Micellization of alkyltriphenylphosphonium bromides in ethylene glycol and diethylene glycol + water mixtures: Thermodynamic and kinetic investigation

Article abstract of DOI:10.1007/s10953-007-9222-6

The thermodynamics of micellization and other micellar properties of alkyl- (C₁₀-, C₁₂-, C₁₄- and C₁₆-) triphenylphosphonium bromides in water + ethylene glycol (EG) (0 to 30% v/v) mixtures over a temperature range of 298 to 318 K and cetyltriphenylphosphonium bromide in water + diethylene glycol (DEG) mixtures (0 to 30% v/v) at 298 K have been studied conductometrically. In all cases, an increase in the percentage of co-solvent results in an increase in the cmc values. On the basis of these results, the thermodynamic parameters, the Gibbs energy (ΔG _m^o), enthalpy (ΔH_m^o ) and entropy (ΔS_m^o ) of micellization have been evaluated. In addition to the conductivity measurements, kinetic experiments have also been done to determine the dependence of observed rate constant for the nucleophilic substitution reaction of p-nitrophenyl acetate and benzohydroxamate ions in the presence of the surfactant cetyltriphenylphosphonium bromide with a varying concentration of EG and DEG ranging from 0 to 50% v/v at pH=7.9 and 300 K. All of the reactions followed pseudo-first-order kinetics. An increase in the surfactant concentration results in an increase in the reaction rate and for a given surfactant concentration, the rate constant decreases as the concentration of co-solvent in the mixture increases. The kinetic micellar effects have been explained by using the pseudophase model. The thermodynamic and structural changes originating from the presence of solvents control the micellar kinetic effects.

Full text of DOI:10.1007/s10953-007-9222-6

J Solution Chem (2008) 37: 59–72
DOI 10.1007/s10953-007-9222-6
Micellization of Alkyltriphenylphosphonium Bromides
in Ethylene Glycol and Diethylene Glycol + Water
Mixtures: Thermodynamic and Kinetic Investigation
Sancheeta Kolay · Kallol K. Ghosh · Amy MacDonald · Jonathan Moulins · Rama
M. Palepu
Received: 13 April 2007 / Accepted: 21 May 2007 / Published online: 29 November 2007
© Springer Science+Business Media, LLC 2007
Abstract The thermodynamics of micellization and other micellar properties of alkyl-
(C10-, C12-, C14- and C16-) triphenylphosphonium bromides in water + ethylene glycol (EG)
(0 to 30% v/v) mixtures over a temperature range of 298 to 318 K and cetyltriphenylphos-
phonium bromide in water+diethylene glycol (DEG) mixtures (0 to 30% v/v) at 298 K have
been studied conductometrically. In all cases, an increase in the percentage of co-solvent re-
sults in an increase in the cmc values. On the basis of these results, the thermodynamic
parameters, the Gibbs energy (ꢀGmo ), enthalpy (ꢀHmo ) and entropy (ꢀSmo ) of micellization
have been evaluated. In addition to the conductivity measurements, kinetic experiments have
also been done to determine the dependence of observed rate constant for the nucleophilic
substitution reaction of p-nitrophenyl acetate and benzohydroxamate ions in the presence
of the surfactant cetyltriphenylphosphonium bromide with a varying concentration of EG
and DEG ranging from 0 to 50% v/v at pH = 7.9 and 300 K. All of the reactions followed
pseudo-first-order kinetics. An increase in the surfactant concentration results in an increase
in the reaction rate and for a given surfactant concentration, the rate constant decreases as
the concentration of co-solvent in the mixture increases. The kinetic micellar effects have
been explained by using the pseudophase model. The thermodynamic and structural changes
originating from the presence of solvents control the micellar kinetic effects.
Keywords Critical micelle concentration · Solvent effect · Kinetics ·
Alkyltriphenylphosphonium bromide · Pseudophase model
1 Introduction
Much effort has been devoted to exploring the nature of micellization and surfactant behav-
ior in polar organic solvents and solvent mixtures [1–8]. Changing the solvent composition
S. Kolay · K.K. Ghosh (
)
ꢀ
School of Studies in Chemistry, Pt. Ravishankar Shukla University, Raipur (C.G.) 492010, India
e-mail: kallolkghosh@yahoo.com
A. MacDonald · J. Moulins · R.M. Palepu
Department of Chemistry, St. Francis Xavier University, Antigonish, Canada

60
J Solution Chem (2008) 37: 59–72
provides an opportunity to study the role of the so-called solvophobic effect, in contrast to
the hydrophobic effect in micellization [9]. The term “solvophobic interaction” has been
coined to describe micellization in non-aqueous polar solvents, by analogy with hydropho-
bic interactions responsible for aggregation in water [10]. However, the ability of water to
form unique hydrogen-bonded networks is not a necessary condition for the aggregation
process. The micelles formed in non-aqueous solvents are similar in many aspects to the
micelles that are formed in water, although, micelle formation is not as favored in such non-
aqueous solvents for a given surfactant [11, 12]. Among the organic solvents studied so far,
ethylene glycol (EG) is of particular interest as it has many characteristics similar to those
of water, and therefore the study of the aggregation behavior of surfactants in water + EG
mixtures provides a better understanding of the function of the liquid structure in the micel-
lization process.
The majority of fundamental studies of the solvent effect on cationic surfactants have
been made with alkyltrimethylammonium bromides and alkylpyridinium bromides [13, 14].
By comparison to these other surfactants, alkyltriphenylphosphonium bromide have not
been given their due attention. The micellization behavior of binary combinations of
alkyltrimethylammonium bromides has been studied by Palepu et al. [15, 16]. Recently,
Palepu et al. [17] studied micellar and associated thermodynamic properties of binary mix-
tures of alkyltriphenylphosphonium bromides in EG + water mixtures. In the present study,
we have used C10-, C12-, C14- and C16-TPB to obtain thermodynamic and structural informa-
tion about water + EG and water + DEG micellar solutions. Critical micelle concentrations
(cmc) and micellar ionization degrees, α, were obtained from conductivity measurements.
The standard Gibbs energy, enthalpy and entropy changes for micellization, ꢀGom, ꢀHmo
and ꢀSmo , respectively, have also been determined to study the energetics of micellization
reactions.
To extend our knowledge of the properties of water + ethylene glycol and water +
diethylene glycol micellar solutions as reaction media, the nucleophilic substitution reac-
tion of p-nitrophenyl acetate was studied in cetyltriphenylphosphonium bromide solutions.
The kinetic micellar effects will be due to the micellar concentration effect. This effect de-
pends upon the transfer of the substrate from the bulk solution to the micelle, upon the
reaction mechanism, and upon the properties of the interfacial region such as local charge,
polarity and water content. A study of this effect thereby gives information about the micel-
lar pseudophase characteristics as a reaction media. Comparisons between the observed rate
constants in water and in the micellar pseudophases in water + EG and water + DEG micel-
lar solutions can be done directly, and hence provide information about the characteristics
of the micellar pseudophase where the reaction occurs.
2 Experimental Section
2.1 Materials
Benzohydroxamic acid was prepared by a literature method [18, 19]. p-Nitrophenyl ac-
etate was obtained from SD fine chemicals. The surfactants employed in this study are decyl
(C10TPB), dodecyl (C12TPB), tetradecyl (C14TPB), and hexadecyl (C16TPB) triphenylphos-
phonium bromides, and were obtained from Caldon Chemicals Canada (distributors for Lan-
caster Synthesis of England). The surfactants were purified as described earlier [15]. Freshly
opened bottles of EG and DEG (Qualigens) were employed in our study. Binary solutions
were prepared employing triply distilled and deionized water.

J Solution Chem (2008) 37: 59–72
61
2.2 Conductivity Measurements
The conductivity experiments were performed on a CDM 83 conductivity bridge operating
at 1000 Hz, with a platinum cell. The cell constant was 0.978 cm−1. A conductometric titra-
tion method was employed. This method involves titrating a known volume of a surfactant
solution into 10 mL of the solvent, which is contained in a thermostatted, jacketed beaker.
For the pure surfactants in the presence of aqueous ethylene glycol, these titrations were
carried out from 298 to 318 K at 5 K increments.
2.3 Kinetics
The reactions were investigated at 300.2 0.2 K with a Varian Cary-50 spectrophotometer
and a Systronics (Type-104) spectrophotometer. The reactions were followed by monitoring
the decreasing concentrations of the reactant p-nitrophenoxide at 400 nm. All of the kinetic
experiments were performed at an ionic strength of 0.1 mol·L−1 (controlled with KCl).
A phosphate buffer was employed to control the solution pH. All reactions were conducted
under pseudo-first-order rate conditions. For all of the kinetic runs, the absorbance versus
time results were fit very well to the first-order-rate equation
ln(A∞ − At ) = ln(A∞ − Ao) − kt.
(1)
The pseudo-first-order rate constants were determined by the method of least squares.
Each experiment was repeated at least twice, and the observed rate constant was found to be
reproducible within a precision of about 3% or better.
3 Results and Discussion
3.1 Micellar Properties in Aqueous Ethylene Glycol and Aqueous Diethylene Glycol
Solutions
Conductivity studies were performed on the surfactants in the presence of ethylene glycol
over a range of temperatures (298 to 318 K) in order to determine the dependency of the
thermodynamic properties for molecular assembly on the chain length, additives, and tem-
perature. The specific conductivity was plotted as a function of the surfactant concentration
in order to determine the cmc and counter-ion binding/ionization for the surfactants at each
temperature. Figure 1 shows the conductivity plot for the C10TPB surfactant at 298.15 K
in water, and in 5% and 10% v/v EG solutions. As indicated in this plot, the cmc value
increases with increasing concentration of EG. Similar behavior was observed in all other
cases. Figure 2 depicts the effect of temperature on the cmc values for C12TPB in 10% EG.
The cmc values as a function of the EG percent are presented in Table 1. The degree of
dissociation of the micelles (α) in the mixed solvent system exhibited very little dependence
on temperature, and therefore the average value of α was used for the calculation of ꢀGom at
all temperatures. It was found that the cmc values of the surfactants decrease with increasing
hydrocarbon chain length at any given temperature, as can be seen in Table 1. Therefore, as
the chain length increases, micelles form at lower concentrations of the surfactant due to a
more pronounced hydrophobic effect.
The cmc values of the surfactants were found to increase in the presence of ethylene gly-
col, as can be seen in Table 1. Ethylene glycol is a structure breaker, breaking up the structure

62
J Solution Chem (2008) 37: 59–72
Fig. 1 Plots of the specific conductivity (κ) versus [C TPB] at different volume-% of EG
10
−1
Fig. 2 Plots of the specific conductivity (Specific conductivity (κ/μ s cm )) versus [C TPB] at different
temperatures in the presence of 10% (v/v) EG
12

J Solution Chem (2008) 37: 59–72
63
Table 1 Cmc and α values of the ATPBs, determined by conductivity method in the presence of ethylene
av
glycol
Surfactant Temperature CMC in
CMC in
5% (v/v)
ethylene
glycol
(mmol·L
α
CMC in
10% (v/v)
ethylene
glycol
(mmol·L
α
CMC in
30% (v/v)
ethylene
glycol
(mmol·L
av
av
(K)
aqueous
media
a
−1
(mmol·L
)
−1
−1
−1
)
)
)
C
10
C
12
C
14
C
16
TPB
TPB
TPB
TPB
298
303
308
313
318
298
303
308
313
318
298
303
308
313
318
298
303
308
313
318
7.21
9.36
9.28
9.44
9.76
10.0
2.15
2.25
2.40
2.63
2.70
0.65
0.66
0.68
0.73
0.76
0.219
0.220
0.221
0.222
0.590 10.2
10.8
0.600 ···
···
11.3
···
11.4
···
12.0
···
1.82
0.58
0.14
0.640 2.17
2.65
0.645 ···
···
2.73
···
2.88
···
2.92
···
0.694 ···
···
0.692 0.71
0.76
0.85
···
1.10
···
1.15
···
0.690 0.28
0.30
0.696 0.68
0.75
0.37
0.78
0.38
0.87
0.40
0.87
a
Taken from [15]
of the water molecules around the hydrophobic chains, thus decreasing the hydrophobic ef-
fect and consequently increasing the cmc value. As the temperature increases, the resulting
increase in thermal motion of the water molecules further decrease the hydrophobic effect,
resulting in increasing cmc values.
Values of the cmc and counter-ion dissociation for the surfactant C16TPB in 10% (v/v)
DEG are given in Table 2. The values for counter-ion binding (β = 1 − αav) generally de-
crease with increasing temperature. As the temperature increases, micelles form at higher
surfactant concentrations. Therefore, fewer micelles will be present at higher temperatures
and fewer counter-ions will be needed to reduce the head group repulsions.
3.2 Thermodynamics of Micellization
Thermodynamic values for the micellization reaction were calculated using equations de-
rived from the charged pseudophase separation model. In this model, micelles are consid-
ered to be a new soluble phase formed in the system at and above the cmc. The cmc can
therefore be thought of as the solubility limit of the monomers.
The Gibbs energy of micellization for each surfactant in its aqueous solution, and in
the presence of 5% (v/v) and 10% (v/v) ethylene glycol, was calculated with the following

64
Table 2 Cmc and α values of
J Solution Chem (2008) 37: 59–72
av
Surfactant
C16TPB
Temperature
(K)
CMC in 10% (v/v)
α
the C TPB determined by
16
diethylene glycol
conductivity method in the
presence of diethylene glycol
−1
(mmol·L
)
298
308
318
0.36
0.40
0.46
0.51
0.57
0.68
Fig. 3 Variation of ln X
of C TPB in 10% (v/v) ethylene glycol with temperature
12
cmc
equation [20, 21]:
ꢀGom = (2 − α)RT lnXcmc
(2)
where α is the degree of dissociation, R is the gas constant, T is temperature, and Xcmc
is the cmc value on the mole fraction scale [14]. Densities of the binary mixtures were
measured using an Anton Parr DMA 5000 density meter and were used to convert the molar
concentration units to the mole fraction scale.
The enthalpies of micellization [14] were calculated using Eq. 3:
ꢀ
ꢁ
∂ lnXcmc
∂T
ꢀHmo = −(2 − α)RT2
.
(3)
Therefore, if the dependence of the cmc values on temperature is known, a plot of ln Xcmc
versus temperature can be constructed. The slope can then be found at each temperature.
These plots were found to be best fit with a second-order polynomial (r2 = 0.99). A typ-
ical plot for C12TPB in 10% (v/v) ethylene glycol is presented in Fig. 3. The entropies of

J Solution Chem (2008) 37: 59–72
65
Table 3 Thermodynamic
parameters of the ATPBs in
5% (v/v) ethylene glycol
o
o
o
ꢀS
Surfactant Temperature ꢀG
ꢀH
m
m
m
−1
−1
−1
−1
(K)
(kJ·mol
)
(kJ·mol
)
(J·K ·mol
)
C
10
C
12
C
14
C
16
TPB
TPB
TPB
TPB
298
303
308
313
318
−31.5
−32.2
−32.7
−33.0
−33.1
14.5
4.1
154
119
83
45
5
−7.0
−18.8
−31.4
298
303
308
313
318
−34.6
−35.5
−36.0
−36.1
−36.6
12.3
3.0
157
127
94
−6.9
−17.5
−28.8
59
25
298
303
308
313
318
−37.7
−38.2
−38.4
−38.8
−39.0
−8.0
−12.4
−16.5
−20.3
−24.8
89
76
63
50
37
298
303
308
313
318
−42.2
−42.1
−42.3
−42.6
−43.0
8.7
4.9
170
155
140
125
110
0.8
−3.5
−8.1
micellization were then calculated from Eq. 4:
ꢀHmo − ꢀGom
ꢀSmo =
(4)
T
The thermodynamics of micellization were calculated for the pure surfactants in aque-
ous solution as well as in the presence of 5% (v/v) and 10% (v/v) ethylene glycol. The
parameter values obtained are given in Tables 3 and 4. The errors in the Gibbs energy and
enthalpy values are estimated to be 0.5 kJ·mol−1, whereas the error in the entropy values
is 5 J·K−1·mol−1. It is evident that the Gibbs energies of micellization decrease as the
hydrocarbon chain length increases. As previously mentioned, the Gibbs energies of micel-
lization give a measure of the ability for micelle formation. It was found that the cmc values
decrease with increasing chain length, and the Gibbs energies of micellization follow the
same trend. This indicates an increased hydrophobic effect for the longer chain surfactants.
The Gibbs energies of micellization become more negative with increasing temperature
in pure water, and also in the presence of co-solvents, for all of the studied surfactants. This
results because the change in size of the logarithm of the cmc is more than compensated for
by the RT term in Eq. 2.
It can be seen from Tables 3 and 4 that the enthalpies of micellization become more nega-
tive with increasing temperature for each surfactant in each solvent. However, the enthalpies
calculated from Eq. 3 could differ from the values determined calorimetrically. The equation
employed to determine the Gibbs energies is only applicable if the aggregation numbers are

66
J Solution Chem (2008) 37: 59–72
Table 4 Thermodynamic
parameters of the ATPBs in 10%
(v/v) ethylene glycol
o
o
o
ꢀS
Surfactant Temperature ꢀG
ꢀH
m
m
m
−1
−1
−1
−1
)
(K)
(kJ·mol
)
(kJ·mol
)
(J·K ·mol
C
10
C
12
C
14
C
16
TPB
TPB
TPB
TPB
298
303
308
313
318
−29.5
−29.8
−30.1
−30.6
−30.9
9.1
4.0
129
112
93
−1.3
−7.0
−13.1
75
56
298
303
308
313
318
−31.9
−31.8
−32.2
−32.5
−33.0
−15.4
−17.8
−20.4
−23.2
−26.1
55
46
38
30
22
298
303
308
313
318
−37.4
−37.8
−38.0
−38.1
−38.2
−5.0
−11.5
−18.0
−24.7
−31.6
109
87
65
43
21
298
303
308
313
318
−39.9
−40.2
−40.3
−40.8
−41.3
11.4
4.8
172
148
123
98
−2.4
−10.0
−18.2
73
Table 5 Thermodynamic
parameters of the CTPBs in the
presence of diethylene glycol at
298 K
o
Surfactant
%
cmc
ꢀG
m
−1
−1
)
(v/v)
(mmol·L
)
(kJ·mol
C
16
TPB
10
20
30
0.36
0.49
0.52
−40.6
−41.6
−42.0
large, and activities are assumed to be equal to their concentrations because the solutions are
so dilute. Therefore, the obtained thermodynamic values should be viewed as approximate.
However, generalizations can still be drawn from the data.
The data indicate that the micellization is favored in general by both the entropy and
enthalpy terms at higher temperatures, whereas it is favored mainly by entropy at lower
temperatures.
From Table 5 it can be seen that the cmc values increase with increasing volume-% of
diethylene glycol. As the amount of diethylene glycol in the media increases, the structure
of the water molecules around the hydrophobic chains becomes destroyed, resulting in the
observed increase of the cmc. The Gibbs energies of micellization were found to become
more negative with increasing concentration of diethylene glycol.

J Solution Chem (2008) 37: 59–72
67
Table 6 Kinetic data for the nucleophilic substitution reaction of p-nitrophenyl acetate and benzohydroxa-
mate ion in the presence of water + EG micellar solutions of cetyltriphenyl-phosphonium bromide cationic
surfactants at 300 K
3
−1
10 /s
obs
[C PPh3Br]
16
k
−1
(mmol·L
)
0% (v/v) EG
10% (v/v) EG
30% (v/v) EG
50% (v/v) EG
Without
BHA
With
BHA
Without
BHA
With
BHA
Without
BHA
With
BHA
Without
BHA
With
BHA
0
0.05
0.07
–
9.84
23.4
35.0
51.7
57.5
64.0
73.3
73.5
0.15
0.17
–
6.90
0.22
0.25
–
3.24
0.29
0.31
–
0.27
0.6
1.0
1.8
2.5
3.6
5.5
7.5
9.1
15.4
22.1
29.5
36.0
43.6
53.0
57.9
58.6
6.68
9.00
8.49
15.0
18.4
23.5
26.9
27.9
2.70
3.40
3.45
3.60
4.80
5.50
5.90
0.11
–
0.21
–
0.29
–
0.38
–
0.13
–
0.31
–
0.42
–
0.53
–
–
–
–
–
0.14
74.7
−1
0.37
0.53
0.59
6.08
−4
−1
−3
−1
Conditions: pH 7.9, μ = 0.1 mol·L KCl, [PNPA] = 1.0 × 10 mol·L , [BHA] = 1.0 × 10 mol·L
,
and pK of BHA = 8.8
a
3.3 Kinetic Studies in Water + Ethylene Glycol and Water + Diethylene Glycol Micellar
Media
All of the kinetic reactions in the present study obeyed pseudo-first-order rate kinet-
ics, where the concentration of the nucleophile is generally ten times greater than that
of the substrate. Pseudo-first-order rate constants (kobs) for the nucleophilic reaction of
p-nitrophenyl acetate and benzohydroxamate ion (Scheme 1) in water + ethylene glycol
and water + diethylene glycol micellar solutions of cetyltriphenylphosphonium bromide are
summarized in Tables 6 and 7.
The observed rate constants (kobs) increase with increasing surfactant concentration, and
then gradually level off. This dependence of the observed rate constant can be explained by
considering that an increase in surfactant concentration results in further incorporation of
the substrate, i.e., p-nitrophenyl acetate, into the micelles where the benzohydroxamate ion
concentration is higher than that in the bulk phase (because cationic micelles bind anionic
nuceophiles). For a given surfactant concentration, the observed rate constant decreases as
the concentration of EG and DEG in the solvent mixture increases. These variations in kobs
upon changing the concentrations of EG and DEG should reflect thermodynamically the
structural changes produced in the micellar solutions by the presence of different amounts
of the organic solvent. The decrease of rate constants resulting from addition of an organic
solvent to water can be explained by taking into account the fact that its presence diminishes

68
J Solution Chem (2008) 37: 59–72
Table 7 Kinetic data for the nucleophilic substitution reaction of p-nitrophenyl acetate and benzohydroxa-
mate ion in the presence of water + DEG micellar solutions of cetyltriphenyl-phosphonium bromide cationic
surfactants at 300 K
3
−1
10 /s
obs
[C PPh3Br]
16
k
−1
(mmol·L
)
0% (v/v) DEG
10% (v/v) DEG
30% (v/v) DEG
50% (v/v) DEG
Without
BHA
With
BHA
Without
BHA
With
BHA
Without
BHA
With
BHA
Without
BHA
With
BHA
0
0.05
0.07
–
9.84
0.11
0.14
–
7.53
0.16
0.18
–
3.88
0.21
0.26
–
2.56
0.6
1.0
1.8
2.5
3.6
5.5
7.5
9.1
23.4
35.0
51.7
57.5
64.0
73.3
73.5
74.7
18.2
23.1
31.6
38.8
44.7
54.4
58.1
59.3
7.05
8.60
9.05
16.1
19.2
23.6
26.6
28.0
2.97
3.51
3.7
0.11
–
0.18
–
0.24
–
0.31
–
4.32
4.93
5.60
6.51
6.75
0.13
–
0.26
–
0.32
–
0.48
–
–
–
–
–
0.14
0.32
0.4
0.52
−1
−4
−1
−3
−1
,
Conditions: pH 7.9, μ = 0.1 mol·L KCl, [PNPA] = 1.0 × 10 mol·L , [BHA] = 1.0 × 10 mol·L
and pK of BHA = 8.8
a
Scheme 1 Nucleophilic substitution reaction of PNPA and BHA in presence of surfactant
the water content and decreases the polarity of the reaction medium. A decrease in polarity
results in a large destabilization of the polar transition state, with respect to the initial state,
thus retarding the reaction.

J Solution Chem (2008) 37: 59–72
69
Scheme 2 Pseudophase model
3.4 The Pseudophase Model
Reactivity occurring in association colloids has been thoroughly studied during the past
several decades [22–25]. It is widely accepted that the rate enhancements observed in these
aggregated systems are largely the result of increases in concentration of reactants in the
interfacial volumes where the reactions occur [24–27]. Quantitative treatments of reactivity
in association colloids frequently are based on the pseudophase model [26–28]. One of the
basic assumptions of this model is that the aggregate constitutes a pseudophase, separated
from the bulk solution where it is dispersed, so that reagents partition between the bulk phase
and the aggregate pseudophase. Thus, bimolecular nucleophilic reactions can be described
as illustrated in Scheme 2.
In Scheme 2, subscripts “bulk” and “m” indicate the aqueous and water + EG and
micellar pseudophase, respectively, and Dn represents the micellized surfactant. That is,
[Dn] = [DT]− cmc, where [DT] is the stoichiometric surfactant concentration and cmc
is the measured critical micelle concentration obtained under the experimental conditions
(i.e., in varying amounts of EG and DEG in the solvent mixtures; the cmc is the minimum
surfactant concentration required to observe any kinetic effect). Scheme 2 considers the
distribution of PNPA between the aqueous bulk phase (aqueous and water + EG) and mi-
cellar pseudophase,KmPNPA. The distribution of the benzohydroxamate ion, BHA, between
both pseudophases is considered through the distribution constant KmBHA. The different re-
activities in the bulk and micellar pseudophases have been taken into account through the
corresponding second-order rate constants k2bulk and k2m. The values of k2bulk were obtained
by studying the reaction in the absence of surfactants.
The concentration of hydroxamate in the micellar pseudophase has been defined as the
local molar concentration within the micelle pseudophase: [HA]T = [HA]m/DnV , where V
is the molar volume in dm3·mol−1 of the reaction region and [Dn]V denotes the fractional
volume of the micelle in which the reaction occurs. We assume that V is equal to the partial
molar volume of the interfacial reaction region in the micellar pseudophase. Micellar bind-
ing of both substrates, PNPA and the benzohydroxamate ion, is governed by hydrophobic
interactions, and the equilibrium constants KmPNPA and KmBHA are expressed by referring these
concentrations to the total volume of the micelle. The observed rate constant, kobs, based on
Scheme 2 and the above considerations, is given by the following equation:
m
k
k2bulk
+
KmPNPAKmBHA[Dn]
2
∇
kobs
=
[BHA]T .
(5)
(1 + KmPNPA[Dn])(1 + KmBHA[Dn])

70
J Solution Chem (2008) 37: 59–72
Fig. 4 Simulated rate-surfactant profiles for the reaction of p-nitrophenyl acetate and benzohydroxamate ion
in the presence of C TPB in water+EG mixtures (lines are predicted values with model, !—0%, "—10%,
16
1—30%, 2—50%)
Fig. 5 Simulated rate-surfactant profiles for the reaction of p-nitrophenyl acetate and benzohydroxamate
ion in the presence of C TPB in water + DEG mixtures (lines are predicted values with model, !—0%,
16
"—10%, 1—30%, 2—50%)

J Solution Chem (2008) 37: 59–72
71
Table 8 Kinetic parameters obtained by applying pseudophase model for the nucleophilic reaction of PNPA
with benzohydroxamate ions in the presence of C TPB cationic micelles
16
0% (v/v)
10% (v/v)
EG
30% (v/v)
EG
50% (v/v)
EG
DEG
DEG
DEG
w
2
−1 −1
s )
k
/(M
91.9
440
28.1
5.0
61.6
90
70.3
150
32.3
5.2
28.9
95
36.2
120
8.7
20.1
90
23.9
110
7.4
PNPA
−1
K
K
/(M
−1
)
m
HA
/(M
)
60
20
10
m
m
2
−1 −1
s )
k
/(M
4.1
4.0
7.8
1.6
1.9
When the data in Tables 6 and 7 are fitted with Eq. 5, Figs. 4 and 5 are obtained. The
agreement between the experimental data and the fitted model is good. This indicates that
the pseudophase model is valid.
The results presented in Table 8 allow us to study the influence of the nature of the
micelles on the reaction of PNPA with varying concentrations of ethylene glycol and di-
ethylene glycol. The micellar binding constants of PNPA and BHA in the C16TPB mi-
celle provide conclusive information on the reactivity patterns. This association constant
of PNPA is obtained by fitting experimental data in micellar systems with the value of
KmPNPA = 440 L·mol−1 for C16TPB micellar systems obtained in the absence of EG and
DEG. The values of the distribution constants of BHA decrease with increasing concentra-
tions of EG and DEG in the reaction medium. Taking into account these micellar parameters,
the changes in the polarity of the interfacial region and aggregation number of the micelles
are the key factors for the decrease in kobs values observed in the presence of these solvents.
Acknowledgements The authors are grateful to Dr. P.R. Dafonte, University of Santiago de Compostela,
Spain for applying the pseudophase model. Dr. Kallol K. Ghosh and Sancheeta Kolay are grateful to Prof.
Rama Pande, Head, for providing laboratory facilities.
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