Antagonism in (conventional anionic-gemini anionic) mixed micelle catalyzed oxidation of D-fructose by alkaline chloramine-T: A kinetic study

Article abstract of DOI:10.1002/kin.20384

The catalytic effect of individual conventional anionic surfactant, namely, sodium lauryl sulfate (NaLS), anionic gemini surfactant, namely, sodium salt of bis(1-dodecenyl succinamic acid) (NaBDS), and mixed surfactant (NaLS + NaBDS) on the rate of oxidat

Full text of DOI:10.1002/kin.20384

Antagonism in
Conventional
(
Anionic–Gemini Anionic)
Mixed Micelle Catalyzed
Oxidation of D-Fructose by
Alkaline Chloramine-T:
A Kinetic Study
NEELU KAMBO, SANTOSH K. UPADHYAY
Department of Chemistry, H. B. Technological Institute, Kanpur 208 002, India
Received 14 May 2008; revised 14 August 2008, 28 August 2008; accepted 28 August 2008
DOI 10.1002/kin.20384
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: The catalytic effect of individual conventional anionic surfactant, namely, sodium
lauryl sulfate (NaLS), anionic gemini surfactant, namely, sodium salt of bis(1-dodecenyl suc-
cinamic acid) (NaBDS), and mixed surfactant (NaLS + NaBDS) on the rate of oxidation of
D-fructose by alkaline chloramine-T has been investigated. The reaction always showed a first-
order dependence of rate with respect to each fructose, alkali, and chloramine-T. The rate was
ꢀ
ꢀꢀ
ꢀ
ꢀꢀ
proportional to (k + k [surfactant]), where k and k are the rate constants in the absence
and presence of the surfactant, respectively. The binding parameters have been evaluated.
The observed catalytic effect of mixed micelle on the rate of oxidation was always less than
the algebraic sum of the catalytic effect of two surfactants when they were taken separately,
suggesting an antagonism (negative synergism) in mixed micelle. The antagonism has also
m
been confirmed by determining critical micelle concentration and interaction parameter (β )
of mixed micelle under the experimental conditions of kinetics, that is, in alkaline medium.
ꢁ
C
2008 Wiley Periodicals, Inc. Int J Chem Kinet 41: 123–132, 2009
INTRODUCTION
Mixed micelles are considered to be more versatile
than the single surfactant and have many applications
[1–4] in surface activity, detergency, pharmaceutical
industries, and so on. Gemini surfactants with two hy-
drophilic and two hydrophobic groups in the molecule
[5–8] have received attention due to their superior
Correspondence to: Santosh K. Upadhyay; e-mail: upadhyay
s k@rediffmail.com.
Present address of Neelu Kambo: Department of Chemistry,
Uttar Pradesh Textile Technology Institute, Kanpur, India.
ꢀ
c 2008 Wiley Periodicals, Inc.

1
24
KAMBO AND UPADHYAY
◦
surface-active properties. Because of the double charge
on ionic gemini surfactants, they interact [9,10] more
strongly in a mixed micelle than a singly charged con-
ventional surfactant.
(25 ± 0.1 C) was measured on an automatic conduc-
tivity meter (Systronic, New Delhi, India) with a con-
ductivity cell type CD-10 with platinum electrodes em-
bedded in glass and having cell constant of 1.00 cm
−1
.
The formation of (surfactant-reducing sugar) ag-
gregates in the case of a normal anionic surfactant,
namely, sodium lauryl sulfate (NaLS) and anionic gem-
ini surfactant, namely, sodium salt of bis(1-dodecenyl
succinamic acid) (NaBDS), and their resistance to
react with oxidant hexacyanoferrate(III) has recently
been observed [11,12]. However, both the surfactants,
that is, NaLS and NaBDS, showed an accelerating ef-
fect on the rate of oxidation of D-fructose by alkaline
chloramine-T, that is, sodium salt of N-chloro-toluene-
p-sulfonamide (CAT), which serves as an effective
oxidant in acidic, basic, or neutral medium [13,14].
To compare the catalytic effect of the two micelles on
the rate, the detail kinetics of the oxidation of fruc-
tose by alkaline chloramine-T has been investigated in
the presence of individual surfactants and also in mix-
ture of the two surfactants (i.e., NaLS + NaBDS). The
results are reported in the present communication.
Aliquots of a stock solution of surfactant at concen-
tration 10-fold the expected CMC were successively
added to 20 mL of water. A burette was used for this
purpose with an accuracy of about 5 μs on the added
aliquot. SufÞcient time was allowed between succes-
sive additions for the system to equilibrate.
Surface Tension Measurement
The surface tension of aqueous solutions of individ-
ual surfactants and mixed surfactant, that is, NaLS,
NaBDS, and NaLS + NaBDS, in the presence of
◦
alkali was measured at 25 C, using the Wilhemy
plate method [17,18] on a tensiometer (DCAT21; Data
Physics, Germany). The observed surface tension (γ )
of various surfactant solutions was plotted against
the log [surfactant]. The plot showed two straight
lines with different slopes. The CMC of the surfac-
tant was determined from the point of intersection of
two straight lines.
EXPERIMENTAL
Materials
The CMC of the NaBDS in aqueous solution (at
5 C) was determined by surface tension and con-
ductivity measurement methods and was found to be
◦
2
−
4
−3
−4
−3
0
.78 × 10 mol dm and 0.90 × 10 mol dm , re-
The chemicals used were chloramine-T (LOBA,
Mumbai, India; AR), D-fructose (Thomas Baker,
Mumbai, India; AR), NaLS (s.d. Þne, Mumbai,
India). Other reagents used—NaOH, NaClO4, and
so on—were of AR grade. NaLS was used as such.
However, its critical micelle concentration (CMC) was
determined from the plot of (surface tension) versus
spectively. The values are in close agreement with the
−4
−3
reported value of NaBDS (1.0 × 10 mol dm at
◦
2
5 C) in the literature [12,16].
Kinetic Measurement
−3
Appropriate quantities of solutions of CAT, NaOH,
log [surfactant] and was observed as 7.8 × 10 mol
3
−3
◦
and surfactant(s) were placed in a 100-cm Jena glass
dm at 25 C, which was in close agreement with the
−3
−3
◦
vessel. The requisite amount of doubly distilled wa-
ter was added so that the volume of reaction mixture
reported CMC (8.0 × 10 mol dm at 25 C) in the
literature [15].
3
was 50 cm after adding fructose solution. The re-
The synthesis and characterization of anionic gem-
ini surfactant (e.g., NaBDS) are reported by Dix [16],
and the same procedure was adopted for the synthesis
of NaBDS.
Double distilled (Þrst time from alkaline KMnO4)
deionized water was used throughout. The stock solu-
tion of chloramine-T was prepared in doubly distilled
water and stored in a dark-colored bottle. The strength
of CAT was checked iodometrically from time to time.
The aqueous solutions of fructose and surfactants were
prepared just before the experiments.
action mixture was placed in a thermostat at desired
◦
temperature ± 0.1 C, and the reaction mixture was al-
lowed to attain the bath temperature. The reaction was
then initiated by adding the requisite amount of fruc-
tose solution placed separately in the same water bath.
The progress of reaction was followed by determining
unreacted CAT iodometrically in aliquots, withdrawn
after regular time intervals. The reaction mixture was
homogeneous.
Determination of the Rate Constant
Conductivity Measurement
log [CAT]t versus time plots were always found to
be linear up to nearly 80%–85% of the reaction
and, therefore, the pseudo-Þrst-order rate constants in
The speciÞc conductivity of a series of solutions of the
surfactant (pure or mixed) at a constant temperature
International Journal of Chemical Kinetics DOI 10.1002/kin

ANTAGONISM IN MIXED MICELLE CATALYZED OXIDATION OF D-FRUCTOSE
125
chloramine-T in both the conditions, that is, in the
presence and the absence of the surfactants, have been
evaluated from slopes of these plots. The observed rate
constants were reproducible within ± 5% in replicate
kinetic runs.
reagent. The corresponding aldonic acid as the prod-
uct during oxidation of reducing sugars has also been
reported earlier [19,20].
RESULTS AND DISCUSSION
Stoichiometry and Products
The reactions were studied at different initial concen-
trations of the reactants in the absence as well as in
the presence of each surfactant. The observed pseudo-
Þrst-order rate constants in the absence of surfactant
(kw) and in the presence of surfactants (kψ)NaLS or
(kψ)NaBDS at different initial concentrations of reac-
tants are reported in Table I. The values of kw or kψ
were nearly the same at various initial [CAT], conÞrm-
ing Þrst-order dependence of the rate with respect to
CAT.
Reaction mixtures containing a known excess of [CAT]
over [fructose] were kept in the presence of NaOH and
◦
in the presence or absence of the surfactant at 40 C for
4 h. The estimation of the unreacted amount of CAT
2
showed a 1:1 stoichiometry between fructose and CAT.
The results are represented as
[
surfactant]
ꢀ
RCOCH2OH + R N · NaCl + H2O
−→
ꢀ
RCOOH + HCHO + R NH2 + NaCl
The effect of alkali was studied at a Þxed ionic
−3
strength μ = 0.2 mol dm maintained by sodium per-
ꢀ
where R and R represent CH2OH(CHOH)2− and
chlorate. The rate constant increased linearly with an
−
CH3C6H4SO2− , respectively.
increase in [fructose] or [OH ]. A plot of (observed
−
The presence of formaldehyde as one of
the products was conÞrmed by forming 2,4-
dinitrophenylhydrozone and comparing it (mp and
Co–TLC) with an authentic sample. p-Toluene sul-
rate constant) versus [OH ] or [fructose] was linear
passing through origin in each case, suggesting Þrst-
order dependence of the rate with respect to each fruc-
tose and alkali.
Addition of p-toluene sulfonamide in the reaction
mixture had no effect on the reaction rate. Addition of
sodium perchlorate in the reaction mixture resulted in a
positive effect on the reaction rate (Table II), indicating
ꢀ
fonamide (R NH2) as a product in the reaction mixture
was detected by paper chromatography, in which ben-
zyl alcohol saturated with water was used as a solvent
with 0.5% vanillin + 0.1% HCl in ethanol as a spray
◦
Table I Effect of [Reactants] on Rate Constants (kw or k ) at 35 C
ψ
−1
)
1
04 (Observed Rate Constant) (s
3
2
2
−
1
(
0 [CAT]
10 [Fructose]
10 [OH ]
mol dm 3)
−
(mol dm
−3
)
−3
(mol dm )
kw
(k )NaLS
ψ
(k )NaBDS
ψ
1.0
1.5
2.0
3.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
0.5
1.0
1.5
3.0
4.0
2.0
2.0
2.0
2.0
2.0
2.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
4.0
5.4
5.4
5.4
5.5
1.1
2.3
3.8
7.6
10.7
1.5
3.8
5.7
7.3
9.2
13.0
6.0
6.1
6.1
6.2
1.5
3.0
4.6
8.4
11.5
2.3
4.2
6.5
8.4
10.7
15.3
7.0
6.9
6.9
6.9
2.3
3.8
5.4
9.6
13.8
3.0
4.6
7.3
9.2
11.5
16.2
8.0
10.0
12.0
16.0
20.0
NaLS] = 1.4 × 10− mol dm
2
−3
.
[
[
−
4
−3
NaBDS] = 5.8 × 10 mol dm
.
−
3
Effect of alkali was studied at Þxed ionic strength μ = 0.2 mol dm maintained by NaClO
4
.
International Journal of Chemical Kinetics DOI 10.1002/kin

1
26
KAMBO AND UPADHYAY
Table II Effect of [NaClO4] on the Rate Constants at
Thus, the various oxidizing species of CAT in alkaline
◦
−
35 C
medium are RN·NaCl, RNHCl, and OCl . RNHCl is
04 (Observed Rate Constant) (s
−1
reported [21] to be a fairly strong acid (pK = 4.55) and
1
)
2
1
(
0 [NaClO4]
thus in alkaline solutions it exists in traces only. There-
−
3
mol dm
)
kw
(k )NaLS
(k )NaBDS
ψ
−
ψ
fore, in the highly alkaline medium, OCl is supposed
to be considered as the main reacting species of CAT.
Nil
5.4
5.7
8.4
6.1
6.5
9.2
6.9
7.3
10.0
−
1
2
0.0
0.0
OCl as the reactive species of CAT has been
suggested during the unanalyzed or catalyzed oxida-
tion of reducing sugars by CAT in alkaline medium
3
−3
[
CAT] = 2.0 × 10− mol dm
.
−
−
2
−3
[19,20]. To conÞrm that OCl is the reactive species
[
[
[
Fructose] = 2.0 × 10 mol dm
.
−
−2
−3
of chloramine-T, the rates of oxidation of fructose by
OH ] = 10.0 × 10 mol dm
.
NaLS] = 1.4 × 10 mol dm and [NaBDS] = 5.8 × 10−4
−
2
−3
−
chloramine-T and OCl were measured separately in
−
3
mol dm
.
alkaline medium under the similar experimental con-
ditions. Nearly the same values of kobs were obtained
when kinetic runs were made in the presence of NaOCl
involvement of similarly charged particles in the rate-
determining step.
−
or CAT, suggesting OCl is the reactive species of CAT.
On the basis of kinetic results, the mechanism for
the oxidation of fructose in absence of surfactant may
be proposed as
The rates were measured at different temperatures,
namely, 35, 40, and 45 C, and the activation param-
eters in the absence as well as in the presence of the
surfactants have been evaluated (Table III) using the
Arrhenius equation and the Eyring plots.
◦
k1
+ OH− ꢁꢀ
−
S
S
+ H2O
(i)
(
Fructose)
(enediol anion)
k
In the Absence of Surfactant
−
−
S +
OCl
−→ products (rds)
(
reacting species of CAT)
Although the oxidation of reducing sugars by alkaline
chloramine-T in the absence of surfactant or any cat-
alyst is reported [19], we have studied the reaction in
the absence of surfactant to compare the results with
those in the presence of the surfactant. The enediol an-
ion of the reducing sugar serves as the reacting species
(
ii)
On the basis of steps (i) and (ii), the rate of disappear-
ance of CAT is obtained as
d[CAT]
−
[11,19,20] of reducing sugars.
−
= kK [S][OH ][CAT]
(4)
1
dt
In aqueous solution, chloramine-T hydrolyzes
13,14] according to Eq. (1)
[
The above rate law (4) explains the experimental re-
sults, that is, the Þrst-order dependence of the rate
with respect to each fructose, alkali, and chloramine-
T. A positive salt effect, which is expected from rate-
determining step (ii), has also been observed experi-
mentally.
RN · NaCl + H2O ꢁꢀ RNH2 + NaClO (1)
−
where R = CH3C6H4SO .
2
The hydrolysis is actually more complicated and
involves different steps depending upon the medium.
In alkaline solutions, it hydrolyzes as
In the Presence of an Individual Surfactant
R · N NaCl + H2OꢁꢀRN · HCl + NaOH (2)
Similar kinetic results and nearly same value of free
energy change in a pure aqueous medium and in the
RNHCl + H2OꢁꢀRNH2 + NaClO
(3)
Table III Activation Parameters for Oxidation of Fructose in Absence and Presence of Surfactants
#
#
#
#
ꢀ
E ± 0.5
ꢀH ± 0.5
−ꢀS ± 1.0
ꢀG ± 1.0
−
1
−1
−1
−1
−1
(
kJ mol
)
log A
(kJ mol
)
(JK mol
)
(kJ mol
)
In the absence of surfactant
In the presence of NaLS
In the presence of NaBDS
65.0
57.4
53.6
7.7
6.4
5.9
62.5
54.8
51.0
97.2
120.8
132.0
92.7
92.3
92.0
International Journal of Chemical Kinetics DOI 10.1002/kin

ANTAGONISM IN MIXED MICELLE CATALYZED OXIDATION OF D-FRUCTOSE
127
presence of the surfactant indicate that the same reac-
tion mechanism is operative in both the media. Large
negative values of entropy change in the presence of
surfactant indicate that a more ordered activated com-
plex is formed in the surfactant media.
tively lower concentrations of NaBDS) in comparison
with that of NaLS. At high surfactant concentrations,
kobs, that is, kψNaLS or kψNaBDS, attained a limiting
value, and there was no increase in the observed rate
constant with a further increase in the concentration of
the surfactant(s).
The kinetic data in the presence of the individ-
ual surfactant have been rationalized in terms of the
pseudophase kinetic model proposed by Menger and
Portnoy [15]. According to this model, the variation of
the rate constant with the surfactant is generally treated
on the assumption that the substrate S is distributed
between the aqueous and micellar pseudophase as
follows:
The effect of the individual surfactant (NaLS or
NaBDS) on the rate of oxidation was studied at three
◦
temperatures, namely, 35, 40, and 45 C, over a wide
range of concentrations of the surfactants. The re-
sults are represented graphically in the form of (ob-
served rate constant) versus [surfactant] plots (Figs. 1a
and 1b). It is observed from Fig. 1 that at the lower
surfactant concentrations the rate is proportional to
ꢀ
ꢀꢀ
ꢀ
ꢀꢀ
(
k + k [surfactant]), where k and k are rate con-
stants in the absence and presence of the surfactant,
respectively. The values of kw, that is, the rate constant
in the absence of the surfactant, were matching with the
intercept of the plot of (the rate constant) versus [sur-
factant] (Figs. 1a and 1b). It was also observed that the
catalytic effect of the anionic gemini surfactant was
more pronounced (more catalytic effect at compara-
Ks
S
+
Dn
SDn
km
kw
products
products
2
2
1
1
8
4
4.0
0.0
6.0
2.0
.0
o
4
5 C
o
40 C
k
o
3
5 C
.0
0
0
1.0
2.0
3.0
4.0
5.0
6.0
2
[NaLS] 10
(a)
−
3
−3
−2
Figure 1 (a) Plot of (k )NaLS versus [NaLS] at various temperatures. [CAT] = 2.0 × 10 mol dm , [fructose] = 2.0 × 10
ψ
−3
−
−2
−3
mol dm , [OH ] = 10.0 × 10 mol dm . (b) Plot of (k )NaBDS versus [NaBDS] at various temperatures. [CAT] =
ψ
−3
−3
−2
−3
−
−2
−3
2
.0 × 10 mol dm , [fructose] = 2.0 × 10 mol dm , [OH ] = 10.0 × 10 mol dm . (Continued)
International Journal of Chemical Kinetics DOI 10.1002/kin

1
28
KAMBO AND UPADHYAY
o
4
5 C
2
2
1
1
8
4
4.0
0.0
6.0
2.0
.0
o
4
3
0 C
o
5 C
.0
0
0
4.0
8.0
12.0
16.0
20.0
24.0
4
[
NaBDS] 10 (mol dm )
(
b)
Figure 1 Continued
2
1
1
0
0
.0
.6
.2
.8
.4
o
NaLS
35 C
NaBDS
o
3
5 C
o
4
0 C
o
4
4
0 C
o
4
5 C
o
5 C
0
0
0.4
0.8
1.2
1.6
0.1
0.2
0.3
0.4
0.5
2
4
−3
−3
Figure 2 Plots of 1/(k − kw)NaLS and 1/(k − kw)NaBDS versus 1/([D] − CMC) [CAT] = 2.0 × 10 mol dm , [fructose]
ψ
ψ
2
−3
−
−2
−3
=
2.0 × 10− mol dm , [OH ] = 10.0 × 10 mol dm
.
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ANTAGONISM IN MIXED MICELLE CATALYZED OXIDATION OF D-FRUCTOSE
129
Table IV Binding Parameters Evaluated From Menger
and Portnoy Model
According to Eq. (5) a plot of 1/(k − k ) versus
ψ
w
1/([D] − CMC) should be linear with an intercept.
By using measured values of kw and kψ, the val-
ues of Ks and km can be determined with the help
of the intercept and the slope of the above linear
plot.
NaLS
NaBDS
Temperature
◦
4
−1
4
−1
(
0 C)
10 km (s
)
Ks 10 km (s
)
KS
2
2
2
35
40
45
16.5
34.0
46.7
8.2
8.0
7.5
17.9
25.6
38.4
4.0 × 10
3.8 × 10
3.3 × 10
Using data of Figs. 1a and 1b, the plots of 1/(kψ −
kw) versus 1/([D] − CMC) were drawn (Fig. 2)
and found to be fairly linear with an intercept in
each case. The values of Ks and km in the case of
each surfactant have been evaluated and are given in
Table IV.
It is observed from Table IV that the value of km
increases with the increase in the temperature. How-
ever, a decrease in Ks with an increase in temperature
was observed. On increasing the temperature, the elec-
trostatic repulsions between the anionic substrate and
anionic surfactants increases, resulting in less binding
between the substrate and surfactant and, consequently,
Ks decreases. The binding constant (Ks) in the case of
gemini surfactant (NaBDS) was much greater than that
in the case of NaLS. This is expected because of more
binding capacity of a gemini surfactant.
where kw and kψ are the observed rate constants in
aqueous and surfactant medium, respectively. km is
the rate constant in micellar medium, and Ks is the
binding/association constant of the substrate with the
surfactant.
On the basis of above model, the following relation
for the observed rate constant (kψ) has been derived
for micellar catalysis:
1
1
(km − kw)
1
=
(
kψ − kw)
+ (
(5)
km − kψ )Ks([D] − CMC)
where [D] is the surfactant concentration.
B
1
1
1
1
8
6
4
2
6.0
4.0
2.0
0.0
.0
C
D
A
.0
.0
.0
0
0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
5
[
Surfactant] 10 (mol dm )
◦
−3
−3
Figure 3 Plots of (conductivity) versus [surfactant] at 25 C in alkaline medium. NaOH = 1.0 × 10 mol dm . NaLS, A;
NaBDS, B; mixed surfactant (α = 0.275 NaLS), C; and (α = 0.385 NaLS), D.
International Journal of Chemical Kinetics DOI 10.1002/kin

1
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KAMBO AND UPADHYAY
5
5
5
4
4
3
3
8.0
4.0
0.0
6.0
2.0
8.0
4.0
A
D
C
B
0
.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
4
+ log [surfactant]
◦
Figure 4 Plots of (surface tension) versus log [surfactant] at 25 C in alkaline medium. Other conditions are the same as in
Fig. 3.
In the Presence of Mixed Surfactants
The synergism or negative synergism (antagonism)
between the two surfactants may be predicted by con-
sidering the CMC of the mixture of the surfactants
To compare the catalytic effect of individual surfac-
tant and mixture of surfactants on the rate of oxida-
tion, the rates were also measured in the presence of
mixture of surfactants (i.e., NaLS + NaBDS) at differ-
ent temperatures. The observed values of (kψ − kw) in
the case of NaLS, NaBDS, and mixture of surfactants
[23]. Furthermore, the nature and the strength of the
interactions between the two surfactants can be deter-
mined [23] by calculating the values of their interaction
parameter (β). It is reported that when CMC of the mix-
ture is larger than the CMC of either surfactant of the
mixture, the antagonism exists in the mixed micelle.
The kinetic studies have been made in alkaline
medium, and in alkaline medium the CMC of the
monomeric, the dimeric, and the mixed surfactant solu-
tions may be much lower than in pure water because the
presence of ions results in a diminution of electrostatic
repulsions between surfactant head groups at the mi-
celle surface and hence CMC decreases. Therefore, the
CMC of pure surfactants, namely, NaLS and NaBDS,
and that of mixture of surfactants, that is, NaLS +
NaBDS, has been determined in both the aqueous and
alkaline medium by conductivity (Fig. 3) and surface
tension (Fig. 4) measurements.
(
i.e., NaLS + NaBDS) at various initial concentrations
of surfactants and temperatures are reported in Table
V. It is observed from Table V that the observed value
of (kψ− kw) for a mixed surfactant was always less
than the algebraic sum of (kψ − kw) for individual sur-
factants (i.e., (kψ− kw)NaLS + (kψ − kw)NaBDS). The
results are in favor of negative synergism (antagonism)
in mixed micelle, which is due to repulsive interactions
between the two surfactants.
The repulsive interactions between different types
of anionic surfactants at the aqueous solution–air in-
terface is believed to result [22] in demixing in the
monolayer. This may be the reason for a decrease in
the catalytic effect in the case of mixed micelle in com-
parison to the algebraic sum of the catalytic effect of
two individual surfactants.
The CMC of pure surfactants, namely, NaLS and
NaBDS, and that of mixture of the surfactants, that is,
International Journal of Chemical Kinetics DOI 10.1002/kin

ANTAGONISM IN MIXED MICELLE CATALYZED OXIDATION OF D-FRUCTOSE
131
NaLS + NaBDS (at two different mole fraction (α) of
NaLS in the total surfactant in the solution phase; α =
0.275 and 0.385), has been determined and is given in
Table VI. It is observed from Table VI that the CMC
of the mixture of surfactants was larger than that of
either individual surfactant (i.e., NaLS or NaBDS). The
results conÞrm the negative synergism (antagonism) in
mixed micelles.
m
The value of β , the interaction parameters for
mixed micelle formation in an aqueous medium, has
also been calculated using following relations:
ꢀ
ꢁ
ꢀ
ꢁ
2
m
1
m
12
m
m
1
X
ln α1C /X C
1
ꢃ =
1 (6)
ꢀ
ꢁ
ꢂ
ꢀ
ꢁ
2
m
m
12
m
1
m
1
− X1 ln (1 − α1) C / 1 − X C2
and
ꢀ
ꢁ
m
m
m
1
ln α1C /X C
ꢀ
βm
=
12
1
(7)
ꢁ
2
m
1
− X1
m
1
where X is the mole fraction of surfactant 1 (NaLS) in
the total surfactant in the mixed micelle. C , C , and
C1 are the CMC for surfactant 1 (NaLS), surfactant 2
m
1
m
2
m
2
(
NaBDS), and their mixture (NaLS + NaBDS) at mole
fraction α1 (0.275 or 0.385), respectively.
m
1
Equation (6) was solved numerically for X , and
interaction parameter (β) for mixed micelles at two
values of α1 (i.e., 0.275 and 0.385) has been obtained
and is reported in Table VI.
A positive value of βm (Table VI) again indicates
an antagonism (negative synergism) in mixed micelle,
which is due to the repulsive interactions between the
m
two surfactants. The value of the β should be constant
and expected to be invariant with respect to change
in composition for a given binary surfactant mixture.
However, in the present studies a signiÞcant variation
(
an increase) in the βm value with respect to the in-
crease in the amount of NaLS is observed. This may
be due to the fact that the mixed micelle is made up
of only NaLS and NaBDS monomers. When NaLS
macromolecules penetrate into the mixed micelles then
it should certainly have a signiÞcant inßuence on the
value of interaction parameters. Such types of results in
binary mixed surfactants are reported in the literature
[24].
The authors thank the Department of Science and Technol-
ogy, New Delhi, India, for the Þnancial support of this work
under the Fast Track Scheme.
International Journal of Chemical Kinetics DOI 10.1002/kin

1
32
KAMBO AND UPADHYAY
◦
Table VI The Interaction Parameters at 25 C
m
1
m
12
−3
m
System
α (NaLS)
X
C
(mol dm
)
β
In aqueous medium (by the conductivity method)a
−
4
4
NaLS + NaBDS
NaLS + NaBDS
0.275
0.385
0.48
0.41
1.80 × 10
2.00 × 10
0.95
2.49
−
−3
−3
In alkaline medium (in the presence of 1.0 × 10 mol dm NaOH)
By the conductivity methodb
NaLS + NaBDS
−
4
4
0.275
0.385
0.45
0.37
1.00 × 10
1.20 × 10
0.31
2.05
−
NaLS + NaBDS
c
By the surface tension method
NaLS + NaBDS
−
4
4
0.275
0.385
0.41
0.34
0.90 × 10
1.10 × 10
0.35
2.44
−
NaLS + NaBDS
a
b
c
−4
−3
−4
−3
CMC of NaLS = 0.80 × 10 mol dm ; CMC of NaBDS = 0.90 × 10 mol dm
.
.
.
−4
−3
−4
−3
−3
CMC of NaLS = 0.58 × 10 mol dm ; CMC of NaBDS = 0.68 × 10 mol dm
CMC of NaLS = 0.50 × 10 mol dm ; CMC of NaBDS = 0.70 × 10 mol dm
−4
−3
−4
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International Journal of Chemical Kinetics DOI 10.1002/kin