constant plays a minor role (30, 31 ). The donor character (which can be expressed by the " d o n o r number" easily determined by experiment (32)) is very weak for benzene and dichloroethane. Therefore, ion pairs are not expected to exist predominantly in these solvents. In order to clarify this important point, we performed Fourier-transform infrared spec-
troscopy experiments on DAP solutions in benzene and dichloroethane at low concentrations and on solutions of propionic acid for comparison. The infrared spectra were recorded from 1500 to 1800 cm -I in order to observe the C - O vibrational bands of propionate ( 1575 cm -~ ) and propionic acid in the monomeric form ( 1755 cm -I ) and the dimeric form (1715 cm-1). The 3500-3700 cm -1 region is also of interest for the detection of the N - H vibrational bands of a primary amine (dodecylamine). It was not possible to see the a m m o n i u m bands because of the high absorption of the solvents in the relevant region of the spectrum. Figures 4 and 5 clearly show that at concentrations lower than 2 × 10 -3 M, the spectra of DAP (in the 1500-1800 cm -~ region) closely resembles that ofpropionic acid in both solvents. Moreover, the characteristic N - H bands of a primary amine are easily detected in dichloroethane. Upon gradual addition of DAP, the C - O bands of propionic acid decrease and those of propionate appear. The concentration in DAP at which the propionate bands appear is in agreement with the operational CMC reported in the literature (13, 25). These findings provide compelling
DAP
~
o
o o
_
1
2.10-3M
0.3
2"10-3M
~
I ~l ~
0"1 A~ o . 0 4 p, /
o ~
0.02
} v~ 10"3M
IA~ ~10-2M
oo,
A
--
.,,,
I
a
0,041.. `
I
0.02 I
,
~
I
I
18o0 1700 1600 1500 180o 1700 1600
FIG. 4. FTIR spectra of DAP and propionic acid in 1,2-dichloroethane. Journal o[Colloid and lnter[~tce Science, VoL 150, No. 2, May 1992
DAP
t/
o J L. ~.~o-'.
" 18o0 17o0
-2 M
0.1
/DA~ 0"01
3700 3600
"~
0-04~- M ~-
i
_
~(©m-1)
477
EFFECT OF AGGREGATION ON REACTIVITY ABSORBANCE
C2HsCOzH
I AA
2.10-3M
0-3
0.1 -2 M
5.10-3M
0.06
OOo31 I
1800
o''
esters by dodecylamine is always higher than by DAP at the same concentration, and the ratio kobs(DA)/kobs(DAP) approaches 1 at very low identical concentrations of DA and DAP. This means that dodecylamine is most likely to be the nucleophilic agent, as in the case of PNPA. This is further supported by the following observations: solutions of dodecylammonium chloride or sodium propionate in benzene at a concentration of 5 × 10-z M at 60°C have no effect on the esters under study. From the experimental results, it can be concluded that (i) the monomeric form of DAP consists of dodecylamine and propionic acid; (ii) at very low concentrations where DAP is in the monomeric form, the esterolytic efficiency of DAP is close to that of dodecylamine; and (iii) as the concentration of DAP increases, its esterolytic efficiency decreases together with the fraction of DAP monomers. The following questions now arise:
2.10 .3 M i
I
1700
i
i
1600
.=
~( crn-1)
FIG. 5. FTIR spectra of DAP and propionic acid in benzene.
evidence of the fact that DAP is in the form of dodecylamine + propionic acid at low concentrations ( < 2 × 10 -3 M ) at which only the monomeric form exists. At higher concentrations, aggregation of DAP occurs in the form of dodecylammonium propionate, with coexistence ofdodecylamine and propionic acid: the fraction of these species should be in accordance with the fraction of monomer predicted by the sequential self-association model C12H25NH3G, ®O2C-C2H5 ~--
aggregated form
(i) Is the reactivity of DAP due only to the monomeric form or is there a contribution of the aggregates? (ii) If there is a contribution of the aggregates, do they act as a whole as kinetic species or should the surfactant molecules in the aggregates (ion pairs) be considered individually? (iii) Is it possible to determine the rate constants relevant to the monomers and that (or those) relevant to the aggregates? To answer these questions, kinetic models should be developed. KINETIC MODELS
Basic Relations for Sequential Indefinite Self-Association with All Molar Equilibrium Constants Equal This multiple-equilibrium model of aggregation can be described as
C,2HzsNH2 + C2HsCO/H monomeric form These results led us to examine the reactivity of dodecylamine alone as compared to that of DAP. The rate of aminolysis of the allophanic
S] + Sl ~ 52
KI2
52 -1- S| ~-- S 3
K23
Sn-l+Sl ~S, with Kl2
=
K23
. . . . .
K,-ln, gn-I
Journal o[ Colloid and lnteff?lce &'ience, Vol.
n = g.
[1]
150, No. 2, May 1992
478
VALEUR AND MONNIER
Let [Si] be the concentration in aggregates containing i surfactant molecules. The total concentration in surfactant is then given by [S]o = [SI] + 2[S2] + 3[$3]
+---
+
0.8 0.6
+n[S.]+...
= IS1] --~2K[$1] 2 +
2
i
0.4-
3K2[S1] 3
• • • + nKn-l[s1]n
f'lt
+
• • • .
0.2-
[2]
0
i 0.05
0.~1
i 0.15
0.~2
i 0.25
0.'3
~' [S]o
Summation of the series leads to
[Sl] [S]o - (1
__ K [ S 1 1 2 )
.
[3]
The fraction of monomer is defined as
FIG. 6. Variations in the fraction of monomer as a functionof the total concentrationofsurfactantfor various values of the equilibrium constant K (expressedin M-l): 10 (1), 20 (2), 30 (3), 50 (4), 90 (5), 150 (6), 230 (7), 350(8/.
[S~]
fl = -
[S]0
"
Then, from Eq. [3] we obtain K[S]0 -
1 - - f l 1/2
[4]
fl
This equation was previously derived by Lo e t a l . (16). fl can then be expressed as a function of K and [ S ]o: f =
1 + 2K[S]o - (1 + 4K[S]o) 1/2 2K2[S]02
[5]
The fraction ofdimer, trimer . . . . . n-mer can be expressed as a function of the fraction of monomer f : dimer:
j ~ _ [$2___]-fl(1
n-mer:
f~-
[S]o
-fl
1/2)
[s,__j]-fl(1--fll/2) "-1.
[S]o
[6]
[7]
The fraction of surfactant in the aggregated form can be written as [ag]
fag-- [S]o-
E ~ 2 [Si]
[S]o =fll/2(l-fli/2).
[8]
The fraction of monomer as a function of [S]o for various values of K (Eq. 5 ) is shown Journal qfCblloid and lnte(/bce Science.
Vol.150,No.2,May1992
in Fig. 6. From the examination of this figure together with Figs. 1, 2, and 3, it can be guessed that a satisfactory agreement will never be obtained by considering that only the monomers are the kinetic species. The slow decrease in the kobs/[DAP] ratio at high DAP concentrations is in favor of the participation of other kinetic species, i.e., the aggregates. Several assumptions can be made, leading to different models. Model I n . The assumptions pertaining to this model are the following: (i) A surfactant molecule acts individually as a kinetic species either in the monomeric form or in an aggregate with pseudo-first-order kinetics; the rate constant is kl for a surfactant molecule in the monomeric form and ka within an aggregate. (ii) ka is assumed to be independent of the size of the aggregate. (iii) The aggregation process is assumed to be a sequential indefinite self-association with all equilibrium constants equal. It should be noted that assumptions (i) and (ii) are usually made in treating kinetic data in aqueous micellar solutions with different reactivities in the bulk and in aggregates. From the above assumptions, the following relations can be easily derived:
479
EFFECT OF AGGREGATION ON REACTIVITY
kob~ = kl[Sl]
kobs = kl[Sl] + k,(2152]
+ kag([52] 31- [53] + [54] -1- • " ")
+ 3[$31 + 4 1 5 4 1 + " • ") or
= k~[Sl] + k , ( [ S ] 0 - [S~]) kob~ = k l f l [ S ] o + k a ( 1 - f l ) [ S ] 0 .
[9]
]gobs
[S]o
- (k, - ka)fl + ka.
[S]o
[101
According to assumption (iii), f~ is given by Eq. [5]. M o d e l Ib. The assumptions are the same as in model Ia but the rate constant for the dimer (k2) is different from that of the other aggregates:
+ k a g ( [ 5 3 ] --[- [ 5 4 ] +
• • .)
= kl[S~] + k2152]
kobs = kl[Sl] + 2k2152]
+ kag([ag] - [$2]).
[17l
Hence
+ k . ( [ S ] 0 - [Sl] - 2[S2]).
[11] kobs
By using Eq. [6], we obtain
[S]0
- ( k l + k2 - 2 k a g ) f
+ kagfl 1/2 + (kag - k2)fl 3/2. - [kl + 2k2 - 3ka]f~ + 2(k~ - k 2 ) f l 3/2 + ka.
[12]
M o d e l Ic. This model is identical to model Ia but the rate constant for the monomer is kl[S~] + k~ [S~ ]2, as in the case of esterolysis in homogeneous solutions (33-37): kobs = k l [ S l ]
[16]
kobs = k~[S~] + k2[$2]
+ k,(3[S3l + 4 1 5 4 1 + " " ")
[S]0
- (kl - kag)f + kagfl 1/2.
M o d e l lib. This model is identical to model IIa but the rate constant for the dimer (k2) is different from that of the other aggregates:
kobs = kt[S~] + 2k21521
kobs
[15]
By using Eq. [8 ], we obtain
Hence, kob~
kobs = k~[S~] + kag[ag].
+ k] [Sl] 2
+k~([Slo-[Sl])
[13]
,o,s k'l f l3/2 + k a.
[14]
K M o d e l IIa. In contrast to model Ia, each aggregate acts as a kinetic species with pseudofirst-order kinetics. The rate constant is kl for the m o n o m e r and k~g for the aggregates, whatever their size:
[18]
These models were checked with the experimental data obtained for the three allophanic esters in benzene and in dichloroethane and for PNPA in benzene. The following procedure was employed: for a given value of K, the fraction of monomer j] is calculated by using Eq. [ 5 ] at each concentration of DAP; then curve fitting of the plot ofkob~/[So] versus J~ by a nonlinear least-squares method is attempted by using Eqs. [10], [12], [14], [16], or [18], the criterion being the reduced X 2. Various values of K are successively tried until the minimum of the X 2 is reached. Model Ia gives excellent agreement, as shown in Figs. 7, 8, and 9 and in Table I. No significant improvement of the quality of the fit is obtained by considering the rate constant for the dimer (k2) to be different from that of the other aggregates (model Ib). Analysis of the kinetic data by means of Eq. [14 ] relevant to model Ic failed to give a value JournalolColloidand lnteffhceScience, Vol. 150, No. 2, May 1992
480
VALEUR AND MONNIER
103
kobs (s'1) ].1
Ar--
©
A E--CH,
/ 0.'01
0~005
AE-H
2.
0:02
o
,,-t
I, I
I
0:04
0:06
0.1' [DAP]
At-~
I J
i i
0:08
I
A E--CH t
1
AE--H I =
1
i£1 E,
FIG. 7. Kinetic data obtained for the allophanic esters in benzene at 26°C and best fit (solid lines) with model la. The parameters corresponding to the best fit are given in Table I.
of k'~ with an acceptable error, and no improvement of the reduced X 2 was obtained with respect to model Ia. With regard to models IIa and lib pertaining to cases where the aggregates are considered as kinetic species, it was not possible to get a satisfactory fit of the data with the relevant equations. Jo trnal ~[ Colloid and Interlace Science,
Vol. 150,No. 2, May 1992
DISCUSSION
The tests of the various kinetic models show that the kinetic data are very well described by model Ia. There is definitely a contribution of the aggregates to the aminolysis of the esters, and each surfactant molecule in the aggregate, not the aggregate as a whole, acts as a kinetic
EFFECT OF AGGREGATION ON REACTIVITY 10 3 kob L2 (s-l)
481
•
CJ~CJ
AE
~)
6.
i,
4,
6.02 o
.1[
0:04
o'.o6
o:oa
o.~' loOP]
I l
I
i
l
J
J
I
AE--CH
3
r't tl,I a"
I
J
,
t
AE--H
I
'
FIG. 8. Kinetic data obtained for the allophanic esters in 1,2-dichloroethane at 26°C and best fit (solid lines) with model Ia. The parameters corresponding to the best fit are given in Table I.
species. This is in contradiction with the conclusions o f O ' C o n n o r and co-workers who stated that each aggregate has its own kinetic identity, i.e., acts as a kinetic species (5, 10). It should be noted that no curve fitting evidenced their statement. T h e fact that model Ic, involving a secondorder dependence on the m o n o m e r concen-
tration, does not provide a better description of the kinetic data than model Ia deserves further attention. At first sight, this is surprising because it is well established that esterolysis in aprotic solvents show first- and higher-order dependence on the a m i n e concentration ( 3 3 37). N o i m p r o v e m e n t in the quality of the fit after adding the term k'~ [S~ ]2 does not m e a n Journal (~]('otloid and Interlace Science, Vol. 150. No. 2, May 1992
482
VALEUR AND MONNIER 10 3 kobs (s-~)
© O.
PNPA
0.~ i
i
0-6
OA
0.2.
olo= I
olo,
0:06
o'.oa
o!1 C~"]
i
-2Y.. ¸
FIG. 9. Kinetic data obtained for PNPA in benzene at 26°C and best fit (solid lines) with model Ia. The parameters corresponding to the best fit are given in Table I.
that this term does not exist, but it m a y be so small with respect to the other terms that it cannot be detected. In fact, it will be shown in the next paper of this series (38) that for the reaction of allophanic esters with dodecylamine in benzene, the second-order term has a much smaller contribution than the fLrstorder one. In contrast, for the reaction of PNPA with dodecylamine in benzene, previous works have shown that the contribution of the general base-catalyzed pathway (resultJournal of Colloid and lnterJace Science, Vol. 150, No. 2, May 1992
ing in second-order dependence on dodecylamine concentration) is m u c h larger than that of the uncatalyzed pathway. However, the mechanism of the reaction of PNPA with DAP is different despite the fact that dodecylamine is still the nucleophilic agent. The variations in ko~ versus DAP or dodecylamine concentration are completely different because, in the reaction with DAP, the d o d e c y l a m m o n i u m ion plays an important role which will be discussed in detail in a forthcoming paper (38).
EFFECT OF AGGREGATION
483
ON REACTIVITY
TABLE I Results of C u r v e Fitting o f the Kinetic D a t a O b t a i n e d for the A l l o p h a n i c Esters a n d P N P A in Benzene a n d 1,2-Dichloroethane at 2 6 ° C K (M-I ) Solvent: benzene AE-H AE-CH3 AE- ql, PNPA Solvent: 1,2-dichloroethane AE-H AE-CH3 AE-~
235 240 225 215
+ 35 + 30 -+ 25 + 25
120 _ 30 195 + 55 175 -+ 35
l0s kl (s-I M -~)
308 277 311 105
l0s ku (s-1M -l)
+ 24 __ 17 + 16 -+ 6
248 + 25 274 - 37 579 -+ 53
X~
(Estimated errors)
14.9 23.7 36.4 5.45
__+0.9 __+0.7 -+0.8 __ 0.25
0.92 0.98 1.26 0.85
(2%) (1%) (3%) (2%)
24.3 25.8 58.9
- 3.0 + 2.4 -+ 3.7
1.40 0.75 0.66
(3%) (3%) (3%)
N o t e . x 2 is the reduced x 2 whose value s h o u l d be close to 1 for a satisfactory fit.
The results of the kinetic analysis by means of model Ia (Table l ) show that the rate constant for the surfactant molecules in the aggregated form (ion pairs) is always much lower than in the monomeric form (dodecylamine + propionic acid) by a factor of nine or more. It is also worth pointing out that the kinetic model provides the equilibrium constant of the self-association process and that its value does not significantly depend on the nature of the ester under study. It is remarkable that the average value of K in benzene (230 _+40 M - t at 26°C) is in excellent agreement with the value of 230 M -1 calculated from vapor pressure osmometry experiments (16 ) (this value is extrapolated from the values of 207 M-~ at 27°C and 70.4 M -I at 37°C by using Van't Hoff's equation). This excellent accordance further confirms the validity of the kinetic model and justifies a posteriori the use of the aggregation model based on sequential indefinite self-association with all molar equilibrium constants equal. It can be also concluded that the substrates at a concentration of 10-4 M do not alter significantly the aggregation process. The values of K obtained in dichloroethane are more scattered, but the average value (around 150 M -1 ) is significantly lower than that in benzene. The difference in polarity of these two solvents may account for the ob-
served difference in the efficiency of self-association. The value of this equilibrium constant in dichloroethane obtained in this work was not reported previously. The values in other organic solvents could be easily determined. The validity of this method of determination of K is supported by the excellent agreement found for K in benzene by the physical and the chemical methods. Such an approach of structural features by chemical kinetics is of great interest. Generalization to other systems is possible, but the reliability of the method may be affected by possible perturbation of the aggregation process by the substrate. A control by a physical method is a prerequisite. Interestingly, Figs. 7 to 9 show that at high concentration in surfactant the variation in kob s tends to be linear. From Eqs. [ 9 ] and [ 5 ], it is indeed easy to show that the asymptotic behavior of kobs is expressed by kobs ~
ka[S]0 +
kl - ka K for
K[S]0>> 1.
[19]
Therefore, it is of interest to note that the slope of the asymptote represents the rate constant ka for the aggregated surfactant and the intercept is (k~ - k a ) / K (Fig. 10). This provides Journal t~l'Colloid and Interlace Science, Vol. 150, No. 2, May 1992
484
VALEUR AND MONNIER available to us. Thanks are also due to Dr. B. Jasse, ESPCI, Paris, for his help in FTIR experiments.
k°bs I Slope: k a
REFERENCES
k1-
ka
...-.............., J ' J
[Sl0 FIG. 10. Illustration of the variations in ko~ versus surfactant concentration showing the asymptotic behavior and involved parameters. an easy w a y to d e t e r m i n e ka p r o v i d e d that the linear part o f the p l o t at high c o n c e n t r a t i o n s is well enough defined. Satisfactory agreement between the values o f ka d e t e r m i n e d b y this m e t h o d a n d those o b t a i n e d b y the general p r o c e d u r e was f o u n d in m o s t cases. F o r instance, in the case AE-cI, in benzene, the range o f c o n c e n t r a t i o n was e x t e n d e d to 0.2 M ; b y t a k i n g the e x p e r i m e n t a l values o f kobs for conc e n t r a t i o n s ranging from 0.06 to 0.2 M, a linear regression in this range yields the slope, i.e., ka, equal to 35.9 × 10 -3 s - l M - l , a value close to that o b t a i n e d by the general p r o c e d u r e (36.4 × 10 -3 s -1 M - l ) . In principle, the rate c o n s t a n t kl c a n be t h e n d e t e r m i n e d from the intercept p r o v i d e d that the e q u i l i b r i u m constant is k n o w n . H o w e v e r , the value o f the intercept was found, in s o m e cases, n o t accurate e n o u g h to p r o v i d e a value o f k l in g o o d agreem e n t with t h a t o b t a i n e d b y the general p r o cedure. It s h o u l d be e m p h a s i z e d that the rate constants for the a l l o p h a n i c esters are higher t h a n those o f P N P A . A d e t a i l e d study o f the m e c h a n i s m s will be r e p o r t e d elsewhere ( 3 8 ) . Alt h o u g h a m i n o l y s i s b y d o d e c y l a m i n e is the c o m m o n feature o f the reaction o f P N P A a n d a l l o p h a n i c esters with D A P , the m e c h a n i s m o f a m i n o l y s i s is different. ACKNOWLEDGMENTS The authors thank Professors J. Prri6 and A. Klarbr, University of Toulouse, for making the allophanic esters Journalq/Colloidand lnterJace&'ience,Vol.150,No.2, May1992
1. Fendler, J. H., and Fendler, E. J., "Catalysis in Micellar and Macromolecular Systems," p. 340. Academic Press, New York, 1975. 2. O'Connor, C. J., Fendler, E. J., and Fendler, J. H., J. Am. Chem. Soc. 95, 3273 (1973). 3. O'Connor, C. J., Fendler, E. J., and Fendler, J. H., J. Chem. Soc. Dalton Trans. 625 (1974). 4. Fendler, J. H., Fendler, E. J., Medary, R. T., and Woods, V. A., J. Am. Chem. Soc. 94, 7288 (1972). 5. O'Connor, C. J., Lomax, T. D., and Ramage, R. E., Adv. Colloid Interface Sci. 20, 21 (1984), and references cited therein. 6. O'Connor, C. J., and Lomax, T. D., Aust. J. Chem. 36, 895 (1983). 7. Farah, J. P. S., El Seoud, M. I., and El Seoud, O. A., J. Org. Chem. 49, 4063 (1984). 8. El Seoud, O. A., Vieira, R. C., and Novaki, L. P., Bull. Chem. Soc. Jpn. 60, 1163 (1987). 9. El Seoud, M. I., Vieira, R. C., and E1 Seoud, O. A., J. Org. Chem. 47, 5137 (1982). 10. O'Connor, C. J., and Lomax, T. D., J. Colloidlnterface Sci. 95, 204 (1983). 11. Sunamoto, J., in "Solution Behavior of Surfactants" (K. L. Mittal and E. J. Fendler, Eds.), p. 767. Plenum, New York, 1982. 12. Fendler, J. H., Fendler, E. J., Medary, R. T., and E1 Seoud, 0. A., J. Chem. Soc. Faraday Trans. 1 69, 280 (1973). 13. Fendler, J. H., Fendler, E. J., Medary, R. T., and E1 Seoud, 0. A., J. Phys. Chem. 77, 1432 (1973). 14. E1 Seoud, O. A., and Ribeiro, F. P., J. Org. Chem. 41, 1365 (1976). 15. El Seoud, O. A., Fendler, E. J., Fendler, J. H., and Medary, R. T., J. Phys. Chem. 77, 1876 (1973). 16. Lo, F. Y. F., Escort, B. M., Fendler, E. J., Adams, E. T., Larsen, R. D., and Smith, P. W., J. Phys. Chem. 79, 2609 (1975). 17. Herrmann, U., and Schelly, Z. A., J. Am. Chem. Soc. 101, 2665 (1979). 18. Muller, N., J. Phys. Chem. 79, 287 (1975). 19. Verbeeck, A., Gelade, E., and De Schryver, F. C., Langmuir 2, 448 (1986). 20. Eicke, H. F., and Denss, A., J. Colloid Interface Sci. 64, 386 (1978). 21. Correll, G. D., Cheser, R. N., Nome, F., and Fendler, J. H., J. Am. Chem. Soc. 100, 1254 (1978). 22. Jean, Y.-C., and Ache, H. J., J. Am. Chem. Soc. 100, 6320 (1978). 23. Monnier, E., Klaebe, A., and Prrir, J., Tetrahedron 41, 3269 (1985).
EFFECT OF AGGREGATION ON REACTIVITY 24. Monnier, E., Botella, J. M., Murillo, A., Klaebe, A., and P6ri6, J., Tetrahedron 42, 1315 (1986). 25. Kitahara, A., Bull. Chem. Soc. Jpn. 28, 234 (1955). 26. Guggenheim, E. A., Philos. Mag. 2, 538 (1926). 27. E1 Seoud, O. A., Fendler, E. J., and Fendler, J. H., Z Chem. Soc. Faraday Trans. 1 70, 450 (1974). 28. El Seoud, O. A., Fendler, E. J., and Fendler, J. H., J. Chem. Soc. Faraday Trans. 1 70, 459 (1974). 29. O'Connor, C. J., and Lomax, T. D., Aust. J. Chem. 36, 917 (1983). 30. Gutmann, V., "Coordination Chemistry in NonAqueous Solutions." Springer-Verlag, New York, 1969. 31. Szwarc, M., in "Ions and Ion Pairs in Organic Reactions" (M. Szwarc, Ed.), p. 1. Wiley-lnterscience, New York, 1972.
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32. Gutmann, V., and Wychera, E., lnorg. Nucl. Chem. Lett. 2, 257 (1966). 33. Menger, F. M., and Smith, J. H., Z Am. Chem. Soc. 94, 3824 (1972). 34. Menger, F. M., and Vitale, A. C., J. Am. Chem. Soc. 95, 4931 (1973). 35. El Seoud, O. A., Martins, A., Barbur, L. P., da Silva, M. J., and Aldrigue, V., J. Chem. Soc. Perkin Trans. 2 1674 (1977). 36. E1 Seoud, O. A., Pivetta, F., E1 Seoud, M. I., Farah, J. P. S., and Martins, A., J. Org. Chem. 44, 4832 (1979). 37. Neuvoven, H., J. Chem. Soc. Perkin Trans. 2 159 (1987). 38. Monnier, E., Peri6, J., KlaOb6, A., and Valeur, B., to be published.
Journal ~!/C~*ltoidand lnleiJace Sciem'e, Vol. 150. No, 2, May 1992