Aqueous solutions of geminal alkylammonium surfactants as a medium for reactions of long-chain amines

Article abstract of DOI:10.1134/S1070363209010071

The formation of surfactant-hydrophobic amine mixed aggregates reduces the pK _a of long-chain amines by 1-1.5 units compared with those in molecular solutions and is an important factor responsible for the high catalytic effect of the system in

Full text of DOI:10.1134/S1070363209010071

ISSN 1070-3632, Russian Journal of General Chemistry, 2009, Vol. 79, No. 1, pp. 42–48. © Pleiades Publishing, Ltd., 2009.
Original Russian Text © A.B. Mirgorodskaya, L.A. Kudryavtseva, 2009, published in Zhurnal Obshchei Khimii, 2009, Vol. 79, No. 1, pp. 44–50.
Aqueous Solutions of Geminal Alkylammonium Surfactants
as a Medium for Reactions of Long-Chain Amines
A. B. Mirgorodskaya and L. A. Kudryavtseva
Arbuzov Institute of Organic and Physical Chemistry, Kazan Research Center, Russian Academy of Sciences,
ul. Akademika Arbuzova 8, Kazan, Tatarstan, 420088 Russia
e-mail: mirgorod@iopc.knc.ru
Received April 1, 2008
а
Abstract―The formation of surfactant–hydrophobic amine mixed aggregates reduces the рK of long-chain
amines by 1–1.5 units compared with those in molecular solutions and is an important factor responsible for the
high catalytic effect of the system in ester bond cleavage. In aqueous solution of geminal surfactants, the rate of
azomethine formation in the reaction of long-chain amines with benzaldehydes is an order-of-magnitude higher
than in ethanol.
DOI: 10.1134/S1070363209010071
An important feature of aqueous micellar solutions
of surfactants is their ability to solubilize chemically
active compounds with various hydrophilic–lipophilic
properties, which considerably extends the possibility
of using such solutions as a reaction medium [1–4].
The solubilization of reagents in surfactant solutions
affects the microenvironment (medium effect) and thus
reactivity of the reagents and their acid–base and
spectral properties, as well as other physicochemical
parameters. Another consequence of solubilization is
concentration of the reagents in a micelle, which
enhances the probability of their reaction contact (cage
effect). These two factors exert a decisive effect of the
kinetics of chemical reactions in the micellar medium,
and they are primarily controlled by the structure of
the surfactant, component ratio in the system, and
response of the latter on reagents and modifying
additives.
aggregation behavior and structural properties of
germinal surfactants have been published [9–11]. The
catalytic effect of micellar surfactant solutions in
nucleophilic substitution reactions have been reported
[12–16].
To gain insight into the feasibility of aqueous
solutions of водных растворов geminal cationic
surfactants as a medium for tractions involving
hydrophobic alkylamines, we suggested to determined
the solubility of these compounds in micellar solutions
of hexamethylenebis(cetyldimethylammonium) bromide
(
Gem-16) and hexamethylenebis(dimethyldodecylam-
monium) bromide (Gem-12) and also to assess their
effect on the basicity and nucleophilicity of amines.
Two processes involving long-chain aliphatic amines
were studied: cleavage of p-nitrophenyl esters of
carboxylic acids and formation of azomethines in
reactions with benzaldehyde. The properties of
geminal surfactants are discussed in comparison with
the behavior of analogous monomeric cationic
surfactants: dodecyltrimethylammonium and cetyltri-
methylammonium bromides.
Over the past decade there has been an outburst of
interest in germinal (dimeric) surfactants and highly
organized systems on their basis. Geminal surfactants
contain two hydrophobic radicals and two head (most
frequently, charged) groups linked by rigid or flexible
spacers. These compounds differ from their
amphiphilic analogs in that they have an order-of-
magnitude lower critical micelle concentrations
Water is an inappropriate medium for reactions
involving long-chain aliphatic amines because of the
restricted solubility of the latter. This problem is
solved in part by using cationic surfactants. The
solubilities of octyl-, decyl-, dodecyl-, and cetylamines
in water and aqueous solutions of geminal surfactants
(
CCM), high surfactant activity, viscoelastic and
wetting properties, and exhibit an unusual morphologic
behavior [5–8]. A series of papers concerning the
42

AQUEOUS SOLUTIONS OF GEMINAL ALKYLAMMONIUM SURFACTANTS
43
Gem-12 and Gem-16 and their analogs dodecyl-
trimethylammonium and cetyltrimethylammonium
bromides were determined by potentiometric titration.
The resulting data (see Fig. 1) show that the surfactants
studied all favor enhanced solubility of long-chain
amines, and, therewith, Gem-16 solutions exhibit the
highest solubilizing ability. Thus, for instance, the
solubility of decylamine in these solutions is 25 times
higher than in water and an order of magnitude higher
than in solutions of a monomeric surfactant (cetyltri-
methylammonium bromide). Amines dissolved in
micellar solutions of the cationic surfactants in study
8
7
6
5
0
0
0
0
0.5
1
0
0
0
0
0
.4
.3
.2
.1
.0
40
1
3
0
2
20
3
1
0
0
have much lower рK values than in water (Table 1).
а
The main reason for this effect consists in preferential
solubilization of the neutral form of amines with the
positively charged micelle surface. The strongest effect
8
10
12
n
on рK (1–1.5 units) is characteristic of Gem-16, in
а
agreement with the higher solubilizing ability of this
surfactant.
2
3
Importantly, it is unprotonated amines that exhibit
nucleophilic properties in chemical reactions. Thus, the
use of cationic surfactants (first of all, Gem-16)
extends the synthetic potential of amines, allowing
reactions to be performed in aqueous solutions in mild
conditions (in weakly alkaline media). This statement
can be illustrated by the nucleophilic substitution
reaction in p-nitrophenyl esters of carboxylic acids.
4
8
10
12
n
14
16
Fig. 1. Effect of the radical chain length in normal primary
aliphatic amines on their solubility in water and aqueous
solutions of cationic surfactants (сsurf 0.005 M, 25°С):
(1) Gem-16, (2) Gem-12, (3) cetyltrimethylammonium
bromide, and (4) no surfactant. Insert: Data on the
solubility of amines in micellar solutions, normalized with
respect to water (n is the number of carbon atoms in the
radical).
Scheme 1 shows two main directions of ester
cleavage in the presence of primary amines in
molecular aqueous solutions: aminolysis (main
reaction) and alkaline hydrolysis (side reaction).
be remembered that this contribution can increase with
increasing pH of the solution and decreasing fraction
of the unprotonated form of the amine. Comparison of
Scheme 1.
RC(O)NHR′ + HOC
6
H
4
NO
2
-p
the kobs = f(c ) dependences for octylamine in
surf
6 4 2
RC(O)OC H NO -p
–
–
Table 1. рK
а
of amines in aqueous micellar solutions (csurf
RC(O)O + OC
6
H
4
NO -p
2
0
.01, camine 0.005 M, 20°С)
Octyl- Decyl- Dodecyl-
amine amine amine
R, R' = C
n
2n+1
H .
Surfactant
–
a
In micellar solutions of cationic surfactants, both
reactions can be accelerated. Studying the kinetics of
ester cleavage in the presence and in the absence of
amines (at the same рН) allows separation of the
contributions of aminolysis and hydrolysis in the
overall reaction rate. The plots of the observed rate
10.6
10.1
9.8
9.4
9.3
9.2
–
Dodecyltrimethylammonumbromide 10.6
Cetyltrimethylammonium bromide
–
9
.9
8.00
8.05
8.00
Gem-12
Gem-16
10.0
9.9
constant (k ) of cleavage of p-nitrophenyl acetate (R =
obs
СН ) versus surfactant concentration are shown in
a
3
а
The рK values of dodecylamine in water and aqueous dodecyltri-
Figs. 2 and 3. As seen, alkaline hydrolysis contributes
very little in the overall reaction rate; however, it will
methylammonium bromide could be determined because of its
poor solubility in these media.
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 79 No. 1 2009

4
4
MIRGORODSKAYA, KUDRYAVTSEVA
–1
k
obs, s
–
1
k
obs, s
0
0
0
0
0
0
0
.30
.25
.20
.15
.10
.05
.00
0
0
0
0
.15
.10
.05
.00
1
2
1
2
3
5
6
4
5
6
7
3
7
, 8
4
0
.000
0.005
0.010
0
.000 0.002 0.004 0.006 0.008 0.010
с
surf, M
с
Gem-16, M
Fig. 2. Plot of the observed rate constants of p-nitrophenyl
acetate cleavage in the presence of amines and in their
absence vs. concentration of cationic surfactants (рН 10.0,
Fig. 3. Plot of the observed rate constants of the reaction of
carboxylic esters with amines vs. surfactant concentration
(сamine 0.0025 M, рН 9.2, 25°С). p-Nitrophenyl acetate,
Gem-16: (1) dodecylamine, (2) decylamine, (3) octyl-
amine, (4) no amine. p-Nitrophenyl laurate, Gem-16:
(5) dodecylamine, (6) decylamine, (7) p-nitrophenyl
laurate, cetyltrimethylammonium bromide, decylamine.
25°С). At саmine 0.0025 M: (1) decylamine, Gem-16; (3) octyl-
amine, Gem-16; (4) octylamine, Gem-12; (5) octylamine,
cetyltrimethylammonium bromide; and (6) octylamine,
dodecyltrimethylammonium bromide. At сamine 0.004 M:
(
1
2) octylamine, Gem-16. In the absence of amine: (7) Gem-
2 and (8) Gem-16.
different micellar solutions shows that the geminal
surfactants studied exhibit a strong catalytic effect in
ester cleavage reactions, and this effect reveals itself at
lower concentrations than in the case of monomeric
analogs. The fraction of the neutral form (α) depends
acetate (Fig. 2, plots 1 and 2). Previously we showed
by self-diffusion NMR and spin-probe ESR [17, 18]
that decylamine and its higher homologs prone to self-
association form with monomeric cationic surfactants
mixed aggregates in which the amine exhibits
enhanced nucleophilicity , for example, in cleavage of
p-nitrophenyl acetate [19, 20]. Probably, alkylam-
monium geminal surfactants, too, tend to form such
associates, which is responsible for the enhanced
catalytic effect of Gem-16 in p-nitrophenyl acetate
aminolysis in going from octylamine to decylamine
and further to dodecylamine (Fig. 3).
on the рK of the amine and the рН of the medium and
а
+
can be calculated from the equation α = K /(K + [H ]).
а
а
At pН 10.0 in aqueous Gem-16, the fractions of
octylamine and decylamine are about 0.56 and 0.86,
respectively. The higher content of the neutral form is
one of the reasons for the higher activity of decylamine
compared to octylamine (Fig. 2). Correct reactivity
comparisons are possible only at equal concentrations
of the neutral forms. This is the case when the
concentration of decylamine is 0.0025 M and that of
octylamine is 0.004 M: The concentrations of the
unprotonated forms of these amines in an aqueous
solution of Gem-16 at рН 10.0 with be the same
The data presented in Fig. 2 were analyzed in terms
of the pseudophase model of micellar catalysis. To this
end, we made use of Eq. (1) that relates kobs to reaction
parameters in the micellar phase [2].
k
m
K
s
с
surf + k
0
(
0.002 M). However, in such conditions, too,
kobs
=
.
(1)
1
+ Kbind
с
surf
decyalmine is more reactive toward p-nitrophenyl
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 79 No. 1 2009

AQUEOUS SOLUTIONS OF GEMINAL ALKYLAMMONIUM SURFACTANTS
45
Here сsurf is the surfactant concentration corrected for
the critical micelle concentration (CCM); k and k ,
rate constants in the aqueous and micellar phases,
respectively; and Kbind, binding constant of the
substrate.
(Table 2). The inhibition of the reaction with p-
nitrophenyl laurate with decylamine with micelles of
cationic surfactants, including geminal, is in conflict
with the observation that these systems are
characterized by increased contents of the neutral
forms of amines. A probable reason for the inhibition
consists in the formation of mixed aggregates between
p-nitrophenyl laurate and long-chain amines in the
absence of surfactants [20]; the rate of aminolysis in
such aggregates is very high. Addition of a surfactant
in such system results in a rearrangement of micelles
and formation of new mixed aggregates. The neutral
decylamine and substrate molecules comprised in these
aggregates can be separated or unfavorably oriented;
as a result, their reaction can be hindered. Thus,
cationic surfactants exhibit substrate specificity in
aminolysis of carboxylic esters, and this specificity is
more pronounced in the case of geminal surfactants
compared to their monomeric analogs.
0
m
It follows from the resulting data (Table 2) that
addition of a long-chain amine to a cationic surfactant
adversely affects substrate– micelle binding. In the
absence of amines, the binding constants of p-nitro-
phenyl acetate with cetyltrimethylammonium and
–
1
Gem-16 are 450 and 2000 l mol , respectively [15]
and in the presence of amines these values decrease
about two times. Nevertheless, the rate of ester
cleavage increases by an order of magnitude and more
(Table 2). The reason for the observed acceleration is a
shift of the рK of the amine (i.e. increase of the
а
fraction of the neural form) and the ability of the amine
to form mixed functionalized aggregates with cationic
surfactants.
We also studied the reaction of long-chain aliphatic
amines with benzaldehyde in aqueous solutions of
geminal surfactants (Scheme 2).
Unlike what is observed with aminolysis of p-
nitrophenyl acetate in the system Gem-16–decylamine
or dodecylamine), the reaction with p-nitrophenyl
(
laurate (R = С Н ) under the same conditions is
1
1
23
Scheme 2.
inhibited (Fig. 3, descending curves). We already faced
the same effect with hydrophobic esters in the case of
monomeric cationic surfactants [18]. As seen from the
kinetic data in Fig. 3, the rate constant of p-nitrophenyl
laurate in the Gem-16–decylamine system is lower
about 7 times compared with aqueous solutions,
whereas with p-nitrophenyl acetate accelera-tion of
about 50 times is observed. In the cetyltrimethyl-
ammonium bromide–decylamine under the same condi-
tions, aminolysis of the acetate accelerates 40 times
and aminolysis of the laurate decelerates 5 times
H C=O
H C=NR
+ RNH2
+ H O
2
This reaction gives rise to azomethine compounds
(Schiff bases) and it forms the basis of the analytical
determination of primary amines in mixtures of amines
with various substitution degrees, as well as of
benzaldehyde. Long-chain amines are used for
Table 2. Parameters of the micelle-catalyzed cleavage of p-nitorphenyl acetate in aqueous solutions of various surfactants in
the presence of long-chain primary amines (сamine 0.0025 M, 25°С)
–
1
–1
–1
Surfactant
Amine
рН
k
0
, s
k
m
, s
K
s
, l mol
CCM, M
0.0005
0.0006
0.0003
0.00002
0.0002
0.00064
k
m
/k
0
Octylamine
Gem-12
10.0
0.009
0.009
0.002
0.013
0.003
0.0035
0.09
0.09
0.028
0.36
0.16
0.22
400
9
Cetyltrimethylammonium bromide
Octylamine
Octylamine
Decylamine
Decylamine
Dodecylamine
1
0.0
9.2
200
10
14
28
53
62
Gem-16
Gem-16
Gem-16
Gem-16
430
10.0
9.2
650
700
9.2
660
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4
6
MIRGORODSKAYA, KUDRYAVTSEVA
–
1
(
in ethanol, 0.00031 s ). The conversion rates of
1
00
octyl-, decyl, and dodecylamine in the presence of
Gem-16 are almost equal to each other and remain
practically invariable as the surfactant concentration is
varied from 0.0025 to 0.02 M. Such an activity
leveling is probably associated with the fact that ionic
surfactants exert the greatest impact on ionic and ion-
molecular processes, whereas the reaction in focus
involves neutral molecules.
1
8
6
4
2
0
0
0
0
2
3
4
It is known that benzaldehyde in alkaline media
tends to disproportionate to form an alcohol and acid,
and it is also readily oxidized in air [22]. Benzoic acid
that is formed in both cases can bind amines in the
reaction in focus and thus decrease the yield of
azomethines.
0
2
4
6
8
10
t, min
Fig. 4. Variation of the content of free amine on its reaction
with benzaldehyde in alcoholic and aqueous micellar media
(сsurf 0.005 M, 25°С): (1) decylamine in ethanol, (2) decyl-
amine in aqueous cetyltrimethylammonium bromide, (3) de-
cylamine in Gem-16, and (4) octylamine in aqueous Gem-16.
To find out what is the contribution of these side
reactions, we performed additional experiments. The
contribution of benzaldehyde disproportionation in
aqueous surfactants solutions was estimated in a
system that contained a tertiary amine instead of
primary. We used dimethyloctylamine and benzyldi-
methylamine, since their рK are close to the рK of
decylamine, and they create a weakly alkaline medium
in aqueous micellar solutions (рН ~10). Potentiometric
titration showed that the conversion of decylamine
after 10-min reaction is more than 90%, whereas those
of the above tertiary amines (due to reaction with
benzoic acid) are lower than 5%, which allows the
disproportionation reaction to be neglected in discus-
sing the results.
manufacturing impregnated resins which, in their turn,
are used to clean up waste waters and industrial vapors
from benzaldehyde [21].
а
а
The formation of azomethine compounds is a
reversible reaction, and it is generally performed in
nonaqueous solvents (alcohols) [22]. An exception is
Schiff bases derived from aniline. These compounds
are sufficiently stable in water. Some examples of their
preparation in aqueous micellar solutions have been
reported [23, 24]. We tried to react long-chain amines
with benzaldehyde in aqueous solutions of Gem-16,
Gem-12, and cetyltrimethylammonium bromide. It was
suggested that the poor solubility of the reagents in
water will result in that their reaction will occur in the
micellar pseudophase. The resulting azomethine
compounds are also hydrophobic and will stay in the
micellar phase, thus preventing hydrolysis.
To avoid oxidation of benzaldehyde, we prepared
micellar solutions with a freshly prepared benzal-
dehyde. The reactions with amines were performed
with a solution of benzaldehyde, that contained no
more than 3% of benzoic acid which was preliminarily
neutralized with alkali. Thus, under our experimental
conditions, the main reaction products of benzaldehyde
with long-chain amines are azomethine compounds.
The reaction progress was followed by monitoring
the concentration of free amine in the reaction medium
by means of potentiometric titration. For the sake of
comparison, the reactions were performed not only in
aqueous micellar solutions of cationic surfactants, but
also in ethanol which is frequently used in azomethine
synthesis. As seen from Fig. 4, the conversion rate of
amines in alcohol is much lower than in micellar
solutions. Geminal surfactants are slightly more
efficient than monomeric analogs. For example, the
observed rate constants of the reaction of decylamine
with benzaldehyde at 25°С in Gem-16 solutions in
The use of alkylammonium surfactants offers an
undeniable advantage of providing the possibility of
preparing azomethine compounds in aqueous media.
The solubilization of the starting reagents and reaction
products in a micelle completely shift the equilibrium
reaction (Scheme 2) to the right. Note that complete
conversion of hydrophilic amines in this reaction is
almost impossible to reach, since the reaction will
partially occur in the aqueous phase, and the
equilibrium will be shifted to the starting compounds.
The high solubilizing activity of Gem-16 with respect
–1
–1
0
.0069 s , in Gem-12 solutions, 0.0041 s , and
–1
cetyltrimethylammonium bromide solutions, 0.0038 s
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 79 No. 1 2009

AQUEOUS SOLUTIONS OF GEMINAL ALKYLAMMONIUM SURFACTANTS
47
to long-chain amines and benzaldehyde allows one to
REFERENCES
deal with high reagent concentrations, which opens up
possibilities for the reaction in focus to find not only
analytical, but also synthetic applications.
1
2
3
. Micellization, Solubilization and Microemulsions,
Mittel, K.L., Ed., New York: Plenum, 1978.
. Bunton, S.A. and Savelli, G., Adv. Phys. Chem., 1986,
vol. 22, p. 213.
EXPERIMENTAL
. Dwars, T., Paetzold, E., and Oehme, G., Angew. Chem.
Int. Ed., 2005, vol. 44, p. 7174.
Commercial
dodecyltrimethylammonium
and
cetyltrimethylammonium bromides (Sigma), long-
chain normal aliphatic amines (Acros Organics), and
p-nitrophenyl acetate and p-nitrophenyl laurate (Fluka)
with main substance contents of 99% were used.
Benzaldehyde (Acros Organics) was distilled im-
mediately before use (bp 178–179°C). The quantity of
benzoic acid appearing in solutions on standing was
controlled by titration with alkali. Geminal surfactants
were synthesized by reactions of N,N'-tetrasubstituted
hexamethylenediamine with alkyl bromides in acetone
followed by double recrystallization from ethanol [16].
4
. Zakharova, L.Ya., Mirgorodskaya, A.B., Zhil`tsova, E.P.,
Kudryavtseva, L.A., and Konovalov, A.I., Izv. Ross.
Akad. Nauk, Ser. Khim., 2004, no. 7, p. 1331.
5
. Menger, F.M. and Keiper, J.S., Angew. Chem., 2000,
vol. 112, p. 1980.
6
. Hait, S.K. and Moulik, S.P., Current Sci., 2002, vol. 82,
no. 10, p.1101.
7. Groth, C., Nyden, M., Holmberg, R., Kanicky, J.R., and
Shah, D.O., J. Surf. Deterg., 2004, vol. 7, no. 3, p. 247.
8
9
. Zana, R., J. Colloid Interface Sci., 2002, vol. 248, no. 2,
p. 203.
The рK values of amines were determined by poten-
а
. Aswal, V.K., De, S., Goyal, P.S., Bhattacharya, S., and
Heenan, R.K., Phys. Rev. E, 1998, vol. 57, no. 1, p. 776.
tiometric titration of their solutions with 0.1 N HCl
using a рН-340 device. The surfactant concentration
was measured in the range 0–0.02 M. In solubilization
studies, amines were added in small portions to
vigorously shaken and thermostated micellar surfactant
solutions until the system got visually inhomogeneous.
Aliquots were then taken and titrated with HCl to
determine the concentration of amine in the solution.
10. Siddiqui, U.S., Ghosh, G., and Kabir-ud-Din, Langmuir,
2006, vol. 22, no. 24, p. 9874.
11. Borse, M.S. and Devi, S., Adv. Colloid Interface Sci.,
006, vols. 123–126, p. 387.
2
1
2. Bhattacharya, S. and Kumar, V.P., J. Org. Chem., 2004,
vol. 69, no. 2, p. 559.
Reaction kinetics were studied in freshly prepared
micellar solutions under pseudofirst-order reaction
conditions. Ester cleavage was studied by spectro-
photometry on a Specord UV–Vis instrument at 25°С.
Reaction progress was followed by measuring the
optical density of solutions at 400 nm (formation of the
p-nitrophenolate anion). Initial substrate concentration
13. Bhattacharya, S. and Kumar, V.P., Langmuir, 2005, vol. 21,
no. 1, p. 71.
1
4. Geng, Y., Romsted, L. S., and Menger, F., J. Am. Chem.
Soc., 2006, vol. 128, no. 2, p. 492.
15. Mirgorodskaya, A.B., Kudryavtseva, L.A., Pankratov, V.A.,
Lukashenko, S.S., Rizvanova, L.Z., and Konovalov, A.I.,
Zh. Obshch. Khim., 2006, vol. 76, no. 10, p. 1696.
–5
5
×10 M, conversion > 90%.
1
1
6. Sekhon, B.S., Resonance, 2004, no. 3, p. 42.
Azomethine formation was followed by the
7. Mirgorodskaya, A.B., Kudryavtseva, L.A., Zuev, Yu.F.,
Arkhipov, V.P., Idiyatullin, Z.Sh., and Kudryavtsev, D.B.,
Izv. Akad. Nauk., Ser. Khim., 2000, no. 2, p. 267.
concentration of amine in the reaction medium,
measured by potentiometric titration. Initial concentra-
tion of amine and aldehyde 0.005 and 0.05 M, respect-
tively. The titrant was 0.02 N aqueous HCl. The
1
8. Mirgorodskaya, A.B., Kudryavtseva, L.A., Zuev, Yu.F.,
and Vylegzhanina, N.N., Zh. Fiz. Khim., 2002, vol. 76,
no. 11, p. 2049.
observed pseudofirst-order constants (k ) were deter-
obs
mined by the equation log (c – c ) = –0.434k t +
∞
t
obs
const, where c и c are the concentrations of the
19. Mirgorodskaya, A.B., Kudryavtseva, L.A., Zakharo-
va, L.Ya., and Bel’skii, V.E., Izv. Ross. Akad. Nauk, Ser.
Khim., 1998, no. 7, p. 1333.
t
∞
reaction product at time t and after reaction comple-
tion. The kobs values were calculated by the least-
squares method. Reported are the mean kobs values
obtained from two parallel runs and differing from
each other by no more than 4%.
20. Mirgorodskaya, A.B., Kudryavtseva, L. A., and Iva-
nov, B.E., Izv. Ross. Akad. Nauk, Ser. Khim., 1996, no. 2,
p. 366.
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 79 No. 1 2009

4
2
8
MIRGORODSKAYA, KUDRYAVTSEVA
1. Babic, K., van der Ham, L., and de Haan, A., React.
Funct. Polym., 2006, vol. 66, no. 12, p. 1494.
Chemistry), Moscow: Nauka, 1970.
23. Doronin, S.Yu., Chernova, R.K., and Gusakova, N.N.,
Zh. Anal. Khim., 2005, vol. 60, no. 5, p. 471.
2
2. Nesmeyanov, A.N. and Nesmeyanov, N.A., Nachala
organicheskoi khimii (Fundamentals of Organic
24. Chernova, R.K., Doronin, S.Yu., and Myznikova, I.V.,
Khim. Tekhnol., 2005, vol. 48, no. 6, p. 113.
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