The nature of the sodium dodecylsulfate micellar pseudophase as studied by reaction kinetics

Article abstract of DOI:10.1021/jp208171w

The nature of the rate-retarding effects of anionic micelles of sodium dodecyl sulfate (SDS) on the water-catalyzed hydrolysis of a series of substituted 1-benzoyl-1,2,4-triazoles (1a-f) has been studied. We show that medium effects in the micellar Stern region of SDS can be reproduced by simple aqueous model solutions containing small-molecule mimics for the surfactant headgroups and tails, namely sodium methyl sulfate (NMS) and 1-propanol, in line with our previous kinetic studies for cationic surfactants (Buurma et al. J. Org. Chem. 2004, 69, 3899-3906). We have improved our mathematical description leading to the model solution, which has made the identification of appropriate model solutions more efficient. For the Stern region of SDS, the model solution consists of a mixture of 35.3 mol dm^-3 H₂O, corresponding to an effective water concentration of 37.0 mol dm^-3, 3.5 mol dm ^-3 sodium methylsulfate (NMS) mimicking the SDS headgroups, and 1.8 mol dm^-3 1-propanol mimicking the backfolding hydrophobic tails. This model solution quantitatively reproduces the rate-retarding effects of SDS micelles found for the hydrolytic probes 1a-f. In addition, the model solution accurately predicts the micropolarity of the micellar Stern region as reported by the E_T(30) solvatochromic probe. The model solution also allows the separation of the individual contributions of local water concentration (water activity), polarity and hydrophobic interactions, ionic strength and ionic interactions, and local charge to the observed local medium effects. For all of our hydrolytic probes, the dominant rate-retarding effect is caused by interactions with the surfactant headgroups, whereas the local polarity as reported by the solvatochromic E_T(30) probe and the Hammett ?? value for hydrolysis of 1a-f in the Stern region of SDS micelles is mainly the result of interactions with the hydrophobic surfactant tails. Our results indicate that both a mimic for the surfactant tails (NMS) and a mimic for the surfactant headgroups (1-propanol) are required in a model solution for the micellar pseudophase to reproduce all medium effects experienced by a variety of different probes. ? 2011 American Chemical Society.

Full text of DOI:10.1021/jp208171w

ARTICLE
pubs.acs.org/JPCB
The Nature of the Sodium Dodecylsulfate Micellar Pseudophase as
Studied by Reaction Kinetics
Lavinia Onel and Niklaas J. Buurma*
Physical Organic Chemistry Centre, School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT,
United Kingdom
S Supporting Information
b
ABSTRACT: The nature of the rate-retarding effects of anionic micelles of sodium
dodecyl sulfate (SDS) on the water-catalyzed hydrolysis of a series of substituted
1-benzoyl-1,2,4-triazoles (1aꢀf) has been studied. We show that medium effects in
the micellar Stern region of SDS can be reproduced by simple aqueous model solutions
containing small-molecule mimics for the surfactant headgroups and tails, namely
sodium methyl sulfate (NMS) and 1-propanol, in line with our previous kinetic studies
for cationic surfactants (Buurma et al. J. Org. Chem. 2004, 69, 3899ꢀ3906). We have
improved our mathematical description leading to the model solution, which has made
the identification of appropriate model solutions more efficient. For the Stern region of SDS, the model solution consists of a
mixture of 35.3 mol dmꢀ3 H2O, corresponding to an effective water concentration of 37.0 mol dmꢀ3, 3.5 mol dmꢀ3 sodium
methylsulfate (NMS) mimicking the SDS headgroups, and 1.8 mol dmꢀ3 1-propanol mimicking the backfolding hydrophobic tails.
This model solution quantitatively reproduces the rate-retarding effects of SDS micelles found for the hydrolytic probes 1aꢀf. In
addition, the model solution accurately predicts the micropolarity of the micellar Stern region as reported by the ET(30)
solvatochromic probe. The model solution also allows the separation of the individual contributions of local water concentration
(water activity), polarity and hydrophobic interactions, ionic strength and ionic interactions, and local charge to the observed local
medium effects. For all of our hydrolytic probes, the dominant rate-retarding effect is caused by interactions with the surfactant
headgroups, whereas the local polarity as reported by the solvatochromic ET(30) probe and the Hammett F value for hydrolysis of
1aꢀf in the Stern region of SDS micelles is mainly the result of interactions with the hydrophobic surfactant tails. Our results
indicate that both a mimic for the surfactant tails (NMS) and a mimic for the surfactant headgroups (1-propanol) are required in a
model solution for the micellar pseudophase to reproduce all medium effects experienced by a variety of different probes.
’ INTRODUCTION
micelles to increase the solubility of hydrophobic compounds
in aqueous solutions.6ꢀ10 In micellar solutions, reactions can be
either accelerated or decelerated compared to the reactions in
aqueous solutions without added cosolutes.11ꢀ13 Remarkable
success in enhancing reaction rates has been achieved by applying
micelles as catalysts (introducing catalytic moieties in micelle-
forming surfactants) and by micelle-assisted catalysis.11,14ꢀ25 In
micelle-assisted catalysis, micelles solubilize the reactants and the
catalyst, placing them in close proximity inside the small volume
of the micellar pseudophase. Although highly effective examples
of micelle-assisted catalysis are available, rational design of cata-
lytic systems based on quantitative data remains elusive. One of
the principal reasons for this is the fact that kinetic schemes, typi-
cally involving at least micellar binding of one or more reactants
and the catalyst and local rate constants in the different pseudo-
phases, often become unreliable. In practice, this means that in-
dividual parameters, such as the rate constant of a reaction in the
micellar pseudophase, cannot be determined or can be deter-
mined only with great difficulty, because of strong parameter
Micelle-forming amphiphiles spontaneously self-aggregate co-
operatively above the critical micelle concentration (cmc), form-
ing highly dynamic aggregates. Although different micelles can
have different morphologies (which can roughly be predicted
from the shape of the constituent surfactants),1 here, we focus
on approximately spherical micelles. For spherical morphology,
one of the most commonly accepted models for the micellar
structure is that proposed by Gruen.2 Gruen’s model features a
rather sharp interface between a dry hydrophobic hydrocarbon
core2ꢀ4 and the so-called Stern region. The Stern region is a
region filled with surfactant headgroups, some of the counterions
(for ionic surfactants), backfolding surfactant tails, and water.
The Stern region thus represents an interfacial zone between the
hydrocarbon core and bulk water. In line with this division in
zones, in the pseudophase formalism,5 micelles and bulk water
are considered to be different reaction regions, exerting different
reaction medium effects. As such, taking into account the clear
differences between the micellar core and the Stern region, these
zones themselves could also be considered as two distinct pseudo-
phases inside the micelles.6
Received: August 24, 2011
The increasing interest over the past several decades in organic
reactivity in aqueous solutions has resulted in widespread use of
Revised:
Published: September 27, 2011
September 27, 2011
r
2011 American Chemical Society
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covariance.26,27 Without access to accurate values for the various
parameters, an in-depth analysis of micelle-assisted catalysis is
nontrivial, to say the least. To address this situation, reliable
model solutions for the micellar pseudophase are required. Such
model solutions not only allow the determination of accurate
estimates of micellar rate constants, but ideally also provide in-
sight into the factors affecting micellar reactivity. For the devel-
opment of such model solutions, we limit our discussion to
medium effects exerted by micelles of nonfunctionalized amphi-
philes on uncatalyzed hydrolysis reactions28 for which reliable
models for data analysis exist.
Scheme 1
As discussed above, to understand the micellar acceleration
and deceleration of reactions, a good understanding of the mi-
cellar pseudophase as a reaction medium is necessary. Although
many kinetic studies of micellar medium effects on various organic
reactions have already been reported,6,11,14,15,29,30 the descrip-
tion of the local reaction environment offered by micelles has
remained obscure. The present work continues our kinetic stud-
ies of micellar effects on the water-catalyzed hydrolysis of a series
of activated amides.31 Previously, we showed that these reactions
occur in the micellar Stern region, and our approach therefore
leads to a description of the micellar Stern region as a reaction
medium.31,32 An analysis of the reaction medium properties of
the Stern region is of wide interest because the majority of reac-
tants used in organic reactions in micellar solutions bind in the
micellar Stern region.6,12,33ꢀ35 This preference for the Stern
region probably stems from its versatility as a binding location be-
cause it contains, in addition to water molecules, highly hydro-
philic surfactant headgroups and hydrophobic domains of back-
folding surfactant tails.
A characteristic feature of the Stern region of ionic micelles
is the high local concentration of headgroups, counterions, and
backfolding surfactant tails residing at the micelle interface.
Calculations have estimated the concentration of headgroups
in the Stern region of spherical ionic micelles to be 1ꢀ3 M
(Mukerjee36), 4ꢀ7 M (Bunton et al.37), and 2ꢀ6 M (Buurma
et al.6). Methods using molecular spectroscopic probes (such as
solvatochromic, fluorescent, and spin-label probes)38ꢀ41 and
reactive probes42,43 have also been used to gain insight into the
properties of the micellar interfacial region and its composition.
Model solutions for the micellar Stern region were found useful
for estimating the interfacial concentrations of water40ꢀ43 and
counterions.42,43 The chemical trapping method developed by
Romsted et al.42,43 for probing the micellar Stern region showed
that the concentrations of headgroups and counterions in the
interfacial region of micelles of cationic surfactants such as cetyl-
trimethylammonium bromide and cetyltrimethylammonium
chloride fall roughly in the range of 1ꢀ3 M. The concentration
of counterions is slightly less than the concentration of head-
groups because of incomplete counterion binding in the Stern
region.
ion, because of the instability of the alkyl aryl sulfate ester pro-
duct, which hydrolyzes rapidly.43 Buurma et al.32 and Mu~noz and
co-workers45 used a more concentrated salt solution containing
4.3 mol dmꢀ3 NMS to model the Stern region of SDS micelles.
Using these salt solutions for modeling the interfacial region of
SDS micelles showed that it was not possible to reproduce the
micellar polarity as reported by the ET(30) probe.32 In addition,
the inhibition exerted by SDS micelles on phenyl chloroformate
hydrolysis was much larger than the rate retardation observed in
the model solution.45 The authors of both studies45,46 concluded
that a better description of micellar effects on the reaction rates
includes the contribution of hydrophobic interactions with the
backfolding hydrocarbon tails, which is not taken into account
using a model solution containing only the headgroup mimic
NMS. In our subsequent kinetic study31 of the interfacial region
of micelles of the cationic surfactants dodecyltrimethylammo-
nium bromide (DTAB) and cetyltrimethylammonium bromide
(CTAB), we used model solutions containing, in addition to the
salt mimicking the surfactant headgroups, 1-propanol as a small-
molecule mimic of the hydrocarbon tails. Deconvolution of the
rate-retarding effects of micelles of DTAB and CTAB on a series
of probe reactions allowed the identification of aqueous model
solutions, consisting of mixtures of tetramethylammonium bro-
mide, mimicking micellar headgroups, and 1-propanol, mimick-
ing the backfolding tails, that largely reproduced the observed
micellar kinetics. This solution also correctly predicted the ET(30)
value for the CTAB Stern region, highlighting the importance of
including hydrophobic interactions in model solutions for the
micellar pseudophase.
In the present work, we test the general validity of such
modeling for an anionic surfactant, namely, SDS. Our goal is to
test whether a concentrated aqueous mixture of the headgroup
mimic NMS and the backfolding-tail mimic 1-propanol repro-
duces the rate-retarding effects of SDS micelles on the hydrolysis
of the same series of activated amides as used in ref 31 (1aꢀf,
Scheme 1). In addition, by improving the mathematical descrip-
tion developed in our earlier work for the identification of the
appropriate model solution,31 we more efficiently achieve a more
complete representation of the micellar Stern region as a reaction
medium. Using the ET(30) solvatochromic probe as a micro-
polarity reporter, we probe the ability of the model solution to
predict the medium properties of the interfacial region of SDS
micelles that were not included in our kinetic modeling. In line
with our previous study, we chose the water-catalyzed pH-
independent hydrolysis of different substituted 1-benzoyl-1,2,
4-triazoles (1aꢀf, Scheme 1) as the probe reaction, because
the series of hydrolytic probes 1aꢀf has the required differences
in sensitivity to environment.31 The reactions occur through a
The interface of sodium dodecyl sulfate (SDS) micelles as a
reaction medium has previously been modeled using aqueous salt
solutions, usually involving sodium methyl sulfate (NMS).32,44,45
Based on their earlier work, Cuccovia et al.44 used aqueous
solutions containing 1.5 mol dmꢀ3 NMS and solutions contain-
ing 1.5 mol dmꢀ3 sodium methylsulfonate as model solutions for
the Stern region of SDS micelles in their chemical trapping
experiments when studying the interfacial concentration of co-
ions Clꢀ and Brꢀ. The chemical trapping method was not used to
determine the interfacial concentration of SDS headgroups, even
though the anionic sulfate group reacts with the arenediazonium
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ARTICLE
dipolar activated complex involving two molecules of water, one
acting as a nucleophile and the other as a general base.47ꢀ49
Table 1. Rate Constants for Hydrolysis in Water without
Added Cosolutes and in the SDS Micellar Pseudophase and
Micellar Binding Constantsa for Para-Substituted 1-Benzoyl-
1,2,4-triazoles 1aꢀf at 25 °C
’ EXPERIMENTAL SECTION
b
probe
σp
kX,water (10ꢀ4 sꢀ1
)
kX,mic (10ꢀ4 sꢀ1
)
KX,mic (103 Mꢀ1
)
Chemicals. Sodium dodecylsulfate (SDS) (99%, Fluka),
sodium methylsulfate (NMS) (98%, TCI), p-anisoyl chloride
(99%, Acros Organics), p-toluoyl chloride (99%, Acros Organics),
benzoyl chloride (99%, Acros Organics), p-chlorobenzoyl chlor-
ide (99%, Aldrich), p-(trifluoromethyl)benzoyl chloride (98%,
Acros Organics), p-nitrobenzoyl chloride (99%, Fluka), 1,2,4-
triazole (purum, g98%, Fluka), p-toluic acid (98%, Aldrich),
p-(trifluoromethyl)benzoic acid (99%, Acros Organics), and
Reichardt’s ET(30) dye (90%, Aldrich) were used as received.
The substituted 1-benzoyl-1,2,4-triazoles 1aꢀf were synthesized
according to literature procedures.50
Spectrophotometric Measurements. Aqueous solutions
were prepared in water purified using an ELGA option-R 7BP
water purifier. Micellar solutions were acidified (HCl) to roughly
pH 5.3. This pH was chosen to achieve conditions of pH-
independent reaction in both the bulk water and the micellar
pseudophase; the observed rate constant for the hydrolysis of
each substituted probe in 100 mM SDS does not change if the pH
is a few tenths of a pH unit above or below 5.3, indicating that
5.3 still lies in the range of pH values where the rate constant
for hydrolysis is pH-independent in the micellar pseudophase.
NMS solutions, 1-propanol solutions, and the model (micelle-
mimicking) solutions were acidified to pH 4. The hydrolytic
probes were injected as 7 μL of a stock solution of 1aꢀf in
acetonitrile into a 1.00-cm-path-length cuvette containing ca.
2.5 mL of an aqueous solution of interest, yielding a total probe
concentration during the reaction of ca. 10ꢀ5 mol dmꢀ3. The
hydrolysis reactions were monitored by parallel kinetic measure-
ments using a JASCO V650 UVꢀvisible spectrophotometer with
an AutoPeltier thermostatting unit with six-position cell changer
PAC-743R. Reactions were followed at 296, 262, 251.5, 262, 253,
and 262 nm for 1aꢀf, respectively, at 25 °C for at least eight half-
lives. The decrease of absorbance with time at the selected
wavelengths was reproduced well by the pseudo-first-order
kinetics rate law
1a
1b
1cc
1d
1e
1f
ꢀ0.28
ꢀ0.14
0.00
4.04 ( 0.05
9.42 ( 0.01
21.00 ( 0.02
36.00 ( 0.02
43.25 ( 0.07
274 ( 8
0.145 ( 0.002
0.39 ( 0.02
1.13 ( 0.06
1.86 ( 0.02
2.60 ( 0.04
26.4 ( 2.2
9.05 ( 0.03
10.07 ( 0.13
3.55 ( 0.04
10.37 ( 0.04
18.19 ( 0.15
4.55 ( 0.18
+0.24
+0.32
+0.81
a Calculated using the MengerꢀPortnoy equation,5 with the cmc set to
7.9 mM (determined using isothermal titration calorimetry, in close
agreement with values in the literature55ꢀ57) and an aggregation number
c
of 64.58 b Hammett substituent constants from ref 59. In acceptable
agreement with kmic and Kmic for 1c and SDS from Fadnavis et al.60
weredetermined by nonlinear least-squares fittingofthe Mengerꢀ
Portnoy equation (vide infra) to the experimental data. Errors
were propagated51 as required. Error margins for the molality of
1-propanol (m1‑propanol) and the molality of NMS (mNMS) in
solution 1 (Tables 4 and 9) represent standard deviations
determined by the singular value decomposition method.52 To
determine the error margins for m 1‑propanol and mNMS in solution
2, 0we added the respective standard deviations to each term
(a X,1‑propanol, a0X,NMS, bX,1‑propanol, bX,NMS and cX) in eq 11 (vide
infra) and also subtracted the respective standard devia-
tions from each term in eq 11. The equation obtained in each
of these two cases was solved numerically using the Levenbergꢀ
Marquardt method53 resulting in two “extreme solutions”. Tak-
ing the two extreme solutions together with the best-fit values for
m1‑propanol and mNMS according to the average first and second
derivatives, we obtained three sets of molalities for the two
mimicking compounds in the model solution. For each mimic,
the average of the three molalities coincides with the optimum
value of the molality in solution 2 (2.8 mol kgꢀ1 for 1-propanol
and 5.5 mol kgꢀ1 for NMS), indicating that the error margins are
symmetric. The error margins for m1‑propanol and mNMS in solu-
tion 2 (Table 4) were determined as standard deviations for these
sets of three values.
obst
At ¼ Afin þ ΔAeꢀk
ð1Þ
where At is the absorbance at time t, Afin is the final absorbance,
ΔA represents the difference between the absorbance at time
zero and Afin, and kobs is the observed pseudo-first-order rate
constant.
Measurements Involving the ET(30) Solvatochromic
Probe. All spectra were recorded at 25 °C, pH 12. The ET(30)
probe was injected as 14 μL of a stock solution in ethanol into a
1.00-cm-path-length cuvette containing 3.2 mL of an aqueous
solution of interest. The UVꢀvisible spectra were recorded using
a JASCO V630 spectrophotometer with a JASCO EHC-716
Peltier unit for temperature control.
HPLC Measurements. High-performance liquid chromato-
graphy (HPLC) experiments were performed using an Agilent
1200 instrument with a ZORBAX Eclipse XDB-C18 4.6 ꢁ 150
mm column. Samples of the reaction mixtures for 1aꢀf were
analyzed as soon as the reactions were finished using the HPLC
method described in the Supporting Information.
Error Margins. Error margins for all observed rate constants
represent standard deviations around average values. Error mar-
gins for micellar rate constants and micellar binding constants
’ RESULTS AND DISCUSSION
For convenience of data analysis, the kinetic experiments are
ideally carried out in the pH range in which the hydrolysis of
substituted 1-benzoyl-1,2,4-triazoles (1aꢀf) is pH-independent
(Scheme 1) in both the aqueous and micellar pseudophases.
Based on kinetic measurements for probe 1d (Figures S1.1 and
S1.2, Supporting Information), a bulk pH of 5.3 appeared to
provide these ideal conditions. To confirm that a bulk pH of 5.3 is
suitable for the other kinetic probes as well, we studied the
hydrolysis of 1aꢀf over a limited range of pH values around 5.3
in the presence of 100 mM SDS and found the observed rate
constants to be invariant around this pH. In addition, the
observed rate constants for hydrolysis of each probe 1aꢀf in
water without added cosolutes at pH 5.3 (Table 1) are in
excellent agreement with those for the corresponding hydrolysis
in water at pH 4.31 The local pH on the surface of SDS micelles is
lower than the bulk pH and can be estimated by applying the
PoissonꢀBoltzmann equation54 that relates the proton activity
at the surface of a charged micelle to that in bulk water in
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Table 2. Relative Rate Constants for Hydrolysis of 1aꢀf in
SDS Micelles and Water at 25 °C
probe
kX,mic/kX,water
ln(kX,mic/kX,water)
1a
1b
1c
1d
1e
1f
0.0359 ( 0.0006
0.041 ( 0.002
0.053 ( 0.003
0.0516 ( 0.0005
0.060 ( 0.001
0.096 ( 0.008
ꢀ3.33 ( 0.02
ꢀ3.18 ( 0.05
ꢀ2.92 ( 0.05
ꢀ2.96 ( 0.01
ꢀ2.81 ( 0.01
ꢀ2.34 ( 0.08
The rate-retarding effects exerted by SDS micelles on the
individual hydrolytic probes are described by the micellar rate
Figure 1. Observed rate constant of hydrolysis of 1c at 25 °C in
solutions containing varying concentrations of SDS at pH 5.3. Experi-
mental data were fitted with eq 2.
constants relative to the rate constants in water, that is, kX,mic
/
kX,water, and the natural logarithms of these relative rate con-
stants, ln(kX,mic/kX,water) (Table 2).
The relative rate constants kX,mic/kX,water for 1aꢀf increase
with Hammett substituent constant (σ). Therefore, the rate-
retarding effect exerted by SDS micelles on the hydrolysis of
1aꢀf decreases with increasing electron-withdrawing ability of
the substituent. A similar trend was found for the hydrolysis of
1aꢀf in CTAB and DTAB micelles (Table 3 in ref 31).
combination with the interfacial electrostatic potential. Based on
the interfacial potential of ꢀ134 mV for SDS micelles,54 the
calculated interfacial pH is approximately 3.0 for a bulk pH of 5.3.
We therefore chose a bulk pH of 5.3 for all kinetic experiments.
The hydrolysis reactions of 1aꢀf all follow pseudo-first-order
kinetics. The rate constants for hydrolysis of 1aꢀf in water
without added cosolutes, kX,water (subscript X indicates the sub-
stituent of the probe as shown in Scheme 1), are presented in
Table 1. The rate constant of hydrolysis increases with increasing
electron-withdrawing ability of the substituent, as expected for a
reaction in which a partial negative charge develops on the
carbonyl group going toward the activated complex.
Next, the effect of micelles on the hydrolysis of 1aꢀf was
studied. For all hydrolytic probes, SDS micelles retard hydrolysis.
Figure 1 shows the kinetic profile for 1c. Kinetic profiles for 1a,b and
1dꢀf are shown in Figure S2.1a,b,dꢀf (Supporting Information).
The kinetic data for hydrolysis of 1aꢀf in the presence of a
range of SDS concentrations at a bulk pH of 5.3 were analyzed
using the nonlinear form of the pseudophase model developed
by Menger and Portnoy5 (eq 2). The pseudophase model as-
sumes an equilibrium between free and micelle-bound substrate
and makes a distinction between the reaction rate constants in
bulk water and in the micellar pseudophase
There is no significant correlation between the micellar
binding constants, KX,mic, for 1aꢀf and the micellar rate con-
stants, kX,mic (Table 1), or between the micellar binding con-
stants, KX,mic, for 1aꢀf and the relative micellar rate constants,
kX,mic/kX,water (Table 2). This lack of correlation is in line with
the hypothesis that all hydrolytic probes 1aꢀf bind in the Stern
region in the micellar pseudophase and that different rate-
retarding effects are not the result of different binding locations
within the micelle (vide infra). Micellar rate constants for all
probes 1aꢀf in SDS micelles are 2ꢀ3 times smaller than kmic for
CTAB and DTAB micelles.31 The fact that observed kmic values
for anionic SDS are lower than for cationic DTAB and CTAB
is in agreement with observations by Bunton et al.61,62 and
Campos-Rey et al.13 regarding the effects of the electrostatic non-
neutrality of ionic micelles on reactions involving partial charges
in the transition state. Here, the partial negative charge on the
carbonyl in the activated complex will be destabilized by the
anionic Stern region, whereas with cationic surfactants, a stabiliz-
ing effect occurs. To determine whether the additional destabi-
lizing effect exerted on the transition state by the local negative
charge of SDS micelles enhances the difference between the
effects of electron-donating and electron-withdrawing substitu-
ents on the transition state, we constructed Hammett plots63,64
(Figure S3.1, Supporting Information) for hydrolysis of 1aꢀf in
bulk water and in the micellar pseudophases of SDS, CTAB, and
DTAB. The Hammett F value equals 1.6 for the reaction in water
and is approximately 2.0 for all micelles, independent of the
headgroup charge. Therefore, for hydrolysis of 1aꢀf, the effects
exerted by the negatively charged interface of SDS micelles do
not depend on the substituent on the hydrolytic probes; other-
wise, the Hammett F values for anionic and cationic micelles
would be different. This finding is in agreement with the effects of
the headgroup mimic NMS, which does not strongly affect the
Hammett F value for hydrolysis of 1aꢀf (vide infra).
kwater þ kmicKmð½surfꢂ ꢀ cmcÞ=N
kobs
¼
ð2Þ
1 þ Kmð½surfꢂ ꢀ cmcÞ=N
where kobs is the observed pseudo-first-order rate constant
defined by eq 1 at a surfactant concentration of [surf], kwater is
the rate constant in water in the absence of added cosolutes, and
kmic is the rate constant under conditions of complete binding of
the substrate to the micelles. Km is the binding constant of the
kinetic probe to SDS micelles, cmc is the critical micelle concen-
tration of the surfactant, and N is the average micellar aggregation
number. Because all hydrolytic probes 1aꢀf bind in the micellar
interfacial region (vide supra), kmic is the rate constant for hy-
drolysis in the micellar Stern region.
From a nonlinear least-squares fit of eq 2 to the experimental
data, micellar rate constants for hydrolysis and micellar binding
constants for SDS were determined (Table 1). The micellar
binding constants for 1aꢀf binding to SDS are similar to the cor-
responding Km values for CTAB (Table 2 in ref 31). However,
the Km values for SDS are on average about 3 times larger than
those for DTAB.31
First Model Solution. To obtain a description of the micellar
Stern region as a reaction medium, the effects of ionic inter-
actions with the headgroups and hydrophobic interactions with
the alkyl tails on the kinetic probes have to be distinguished. We
previously31 achieved such a separation of the kinetic effects
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Table 3. Sensitivities of the Rate Constants of Hydrolysis of
the Probes 1aꢀf to 1-Propanol and NMS in Accordance with
the Mathematical Description Leading to Solution 1
a
b
probe
aX,1‑propanol
aX,NMS
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
ꢀ0.547 ( 0.009
ꢀ0.527 ( 0.004
ꢀ0.539 ( 0.007
ꢀ0.516 ( 0.006
ꢀ0.517 ( 0.007
ꢀ0.510 ( 0.016
a aX,1‑propanol is the first-order derivative of the logarithm of the
observed rate constant in the presence of 1-propanol relative to that
in water with respect to the molality of 1-propanol. b aX,NMS is the first-
order derivative of the logarithm of the observed rate constant in the
presence of NMS relative to water with respect to the molality of NMS
(eqs 3 and 4).
to those in water as a function of the molalities of NMS and
1-propanol, respectively, reflect the 1:1 interactions, or pair-
wise interactions, between each cosolute and probes 1aꢀf,65,66
and these are summarized in Table 3.
The data in Table 3 are in good agreement with our previous
findings,31 showing that the rate-retarding effects of added
1-propanol are different for the different substituted probes.
The rate-retarding effects of NMS are larger than those of
1-propanol and vary only slightly in the series 1aꢀf. The rate-
retarding effect of NMS on the hydrolysis of 1c determined here
is in good agreement with the G(c) value for the same combina-
tion of hydrolytic probe and cosolute determined by Noordman
et al.67 In addition, we note that the work by Noordman et al.67
also suggests that results rather similar to those reported here for
NMS would have been obtained if sodium ethyl sulfate had been
used as a headgroup mimic. The effects of NMS on the hydrolysis
of 1aꢀf are reminiscent of the effects of TMAB,31 where the
slopes aX,TMAB, obtained by fitting ln(kX,TMAB/kX,water) versus
mTMAB, were found to vary only slightly with the substituent.
However, the values of aX,NMS are on average 2 times those of aX,
TMAB. Therefore, the hydrolysis of all of the probes is more
retarded by added NMS than by added TMAB.
Figure 2. Linear fit (dotted line) and second-order polynomial fit (solid
line) of the individual effects of (a) 1-propanol and (b) NMS on the
observed rate constant of hydrolysis of probe 1d at 25 °C versus the
(a) 1-propanol molality and (b) NMS molality.
exerted by DTAB and CTAB micelles on hydrolysis of 1aꢀf
using tetramethylammonium bromide (TMAB) as a mimic for
the surfactant headgroups and 1-propanol as a mimic for the
backfolding surfactant tails. In the present study, the rate-retarding
effects of SDS headgroups are mimicked using NMS, and the
effects of the hydrocarbon chains are again modeled using 1-
propanol. The sensitivities of hydrolytic probes 1aꢀf to added
NMS and 1-propanol were determined separately in the molality
range of 0ꢀ5 mol kgꢀ1 for each mimicking compound. Figure 2
summarizes the kinetic data for 1d, with data for 1aꢀc,e,f in
Figures S4.1aꢀc,e,f and S5.1aꢀc,e,f (Supporting Information).
Using our previously developed approach,31 we quantify the
sensitivities of the hydrolysis rate constants of 1aꢀf to each
modeling compound by the slopes of the logarithms of the
As in our previous work,31 we assume that the micellar rate-
retarding effect for each hydrolytic probe corresponds to the sum
of the effects of the two mimicking compounds
!
!
!
kX, 1-propanol
kX, NMS
kX, mic
relative rate constants, ln(kX,NMS/kX,water) and ln(kX,1‑propanol
/
ln
þ ln
¼ ln
ð5Þ
kX, water
kX, water
kX, water
kX,water), versus the molality of the cosolute, namely mNMS and
m1‑propanol. The subscript X again refers to the substituent on the
hydrolytic probe. The slopes were obtained by analyzing ln-
(kX,NMS/kX,water) versus mNMS and ln(kX,1‑propanol/kX,water) ver-
sus m1‑propanol in terms of eqs 3 and 4, respectively (Figure 2a,b).
By substituting eqs 3 and 4 into eq 5, we obtain
X, 1-propanolm1-propanol þ aX, NMSmNMS ¼ cX
a
ð6Þ
!
kX, NMS
ln
¼ aX, NMSmNMS
ð3Þ
ð4Þ
where cX is the natural logarithm of the micellar rate constant
relative to water. Equation 6 can be written for each substituted
probe 1aꢀf taking into account the different sensitivities of the
different probes to added 1-propanol and NMS as quantified by
kX, water
!
kX, 1-propanol
kX, water
ln
¼ aX, 1-propanolm1-propanol
aX,NMS and aX,1‑propanol
.
Alternatively, ln(kX,mic/kX,water) can be interpreted as the dif-
ference in activation Gibbs energy in water and in the micelle, or
the equivalent difference in the Gibbs energy changes for binding
to micelles of the reactant state and transition state (eq 7), with
Slopes aX,NMS and aX,1‑propanol (eqs 3 and 4), that is the first-
order derivatives of the logarithms of the rate constants relative
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Table 4. Molalities and Molar Concentrationsa of 1-Propanol
and NMS in Solution 1 and Solution 2
through aX,1‑propanolm1‑propanol, and by SDS headgroups, repro-
duced through aX,NMSmNMS
.
The mimicking aqueous solution of the micellar pseudophase
should be the same for all probes and therefore contains the two
cosolutes in the same molalities, m1‑propanol and mNMS, for all
probes 1aꢀf. This is made explicit by rewriting the set of all eqs 6
in matrix form as
mol kgꢀ1
1-propanol NMS
mol dmꢀ3
NMS
1-propanol
water
solution 1 3.4 ( 0.2 4.5 ( 0.1 2.2 ( 0.1 2.88 ( 0.05 35.2 ( 0.3
0
1
0
1
solution 2 2.8 ( 0.2 5.5 ( 0.3 1.8 ( 0.1
3.5 ( 0.2 35.3 ( 0.8
aMeO, 1-propanol aMeO, NMS
cMeO
a Molar concentrations were calculated using the experimentally de-
termined densities of solution 1 and solution 2 at 25 °C (1.15 and
1.21 g cmꢀ3, respectively).
B
B
B
B
B
B
C
C
C
C
C
C
B
C
C
C
C
C
C
aMe, 1-propanol
aH, 1-propanol
aCl, 1-propanol
aMe, NMS
aH, NMS
aCl, NMS
c
B Me
!
B
B
m1-propanol
mNMS
cH
B
¼
B
cCl
B
B
@
C
C
A
B
B
@
C
C
A
a
aF CO, NMS
cF CO
F3CO, 1-propanol
3
3
Table 5. Rate-Retarding Effects of 1-Propanol and NMS in
Solution 1 on the Hydrolysis of Substituted Probes 1aꢀf at
25 °C
a
a
c
NO2, 1-propanol
NO2, NMS
NO2
ð9Þ
a,b
a,b
aX,1‑propanolm1‑propanol
aX,NMSmNMS
Equation 9 represents an overdetermined system that cannot be
solved exactly. By applying singular value decomposition,52
solution we refer to as solution 1 in Table 4 was determined.
a
1a
1b
1c
1d
1e
1f
ꢀ0.81 ( 0.05
ꢀ0.80 ( 0.05
ꢀ0.69 ( 0.05
ꢀ0.52 ( 0.03
ꢀ0.45 ( 0.03
ꢀ0.20 ( 0.01
ꢀ2.48 ( 0.06
ꢀ2.39 ( 0.04
ꢀ2.45 ( 0.05
ꢀ2.34 ( 0.05
ꢀ2.35 ( 0.05
ꢀ2.31 ( 0.08
The required molalities for both 1-propanol and NMS are
nonzero and (statistically) significant, showing that both 1-
propanol and NMS are required to reproduce the observed
micellar kinetics for 1aꢀf. Based on the molalities of NMS and
1-propanol in solution 1 (Table 4) and the sensitivities of the rate
constants for hydrolysis of the kinetic probes to the presence of
NMS and 1-propanol (Table 3), the contributions of interactions
with the surfactant tails and interactions with the surfactant
headgroups to the overall observed rate retardation can be
calculated (Table 5).
a aX,1‑propanol and aX,NMS are the first derivatives of the logarithms of the
rate constants relative to those in water with respect to the molality of
1-propanol and NMS, respectively (Table 3). m1‑propanol and mNMS
have the values of the molalities of 1-propanol and NMS, respectively, in
solution 1 (Table 4).
b
Table 5 shows that the product aX,NMSmNMS is between 3 (1a)
the caveat that the reactant state includes two molecules of
water31,32
and 11 (1f) times larger than the product aX,1‑propanolm1‑propanol
.
Therefore, the micellar stabilization of the reactant state relative
to the transition state for the hydrolysis reactions studied here is
mainly due to ionic interactions of 1aꢀf with SDS headgroups.
However, although ionic interactions make the largest contribu-
tion to the observed rate-retarding effects, other properties of the
Stern region of SDS such as those quantified by the ET(30) value
and the Hammett F value for hydrolysis of 1aꢀf cannot be
reproduced by a solution of NMS alone and require the inclusion
of 1-propanol (vide infra).
The hydrolysis of 1aꢀf was studied in solution 1 to test
whether solution 1 indeed reproduces experimentally the micel-
lar rate effects exerted by SDS, as eq 9 predicts it should. As
shown in Figure 3a and Table 6, solution 1 does not fully repro-
duce the rate-retarding effects exerted by the Stern region of SDS
micelles.
Second Model Solution. To decrease the deviations in the
experimentally observed rate effects for our model solution from
the micellar rate effects, we improved the mathematical descrip-
tion leading to the model solution. The plots describing the
kinetic effects of the two mimicking compounds on hydrolysis of
1aꢀf (Figure 2a,b) start to deviate from linearity at high cosolute
concentrations. This is particularly the case for added NMS at
molalities above 3 mol kgꢀ1. The deviations suggest that higher-
order interactions65 (higher than pairwise) of cosolutes with re-
actants 1aꢀf cannot be neglected for concentrated solutions of
mimicking compounds.
!
ΔqGθX, water ꢀ ΔqGXθ, mic
kX, mic
ln
¼
¼
kX, water
RT
ΔmicGθXðRÞ ꢀ ΔmicGXθ ðACÞ
ð7Þ
RT
where Δ‡GθX,water and Δ‡GθX,mic are the standard molar activa-
tion Gibbs energies for the hydrolysis reaction in pure water
and in the micellar pseudophase, respectively; ΔmicGθX(R) and
ΔmicGθX(AC) are the standard molar Gibbs energy differences
for binding to micelles of reactant (R) and activated complex
(AC), respectively; and RT is the product of the gas constant and
the absolute temperature. Equation 7 shows that the micellar
rate-retarding effect exerted on the hydrolysis of each probe 1aꢀf
is caused by a more pronounced stabilization of the reactant state
by binding to micelles in comparison with the stabilization of the
transition state by binding to micelles.
Substitution of eq 7 into eq 6 leads to the equation
aX, 1-propanolm1-propanol þ aX, NMSmNMS
ΔmicGXθ ðRÞ ꢀ ΔmicGXθ ðACÞ
¼
ð8Þ
RT
Equation 8 highlights that the difference between the stabiliza-
tion of the initial state by binding to micelles and the stabilization
of the transition state by binding to micelles is due to the
combination of the effects exerted by surfactant tails, reproduced
As shown in Figure 2, the effects exerted by NMS (and, to
some extent, by 1-propanol) are better reproduced using second-
order polynomials instead of linear fits. This suggests that our
model could be improved by the introduction of quadratic terms
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ARTICLE
in the mathematical description of the kinetic effects exerted by
the model solutions. By adding quadratic terms to eq 6, one
obtains
respect to the molalities of 1-propanol and NMS, respectively.
The mixed second-order derivative of the logarithms of the
relative rate constants with respect to the molalities of 1-propanol
and NMS is not included in eq 10 because this term is not
accessible experimentally using separate solutions of 1-propanol
and NMS. A mixed second-order derivative would describe 2:1
interactions between 1-propanol, NMS, and the kinetic probe.
An evaluation of the mixed second-order derivative would
require the experimental determination of the rate-retarding
effects exerted on hydrolysis of 1aꢀf for a series of solutions
containing both 1-propanol and NMS. Our previous31 method
for accounting for the nonlinear rate-retarding effects at high
molalities of 1-propanol and salt partially addressed the missing
cross term, but at great experimental expense (vide infra).
1
a0X, 1-propanolm1-propanol
þ
bX, 1-propanolm1-propanol
2
2
1
þ a0X, NMSmNMS
þ
b
X, NMSmNMS ¼ cX
ð10Þ
2
2
Here, a0X,1‑propanol and a0X,NMS have the same meaning as aX,1‑propanol
and aX,NMS in eq 6 (vide supra), but whereas aX,1‑propanol and aX,NMS
are determined from a linear fit, a0X,1‑propanol and a0X,NMS are de-
termined by a second-order polynomial fitting of the same experi-
mental data (see Figure 2a,b for examples). Parameters bX,1‑propanol
and bX,NMS denote the second-order derivatives (hence the
The values of all derivatives a0X,1‑propanol, a0X,NMS, bX,1‑propanol
,
1
factor /2) of the logarithms of the relative rate constants with
and bX,NMS in eq 10 for different substituted hydrolytic probes
are collected in Table 7.
As before, the system of eqs 10 can be written in matrix form as
0
1
1
1
a0MeO, 1-propanol
bMeO, 1-propanol aM0 eO, NMS
bMeO, NMS
bMe, NMS
bH, NMS
B
C
B
B
B
B
2
1
2
1
C
C
C
C
0
a
bMe, 1-propanol
bH, 1-propanol
bCl, 1-propanol
a0Me, NMS
a0H, NMS
a0Cl, NMS
Me, 1-propanol
2
1
2
1
B
B
B
B
B
B
B
B
B
B
B
C
C
C
C
C
C
C
C
C
C
C
0
aH, 1-propanol
2
1
2
1
0
aCl, 1-propanol
bCl, NMS
2
1
2
1
a0
bF CO, 1-propanol aF0 CO, NMS
bF CO, NMS
3
3
F3CO, 1-propanol
3
2
1
2
1
B
@
C
A
a0NO , 1-propanol
bNO , 1-propanol aN0 O , NMS
bNO , NMS
2
2
2
2
2
2
0
1
cMeO
cMe
cH
0
1
B
B
C
C
m1-propanol
B
B
B
B
B
C
C
C
C
C
B
B
C
C
2
m1-propanol
B
B
@
C
C
A
ꢁ
¼
ð11Þ
mNMS
mNMS
cCl
B
B
@
C
C
A
2
c
F3CO
c
NO2
Equation 11 cannot be solved using singular value decomposi-
tion. Solving eq 11 numerically using the LevenbergꢀMarquardt
method53 results in the solution referred to as solution 2
(Table 4). As for solution 1, the molalities of NMS and 1-propanol
in solution 2 are nonzero and (statistically) significant, indicating
that both components are essential in the micelle-mimicking
solution. The individual rate-retarding effects of NMS and
1-propanol in solution 2 are calculated using the molalities of
NMS and 1-propanol in solution 2 and the first and the second
derivative for each of the two mimics. Table 8 lists these indivi-
dual contributions.
Figure 3. Rate-retarding effects of micelles (b) exerted on the hydro-
lysis of 1aꢀf reproduced by the calculations underpinning our (a, Δ)
first- and (b, r) second-order models and experimentally by the kinetic
effects of (a, O) solution 1 and (b, )) solution 2 on the hydrolysis of
1aꢀf. The rate-retarding effects are plotted as a function of the Hammett
substituent constants (σp).
Table 8 again shows that the largest part of the overall rate-
retarding micellar effect is mimicked by NMS. Nevertheless,
Table 6. Kinetic Effects Exerted by Solution 1 and Solution 2 Relative to Those Exerted by SDS Micelles at 25 °C
kX,solution 1 (10ꢀ4 sꢀ1
)
kX,solution 2 (10ꢀ4 sꢀ1
)
ln(kX,solution 1/kX,mic
)
ln(kX,solution 2/kX,mic)
1a
1b
1c
1d
1e
1f
0.356 ( 0.001
0.884 ( 0.006
2.155 ( 0.001
5.14 ( 0.01
7.17 ( 0.01
50.8 ( 0.5
0.203 ( 0.003
0.531 ( 0.01
1.255 ( 0.004
2.98 ( 0.01
4.20 ( 0.01
28 ( 4
0.89 ( 0.01
0.81 ( 0.05
0.65 ( 0.05
1.01 ( 0.01
1.01 ( 0.01
0.65 ( 0.08
0.37 ( 0.02
0.31 ( 0.05
0.10 ( 0.05
0.47 ( 0.01
0.48 ( 0.01
0.06 ( 0.16
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The Journal of Physical Chemistry B
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Table 7. Sensitivities of the Rate Constants for Hydrolysis of
Probes 1aꢀf to 1-Propanol and NMS in Accordance with the
Mathematical Description Leading to Solution 2
Table 8. Rate-Retarding Effects of 1-Propanol and NMS in
Solution 2 on the Hydrolysis of Probes 1aꢀf at 25 °C
a0X,1‑propanolm1‑propanol
+
a0X,NMSmNMS
+
a
a
b
b
a0X,1‑propanol
a0X,NMS
1/2bX,1‑propanol
1/2bX,NMS
2 a,b
2 b,c
probe
1/2bX,1‑propanol(m1‑propanol
)
1/2bX,NMS(mNMS
)
1a ꢀ0.212 ( 0.008 ꢀ0.58 ( 0.01
ꢀ0.007 ( 0.002 0.016 ( 0.003
1a
1b
1c
1d
1e
1f
ꢀ0.64 ( 0.06
ꢀ0.63 ( 0.07
ꢀ0.55 ( 0.06
ꢀ0.42 ( 0.04
ꢀ0.36 ( 0.04
ꢀ0.17 ( 0.02
ꢀ2.69 ( 0.17
ꢀ2.65 ( 0.09
ꢀ2.63 ( 0.13
ꢀ2.52 ( 0.12
ꢀ2.45 ( 0.16
ꢀ2.42 ( 0.26
1b ꢀ0.213 ( 0.01 ꢀ0.555 ( 0.006 ꢀ0.005 ( 0.002 0.013 ( 0.001
1c ꢀ0.187 ( 0.008 ꢀ0.571 ( 0.009 ꢀ0.004 ( 0.002 0.017 ( 0.002
1d ꢀ0.149 ( 0.005 ꢀ0.549 ( 0.008 ꢀ0.0008 ( 0.001 0.016 ( 0.002
1e ꢀ0.124 ( 0.006 ꢀ0.565 ( 0.01 ꢀ0.002 ( 0.001 0.022 ( 0.003
1f ꢀ0.056 ( 0.004 ꢀ0.555 ( 0.02 ꢀ0.001 ( 0.001 0.021 ( 0.005
a a0X,1‑propanol and a0X,NMS are the first-order derivatives of the logarithms
of the rate constants relative to those in water with respect to the
molalities of 1-propanol and NMS, respectively (eqs 10 and 11).
b bX,1‑propanol and bX,NMS are the second-order derivatives of the loga-
rithms of the rate constants relative to water with respect to the
molalities of 1-propanol and NMS, respectively (eqs 10 and 11).
a a0X,1‑propanol and bX,1‑propanol are the first- and second-order derivatives,
respectively, of the logarithms of the rate constants relative to water with
respect to the molality of 1-propanol (Table 7). b m1‑propanol and mNMS
are the molalities of 1-propanol and NMS, respectively, in solution 2
(Table 4). c a0X,NMS and bX,NMS are the first- and second-order deriva-
tives, respectively, of the logarithms of the rate constants relative to water
with respect to the molality of NMS (Table 7).
although the contributions to the overall rate-retarding effect
that are mimicked by 1-propanol are relatively small, they vary
rather strongly between the hydrolytic probes. This variation
in rate-retarding effects between hydrolytic probes results in
the difference in the Hammett F values between reaction in bulk
water and in the micellar pseudophase. Consequently, this
change in Hammett F value cannot be accounted for without
the inclusion of 1-propanol in the model solutions, which, in turn,
explains why the calculated molalities of 1-propanol and NMS
in the mimicking solutions are both nonzero and statistically
significant.
The hydrolysis-rate-retarding effects experienced by 1aꢀf in
solution 2 were determined experimentally and compared to the
kinetic effects exerted by micelles and to the kinetic effects of
solution 1. Figure 3a,b and Table 6 show that, for all substituted
probes 1aꢀf, the rate-retarding effects of SDS micelles are experi-
mentally reproduced considerably better by solution 2 than by
solution 1.
The fact that solution 2 reproduces the micellar data better
than solution 1 shows the merit of including both 1:1 and 2:1
interactions over extrapolating the 1:1 interactions from rela-
tively dilute aqueous solutions of the cosolutes into the more
concentrated regimes. Although solution 2 is better, it still does
not retard the hydrolysis of 1aꢀf to exactly the same extent as
SDS micelles, with rate constants overestimated by up to a factor
of 1.6. Nevertheless, this indicates that at least 83% of the change
in Δ‡Gθ has been accounted for. The remaining deviations
between the rate-retarding effects exerted by solution 2 and the
corresponding rate-retarding effects exerted by the Stern region
of SDS micelles are attributed to the lack of terms describing the
cross interactions between the two mimicking compounds in
eqs 10 and 11, that is the mixed derivatives (vide supra).
Previously,31 we derived a second-generation model solution
for CTAB micelles by taking the first model solution as a ref-
erence and determining correction terms for the molalities of 1-
propanol and tetramethylammonium bromide (TMAB) in solu-
tion1 usingsingular valuedecomposition. This methodofderiving
solution 2 required the experimental determination of the rate-
retarding effects exerted on hydrolysis of 1aꢀf in solutions con-
taining both 1-propanol and TMAB in high molalities, namely
around the molalities in solution 1. Our present improved mathe-
matical description leading to solution 2 represents a faster method
of directly deriving the second model solution because it does not
require additional experimental data.
To test the generality of the results obtained with the kinetic
probes, another type of probe, namely the solvatochromic ET(30)
probe, was used in an experiment to assess the predictive value of
our model solutions for processes unrelated to those used to
develop the model solutions themselves. The ET(30) probe is
considered one of the most useful indicators for the polarity of its
environment.68,69 In aqueous micelle solutions, the solvatochro-
mic probe binds to the micellar Stern region,38,70 and for micelles
formed by cationic surfactants such as cetyltrimetylammonium
chloride and dodecyltrimetylammonium chloride, the ET(30)
value was found to vary with surfactant concentration.40 For
anionic SDS, the position of the longest-wavelength absorbance
band of a solvatochromic merocyanine dye analogous to the
ET(30) dye has been reported41 to be virtually constant with
SDS concentration in the range of 0.016ꢀ0.204 mol dmꢀ3. To
confirm that the ET(30) value does not change with SDS concen-
tration above the cmc, we determined the ET(30) value for
solutions in the range of 0.01ꢀ0.1 mol dmꢀ3 SDS. The position
of the longest-wavelength absorbance band was found to be prac-
tically constant, namely 498.4 ( 0.5 nm, corresponding to an
ET(30) value of 57.4 kcal molꢀ1. The ET(30) value of 57.4 kcal
molꢀ1 is in good agreement with the value of 57.5 kcal molꢀ1
reported in the literature.70
The ET(30) value for solution 2 equals the ET(30) value of
57.4 kcal molꢀ1 for the SDS micellar medium, whereas the
ET(30) value for solution 1 is 57.0 kcal molꢀ1. Hence, as reported
by the solvatochromic dye, the micropolarity of solution 2 is
identical to that of the Stern region of SDS micelles. To confirm
that this is a significant result, the ET(30) values for aqueous
solutions of different concentrations of NMS and 1-propanol, in
the ranges of 2.5ꢀ6.5 mol kgꢀ1 for NMS and 2.0ꢀ3.5 mol kgꢀ1
for 1-propanol (i.e. around the molalities in solution 2) were
determined. This experiment probes the sensitivity of the solva-
tochromic probe to changes in concentration of the two mi-
micking compounds. As shown in the Supporting Information
(Figure S6.1), the ET(30) value is not very sensitive to changes in
the molality of NMS and is almost completely determined by the
molality of 1-propanol, in line with an earlier report71 showing
that highly polar solutes have only a small effect on the polarity
of aqueous solutions. These relative sensitivities are the exact
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The Journal of Physical Chemistry B
ARTICLE
opposite of the relative sensitivities of our hydrolytic probe
reactions. According to the solvatochromic probe, solution 2
fully reproduces the polarity of the micellar interfacial region,
whereas the polarity of solution 1 is close to that of SDS micelle
interface. The result obtained with the ET(30) probe confirms
the outcome of our kinetic analysis, namely solution 2 repro-
duces the interfacial region of SDS micelles better than solu-
tion 1. Because the solvatochromic probe was not used in the
construction of the model solutions, the identical ET(30) value
for solution 2 and the micellar pseudophase demonstrates that
solution 2 can be used to predict medium-controlled properties of
the Stern region of SDS micelles that were not included in our
modeling. The fact that solution 2 accurately reproduces the polarity
of the Stern region as reported by the ET(30) probe, despite the
relative sensitivities of the ET(30) probe to 1-propanol and NMS
being the exact opposite of the sensitivities of our hydrolytic probes,
confirms that both 1-propanol and NMS are required to reproduce
the properties of the micellar Stern region studied here.
In our kinetic study of the SDS micellar pseudophase, the
linear alkyl group of 1-propanol mimics the surfactant back-
folding tail in the micellar Stern region. However, the hydroxyl
in 1-propanol is not representative of the hydrocarbon tail of
the surfactant and, in fact, more closely resembles water. In that
sense, 1-propanol in solution 2 also reproduces a small fraction of
water in the SDS micellar pseudophase. In line with this fact,
product analysis using HPLC (Supporting Information, section
S7) revealed that some ester formation occurs in addition to
hydrolysis in solution 2. Further detailed product analysis at
various water/1-propanol ratios shows that, in these mixtures,
the reactivity of 1-propanol, leading to ester formation, is twice
the reactivity of water, leading to hydrolysis (Supporting Infor-
mation, section S8). Because the reactivity of the hydroxyl in
1-propanol is similar to that of water, we define the “effective
water concentration” in solution 2, [H2O]effective, as
of the hydrolytic probe and if more hydrophobic probes are
expected to bind more, or deeper, in the hydrophobic micellar
core, then an increase in Kmic (Table 1) should correspond to a
decrease in the relative rate constant kX,mic/kX,water (Table 2).
The fact that we did not find such a correlation suggests that
differential binding sites are not an important factor behind the
differences in rate-retarding effects. We therefore assume that, in
line with the above-mentioned literature reports, all of the sub-
stituted probes bind in the same zone in the Stern region.
As in the case of the deceleration of the hydrolysis of 1aꢀf by
micelles of CTAB and DTAB, the rate-retarding effects exerted
by micelles of SDS on the hydrolysis of 1aꢀf are due to the
particular features of the micellar pseudophase as a local reaction
medium in comparison with the reaction environment as offered
by bulk water. The main factors affecting the reactivity in the SDS
micellar pseudophase are (1) the lower local concentration/
activity of water, (2) the lower polarity and direct hydrophobic
interactions with the surfactant tails, (3) the high ionic strength
and direct interactions with the headgroups, and (4) the local
charge in the Stern region. We now evaluate these factors.
The concentration of water (factor 1) in the second model
solution is 35.3 mol dmꢀ3 (Table 4). This represents a lower
estimate of the water concentration in the micellar Stern region
(vide supra), and a better estimate is 37.0 mol dmꢀ3. The hy-
drolysis of 1aꢀf is second-order in water (Scheme 1). To esti-
mate the kinetic effect of the lower local concentration of water,
we express the pseudo-first-order rate constants for hydrolysis of
1aꢀf in water, kX,water, and in the micellar pseudophase, kX,mic, as
functions of the water concentrations in bulk water, [H2O]bulk
and in the micellar Stern region, [H2O]mic
,
2
kX, water ¼ k0X, water½H2Oꢂbulk
ð13Þ
2
kX, mic ¼ k0X, mic½H2Oꢂmic
ð14Þ
where k0X,water and k0X,mic are the third-order rate constants for
hydrolysis in bulk water and in the micellar Stern region, respec-
tively. Using the effective water concentration in solution 2 of
37.0 mol dmꢀ3 gives a squared ratio ([H2O]mic /[H 2O]bulk)2 of
0.44. The lower concentration of water in the micellar pseudo-
phase (factor 1) therefore accounts for only a ca. 2-fold decrease
in the pseudo-first-order rate constants for hydrolysis of 1aꢀf.
Because kX,mic is on average 18-fold lower than kX,water, the de-
creased water concentration explains only 12% of the rate-
decreasing effect of hydrolysis exerted by SDS micelles.
Possibly a better way to account for the effects related to water
reactivity is through its activity (factor 1). A high ionic strength,
as well as added alcohols, leads to a decrease in the activity of
water, but the extent of this decrease depends on the nature of the
solutes.75 Solution 2 has an ionic strength of 3.5 mol dmꢀ3 (vide
infra) and contains a high concentration of 1-propanol, suggest-
ing that the activity of water in this solution is likely lower than
that in bulk water. The individual effects exerted on the water
activity by these two factors (i.e. the ionic strength and the
concentration of 1-propanol) overlap and cannot be separated.
The decrease in the activity of water could be fully due to the
decrease in water concentration or could be caused by a combi-
nation of a decrease in the concentration of water and a decrease
in the activity coefficient of water. To determine whether the
activity coefficient of water in solution 2 differs from that in
pure water, it is necessary to know the interfacial water activity
relative to the activity of pure water. As found by Angeli et al.,76
½H2Oꢂeffective≈½H2Oꢂreal þ ½1-propanolꢂ
ð12Þ
(For a derivation and explanation of the apparent disappearance
of a factor of 2, see section S8 in the Supporting Information.)
Here, [H2O]real is the real concentration of water, and [1-pro-
panol] is the concentration of 1-propanol in solution 2. Equation
12 accounts for the (small) rate effect exerted by the reactivity of
the hydroxyl functional group in 1-propanol, which does not
represent polarity and hydrophobic effects as exerted by the hy-
drophobic tails of the surfactants (vide infra). Equation 12 gives
an effective concentrationof water in solution 2 of 37.0mol dmꢀ3
,
suggesting that the water concentration in the interfacial region
of SDS micelles is 37.0 mol dmꢀ3
Factors Determining the Deceleration of the Hydrolysis of
1aꢀf by SDS Micelles. The relative micellar rate constant kX,mic
.
/
kX,water is not constant for all probes 1aꢀf and lies in the range of
0.03ꢀ0.09 (Table 2). A potential source for the differences in the
rate-retarding effects exerted by SDS micelles on the different
probes could, in principle, be solubilization in different locations
in the SDS micellar pseudophase for different hydrolytic probes.
However, we have previously31 shown that all of the kinetic
probes bind in the micellar Stern region, in line with findings by
other authors for a wide range of molecules, such as benzophe-
none; butyronitrile; primary alcohols; solvatochromic indicators
such as p-nitroanisol, p-nitroaniline, and the ET(30) probe;34,35,72
and even benzene up to a critical concentration.73,74 In addition,
if one assumes that Kmic primarily represents the hydrophobicity
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using the pseudophase formalism for the experimentally ob-
served equilibrium of hydration of p-alkyloxy-α-α-α-trifluoroa-
cetophenone, the water activity in the interfacial region of SDS
micelles relative to the activity of pure water equals 0.6. The value
of 0.6 coincides with the value of the effective concentration of
water in solution 2 relative to the concentration of water in pure
water. On the basis of the results of Angeli et al.,76 the activity
coefficient of water in solution 2 equals the activity coefficient of
bulk water. Therefore, the activity coefficient of water does not
appear to contribute to the lower activity of water in the micellar
pseudophase. This conclusion is in line with the observation by
Rispens et al.77 that “variations in the water reactivity ... hardly
play a role in the observed medium effects [on the hydrolysis of
an activated ester].” Similarly, Bunton et al.78 and De Albrizzio
and Cordes79 found the water reactivity in the Stern region of
SDS to be very similar to the water reactivity in bulk water. In
summary, although the local concentration of water in the mi-
cellar Stern region of SDS is lower than that in bulk water and the
activity coefficient of water might be lower than unity, the
resulting overall rate-retarding effect on the hydrolysis of 1aꢀf
is unlikely to exceed a factor of 2.
With respect to the lower polarity of the micellar Stern region
(factor 2), we note that polarity probes show that typical model
solutions for the micellar pseudophase (i.e., binary mixtures such
as n-alcohol/water, 1,4-dioxane/water, acetonitrile/water) are
less polar than bulk water.40,70,80 The ET(30) value for pure water
is 63.1 kcal/mol,68 whereas for solution 2, the ET(30) value is
57.4 kcal/mol; that is, the ET(30) probe reports a decrease in the
polarity on going from bulk water to our second model solution.
The ET(30) value is more sensitive to the change in concentra-
tion of 1-propanol than to the change in concentration of NMS
(vide supra). In addition the ET(30) value for 4.2 mol dmꢀ3
NMS, which is above the NMS concentration in solution 2,
of 62.6 kcal/mol32 is close to the ET(30) value of pure water
(63.1 kcal/mol).68 Because NMS does not contribute signifi-
cantly to the decreased polarity of solution 2 compared to bulk
water, the kinetic effects of the lower polarity of solution 2 on
1aꢀf hydrolysis are dominated by the effect of 1.8 mol dmꢀ3
1-propanol. The lower polarity of the micellar pseudophase com-
pared to the polarity of pure water contributes to the decrease in
the rate of hydrolysis reactions in the presence of micelles.45,81
The usual interpretation of this observation involves the higher
polarity of the transition states (Scheme 1) compared to the
polarity of the substituted substrates: a less polar medium is less
favorable for hydrolysis. Therefore, the lower polarity of the
Stern region of SDS micelles is responsible for part of the rate-
retarding effects on the hydrolysis of 1aꢀf. In addition to its
effect on the local polarity, 1-propanol also engages in direct hy-
drophobic interactions with the probes used here, as well as with
related hydrolytic probes, retarding hydrolysis.66,82ꢀ85 Because
added 1-propanol contributes to rate retardation through hydro-
phobic interactions with the hydrolytic probe and through the
decrease in local polarity, these two effects cannot be separated.
Nevertheless, it is of interest (vide infra) that the rate-retarding
effect of 1-propanol varies between different hydrolytic probes,
indicating that different reactions display different sensitivities to
hydrophobic interactions, giving rise to changes in the Hammett
F value for hydrolysis of 1aꢀf. The effects of interactions with the
hydrophobic surfactant tails of SDS, be they through direct hy-
drophobic interactions or through decreased local polarity, thus
depend on the sensitivity of the reaction kinetics to such inter-
actions, but in general, they can be modeled through 1.8 mol dmꢀ3
1-propanol. It should be noted that, although headgroup effects
dominate the rate-retarding effect exerted by SDS micelles (vide
infra), the increased Hammett F value for hydrolysis of 1aꢀf
in SDS micelles is the result of hydrophobic interactions and
decreased local polarity, with negligible contribution from head-
group effects.
In addition to the local polarity and hydrophobic interactions,
another factor to consider is the high ionic strength and direct
interactions with the ionic groups in the Stern region of ionic
micelles (factor 3).45,86 In our model, the effects of ionic strength
and direct ionic interactions are modeled by NMS. As argued
above, the rate-retarding effects exerted in solution 2 by NMS on
hydrolysis of probes 1aꢀf cannot be attributed to a contribution
of NMS to the decrease in polarity. Table 8 shows that the
deceleration due to NMS in solution 2 represents at least 81% of
the total rate-retarding effect exerted by solution 2 for all probes.
Differences in the stabilization of the reactant state and the
activated complex by specific interactions with NMS could also
influence the reactivity of probes 1aꢀf in hydrolysis. To under-
stand whether specific interactions with NMS contribute to the
retardation of the rates of hydrolysis of 1aꢀf, we compared the
kinetic effects exerted by NMS with those exerted by other salts.
If the kinetic effects do not depend on the nature of the salt, then
the decelerating effects (Figure 2b) exerted by NMS on hydro-
lysis of 1aꢀf, as quantified by the slopes of ln(kX,NMS/kX,water
)
versus NMS molality, should be the same as the rate-retarding
effects exerted by tetrametylammonium bromide (TMAB) on
the hydrolysis of 1aꢀf or the rate-retarding effect of NaCl on 1c,
for example. However, the slopes describing the sensitivities of
the rates of hydrolysis to NMS (aX,NMS in Table 3) are higher by
a factor of about 2 compared to the slopes representing the
sensitivities of the hydrolysis rates to TMAB (Table 4 in ref 31).
Therefore the rates of hydrolysis of 1aꢀf are more retarded by
NMS than by TMAB. Similarly, the rate-retarding effect of NaCl
on the hydrolysis of 1c as quantified through the pairwise
interaction parameter GP(S) by Noordman et al.87 corresponds
to a slope of ln(kX,NaCl/kX,water) versus NaCl molality of ꢀ0.25.
We therefore conclude that the large rate-retarding effects
exerted by NMS in solution 2 on the hydrolysis of 1aꢀf result
from the combination of the kinetic effects due to the high ionic
strength with effects caused by specific interactions of 1aꢀf with
NMS. For the micellar solutions, this indicates that the combined
effects of high local ionic strength and direct interactions be-
tween the sulfate headgroups of SDS and hydrolytic probes 1aꢀf
dominate the observed rate-retarding effects and that the effects
of ionic strength and specific ionic interactions can be modeled
through 3.5 mol dmꢀ3 NMS. Nevertheless, although the effects
of ionic strength and specific ionic interactions might dominate
the observed rate-retarding effects, 1-propanol is still required
in an effective micelle-mimicking solution to account for local
polarity and hydrophobic interaction effects (vide supra).
The local negative charge in the Stern region of anionic SDS
micelles (factor 4) has a destabilizing effect on the partial nega-
tive charge developing in the activated complex (Scheme 1).
The local positive charge in the interfacial region of cationic
micelles of CTAB and DTAB has the opposite effect, stabilizing
the activated complex.31 The combined effect of the electro-
static non-neutrality in the micellar interfacial region on the
transition state13,61,62 and specific interactions with surfactant
headgroups explains why the micellar rate constants for SDS
micelles (Table 1) are smaller by a factor of ca. 2.5 than
those for CTAB and DTAB micelles.31 The effect of the
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non-neutrality of the micellar Stern region and the effect of
specific interactions with the surfactant headgroups are not ne-
cessary orthogonal. We therefore make no attempt to separate
the individual contributions. We note, however, that our model
solution generally reproduces micellar kinetics well, despite the
fact that it can obviously not be overall negatively charged. This
suggests that a significant part of the rate-retarding effect of the
electrostatic non-neutrality of the micellar Stern region is repro-
duced through direct interactions between the hydrolytic probes
and negatively charged methyl sulfate. The implication of this
conclusion for the micellar Stern region is that the local charge as
a medium effect per se on the hydrolysis of 1aꢀf might be of less
importance than more specific interactions with the negatively
charged headgroups themselves.
Table 9. Molalities and Molar Concentrationsa of 1-Propanol
and Saltb in Solution 1 for SDS, DTAB, and CTAB Micelles
mol kgꢀ1
saltb
mol dmꢀ3
saltb
1-propanol
1-propanol
water
SDS
3.4 ( 0.2
4.5 ( 0.1 2.2 ( 0.1
1.5 ( 0.6 5.1 ( 0.6
4.9 ( 0.3 2.6 ( 0.3
2.88 ( 0.05 35.2 ( 0.3
DTAB 9.3 ( 0.9
CTAB 5.0 ( 0.5
0.8 ( 0.3
2.6 ( 0.2
30 ( 1.8
29 ( 0.8
a Molar concentrations were calculated using the experimentally deter-
mined densities at 25 °C of the first model solutions for SDS, DTAB,
and CTAB micelles (1.15, 0.97, and 1.08 g cmꢀ3, respectively). b NMS
for SDS and tetramethylammonium bromide (TMAB) for DTAB
and CTAB.
Comparison of the Description of the Stern Region of SDS
Micelles by Model Solutions 1 and 2 with Previous Repre-
sentations. The concentrations of NMS in the model solutions
(2.9 mol dmꢀ3 in solution 1 and 3.5 mol dmꢀ3 in solution 2)
provide estimates of the concentration of surfactant headgroups
in the Stern region of SDS micelles. Both estimates are between
our previously estimated limits of 2.5ꢀ5.4 mol dmꢀ3, calculated
by considering the Stern region of SDS micelles as a layer
between two concentric spheres.6
to interactions with surfactant headgroups and hydrocarbon tails
that are reflected in the relative contributions of the two terms
aX,NMSmNMS and aX,1‑propanolm1‑propanol. For example, the rela-
tive effects of the two mimics are different in the case of the
ET(30) probe, which is more sensitive to 1-propanol than to
NMS. The effects exerted by 1-propanol and NMS on the value
of the wavelength at the maximum of absorbance in the visible
range (λmax) of the ET(30) probe are estimated as am1‑propanol
and bmNMS (section S2 in Supporting Information), which are
(27.1( 3.2) nm and (ꢀ1.1 ( 1.6) nm, respectively. These values
clearly show that the effects of the micellar Stern region on the
ET(30) solvatochromic probe are dominated by polarity and
hydrophobic effects as mimicked by 1-propanol. The fact that the
hydrolysis of phenyl chloroformate is much less retarded by 4.3
mol dmꢀ3 NMS than by SDS micelles represents another
example.45 As for the ET(30) probe, phenyl chloroformate
(PhOCOCl) hydrolysis is probably more sensitive to interac-
tions with the surfactant tails than to interactions with SDS
headgroups; that is, in terms of eq 8, aPhOCOCl,1‑propanolm1‑propanol
is larger than aPhOCOCl,NMSmNMS. These two examples clearly
illustrate the importance of modeling both hydrophobic and
ionic interactions when developing universal model solutions for
the micellar pseudophase.
Comparison of SDS Micelles with DTAB and CTAB Micelles
in Terms of the Model Solution for the Stern Region.
Analogous to our previous studies of cationic micelles of DTAB
and CTAB,31 we reproduce the Stern region of SDS micelles by a
model solution containing a mimic of the headgroup (NMS) and
a mimic of the backfolding surfactant tail (1-propanol). Applying
our previous mathematical description, based on first-order deri-
vatives, that led to the model solutions for micelles of DTAB and
CTAB, we found the first model solution for SDS micelles.
Comparison of the concentrations of salt and 1-propanol in
the first model solutions for SDS, DTAB, and CTAB micelles
(Table 9) shows that the local concentration of the backfolding
surfactant tails in the case of SDS micelles more closely resembles
the corresponding concentration for CTAB micelles than the
respective concentration for DTAB micelles. In addition, the
micellar binding constants (Km) for 1aꢀf binding to SDS are
closer to the corresponding Km values for CTAB, but ca. 3 times
larger than the micellar binding constants for DTAB.31 Our results
therefore suggest that the interfacial region of SDS micelles
is structurally more similar to the Stern region of CTAB micelles
than to the Stern region of DTAB micelles.
According to solution 2, the effective concentration of water in
the Stern region of SDS micelles is 37.0 mol dmꢀ3. This value is
in agreement with the interfacial water concentration at the
average solubilization site of merocyanine dye BuQMBr2 in SDS
micelles of 38.9 mol dmꢀ3, as determined by Martins et al.41 by
comparison of the ET(BuQMBr2) values for SDS micelles with a
plot of ET(BuQMBr2) versus concentration of water in solutions
of 1-propanol. The ratio between the NMS and water concen-
trations of 10.6 is in reasonable agreement with a hydration
number per surfactant of 8ꢀ9, as determined by Bales et al.88 for
SDS micelles with an aggregation number of approximately 63.
An important merit of the present model solutions over the
simple salt solutions and aqueous alcohol solutions used pre-
viously for mimicking the Stern region of SDS micelles32,45 is that
solution 1 and solution 2 have the ability to reproduce both ionic
and hydrophobic interactions experienced by a probe bound in
the micellar interfacial region. The importance of using both
headgroup and tail mimics is illustrated by the observation that
the significant rate retardations can be accounted for only on the
basis of interactions with the surfactant headgroups, as modeled by
NMS, whereas the change in Hammett F value can be accounted
for only through the lower local polarity and hydrophobic inter-
actions with the surfactant tails, as mimicked by 1-propanol.
Similarly, the inclusion of 1-propanol in the model solution
allowed us to correctly predict the micellar ET(30) value, which
we were unable to do using a concentrated salt solution alone.32
In both model solutions, the molality of NMS is higher than
the molality of 1-propanol (Table 4). Additionally, for all probes
1aꢀf, the sensitivity to NMS is larger than the sensitivity to
1-propanol (aX,NMS is at least 2 times aX,1‑propanol; Table 3).
Consequently, the rate-retarding effects exerted on the hy-
drolysis of 1aꢀf by SDS headgroups as mimicked by NMS
(aX,NMSmNMS) are larger than the effects exerted by the surfac-
tant tails as mimicked by 1-propanol (aX,1‑propanolm1‑propanol
)
(Table 5). The sum of the effects exerted by micellar headgroups
and surfactant tails dictates the magnitude of the difference be-
tween the stabilization of the reactant state by binding to micelles
and the stabilization of the transition state by binding to micelles
(eq 8). However, different probes can have different sensitivities
The molalities of 1-propanol and TMAB in solution 2 for
CTAB micelles are 7.7 and 5.7 mol kgꢀ1, respectively.31 The den-
sity of this solution was determined to be 1.04 g dmꢀ3, allowing
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The Journal of Physical Chemistry B
ARTICLE
the calculation of the molar concentrations of 1-propanol and
’ ASSOCIATED CONTENT
TMAB in solution 2 for CTAB micelles as 3.4 and 2.5 mol dmꢀ3
,
S
Supporting Information. Kinetic effects of SDS micelles
b
respectively. Therefore, the second-order solutions for SDS
micelles (Table 4) and CTAB micelles are less similar to each
other than are the first-order solutions for SDS micelles and
CTAB micelles (Table 9). Comparison of the concentrations of
1-propanol in the model solutions for SDS and CTAB suggests
that backfolding surfactant tails have a greater effect on the local
reaction medium in CTAB than in SDS. The opposite is the case
for the effect of the ionic headgroups.
on hydrolysis of 1d at different values of bulk pH; rate constants
of hydrolysis for 1aꢀf in aqueous solutions of SDS; Hammett
plots for hydrolysis of 1aꢀf in water and in the Stern regions of
SDS, CTAB, and DTAB micelles; rate constants of hydrolysis for
1aꢀf in aqueous solutions of sodium methylsulfate and 1-pro-
panol; sensitivity of the solvatochomic ET(30) probe to molality
of added 1-propanol and NMS; HPLC analyses of reaction
products; and rate constants of hydrolysis and esterification
and calculation of the effective water concentration. This material
is available free of charge via the Internet at http://pubs.acs.org.
’ CONCLUSIONS
The Stern region of SDS micelles has been modeled by con-
centrated solutions of surfactant headgroup mimic NMS and sur-
factant tail mimic 1-propanol. A first model solution (solution 1)
was derived by singular value decomposition of extrapolated linear
fits of experimental rate-retarding effects of NMS and 1-propanol
on a series of hydrolytic probes. Solution 1 reproduces approxi-
mately one-half of the experimentally observed micellar rate
retardations for the hydrolytic probes. We attribute this discre-
pancy to the fact that nonlinear contributions to the rate-
retarding effects of NMS and 1-propanol cannot be neglected
at high concentrations. We therefore improved our mathematical
approach to the deconvolution of micellar effects by incorporat-
ing quadraticterms inthe equationsreproducingtherate-retarding
effects of the mimicking compounds and incorporating the terms
in our matrix equation. Numerically solving the system of non-
linear equations thus obtained, we determined a second model
solution (solution 2) that reproduces the rate-retarding effects of
SDS micelles to within a factor of 1.6. Solution 2 also correctly
predicts the micropolarity of SDS micelles as reported by the
solvatochromic ET(30) probe. The second model solution can
therefore be used to estimate rate constants for reactions occur-
ring at the surface of SDS micelles and similar medium-sensitive
properties, when a direct determination of these is not possible.
In addition to predicting medium effects on reactions, our
approach also allows the dissection of the overall medium effect
into contributions originating from surfactant headgroups and
surfactant tails, that is from ionic and hydrophobic interactions.
For the hydrolysis of 1aꢀf, we showed that the water activity and
the local charge are not important contributors to the rate-
retarding effects. The dominant rate-retarding effects result from
the combination of high ionic strength and direct interactions
with the surfactant headgroups as modeled by NMS. The combi-
nation of hydrophobic interactions and the decreased local
polarity as modeled by 1-propanol also make a contribution to
rate retardation, but the importance of these is more obvious in
that they are required to explain the increased Hammett F in the
micellar pseudophase, as well as the micellar ET(30) value. The
combination of these observations, that is significantly decreased
rate constants for hydrolysis and increased Hammett F value, can
only be reproduced using our model solution containing both
headgroup and tail mimics. We anticipate that the ability to sepa-
rate the different contributions allows the design of alternative
surfactants with tailored properties for a variety of reactions.
Our current results for anionic SDS micelles, in combination
with our previous results for cationic micelles of DTAB and
CTAB, suggest that our approach is generally valid for micelle-
forming surfactants and probably for vesicle-forming surfactants
as well.
’ AUTHOR INFORMATION
Corresponding Author
*Tel.: +44 (0)29 208 70301. Fax: +44 (0)29 208 74030. E-mail:
buurma@cardiff.ac.uk.
’ ACKNOWLEDGMENT
We thank EPSRC for funding (EP/D001641/1) and the POC
Centre research groups at Cardiff University for useful discussions.
’ REFERENCES
(1) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc.,
Faraday Trans. 2 1976, 72, 1525–1568.
(2) Gruen, D. W. R. Prog. Colloid Polym. Sci. 1985, 70, 6–16.
(3) Clemett, C. J. J. Chem. Soc. A: Inorg., Phys., Theor. Chem. 1970,
2251–2254.
(4) Bocker, J.; Brickmann, J.; Bopp, P. J. Phys. Chem. 1994, 98,
712–717.
(5) Menger, F. M.; Portnoy, C. E. J. Am. Chem. Soc. 1967, 89,
4698–4703.
(6) Buurma, N. J. Adv. Phys. Org. Chem. 2009, 43, 1–37.
(7) Dwars, T.; Paetzold, E.; Oehme, G. Angew. Chem., Int. Ed. 2005,
44, 7174–7199.
(8) Tas-cioglu, S. Tetrahedron 1996, 52, 11113–11152.
(9) Li, C. J.; Chen, L. Chem. Soc. Rev. 2006, 35, 68–82.
(10) Iglesias, E. J. Phys. Chem. B 2001, 105, 10287–10294.
(11) Khan, M. N. Micellar Catalysis; CRC Press: Boca Raton, FL,
2007.
(12) Bunton, C. A. Adv. Colloid Interface Sci. 2006, 123ꢀ126,
333–343.
(13) Campos-Rey, P.; Cabaleiro-Lago, C.; Hervꢀes, P. J. Phys. Chem. B
2010, 114, 14004–14011.
(14) Onel, L.; Buurma, N. J. Annu. Rep. Prog. Chem. B: Org. Chem.
2009, 105, 363–379.
(15) Onel, L.; Buurma, N. J. Annu. Rep. Prog. Chem. B: Org. Chem.
2010, 106, 344–375.
(16) Buurma, N. J. Annu. Rep. Prog. Chem. B: Org. Chem. 2011,
107, 328–348.
(17) Marin, M. A. B.; Nome, F.; Zanette, D.; Zucco, C.; Romsted,
L. S. J. Phys. Chem. 1995, 99, 14572.
(18) Krasovskiy, A.; Duplais, C.; Lipshutz, B. H. J. Am. Chem. Soc.
2009, 131, 15592–15593.
(19) Lipshutz, B. H.; Chung, D. W.; Rich, B. Org. Lett. 2008, 10,
3793–3796.
(20) Lipshutz, B. H.; Ghorai, S.; Aguinaldo, G. T. Adv. Synth. Catal.
2008, 350, 953–956.
(21) Lipshutz, B. H.; Petersen, T. B.; Abela, A. R. Org. Lett. 2008,
10, 1333–1336.
(22) Lipshutz, B. H.; Taft, B. R. Org. Lett. 2008, 10, 1329–1332.
13210
dx.doi.org/10.1021/jp208171w |J. Phys. Chem. B 2011, 115, 13199–13211

The Journal of Physical Chemistry B
ARTICLE
(23) Nishikata, T.; Abela, A. R.; Lipshutz, B. H. Angew. Chem., Int. Ed.
2010, 49, 781–784.
(59) Exner, O. Correlation Analysis in Chemistry; Plenum Press:
London, 1978.
(24) Nishikata, T.; Lipshutz, B. H. Org. Lett. 2010, 12, 1972–1975.
(25) Mubofu, E. B.; Engberts, J. B. F. N. J. Phys. Org. Chem. 2007, 20,
764–770.
(26) Rispens, T.; Engberts, J. B. F. N. J. Org. Chem. 2002, 67, 7369–
7377.
(60) Fadnavis, N.; Engberts, J. B. F. N. J. Org. Chem. 1982, 47,
152–154.
(61) Bunton, C. A.; Gillitt, N. D.; Mhala, M. M.; Moffatt, J. R.;
Yatsimirsky, A. K. Langmuir 2000, 16, 8595–8603.
(62) Bunton, C. A. J. Phys. Org. Chem. 2005, 18, 115–120.
(63) Hammett, L. P. Chem. Rev. 1935, 17, 125–136.
(64) Hammett, L. P. J. Am. Chem. Soc. 1937, 59, 96–103.
(65) Otto, S.; Engberts, J. B. F. N. Org. Biomol. Chem. 2003, 1,
2809–2820.
(66) Engberts, J. B. F. N.; Blandamer, M. J. J. Phys. Org. Chem. 1998,
11, 841–846.
(67) Noordman, W. H.; Blokzijl, W.; Engberts, J. B. F. N.; Blandamer,
M. J. J. Org. Chem. 1993, 58, 7111–7114.
(27) Rispens, T.; Engberts, J. B. F. N. J. Org. Chem. 2003, 68, 8520–
8528.
(28) The hydrolysis reactions used in the work presented here are
not strictly uncatalyzed because one of the water molecules involved in
the rate-determining step acts as a general-base catalyst. Here, however,
catalysis by water provides an additional handle on the water concentra-
tion in the micellar Stern region
(29) Cordes, E. H.; Dunlap, R. B. Acc. Chem. Res. 1969, 2, 329–337.
(30) Bunton, C. A. Catal. Rev.ꢀSci. Eng. 1979, 20, 1–56.
(31) Buurma, N. J.; Serena, P.; Blandamer, M. J.; Engberts, J. B. F. N.
J. Org. Chem. 2004, 69, 3899–3906.
(68) Reichardt, C. Chem. Rev. 1994, 94, 2319–2358.
(69) Silva, P. L.; Trassi, M. A. S.; Martins, C. T.; Seoud, O. A. E.
J. Phys. Chem. B 2009, 113, 9512–9519.
(32) Buurma, N. J.; Herranz, A. M.; Engberts, J. B. F. N. J. Chem. Soc.,
Perkin Trans. 2 1999, 113–119.
(70) Zacharlasse, K. A.; Van Phuc, N.; Kozankiewicz, B. J. Phys.
Chem. 1981, 85, 2676–2683.
(33) Menger, F. M. Acc. Chem. Res. 1979, 12, 111–117.
(34) Vitha, M. F.; Dallas, A. J.; Carr, P. W. J. Phys. Chem. 1996, 100,
5050–5062.
(35) Vitha, M. F.; Weckwerth, J. D.; Odland, K.; Dema, V.; Carr,
P. W. J. Phys. Chem. 1996, 100, 18823–18828.
(36) Mukerjee, P. J. Phys. Chem. 1962, 66, 943–945.
(37) Bunton, C. A.; Nome, F.; Quina, F. H.; Romsted, L. S. Acc.
Chem. Res. 1991, 24.
(71) Asaad, N.; Otter, M. J. D.; Engberts, J. B. F. N. Org. Biomol.
Chem. 2004, 2, 1404–1412.
(72) Menger, F. M. Acc. Chem. Res. 1979, 12, 111–117.
(73) Hawrylak, B. E.; Marangoni, D. G. Can. J. Chem. 1999, 77,
1241–1244.
(74) Fendler, J. H.; Patterson, L. K. J. Phys. Chem. 1971, 75, 3907.
(75) Blandamer, M. J.; Engberts, J. B. F. N.; Gleeson, P. T.; Reis,
J. C. R. Chem. Soc. Rev. 2005, 34, 440–458.
(38) Grieser, F.; Drummond, C.J. J. Phys. Chem. 1988, 92, 5580–5593.
(39) Jose, B. J.; Bales, B. L.; Peric, M. J. Phys. Chem. B 2009, 113,
13257–13262.
(40) Novaki, L. P.; El Seoud, O. A. Phys. Chem. Chem. Phys. 1999, 1,
1957–1964.
(76) Angeli, A. D.; Cipiciani, A.; Germani, R.; Savelli, G.; Cerichelli,
G.; Bunton, C. A. J. Colloid Interface Sci. 1988, 121, 42–48.
(77) Rispens, T.; Cabaleiro-Lago, C.; Engberts, J. B. F. N. Org.
Biomol. Chem. 2005, 3, 597–602.
(78) Bunton, C. A.; Huang, S. K. J. Org. Chem. 1972, 37, 1790–&.
(79) De Albrizzio, J. P.; Cordes, E. H. J. Colloid Interface Sci. 1979,
68, 292–294.
(41) Martins, C. T.; Lima, M. S.; El Seoud, O. A. J. Phys. Org. Chem.
2005, 18, 1072–1085.
(42) Soldi, V.; Keiper, J.; Romsted, L. S.; Cuccovia, I. M.; Chaimovich,
H. Langmuir 2000, 16, 59–71.
(80) Tada, E. B.; Novaki, L. P.; El Seoud, O. A. Langmuir 2001, 17,
652–658.
(43) Romsted, L. S. Langmuir 2007, 23, 414–424.
(44) Cuccovia, I. M.; Agostinho-Neto, A.; Wendel, C. M. A.;
Chaimovich, H.; Romsted, L. S. Langmuir 1997, 13, 5032–5034.
(45) Mu~noz, M.; Rodríguez, A.; Del Mar Graciani, M.; Moyꢀa, M. L.
Int. J. Chem. Kinet. 2002, 34, 445–451.
(46) Buurma,N. J., Ph.D. Thesis, Universityof Groningen, Groningen,
The Netherlands, 2003.
(47) Fife, T. H.; Jao, L. K. J. Am. Chem. Soc. 1969, 91, 4217–4220.
(48) Karzijn, W.; Engberts, J. B. F. N. Tetrahedron Lett. 1978, 19,
1787–1790.
(81) Possidonio, S.; Siviero, F.; El Seoud, O. A. J. Phys. Org. Chem.
1999, 12, 325–332.
(82) Buurma, N. J.; Pastorello, L.; Blandamer, M. J.; Engberts, J. B. F.
N. J. Am. Chem. Soc. 2001, 123, 11848–11853.
(83) Benak, H.; Engberts, J. B. F. N.; Blandamer, M. J. J. Chem. Soc.,
Perkin Trans. 2 1992, 2035–2038.
(84) Blandamer, M. J.; Blundell, N. J.; Burgess, J.; Cowles, H. J.;
Engberts, J. B. F. N.; Horn, I. M.; Warrick, P., Jr. J. Am. Chem. Soc. 1990,
112, 6854–6858.
(85) Blokzijl, W.; Blandamer, M. J.; Engberts, J. B. F. N. J. Org. Chem.
1991, 56, 1832–1837.
(49) Engbersen, J. F. J.; Engberts, J. B. F. N. J. Am. Chem. Soc. 1975,
97, 1563–1568.
(86) El Seoud, O. A.; Ruasse, M. F.; Possidonio, S. J. Phys. Org. Chem.
2001, 14, 526–532.
(87) Noordman, W. H.; Blokzijl, W.; Engberts, J. B. F. N.; Blandamer,
M. J. J. Chem. Soc., Perkin Trans. 2 1995, 1411–1414.
(88) Bales, B. L.; Messina, L.; Vidal, A.; Peric, M.; Nascimento, O. R.
J. Phys. Chem. B 1998, 102, 10347–10358.
(50) Mooij, H. J.; Engberts, J. B. F. N.; Charton, M. Recl. Trav. Chim.
Pays-Bas 1988, 107, 185–189.
(51) Bevington, P. R.; Robinson, K. D. Data Reduction and Error
Analysis for the Physical Sciences, 3rd ed.; McGraw-Hill: New York, 2003.
(52) Atkinson, K. E. An Introduction to Numerical Analysis, 2nd ed.;
Wiley: New York, 1988.
(53) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.: Vetterling, W. T
Numerical Recipes in Pascal; Cambridge University Press: Cambridge,
U.K., 1990.
(54) Fernandez, M. A. S.; Fromherz, P. J. Phys. Chem. 1977, 81,
1755–1761.
(55) Wang, G.; Olofsson, G. J. Phys. Chem. 1995, 99, 5588–5596.
(56) Thevenot, C.; Grassl, B.; Bastiat, G.; Binana, W. Colloids Surf. A:
Physicochem. Eng. Aspects 2005, 252, 105–111.
(57) Fuguet, E.; Rꢁafols, C.; Rosꢀes, M.; Bosch, E. Anal. Chim. Acta
2005, 548, 95–100.
(58) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physico-Chemical
Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier:
Amsterdam, 1993.
13211
dx.doi.org/10.1021/jp208171w |J. Phys. Chem. B 2011, 115, 13199–13211