Origin of autocatalysis in the biphasic alkaline hydrolysis of C-4 to C-8 ethyl alkanoates

Article abstract of DOI:10.1021/jp982765n

The alkaline hydrolysis of C-4 to C-8 (butanoate to octanoate) ethyl esters shows autocatalytic kinetics when performed under two-phase conditions without any mixing solvent. Alkanoate anions and ethanol are the products of the reaction. A dynamic model is proposed that describes quantitatively this kinetic behavior. The model includes the main processes occurring in the biphasic medium and the corresponding thermodynamic calculations of the average size and stoichiometry of the molecular aggregates. Modeling indicates that salting-in and solvent effects caused by the alkanoate anions and ethanol determine the autocatalytic kinetics in the hydrolysis of C-4 ethyl ester where no aggregation occurs. In the C-5 to C-8 experiments, ester-containing micelles (ECM) are mainly formed by cooperative aggregation of alkanoate anions with ester molecules. ECM is formed only after a threshold concentration of the alkanoate anion has been reached. In a phase-transfer-like process, ECM carries ester molecules into the aqueous phase, where hydrolysis takes place yielding alkanoate anions. Additionally, in C-6 and C-7 ethyl ester hydrolysis, autocatalysis appears to be delayed, since acceleration only starts after the extent of hydrolysis has reached a certain level. A transient storage of alkanoate anions in a reservoir has been assumed to explain this delay. Collective adsorption of alkanoate anions at the oil-water interface, which occurs without any threshold concentration, could play the role of such a transient storage. The model also shows that empty micelles are without any kinetic importance, since they are formed at the end of reaction after the ester is completely depleted.

Full text of DOI:10.1021/jp982765n

10552
J. Phys. Chem. A 1998, 102, 10552-10559
Origin of Autocatalysis in the Biphasic Alkaline Hydrolysis of C-4 to C-8 Ethyl Alkanoates
†
‡
T. Buhse, D. Lavabre, R. Nagarajan, and J. C. Micheau*
Laboratoire des IMRCP, UMR au CNRS no. 5623, UniVersit e´ Paul Sabatier, 118 Route de Narbonne,
F-31062 Toulouse, France
ReceiVed: June 25, 1998; In Final Form: September 30, 1998
The alkaline hydrolysis of C-4 to C-8 (butanoate to octanoate) ethyl esters shows autocatalytic kinetics when
performed under two-phase conditions without any mixing solvent. Alkanoate anions and ethanol are the
products of the reaction. A dynamic model is proposed that describes quantitatively this kinetic behavior.
The model includes the main processes occurring in the biphasic medium and the corresponding thermodynamic
calculations of the average size and stoichiometry of the molecular aggregates. Modeling indicates that salting-
in and solvent effects caused by the alkanoate anions and ethanol determine the autocatalytic kinetics in the
hydrolysis of C-4 ethyl ester where no aggregation occurs. In the C-5 to C-8 experiments, ester-containing
micelles (ECM) are mainly formed by cooperative aggregation of alkanoate anions with ester molecules.
ECM is formed only after a threshold concentration of the alkanoate anion has been reached. In a phase-
transfer-like process, ECM carries ester molecules into the aqueous phase, where hydrolysis takes place yielding
alkanoate anions. Additionally, in C-6 and C-7 ethyl ester hydrolysis, autocatalysis appears to be delayed,
since acceleration only starts after the extent of hydrolysis has reached a certain level. A transient storage of
alkanoate anions in a reservoir has been assumed to explain this delay. Collective adsorption of alkanoate
anions at the oil-water interface, which occurs without any threshold concentration, could play the role of
such a transient storage. The model also shows that empty micelles are without any kinetic importance, since
they are formed at the end of reaction after the ester is completely depleted.
I. Introduction
aggregates, and consequently, they cannot build host aggregates
for a micelle-mediated phase transfer.
Biphasic liquid-liquid reactions are of particular interest in
Surprisingly, the experimental results reported in this publica-
tion show that the kinetic behavior of the biphasic alkaline
hydrolysis of C-4 to C-8 ethyl alkanoates is always autocatalytic
whatever the chain length, i.e., even if micellization does not
occur within the experimental concentration range.
many fields of chemistry such as industrial and chemical
1
2
3
engineering, organic synthesis, phase-transfer catalysis, mo-
4
5
lecular and chiral recognition, membrane chemistry, and
prebiotic chemistry.6 Despite this broad interest, extensive
kinetic studies are scarce.
To understand this unexpected kinetic behavior, we present
an improved kinetic model for this specific type of two-phase
reaction. The model takes into account the results of thermo-
dynamic calculations that have been performed to estimate the
average size and stoichiometry of sodium alkanoate ester
containing aggregates. The respective values were used as fixed
parameters in the kinetic model. By application of the method
of inverse treatment, a curve fitting of experimental kinetic data
was realized.
However, owing to its highly autocatalytic behavior, the
biphasic alkaline hydrolysis of ethyl octanoate (Luisi experi-
ment) became a prominent example for the kinetics of two-
7
phase reaction systems. This reaction shows a pronounced
induction period in which the medium remains biphasic and
almost at its initial composition. This induction period is then
followed by a rapid clarification, yielding a transparent single-
phase aqueous solution of ethanol and micellized sodium
octanoate as the final hydrolysis products. The highly nonlinear
kinetics of this reaction system has been attributed by the
previous authors to so-called “micellar autocatalysis”.
II. Experiments
8
In a recent study, we revisited the Luisi experiment. The
1
. Biphasic Alkaline Hydrolysis of C-4 to C-8 Ethyl
analysis of new kinetic data, obtained in a well-stirred reactor,
enabled us to propose and to confirm quantitatively a mechanism
involving a micelle-mediated phase transfer at the origin of the
autocatalytic behavior.
Alkanoates. Ethyl esters of C-4 to C-8 (i.e., ethyl butanoate to
ethyl octanoate) have been chosen on the basis of thermody-
namic and physicochemical properties that show significant
variations vs the chain length.
From our previous conclusions, one can expect that the
biphasic alkaline hydrolysis of ethyl alkanoates with short
aliphatic chain lengths would not display such an autocatalytic
behavior. In these cases and under our experimental conditions
the corresponding sodium alkanoates hardly form molecular
The kinetics of the alkaline hydrolysis of ethyl alkanoates
has been monitored by measuring the volume of the residual
oil phase vs time (see Experimental Section). Whatever the
aliphatic chain length, the kinetics at 80 °C shows an accelera-
tion effect. The maximum of the reaction rate is situated near
the clarification point where the medium becomes monophasic.
For ethyl octanoate (C-8), an induction period is observed during
which hydrolysis is very slow. However, after this induction
period, rapid hydrolysis occurs. For intermediate chain lengths
†
Present address: Department of Chemistry, Wake Forest University,
Winston-Salem, NC 27109.
‡
Permanent address: Department of Chemical Engineering, The Penn-
sylvania State University, University Park, PA 16802.
1
0.1021/jp982765n CCC: $15.00 © 1998 American Chemical Society
Published on Web 12/02/1998

Autocatalysis in Hydrolysis
J. Phys. Chem. A, Vol. 102, No. 51, 1998 10553
TABLE 1: Effect of Initial Addition of Reaction Products
on the Kinetics of the Biphasic Alkaline Hydrolysis of C-4
measurements using CDCl3 as solvent have shown that during
the C-6 reaction the volumic ratio of ethanol within this phase
remained always less than 8%.
(60 °C), C-6 (80 °C), and C-8 (80 °C) Ethyl Alkanoates
(
EtOH is Ethanol, and S is Sodium Butanoate in C-4, and
a
The second phase is the interfacial phase (int), which
corresponds to a small volume in which the density profiles of
ester and water are functions of the distance from their respective
bulk phases. This is supported by molecular dynamics simula-
tions of a water-oil interface in the presence of micelles
Sodium Octanoate in C-8)
concentration
mol L ) of the clarification clarification
observed
calcd
-
1
(
chain
additive
additive
time (min)
time (min)
C-4 (60 °C) none
0
0.02
0.8
0.8
0
1.36
0
0.05
1
25
29
17
11
60
15
95
87
40
55
42
18
18
14
10
32
25
9
performed by Karaborni et al. The authors show that the
C-4 (60 °C)
C-4 (60 °C)
S
S
24
15
interface is rough, that there are surfactant molecules adsorbed
at the oil surface, and that the thickness of the interface layer is
of about one micellar diameter.
The third phase is the aqueous phase (aq) that initially
contains hydroxide and sodium ions. During the reaction, several
other species accumulates in this phase: dissolved ester (Eaq),
free surfactant molecules (S), ester-containing micelles that
consist of g′ surfactants and p ester molecules (ECM), empty
micelles (M), and ethanol (EtOH).
C-4 (60 °C) EtOH
15
C-6
C-6
C-8
C-8
C-8
C-8
C-8
C-8
C-8
C-8
C-8
C-8
none
EtOH
none
EtOH
EtOH
S
60
20
95
90
45
0.01
0.02
0.035
0.05
0.075
0.1
40
S
22.5
17
S
S
16.5
14
12.5
23
S
For the purpose of modeling the following variables and
parameters have been considered.
S
C-8
final
solution
1.55 mL
1
. Variables. The number of moles of compound X in phase
j is written as Xj.
a
Observed times of clarification are known with an accuracy of (5
Eorg: ester in the bulk organic phase
min. Calculated times of clarification are from kinetic modeling.
Eint: ester in the interfacial phase
(C-7 and especially C-6), the shape of the induction period is
somewhat different. In these cases, hydrolysis occurs at a slow
constant rate until around 13% and 35%, respectively, of the
initial ester has been consumed. After that, acceleration and
clarification take place. For short-chain esters (C-5 and espe-
cially C-4), no significant induction period can be detected under
our experimental conditions. However, also in these cases the
kinetic curves show a characteristic convex shape, indicating
autocatalytic dynamics.
In all cases, the reaction yields an equimolar mixture of
ethanol and sodium alkanoate. Total depletion of the ester at
the end of reaction has been confirmed by IR spectroscopic
analysis to correspond exactly to the formation of an equivalent
amount of sodium alkanoate in the aqueous phase.
E
aq: ester dissolved in the aqueous phase
Saq: surfactant monomers dissolved in the aqueous phase
EtOH: ethanol dissolved in the aqueous phase
-
OH : hydroxide ions in the aqueous phase
ECM: ester-containing micelles in the aqueous phase
AS: adsorbed surfactant in the interfacial phase
M: empty micelles in the aqueous phase
2
. Effect of Reaction Products. A series of complementary
experiments have been performed to study the kinetic effect of
the initial addition of reaction products, i.e., of ethanol, sodium
alkanoate, and the final reaction solution itself, which was
obtained from a previous experiment. These studies allow us
to confirm the autocatalytic nature of the reaction and to
characterize the specific autocatalytic species. Indeed, results
listed in Table 1 show that the initial addition of sodium
alkanoates and aliquots of final reaction solutions exhibit
significant catalytic effects. In the C-8 case, ethanol displays
Vorg: volume of the bulk organic phase
Vint: interfacial volume
Vaq: volume of the aqueous phase
[X] : molar concentration of X in phase j, [X] ) X /V
j
j
j
j
-
1
only poor catalytic activity (for instance, addition of 1 mol L
ethanol has less effect than the addition of 3.5 × 10 mol L
-2
-1
ri: rate of process i, written in mol min-1 according to the
sodium octanoate). However, in the case of C-4, both butanoate
and ethanol account for the rate acceleration.
mass balance equations
2
. Parameters
III. Kinetic Model
ki: rate constant of process i with usual units
We considered for the proposed kinetic model the main
reactive species and macroscopic physicochemical processes
expected to be involved in an oil-water biphasic hydrolysis
reaction of long-chain ethyl esters.
g′: weight average aggregation number of sodium
alkanoate in ECM
The liquid-liquid reaction system has been regarded to
consist of three phases. One phase is the organic phase (org),
which is considered to contain solely neat ester. Tests using
sodium alkanoates or water have shown that their dissolution
in the ester phase is negligible. Moreover, 200 MHz NMR
p: average number of solubilized ester molecules in ECM
g: weight average aggregation number of empty
micelles M

10554 J. Phys. Chem. A, Vol. 102, No. 51, 1998
Buhse et al.
-
1
TABLE 2: Estimated Parameter Values from Thermodynamic Calculations at T ) 80˚C and in the Presence of 3 mol L Salt
(
See Appendix 2 for Details)a
C-4 (60 °C)
C-4 (80 °C)
C-5
C-6
C-7
C-8
s (mol L-1)
4.1 × 10
-3
5.5 × 10
-3
1.7 × 10
0.149
0.64
4
-3
5.3 × 10
0.166
0.71
5
-4
1.6 × 10
0.182
0.78
14
2.2
-4
5.1 × 10
0.199
0.85
29
4.5
-5
V (L)
0.132
0.132
0.56
R (L mol-1)
0.56
g′
p
1.4
1.5
g
12
1
3.5 × 10
24
0.3
9.2 × 10
36
47
-
1
-2
-2
cmc (mol L
K
)
8.3 × 10
2.5 × 10
1
-g g-1
-3
+8
+34
+70
m
mol
L
2.6 × 10
1.1 × 10
a
The micellization equilibrium constant24 is K
cmc for C-6 and C-8 have been checked experimentally to be =0.46 and =2.5 10 mol L , respectively, at room temperature and in the presence
mol L salt.
/k-8 ) cmc1-g/(2g ). C-4 does not aggregate under our experimental conditions. Values of
2
m
) k
8
-
2
-1
-
1
3
-
1
Step 2: Dissolution of the Ester in the Aqueous Phase. This
is regarded as an equilibrium between the ester located at the
interface (Eint) and the ester dissolved in the aqueous phase (Eaq).
Since the solubility of a solute in a solvent is independent of
the available quantity of the solute (here, the bulk organic phase),
the process of dissolution has been simply described by zero-
order kinetics. However, we also considered that the solubility
of long-chain alkyl esters in water varies with the presence of
dissolved additives. In our case these are ethanol and sodium
alkanoate formed during the reaction process. Ethanol displays
a solvent effect and sodium alkanoate a so-called salting-in
s: solubility of the ester in the aqueous phase (mol L )
R: correction factor related to solvent and salting-in
-
1
effects (L mol )
cmc: critical micellar concentration
CAC: critical aggregation concentration
V: molar volume of neat ester
a: molar area of neat ester
11
effect, both increasing the solubility of the ester in the aqueous
phase. The reversal process (phase separation) has been
considered to be of first order with a rate ensuring that at
equilibrium the actual saturation concentration of ethyl al-
kanoates is reached. Solubility values and the salting-in and
solvent-correcting factor (R) have been estimated by thermo-
D: mean oil droplet diameter
3
. Reaction Scheme. The sequence network for the biphasic
alkaline hydrolysis of C-4 to C-8 ethyl alkanoates can be
summarized by the following steps: (1) formation of a free
organic aqueous interface by macromixing, (2) dissolution of
ester in the aqueous phase, (3) hydrolysis of the ester, (4)
formation of ester-containing micelles by cooperative aggrega-
tion, (5) adsorption of surfactant monomers at the interface, (6)
formation of ester-containing micelles through collective de-
sorption, (7) dissociation of ester-containing micelles and phase
transfer, and (8) formation of empty micelles. The eight steps
are
-
1
dynamic calculations at an ionic strength of 3 mol kg (see
Table 2 and section 2 of Appendix).
Step 3: Hydrolysis of Ethyl Alkanoates. This reaction has
1
2
been studied by Evans et al. under monophasic conditions.
Second-order rate constants and activation energies have been
determined in binary mixtures of 85% ethanol/15% water (v/v)
and 70% acetone/30% water (v/v). From these studies, it appears
that the values of the rate constants increase with the water
content in the reaction medium and that they are almost
independent of the chain lengths of the esters. Activation
Eorg a Eint
Eint a Eaq
(1)
(2)
-1
energies were found to be of 63 kJ mol in aqueous ethanol.
From these reported values, the second-order rate constant k3
-
E + OH f S + EtOH
(3)
(4)
(5)
for the alkaline hydrolysis in pure water has been estimated to
aq
aq
-
1
-1
be about 60 L mol min for the C-4 to C-8 esters at 80 °C
g′S + pE a ECM
and 17 L mol min-1 at 60 °C. Hydrolysis occurring inside
the interfacial volume has been neglected because of the
expected lack of hydroxide ions in this pseudophase.
-1
aq
int
(
g′)S + (p)E a AS
aq int
Steps 4-6: Stepwise CooperatiVe Aggregation, One-Step
AS f ECM
(6)
(7)
9
Adsorption, and CollectiVe Desorption. Karaborni et al. identi-
fied by molecular dynamics calculations the formation of ester-
containing micelles (ECM) in oil-water-surfactant systems.
Both take place in the interfacial volume. The first one (step 4)
involves the direct formation of ECM aggregates at the oil-
water interface by a cooperative aggregation, while the second
one (step 6) corresponds to a collective desorption of adsorbed
surfactant molecules (AS) at the oil-water interface.
ECM a g′S + pE
aq
aq
gS a M
(8)
aq
Step 1: Formation of a Free Organic/Aqueous Interface. This
process corresponds to the dispersion of ester in water. It has
10
been studied by Polat and Chander using an experimental setup
quite similar to ours. Kinetic data show that the dispersion
proceeds rapidly. In the early stage of stirring, the change in
the median oil droplet size as a function of time follows
approximately first-order behavior. On this basis, first-order
reversible steps between the organic phase (Eorg) and the
interface (Eint) were chosen to represent the dispersion of the
ester in the aqueous phase.
Step 4 corresponds to the stepwise cooperative aggregation
of g′ surfactant monomers incorporating p ester molecules
coming from the interface. The process can be described by a
Becker-D o¨ ring-like model similar to that of Anianson and
1
3
14
Wall or Wattis and Coveney. It results in a size distribution
where g′ and p are average values. As already described in our
previous paper, it is reasonable for kinetic modeling purposes

Autocatalysis in Hydrolysis
J. Phys. Chem. A, Vol. 102, No. 51, 1998 10555
Figure 1. Kinetics of the biphasic alkaline hydrolysis of C-4 to C-8
ethyl alkanoates (dots): (continuous line) model fitting at 80 °C; (dashed
line) model fitting of the C-4 experiment at 60 °C.
Figure 2. Skeleton mechanism of the autocatalytic biphasic hydrolysis
of ethyl alkanoates showing the main reaction pathways and the various
reacting species located in the three phases or pseudophases.
to reduce this multistep description into a high order (g′ + p)
one-step aggregation with a reversal first-order dissociation. The
high-order rate law gives rise to a threshold value in the
surfactant concentration that corresponds to a critical aggregation
concentration (CAC) above which ECMs are formed.
Step 5 is the adsorption of surfactant monomers at the free
interface. Second-order kinetics were used to describe the
adsorption that is assumed to occur without any threshold
concentration. Since the adsorbed surfactant is a precursor of
ECM and to ensure mass balance, the same stoichiometry (g′
and p) has been used for the description of AS as for ECM.
In step 6, ECM is the result of the detachment of a bud of
AS, i.e., a collective desorption of surfactant and ester molecules
from the adsorbed surfactant layer. This process has been
described by a first-order reaction.
sensitive have been adjusted to the best fit. These parameters
values are given in Table 3 (see section 1 of Appendix for a
complete survey of parameters values used for modeling).
Values of k-2 obtained by numerical fitting show that under
our experimental conditions, solubilization times are about 0.1
1
5
min, which is in agreement with literature data. They are also
in accordance with the expected tendency that solubility
decreases and time of dissolution increases with increasing
aliphatic chain length of the ester. Another strong trend is
expressed by the value of k4. This parameter corresponds to
the equilibrium constant for the formation of ester-containing
micelles (ECM). As expected, aggregation equilibrium constants
increase with increasing chain length.
The difference between step 4 and steps 5 and 6 is mainly
due to their kinetic rate law rather than to their net chemical
results.
3
. Analysis of Time Profiles. a. C-4 Experiments. Satisfac-
tory curve fitting of kinetic data at 60 and 80 °C was obtained.
It strongly indicates that only solvent and salting-in effects
Step 7: Phase Transfer. Coming either from the cooperative
or collective pathway, ester-containing micelles (ECM) are
dispersed in the bulk aqueous phase where they dissociate,
releasing g′ surfactant and p ester molecules. The dissociation
rate of ester-containing micelles has been taken to be first order.
Step 8: Formation of Empty Micelles. This process has been
described by a one-step high-order aggregation and a reversal
first-order dissociation process. The numerical values of g and
cmc used for the kinetic modeling were obtained from thermo-
dynamic calculations (see section 2 of Appendix, Figure 3, and
Table 2).
(leading to an increase of the solubility of ethyl butanoate in
the aqueous phase) are at the origin for the weak autocatalytic
behavior of this system.
b. C-5 Experiments. The interpretation of the kinetics requires
the consideration of both salting-in and solvent effects and
cooperative phase transfer by ECM.
c. C-6 and C-7 Experiments. In this case, the beginning of
the acceleration period takes place only after a relatively large
amount of ester has been already hydrolyzed. Satisfactory data
fitting failed when only R and cooperative phase-transfer effects
were considered. Adsorption of the surfactant at the oil-water
interface has to be taken into account as well. The adsorbed
surfactant AS acts as a transient reservoir for a part of surfactant
molecules that are trapped at the interface. These trapped
surfactant molecules are consequently not available for the
subsequent phase-transfer process. For the C-7 experiments,
critical aggregation concentration or CAC is readily reached,
the cooperative formation of ester-containing micelles (ECM)
is the predominant process, and AS accumulates moderately.
The behavior of the C-6 experiments is more difficult to interpret
because modeling shows a high transient value of AS. This high
value could be understood either by considering that the
roughness of the interface could provide a sufficiently large
interfacial volume or by assuming that “AS” would not be really
adsorbed at the interface but is rather located in the bulk aqueous
phase as nontransporting ester-containing micelles.
The skeleton mechanism in Figure 2 shows the reaction
pathways and the reactive species in their respective phases
(organic, interfacial, and aqueous).
IV. Results and Discussion
. Equilibrium Thermodynamics Calculations. Equilibrium
1
parameters that were used in the model were predicted by
thermodynamic calculations. Figure 3 shows the dependency
of g′, p, and g on the total surfactant concentration. Although
these values depend on the concentration of the surfactant, we
considered an approximate final concentration of sodium
-
1
alkanoates in our experiments to be around [Stot] ) 1 mol L ,
which corresponds to the concentration that has been reached
when the reaction rate is at its maximum. The values that are
gathered in Table 2 were used throughout the fitting procedure.
2
. Kinetic Curve-Fitting Calculations. Each experiment has
d. C-8 Experiments. In this case, cooperative aggregation is
the only source of ester-containing micelles (ECM) and phase
been fitted separately. Some parameters that appeared to be

10556 J. Phys. Chem. A, Vol. 102, No. 51, 1998
Buhse et al.
Figure 3. Weight average aggregation number vs the total concentration of surfactant for ester-containing micelles (g′ and p) and micelles (g).
TABLE 3: Values of the Parameters Obtained from Fitting of Kinetic Experimental Dataa
C-4 (60 °C)
C-4 (80 °C)
C-5
C-6
C-7
C-8
k
k
k
k
k
-2
13.05
-
18.7
-
16
14.1
1.61 × 10
150
0.10
1.50
5.35
4.76
+
1
+6
+19
+49
4
1.87 × 10
2.06 × 10
1.11 × 10
5
-
-
-
23.1
-
6
-
-
-
-
-
0.53
1.65
-
7
1.59
1.42
a
k
-2, k
6
, and k
7
are first order, k
5
is second order, and k
4
is (g′ + p)th order. The sign (-) indicates that it has not been necessary to activate the
corresponding process.
experimental results (Table 1) showing the weak catalytic
activity of ethanol and the strong catalytic effect of a small
quantity of sodium octanoate.
V. Conclusion
Although we are aware that drastic simplifications have been
made in our model, we think that the main reacting species,
paths, couplings, and features of the kinetics have been correctly
identified. As a general property, the rate of oil-water biphasic
reaction is independent of the remaining amount of supernatant
organic phase. As a consequence, biphasic reactions display
intrinsically zero-order kinetics. However, if the reaction
products are able to change the physicochemical properties of
the interface, for instance, by increasing the saturation concen-
tration of the organic solute in the aqueous phase, autocatalytic
behavior is expected. During the biphasic alkaline hydrolysis
of C-4 to C-8 ethyl alkanoates, several phenomena alter the
interfacial properties and increase the solubility of the ester in
the aqueous phase. For ethyl butanoate (short chain length), only
the salting-in and solvent effect by the reaction products
accounts for the autocatalytic kinetics. For longer chain lengths
(C-5 to C-8) cooperative stepwise formation of ester-containing
micelles (ECM) (occurring with a threshold concentration) and
subsequent phase transfer have to be taken into account.
However, for intermediate chain lengths (C-6 and C-7), kinetic
modeling shows that there is also a transient capture of surfactant
molecules that proceeds without any threshold concentration.
Those surfactant molecules are temporarily withdrawn from the
cooperative phase. Empty micelles have to be considered as an
inactive end product. They can be omitted during kinetic
modeling without any effect on curve fitting.
Figure 4. Calculated time profiles of surfactant-containing species
during the biphasic alkaline hydrolysis of C-6 and C-7 ethyl alkanoates
using the fitted model parameters.
transfer is the main process. Formation of ECM occurs at a
critical aggregation concentration (CAC) that is smaller than
the cmc of the empty micelles. Model calculations show that
the phase-transfer equilibria of steps 4 and 7 are strongly
displaced toward the transportation of the ester from the organic
to the aqueous phase. This phenomenon is likely due to the
ester gradient concentration between the two phases. Consider-
ing collective adsorption-desorption at the interfacial volume
is not necessary for a satisfactory curve fitting. The salting-in
effect due to the accumulation of sodium octanoate monomers
in the aqueous phase is not important because the corresponding
CAC and cmc are small. This reasoning is supported by the
Liquid-liquid biphasic reactions in which products have an
influence on the interfacial properties appear to be a new class
of nonlinear chemical systems; kinetic studies are at the
beginning. Highly nonlinear behavior giving rise to kinetic
bistability in a CSTR has been recently studied in the biphasic
1
6
alkaline hydrolysis of ethyl octanoate. Further examples of
such systems could be found in “classic” organic chemistry like

Autocatalysis in Hydrolysis
J. Phys. Chem. A, Vol. 102, No. 51, 1998 10557
the sulfonation of aromatic compounds, N-oxidation of amines,
nucleophilic substitution of alkyl halides, or acetalization of
sugars when performed under biphasic conditions.
(f) The back reaction of step 7 denotes a cooperative stepwise
aggregation of g′ surfactant molecules with p ester molecules
such as in step 4. For this reason, its reaction order (g′ + p)
and rate constant have been taken to be the same (k-7 ) k4).
(b) Differential and Algebraic Equations. Corresponding
differential and algebraic equations are shown below.
VI. Experimental Section
Reagents. Reagents of highest purity commercially available
(
Fluka) were used without further purification. Alkyl chains are
d[E ]/dt ) -r + r
-1
org
1
C-4 butanoate, C-5 pentanoate, C-6 hexanoate, C-7 heptanoate,
and C-8 octanoate. Sodium hydroxide (pro analysi) was
purchased from Prolabo, and water was doubly distilled.
Biphasic Hydrolysis of Ethyl Alkanoates. The reactions
were performed in a thermostated (T ) 80 or 60 °C) round-
bottom two-neck 250 mL flask under reflux. Macromixing of
the two phases (70 mL of aqueous 3 M NaOH and 23 mL of
ester) was achieved by magnetic stirring at 800 ( 5 rpm with
an ellipsoidal magnetic bar of about 25 mm × 6 mm size. Initial
d[E ]/dt ) r - r - r + r - p(r - r + r - r )
int
1
-1
2
-2
4
-4
5
-5
d[E ]/dt ) r - r - r + p(r - r )
aq
2
-2
3
7
-7
d[S]/dt ) r - g′(r - r + r - r - r + r ) -
3
4
-4
5
-5
7
-7
g(r - r )
8
-8
-
amounts were the following: OH at 0.21 mol and Eorg at 0.163,
d[EtOH]/dt ) r3
0
(
.168, 0.156, 0.140, 0.125, and 0.116 mol for, respectively, C-4
60°), C-4 (80°), C-5, C-6, C-7, and C-8 experiments.
Kinetic Measurements. At fixed time intervals the reaction
-
d[OH ]/dt ) -r
3
mixture was poured into a graduated volumetric cylinder, and
after phase separation (within a few seconds) the volume of
the residual organic phase was measured. Time elapsed during
the measurements was taken off.
d[ECM]/dt ) r - r + r - r + r
-7
4
-4
6
7
d[M]/dt ) r - r
8
-8
Model Calculations. Model calculations and fitting of the
experimental kinetic curves have been performed on a worksta-
tion HP 9000-710. The general algorithm used combines a
d[AS]/dt ) r - r - r6
5
-5
Vint ) (Eint + (g′ + p)AS)V
Vaq ) V - E V - V
17
semiimplicit Runge-Kutta method for the numerical integra-
tion of the differential equations and a nonlinear minimization
18
tot
org
int
procedure. Fitting calculations have been started using estima-
tions of the unknown parameters.
Vexp ) (Eorg + Eint + pAS)V
VII. Appendix
where the total reacting volume (Vtot) is assumed to be constant.
The experimentally measured volume (Vexp) of the organic phase
after decanting and phase separation corresponds to the ester
in the bulk phase (Eorg), in the interface (Eint), and in the
adsorbed layer (ester part in AS). The molar volume V has been
taken to be equal for the ester and the corresponding sodium
alkanoate.
1. Modeling Techniques. (a) Rate Laws. The following rates
laws and rate constants have been used for the model:
r
k
comments
r
r
r
1
) k
1
E
org
-1 ) k-1
) k-2
k
k
k
1
) 7.75
a
b
c
3
E
aq
int
-1 ) 1.66 × 10
2
V
s
2
) k-2
s
2. Solution Thermodynamic Properties of Sodium Al-
kanoates and Ethyl Alkanoates. a. Solubility of Ethyl Al-
kanoates in Water. The correlation of experimental solubility
exp(R([EtOH] + [S])
r
-2 ) k-2
E
aq
k
k
-2
d
aq OH-Vaq
-1
) 60 (80 °C);
7 (60 °C)
r
3
) k
3
E
3
20
data of ethyl alkanoates in water at 298 K yields ∆Gs°) 1.317
1
′
p
-1 -1
g
+ 0.688N expressed in units of kcal mol K , and N denotes
r
r
r
r
r
r
r
r
r
4
) k
4
[Saq] [Eint] Vint
k
1
k
1
k
k
k
k
4
de
b
d
b
d
d
f
-4 ) k-4 ECM
the number of carbon atoms in the alkanoate (N ) 8 for
5
) k
5
E
int[Saq
]
5
octanoate). Here, ∆G° is the free energy change associated
s
-5 ) k-5AS
with dissolution and is equal to RT ln X where X is the mole
fraction solubility. Experimental data on the dependence of
solubility on temperature and salt concentration for ethyl
alkanoates are not available. Therefore, the corrections for
temperature and salt effects have been made using information
available for alkanes. The corrections are made using group
6
) k
) k
6
AS
6
7
7
ECM
[Saq] [Eaq] Vaq
[Saq] Vaq
7
4
8
g′
p
-7 ) k
4
g
8
) k
8
) K
m
-8 ) k-8
M
1
b
The table comments refer to the following.
a) Assuming spherical and smooth ester droplets, the ratio
contribution procedure and account for all the CH and CH3
groups in the ethyl alkanoate but ignore any correction for the
2
(
-
9
-3
Eint/Eorg ) k1/k-1 ) (6/D)(V/a) = 7 × 10 /D ) 4.67 × 10
COO group. In the presence of NaCl, the free energy ∆G°/RT
s
for a spherical droplet diameter of 1.5 µm.19
changes by 0.384C for the CH3 group and by 0.064C for the
CH2 group, where C is the molar concentration of the added
(
b) For the sake of simplicity, k-4, k-5, and k-8 have been
3
21
taken arbitrarily at unity and k-1 ) 1.66 × 10 assuming that
salt. We do not have information about this correction term
the corresponding equilibria are rapid.
at other temperatures, and therefore, this correction is taken as
(
c) The same value of R has been taken for EtOH and the
temperature-independent. From solubility data for alkanes,20 we
surfactant.
know that ∆G°/RT for the CH2 group is 1.496 at 298 K and
s
(
(
d) Adjusted parameters values are from Table 3.
e) Surfactant concentration at the interface is assumed to be
1.311 at 353 K. For the CH3 group, ∆G°/RT is 3.536 at 298 K
and 3.548 at 353 K. Therefore, the change in temperature from
298 to 353 K will cause a change in solubility given by
s
equal to those in the aqueous phase.

10558 J. Phys. Chem. A, Vol. 102, No. 51, 1998
Buhse et al.
∆
G°/RT of -0.185 for CH2 and 0.012 for CH3. Taking into
Quantitative methods for a priori estimation of the salting-in
constant k are not sufficiently well-developed, and hence,
experimental estimates based on measured solubility data are
more commonly used. The magnitude of k will depend on both
the organic salt (sodium alkanoate) and the solute molecule
s
account the salt and temperature effects on solubility, we can
calculate the solubility at 353 K and 3 M NaOH using the
solubility information at 298 K and 0 M NaOH as follows:
ln X(T)353K,C)3M) ) ln X(T)298K,C)0M) +
(ethyl alkanoate). k has been found to increase linearly with
[
0.185nCH2 - 0.012nCH3] - C[0.064nCH2 + 0.384nCH3]
the alkyl chain length of large organic salts. The influence of
long-chain quaternary ammonium salts (carbon numbers be-
tween 4 and 12) on the aqueous solubility of benzoic acid is
The first correction term is for the temperature dependence, and
the second is for the salt dependence. The number of methylene
and methyl groups in ethyl alkanoate are denoted by nCH and
nCH , respectively. The mole fraction solubility data are con-
verted to molar concentration by multiplying by 55.55.
b. Estimation of Parameter R Representing Solubility En-
hancement Caused by ethancol and Sodium Alkanoate. The
solubility of ethyl alkanoate in water is affected by the presence
of ethanol and sodium alkanoate. Both contribute to an increase
in the aqueous solubility of ethyl alkanoates by modifying the
structure of water. To describe the influence of ethanol, we view
the problem as that of the solubility of ethyl alkanoate in a mixed
solvent consisting of ethanol and water. The solubility in the
mixed solvent (Xmix) can be related to the solubility in the pure
solvents of water and ethanol (XW and XE) by applying the
framework of any suitable solution theory. The Flory-Huggins
-
1
accounted for by values of k in the range 0.35-0.91 M , with
-
1
k having a methylene group contribution of 0.07 M . We note
that the incremental variation in the parameter R, which accounts
for the influence of ethanol on the solubility of ethyl alkanoates,
is also 0.07 per methylene group (see Table 2). Since no direct
measurement of k relevant to our system is presently available
and since the incremental variation in R is comparable to that
in k for an analogous system, k is equated to R for simplifying
our kinetic calculations. In summary, the solubility X of ethyl
alkanoates in the presence of ethanol and sodium alkanoate has
been calculated using the relation
2
3
X ) X(EtOH)0,S)0) exp R([EtOH]+[S])
where [EtOH] and [S] are the molar concentrations of ethanol
and sodium alkanoate in the aqueous solution and values of R
are those listed in Table 2.
2
2
solution model yields
ln Xmix ) φ ln X + φ ln X + ø φ φ
WE E W
c. Calculation of Micellization Variables g, cmc, and Km for
Sodium Alkanoates. The aggregation characteristics of sodium
alkanoates (Cn-1H2n-1COONa) such as the cmc, the average
aggregation number of micelles, the variance of the micelle size
distribution, and the micellization equilibrium constant (step 8
in the reaction scheme of section III.3) can all be predicted a
priori using the molecular thermodynamic theory formulated
w
W
E
E
where φW and φE denote the volume fractions of water and
ethanol in the mixed solvent and øWE is the interaction parameter
between water and ethanol. Since the interaction term in the
above equation is less important compared to the other terms,
the above expression reduces to
2
3
by Nagarajan and Ruckenstein. For a surfactant solution
containing micelles of various aggregation numbers g, the
equilibrium condition of a minimum in the Gibbs free energy
stipulates
XE
XE
Xmix ) X exp φ ln
) X exp 0.0585 ln CE
)
W
E
W
[
XW]
[
]
XW
X exp[RC ]
W
E
µ° + kT ln X ) g(µ° + kT ln X )
The volume fraction φE and the molar concentration CE of
ethanol are related by φE ) 0.0585CE, and R denotes the factor
g
g
1
1
where X1 and Xg are the mole fractions of the singly dispersed
molecules and aggregates of size g, respectively, and are their
respective standard chemical potentials, defined as those cor-
responding to infinitely dilute solution conditions. Expressions
for the standard chemical potentials have been developed in
ref 23, and the methods of calculating the equilibrium micel-
lization properties have been described in ref 23 and also in
our previous paper, ref 8.
The predicted results summarized in Table 2 and Figure 3
correspond to the experimental conditions of 80 °C and the
presence of 3 M NaCl in the surfactant solution. The weight-
average aggregation number g as a function of the total
concentration Xtot ()X1 + ∑gXg) of sodium alkanoate in solution
is plotted in Figure 3. The mole fractions X are converted to
molar concentrations C by multiplying by 55.5. One may notice
that for the C4 alkanoate, no aggregate formation occurs up to
a concentration of 2 M. For other tail lengths, one can observe
that the aggregation number is increasing with increasing
surfactant concentration. This is a typical behavior anticipated
when the aggregation numbers are small. Indeed, this behavior
corresponds to a somewhat polydispersed distribution of ag-
gregates in solution. The aggregation numbers listed in Table
2 are the values predicted corresponding to a concentration of
1 M sodium alkanoate but have been used as constants in the
kinetic model calculations. A sharp transition in the plot of X1
0.0585 ln(XE/XW). To calculate R, the known group contributions
at 25 °C to ln XE and ln XW, namely, -0.178kT and -0.935kT
for CH2 and CH3 groups when ethanol is the solvent and
-1.425kT and -3.875kT when water is the solvent, are used.
Since the contribution of the polar COO group would be
comparable in both solvents, the ratio ln(XW/XE) is not signifi-
cantly affected by it. Further, the temperature dependencies of
XE and XW would approximately cancel each other, and thus,
to a first approximation, R is temperature-independent. The
values of R calculated in this manner are listed in Table 2.
The influence of sodium alkanoates on the solubility of ethyl
alkanoates can be described by the concept of salting-in/salting-
out applied to solutions containing salts. The solubility of an
organic nonelectrolyte solute in the presence of a salt can be
represented as
X(C)
ln
) kC
X(C)0)
where k is the salting-in/salting-out equilibrium constant and C
is the molar concentration of the salt. For inorganic salts, k is
a negative constant and the solute is salted-out. For an organic
salt (sodium alkanoate, in the present case), depending upon
the importance of the organic part, the constant k can be positive
and the solute is salted-in.

Autocatalysis in Hydrolysis
J. Phys. Chem. A, Vol. 102, No. 51, 1998 10559
against the total concentration Xtot ) X1 + ∑gXg is used to
predict the cmc values listed in Table 2. The micellization
equilibrium constant Km is calculated from the predicted cmc
and g.
363-374 (ISBN: 0-8493-7694-7).
(
7) (a) Bachmann, P. A.; Luisi, P. L.; Lang, J. Nature 1992, 357, 57-
5
9. (b) Chizmadzhew, Y. A.; Maestro, M.; Mavelli, F. Chem. Phys. Lett.
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are small. The values of g′ and p listed in Table 2 are those
predicted at a total surfactant concentration of 1 M but have
been used as constants for performing the kinetic model
calculations.
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