Cycloadditions in mixed aqueous solvents: The role of the water concentration

Article abstract of DOI:10.1002/poc.926

We examined the kinetics of a series of cycloaddition reactions in mixtures of water with methanol, acetonitrile and poly(ethylene glycol) (MW 1000). The reactions include the Diels-Alder (DA) reaction between cyclopentadiene and N-n-butylmaleimide or acridizinium bromide, the retro-Diels-Alder (RDA) reaction of 1,4,4a,9a-tetrahydro-4a-methyl-(1α,4α,4aα,9aα)-1,4- methaneanthracene-9,10-dione and the 1,3-dipolar cycloaddition of benzonitrile oxide with N-n-butylmaleimide. Plots of logk vs the molar concentration or volume fraction of water are approximately linear, but with a characteristic break around 40 M water. This break, absent for the RDA reaction, is ascribed to hydrophobic effects. Comparison with aqueous mixtures of the more hydrophobic 1-propanol shows that these mixtures induce qualitatively similar effects on the rate, but that preferential solvation effects cause the mixtures of 1-propanol to exhibit a more complex behavior of logk on composition. The results are analyzed using the Abraham-Kamlett-Taft model. The solvent effects in aqueous mixtures are not satisfactorily described by this model. For some cycloadditions, small maxima in rate are observed in highly aqueous mixtures of alcohols. The origin of these maxima and the aforementioned breaks is most likely the same. Copyright

Full text of DOI:10.1002/poc.926

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2005; 18: 725–736
Published online 5 May 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/poc.926
Cycloadditions in mixed aqueous solvents:
the role of the water concentrationy
Theo Rispens and Jan B. F. N. Engberts*
Physical Organic Chemistry Unit, Stratingh Institute, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
Received 19 January 2005; revised 17 February 2005; accepted 22 February 2005
ABSTRACT: We examined the kinetics of a series of cycloaddition reactions in mixtures of water with methanol,
acetonitrile and poly(ethylene glycol) (MW 1000). The reactions include the Diels–Alder (DA) reaction between
cyclopentadiene and N-n-butylmaleimide or acridizinium bromide, the retro-Diels-Alder (RDA) reaction of
1,4,4a,9a-tetrahydro-4a-methyl-(1ꢀ,4ꢀ,4aꢀ,9aꢀ)-1,4-methaneanthracene-9,10-dione and the 1,3-dipolar cycloaddi-
tion of benzonitrile oxide with N-n-butylmaleimide. Plots of logk vs the molar concentration or volume fraction of
water are approximately linear, but with a characteristic break around 40 M water. This break, absent for the RDA
reaction, is ascribed to hydrophobic effects. Comparison with aqueous mixtures of the more hydrophobic 1-propanol
shows that these mixtures induce qualitatively similar effects on the rate, but that preferential solvation effects cause
the mixtures of 1-propanol to exhibit a more complex behavior of logk on composition. The results are analyzed using
the Abraham–Kamlett–Taft model. The solvent effects in aqueous mixtures are not satisfactorily described by this
model. For some cycloadditions, small maxima in rate are observed in highly aqueous mixtures of alcohols. The
origin of these maxima and the aforementioned breaks is most likely the same. Copyright # 2005 John Wiley & Sons,
Ltd.
KEYWORDS: cycloadditions; mixed aqueous solvents; water; Diels–Alder reaction
INTRODUCTION
To obtain a more complete picture of the reactivity in
aqueous environments, we have studied a series of DA
reactions in mixtures of water with several ‘hydrophilic’
cosolvents/cosolutes: polyethylene glycol (average mol.
weight 1000) (PEG1000), methanol, and acetonitrile.
Methanol and acetonitrile have a much smaller tendency
to solvate molecules preferentially in an aqueous envir-
onment, compared with, e.g., 1-propanol. Methanol is,
like water, both a good hydrogen-bond donor and accep-
tor. Acetonitrile, on the other hand, is a poor hydrogen-
bond donor and only a relatively weak hydrogen-bond
acceptor. This difference is nicely reflected, for instance,
in the thermodynamics of mixing. Methanol mixes with
water exothermically, whereas acetonitrile does so en-
dothermically, because it ruptures the hydrogen-bond
network of water without forming (strong) hydrogen
bonds itself. PEG is a good hydrogen-bond acceptor,
but is unable to donate hydrogen-bonds.
The reactions studied (I–IV) are shown in Scheme 1.
They include the DA reaction between cyclopentadiene
(1) and N-n-butylmaleimide (2) [reaction (I)], the DA
reaction between 1 and acridizinium bromide (4) [reac-
tion (II)], the retro-Diels–Alder (RDA) reaction of
1,4,4a,9a-tetrahydro-4a-methyl-(1ꢀ,4ꢀ,4aꢀ,9aꢀ)-1,4-
methaneanthracene-9,10-dione (6) [reaction (III)] and
the 1,3-dipolar cycloaddition (DC) between benzonitrile
oxide (8) and 2 [reaction (IV)]. Reaction (I) is an example
Diels–Alder (DA) reactions in aqueous media have
been studied thoroughly1 since the pioneering work of
Breslow’s group in the early 1980s.2 In particular, salt
solutions of both salting-in and salting-out agents3 and
mixtures of water with alcohols (ethanol, propanol)4,5
have been used frequently as the reaction medium.
Nevertheless, aqueous Diels–Alder (DA) reactions have
not revealed all their secrets yet. It has been well
established that no single interaction mechanism is re-
sponsible for the dependence of the rate constants on the
composition of (aqueous) solvent mixtures. Solvent po-
larity, hydrogen bonding and enforced hydrophobic inter-
actions are important factors that may affect the rate
constant. Aqueous mixtures with hydrophobic cosolvents
such as 1-propanol are particularly complex, as prefer-
ential solvation effects may become significant, which
hampers the search for correlations of reaction rates with
composition. It is therefore surprising that little attention
has been given to aqueous mixtures of, e.g., methanol, or
other ‘simpler’ cosolvents.
*Correspondence to: J. B. F. N Engberts, Physical Organic Chemistry
Unit, Stratingh Institute, University of Groningen, Nijenborgh 4, 9747
AG Groningen, The Netherlands.
E-mail: j.b.f.n.engberts@rug.nl
ySelected paper presented for a special issue dedicated to Professor
Otto Exner on the occasion of his 80th birthday.
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 725–736

726
T. RISPENS AND J. B. F. N. ENGBERTS
Scheme 1
of a typical DA reaction, in which the dienophile is
capable of accepting hydrogen bonds, which promotes
the rate of the reaction. Reaction (II), on the other hand,
involves two reactants that are not or only very weakly
susceptible to hydrogen-bond formation. Comparison of
reactions (I) and (II) may offer insight into the contribu-
tion of (direct) hydrogen bonding to changes in rate. The
RDA reaction (III) reflects the reverse process of reaction
(I). The activation process of this reaction can be influ-
enced by hydrogen-bond formation, but association of
two reactions (as part of the reaction) is absent. There-
fore, hydrophobic effects play only a minor role in
governing the rate of this reaction. Finally, reaction
(IV) involves two relatively polar substrates, that are
both susceptible to hydrogen bonding. A summary is
provided in Table 1.
RESULTS AND DISCUSSION
Aqueous mixtures of methanol,
acetonitrile, 1-propanol and PEG1000
In Figs 1–4, the logarithms of the rate constants (logk) are
plotted against the concentration of water for reactions
Table 1. Sensitivity of the rate constants of reactions I–IV
Reaction
Hydrogen bonding
Hydrophobic effects
(I)
þ
0
þ
þ
0
þ
Figure 1. Log k vs the concentration of water for the reaction
of 1 with 2 at 25 ꢁC in mixtures of water with PEG1000 (&),
methanol (~), acetonitrile (ꢂ) and 1-propanol (*; values for
ethyl- rather than n -butylmaleimide are indicated with ꢃ). k
has units Mꢄ1 sꢄ1
(II)
(III)
(IV)
þ
a
ꢀ
a
Hydrogen bonding to both reactants influence rate in opposite ways.
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CYCLOADDITIONS IN MIXED AQUEOUS SOLVENTS
727
Figure 4. Log k vs the concentration of water for the reaction
of 2 with 8 at 25 ꢁC in mixtures of water with PEG1000 (&),
methanol (~), acetonitrile (ꢂ) and 1-propanol (*). k has
units Mꢄ1 sꢄ1
Figure 2. Log k vs the concentration of water for the reaction
of 1 with 4 at 25 ꢁC in mixtures of water with PEG1000 (&),
methanol (~), acetonitrile (ꢂ) and 1-propanol (*). k has
units Mꢄ1 sꢄ1
(I)–(IV) in mixtures of water with methanol, acetonitrile
and PEG1000. We chose to plot the data against the molar
concentration of water because the concentration is a
measure of the amount of water present per unit volume,
independent of the size of the cosolvent molecules, in
contrast to the mole fraction scale. The volume fraction
of water also scales with the (molar) concentration of
water, although only insofar as the solvents mix ideally.
The non-ideal part is only a minor contribution, although
typically a few percent. Interestingly, linear dependences
are found of logk on [H2O] over large ranges of concen-
trations, with one (or two) relatively sharp bends.
For comparison, aqueous mixtures of 1-propanol were
also examined. Although the data for 1-propanol roughly
follow the same patterns found for methanol and acet-
onitrile, no linear dependence of logk on the concentra-
tion of water is observed. This behavior is attributed to
preferential solvation effects. Nevertheless, one essential
feature is evident for all cosolvents: in the water-rich
regime there is a sudden change in slope at around 40 M
water (except for the RDA reaction; see below). Gener-
ally, the breaks occur at a somewhat higher concentration
for acetonitrile than for methanol, with the break for 1-
propanol in between. The breaks may reflect the ability of
the water to maintain its hydrogen-bond network in the
different mixtures (see below).
Disregarding reaction (III) for the moment, when
comparing methanol and acetonitrile, the rate constants
are invariably larger in methanol or aqueous mixtures of
methanol than in acetonitrile or aqueous mixtures of
acetonitrile. This is as expected, since methanol is more
polar and capable of donating hydrogen bonds. Starting
from either pure methanol or acetonitrile, logk increases
linearly with the concentration of water over an extended
range (up to 35–45 M), although for methanol a deviation
is found at low concentrations of water in the case of
reaction (I). The slopes are nearly identical for methanol
and acetonitrile in each case. This is remarkable: one
would expect the slope to be higher for acetonitrile,
because the hydrogen-bond donating capacity varies
more dramatically in aqueous mixtures of acetonitrile
(based on ꢀ; see below).
In the water-rich regions, the slopes of logk vs [H2O]
become close to zero, and occasionally slightly negative.
In the latter case, a maximum in rate constant is observed
around 40 M water.
Solutions of PEG1000 were also studied, up to a
concentration of 500 g lꢄ1. At still higher concentrations
of PEG1000, the increased viscosity prohibited an accu-
rate determination of rate constants. In cases, where
maxima for the rate constants were found for alcohols
[reactions (II) and (IV)], PEG1000 displays a similar
pattern, and the maxima even exceed those found for 1-
propanol. However, this is not a general observation: for
the reaction of cyclopentadiene with naphthoquinone, a
Figure 3. Log k vs the concentration of water for the
unimolecular reaction of 6 at 40 ꢁC in mixtures of water
with PEG1000 (&), methanol (~), acetonitrile (ꢂ) and 1-
propanol (*). k has units sꢄ1
Copyright # 2005 John Wiley & Sons, Ltd.
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728
T. RISPENS AND J. B. F. N. ENGBERTS
maximum was found in mixtures of water with 2-methyl-
2-propanol,4 but not in aqueous solutions of PEG400.6 In
any case, the maxima are not just a peculiarity, caused
only by hydrophobic cosolvents, such as propanol or
butanol. Even methanol may induce an additional accel-
eration, albeit smaller than that found for 1-propanol.
For the RDA reaction, the characteristic changes in
slope at around 40 M water are absent. For methanol, two
linear areas are found, between 0 and 15 M and between
15 and 55 M. For acetonitrile, logk is linear with [H2O]
over the entire range of composition. We suggest that the
origin of the changes in slope of logk vs [H2O] around
40 M water for the other reactions lies in hydrophobic
effects, as for the RDA reaction changes in hydrophobi-
city (during the activation process) are minor.7
Comparing reactions (I) and (II), the behavior of logk
in the various mixtures is qualitatively similar, despite the
fact that reaction (II) is not directly influenced by hydro-
gen bonds. The magnitudes of the changes in rate con-
stant are much larger for reaction (I) than for reaction (II),
however. A similar behavior (large linear regions, parti-
cularly for acetonitrile, with changes in slope in the
water-rich region) may result from the fact that the under-
lying mechanisms responsible for determining the rate
variations are the same, and only the solvent sensitivities
of the various reactions are different. This would rule out
direct hydrogen bonding as an important contributor to
changes in rate, which is not in line with previous
results.1 Alternatively, the other factors that influence
the rate (in particular solvent polarity) and direct hydro-
gen-bond interactions vary with solvent composition in a
similar manner, either coincidentally, or because of a
more fundamental reason.
parameter scales such as ET(30),9 and multiparameter
scales, such as the Abraham–Kamlett–Taft (AKT) model
(see below). Single-parameter scales try to avoid the
difficult task of attributing complex trends in, for exam-
ple, rate constants to variations in several ‘fundamental’
properties (e.g. electron-pair donating ability), by captur-
ing them into a single, composite parameter. Such corre-
lations naturally will be satisfactory only if the process
under consideration bears some resemblance to the one
on which the scale is based. Its main advantage is its
simplicity. A major drawback is that correlations are still
difficult to interpret. The multiparameter approach aims
at more transparent correlations. Although usually em-
pirical in nature, the individual parameters have a more
fundamental flavor, capturing a single solvent property at
a time. The AKTapproach,10 in its basic form, recognizes
three aspects of solvation effects: dipolarity/polarizabil-
ity (ꢁꢅ), hydrogen-bond acidity (ꢀ) and hydrogen-bond
basicity (ꢂ). The parameters are derived from spectral
changes (UV–visible, NMR) for probe molecules that are
sensitive to changes in these properties to various extents.
Often, additional parameters that account for ‘solvopho-
bicity’ are included, such as the Hildebrand solubility
parameter (ꢃ2), based on the enthalpy of vaporization per
unit volume of the solvent, or the solvophobicity para-
meter (Sp), based on transfer parameters of low molecu-
lar weight alkanes and noble gases from organic solvents
to water.11
For a variety of DA reactions, rate constants were
found to correlate with one or more properties of the
solvents.12–20 In most cases, the AKT model10 was used
to account for different aspects of solvent polarity.
Usually, only pure solvents are taken into account, and
often water is not included in the analyses. Desimoni
et al.12 analyzed solvent effects on a wide range of DA
reactions and, based on that analysis, made a division into
three types of DA reactions: type A, reactions that are
mainly affected by the hydrogen-bond donor capacity ꢀ
of the solvent, although significant contributions of ꢁꢅ are
sometimes also present; type B, reactions that mainly
respond to changes in ꢂ; and type C, reactions that are
insensitive to both ꢀ and ꢂ. In another study,14 satisfac-
tory fits were obtained with contributions of ꢀ, ꢁ and Sp.
Upon inclusion of water, the contribution of Sp vastly
increased. Mayoral and co-workers analyzed several DA
reactions in a range of solvents, including aqueous
mixtures.15,17,18 Again, ꢀ and Sp were found to be im-
portant. Their relative contributions differed substantially
when only aqueous mixtures or only (non-aqueous)
solvents were taken into account.
For the DC reaction (IV), the rate constants are hardly
affected by changes in medium (k varies by a factor of
< 2.5 in the case of methanol and < 4 in case of
acetonitrile). For this reaction we found that the different
types of interactions that affect the rate oppose each
other, resulting in modest overall medium effects.8 De-
spite this, the qualitative picture again is strikingly
similar to that for reactions (I) and (II).
Correlations with the composition
of the medium
In order to elucidate the origins of these solvent effects,
we consider different approaches to rationalizing the
data. In particular, attempts were made to fit the data to
a multiparameter model, and comparisons are made with
standard Gibbs energies of transfer in mixed aqueous
solvents.
The single-parameter ET(30) polarity scale does not
account for the observed trends in logk presented in the
previous section. Instead, we have attempted to rationa-
lize the observed trends in rate constants of the different
reactions in terms of the AKT model, using the equation
Linear multiparameter models. Properties of sol-
vents, in particular solvent polarity, have been captured
in a multitude of empirical scales, among them single-
logk ¼ constant þ aꢀ þ bꢂ þ pꢁꢅ þ sSp
J. Phys. Org. Chem. 2005; 18: 725–736
ð1Þ
Copyright # 2005 John Wiley & Sons, Ltd.

CYCLOADDITIONS IN MIXED AQUEOUS SOLVENTS
729
The coefficients a, b, p and s describe the relative
contributions (they are not directly comparable with
each other, as the scales for ꢀ, ꢂ, ꢁꢅ and Sp are arbitrary
and only have indirect physical meaning; to circumvent
this, ‘standardized coefficients’ may be calculated14) of
the different solvent properties, described by ꢀ, ꢂ, ꢁꢅ and
Sp. For mixtures of water with methanol, values are
available for all parameters. For acetonitrile as the
cosolvent, values of ꢀ, ꢂ and ꢁꢅ are available, and values
of Sp were estimated. Mixtures with 1-propanol were not
taken into consideration, as preferential solvation effects
are expected to interfere. The aqueous PEG mixtures will
only be considered qualitatively, because no reasonable
estimates for Sp could be made. In all cases, some
parameters did not contribute significantly to the fit,
and fits without these parameters were performed subse-
quently. A set of parameters used in a fit will be placed in
braces, e.g. fꢀ; ꢁꢅg means a fit only including ꢀ and ꢁꢅ.
Although the aim was to study the contributions of the
different properties in aqueous mixtures, pure solvents
were also considered. The motivation was twofold. First,
comparing results obtained for a series of solvents with
those obtained for the mixures might be considered a
consistency check. Alternatively, comparison may point
out qualitative or quantitative differences between aqu-
eous mixtures and non-aqueous solvents. Second, the
parameters ꢁꢅ and Sp, although poorly correlated for
pure solvents (r ¼ 0:620 for all solvents considered in
this paper; r ¼ 0:495 when water is omitted), turned out
to be much better correlated in mixtures of water with
methanol or acetonitrile (r ¼ 0:951).
results are also presented, with smaller but still satisfac-
tory regression coefficients. For a number of fits, calcu-
lated values of logk are shown in Fig. 5, together with the
experimental values.
For reaction I, when only mixtures are considered, the
best fit is obtained with fꢀ; ꢁꢅg, but with fꢀ; Spg a good
fit is also obtained. Perhaps the most striking result is the
close similarity in behavior of logk and ꢁꢅ in water–
methanol mixtures. For pure solvents, on the other hand,
an acceptable fit is obtained only for fꢀ; Spg. This result
can be accounted for because water was included in the
fit. Sp ranges from 0 to 0.35 for organic solvents, but for
water Sp ¼ 1. Therefore, a much larger rate in water than
in organic solvents is conveniently captured by Sp. The
inclusion of water usually amplifies the contribution of
Sp.14 Including the (other) pure solvents in the fits for the
mixtures yields the best fit with fꢀ; Spg (r ¼ 0:979; for
fꢀ; ꢁꢅg, r ¼ 0:88). The coefficients are within error
margins consistent with each other. One interesting point
to note is that although ꢀ contributes significantly, its
characteristic pattern in mixtures of water and acetoni-
trile, with a drastic increase at low concentrations of
water, is not reflected in the experimental logk.
For reaction (II), the series of pure solvents did not give
a proper fit. This result may be due in part to the limited
number of points (8). Nevertheless, the dependence of
logk on the solvent is complex and may not be fully
captured by the AKT model. For aqueous mixtures, a
strange result is obtained. Two mutually exclusive com-
binations of parameters give reasonable fits (fꢀ; ꢁꢅg,
r ¼ 0:963; fꢂ; Spg, r ¼ 0:979). With fꢂ; Spg, unlike
fꢀ; ꢁꢅg, the characteristic maxima in the plots of logk
vs the concentration of water could be reproduced.
The results in Table 2 only include parameters that
contribute significantly. In a few instances, alternative
Table 2. Summary of fits using the AKT modela
Reaction
(I)
System
Mixturesb
a
b
p
s
r
1.42 (0.17)
1.08 (0.30)
0.88 (0.22)
0.92 (0.17)
—
—
—
—
—
4.16 (0.24)
—
—
0.991
0.975
0.981
0.979
0.979
0.963
2.45 (0.23)
2.09 (0.34)
2.33 (0.16)
1.34 (0.07)
—
Pure solvents (7)c
All
Mixtures
—
—
(II)
III
1.86 (0.24)
—
—
1.53 (0.19)
0.58 (0.13)
Pure solvents (8)d
All
Mixtures
ꢂ
ꢂ
ꢂ
ꢂ
ꢂ
e
e
e
e
e
0.44 (0.11)
0.43 (0.11)
0.65 (0.13)
0.80 (0.07)
0.74 (0.13)
0.82 (0.06)
0.75 (0.07)
—
—
—
1.27 (0.19)
—
—
1.13 (0.09)
—
0.909
0.984
0.975
0.986
0.958
0.975
0.970
0.977
—
—
—
—
1.77 (0.18)
1.01 (0.15)
—
1.09 (0.10)
—
—
Pure solvents (10)d
All
—
1.03 (0.32)
—
0.93 (0.10)
0.88 (0.04)
—
1.46 (0.16)
(IV)
Mixtures
Pure solvents (13)f
All
ꢂ
ꢂ
ꢂ
ꢂ
ꢂ
e
e
e
e
e
—
0.37 (0.13)
—
0.635 (0.09)
0.775
a
Error margins given in parentheses.
Aqueous mixtures of methanol and acetonitrile.
Some values taken from Ref. 21.
Some values taken from Ref. 5.
No acceptable fit with any combination of parameters could be obtained.
Values from Ref. 8.
b
c
d
e
f
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730
T. RISPENS AND J. B. F. N. ENGBERTS
Figure 5. Overview of logk values in mixtures of water with methanol (left) and acetonitrile (right) as determined from various
fits (open symbols). Experimental values are indicated with closed squares
Copyright # 2005 John Wiley & Sons, Ltd.
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CYCLOADDITIONS IN MIXED AQUEOUS SOLVENTS
731
Mathematically, this pattern is caused by the fact that ꢂ
increases on going from pure water to mixtures of water
with either methanol or acetonitrile. This reaction falls
into Desimoni et al.’s category B,13 thus sensitive to ꢂ, in
line with the result from our fit. On the other hand, logk
also increases in mixtures of water with PEG, for which ꢂ
was found to be constant up to 40 wt% of PEG.22 There-
fore, at least for mixtures of water and PEG, a sensitivity
for ꢂ cannot explain a rate increase relative to water.
When pure solvents and mixtures are combined, the most
satisfactory fit is obtained with fꢀ; ꢁꢅg, but the correla-
tion becomes much less satisfactory (r ¼ 0:909), con-
sidering that the majority of data points (ꢆ20) included
in the fit are those for the mixtures (for which r ¼ 0:963).
For reaction (III), good fits were obtained with either
fꢀ; ꢁꢅg or fꢀ; Spg. This is true for pure solvents (10),
mixtures or a combination. For pure solvents, fꢀ; ꢁꢅg
produces the better fit. This result was expected because
this reaction does not involve the association of two
reactants during the activation process; solvophobic ef-
fects play only a minor role. It is therefore strange that
(also) for pure solvents, for which ꢁꢅ and Sp correlate
poorly, a good fit is obtained with fꢀ; Spg. This result
confirms that results from multiparameter analyses
should not be interpreted on a simple basis. Overall, the
fits with fꢀ; ꢁꢅg give the most consistent results. The
relative contributions of ꢀ and ꢁꢅ are both larger than
those found by Desimoni et al.13 for this reaction at
90 ꢁC, but the ratio ꢀ=ꢁꢅ is the same (note that they did
not include water in the fit). Therefore, at higher tem-
peratures, the reaction rate is less dependent on the
solvent (the values of ꢀ and ꢁꢅ have, in fact, been deter-
mined at 25 ꢁC, and may not be applicable to systems at
temperatures as high as 90 ꢁC).
water with methanol, ꢀ is nearly constant. Therefore, the
similar trends observed for logk in both types of mixtures
point towards a weak dependence on the hydrogen-bond
donating capacity. This conclusion is not fully confirmed
by the fits, which reveal significant contributions of ꢀ, but
the deviation of the calculated values of logk from the
experimental values in acetonitrile-rich water–acetoni-
trile mixtures [especially for reaction (III)] shows that the
contribution of ꢀ may be overestimated. In any case, the
model at best only partially reproduced the characteristic
trends in logk observed in these aqueous mixtures.
Transfer parameters and the log-linear model.
Another method for rationalizing trends in rate constants
considers initial state (IS) and transition state (TS) effects
separately (within the framework of transition state
theory). This method requires that transfer parameters
of the reactants are known. Those of the activated com-
plex (AC) can be derived subsequently from those of
the reactants in combination with the activation para-
meters. We did not determine transfer parameters for
the reactants. Nevertheless, a qualitative discussion is
worthwhile.
For the DA reaction between cyclopentadiene (1) and
methyl vinyl ketone (MVK), resembling reaction (I),
transfer parameters have been determined for aqueous
mixtures of 1-propanol (Fig. 6).4 They reveal a minor
dependence of ÁtrGꢁ(TS) on the solvent composition;
especially for [H2O] > 30 M, ÁtrGꢁ(TS) is nearly con-
stant, and increases slightly. For several other DA reac-
tions, ÁtrGꢁ(TS) from water to organic solvents was
very small21,23 and the small dependence of ÁtrGꢁ(TS)
on the nature of the reaction medium may be a general
phenomenon.
For reaction (IV), the results loosely resemble those for
reaction II. Trends in logk among pure solvents are not
satisfactorily described by the AKT model, as expected
for a reaction with a particularly complicated dependence
of logk on the solvent.8 For aqueous mixtures of methanol
or acetonitrile, on the other hand, a good fit is obtained
with ꢂ and Sp. Again, only the rate profiles for mixtures
of water with methanol or acetonitrile are properly
described; the higher maxima in aqueous mixtures of
1-propanol, 2-methyl-2-propanol or PEG1000 cannot be
explained by a dependence on ꢂ.
For both 1 and MVK, two approximately linear regions
are observed, with a bend, which for 1 occurs in the same
region as found for logk. The dependence of ÁtrGꢁ(1) is
particularly noteworthly. Inspection of Gibbs energies of
transfer from water to aqueous solvent mixtures [data
In summary, for reactions (I) and (III), the AKT model
does a fair job and fꢀ; ꢁꢅg or fꢀ; Spg suffice to describe
trends in logk, both in pure solvents and in aqueous
mixtures. For reactions (II) and (IV), logk cannot be
correlated accurately for pure solvents. In aqueous mix-
tures of methanol or acetonitrile, fꢂ; Spg can account for
the observed trends, including the small rate maxima, but
as the same observations for aqueous PEG solutions
cannot be described in this manner, this result may not
have physical significance. In mixtures of water with
acetonitrile, ꢀ varies considerably, and strongly non-
linearly with the concentration of water. In mixtures of
Figure 6. Gibbs energies of transfer (ÁtrGꢁ) for 1 (*), MVK
(&) and the AC (~), for the reaction of 1 with MVK in
mixtures of water with 1-propanol (relative to 1-propanol)4
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732
T. RISPENS AND J. B. F. N. ENGBERTS
were collected from the literature, as cited in the text, in
many cases, only solubilities were reported, which were
converted to ÁtrG, all data were converted to the molar
¨
concentration scale (Ben-Naım standard state), according
to the procedures described in Ref. 24, to allow compar-
ison] reveals that for a multitude of organic compounds, a
similar pattern is found, with a small initial decrease in
ÁtrGꢁ down to [H2O] ꢇ 40 M and a sharper decrease for
[H2O] 40 M.25–38 Especially small, purely hydrophobic
<
ꢆ
solutes such as (gaseous) alkanes and benzene show this
behavior; the effect becomes more prominent for the
more hydrophobic cosolutes, in particular 2-methyl-2-
propanol, and at lower temperatures. For the alkanes, at
elevated temperatures ÁtrGꢁ initially slightly decreases;
at room temperature ÁtrGꢁ is essentially constant up to
[H2O] ꢇ 40 M, and at lower temperatures initially even a
small increase in ÁtrGꢁ is found, resulting in a small
maximum around 40 M water. The origin of this effect
undoubtedly follows from the characteristic way in which
water hydrates apolar substrates. In ‘pure’ water, hydro-
phobic hydration shells form around apolar solutes upon
dissolution. This is a cooperative process involving many
water molecules and is a special feature of water. How-
ever, mixing water with more and more cosolvent ulti-
mately leads to the remaining water acting as ‘normal’
solvent molecules. Or, looking at it another way, when
adding water to, for example, ethanol, the solution be-
comes more polar, as more and more water molecules are
present, which will form hydrogen bonds with a solute if
possible. When the mixture contains more and more
water, at a certain point (atꢆ40 M water), water starts to
form three-dimensional hydrogen-bonded clusters of
‘bulk-like’ water. Now, hydrophobic hydration becomes
increasingly important. Compared with pure ethanol, an
apolar substrate will be increasingly less comfortable with
increasing amounts of water (the Gibbs energy increases).
This trend continues when hydrophobic hydration sets in,
but to a lesser extent, as hydrophobic hydration is less
strenuous than the (at this point hypothetical) alternative,
‘normal’ mode of solvation. Widely varying values for
ÁtrHꢁ and ÁtrSꢁ in this regime accompany this transition.
For many other organic compounds, usually bear-
ing (several) polar groups, ÁtrGꢁ is almost a linear
function of the volume fraction of water (linear with
[H2O]).29,33,39–51 This pattern is expressed by the so-
called log-linear model,46 which simply states that
logSm ¼ f logSx þ ð1 ꢄ fÞlogSw, where Sm, Sx and Sw
are the solubilities in the mixture, the cosolvent and
water, respectively, and f is the volume fraction. We
note that ÁtrG is the Gibbs energy of transfer of a solute
from solvent 1 to solvent 2 at 1 M, under the assumption
the conditions resemble those at infinite dilution. This is
approximately the same as ꢄRT lnðS2=S1Þ, the main
difference being possible contributions of solute-solute
interactions to the solubility, especially when the solubi-
lity is high. In cases where correction factors (activity
coefficients) have been determined, they usually turn out
Figure 7. Gibbs energies of transfer (ÁtrGꢁ) for betaine-30
from water to mixtures of water with acetonitrile (&) or
ethanol (*), calculated from solubility data39
to be small. Plots consisting of two linear parts are also
sometimes encountered.33,49,51–54 However, when a so-
lute has a more complex structure, with polar and apolar
parts combined in a single molecule, different parts of the
solute molecule may become preferentially solvated by
either of the solvents in mixed solvents, and ÁtrGꢁ
becomes a more complex function of the composi-
tion.36,42,53,55–63 Indeed, ÁtrGꢁ can even pass through a
minimum. A good example of both types of behavior is
shown by betaine-30, for which ÁtrGꢁ is nearly a linear
function of the volume fraction in water–ethanol mix-
tures, but passes through a minimum in water–acetoni-
trile mixtures (Fig. 7).
That ÁtrGꢁ is often a linear function of the volume
fraction over all or parts of the composition range in
aqueous solvent mixtures is in line with the kinetic data
for DA reactions: if ÁtrGꢁ is a linear function of volume
z
fraction for both IS and TS, Á Gꢁ (or logk) will also form
a linear plot. We note that if a particular functional group
in one of the reactants causes a deviation from linearity in
ÁtrGꢁ(IS), and if this group is not involved in the
activation process, because its position is remote from
the reaction center, it will do so for ÁtrGꢁ(TS) likewise,
and this non-linearity cancels in ÁzGꢁ. Recently, we
found a nearly linear dependence of logk on the concen-
tration of water for the hydrolysis of p-methoxyphenyl-
2,2-dichloroacetate in binary aqueous mixtures of
acetonitrile, tetrahydrofuran and PEG400.64
One phenomenon that may in part be rationalized in
terms of transfer parameters is the small rate enhance-
ment, sometimes found in highly aqueous mixtures.
Suppose the Gibbs energy of the AC, a species that is
apparently not very sensitive to changes in medium,
decreases slightly with decreasing water content (on
going from water to aqueous solvent mixtures). If the
IS follows the pattern in ÁtrGꢁ found for, e.g., 1, the
resulting ÁzGꢁ will also reflect this pattern (in reverse),
and in some cases a minimum in ÁzGꢁ (maximum in rate
constant) is observed. This pattern is illustrated in Fig. 8.
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CYCLOADDITIONS IN MIXED AQUEOUS SOLVENTS
733
That ÁtrGꢁ is related to the volume fraction is most
likely due to the fact that the probability of finding
solvent 1 or 2 at a particular position in the solvation
shell around a solute (in the condensed phase) depends on
the volume fraction. Hence, in the absence of widely
differing strengths of interactions, the solute–solvent
interactions constituting the total solvation (and ÁtrGꢁ)
are the average with respect to the volume fraction. We
note that in a thermodynamic approach, often the mole
fraction scale is used, as chemical potentials are usually
described referring to partial vapor pressures, which are
related to mole fractions. Although this is formally a
correct approach, it neglects the structure of a condensed
liquid phase, where any molecule is necessarily sur-
rounded by (solvated by) other molecules. Although the
volume fraction scale also has its drawbacks, it does
recognize this fact and accounts for differences in size
between solvent molecules.
Figure 8. Illustration of a combination of Gibbs energies of
transfer for an IS and a TS that will lead to a minimum in
ÁzGꢁ (maximum in rate) at [H2O] ꢇ 40 M
When one solvent strongly interacts with the solute, this
interaction can be regarded as binding, and a binding
curve will be observed instead. However, if the two
solvents have comparable, strong interactions, this effect
is strongly moderated (for specific interactions, such as
hydrogen bonds, the ratio of the number densities will
describe the average solvation; if one or both solvents bear
several functional groups that are able to act as ‘binding
sites’, the number densities of these groups, rather than of
the solvent molecules, will be the determining factor).
In many cases, the mode of solvation is intermediate
between these two extremes; commonly referred to as
preferential solvation. Because Sp is derived from Gibbs
energies of transfer, it is not surprising that Sp also
correlates approximately linearly with the volume frac-
tion in mixed solvents. (One could argue that Sp contains
In line with the temperature dependence of ÁtrGꢁ of
alkanes in aqueous mixtures (see above), kmax=kw was
found to decrease with temperature for reaction (IV).
Regardless of whether a maximum is observed or not, a
sudden change in slope of logk vs the concentration of
water is observed almost invariably for any DA reaction.
In most cases, this can be explained by assuming that
ÁtrGꢁ(IS) resembles the pattern found for 1, and that
ÁtrGꢁ of the (less hydrophobic) TS varies little (and
linearly) with composition. The ‘reduction in hydropho-
bicity’ as an integral part of the activation process is
reflected in the activation Gibbs energy, with a character-
istic bend at [H2O] ꢇ 40 M. Only for RDA reactions, for
which the hydrophobicity hardly changes on going from
the IS to the TS, is this phenomenon absent.
Figure 9. Values of logðendo=exoÞ for 1 þ MVK in mixtures of water with methanol (~), ethanol (^), 1-propanol (*), and
2-methyl-2-propanol (!), re-plotted versus the molar concentration of water. Inset: plotted versus the mole fraction of water4
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 725–736

734
T. RISPENS AND J. B. F. N. ENGBERTS
information about only part of the ‘solvophobicity’. A
function ÁGtr ¼ ax þ b, with x a constant for a given
solute, was fitted for compilation of several hydrophobic
compounds.11 Values of a were normalized to give Sp;
but also b varies considerably and that information is just
not used.)
with consistent sets of parameters (important contribu-
tions of fꢀ; Spg and fꢀ; ꢁꢅg, respectively). Overall,
solvent effects in aqueous mixtures were not satisfacto-
rily described. The results call for a further study of the
role of the hydrogen-bond donor capacity.
Small maxima in the rate constant are sometimes
observed for cycloadditions in highly aqueous media, at
around 40 M water. The maxima seem to be the outcome
of the different dependences of the Gibbs energies of
transfer of the initial state and the transition state. The
former follow a pattern, characteristic for many hydro-
phobic compounds, where ÁtrGꢁ changes little down to
about 40 M water, after which it decreases considerably.
The latter are characteristic for a more polar compound,
with a more gradual decrease in ÁtrGꢁ.
In Fig. 9, logðendo=exoÞ is plotted for the reaction of 1
with MVK in aqueous mixtures of alcohols. Except for 1-
propanol, logðendo=exoÞ is linear with [H2O] over the
entire range of composition, albeit with some scattering.
Because logðendo=exoÞ is determined solely by the differ-
ence in Gibbs energy of the TS, this is not an unexpected
result.Themorecomplicatedtrendsinlogk aredue(atleast
in part) to IS effects. As the TS is thought not to be very
hydrophobic, this pattern shows that in the absence of
hydrophobic effects, (and in the absence of preferential
solvation effects), trends in transfer Gibbs energies in
water–alcoholmixturesarelinearwiththevolumefraction.
In conclusion, the solvent dependence of ÁzGꢁ may be
understood in terms of ÁtrGꢁ of IS and TS. The linear
trends in ÁzGꢁ over large parts of the volume fraction (or
molar concentration) of water reflect the often found
linear dependence of ÁtrGꢁ on the volume fraction.
Moreover, the breaks around 40 M water reflect ÁtrGꢁ
for many hydrophobic compounds, including 1. A weak
composition dependence of ÁtrGꢁ for the hydrophobic IS
before the break, combined with an also weak yet slightly
larger decrease in ÁtrGꢁ of the more polar TS, may even
turn the break into a maximum. A drawback of this
thermodynamic approach is that it provides less insight
at the mechanistic level than the AKT approach.
EXPERIMENTAL
Materials
N-n-Butylmaleimide (2)21 and 1,4,4a,9a-tetrahydro-4a-
methyl-(1ꢀ,4ꢀ,4aꢀ,9aꢀ)-1,4-methaneanthracene-9,10-
dione (6)5 have been synthesized previously. All other
materials were obtained from commercial suppliers, and
were of the highest purity available. Solvents were either
of analytical grade or distilled; acetonitrile was purified
over basic aluminium oxide prior to use. Acridizinium
bromide (4) was prepared by a literature procedure;65,66
H-NMR (D2O): ꢃ 9.92 (s, 1H), 9.02 (d, J ¼ 7.5 Hz, 1H),
8.84 (s, 1H), 8.36 (d, J ¼ 9.3 Hz, 1H), 8.29 (d, J ¼ 8.6 Hz,
1H), 8.18 (d, J ¼ 8.6 Hz, 1H), 7.80–8.06 (m, 4H).
CONCLUSIONS
Kinetic experiments
For a number of different types of cycloadditions, mix-
tures of water with hydrophilic cosolvents and hydro-
phobic cosolvents affect reaction rates in a qualitatively
similar manner. The interesting pattern of logk, that changes
little in highly aqueous mixtures but (much) more strongly
at lower concentrations of water, is observed for different
kinds of cosolvents, regardless of their nature.
For the more hydrophilic cosolvents, extensive linear
dependences of logk on either the concentration or the
volume fraction of water are found. This pattern reflects
the thermodynamics of transfer of solutes from one sol-
vent (mixture) to another. In cases where no peculiarities
resulting from hydrophobic effects are expected, linear
dependences on the concentration or volume fraction of
water over the entire range of composition are found, e.g.
for logk (reaction III) or logðendo=exoÞ (reaction of
cyclopentadiene with MVK4). For more hydrophobic
cosolvents such as 1-propanol, preferential solvation
effects result in deviations from the linear trends.
Cyclopentadiene (1) + N-n-butylmaleimide (2)
or acridizinium bromide (4). Kinetic measurements
were performed using UV–visible spectroscopy (Perkin-
Elmer Lambda 5 spectrophotometer). Cuvets containing
the reaction mixture together with 2 or 4 were thermo-
stated at 25.0 ꢁC. After the addition of cyclopentadiene
(concentrated solution in acetonitrile), the reaction was
monitored at 298 or 376 nm, respectively. Rate constants
for 2 were obtained by conventional pseudo-first-order
kinetics, and rate constants were reproducible to within
3%. For 4, rate constants were determined using initial
rate kinetics, and rate constants were reproducible to
within 4%. Rate constants are the average of at least
three independent experiments. Stock solutions of 2 and 4
were made in acetonitrile and methanol, respectively.
In all cases, cyclopentadiene was used in excess. Typical
conditions were [1] ¼ 0.5–4 mM for 2 and 2–60 mM for 4;
[2] ¼ 0.05 mM; [4] ¼ 0.05–0.1 mM.
For reactions (I) and (III), a multiparameter analysis
using the AKT model reproduces solvent effects for pure
organic solvents and aqueous mixtures reasonably well,
Benzonitrile oxide (8) + N-n-butylmaleimide (2).
Kinetic measurements were performed as described
previously.67 Rate constants are the average of at least
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CYCLOADDITIONS IN MIXED AQUEOUS SOLVENTS
735
three independent experiments and were reproducible to
within 3%. Typical conditions were [2] ¼ 1–10 mM;
[8] ꢇ 0.025–0.05 mM.
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