Cyclodextrin-surfactant binding constant as driven force for uncomplexed cyclodextrin in equilibrium with micellar systems

Article abstract of DOI:10.1016/j.cplett.2010.09.017

Mixed systems formed by surfactants, sodium alkylsulfonates, and β-cyclodextrin have been studied by using the solvolysis of 4-methoxybenzenesulfonil chloride (MBSC) as a chemical probe. The kinetic analysis allows us to obtain the percentage of uncomplex

Full text of DOI:10.1016/j.cplett.2010.09.017

Chemical Physics Letters 499 (2010) 70–74
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Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Cyclodextrin-surfactant binding constant as driven force for uncomplexed
cyclodextrin in equilibrium with micellar systems
1
⇑
M. Cepeda , R. Daviña, L. García-Río , M. Parajó
Departamento de Química Física, Facultad de Química, Universidad de Santiago, 15782 Santiago, Spain
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 7 May 2010
In final form 5 September 2010
Available online 9 September 2010
Mixed systems formed by surfactants, sodium alkylsulfonates, and b-cyclodextrin have been studied by
using the solvolysis of 4-methoxybenzenesulfonil chloride (MBSC) as a chemical probe. The kinetic anal-
ysis allows us to obtain the percentage of uncomplexed cyclodextrin in equilibrium with the micellar
media and its variation with the alkyl chain length of the surfactant. Competition between surfactant
complexation by the cyclodextrin and self-aggregation to form micelles is the driving force for the per-
centage of uncomplexed cyclodextrin in equilibrium with the micellar system and its variation with the
surfactant chain length.
Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction
in equilibrium with the cyclodextrin is sufficient for the micelliza-
tion process to begin. (ii) The critical micelle concentration has
Since their discovery, cyclodextrins have been the objective of a
large number of studies, specially focused on their ability to form
inclusion complexes [1,2]. The formation of the inclusion com-
pounds greatly modifies the physical and chemical properties of
the guest molecule, mostly in terms of water solubility. This is
the reason why cyclodextrins have attracted much interest in
many fields, especially pharmaceutical applications: because inclu-
sion compounds of cyclodextrin with hydrophobic molecules are
able to penetrate body tissues, these can be used to release biolog-
ically active compounds under specific conditions [3]. Of particular
interest is the effect of cyclodextrins on the self-organization pro-
cesses involving surfactants in which the presence of these macro-
cycles introduces a new equilibrium, which in turn competes with
aggregation [4]. Traditionally, supramolecular complexes, of which
CDs are a simple class of host molecules, have been characterized
by X-ray crystallography or by determining thermodynamic
parameters. These structural measurements provide information
on the system when it is equilibrium but do not convey any kinetic
understanding of the association and dissociation processes [5].
Our group has developed a kinetic model that accounts for reac-
tivity in mixed surfactant-CD systems [6]. This model has enabled
us to highlight certain characteristics of mixed surfactant-CD sys-
tems: (i) At surfactant concentrations lower than the micellization
point a complexation equilibrium between the surfactant and the
cyclodextrin is established. As the surfactant concentration in-
creases, the concentration of uncomplexed surfactant monomers
been found to shift to higher values in presence of CD. The critical
micelle concentration of a micellar system in the presence of cyclo-
dextrin is equivalent to the combined concentrations of surfactant
monomers complexed to the CD and of free dissolved monomers in
equilibrium with the micellized surfactant. (iii) Once the micelliza-
tion process has begun, interactions will not be established be-
tween the CD and the micellar system.
Previous studies have shown that the percentage of uncom-
plexed CD in equilibrium with the micellar system increases with
the chain length of the surfactant [7–9]. This behaviour has been
explained by considering simultaneous competitive equilibria: (i)
surfactant complexation by the cyclodextrin yields
a higher
uncomplexed cyclodextrin in equilibrium with the micellar system
on decreasing the binding constant of the surfactant by b-CD. This
can be achieved by decreasing the alkyl chain length of the surfac-
tant. (ii) Surfactant self-association yielding micelles. As higher is
the tendency of surfactants to form micelles (smaller the cmc)
higher is the percentage of uncomplexed cyclodextrin. It should
be noted that both factors are present simultaneously. In previous
studies [7–9] we have used surfactants where the main factor is its
self-association yielding a higher percentage of uncomplexed
cyclodextrin on decreasing the cmc. In the present study we are
searching for surfactants where the surfactant binding by the
b-CD is dominant in reporting the uncomplexed cyclodextrin. In
this way we need to use surfactants with very large cmc (i.e. short
alkyl chains). Therefore we studied mixed systems formed by anio-
nic surfactants with different chain lengths and b-CD. As chemical
probe we used the hydrolysis of the 4-methoxybenzenesulfonil
chloride (MBSC), a molecule whose geometry and polarity is suit-
able for complex formation with b-CD and whose basic hydrolysis
has been previously studied in water and water:organic solvent
⇑
Corresponding author. Fax: +34 981595012.
E-mail address: luis.garcia@usc.es (L. García-Río).
Permanent address: Facultad de Química, Pontificia Universidad Católica de Chile,
1
Casilla 306, 6094411 Santiago, Chile.
0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2010.09.017

M. Cepeda et al. / Chemical Physics Letters 499 (2010) 70–74
71
mixtures [10]. The results obtained confirm that, contrary to the
expectations, the percentage of uncomplexed CD decreases with
the number of carbons of the chain, meaning that the percentage
of uncomplexed CD decreases with the hydrophobic character of
the surfactant.
than the cmc, a clear decrease in kobs can be observed due to the
presence of micellar aggregates. These inhibitions are due to the
substrate incorporation into the micelles where the rate of solvo-
lytic reaction is smaller than in bulk water. The formalism of the
micellar pseudophase [11,12] was applied to obtain a quantitative
interpretation of the experimental results. Two well-differentiated
environments were considered: water and a micellar pseudophase
between which the MBSC is distributed.
2. Experimental section
By considering that the solvolysis can take place simultaneously
in water, kw, and at the micellar pseudophase, km, it is possible to
derive the following equation, which relates the observed rate con-
stant with the surfactant concentration. (Eq. (1)).
Sodium decane sulfonate (C10SO3Na), sodium octane sulfonate
(C8SO3Na), sodium hexane sulfonate (C6SO3Na) and sodium butane
sulfonate (C4SO3Na) were Aldrich products of the highest available
purity and were used without further purification. b-CD was sup-
plied by Cyclolab. Stocks solutions of MBSC were prepared in ace-
tonitrile due to its low solubility in water. The final acetonitrile
concentration in the reaction medium was 1% (v/v). Surfactant-
CD systems were prepared by mixing appropriate volumes of stock
aqueous solutions of CD and surfactant. Kinetics runs were initi-
ated by injecting a stock solution of MBSC into the mixed system
in a 1 cm cuvette.
Reaction kinetics were recorded by measuring absorbance due
to MBSC at 270 nm in a Cary 100 UV–Vis spectrophotometer with
a cell holder thermostated at (25.0 0.1)°C. The MBSC concentra-
tion was always approximately 1.2 ꢀ 10ꢁ4M. The absorbance-time
data of all kinetic experiments were fitted by first-order integrated
equations, and the values of the pseudo-first-order rate constants,
kobs, were reproducible to within 3%. The critical micelle concentra-
tion of the mixed system was obtained kinetically.
kw þ kmKm½Dnꢂ
kobs
¼
ð1Þ
1 þ Km½Dnꢂ
where Km is the distribution constant of MBSC between the water
and the micellar pseudophase, Km=[MBSC]m/([MBSC]w[Dn]); [Dn]
is the concentration of micellized surfactant, [Dn] = [Surfactant]Tꢁ
cmc; and [Surfactant]T is the total concentration of the surfactant.
If we consider that the solvolysis reaction takes place only in the
aqueous medium we should simplify Eq. (1) to Eq. (2)
kw
kobs
¼
ð2Þ
1 þ Km½Dnꢂ
Critical micelle concentration values are required to fit Eq. (2) to
the experimental results. The critical micelle concentration can be
obtained kinetically as the minimal surfactant concentration nec-
essary to observe an appreciable change in kobs. Obtained values
are shown in Table 1. Fitting the experimental results to Eq. (2)
(lines showed in Figure 1 left) by a nonlinear regression method
provided the value of the distribution constant of the MBSC be-
tween the water and the micellar pseudophase (Km). These values
along with the cmc values obtained experimentally are given in Ta-
ble 1.
3. Results and discussion
3.1. Solvolysis of MBSC in the presence of anionic micelles
The influence of the concentration of C4SO3Na; C6SO3Na;
C8SO3Na and C10SO3Na on the solvolytic rate constant of MBSC
has been studied in a wide interval of concentrations that includes
both the regions prior to the cmc, where the molecules of surfac-
tant are presented as monomers dispersed in the solution, and
the regions after the cmc where the surfactant molecules are asso-
ciated to form micelles. The effect of the surfactant concentration
on the pseudo-first-order rate constant, kobs, for the hydrolysis of
the MBSC is shown in Figure 1.
The binding constant of MBSC to the micellar system increases
with the length of the surfactant hydrocarbon chain so does its
hydrophobity too. Likewise, as the length of the surfactant hydro-
carbon chain increases the critical micelle concentration decreases.
3.2. Solvolysis of MBSC in presence of cyclodextrins
As can be seen from Figure 1, the pseudo-first-order rate con-
stant remains practically unchanged on increasing the surfactant
concentration up until the cmc. At surfactant concentrations higher
The influence of b-CD concentration on the rate of solvolysis of
MBSC was studied. This effect is shown in Figure 1-right. As can be
observed, addition of b-CD to the reaction medium inhibits the
Figure 1. Left: Influence of the alkyl sulfonate concentration on the pseudofirst order rate constant for solvolysis of MBSC at 25.0 °C. ( )C6SO3Na; ( )C8SO3Na and
)C10SO3Na. Lines correspond to the fit of Eq. (2) to the experimental data. Right: Influence of b-CD concentration on the pseudo-first-order rate constant, kobs, for the
hydrolysis of MBSC at 25.0 °C. Curves represent the fits of the experimental data to Eq. (3).
(

72
M. Cepeda et al. / Chemical Physics Letters 499 (2010) 70–74
Table 1
the cyclodextrin and the surfactant. The formation of these
inclusion complexes displaces the MBSC towards the aqueous
medium, where the reaction rate is higher than inside the CD
cavity and, as a consequence, the observed rate constant of the
reaction increases. The competitive formation of the CD-surfac-
tant inclusion complexes occurs until the concentration of sur-
factant monomers reaches the value at which the micellization
process begins. Once micelles have been formed, the typical
inhibiting effect that they have on the hydrolysis of MBSC is ob-
served. Therefore, the maximum observed in the plot of kobs ver-
sus surfactant concentration can be attributed to the
micellization point, where the kinetic effects caused by the for-
mation of an inclusion complex between the surfactant and
the CD (catalytic effect on kobs) and for the formation of micelles
(inhibitory effect on kobs) are compensated.
Critical micelle concentration obtained experimentally and results obtained by fitting
the experimental data to Eq. (2) and Eq. (4) for the hydrolysis of MBSC in the presence
of surfactant and in mixed systems surfactant: b-CD. kw = (6.0 0.1) ꢀ 10ꢁ3sꢁ1
;
kCD = (1.43 0.03) ꢀ 10ꢁ4sꢁ1; KCD = (1.89 0.01) ꢀ 103Mꢁ1 [b-CD] = 2.6 ꢀ 10ꢁ3M.
;
Surfactant
cmc/M
cmcCD/M
KN/Mꢁ1
Km/Mꢁ1
%CDf
C4SO3Na
C4SO3Na + b-CD
C6SO3Na
C6SO3Na + b-CD
C8SO3Na
C8SO3Na + b-CD
0.75
1.1 0.1
1.1 0.1
4.1 0.8
4.1 0.8
0.8
7
1
31.8
7.5
0.20
0.13
0.04
0.3
200 25
25
25
55
55
3
3
5
5
0.12
0.04
1500 100
(10 2) ꢀ 103
3.6
C
C
10SO3Na
10SO3Na + b-CD
3.2
hydrolysis of MBSC. The experimental behaviour can be explained
by considering a mechanistic behaviour where MBSC bind the
cyclodextrin and the solvolytic reaction takes place simultaneously
in water, kw, and through the MBSC-CD complex [13], kCD. The
dependence of kobs on the concentration of b-CD is expressed by
(Eq. (3)).
In order to explain the experimental behaviour we considered
that the solvolysis proceeds exclusively through the free substrate
in aqueous medium (Scheme 1). As we have seen before the rate
constants for the reaction in the micelles (km) are negligible com-
pared to kw. We assume also that there is uncomplexed cyclodex-
trin coexisting with the micellar system and that there are no
interactions of any sort between the CD and the micellar system
once the micellization process begins.
kw þ kCDKCD½CDꢂ
kobs
¼
ð3Þ
1 þ KCD½CDꢂ
This mechanistic scheme allows us to derive the following
expression for the rate constant.
where KCD is the equilibrium binding constant of the substrate to
the cyclodextrin, kCD is the rate constant for the reaction in the
cyclodextrin complex, and kw is the rate constant for the hydrolysis
in the aqueous medium. The good fit of the experimental data to
this last equation (Figure 1-right) allows us to obtain the binding
kw þ kCDKCD½CDꢂf
kobs
¼
ð4Þ
1 þ KCD½CDꢂf þ Km½Dnꢂ
To solve Eq. (4) it is necessary to obtain the concentration of
uncomplexed cyclodextrin, [CD]f, for each surfactant concentration
as well as the values of [Dn]. The concentration of free CD can be
obtained by means of a simulation procedure, supposing that the
complex formed between the surfactant molecules and the CD
has a stoichiometric ratio [14,15] of 1:1, as well as for the CD-MBSC
complex. The complexation constant for binding of the substrate
by CD, KCD, surfactant molecules by the cyclodextrin, KN, and sub-
strate by the micellar system, Km, are expressed as.
constant of MBSC to the cavity of the cyclodextrin: KCD
=
(1.89 0.01) ꢀ 103Mꢁ1. and the solvolytic rate constant inside the
cavity of the CD, kCD = (1.43 0.03) ꢀ 10ꢁ4 sꢁ1
.
3.3. Solvolysis of MBSC in surfactant/cyclodextrin mixed systems
The study of the mixed system was carried out with experi-
ments in which the b-CD concentration was kept constant
(2.6 ꢀ 10ꢁ3M) and the surfactant concentration was varied from
values clearly lower than the cmc to values beyond the micelliza-
tion point. The influence of the mixed system on the hydrolysis
of MBSC rate constant is shown in Figure 2.
From a qualitative point of view, the observed behaviour is
the same in all cases; the value of kobs increases to a maximum
as the concentration of surfactant increases. This increase is due
to the competitive formation of inclusion complexes between
½MBSC ꢁ CDꢂ
½MBSCꢂ ½CDꢂf
½Surf ꢁwCDꢂ
½MBSCꢂm
KCD
KN
¼
Km
¼
½MBSCꢂw½Dnꢂ
¼
ð5Þ
½Surfmonꢂ½CDꢂf
The mass balances for the total concentrations of cyclodextrin,
surfactant and substrate: [{CD}]_T = [{CD}]_f + [{MBSC - CD}] +
[{Surf - CD}]; [{Surf}]_T = [{Surf_{mon}}] + [{D_n}] + [{Surf - CD}]
Figure 2. Influence of the surfactant concentration on the observed rate constant
for the hydrolysis of MBSC at 25.0 °C in the presence of b-CD. ( ) C10SO3Na, (
)
C8SO3Na, ( ) C6SO3Na, ( ) C4SO3Na.
Scheme 1.

M. Cepeda et al. / Chemical Physics Letters 499 (2010) 70–74
73
and [{MBSC}]_T = [{MBSC}]_w + [{MBSC - CD}] + [{MBSC}]_m are
combined with binding constants to give a third-order equation
for the concentration of uncomplexed cyclodextrin:
3
2
a
a
½CDꢂf þ b½CDꢂf þ
¼ KNKCD
c
½CDꢂf ꢁ ½CDꢂT ¼ 0
ð6Þ
ð7Þ
ð8Þ
ð9Þ
b ¼ KN þ KCD þ KNKCDð½SurfꢂT ꢁ ½CDꢂT þ ½MBSCꢂTÞ
¼ 1 þ KNð½SurfꢂT ꢁ ½CDꢂTÞ þ KCDð½MBSCꢂT ꢁ ½CDꢂTÞ
c
These equations were solved for different values of KN allowing
us to obtain the concentration of uncomplexed cyclodextrin for
each surfactant concentration. Using the [CD]f values and with
the [Dn] values, we can fit the experimental kobs values to Eq. (4).
The value of KN for which we obtain the best root-mean-square
deviation (v
2) values in fitting Eq. (4) to the experimental results
was taken as optimal. The validity of this model was tested by fit-
ting Eq. (4) to the experimental data by means of a two-tier opti-
mization process in which the optimized variable was KCD, and
the values obtained in the simple systems were taken as constants.
As can be seen in Table 1 the binding constant of MBSC to the
cyclodextrin is independent of the presence of surfactants. More-
over the binding constant of MBSC to the micelle, Km, is strongly
dependent on the hydrophobicity of the surfactant but indepen-
dent on the presence or absence of b-CD. The insensitivity of Km
to the presence of b-CD is in agreement with the absence of inter-
action between the cyclodextrins and micelles once they have been
formed.
Figure 3. Influence of the surfactant alkyl chain length on the free energy per
aggregated molecule of surfactant (
D
GM,
) and on the free energy of surfactant
complexation by b-CD ( GC, ) at 25.0 °C.
D
D
GM ¼ RT ln cmc0
ð11Þ
´
where cmc is the critical micelle concentration in mole fraction
units. Moreover, from the binding constants of the alkyl sulfonate
surfactants to the cavity of the cyclodextrins we can evaluate the
complexation free energy,
DGC. Figure 3 shows the variation of
D
GM and GC with the alkyl chain length of the surfactant. As can
D
The most important aspect of the results obtained in the pres-
ent study that should be remarked is the kobs value in the maxi-
mum of the plot kobs vs. surfactant concentration (Figure 2). This
value is lower than the value obtained in bulk water and is due
to the presence of uncomplexed cyclodextrin at the micellization
point. The difference between kobs in bulk water and in the mixed
system increases on decreasing the alkyl chain length of the surfac-
tant. In Table 1 we present the percentage of uncomplexed cyclo-
dextrin obtained from a calibration procedure. For any surfactant
concentration, it is possible to obtain the concentration of uncom-
plexed cyclodextrin from a calibration curve. The calibration curve
can be obtained by regrouping Eq. (3) and using previously ob-
tained values for KCD = (1.89 0.01) ꢀ 103 Mꢁ1; kCD = (1.43 0.03)
be observed for alkylsulfonates with very short alkyl chain length,
C4SO3Na, micellization is favored against of surfactant-CD complex-
ation. Because the percentage of uncomplexed cyclodextrin is a
consequence of the balance between micellization and CD-surfac-
tant complexation, on increasing the weight of micellization vs.
CD-surfactant complexation we expect to increase the percentage
of uncomplexed cyclodextrin. If we increase the alkyl chain length
of the surfactant, CD-surfactant complexation is energetically more
favorable than micellization and as a consequence the percentage
on uncomplexed cyclodextrin decreases on increasing the alkyl
chain length on going from C4SO3Na to C10SO3Na.
ꢀ 10ꢁ4 sꢁ1 and kw = (6.0 0.1) ꢀ 10ꢁ3 sꢁ1
.
kw ꢁ kobs
4. Conclusions
½CDꢂf ¼
ð10Þ
KCDðkobs ꢁ kCD
Þ
Mixed systems formed by surfactants and cyclodextrins are
characterized by the presence of a non-negligible amount of
uncomplexed cyclodextrin in equilibrium with the micellar system
once the micelles have been formed. In this way traditional ideas
that micelles are formed only once the complexation ability of
cyclodextrins have been saturated should be removed. The exis-
tence of an appreciable percentage of uncomplexed cyclodextrin
is a consequence of the competitive equilibria of CD-surfactant
complexation and surfactant self-assembly to form micelles. The
balance between both equilibria determines the influence of the
hydrophobic character of the surfactant on the percentage of
uncomplexed cyclodextrin. In this study we have shown that on
decreasing the alkyl chain length of the surfactant micellization
is more important than complexation by the cyclodextrin and
the precentage of uncomplexed cyclodextrin increases.
Results in Table 1 show that the percentage of uncomplexed
cyclodextrin in equilibrium with the micellar system increases
on decreasing the hydrophobic character of the surfactant. This
behaviour is contrary with that previously reported in our labora-
tory [7–9] where the percentage of uncomplexed cyclodextrin in-
creases on increasing the alkyl chain length of the surfactant for
surfactants with alkyl chain larger than ten carbon atoms. Tradi-
tional ideas on mixed CD-surfactant systems consider that the mic-
ellization process only begins once the complexation capacity of
the cyclodextrin has been saturated. Thus supposition implies
the absence of uncomplexed CD in equilibrium with the micellar
system. Our results indicate that this vision should be modified.
We should consider that the complexation equilibrium of the sur-
factant by the CD and the autoassociation of the surfactant (micel-
lization) take place simultaneously. The balance between both
processes will be the cause of the existence of uncomplexed CD
in equilibrium with the micellar system and its variation with
the nature of the surfactant.
Acknowledgments
The total free energy per aggregated molecule of surfactant [16]
in the micelles can be evaluated from the experimental cmc values,
using the following equation:
This work was supported by the Ministerio de Ciencia y Tec-
nología (Project CTQ2008-04420/BQU) and Xunta de Galicia (PGI-
DIT07-PXIB209041PR).

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M. Cepeda et al. / Chemical Physics Letters 499 (2010) 70–74
[8] B. Dorrego, L. Garcia-Rio, P. Herves, J.R. Leis, J.C. Mejuto, J. Perez-Juste, J. Phys.
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