Comparative study of nitroso group transfer in colloidal aggregates: Micelles, vesicles and microemulsions

Article abstract of DOI:10.1039/b209539d

A kinetic study was carried out on nitroso group transfer from N-methyl-N-nitroso-p-toluenesulfonamide (MNTS) to different secondary amines: morpholine (MOR), piperazine (PIP), dimethylamine (DMA) and piperidine (PIPER) in micelles of dodecyltrimethylammonium bromide (LTABr) and in vesicles of dioxadecyltrimethylammonium chloride (DODAC). Amine nucleophiles were chosen on the basis of their hydrophobicity and basicity. The observed rate constant, k_obs, shows opposite behavior in micelles and vesicular systems. k_obs for micelle systems decreases as the surfactant concentration increases. This behavior can be interpreted according to the distribution of the reagents among the different pseudophases of the system and the physicochemical properties of the latter. It has been observed that the product of the rate constant in the micellar pseudophase and the distribution constant of the amine, k₂^mK_m^R2NH, retains a sequence similar to the reactivity observed in water. The differences observed can be explained on the basis of the different hydrophobicity of the amines and consequently different values of K_m^R2NH. In all cases a catalytic effect on the addition of vesicles was observed reaching a limiting value of k_obs. The kinetic behavior can be explained quantitatively on the basis of a single pseudophase model, k₂^vK_v^R2NH in the vesicular systems of DODAC displays a variation which is analogous with the micellar systems but approximately 35 times greater, which in turn indicates the greater hydrophobic character of the vesicles of DODAC by comparison with the micelles of LTABr. In AOT/isooctane/water microemulsions we have found similar behavior where the product is approximately 22 times lower than in vesicles, indicating that the polarity of the interface of the microemulsions is greater than that of the micelles of LTABr and smaller than that of DODAC vesicles. The comparative analysis of the reactivities in the interface of the microemulsion and in an aqueous medium shows that the reactive position in the interface changes as the hydrophobic character of the amine varies.

Full text of DOI:10.1039/b209539d

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Comparative study of nitroso group transfer in colloidal aggregates:
micelles, vesicles and microemulsions
a
L. Garc ´ı a-R ´ı o,* P. Herv e´ s, J. C. Mejuto, J. P e´ rez-Juste and P. Rodr ´ı guez-Dafonte
b
b
b
b
a
Departamento de Qu ı´ mica F ı´ sica, Facultad de Qu ı´ mica, Universidad de Santiago de
Compostela, 15782, Santiago, Spain
Departamento de Qu ı´ mica F ı´ sica, Facultad de Ciencias, Universidad de Vigo, Spain
b
Received (in London, UK) 30th September 2002, Accepted 15th November 2002
First published as an Advance Article on the web 19th December 2002
A kinetic study was carried out on nitroso group transfer from N-methyl-N-nitroso-p-toluenesulfonamide
MNTS) to different secondary amines: morpholine (MOR), piperazine (PIP), dimethylamine (DMA) and
(
piperidine (PIPER) in micelles of dodecyltrimethylammonium bromide (LTABr) and in vesicles of
dioxadecyltrimethylammonium chloride (DODAC). Amine nucleophiles were chosen on the basis of their
hydrophobicity and basicity. The observed rate constant, kobs , shows opposite behavior in micelles and
vesicular systems. kobs for micelle systems decreases as the surfactant concentration increases. This behavior can
be interpreted according to the distribution of the reagents among the different pseudophases of the system and
the physicochemical properties of the latter. It has been observed that the product of the rate constant in the
m
2
R NH
micellar pseudophase and the distribution constant of the amine, k
the reactivity observed in water. The differences observed can be explained on the basis of the different
2
K
m
, retains a sequence similar to
2
R NH
hydrophobicity of the amines and consequently different values of K
addition of vesicles was observed reaching a limiting value of kobs . The kinetic behavior can be explained
m
. In all cases a catalytic effect on the
v
2
2
R NH
quantitatively on the basis of a single pseudophase model. k K
in the vesicular systems of DODAC
v
displays a variation which is analogous with the micellar systems but approximately 35 times greater, which in
turn indicates the greater hydrophobic character of the vesicles of DODAC by comparison with the micelles of
LTABr. In AOT/isooctane/water microemulsions we have found similar behavior where the product is
approximately 22 times lower than in vesicles, indicating that the polarity of the interface of the microemulsions
is greater than that of the micelles of LTABr and smaller than that of DODAC vesicles. The comparative
analysis of the reactivities in the interface of the microemulsion and in an aqueous medium shows that the
reactive position in the interface changes as the hydrophobic character of the amine varies.
ability of micelles to take up all kinds of molecules. The bind-
Introduction
ing is generally driven by hydrophobic and electrostatic inter-
actions. The take-up of solutes from the aqueous medium into
the micelle is close to diffusion controlled, whereas the resi-
dence time depends on the structure of the surfactant molecule
Surfactants, or amphiphiles, are surface-active nonionic mole-
cules or organic salts which, either alone or in combination with
a wide variety of other ionic and nonionic solutes, aggregate
spontaneously and with a high degree of cooperativity in solu-
tion to form a variety of assemblies (or association colloids)
whose structures depend both on the solution composition and
ꢀ4
ꢀ6
8
and the solubilizate and is often of the order of 10 –10 s.
Solubilization is usually treated in terms of a pseudophase
model in which the bulk aqueous phase is regarded as one
phase and the micellar pseudophase as another. The time-aver-
aged location of different solubilizates in or at a micelle has
1,2
on the structures of the components, primarily the surfactant.
Micelles are highly dynamic, often polydisperse aggregates
3
formed from single-chain surfactants beyond the critical
9
been a topic of contention. Apart from saturated hydrocar-
bons, there is usually a preference for binding in the interfacial
micelle concentration, cmc. Micellization is primarily driven
by bulk hydrophobic interactions between the alkyl chains of
the surfactant monomers and usually results from a favorable
1
0
region, that is, at the surface of the micelle. Such binding
locations offer possibilities for hydrophobic interactions and
avoid unfavorable disturbances of the interactions between
the alkyl groups of the surfactant molecules in the core of
the aggregate. The preferential binding of aromatic molecules
at the micellar surface has been explained at least in part by the
ability of the p-system of the molecule to form a weak hydro-
4
entropy change. The overall Gibbs energy of the aggregate for
ionic surfactants is a compromise of a complex set of interac-
5
tions, with major contributions from headgroup repulsions
and counterion binding. It has long been known that aqueous
micelles can influence chemical reaction rates and equilibria.
Early studies of micellar effects on reaction rates and equilibria
1
1
gen bond with water.
Surfactant vesicles, like the systems based on spherical dou-
ble layers, constitute a rather more realistic model of biological
1
b,6
are described in extensive monographs.
Much of the
impetus for the study of reactions in micelles is that they
model, to a limited extent, reactions in biological assemblies,
and the term ‘‘biomimetic chemistry’’ has been coined to
describe this general area of study.
1
2
membranes than closed single-layer surfaces. In fact, vesicles
(or liposomes) have the bilayer structure of biological mem-
branes and they have been proposed as possible precellular
1
3
Micellar catalysis of organic reactions has been extensively
studied. This type of catalysis is critically determined by the
systems. Vesicles share the ability of micelles to accelerate
certain chemical reactions by trapping and concentrating the
7
3
72
New J. Chem., 2003, 27, 372–380
DOI: 10.1039/b209539d
This journal is # The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2003

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6
a,d
reagents.
gates and they can be obtained by different preparation meth-
Vesicles are thermodynamic metastable aggre-
1
4
ods. The most widely used choices in this respect are
sonication and ethanol injection methods, which yield small
vesicles (diameter approximately in the range 30–50 nm).
Also extrusion methods are used for the production of large
unilamellar vesicles. Salt concentration and pH significantly
control the degree of vesicle packing and hence vesicle size.
Vesicles formed by sonicating dialkylmethylammonium salts
are stable over the range pH 1–13.
The vesicles can inhibit chemical reactions encapsulating
one of the reagents in the internal compartment, or can cat-
alyze reactions concentrating the reagents in the water–bilayer
interface, acting as microreactors.
the vesicles is greater than that of the micelles, and depends
on the size of the aggregate, which is greater for the small vesi-
cles prepared by sonication than for the large vesicles prepared
by chloroform injection. The reason for this influence of the
size of the vesicle on its catalytic activity is fundamentally that
the degree of dissociation of the counterion of the vesicle
1
5
1
6
1
7
1
8
1
9
1
9,20
The catalytic capacity of
2
1
Scheme 1
2
2
piperazine (PIP), dimethylamine (DMA) and piperidine
PIPER) were chosen on the basis of their hydrophobicity,
(
29a
1
5b,21b
basicity and reactivity in water against the nitroso group.
Given that this reaction had already been studied previously
in our laboratory in microemulsions of AOT/isooctane/water
all we need do is reanalyze the results obtained to make them
compatible with the distribution constants and reactivity
constants obtained in the micellar systems.
The aim of the study will be to compare the sequences of
reactivity observed in different colloidal systems. In this way
we can obtain information about the specific properties pre-
sented by the interfaces of these three colloidal aggregates.
The results obtained have shown parallel behavior in the differ-
ent colloidal media studied.
2
2
and its capacity to solubilize reagents are affected by the size
of the aggregate. In addition an adequate selection of the vesi-
cular surfactant and the reagents enables us to find different
1
9,23
reactivities in the internal and external interface,
observing
in these cases biphasic kinetic behavior in which the permea-
tion through the bilayer of one of the reagents is the determin-
ing stage of the reaction.
The influence of microemulsions on chemical reactivity has
been studied to a lesser extent, mainly in those cases in which
the reagents can be distributed throughout the different pseu-
dophases of the system. In our laboratory we have developed
a kinetic model based on the formalism of the pseudophase
which has been applied satisfactorily to nitroso group transfer
2
4,25
in microemulsions of AOT/isooctane/water.
Experimental
In the literature there exist doubts about the existence of a
parallelism between the behavior observed in micelles and in
microemulsions. The results obtained on studying the forma-
tion of 5-hexadecyl-7-methylindazole from 2,6-dimethyl-4-
hexadecylbenzenediazonium tetrafluoroborate indicate that the
interfacial basicity of cationic microemulsions is less than that
which corresponds with the micellar systems of the same sign,
considering that this property is due to the high concentration
of counterions present in the interfacial zone in the microemul-
All reagents were Merck or Sigma-Aldrich products of the
maximum commercially available purity. Amines (Aldrich)
were purified by distillation under an argon atmosphere prior
to use. DODAC (Fluka) was used as supplied. All aqueous
solutions were prepared by weight using double-distilled water.
ꢁ
Reaction kinetics were recorded at 25 C in a MILTON
ROY SPECTRONIC 3000 diode array spectrophotometer
equipped with thermostated cell carriers. The disappearance
of the absorbance at 270 nm due to MNTS consumption
was followed. The MNTS concentration (approximately
2
6
sions. In the same way the studies carried out on micellar and
vesicular systems indicate that the vesicular interface has a
2
7
ꢀ5
more hydrophobic character. However this greater hydro-
phobic character does not always constitute a greater catalytic
or inhibiting efficiency in these systems when they are com-
4 ꢂ 10 M) was always very much lower than the concentra-
tion of amine (0.1 M). The kinetic data always fitted the first-
order integrated rate equation satisfactorily (r > 0.999), eqn.
1; in what follows, kobs denotes the pseudo first order rate con-
stant. For the reactions in vesicles, reagents were always added
to the reaction cell in the same order: first the presonicated
DODAC, followed by the solution providing MNTS, and
finally the amine.
2
8
pared with the micellar aggregates. Engberts and Rispens
observed greater catalytic efficiency for Diels–Alder reactions
when micelles of Cu(DS) were used than when vesicles of
2
Cu(dDP) were used. However the catalysis was observed for
2
metallovesicles at lower concentrations than for metallomi-
celles, which is due to the lower critical vesicular concentration
of Cu(dDP) in comparison with the critical micellar concen-
2
tration of Cu(DS) . As a result, hydrophobic microdomains
2
lnðAt ꢀ A1Þ ¼ lnðAo ꢀ A1Þ ꢀ kobst
ð1Þ
1
8
DODAC vesicles were prepared by sonication. Typically,
70–90 mg of solid DODAC were dispersed in 12–15 mL of
are present at lower concentrations, to which both the diene
and the dienophile can bind efficiently.
ꢁ
water, sonicated for 25 min at 53–60 C with a Branson 250
This article presents a comparative study of the reactivity in
strongly differentiated three colloidal media: dodecyltrimethyl-
ammonium bromide micelles, microemulsions of sodium bis(2-
ethylhexyl)sulfosuccinate (AOT)/isooctane/water and vesicles
of dioctadecyldimethylammonium chloride (DODAC). For
this study we have used a reaction of which we have wide
experience, the nitroso group transfer from N-methyl-N-
nitroso-p-toluenesulfonamide (MNTS) to secondary amines
sonicator, centrifuged, and passed through a 0.45 mm filter to
remove tip debris. Since the age of the vesicle preparations
was found to affect the observed reaction kinetics, all reactions
were carried out in vesicular media prepared within the preced-
ing 6 hours. The effect of the age of the vesicle on kinetics is
attributed to a gradual increase in the average size and polydis-
persity of the vesicle populations, a process which is acceler-
3
3
ated by the presence of salts.
The size and shape of vesicles depends on the duration of
sonication and the temperature at which it is carried out. Tur-
(
in an aqueous medium, a micellar medium, in non-aqueous
Scheme 1). This reaction has been studied in our laboratory
2
9
30
3
1
ꢁ
solvents
water.
and in microemulsions of AOT/isooctane/
The amines used, namely: morpholine (MOR),
bidity measurements have shown that below 36 C the
DODAC double layer forms a continuous macroscopic sheet
2
4,25,32
New J. Chem., 2003, 27, 372–380
373

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at the surface of the aqueous medium rather than a dispersion
3
4
of vesicles. Sonication at higher temperatures gives rise to
multicompartment vesicles which, if sonication is continued,
split into smaller single-compartment vesicles. We character-
ꢁ
ized our preparations at 25 C by performing dynamic light
ꢁ
ꢁ
scattering measurements at scattering angles of 90 and 120
+
using Ar laser irradiation (l ¼ 514.5 nm) and an ALV-5000
digital correlator. Correlation functions fitted by the CONTIN
and cumulant methods afforded hydrodynamic radius values
3
5
˚
of 200 A at 90 and 120 and polydispersity values of 0.1–0.2;
these values are in keeping with those reported by Fendler
for single-compartment vesicles.
Turbidity measurements were carried out at 25 C in a
MILTON ROY SPECTRONIC 3000 diode array spectro-
photometer equipped with thermostated cell carriers. The
turbidity was monitored as a function of time following the
changes in absorbance at l ¼ 400 nm.
ꢁ
ꢁ
2
0d
Scheme 2
ꢁ
of the amine, R
through the distribution constant K
2
NH, between both pseudophases is considered
2
R NH
m
. The different reac-
tivities in the aqueous and micellar pseudophases have been
taken into account through the corresponding second order
w
2
m
2
w
2
rate constants: k
and k
. The values of k
have been
obtained by studying the reaction in the absence of the surfac-
tant and are compatible with those obtained previously in the
presence of different quantities of organic cosolvent (acetoni-
trile or dioxane).
The amine concentration in the micellar pseudophase has
been defined as the local, molar concentration within the
Results and discussion
2
9a
Nitroso group transfer in LTABr micelles
We studied the nitrosation reaction of various aliphatic
amines: morpholine (MOR), piperazine (PIP), dimethylamine
¯ ¯
/[D ]V, where V
micellar pseudophase: [R
2
NH]
is the molar volume in dm mol of the reaction region and
m
¼ [R
2
NH]
m n
3
ꢀ1
(
DMA) and piperidine (PIPER), by N-methyl-N-nitroso-p-
¯
n
[D ]V denotes the micellar fractional volume in which the reac-
toluenesulfonamide (MNTS) in the presence of micelles of
LTABr (0–0.25 M) keeping constant the total amine concen-
¯
tion occurs. We assume V is equal to the partial molar volume
of the interfacial reaction region in the micellar pseudophase,
tration ([R
2
NH] ꢃ 0.25 M). The addition of the surfactant in
3
7
3
ꢀ1
determined by Bunton as 0.14 dm mol . Micellar binding
of both substrates, MNTS and R NH, is governed by hydro-
phobic interactions, and the equilibrium constants K
concentrations which are higher than its critical micellar con-
centration gives rise to an inhibition of the reaction (see
Fig. 1). The influence of cationic micelles on the reaction rate
can be quantitatively analyzed according to the model of the
micellar pseudophase.
cationic micelles does not change the base ionization equilibria
2
MNTS
m
2
R NH
and K
m
are expressed by referring these concentrations
6
,36
to the total volume of the reaction mixture. The expression
for the observed rate constant, kobs , based on Scheme 1 and
on the above considerations, is given by the following equa-
tion.
We assume that the presence of
3
0c
of the amine in water as we have done previously. Under
these experimental conditions, Scheme 2 can be proposed.
In this scheme subscripts w and m indicate aqueous and
m
k
w
2
MNTS R2NH
m
k þ
2
K
K
m
½Dnꢄ
micellar pseudophases, respectively, and D
n
represents the
ꢀ
V
MNTS
kobs ¼
½R2NHꢄT
ð2Þ
micellized surfactant, that is [D ] ¼ [D ] ꢀ cmc, where [D ] is
R2NH
n
T
T
ð1 þ Km
½DnꢄÞð1 þ Km
½DnꢄÞ
the stoichiometric surfactant concentration and cmc the
critical micelle concentration, obtained under the experi-
mental conditions as the minimum surfactant concentration
required to observe any kinetic effect (typical values being
Second order rate constants at the micellar interface and
association constants of the neutral form of the amine to
LTABr micelles were obtained by fitting eqn. 2 to the experi-
mental data.
Fig. 2 shows the correspondence of the experimental data
to the rate equation rewritten in the following form for the
ꢀ
3
(
8–15) ꢂ 10 M).
Scheme 2 considers the distribution of MNTS between the
MNTS
aqueous and micellar pseudophases, K
m
. This association
constant has been previously obtained from studies of acid and
3
basic hydrolysis of MNTS in micellar systems with a value
0b
MNTS
ꢀ1
of Km
¼ 132 M . The distribution of the neutral form
Fig. 2 Fitting of experimental data for nitrosation of piperidine (X,
[PIPER] ¼ 0.26 M, left axis), piperazine (S, [PIP] ¼ 0.25 M, right
axis), dimethylamine (`, [DMA] ¼ 0.09 M, left axis) and morpholine
(L, [MOR] ¼ 0.27 M, right axis) by MNTS in LTABr micelles at
Fig. 1 Influence of LTABr micelles on the observed rate constant of
nitrosation of piperidine (X, [PIPER] ¼ 0.26 M, left axis), piperazine
(
S, [PIP] ¼ 0.25 M, left axis) and morpholine (L, [MOR] ¼ 0.27 M,
ꢁ
ꢁ
right axis) by MNTS at 25 C.
25 C according to eqn. 3.
3
74
New J. Chem., 2003, 27, 372–380

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nitrosation of piperidine
that found in water, however they behave differently from
the reactivity sequence in the aqueous medium, k2
w
,
m
k
w
2
2
MNTS R2NH
m
MNTS
k þ
K
K
m
½Dnꢄ
26:56:8:1 for the same amines. Whereas in water the transfer
of the nitroso group from the MNTS to the piperidine is 26
times faster than when the least reactive amine is involved,
in micelles this difference in reactivity increases by 3.6 times.
This increase in reactivity in the micellar medium with regard
to the aqueous medium is only 1.6 times that for dimethyl-
amine. However there are no divergences in the case of the
piperazine.
kobsð1 þ Km
½DnꢄÞ
ꢀ
V
1 þ K
¼
ð3Þ
R2NH
m
½
using the value of K
R2NHꢄT
½Dnꢄ
MNTS
ꢀ1
m
¼ 132 M previously obtained.
w
2
ꢀ1
From this fit we obtain a value of k ¼ (0.21 ꢅ 0.1) M
ꢀ1
s
which is compatible with the value obtained previously
2
9a
in an aqueous medium.
Likewise we obtain a value of
¼ (2.6 ꢅ 0.3)M for the incorporation of the piperi-
ꢀ1
M
R
2
NH
ꢀ1
K
m
m
ꢀ3
dine into the micelles of LTABr and k ¼ 5.0 ꢂ 10
2
ꢀ
1
m
s
. This value of k
2
indicates that the reaction rate in the
Stability of vesicles
micelle is 42 times lower than in the aqueous medium, a result
which is compatible with the expected polarity for the interface
of the micelle of LTABr and for the solvent effect on the rate of
A very important aspect to take into account when dealing
with vesicles as a reaction medium is their stability and the
behavior which they will exhibit towards the reagents added
to the medium. When an additive is added to a vesicle obtained
by sonication, passive transport of water as well as substrates
will occur with the purpose of compensating the slopes of the
concentration which prevail between the internal water and the
external water of the system. In fact it is known that the vesi-
2
9a,31b
nitrosation of amines by MNTS.
The behavior observed for the nitrosation of morpholine,
dimethylamine and piperazine is slightly different. As we can
observe in Fig. 2 the representation of
½
Aꢄ
½Bꢄ
½Bꢄ
A
oi
i
B
oi
i
K
K
¼
¼
Z
K
K
¼
¼
Z
½
Aꢄ
39
o
o
cles obtained from DODAC present ideal osmotic behavior.
½
Aꢄ
½Bꢄ
A
wi
i
B
wi
i
Due to the osmotic gradient, when a reagent is added which
does not have a permeable membrane, there will be a reduction
in the vesicular size. This reduction of a medium size constitu-
tes an increase in the turbidity of the system (measured by
means of spectrophotometry at l ¼ 400 nm). Keeping in mind
that the membranes of the DODAC are impermeable to mole-
W
W
½
Aꢄ
½Bꢄ
w
w
n
vs. [D ] is perfectly linear. In the denominator of rate eqn. 3 the
term which corresponds to the association constant of the
unprotonated amine to the LTABr micelles, K
2
R NH
m
, does
3
8
not appear because, as will be seen, the value which can be
estimated for that equilibrium constant turns out to be very
small. This means that the amount of micellar-bound amine
is stoichiometrically negligible with respect to the total amine,
although this small amount has kinetic relevance. In this way
eqn. 3 can be simplified as:
39
cules such as urea or sucrose, it is possible that this same
problem of stability of the vesicle would prevail in our experi-
mental conditions, in which the vesicle is subjected to an
important osmotic slope through the addition of appreciable
concentrations of amine.
In the presence of amine we have observed an increase in the
turbidity of the system. An increase in the turbidity can be
attributed to the breakage/rupture of the vesicles or to the
fusion of the vesicles or to the possible fragments of bilayer
MNTS
m
kobsð1 þ K
½DnꢄÞ
ð4Þ
½
R2NHꢄT
3
9
Fig. 2 shows by way of example the fulfilment of eqn. 4 for
the nitrosation of morpholine, dimethylamine and piperazine
present in the sonicated medium. The increase in turbidity
is greater when the concentration of DODAC present in the
medium is greater. However in all cases we have observed a
period of induction which is greater than or equal to 9–10 min-
utes, for which no quantifiable variations were observed in the
turbidity of the system.
w
2
ꢀ3
by MNTS, obtaining the values of k ¼ (8.0 ꢅ 0.5) ꢂ 10
ꢀ
1
ꢀ1
w
ꢀ2
ꢀ1
ꢀ1
w
M
(
s
;
k
2
¼ (6.3 ꢅ 0.2) ꢂ 10
M
for the nitrosation of morpholine,
s
and
k
2
¼
ꢀ
1
ꢀ1 ꢀ1
4.5 ꢅ 0.1) ꢂ 10 s
piperazine and dimethylamine respectively, which are compati-
M
2
9a
ble with those obtained previously in an aqueous medium.
m
To illustrate the behavior observed, and by way of example,
Figs. 3 and 4 show the increase in absorbance at 400 nm which
corresponds with vesicles of DODAC in the presence of two
amines: dimethylamine (Fig. 3) and piperidine (Fig. 4). Similar
behavior has been found for the rest of the studied amines. The
2
R NH
Likewise we obtain for the product k
s
2
K
K
m
m
the values
¼ 8.1 ꢂ 10
m
R
2
NH
ꢀ4
ꢀ2 ꢀ1
m
R
2
NH
ꢀ4
k2
M
K
¼ 1.4 ꢂ 10
M
; k
m
2
ꢀ
2
ꢀ1
m
R
2
NH
ꢀ2
ꢀ2 ꢀ1
s
and k
2
K
m
¼ 1.3 ꢂ 10
M
s
for morpho-
line, piperazine and dimethylamine respectively. Table 1 shows
the results obtained for the different kinetic parameters in the
nitrosation of amines by MNTS in micelles of LTABr.
The results presented in Table 1 allow us to study the influ-
m
2
R NH
ence of the nature of the amine on the product k2 Km
the nitrosation of amines by MNTS in micelles of LTABr. The
for
m
2
2
R NH
m
product k
K
presents the following sequence 93:93:6:1
for piperidine, dimethylamine, piperazine and morpholine
respectively. These values present a sequence in parallel with
Table 1 Kinetic parameters obtained by applying the pseudophase
model for the nitroso group transfer from MNTS to different amines
in presence of LTABr micelles and DODAC vesicles
a
w
m
R
2
NH
m
R
2
NH
v
2
R NH
k
2
/
1
k
2
/
K
m
/
k
2
K
m
/
k
2
K
v
/
ꢀ
ꢀ1
ꢀ1 ꢀ1
ꢀ1
ꢀ2 ꢀ1
ꢀ2 ꢀ1
Amine
M
s
M
s
M
M
s
M s
1
ꢀ3
ꢀ2
ꢀ2
ꢀ4
ꢀ4
ꢀ1
Piperidine
Dimethylamine 4.5 ꢂ 10
2.1 ꢂ 10ꢀ 5.0 ꢂ 10
2.6
—
—
—
1.3 ꢂ 10
1.3 ꢂ 10
8.1 ꢂ 10
1.4 ꢂ 10
4.8 ꢂ 10
4.6 ꢂ 10
2.4 ꢂ 10
4.9 ꢂ 10
ꢀ
ꢀ
1
2
3
ꢀ1
ꢀ2
ꢀ3
—
—
—
Piperazine
Morpholine
6.3 ꢂ 10
Fig. 3 Turbidity measurements of DODAC vesicles in the presence
ꢁ
8.0 ꢂ 10ꢀ
of dimethylamine, [DMA] ¼ 0.1 M, T ¼ 25.0 C. (S) [DODAC] ¼
ꢀ3
ꢀ3
a
MNTS
¼ 132 Mꢀ1; K MNTS
v
¼ 380 Mꢀ1
7.00 ꢂ 10
M; (X) [DODAC] ¼ 5.60 ꢂ 10
M; (L) [DODAC] ¼
ꢀ3
K
m
.
ꢀ3
4
.00 ꢂ 10 M and (K) [DODAC] ¼ 2.00 ꢂ 10 M.
New J. Chem., 2003, 27, 372–380
375

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Fig. 6 Influence of DODAC vesicles on the observed rate constant of
nitrosation of morpholine (X, [MOR] ¼ 0.10 M, left axis) and piper-
ꢁ
azine (S, [PIP] ¼ 0.10 M, right axis) by MNTS at 25 C.
Fig. 4 Turbidity measurements of DODAC vesicles in the presence
ꢁ
of piperidine, [PIPER] ¼ 0.1 M, T ¼ 25.0 C. (S) [DODAC] ¼
ꢀ
3
3
ꢀ3
ꢀ3
7
4
3
.00 ꢂ 10
M; (X) [DODAC] ¼ 6.40 ꢂ 10
M; (L) [DODAC] ¼
ꢀ
.40 ꢂ 10 M; (`) [DODAC] ¼ 4.00 ꢂ 10 M and (K) [DODAC] ¼
The application of the formalism of the pseudophase in
combination with the mass action model (Scheme 3) allows
us to obtain the following rate equation which is analogous
with that obtained for micelles of LTABr.
ꢀ3
.60 ꢂ 10 M.
observed results allow us to optimize the conditions of the
reaction to obtain a reaction half life at least 5 times shorter
that this induction period to ensure that there is no influence
of turbidity upon the absorbance/time data.
kobsð1 þ K mM NTS½DnꢄÞ
k
m
w
2
2
MNTS R2NH
m
¼
k þ
K
K
m
½Dnꢄ ð5Þ
ꢀ
V
½
R2NHꢄT
In order to obtain this equation we have assumed that the
distribution of the amine between the two pseudophases
Nitroso group transfer in DODAC vesicles
(
cular compartment) is governed by the association equilibrium
DODAC film and both bulk aqueous medium and intravesi-
The effect of the presence of DODAC vesicles on the nitro-
sation of amines by MNTS was studied at constant amine con-
2
R NH
constant, K
similar distribution equilibrium kv
be able to take place simultaneously in the aqueous pseudo-
v
. The nitrosating agent, MNTS, presents a
centration (typically [R NH] ¼ 0.10 M) and DODAC
MNTS
2
, and the reaction will
ꢀ
3
concentrations ranging from 0 to 6.30 ꢂ 10 M. Unlike the
behavior detected in micelles of LTABr, the values of the rate
constant observed, kobs , rose with DODAC concentration in
all cases (see Figs. 5–6).
w
v
phase, k2 , and the vesicular pseudophase, k . The vesicular
concentration of the amine has been defined as the local con-
2
centration within the vesicular pseudophase: [R NH] ¼
2
v
To carry out a quantitative interpretation of the experimen-
tal results we should take into account the formalism of the
pseudophase, while bearing in mind that the rate of transmem-
brane equilibration of fairly low molecular weight hydropho-
bic substrates (such as both amine and MNTS) is fast in
relation to the time scale of the transnitrosation reaction. This
high mobility of both MNTS and amine inside the DODAC
bilayer means that the permeation of one of these reagents will
never be the rate-determining step of the reaction and hence
our system will be under chemical control. In this case, inner
and outer reaction (bulk water and intravesicular water) can-
not be discriminated. This leads to a pure monophasic chemi-
cal process similar to that observed in LTABr micelles.
3
¯
/[DODAC]V, where V is the molar volume in dm
¯
[
R
2
NH]
v
ꢀ1
¯
mol of the reaction region and [DODAC]V denotes the vesi-
cular fractional volume in which the reaction occurs. We
¯
assume V is equal to the partial molar volume of the interfacial
3
reaction region in the vesicular pseudophase (0.54 dm
mol ).
ꢀ1 21b,22
For the application of eqn. 5 to the experimental results we
will consider that all the DODAC in the medium was incorpo-
rated in vesicles, although there is a surfactant concentration
(
critical vesicular concentration, cvc) threshold, somewhere
ꢀ6
40
in the range (4–8) ꢂ 10 M, below which vesicles do not
form, much lower than typical values of critical micellar con-
centration (cmc). Its threshold is not, like the cmc of micellar
media, the result of a dynamic equilibrium between free and
vesicular surfactant; once formed, vesicles are not destroyed
by dilution, and have, in fact, been detected at surfactant con-
centrations as low as 10 M, which is far below the concen-
trations used in this work. For this reason, in the case it would
be a good approximation that [D ] is equal to the total
ꢀ
8
41
n
DODAC concentration.
This expression predicts that kobs increases with DODAC
concentration until all the reagents are incorporated in the
DODAC bilayer, after which the value of the observed
rate constant, kobs , will fall due to the dilution of reactive
species among an excess of vesicles. Although no clear fall in
at high DODAC concentrations was observed experimen-
tally (it was not possible to use DODAC concentrations
ꢀ
3
greater than 7 ꢂ 10 M because of the appearance of turbid-
MNTS
ity, due to fusion of vesicles). For the fitting procedure
the value of k
of kv
v
was kept constant and equal to the value
Fig. 5 Influence of DODAC vesicles on the observed rate constant of
nitrosation of dimethylamine (X, [DMA] ¼ 0.10 M) and piperidine (S,
MNTS
ꢀ1
¼ 380 M
obtained in previous works from
the basic and acid hydrolysis of MNTS in this medium and
ꢁ
[
PIPER] ¼ 0.10 M) by MNTS at 25 C.
3
76
New J. Chem., 2003, 27, 372–380

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Scheme 3
4
2
by spectroscopic techniques. In this way eqn. 5 can be rewrit-
ten as:
lowest concentration of DODAC which can be reached in
comparison with [LTABr]. In fact we have previously obtained
for the association constant of piperidine at micelles of LTABr
v
k
2
R NH
ꢀ1
w
2
MNTS R2NH
k þ Kv
Kv
½DODACꢄ
a value of K
character of DODAC must cause an increase in K
m
¼ (2.6 ꢅ 0.3) M . The more hydrophobic
2
ꢀ
2
R NH
V
kobs ¼
½R2NHꢄT
ð6Þ
v
in
, in such a way that we could suppose
R2NH
½DODACꢄÞð1 þ K vM NTS½DODACꢄÞ
ð1 þ Kv
2
R NH
comparison with K
m
R
2
NH
ꢀ1
that K
v
ꢃ 10 M . However, even with this value of
v
R
2
NH
2
R NH
K
v
we would have 1 ꢆ K
[DODAC] since the
MNTS
The representation of kobs(1 + Kv
vs. [DODAC] presents a perfectly linear dependence for all the
amines studied (see Figs. 7 and 8). The existence of this linear
[DODAC])/[R NH]T
2
maximum [DODAC] which we can reach is [DODAC] ꢃ
ꢀ3
6
.0 ꢂ 10 M.
We have obtained the following values for the product
for nitroso group transfer from MNTS to
2
2
R NH
dependence is a consequence of the fact that 1 ꢆ K
v
v
2
R NH
k K
piperidine,
k
v
2
[
DODAC], in such a way that eqn. 6 can be simplified to:
v
K
R
v
NH
ꢀ2
ꢀ1
s ;
; piperazine, k
k
2
¼ 0.48
M
dimethylamine,
2
v
v
R
2
NH
ꢀ2 ꢀ1
v
R NH
v
2
K
v
¼ 0.46 M
s
2
K
¼ 2.4 ꢂ
k
w
2
MNTS R2NH
Kv Kv
k þ
½DODACꢄ
½DODACꢄÞ
ꢀ
2
ꢀ2 ꢀ1
v
R
2
NH
ꢀ3 ꢀ2
MNTS
kobsð1 þ Kv
½DODACꢄÞ
2
ꢀ
V
10
M
s
and morpholine k
ꢀ1
. If we compare the relative values of the rate of nitrosation
2
K
v
¼ 4.9 ꢂ 10
M
¼
R2NH
s
½
R2NHꢄT
ð1 þ Kv
of these amines by MNTS in water we obtain a reactivity
sequence: PIPER:DMA:PIP:MOR (reactivity sequence 26:
ð7Þ
From the fit of eqn. 7 to the experimental data we obtain the
and of the product k which are shown in
Table 1. It is important to point out that in all cases the value
v
2
R NH
v
5
6:6:1), while on comparing the product k K
we obtain
2
w
v
K
R
v
2
NH
98:95:4.8:1 for the same amines. The absence of parallelism
must be due to the different association constants of the amines
at the DODAC vesicle, in such a way that piperidine will pre-
values of k
2
2
w
of k
medium.
The experimental results obtained show the existence of a
strong parallelism between the vesicles of DODAC and the
2
is analogous to that observed previously in an aqueous
2
R NH
sent a value of Kv
zine will present a value of K
superior to that of DMA while pipera-
2
R NH
v
which is slightly lower. This
sequence of association constants must be parallel to the
hydrophobicity of the amines such as we observe in micelles
of LTABr and in microemulsions of AOT/isooctane/water.
2
R NH
micelles of LTABr. The fact that 1 ꢆ K
v
[DODAC] seems
contradictory with the results existing in the literature which
indicate that the vesicular interfaces are more hydrophobic
than the micellar interfaces. In accordance with this observa-
v
2
R NH
The values of k
can be compared with the analogous values obtained in
2
K
v
obtained in vesicles of DODAC
m
micelles of LTABr, k Km
2
R NH
R
2
NH
. The values obtained for the
for the nitrosation of piperi-
2
tion it is necessary to check that K
its analogue for the association of amines to micelles, K
This result seems to contradict the fact that for the nitrosation
of piperidine in vesicles it follows that 1 ꢆ K
whereas in micellar systems this approximation is not correct
see previous discussion and Fig. 2). The behavior observed
v
should be greater than
v
quotient k K
R
v
2
NH
m
/k2 Km
R NH
2
R
2
NH
2
m
.
dine, dimethylamine, piperazine and morpholine are
37:35:29:35 respectively. These values indicate that there exists
a parallelism between the behavior in micellar systems and
vesicular systems. The difference in behavior can be attributed
for the most part to the difference between the values of the
2
R NH
v
[DODAC],
(
experimentally in this study is justified on the basis of the
Fig. 7 Fitting of experimental data for nitrosation of piperidine (X,
Fig. 8 Fitting of experimental data for nitrosation of piperazine (X,
[PIP] ¼ 0.10 M) and morpholine (S, [MOR] ¼ 0.10 M) by MNTS in
[
MNTS in DODAC vesicles at 25 C according to eqn. 7.
PIPER] ¼ 0.10 M) and dimethylamine (S, [DMA] ¼ 0.10 M) by
ꢁ
ꢁ
DODAC vesicles at 25 C according to eqn. 7.
New J. Chem., 2003, 27, 372–380
377

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association constants of the amines at the vesicular and
micellar interphases. It is to be expected that K
constants have been defined thus:
2
R NH
in vesicles
in micelles of
v
NH
w
o
R
2
k2
k2
ꢀ
of DODAC would be greater than K
m
W
Z
i
k
ꢀ
2
Vw
Vo
LTABr, due to the greater length of the hydrocarbon chain
of DODAC (18 carbon atoms) vs. LTABr (12 carbon atoms).
In fact in micellar systems it can be observed that the associa-
tion constant of MNTS at the micelles increases three times as
the length of the hydrocarbon chain of the tensioactive
increases from 12 carbon atoms (LTABr) to 18 carbon atoms
þ
þ
ꢀ
A
wi wi
B
A
oi oi
B
Vi K K
K K
½Aꢄ ½Bꢄ
T
T
rate ¼
!
ꢀ
ꢁ
½AOTꢄ
W
A
wi
Z
W
Z
B
1
þ K
þ
1 þ K þ
K
wi
A
oi
B
K
oi
Therefore, although the rate constants in the pseudophases
of the microemulsion are directly comparable with the rate
constants in an aqueous, micellar or vesicular medium, the dis-
tribution constants between the pseudophases of the micro-
emulsion and the micellar or vesicular systems are not. To
make these constants compatible we must take into account
that
(
OTACl). Likewise this difference should increase as a conse-
quence of the existence of a double hydrocarbon chain in
DODAC against the simple chains present in micellar systems
based on quaternary ammonium salts. The existence of parallel
v
2
R
2
NH
m
2
2
R NH
behavior for k
K
v
/k
K
m
indicates that the proper-
ties of the micellar interphase of LTABr and the vesicular
interphase of DODAC are parallel.
½
Aꢄ ½H2Oꢄ
A
wi
i
K
¼
½
Aꢄ ½AOTꢄ
w
Nitroso group transfer in AOT/isooctane/water microemulsions
and that
The nitroso group transfer from N-methyl-N-nitroso-p-tolue-
nesulfonamide (MNTS) to several amines has been studied
½
Aꢄ
1
A
m
m
K
¼
2
4
½
Aꢄ ½LTABrꢄ
previously in AOT/isooctane/water microemulsions. How-
ever, and for the purpose of comparison, it is necessary to
recalculate the distribution constants of the amines between
the different pseudophases. The application of the formalism
of the pseudophase allows us to explain the reactivity in micro-
emulsions considering the existence of three well differentiated
microenvironments: a continuous medium formed by the
alkane, an aqueous microdroplet and an interphase or ten-
sioactive film which separates both microenvironments. For
any general reaction, A + B ! Products, we can obtain a reac-
tion scheme like that which is shown below (Scheme 4) for
which we assume that the distribution of the reagents through-
out the different pseudophases is governed by distribution con-
stants for the incorporation of the reagents from the
w
in such a way that for the purpose of comparison we could
4
3
A
A
write
K
wi ¼ [H
2 m
O]K . The values of the equilibrium con-
stants are not directly comparable since the tensioactives do not
have the same structure (LTABr, DODAC and AOT) and the
properties of the microenvironments of a microemulsion,
whether micellar or vesicular, are the same. However, it would
be interesting to compare sequences of rate constants as the
nature of the amine varies and so determine its possible reper-
cussions on the rate constants of the interphases.
Table 2 shows the equilibrium constant for the distribution
A
of the different amines and MNTS written in the form Kwi
/
H O] and K /[isooctane], as well as the rate constants
A
[
obtained for nitroso group transfer in the interphase. Likewise
2 oi
A
B
continuous medium, oil, to the interphase: Koi and Koi
and by distribution constants for the incorporation of the
,
A
wi
m
i
the said table also shows the values of the product K k /
2
R
2
NH
A
[H
K
2
O] with the aim of comparing it with K
2
m
k
2
and
reagents from the aqueous medium to the interphase: Kwi
and Kwi . If the reagents are distributed throughout the differ-
R
NH
v
B
v
k .
2
R
2
NH
v
R
2
NH
i
We can obtain the quotient K
v
k
2
/(Kwi
2 2
/[H O])k
ent pseudophases of the system we can assume that the reac-
tion can occur simultaneously in the continuous medium, the
for the nitrosation of dimethylamine, piperazine and morpho-
line as 20:26:24 respectively. Likewise as the analogous quoti-
ent for comparing the reactivity between microemulsions and
0
interphase and the aqueous medium with rate constants: k
2
,
i
w
k2 and k2 respectively. From these considerations we can
obtain the following expression for the rate of the reaction
R
2
NH
m
R
2
NH
i
micelles, K
m
k
2
/(Kwi
2 2
/[H O])k allows us to obtain
values of 0.5:0.9:0.7 for these same amines respectively. The
results obtained indicate that the greatest kinetic effect is
observed for the vesicles of DODAC, and the effect produced
by the LTABr micelles and the microemulsions of AOT/isooc-
tane/water is very similar.
¯
assuming that V , V and V are the molar volumes of the
¯
¯
o
i
w
oil, the interphase and the water respectively:
MNTS
v
kobsð1 þ Kv
½DODACꢄÞ
k
2
w
2
MNTS R2NH
Kv Kv
¼
k þ
½DODACꢄ
ð8Þ
ꢀ
V
½
R2NHꢄT
The existence of a parallelism between the quotients
R NH
2
v
k /(K
R NH
2
i
R NH
2
m
k2 /(Kwi
2
R NH
Kv
/[H O])k ;
2
Km
/
indicates that the effect
2
wi
2
i
R
v
2
NH
v
2
R
2
NH
m
[H
2
O])k
2
and K
k
/K
m
k
2
where W and Z are the molar relationships W ¼ [H O]/[AOT]
2
produced by the micellar interphases of the LTABr, vesicles
of DODAC and microemulsions of AOT on the transfer reac-
tivity of the nitroso group to/at amines is similar. As has been
discussed previously the experimental conditions have not
allowed us to obtain the values of the bimolecular rate con-
stants in the micellar and vesicular interphases, but to obtain
its product with the association constant of the amine to/at
the said interphases. In the case of the microemulsions of
and Z ¼ [isooctane]/[AOT] and where the distribution
AOT/isooctane/water the experimental conditions have
i
allowed us to obtain the values of k
with the values obtained for the same reaction in an aqueous
2
which can be compared
w
2
medium, k . The conclusions reached on the basis of this
comparison will be able to be extrapolated to the micellar
and vesicular systems since the constancy of comparing values
m
R
2
NH
v
R
2
NH
i
2
R NH
of the products of k
2
K
m
; k
2
K
v
and k
2
K
wi
/
O] has been verified. The relationship k /k is the same
w
2 2
i
[H
2
at 20; 70; 27; 12; 41 and 33 for the nitrosation of pyrrolidine,
piperidine, dimethylamine, piperazine, N-methylbenzylamine
Scheme 4
3
78
New J. Chem., 2003, 27, 372–380

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Table 2 Kinetic parameters obtained by applying the pseudophase model for nitroso group transfer from MNTS to different amines in AOT/iso-
octane/water microemulsions. Data from ref. 24
w
2
ꢀ1 ꢀ1
A
a
O]
A
a
i
2
ꢀ1 ꢀ1
A
i
b
Amine
k
/M
s
K
wi /[H
2
K
oi /[isooctane]
k
/M
s
wi 2 2
K k /[H O]
ꢀ
2
6.33 ꢂ 10ꢀ3
2.4 ꢂ 10ꢀ2
Pyrrolidine
Piperidine
0.83
0.15
—
20.7
4.25
13.8
4.23
4.22 ꢂ 10
ꢀ1
ꢀ1
ꢀ2
ꢀ2
ꢀ3
ꢀ3
ꢀ2
2.1 ꢂ 10
4.3 ꢂ 10
4.1 ꢂ 10
6.3 ꢂ 10
8.0 ꢂ 10
3.0 ꢂ 10
1.6 ꢂ 10
1.00 ꢂ 10
5.33 ꢂ 10
Dimethylamine
N-Methylbenzylamine
Piperazine
1.5
—
ꢀ3
ꢀ3
ꢀ4
ꢀ4
0.17
0.84
—
33.1
9.06 ꢂ 10
ꢀ4
Morpholine
2.4 ꢂ 10
2.02 ꢂ 10
a
ꢀ1
b
ꢀ2 ꢀ1
M s .
M
.
and morpholine respectively. Within this reactivity sequence
we can distinguish three types of behavior: piperazine (the least
hydrophobic amine) presents an inhibition of 12 times, N-
methylbenzylamine and piperidine (the most hydrophobic
amines) present an inhibition of 41 and 70 times respectively,
while for the amines with intermediate hydrophobicity (pyrro-
lidine, dimethylamine and morpholine) the inhibition observed
is approximately 25 times in all cases.
formalism of the pseudophase in an analogous way to that
obtained in LTABr micelles. The obtained values for
v
2
R NH
k
2
K
v
show different behavior which is parallel with that
obtained in micelles of LTABr. In fact the quotient
v
2
R
2
NH
m
K
2
R NH
k
K
v
/k
2
m
is practically constant and independent
of the nature of the amine, with a value in the region of 35.
This behavior is consistent with the interphase of the vesicle
being more hydrophobic than that of the micelles.
This hydrophobic/hydrophilic balance with the distribution
of the amines is found throughout the different pseudophases
of the microemulsion. In this way the piperazine is distributed
solely between the aqueous microdroplet and the interphase,
whereas piperidine and N-methylbenzylamine will be found
to be distributed between the continuous medium and the
interphase of the microemulsion. The other three amines are
found to be distributed throughout the three pseudophases
of the system. The different distributions of the amines
throughout the system will give rise to different zones of resi-
dence within the interphase of the microemulsion: the most
hydrophobic amines will be in nearer to the head groups in a
more hydrated medium, and therefore the decrease in the rate
with respect to the aqueous medium will be small. The most
hydrophobic amines (N-methylbenzylamine and piperidine)
will be found in an interfacial zone nearer to the continuous
medium where the hydration will be less. Consequently the
inhibition with regard to the aqueous medium will be lower.
The amines with intermediate hydrophobicity will be distribu-
ted between the former in such a way as to make their kinetic
behavior intermediate.
To compare these experimental results with those obtained
previously in microemulsions of AOT/isooctane/water it is
necessary to obtain the product of the bimolecular rate con-
stant at the interphase of the microemulsion with the distribu-
tion constant of the reagents from water to the interphase,
which has been defined in the same way as in micellar systems:
i
R
2
NH
m
2
R NH
k
2
K
wi
/[H
micellar systems or k
2
O] (analogous with the product k
K
v
2
K
m
in
in vesicular systems). The rela-
v
2
NH
2
R NH
R
2
v
R
2
NH
i
tive values of K
v
k
2
/(Kwi
2 2
/[H O])k for the nitrosa-
tion of dimethylamine, piperazine and morpholine are
approximately constant and in the region of 23. These values
indicate than the interphase of the microemulsion will be less
hydrophobic than the vesicular interphase and more hydro-
phobic than that of the micelles of LTABr. The comparison
of the bimolecular rate constants at the interphase of the
w
i
2 2
microemulsion and in the aqueous medium, k /k , shows
three types of behavior which are well differentiated according
to the hydrophobicity of the amines, which reflect the amine
localization in different zones of the interphase of the micro-
emulsion. These zones of the interphase of the microemulsion
will have different polarities and consequently will give rise to
different effects on the rate of the reactions.
Conclusions
Acknowledgements
The behavior observed for nitroso group transfer from MNTS
to different secondary amines in micelles of LTABr has been
explained by means of the application of the formalism of
the micellar pseudophase. The obtained values for the product
of the rate constant in the micellar pseudophase with the asso-
The authors thank the Spanish Ministry of Education and
Culture (PB98-01098) and Xunta de Galicia (PGODT00P-
XI20907PR) for financial support.
m
2
R NH
ciation constant of the amines at the micelle, k2 Km
not present the same sequence of behavior as for the reactivity
, do
References
w
in an aqueous medium, k2 . This apparent anomaly may be
1
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R NH
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R NH
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5
6
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38 If we assume that the quotient k
2
/k
2
takes the same value for
the nitrosation of piperidine, piperazine and morpholine by
2
R NH
2
0
1
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MNTS, we can estimate the value of K
m
for the last two
m
R
2
NH
ꢀ4
ꢀ2 ꢀ1
amines using the values of k
¼ 8.1 ꢂ 10
2
K
m
¼ 1.4 ꢂ 10
M s
. The values obtained for
m
R
2
NH
ꢀ4
ꢀ2 ꢀ1
and k
2
NH
K
m
M
s
R
2
R
2
NH
ꢀ1
R
2
NH
ꢀ1
(
c) M. A. Carmona-Riveiro, L. S. Yoshida, A. Sesso and H.
K
m
are K ꢃ 0.73 M and K
pholine and piperazine respectively. These values mean that the
m
m
ꢃ 0.54 M for mor-
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R NH
2
m
product K
n
[D ] is always lower that 0.18 in such a way as
2
for it to be compatible with the simplification of eqn. 3.
39 A. M. Carmona-Riveiro, L. S. Yoshida and H. Chaimovich,
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2
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A
A
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43 The equality is established to mean that Kwi and K
m
have the
same dimensions. At no time do we claim that there exists a
numerical equality between both types of association constants
as they reflect microenvironments which are very well differen-
tiated.
24
3
80
New J. Chem., 2003, 27, 372–380