4-Heptanone cyclic diperoxide: Improved preparation method and solvent effect on its thermolysis in solution

Article abstract of DOI:10.1002/kin.20600

Cyclic organic peroxides have interesting pharmacological properties and are used at industrial level as polyfunctional initiators of polymerization, and so their preparation through novel methods has attracted the attention of numerous researchers. White crystals of 4-heptanone cyclic diperoxide (HDP) can be obtained in acidic media at-1°C by a reaction between 4-heptanone and hydrogen peroxide. Its thermal decomposition was studied in acetone, cyclohexane, acetonitrile, ethyl acetate, ethanol, 2-propanol, 2-butanol, and 1,4-dioxane at temperatures higher than 120°C, showing a behavior accordingly with a pseudo-first-order kinetic law up to at least 80% HDP conversion. It was demonstrated that an increase in solvent polarity is accompanied by an increase in reaction rates. The effect of solvent polarity on the thermal decomposition rate constant values can be associated with a reaction mechanism involving a more dipolar-activated complex than the diperoxide initial molecule. The activation parameters varied widely from 31.2 to 46.6 kcal mol^-1 and-1.33 to 31.7 cal mol^-1 K^-1 when going from ethanol to cyclohexane as reaction solvents, respectively. An enthalpy-entropy compensation effect was observed in all solvents. Specific interactions between the oxygen atoms from the peroxidic bond and the hydrogen atom bonded to C2 and/or from the OH group can be taken into account to explain that the existence of the compensation effect does not mean that an isokinetic relationship consequently can be established. The kinetic results showed that an isokinetic relationship is observed only for a group of solvents.

Full text of DOI:10.1002/kin.20600

4-Heptanone Cyclic
Diperoxide: Improved
Preparation Method and
Solvent Effect on Its
Thermolysis in Solution
´
´
KARINA NESPRIAS, MARIANGELES IGLESIAS, SONIA RIVAS, ELIDA ALVAREZ, GASTON
˜
BARRETO, NORA EYLER, ADRIANA CANIZO
Department of Chemistry, Engineering Faculty, National University of the Center of Buenos Aires Province,
del Valle Avenue N◦ 5737, (B7400JWI) Olavarr´ıa, Buenos Aires, Argentina
Received 14 February 2011; revised 14 July 2011; accepted 14 July 2011
DOI 10.1002/kin.20600
Published online 2 September 2011 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: Cyclic organic peroxides have interesting pharmacological properties and are used
at industrial level as polyfunctional initiators of polymerization, and so their preparation
through novel methods has attracted the attention of numerous researchers. White crystals of
4-heptanone cyclic diperoxide (HDP) can be obtained in acidic media at −1◦C by a reaction
between 4-heptanone and hydrogen peroxide. Its thermal decomposition was studied in ace-
tone, cyclohexane, acetonitrile, ethyl acetate, ethanol, 2-propanol, 2-butanol, and 1,4-dioxane
at temperatures higher than 120◦C, showing a behavior accordingly with a pseudo-first-order
kinetic law up to at least 80% HDP conversion. It was demonstrated that an increase in solvent
polarity is accompanied by an increase in reaction rates. The effect of solvent polarity on the
thermal decomposition rate constant values can be associated with a reaction mechanism in-
volving a more dipolar-activated complex than the diperoxide initial molecule. The activation
parameters varied widely from 31.2 to 46.6 kcal mol−1 and −1.33 to 31.7 cal mol−1 K−1 when
going from ethanol to cyclohexane as reaction solvents, respectively. An enthalpy–entropy
compensation effect was observed in all solvents. Specific interactions between the oxygen
atoms from the peroxidic bond and the hydrogen atom bonded to C2 and/or from the OH
group can be taken into account to explain that the existence of the compensation effect does
not mean that an isokinetic relationship consequently can be established. The kinetic results
showed that an isokinetic relationship is observed only for a group of solvents. ꢀ 2011 Wiley
C
Periodicals, Inc. Int J Chem Kinet 43: 657–666, 2011
INTRODUCTION
Correspondence to: Adriana Can˜izo; e-mail: acanizo@fio
.unicen.edu.ar.
Contract grant sponsor: National University of the Center of
Buenos Aires Province (UNCPBA).
During the past decade, the chemistry of cyclic per-
oxides has enjoyed a renaissance with the increasing
appreciation that such compounds are found widely
in nature, often have interesting pharmacological
c
ꢀ
2011 Wiley Periodicals, Inc.

658
NESPRIAS ET AL.
properties, and are used at the industrial level as poly-
functional initiators of polymerization. Also, a number
of studies have been undertaken concerning the ex-
amination of the behavior of cyclic organic peroxide
to know the kinetics and mechanism of their decom-
position reactions in different solvents. New synthetic
methods or alternative techniques that involve greater
yields of peroxide compound in a shorter preparation
time have been reported [1–4].
In this work, an improved procedure for
the preparation of 3,3,6,6-tetra-n-propyl-1,2,4,5-
tetraoxacyclohexane (HDP; Eq. (1)) and a kinetic study
of its thermal decomposition reaction in solution are
reported. The reactions were carried out in solvents of
different physicochemical properties at different tem-
peratures. The solvent effects on the rate constants and
on the activation parameters of the thermolysis of this
organic peroxide molecule were discussed.
The correlation between structure and reactivity has
been the most relevant aim in physical organic chem-
istry. In that sense, the effect of solvent polarity on
the thermal decomposition rate constant and activa-
tion parameter values of various cyclic diperoxides
and triperoxides derived from aliphatic ketones has
been carried out [3,5–9]. Information concerning sub-
stituent and solvent effects on chemical reactivity can
be correlated in a variety of ways. Such relationships
fall into a large class of linear free-energy relationships
(LFER), also called extrathermodynamic relationships
or correlation equations [10]. The observation and re-
porting of linear relationships between entropies and
enthalpies of activation have become common in ki-
netic studies of groups of similar organic reactions.
Such a group might comprise, for example, a series
of thermal decompositions of a single compound in
several different solvents, or it might be a series of
reactions differing only in one of the reactants. If the
enthalpy and entropy changes are temperature indepen-
dent, then the enthalpy of activation changes (ꢀH‡)
must be directly proportional to the entropy of acti-
vation changes (ꢀS‡) for the reaction series (this be-
havior has been called the “compensation effect” or
“enthalpy–entropy compensation”) [11]. Two extreme
situations should be noted: (1) If ꢀH‡ is constant for
all the reaction series, the reaction series is entirely
entropy controlled; it is said to be isoenthalpic and the
ln (k/T ) vs. 1/T plots are parallel lines. (2) If ꢀS‡ is
constant, the series is enthalpy controlled; it is said to be
isoentropic [12].
Historically, the compensation effect and the isoki-
netic relationship were considered to be synonymous.
Furthermore, it was demonstrated that the occurrence
of one does not necessarily imply the occurrence of the
other [13]. Different statistical criteria may be used to
decide the existence of each effect. When the correla-
tion coefficient for the compensation effect has a value
closely to the unit, it is considered that the compensa-
tion is better. On the other hand, the only unambiguous
evidence for an isokinetic relationship is the intersec-
tion of all ln k [or ln (k/T )] vs. 1/T plots for the series
at a common point [14–16]. This isokinetic behavior is
commonly found for reaction series in which only one
reaction mechanism is followed [17].
(1)
EXPERIMENTAL
Preparation of 3,3,6,6-tetra-n-propyl-
1,2,4,5-tetraoxacyclohexane
This cyclic peroxide was prepared by an alternative
method to that reported in the literature [18]. In this
work, HDP was obtained by dropwise addition of
5.7 mL of hydrogen peroxide (30%, 0.056 mol) to a
vigorouslystirredmixtureof 14gof sulfuricacid(70%,
v/v) and 7 mL of 4-heptanone (0.050 mol) cooled at
−1◦C.
After 2 h of reaction, the mixture was extracted
twice with 50 mL of purified light petroleum ether (35–
60◦C) and the organic phase was freed of exceeding
hydrogen peroxide with aqueous saturated solution of
ammonium chloride, washed with cold distilled water
(0◦C) until the exceeding acid was eliminated, and
then dried over anhydrous sodium sulfate. The organic
solvent was evaporated at ambient temperature, and the
residue was left overnight in a desiccator.
The white solid obtained (54.4% crude product) was
twice recrystallized from boiling methyl alcohol. The
colorless crystals (m.p., 47.0–47.5, 47.0–48.0◦C [18])
actually correspond to HDP molecule prepared by an
improved method. Its purity was also checked by gas
chromatography (GC) and Fourier transform infrared
(KBr) absorption bands.
Caution: HDP must be handled with care because
it can be detonated by shock.
Materials
Acetone, cyclohexane, acetonitrile, ethyl acetate,
ethanol, 2-propanol, 2-butanol, and 1,4-dioxane were
purified with the appropriate techniques [19,20], and
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PREPARATION AND THERMOLYSIS OF 4-HEPTANONE CYCLIC DIPEROXIDE
659
their purity was checked by GC analysis. Alcohols used
as solvents were distilled from ethylenediaminote-
traacetic acid disodium salt to remove traces of metallic
ions [21]. Sublimed naphthalene was employed as an
internal standard in quantitative GC determinations.
heated up to 200◦C at a rate of 20◦C/min. Only 4-
heptanone organic product was identified by GC with
FID, as was described in the Kinetic Methods section.
RESULTS AND DISCUSSION
Kinetic Methods
Pyrex glass tubes (7 cm long × 4 mm internal diame-
ter [i.d.]) half filled with the appropriate HDP solution
were thoroughly degassed under vacuum at −196◦C
and then sealed with a flame torch. To carry out the
experiment, the ampoules were immersed in thermo-
static silicone oil bath ( 0.1◦C) and withdrawn after
predetermined times, stopping the reaction by cooling
them in an ice-water bath (0◦C).
The HDP remaining in the solution and the 4-
heptanone organic product were determined by GC
(internal standard method) in a DB-5 capillary col-
umn (5% biphenyl–95% dimethyl polysiloxane, 30 m
× 0.32 mm i.d., 0.25-mm film thickness) installed in a
Konik-2000C gas chromatograph, with nitrogen as car-
rier gas and flame ionization detection (FID) (250◦C).
Injection port was fixed at 150◦C in split mode. HDP
retention time under programmed conditions (80◦C,
3 min, 10◦C/min, 170◦C, 15 min) was 20.3 min.
The corresponding pseudo-first-order rate constant
values were calculated from the slope of the line ob-
tained by a least-mean-square treatment of the reaction
data when plotting the values of the ln [HDP] concen-
tration vs. reaction times.
This paper describes a new method of preparation of
4-heptanone cyclic diperoxide (HDP) that is an alterna-
tive to that reported in the literature [18]. This improved
technique obviated the addition of acetanhydride as re-
action solvent. The reaction was initiated by drop-wise
addition of H2O2 to a mixture of 4-heptanone in acidic
media at −1◦C instead of adding ketone to the acidic
H2O2 at 15◦C. The molar yield of white crystals of
4-heptanone diperoxide raised with the present method
was ca. 54.4% in 2 h of reaction, whereas Dilthey et al.
[18] obtained only a yield of 35.2%.
The thermal decomposition reaction of HDP has
been studied in solution at a temperature range of 120–
170◦C (Table I) and at an initial concentration of ca.
2 × 10−2 M. It was found that the kinetic behavior of
this system agrees with a pseudo-first-order kinetic law
up to at least 80% of HDP conversion. It seems that
under the experimental conditions of the present work,
there are no contributions from second-order processes
inducing the decomposition of HDP. The experimen-
tal rate constant values, kexp, obtained in solvents
with different physicochemical properties are shown in
Table I.
Enthalpy and entropy of activation were obtained
from the experimental rate constant values at different
temperatures in intervals of at least 30˚C in each sol-
vent. Linear regression analysis of ln (k/T ) vs. 1/T ,
according to the Eyring equation, allowed the calcula-
tion of the enthalpy of activation from the slope and
the entropy of activation from the intercept. The errors
on the activation parameters were worked out by the
Arrhenius equation method using a least-mean-square
data treatment [22].
The temperature dependence of the kexp values for
the thermal decomposition reaction of HDP in solution
follows the Arrhenius equation with good accuracy for
most solvents investigated. The linearity of the Arrhe-
nius equation plots in a relatively large temperature
interval (ca. 30◦C, Table I) suggests that the calculated
activation-parameter values for the HDP reaction in
solution belong to a single process, which could be its
unimolecular thermal decomposition through the O–
O bond cleavage to form the intermediate biradical 1
(Eq. (1)) as the initial bond-breaking step [5].
The biradical species 1 (Eq. (1)) can reform the
diperoxide molecule or undergo either C O bond
cleavage to give 4-heptanone (Eq. (2)) or O O bond
cleavage to give a biradical species 2 (Eq. (3)), which
can undergo C C bond cleavage to give n-propyl and
butanoate radicals (Eq. (4)). Butanoate radicals can
abstract a hydrogen atom from solvent to give bu-
tanoic acid (Eq. (5)) or take part in some radical re-
action to form n-propylbutanoate (Eq. (6)). A radical–
radical coupling reaction between two n-propyl radi-
cals may explain the detection of n-hexane as a product
(Eq. (7)).
Product Analysis
The reaction products were identified by GC–MS anal-
ysis in a Rtx-5MS capillary column (5% biphenyl–95%
dimethyl polysiloxane, 30 m × 0.25 mm i.d., 0.25-μm
film thickness) installed in a Thermo Quest Race 2000
CG model gas chromatograph with helium as carrier
gas (0.5 mL min−1) and the injection port at 150◦C in
split mode (split ratio 1:33). The detection was carried
out with a Finnigan Polaris ion-trap MS detector with
the transfer line at 275◦C and the ion source at 200◦C.
The oven was maintained at 50◦C for 3 min and then
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660
NESPRIAS ET AL.
Table I Pseudo-First-Order Rate Constant Values (kexp) for the Thermal Decomposition Reaction of HDP in Different
Solvents
Solventa
Temperature (◦C)
k
exp
(×10−4s−1
0.167
0.896
1.47
)
rb
Cyclohexane (ETN: 0.006)
140.0
150.0
160.0
170.0
140.0
150.0
160.0
170.0
130.0
140.0
150.0
160.0
130.0
140.0
150.0
160.0
130.0
141.4
145.0
151.0
166.0
140.0
150.0
155.0
160.0
165.0
120.0
130.0
140.0
150.0
130.0
140.0
150.0
160.0
0.981
9.59
1,4-Dioxane (ETN: 0.164)
Acetone (ETN: 0.355)
Acetonitrile (ETN: 0.460)
Toluenec (ETN: 0.099)
0.170
0.730
2.16
0.999
0.999
0.998
0.993
7.99
0.220
0.620
1.83
5.23
0.17
0.67
2.36
5.83
0.116
0.563
0.590
1.68
6.51
0.350
1.17
1.86
2.30
5.60
0.190
0.500
1.38
3.41
1.85
4.65
16.7
27.3
Ethyl acetate (ETN: 0.228)
0.989
Ethanol (ETN: 0.654)
0.999
0.992
2-Propanol (ETN: 0.546)
2-Butanol (ETN: 0.506)
130.0
140.0
150.0
160.0
1.47
5.66
13.4
29.1
0.994
1-Propanold (ETN: 0.617)
150.0
5.91
aNormalized solvent polarity parameter values ET [30] are in parentheses.
bCorrelation coefficient according to the Arrhenius equation.
cRate constant value from [7].
d Rate constant value from [23].
(2)
(3)
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PREPARATION AND THERMOLYSIS OF 4-HEPTANONE CYCLIC DIPEROXIDE
661
alcohols. Although the correlation between reactivity
of HDP at 150◦C and ETN is not exactly linear, the
trend demonstrates that an increase in the solvent po-
larity is accompanied by an increase in reaction rates
(Fig. 1). This trend could be considered as evidence
in support of a reaction mechanism involving a more
dipolar-activated complex than the diperoxide initial
molecule.
(4)
(5)
(6)
(7)
The presence of 4-heptanone as one of the peroxide
decomposition products was recognized through the
interpretation of mass spectrum and also by compari-
son of its retention time with that obtained by injecting
an authentic sample of this compound in a gas chro-
matograph with FID. Hexane, n-propylbutanoate, bu-
tanoic acid, and propane were identified qualitatively
by interpretation of their mass spectrum.
Considering that the activated complex represented
by the biradical species 1 (Eq. (1)) is more polar
than the diperoxide reactant molecule, it is easy to
interpret through the Kirkwood formula [25] that the
rate of reaction increases with the dielectric constant
of the medium. This is because a higher dielectric
constant favors the production of any highly dipolar
species. In this way, acetone has a Kirkwood func-
tion value 2.3 times higher than cyclohexane, with
a ratio keaxcpetone/kecxypclohexane is close to 2. On the other
hand, as seen from Figs. 1 and 2, although the four
aliphatic alcohols have very similar dielectric con-
stants, dipolar moments (ETN), and Kirkwood function
[(εr − 1)/(2εr + 1)] values, when used as solvents they
lead to different reaction rates (Figs. 1 and 2). The
thermal decomposition of HDP can be accelerated by
a factor close to 5 on going from ethanol as solvent
to a secondary alcohol like 2-propanol. This obser-
vation strongly suggests that the polarizability of the
solvent is an important factor in stabilizing the dipolar-
activated complex of this reaction. In addition, it is
possible to postulate an interaction between hydrogen
atoms of the OH group (or hydrogen atoms bonded
to C2 in secondary alcohols) and the oxygen atom of
the O O function, favoring this bond rupture. As it
was described in a recent paper [26], when ethanol
is the reaction solvent only the hydrogen atom of the
Organic chemists have usually attempted to under-
stand the solvent effects in terms of solvent polarity.
In 1968, Reichardt and Dimroth [24] proposed an em-
piric solvent-polarity parameter, denominated as ET
[30], which is based on the transition energy for the
longest wavelength solvatochromic absorption band
of the pyridinium-N-phenoxide betaine dye. A clas-
sification of the solvents according to their normal-
ized ETN values [25] gives three groups related with
specific solute/solvent interactions: 1-protic hydrogen
bonding donor (HBD) solvents (ETN ca. 0.5–1), 2- dipo-
lar non-HBD solvents (ETN ca. 0.3–0.5), and 3-apolar
non-HBD solvent (ETN ca. 0–0.3). In the present work,
various solvents included in these groups were used
as reaction media (Table I), showing that HDP is less
reactive in apolar solvents (cyclohexane, toluene [7],
and 1,4-dioxane) than in protic-HBD solvents (ethanol,
1-propanol, 2-propanol, and 2-butanol) according to
the kexp values at 150◦C (Table I, Fig. 1). Probably, the
specific interactions between protic-HBD solvents and
the O O bond in the HDP molecule are responsible
for the differences in the kinetic behavior of HDP in
–6
–7
–6
–7
–8
–9
–8
–10
–11
–12
–9
–10
0
0.2
0.4
0.6
0.8
0.15
0.25
0.35
0.45
N
ε
ε
(
r + 1)
r – 1)/(2
ET
Figure 2 Correlation between ln k
and the Kirkwood
Figure 1 Correlation between the natural logarithm of the
rate constant value of HPD thermolyses at 150◦C, and ETN
exp
function, (εr − 1)/(2εr + 1), for the thermal decomposition
reaction of HDP in solution ( , aliphatic alcohols).
values of the solvents ( , aliphatic alcohols).
•
•
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662
NESPRIAS ET AL.
50
Cyclohexane
1,4-Dioxane
45
40
35
30
25
Toluene
Acetonitrile
Ethyl acetate
Acetone
Ethanol
2-Butanol
2-Propanol
–5
0
5
10
15
20
25
30
35
S#, cal mol–1 K–1
Δ
Figure 3 Enthalpy–entropy compensation for the thermal decomposition reaction of HDP in different solvents.
OH group interacts with the O O bond of the cyclic
organic peroxide.
compensation effect; thus it is easy to deduce that the
higher the correlation coefficient is the better the com-
pensation will be. The representation of the enthalpy–
entropy compensation [27] between the activation pa-
rameters for the thermolysis of HDP in nine different
solvents (Table II) and Eq. (8) shows a relatively good
linear dependence (r = 0.994; Fig. 3). It is important
to emphasize that the correlation improves when the
secondary alcohols are excluded (r = 0.999; dashed
line in Fig. 3). The slope of the line in Fig. 3 (β in
Eq. (8)) is the temperature at which the rate constant
is identical for all concerned reactions, and it is known
as the isokinetic temperature. The family of reactions
corresponding to the thermal decomposition of HDP
in solution has a β value of 216◦C (or 187◦C without
considering the secondary alcohols). These values are
The compensation effect in the thermal decompo-
sition reaction of HDP in solution can be observed
through the linear relationship between the enthalpies
and entropies of activation (Fig. 3). The experimen-
tal enthalpy and entropy of activation of HDP varied
widely from 31.2 to 46.6 kcal mol−1 and from −1.33
to 31.7 cal mol−1
K
−1, respectively, when going from
ethanol to cyclohexane as reaction solvents. These vari-
ations in activation parameters are large as compared
with the probable errors of these determinations. As a
consequence of this strong compensation, ꢀG‡ values
remained nearly constant (ꢀꢀG‡ = 2.5 kcal mol−1).
The correlation coefficient of the linear plot (Fig. 3)
can be used as a criterion to judge the existence of the
Table II Activation Parameters for the Thermal Decomposition Reaction of HDP in Different Solvents
◦
Solvent
ꢀH‡ (kcal mol−1
)
ꢀS‡ (cal mol−1 K−1
)
ꢀG‡a (kcal mol−1
)
ke1x5p0 C(×10−4 s−1
)
Cyclohexane
Toluene
1,4-Dioxane
Acetone
Acetonitrile
Ethyl acetate
Ethanol
2-Propanol
2-Butanol
46.6 0.4
39.8 1.2
46.5 0.9
36.0 0.5
40.6 1.2
36.8 2.1
31.2 0.3
31.9 1.5
33.5 1.2
31.7 4.8
17.0 2.9
31.6 2.2
8.79 1.1
19.9 2.8
9.57 4.9
−1.33 0.7
2.97 3.8
6.62 2.9
33.2 0.4
32.7 1.2
33.2 0.9
32.3 0.5
32.2 1.2
32.8 2.1
31.8 0.7
30.7 1.5
30.7 1.2
0.896
1.26b
0.73
1.83
2.36
1.17
3.41
16.7
13.4
aCalculated at 150◦C.
bkexp value calculated at 150◦C from [7].
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PREPARATION AND THERMOLYSIS OF 4-HEPTANONE CYCLIC DIPEROXIDE
663
–2
–2.5
–3
–3.5
–4
Experimental data
Mapped back from Eq. (10)
Lineal (experimental data)
–4.5
–5.00
–4.50
–4.00
log k2 140 C
Figure 4 Isokinetic relationship according to Eq. (9) for the unimolecular decomposition of HDP in solution.
–3.50
–3.00
–2.50
°
well outside of the temperature interval where the ki-
netic experiments have been performed (120–170◦C).
not necessarily synonymous and the occurrence of one
does not necessarily imply the occurrence of the other.
On the other hand, Exner suggested a simple method
to evaluate the isokinetic relationship [31]. It consists
of plotting the decimal logarithms of the rate con-
stants for the same reaction at two different temper-
atures (log k1 against log k2, with T1 > T2). When
this representation is linear, it can be considered by
itself an isokinetic relationship for the series (Fig. 4).
The reason that this plot is a reliable test for such a
relationship is that the errors in k1 and k2 are inde-
pendent (unlike the errors in ꢀH‡ and ꢀS‡). Exner
[31] showed that a linear function between the origi-
nal coordinates (log k1 vs. log k2; Fig. 4) also required
a linear function between the transformed coordinates
and vice versa (E‡ vs. log A; Fig. 5) according to
ꢀH‡ = ꢀH◦ + βꢀS‡
(8)
Some authors [28,29] have suggested, on the basis
of thermodynamic arguments, that the actual source of
the compensation effect (Fig. 3) should be related to
contributions due to solvent reorganization on forming
the transition state. HDP decomposes via the formation
of a more polar biradical (1 in Eq. (1)) as an interme-
diate species, and the polar solvent molecules (i.e.,
aliphatic alcohols) should adopt specific orientations
for biradical stabilization. This phenomenon may be
considered as “freezing” of the solvent molecules in
the transition state, and it results in lower activation
entropy values than that in apolar solvents.
150◦C
Eqs. (9) and (10). The correlation between log k
exp
◦
vs. log ke1x4p0 C for the thermal decomposition of HDP in
However, it is well recognized that the errors in
ꢀH‡ and ꢀS‡ are correlated because they are calcu-
lated from the same set of data. It was Petersen [30]
who postulated that a linear enthalpy–entropy relation-
ship can never be, by itself, a sufficient demonstration
of an isokinetic relationship. He analyzed the errors
in ꢀH‡ and ꢀS‡, showing that the error in ꢀS‡ is
directly proportional to the error in ꢀH‡. Hence, a
reaction series could generate an apparent isokinetic
relationship solely through the operation of this error
effect, which predicts that a plot of ꢀH‡ against ꢀS‡
will be linear. Later, Liu and Guo [13] demonstrated
that the compensation effect and isokinetic effect are
different solvents constitutes a useful LFER to evaluate
solvent–reactivity effects.
ꢀ
ꢁ
T1
T2
T1
log A =
log k1
−
log k2
(9)
T1 − T2
2.303RT1T2
E‡
=
(log k1 − log k2) (10)
T1 − T2
According to this method, the isokinetic temperature
can be obtained applying Eq. (11) [10,13], where
b = 0.8624 is the graphical estimated slope of the
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NESPRIAS ET AL.
70000
–1
#
50000
30000
Experimental data
Mapped back from Eqs. (9 and 10)
Lineal (experimental data)
10000
10
15
20
25
30
35
40
45
50
55
60
ln A
Figure 5 Isokinetic relationship according to Eq. (10) for the unimolecular decomposition of HDP in solution.
0
–4
9
(a)
7
5
–8
(b)
3
β–1
β–1
–12
–16
–20
1
–1
–3
0.0018
0.0022
0.0026
1/T
Figure 6 Dependence of S on the supposed isokinetic temperature β for HDP thermal decomposition in solution. (a) All
u
solvents included, β = 248◦C and (b) secondary alcohols excluded, β = 208◦C. [Color figure can be viewed in the online issue,
which is available at wileyonlinelibrary.com.]
straight line determined by Eq. (9) in Fig. 4. A β value
varied from 226◦ to 175◦C with all solvents included
or with secondary alcohols excluded, respectively.
at some temperature T = β. As β is not known a
priori, the residual sum of squares (Su in Fig. 6) is
calculated for trial values of β until a minimum is
found. This method was often called the Exner–Linert
method because Linert [17] had significantly improved
the calculation procedure and the understandability of
the method.
Analysis of the temperature-dependent rate con-
stants indicates that there is no temperature such that
all the rate constants of the set of reaction are close to
each other. It seems that different isokinetic groups
can be differentiated (Fig. 6). For example, the Su
β = T1T2(b − 1)/(bT1 − T2)
(11)
Later, Exner [15] gave a stricter but more sophisti-
cated method to test the isokinetic relationship based
on least-squares fitting. In the method, linear regres-
sions of experimental Arrhenius plots are done indi-
vidually for each reaction of the series and under the
isokinetic constraint that all regressions lines intersect
International Journal of Chemical Kinetics DOI 10.1002/kin

PREPARATION AND THERMOLYSIS OF 4-HEPTANONE CYCLIC DIPEROXIDE
665
function presents different minimum values if all sol-
vents were included in the calculation or when sec-
ondary alcohols were excluded. Thus the isokinetic
temperature values according to this method were 248
or 208◦C, respectively. It seems appropriate to con-
sider again that the secondary alcohols have a strong
interaction through two hydrogen atoms with the per-
oxide bond. That interaction could alter HDP reactivity,
reaching the highest kexp values in these solvents. The
isokinetic temperature values calculated by different
methods including all solvents studied or excluding
secondary alcohols were higher than the experimental
temperature. However, these β values obtained with
Eq. (11) (Fig. 4) are subject to error problems because
they were determined considering kinetic parameters
at only two temperatures in a narrow temperature range
(ꢀT = 10◦C).
the intermediate biradical species 1. Thus, the rate of
reaction is determined mainly by the environmental
molecules.
Finally, the kinetic results of the thermal decompo-
sition reaction of HDP in several solvents reveal the
occurrence of the enthalpy–entropy compensation ef-
fect, whereas the isokinetic effect is observed only for
a group of solvents.
AIC is a member of the Consejo Nacional de Investigaciones
Cient´ıficas y Tecnolo´gicas. GPB is a fellowship holder of the
CONICET.
In summary, the compensation effect can occur
when ꢀG‡ is approximately constant within the reac-
tion series, whereas ꢀH‡ and ꢀS‡ vary significantly,
as was observed in the previous work [16]. On the
other hand, the establishment of the compensation ef-
fect does not imply that the isokinetic relationship is
operative at the same time, as it is shown in Figs. 3
and 6.
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