The nature of the micellar Stern region as studied by reaction kinetics. 2

Article abstract of DOI:10.1021/jo049959l

The nature of rate-retarding effects of cationic micelles on the water-catalyzed hydrolyses of a series of para-substituted 1-benzoyl-1,2,4-triazoles (1a-f) and 1-benzoyl-3-phenyl-1,2,4-triazole (2) has been studied using kinetic methods. A comparison is drawn between medium effects in the micellar Stern region and in model solutions for the micellar Stern region. Simple model solutions involving concentrated aqueous solutions of a small ionic molecule resembling the surfactant headgroup, as reported before, were improved. New model solutions for alkyltrimethylammonium bromide micelles contain both tetramethylammonium bromide (TMAB), mimicking micellar headgroups, and 1-propanol, mimicking hydrophobic tails. The rate-retarding effect of micelles on the hydrolysis of 1a-f and 2 is caused by the high concentration of headgroups as well as by hydrophobic tails in the Stern region where 1a-f and 2 bind to the micelle. Individual contributions of these interactions are quantified. Rate-retarding effects found for different probes, with different sensitivities for interactions as they occur when the probe binds to the micellar Stern region, as well as the micellar Stern region's micropolarity as reported by the E_T(30) probe, are satisfactorily reproduced by new model solutions containing both TMAB and 1-propanol.

Full text of DOI:10.1021/jo049959l

Th e Na tu r e of th e Micella r Ster n Region As Stu d ied by Rea ction
Kin etics. 2†,1
Niklaas J . Buurma,§ Paola Serena,§ Michael J . Blandamer,‡ and J an B. F. N. Engberts*,§
Physical Organic Chemistry Unit, Stratingh Institute, University of Groningen, Nijenborgh 4,
9747 AG Groningen, The Netherlands, and Department of Chemistry, University of Leicester, Leicester,
LE1 7RH, United Kingdom
j.b.f.n.engberts@chem.rug.nl
Received J anuary 6, 2004
The nature of rate-retarding effects of cationic micelles on the water-catalyzed hydrolyses of a series
of para-substituted 1-benzoyl-1,2,4-triazoles (1a -f) and 1-benzoyl-3-phenyl-1,2,4-triazole (2) has
been studied using kinetic methods. A comparison is drawn between medium effects in the micellar
Stern region and in model solutions for the micellar Stern region. Simple model solutions involving
concentrated aqueous solutions of a small ionic molecule resembling the surfactant headgroup, as
reported before,1 were improved. New model solutions for alkyltrimethylammonium bromide micelles
contain both tetramethylammonium bromide (TMAB), mimicking micellar headgroups, and
1-propanol, mimicking hydrophobic tails. The rate-retarding effect of micelles on the hydrolysis of
1a -f and 2 is caused by the high concentration of headgroups as well as by hydrophobic tails in
the Stern region where 1a -f and 2 bind to the micelle. Individual contributions of these interactions
are quantified. Rate-retarding effects found for different probes, with different sensitivities for
interactions as they occur when the probe binds to the micellar Stern region, as well as the micellar
Stern region’s micropolarity as reported by the ET(30) probe, are satisfactorily reproduced by new
model solutions containing both TMAB and 1-propanol.
In tr od u ction
in surfactants has been achieved.10 However, we limit
discussion solely to “medium effects” as they occur in
solutions of unfunctionalized micelle-forming amphiphiles.
Micelle-forming surfactants self-aggregate in a coop-
erative manner, forming stable but highly dynamic
clusters above the critical micelle concentration (cmc).
Gruen described a realistic model for a micelle2 which
involves a rather sharp interface between two distinctly
different “zones” making up a micelle: (i) a dry2,3
hydrophobic hydrocarbon core surrounded by (ii) a region
filled with surfactant headgroups, part of the counterions
(in case of ionic surfactants) and water, viz. the Stern
region. The Stern region is an interfacial region between
the hydrocarbon core and bulk water (the third “zone”
in micellar solutions). This model has been validated for
both ionic and nonionic micelles using molecular dynam-
ics simulations.4,5
The exact mechanism of micellar acceleration and
deceleration has remained obscure because a good de-
scription of the local reaction environment offered by
micellar binding sites, often referred to as the “micellar
pseudophase”, is lacking. The present (and our previous1)
study investigated mechanistic aspects of micellar effects
on water-catalyzed hydrolysis reactions to develop a
satisfactory description of the micellar pseudophase as
a reaction medium. Nevertheless, the distinct differences
between micellar core and Stern region make it impos-
sible to describe the complete micelle as a homogeneous
“entity” or “(pseudo)phase”. Descriptions of medium
effects exerted by micelles describe either the Stern
region or the hydrocarbon core, depending on the binding
location of the (reactive) probes that are used.
In micellar solutions, reactions can be either accelerated
or inhibited compared to the reaction in aqueous solu-
tions without added cosolutes.6-8 Remarkable success in
enhancing reaction rates9 introducing catalytic moieties
* Author to whom correspondence should be addressed. Fax: +31
50 363 4296.
(7) Berezin, I. V.; Martinek, K.; Yatsimirskii, A. K. Russ. Chem. Rev.
1973, 42, 787-802.
† Taken in part from the Ph.D. thesis of N.J .B., 2003, University of
Groningen.
(8) Engberts, J . B. F. N. Pure Appl. Chem. 1992, 64, 1653-1660.
(9) The difference between reaction rates and reaction rate constants
should be noted. Due to compartmentalization, concentrations of
reactants inside micelles can be higher so that, notwithstanding lower
reaction rate constants, reaction rates can still be higher than observed
in bulk water.
§ University of Groningen.
‡ University of Leicester. E-mail: mjb@le.ac.uk.
(1) Part 1: Buurma, N. J .; Herranz, A. M.; Engberts, J . B. F. N. J .
Chem. Soc., Perkin Trans. 2 1999, 113-119.
(2) Gruen, D. W. R. Prog. Colloid Polym. Sci. 1985, 70, 6-16.
(3) Clemett, C. J . J . Chem. Soc. A 1970, 2251-2254.
(4) Bo¨cker, J .; Brickmann, J .; Bopp, P. J . Phys. Chem. 1994, 98,
712-717.
(10) Examples of surfactants equipped with catalytically active
headgroups can be found among others in the following: (a) Otto, S.;
Engberts, J . B. F. N.; Kwak, J . C. T. J . Am. Chem. Soc. 1998, 120,
9517-9525. (b) Sirieix, J .; de Viguerie, N.; Riviere, M.; Lattes, A. New
J . Chem. 1999, 23, 103-109. (c) Ghosh, K. K.; Pandey, A.; Roy, S. J .
Phys. Org. Chem. 1999, 12, 493-498. (d) Tagaki, W.; Chigira, M.;
Amada, T.; Yano, Y. J . Chem. Soc., Chem. Commun. 1972, 219-220.
(5) Shelley, J .; Watanabe, K.; Klein, M. L. Int. J . Quantum Chem.:
Quantum Biol. Symp. 1990, 17, 103-117.
(6) Bunton, C. A. Catal. Rev.sSci. Eng. 1979, 20, 1-56.
10.1021/jo049959l CCC: $27.50 © 2004 American Chemical Society
Published on Web 05/05/2004
J . Org. Chem. 2004, 69, 3899-3906
3899

Buurma et al.
SCHEME 1
A prerequisite for understanding the reaction medium
offered by micelles is to know where reaction occurs. A
micelle offers several binding sites for relatively apolar
molecules. These include the hydrophobic core and
hydrophobic binding sites located in the Stern region. The
latter region is particularly flexible in binding molecules
as it contains, apart from water molecules, highly hy-
drophilic surfactant headgroups and hydrophobic do-
mains due in part to backfolding of surfactant tails.2-4
In our previous study,1 we showed that the water-
catalyzed hydrolysis reactions of activated amides take
place in the micellar Stern region. This conclusion agrees
with the binding locations found using a variety of
techniques for many other, especially aromatic, mol-
ecules.11
stituted 1-benzoyl-1,2,4-triazoles (1a -f) and 1-benzoyl-
3-phenyl-1,2,4-triazole (2).
In view of the literature evidence mentioned above, the
kinetic probes used in the study reported here almost
certainly bind in the micellar Stern region. Hence, the
experiments effectively provide information about the
reaction medium properties of the Stern region. The aim
of this study was to model the medium properties of the
micellar Stern region in terms of aqueous solutions
comprising compounds mimicking molecules and parts
of molecules present in the Stern region.
A key feature of the micellar Stern region is the
concentration of headgroups and counterions. The con-
centration of headgroups in the Stern region12-14 lies in
the range of 3-5 mol dm-3, though recent work suggested
lower values.15 In our previous work, we determined
upper limits for the concentration of headgroups in the
Stern regions of n-dodecyltrimethylammonium bromide
(DTAB), n-hexadecyltrimethylammonium bromide (CTAB),
and sodium n-dodecyl sulfate (SDS) of approximately 4
M.1 The concentration of counterions is slightly less due
to incomplete counterion binding, locally creating an
electrically nonneutral environment.
In our preceding study,1 we showed that rate-retarding
effects exerted by micelles on certain hydrolysis reactions
can be largely explained in terms of salt effects. However,
the success of modeling the micellar Stern region using
a concentrated salt solution depends on the reaction
chosen to probe the Stern region’s properties as a reaction
medium.1,16 In this study we incorporate in the mimic
both polar and apolar components with the aim of
inducing medium effects still more representative of the
Stern region.
The reactions proceed via a dipolar activated complex
in which two water molecules, one acting as a nucleophile
and the other as a general base, are involved with three
protons in flight (Scheme 1).17-19
Kinetic data for reactions in micellar solutions are
analyzed using eq 1 in a nonlinear least-squares fitting
procedure. Equation 1 represents the nonlinear form of
the Menger-Portnoy equation:20
k(mc ) 0) + kmicKm([surf] - cmc)/N
kobsd
)
(1)
1 + Km([surf] - cmc)/N
Here kobsd is the observed rate constant at a surfactant
concentration [surf], k(mc ) 0) is the rate constant in
water without added cosolute (pH ) 4.0),21 and kmic is
the rate constant under conditions of complete binding
of the substrate to the micelles. For the present system,
the micellar rate constant kmic is the rate constant for
reaction in the micellar Stern region. N is the aggregation
number of the micelle, Km is the binding constant of the
kinetic probe to the micelle (the kinetic probe residing
in the Stern region), and cmc is the critical micelle
concentration of the surfactant.
In addition to micellar rate constants kmic and micellar
binding constants Km, transition-state pseudoequilibrium
constants KAC can be determined.22,23 Transition-state
pseudoequilibrium constants KAC are hypothetical bind-
A
Kin etic Mod el for Rea ction s in Micella r
Solu tion s
The hydrolytic reactions described here are the water-
catalyzed, pH-independent hydrolysis reactions of sub-
(17) Fife, T. H.; McMahon, D. M. J . Am. Chem. Soc. 1969, 91, 7481-
7485.
(18) Karzijn, W.; Engberts, J . B. F. N. Tetrahedron Lett. 1978, 1787-
1790.
(11) See, for example: (a) Menger, F. M. Acc. Chem. Res. 1979, 12,
111-117. (b) Vitha, M. F.; Dallas, A. J .; Carr, P. W. J . Phys. Chem.
1996, 100, 5050-5062 and references therein.
(19) Engbersen, J . F. J .; Engberts, J . B. F. N. J . Am. Chem. Soc.
1975, 97, 1563-1568.
(20) Menger, F. M.; Portnoy, C. E. J . Am. Chem. Soc. 1967, 89,
4698-4703.
(12) Bunton, C. A.; Nome, F.; Quina, F. H.; Romsted, L. S. Acc.
Chem. Res. 1991, 24, 357-364.
(21) For the present reactions, the minor decrease in rate constant
before the cmc indicates that rate-retarding effects below the cmc are
small, justifying our choice of k(mc ) 0). It should also be noted that
micellar rate constants for substrates bound to spherical micelles can
only be determined as long as the surfactant concentration is below
the concentration at which wormlike micelles start to form. This poses
an upper limit on the concentration range in which relevant results
can be obtained.
(13) Mukerjee, P. J . Phys. Chem. 1962, 66, 943-945.
(14) Menger, F. M.; Yoshinaga, H.; Venkatasubban, K. S.; Das, A.
R. J . Org. Chem. 1981, 46, 415-419.
(15) (a) Chaudhuri, A.; Loughlin, J . A.; Romsted, L. S.; Yao, J . H.
J . Am. Chem. Soc. 1993, 115, 8351-8361. (b) Soldi, V.; Keiper, J .;
Romsted, L. S.; Cuccovia, I. M.; Chaimovich, H. Langmuir 2000, 16,
59-71.
(16) Munoz, M.; Rodriguez, A.; Graciani, M. D.; Moya, M. L. Int. J .
Chem. Kinet. 2002, 34, 445-451.
(22) Kurz, J . L. J . Am. Chem. Soc. 1963, 85, 987-991.
(23) Kraut, J . Science 1988, 242, 533-540.
3900 J . Org. Chem., Vol. 69, No. 11, 2004

Nature of the Micellar Stern Region
TABLE 1. Over view of th e Hyd r olysis Ra te Con sta n ts
of 1-Ben zoyl-1,2,4-tr ia zoles 1a -f a t 298.15 K
ing constants of the activated complex to the micelle. For
the system under study, KAC is given by eq 2.
kx(mc ) 0)/
30
probe
σp
10-4 s-1
k
micKm
k
mic′[H2O]mic2Km
KAC
)
)
(2)
1a
1b
1c
1d
1e
1f
-0.28
-0.14
+0.00
+0.24
+0.32
+0.81
4.1
9.4
21.2
36.0
43.1
278
2
k(mc ) 0)
kw′[H2O]w
In eq 2, kw′ and kmic′ are the third-order rate constants
(rate of reaction of probe P: d[P]/dt ) kz′[P][H2O]z2, where
z represents subscripts mic and w in eq 2) in bulk water
and in the micellar Stern region, respectively. [H2O]w is
the water concentration in water, and [H2O]m is the water
concentration in the micelle, i.e. in the Stern region.
ionic headgroups and of the hydrophobic tails leading to
a satisfactory reproduction of the behavior of all tested
probes. It should be noted that ionic interactions do not
only include the effect of the charges of the surfactant
headgroups29 but instead are defined to include all rate-
influencing effects of the surfactant headgroups, i.e.
charge, effect on local water activity, and direct 1:1
interactions with the hydrolytic probe.
An Exten d ed Mod el of th e Micella r Ster n Region
Concentrated salt solutions may effectively reproduce
the medium effects exerted by the micellar Stern region
on one (series of) probe(s) but not on another series. For
example, medium effects on the solvatochromic ET(30)
probe24 in the Stern region cannot be accounted for solely
on the basis of the polarity of a concentrated salt
solution.1
Resu lts a n d Discu ssion
Rate constants for hydrolysis of 1a -f in water without
added cosolutes, kx(mc ) 0), together with the Hammett
substituent constants σp are summarized in Table 1
30
(subscript x indicates the probe molecule).
It is shown that the rate of hydrolysis increases with
increasing electron-withdrawing ability of the para-
substituent, as expected for a reaction in which a (partial)
negative charge develops on the carbonyl group going
toward the activated complex (Scheme 1). The hydrolysis
of all of these probes is retarded in solutions containing
micelles of CTAB and DTAB (examples given in Figure
1).
Similarly, the hydrolysis of phenyl chloromethanoate
is not nearly as much retarded in salt solutions as in
micellar solutions.16 Another indication is the failure of
3, a hydrolytic probe that is particularly sensitive to
hydrophobic interactions, to show a relation between the
charge of the Stern region and the rate-retarding effect,1
as was also observed by others for the hydrolysis of
4-nitrophenyl 2,2-dichloropropanoate.25,26
If the ET(30) probe is a good micropolarity reporter,
the micropolarity of the micellar Stern region is consider-
ably lower than expected on the basis of the concentrated
salt solutions used as mimics of the Stern region. This
lower polarity is envisaged to be primarily caused by
interactions of the probes with the hydrophobic tails of
the surfactants in the Stern region.
In this context, we chose the hydrolysis of a series of
substituted 1-benzoyl-1,2,4-triazoles 1a -f27 in the pres-
ence of micelles of DTAB and CTAB for detailed analysis.
The Stern region of micelles of ionic surfactants is
modeled by including both hydrophobic and ionic interac-
tions. Our new model solutions contain both salt, mim-
icking ionic interactions, and 1-propanol, mimicking
hydrophobic interactions.28 We separate the effect of the
From a nonlinear least-squares fit to eq 1, micellar rate
constants for hydrolysis and micellar binding constants
were determined (Table 2).
There is no appreciable trend in the micellar binding
constants of 1a -f (Table 2) with substituent constant
(Table 1). However, micellar binding constants for CTAB
on average are about three times larger than those for
DTAB. For comparison of the rate-retarding effects on
the hydrolysis of the individual hydrolytic probes, the
relative rate constants of hydrolysis in aqueous solutions
of DTAB and CTAB and the logarithms of these relative
rate constants are given in Table 3.
For 1d -f, micelles of CTAB retard hydrolysis more
than micelles of DTAB. However, micelles of DTAB
retard the hydrolysis of 1a ,b more compared with mi-
celles of CTAB (Table 3). Apart from these rather unusual
rate effects, ln(kx,mic/kx(mc ) 0)) tends to increase (de-
crease in absolute value) with increasing σp.
We improved our previous model for the micellar Stern
region1 by adding a compound mimicking the interactions
with the alkyl tails of the surfactants. 1-Propanol was
used as added cosolute being the highest linear32 alcohol
(24) Reichardt, C. Chem. Rev. 1994, 94, 2319-2358.
(25) El Seoud, O. A.; Ruasse, M. F.; Possidonio, S. J . Phys. Org.
Chem. 2001, 14, 526-532.
(26) In our opinion, the conclusion in ref 25 that the rate-retarding
effect brought about by the micelles is not a salt effect is unwarranted.
The conclusion has been based on activation parameters of the reaction
occurring in the micelle. However, these activation parameters will
include effects of the thermodynamics of micellization changing with
temperature.
(27) A series of probes with different substituents was used before
in a study of micellar medium effects in terms of Hammett F-values.
See: Brinchi, L.; Di Profio, P.; Germani, R.; Savelli, G.; Spreti, N.;
Bunton, C. A. Eur. J . Org. Chem. 2000, 3849-3854.
(28) Recently, similar attempts at including both “headgroup mim-
ics” and “tail mimics” in model solutions for the micellar Stern region
have been made. However, these tertiary solutions either (i) do not
distinguish between the rate effects of headgroup mimic and tail mimic
(refs 25 and 40) or (ii) seem to reproduce the rate of a single reaction
only (Tada, E. B.; Ouarti, N.; Silva, P. L.; Blagoeva, I. B.; El Seoud, O.
A.; Ruasse, M.-F. Langmuir 2003, 19, 10666-10672).
(29) Fernandez, M. S.; Fromherz, P. J . Phys. Chem. 1977, 81, 1755-
1761.
(30) Exner, O. In Correlation Analysis in Chemistry; Chapman, N.
B., Shorter, J ., Eds.; Plenum: London, 1978; pp 439-540.
J . Org. Chem, Vol. 69, No. 11, 2004 3901

Buurma et al.
F IGURE 1. Rate constants of hydrolysis of 1c at 298.15 K in solutions containing micelles of DTAB (left) and CTAB (right).
TABLE 2. Over view of Micella r Ra te Con sta n ts of Hyd r olysis a n d Micella r Bin d in g Con sta n tsa of P a r a -Su bstitu ted
1-Ben zoyl-1,2,4-tr ia zoles 1a -f a t 298.15 K
k
x,CTAB/10-4 s-1
k
x,DTAB/10-4 s-1
Kx,CTABb/103 dm3 mol-1
Kx,DTABc/103 dm3 mol-1
1a
1b
1c
1d
1e
1f
0.34 ( 0.03
0.78 ( 0.08
2.5 ( 0.2
5.4 ( 0.2
7.0 ( 0.1
67 ( 3
0.25 ( 0.04
0.70 ( 0.06
2.4 ( 0.3
9.3 ( 0.3
10.3 ( 0.4
3.44 ( 0.07
13.9 ( 0.4
21.0 ( 0.3
6.4 ( 0.3
3.1 ( 0.2
3.4 ( 0.1
1.5 ( 0.1
4.2 ( 0.1
6.0 ( 0.1
1.4 ( 0.2
6.67 ( 0.10
8.4 ( 0.2
74 ( 12
a
Cmcs set to 0.9 and 14.0 mM for CTAB and DTAB, respectively. These are the average values of the cmcs determined from initial
curve-fitting with unrestricted cmcs. Based on an aggregation number of 110.31 c Based on an aggregation number of 70.31
b
TABLE 3. Rela tive Ra te Con sta n ts of Hyd r olysis of 1a -f Ta k in g P la ce in Micelles of DTAB a n d CTAB a t 298.15 K
CTAB
DTAB
k
x,mic/kx(mc ) 0)
ln[kx,mic/kx(mc ) 0)]
kx,mic/kx(mc ) 0)
ln[kx,mic/kx(mc ) 0)]
1a
1b
1c
1d
1e
1f
0.08
0.08
0.12
0.15
0.16
0.24
-2.5 ( 0.1
0.06
0.07
0.12
0.19
0.20
0.27
-2.8 ( 0.2
-2.6 ( 0.1
-2.1 ( 0.3
-1.68 ( 0.02
-1.63 ( 0.02
-1.3 ( 0.2
-2.5 ( 0.1
-2.14 ( 0.06
-1.90 ( 0.04
-1.82 ( 0.02
-1.42 ( 0.03
completely miscible with water at 298.15 K. In addition,
widely accepted micelle models suggest that on average
about 2-3 methylene units are in contact with water.2
The effects of ionic headgroups and alkyl tails as mim-
icked by TMAB and 1-propanol, respectively, have to be
distinguished. Ideally, trends in sensitivity toward the
presence of these two compounds should be different
within the series of hydrolytic probes. By analogy with
1:1 interactions in (aqueous) solutions (see ref 33 for short
reviews), we quantify rate-retarding effects exerted by
the two mimicking compounds using the slopes of plots
of the logarithm of the relative rate constant of hydrolysis
as a function of molality of cosolute mc, eq 3.34,35
2
ln[k(mc)/k(mc ) 0)] )
2G(c)mc - NMlφmc (3)
RTmo
Here k(mc) is the (pseudo-)first-order rate constant for
hydrolysis in an mc molal aqueous solution of cosolute c;
k(mc ) 0) is the rate constant in the absence of added
cosolute, R is the gas constant, and T is the absolute
temperature. G(c) is the difference [gcx - gcq] in interac-
tion Gibbs energies between the cosolute c and the
reactants x on one hand and the cosolute c and the
activated complex q on the other hand. Ml is the molar
mass of water, N is the number of water molecules
involved in the rate-determining step, and φ is the
practical osmotic coefficient for the aqueous solution
where the molality of added solute is mc. In this study,
N equals 2 (vide supra). Since the solutions are very
dilute, φ can be taken as unity; mo, 1 mol kg-1, is the
molality of the solute reference state. In short, NMlφmc
gives the change in water activity upon addition of mc
(31) van Os, N. M.; Haak, J . R.; Rupert, L. A. M. Physico-Chemical
Properties of Selected Anionic, Cationic and Nonionic Surfactants;
Elsevier: Amsterdam, 1993.
(32) Hydrophobic interactions are rather dependent on size and
shape of the hydrophobic (parts of) molecules involved; see e.g.:
Southall, N. T.; Dill, K. A. J . Phys. Chem. B 2000, 104, 1326-1331.
We therefore restricted our choice of alcohols for our mimicking solution
to linear alcohols. The actual choice of linear alcohol is expected to be
unimportant as all short-chain linear alcohols retard the hydrolysis
reactions of activated amides in similar ways following an additivity
scheme (see ref 35 and the following: Buurma, N. J .; Pastorello, L.;
Blandamer, M. J .; Engberts, J . B. F. N. J . Am. Chem. Soc. 2001, 123,
11848-11853).
(34) Blokzijl, W.; Engberts, J . B. F. N.; Blandamer, M. J . J . Phys.
Chem. 1987, 91, 6022-6027.
(35) Blokzijl, W.; Engberts, J . B. F. N.; Blandamer, M. J . J . Am.
Chem. Soc. 1990, 112, 1197-1201.
(33) (a) Engberts, J . B. F. N.; Blandamer, M. J . J . Phys. Org. Chem.
1998, 11, 841-846. (b) Otto, S.; Engberts, J . B. F. N. Org. Biomol.
Chem. 2003, 1, 2809-2820.
3902 J . Org. Chem., Vol. 69, No. 11, 2004

Nature of the Micellar Stern Region
F IGURE 3. Relative rate-retarding effects of CTAB micelles
on the hydrolysis of 1a -f at 298.15 K as a function of Hammett
substituent constant. Dotted line indicates the division be-
tween rate-retarding effects attributed to interactions with
ionic surfactant headgroups as modeled by TMAB (upper
section) and rate-retarding effects attributed to interactions
with surfactant alkyl tails as modeled by 1-propanol (lower
section). The dotted and the solid lines cross at σp ) 1.13 (see
text for details).
F IGURE 2. Rate-retarding effects of 1-propanol (b) and
TMAB (O) on the hydrolysis of probes 1a -f at 298.15 K as a
function of Hammett substituent constants.
TABLE 4. Con cen tr a tion Dep en d en ce (k g m ol-1) of
Ra te-Reta r d in g Effects of 1-P r op a n ol a n d TMAB on th e
Hyd r olysis of Su bstitu ted 1-Ben zoyl-1,2,4-tr ia zoles 1a -f
a t 298.15 K
retardation is caused by interactions with ionic head-
groups (Figure 3).
∂ln{kx(m1-propanol)/
kx(mc ) 0)}/∂m1-propanol
∂ln{kx(mTMAB)/
kx(mc ) 0)}/∂mTMAB
Hydrolysis of a probe with a substituent with σp ) 1.13
is expected to be solely retarded by ionic interactions.
Because rate retardation by ionic interactions as modeled
by TMAB is approximately constant for all hydrolytic
probes, the horizontal dotted line at ln[kx,CTAB/kx(mc ) 0)]
) -1.0 indicates the constant “ionic contribution” to the
rate-retarding effect for all hydrolytic probes. As the rate
retardation (expressed in terms of logarithm of the
relative rate retardation; vide supra) by ionic interactions
is approximately -0.25 kg mol-1 for TMAB, the micellar
rate-retarding effect attributed to ionic interactions of
-1.0 corresponds to a model solution of -1.0/-0.25 mol
kg-1 ) 4 mol kg-1 in TMAB. The slope of the remainder
of the rate-retarding effect, attributed to hydrophobic
interactions, as a function of substituent parameter
equals 1.07. As a slope of 0.17 is expected for a 1 mol
kg-1 solution, we estimate a model solution for the
micellar Stern region to be approximately 1.07/0.17 ) 6
mol kg-1 in 1-propanol.
1a
1b
1c
1d
1e
1f
-0.236 ( 0.005
-0.232 ( 0.006
-0.201 ( 0.005
-0.151 ( 0.003
-0.131 ( 0.003
-0.058 ( 0.002
-0.306 ( 0.015
-0.240 ( 0.007
-0.258 ( 0.006
-0.259 ( 0.007
-0.226 ( 0.002
-0.240 ( 0.007
2
molal of a cosolute and 2/RTmo G(c)mc gives the inter-
solute interactions upon addition of mc molal of a coso-
lute. Equation 3 is used to obtain G(c) values which may
be subsequently analyzed using a group-additivity ap-
proach. For the present case, it should be noted that G(c)
often follows a group-additivity pattern and that interac-
tions with different cosolutes are expected to be addi-
tive.33 For dilute solutions for which eq 3 is valid, ln[k(mc)/
k(mc ) 0)] varies linearly with molality mc.
In the present case, the rate-retarding effects of TMAB
and 1-propanol were determined in the ranges from 0
up to (at most) 5 mol kg-1 and from 0 up to 3.6 mol kg-1
respectively (Table 4).
,
An alternative approach uses equations used in the
study of 1:1 interactions in aqueous solutions.34 The rate-
retarding effect in an aqueous solution containing 1-pro-
panol and TMAB can be described as the sum of effects
caused by added TMAB and 1-propanol:
The necessary difference in sensitivity trends exists.
Whereas the variation in the effect of TMAB on the
hydrolysis of 1a -f is relatively modest, the rate-retarding
effect of 1-propanol varies substantially with the Ham-
mett substituent constant (Figure 2).
kx(m1-propanol
kx(mc ) 0)
)
This difference allows the calculation of individual
molalities of the headgroup mimic and the tail mimic as
required for a solution mimicking the micellar Stern
region. These calculated molalities are assumed to reflect
the relative importance of ionic interactions and hydro-
phobic interactions in the Stern region. For a graphical
solution, the rate-retarding effect of 1-propanol on the
hydrolysis reactions decreases roughly linearly with
substituent parameter σp. Hence, there is a hypothetical
hydrolytic probe with a (hypothetical) substituent for
which hydrolysis is not retarded by 1-propanol. This
hypothetical substituent has a σp of about 1.13. A plot of
ln(kx,mic/kx(mc ) 0)) as a function of σp can now be divided
into two parts, viz. a part where rate retardation is
caused by hydrophobic interactions and a part where rate
∂ln
[
]
m1-propanol
+
∂m1-propanol
kx(mTMAB
)
∂ln
[
]
kx(mc ) 0)
∂mTMAB
kx,mic
mTMAB ) ln
(4)
[
]
kx(mc ) 0)
Equation 4 is more conveniently written in the form of
eq 5:
ax,1-propanolm1-propanol + ax,TMABmTMAB ) cx (5)
Here, ax,1-propanol is the derivative of the logarithm of the
J . Org. Chem, Vol. 69, No. 11, 2004 3903

Buurma et al.
TABLE 5. Mola lities a n d Con cen tr a tion sa of 1-P r op a n ol
a n d TMAB in Soln .1 for Bin d in g Sites of 1a -f in Micelles
of DTAB a n d CTAB
SCHEME 2
DTAB
CTAB
mc/mol kg-1 cc/mol dm-3 mc/mol kg-1 cc/mol dm-3
1-propanol
TMAB
water
9.3 ( 0.9
1.5 ( 0.6
5.1
0.8
30
5.0 ( 0.5
4.9 ( 0.3
2.6
2.6
29
a
Concentrations were calculated using the (experimentally
determined) densities of the “first-order solutions” Soln.1 at 298.15
K (densities of the first-order solutions for CTAB and DTAB are
1.079 and 0.975 g cm-3, respectively).
TABLE 6. Com p a r ison of Soln .1 a n d th e Micella r
System for CTAB a t 298.15 K
calc
kx,mic
/
kx,Soln.1
/
kx,Soln.1
/
ln(kx,mic/
kx,Soln.1)
10-4 s-1
10-4 s-1
10-4 s-1 a
relative rate constant with respect to molality of 1-pro-
panol, ax,TMAB is the same derivative with respect to the
molality of TMAB, and cx is the logarithm of the relative
micellar rate constant. For a model solution consistently
describing the micellar Stern region of the micelles
formed by a certain surfactant, this equation should hold
for all the hydrolytic probes in combination with this
surfactant. Hence, for a given surfactant, there is a model
solution of m1-propanol mol kg-1 in 1-propanol and mTMAB
mol kg-1 in TMAB in which the hydrolysis reactions of
all hydrolytic probes 1a -f are retarded to the same
extent as in the micellar Stern region. Hence, for every
surfactant a set of linear equations is given by eq 5. In
its extended form, these equations form the matrix given
in eq 6:
1a
1b
1c
1d
1e
1f
0.34 ( 0.03
0.78 ( 0.08
2.5 ( 0.2
5.4 ( 0.2
7.0 ( 0.1
67 ( 3
0.54 ( 0.04
1.45 ( 0.03
3.71 ( 0.24
8.0 ( 0.1
0.28
0.92
2.21
4.76
7.41
64.6
-0.463
-0.620
-0.399
-0.402
-0.386
-0.132
10.28 ( 0.07
77.7 ( 5.6
a
Calculated using eq 6.
determined for the solution mimicking CTAB made
according to Table 5, i.e. in Soln.1(CTAB) (Table 6).
According to Table 6, rate constants for hydrolysis of
individual probes in the model solution are only slightly
higher than those in the CTAB Stern region. This
discrepancy is attributed to the fact that hydrolysis data
for 1a -f in binary aqueous solutions of TMAB or 1-pro-
panol as determined at intermediate molalities have been
extrapolated to higher molalities. In addition, the final
solution is a ternary solution, introducing further devia-
tions from the extrapolations for binary solutions. An
encouraging observation is that the ET(30) value for the
mimicking solution (55.8 kcal mol-1) is in far better
agreement with the value for CTAB micelles (53.5 kcal
mol-1) than the ET(30) values of the model solutions
containing only TMAB.1 Further, we calculated the
expected micellar (CTAB and DTAB) rate constant of
hydrolysis for 2. Using the molalities (and concentrations)
determined here, together with the G(c) value of 1-pro-
panol for hydrolysis of 2 determined previously35 and the
dependence of the hydrolysis of 2 in aqueous solutions
containing TMAB on molarity (Figure 2 in ref 1), the rate
constant of the hydrolysis of 2 in the Stern region of
aMeO,1-propanol aMeO,TMAB
aMe,1-propanol aMe,TMAB
aH,1-propanol aH,TMAB
aCl,1-propanol aCl,TMAB
cMeO
cMe
cH
m1-propanol
)
(6)
cCl
[
]
mTMAB
a
a
c
F3CO,1-propanol
NO2,1-propanol
F3CO,TMAB
F3CO
[
]
[
]
a
a
c
NO2,TMAB
NO2
Overdetermined (not exact) matrix systems of the form
in eq 6 can be solved using singular value decomposi-
tion.36 The entries in vector cx and matrix ax,c are given
in Tables 3 and 4, respectively. With application of the
singular value decomposition method, a calculated model
solution mimicking the micellar Stern region of a CTAB
micelle is described in Table 5. The solution describes a
“first-order solution” of eq 6, based entirely on extrapo-
lated 1:1 interactions. This solution will be referred to
as Soln.1.
CTAB micelles is expected to be (1.4 ( 0.4) × 10-4 s-1
.
Experimentally, a micellar rate constant of (0.67 ( 0.08)
× 10-4 s-1 is observed.1 Similarly, the rate constant for
the hydrolysis of 2 in DTAB micelles is expected to be
(1.1 ( 0.3) × 10-4 s-1, in good agreement with the
experimental micellar rate constant1 of (1.26 ( 0.05) ×
10-4 s-1. In other words, the model predicts reasonably
well reaction rates for reactions that were not used in
the development of the model.
The salt concentrations in Table 5 are lower than those
in the concentrated salt solutions described in our previ-
ous paper1 where the salt was taken as the sole origin of
rate retardation. Nevertheless, the salt concentrations
match the calculated concentration ranges given in our
previous report but now at the lower end of the calculated
range. In fact, the value of 2.6 mol dm-3 is in reasonable
agreement with the concentrations of bromide anions (1.6
mol dm-3) and ionic headgroups (2.0 mol dm-3 assuming
a counterion binding of 0.8) as determined by the Rom-
sted group using their arenediazonium probe.15 Rate
constants for hydrolysis of 1a -f37 and ET(30) value were
Using the results of the analysis, we describe the
micellar binding and micellar inhibition in a single
scheme (Scheme 2, different contributions not drawn to
scale).
Both reactant (R) and activated complex (AC) bind to
the micelle in the Stern region (Table 2). However, R
binds much more strongly than AC, causing the rate
retardation. We divide the Gibbs energy of binding of R
to the micelle into a “dynamic” part, causing rate effects,
(36) Atkinson, K. E. An Introduction to Numerical Analysis; 2nd ed.;
Wiley: New York, 1988.
(37) The 1-propanolysis of 1a -f is expected to make a negligible
contribution to the observed rate constants (see ref 35).
3904 J . Org. Chem., Vol. 69, No. 11, 2004

Nature of the Micellar Stern Region
and a “passive” part, not causing rate effects (cf. a related
division into passive and dynamic interactions in ref 38,
for the present case the passive interactions correspond
to KAC). Using eq 6, the dynamic part has been divided
into rate-retarding effects caused by interactions with
ionic groups (as quantified by ax,TMABmTMAB) and effects
caused by interactions with hydrophobic groups (as
quantified by ax,1-propanolm1-propanol). For probes for which
the dynamic part of the Gibbs energy of binding to the
micelle is the same (i.e. probes with the same kinetic
sensitivity toward hydrophobic and ionic interactions but
for which the passive part is different), a linear relation
between pKm and pKAC with a slope of 1 is expected.
Indeed, such a linear relation is found for probes of which
only the hydrophobicity is increased by elongating an
alkyl chain remote from the reaction center.39 Similarly,
the reason for the absence of a correlation between rate-
retarding effects, micellar binding constants, and hydro-
phobicity of the surfactants constituting the micelle as
found in this study stems from different and uncorrelated
passive and dynamic contributions to the Gibbs energy
of binding to the micelles.
F IGURE 4. Representative examples of the rate-retarding
effect of (additional) added 1-propanol on the hydrolysis of 1a
(O), 1b (4), 1d (b), and 1f (3) at 298.15 K at a constant TMAB
molality mTMAB of 4.85 mol kg-1, using Soln.1 as reference.
solution, it would be useful to have a real solution
accurately reproducing rate constants in the micellar
Stern region. In the study of bimolecular reactions
occurring in the Stern region, it is often especially
difficult to determine independently binding constants
for both reactants and the micellar rate constant.40-42 We
therefore extended the model for CTAB to prepare a
solution that includes the nonlinear rate-retarding effects
at high molalities of TMAB and 1-propanol (vide supra).
We determined these rate-retarding effects at high
molality in much the same way as was used at low
molality. Instead of using rate constants in water without
added cosolute as reference points, rate constants in
Soln.1, kx(mTMAB ) 4.85, m1-propanol ) 5.00), denoted as
kx(Soln.1), were taken as reference points. Rate constants
for hydrolysis of the hydrolytic probes in the presence of
The present analysis, separating the contributions of
hydrophobic and ionic interactions, uses the differences
in rate-retarding effects caused by hydrophobic interac-
tions and ionic interactions. However, additional effects
causing differences in rate-retarding effects have not been
included in the present model. Three of these effects are
readily identified, and their source, effect, and importance
can be estimated.
First, different hydrolytic probes could bind in different
zones of the micelle (or their distribution over different
zones of the micelle could change1) and therefore experi-
ence different interactions. However, the kinetic probes
used in this study are structurally similar and are all
expected to reside in the micellar Stern region.11 Hence,
any difference in rate effect caused by a difference in
binding locations is expected to be of minimal importance.
Second, the electrostatic nonneutrality of the micellar
Stern region can (de)stabilize charges developing in the
activated complex. In the present case, the partial
negative charge on the AC will be stabilized by the
effectively cationic Stern region. This effect will be
modified by other factors (de)stabilizing the partial
negative charge, e.g. (de)stabilization by substituent
effects. Hence, different probes can be differently stabi-
lized by the cationic nature of the micellar Stern region.
Third, the local pH in the Stern region may be different
from the bulk pH. The local pH on the micellar surface
can be calculated from the bulk pH and the micellar
surface charge using the Poisson-Boltzmann equation.29
For a bulk pH of 4.0, the pH in the micellar Stern region
of CTAB is calculated to be approximately 6.5. Experi-
ments using 1e indicate that hydroxide-ion catalyzed
hydrolysis contributes less than 5% to the rate constant
of hydrolysis of 1e in the “second-order solution” (vide
infra) at pH 6.5. This suggests that, for the system
studied here, hydroxide-ion catalyzed hydrolysis as a
result of the different pH is not an important factor.
Notwithstanding the fact that conclusions about the
micellar binding sites can be drawn from the first-order
high molalities of TMAB and 1-propanol, kx(mTMAB
1-propanol), were determined in solutions where TMAB
,
m
and 1-propanol molalities were around 4.85 and 5.00 mol
kg-1, respectively, i.e. around the molalities in Soln.1.
Plots of ln[kx(mTMAB, m1-propanol)/kx(Soln.1)] as a function
of 1-propanol molality around the 1-propanol molality of
Soln.1 and at a constant mTMAB of 4.85 mol kg-1 are not
linear (Figure 4).
Nevertheless, a linear fit, forced through the reference
point provided by Soln.1, was used to obtain δln[kx(4.85,
m
1-propanol)/kx(Soln.1)]/δm1-propanol (denoted ax,1-propanolSoln.1).
For the dependence on mTMAB, only one additional data
point (for every probe) was determined as an indication
of δln[kx(mTMAB
,
5.00)/kx(Soln.1)]/δmTMAB (denoted
ax,TMABSoln.1). The calculated slopes are given in Table 7.
An improved estimate of the molalities for a model
solution accurately reproducing micellar rate constants
can be determined starting from the first-order solution.
Equation 6 with cx ) ln(kx,mic/kx(Soln.1)) (the residual of
the first-order model solution) and with ax,1-propanol and
Soln.1
Soln.1
ax,TMAB set to ax,1-propanol
and ax,TMAB
(Table 7),
(40) Rispens, T.; Engberts, J . B. F. N. J . Org. Chem. 2002, 67, 7369-
7377.
(41) Rispens, T.; Engberts, J . B. F. N. J . Org. Chem. 2003, 68, 8520-
8528.
(42) It is expected that the micellar rate constants as reported in
refs 40 and 41 will be reasonably well reproduced by the model
solutions reported here. This is expected because water concentrations
are less than 30 M in all the presented model solutions.
(38) Kirby, A. J . Angew. Chem., Int. Ed. Engl. 1996, 35, 707-724.
(39) Tee, O. S.; Yazbeck, O. J . Can. J . Chem 2000, 78, 1100-1108.
J . Org. Chem, Vol. 69, No. 11, 2004 3905

Buurma et al.
TABLE 7. Ra te-Reta r d in g Effects of 1-P r op a n ol a n d
TMAB on th e Hyd r olysis of Su bstitu ted
1-Ben zoyl-1,2,4-tr ia zoles 1a -f a t 298.15 K for Mola lities
a r ou n d Soln .1
Con clu sion s
The failure of concentrated salt solutions to reproduce
polarity-related properties of the micellar Stern region1
indicated the necessity of expanding our previous model
mimicking the Stern region in such a way that rate-
retarding hydrophobic interactions are correctly taken
into account. For DTAB and CTAB, this has been
accomplished by modeling the micellar Stern region using
an aqueous solution containing both 1-propanol, mimick-
ing hydrophobic surfactant tails, and TMAB, mimicking
ionic surfactant headgroups. The molalities of TMAB and
1-propanol in these solutions can be determined graphi-
cally and mathematically, using singular value decom-
position. We distinguish two “types” of model solutions,
viz. first-order and second-order solutions. First-order
solutions are determined from the rate-retarding effects
of 1-propanol and TMAB at intermediate molalities and
indicate the relative importance of ionic and hydrophobic
groups in the micellar Stern region. Second-order solu-
tions can be derived from first-order solutions and take
into account the nonlinear rate retardations at high
molalities of cosolutes. Second-order solutions can be used
to obtain estimates of micellar rate constants for reac-
tions of which the micellar rate constants cannot be
determined directly. The present approach can be used
for both micellar and vesicular systems and probably has
an even wider applicability.
Soln.1
Soln.1
ax,1-propanol
kg mol-1
/
ax,TMAB
/
kg mol-1
1a
1b
1c
1d
1e
1f
-0.128 ( 0.005
-0.160 ( 0.008
-0.160 ( 0.008
-0.080 ( 0.008
-0.078 ( 0.005
+0.022 ( 0.019
-0.13a
-0.19
-0.19
-0.18
-0.22
-0.19
a
Error has been set to 0.01 kg mol-1 for all entries in this
column.
respectively, yields a correction term for the “first-order
solution” equal to +2.7 ( 0.9 mol kg-1 for 1-propanol and
+0.8 ( 0.4 mol kg-1 for TMAB. Therefore the “second-
order solution” (Soln.2) should contain 7.7 ( 0.9 mol kg-1
1-propanol and 5.7 ( 0.4 mol kg-1 TMAB. We tested this
second-order solution. The rate constant for hydrolysis
of 1e, which is most sensitive to ionic interactions, equals
7.6 × 10-4 s-1, in good agreement with the micellar rate
constant of (7.0 ( 0.1) × 10-4 s-1. The ET(30) value, which
is most sensitive to hydrophobic interactions, equals 54.4
( 0.2 kcal mol-1, in reasonable agreement with the
micellar value1 of 53.5 kcal mol-1 (90% of the decrease
in excitation energy accounted for).43 In addition, the rate
constant for hydrolysis of 2 in Soln.2 is (9.5 ( 0.5) × 10-5
s-1, in reasonable agreement with the micellar rate
constant of (6.7 ( 0.8) × 10-5 s-1 (88% of the increase in
Gibbs energy of activation accounted for). Therefore,
reasonable estimates of micellar rate constants and even
micropolarity, as determined using the ET(30) probe, can
be obtained using the present model solution for CTAB.
Furthermore, the results obtained for 2 and the ET(30)
probe (both were not used in the optimization of our
model) suggest that this can also be done for reactions
and properties that were not included in the construction
of the model. Hence, the present model is the first to be
able to reproduce a diverse range of medium-controlled
properties of the micellar Stern region and it indicates
that other effects that were not included in the analysis
(vide supra) play only a minor role.
Exp er im en ta l Section
Substituted 1-benzoyl-1,2,4-triazoles (1a -f) and 1-benzoyl-
3-phenyl-1,2,4-triazole (2) were synthesized according to lit-
erature procedures.44 The ET(30) probe was kindly provided
by Prof. Dr. Chr. Reichardt. Micellar solutions were 1 × 10-4
mol dm-3 in HCl, and model compound solutions were acidified
to pH 4 to achieve conditions for pH-independent hydrolysis.
All solutions were made in water that was distilled twice in
an all-quartz apparatus. Surfactants and salts were dried
before use. If solutions were made volumetrically, the mass of
all components of the solutions was determined to know both
solute and solvent concentration. If model solutions were made
by weight, the density was determined. Reactions were fol-
lowed at 260, 262, 252, 262, 253, and 262 nm for 1a -f,
respectively, and at 273 nm for 2, at 298.15 ( 0.2 K for at
least 6 half-lives. Good to excellent pseudo-first-order kinetics
were obtained, the error in the rate constants being 2% or less
for the micellar solutions and the dilute solutions but up to
10% for the concentrated solutions.
The present model is not limited to alkyltrimethylam-
monium bromide surfactants. Comparable model solu-
tions can also be determined for other surfactants, both
micelle- and vesicle-forming, provided the salt mimicking
the micellar headgroups is appropriate. Availability of
solutions mimicking the micellar Stern region is espe-
cially helpful for determining factors underlying either
micellar catalysis or inhibition of bimolecular (or higher
molecularity) reactions. Despite the emphasis on reaction
kinetics in this study, virtually any property of the
micellar Stern region can be used in similar analyses.
The probes were injected as 6 µL of a stock solution of 1a -f
or 2-5 µL of a stock solution of 2 in cyanomethane into a 1
cm quartz cuvette of ca. 2.5 mL yielding a total probe
concentration during the reaction of ca. 10-5 mol dm-3. These
concentrations were chosen to have absorbance changes not
larger than 0.6.
The measurements involving the ET(30) probe were per-
formed at pH 11. The ET(30) probe was injected as <6 µL of a
stock solution of the solvatochromic probe in EtOH.
The singular value decomposition method was used as
implemented in Mathcad 2001 Professional by Mathsoft Inc.
Ack n ow led gm en t. Marie J etta den Otter is grate-
fully acknowledged for her contribution to this work.
(43) The relatively high sensitivity of the ET(30) probe toward
hydrophobic interactions provides a possibility for a quick test of the
nature of the micellar Stern region. The ET(30) probe can be used
mainly for the interactions with the alkyl tails whereas 1e is mainly
suitable for the interactions with the ionic headgroups. This results
in a 2 × 2 matrix with one row strongly dependent on TMAB molality
and one row mainly dependent on 1-propanol molality, yielding a
reasonable first indication of the Stern region as a reaction medium.
J O049959L
(44) (a) Staab, H. A.; Lu¨king, M.; Du¨rr, F. H. Chem. Ber. 1962, 95,
1275-1283. (b) Karzijn, W. The water- and hydroxide-ion catalyzed
hydrolysis of 1-acyl-1,2,4-triazoles. Ph.D. Thesis, University of Gronin-
gen, 1979. (c) Mooij, H. J .; Engberts, J . B. F. N.; Charton, M. Recl.
Trav. Chim. Pays-Bas 1988, 107, 185-189.
3906 J . Org. Chem., Vol. 69, No. 11, 2004