Kinetics of thermal conversions of monoterpenic compounds in supercritical lower alcohols

Article abstract of DOI:10.1134/S0023158410020035

The most important information concerning thermal conversions of vegetable terpenes (α-pinene, β-pinene, turpentine, and cis-verbenol) in supercritical lower alcohols is systematized. The kinetics of selected reactions is reported and is compared with the kinetics of the same reactions in the gas and liquid phases. Thermodynamic calculations of the phase states and kinetic parameters are presented for a number of multicomponent multiphase systems containing terpenes and lower alcohols. The effect of the supercritical solvent pressure on the rate and selectivity of the selected reactions is reported.

Full text of DOI:10.1134/S0023158410020035

ISSN 0023ꢀ1584, Kinetics and Catalysis, 2010, Vol. 51, No. 2, pp. 162–193. © Pleiades Publishing, Ltd., 2010.
Original Russian Text © V.I. Anikeev, A. Ermakova, A.M. Chibiryaev, I.V. Kozhevnikov, 2010, published in Kinetika i Kataliz, 2010, Vol. 51, No. 2, pp. 176–209.
Kinetics of Thermal Conversions of Monoterpenic Compounds
in Supercritical Lower Alcohols
a
a
b
a
V. I. Anikeev , A. Ermakova , A. M. Chibiryaev , and I. V. Kozhevnikov
a
Boreskov Institute of Catalysis, Siberian Branch,
Russian Academy of Sciences, Novosibirsk, 630090 Russia
Novosibirsk Institute of Organic Chemistry, Siberian Branch,
b
Russian Academy of Sciences, Novosibirsk, 630090 Russia
eꢀmail: anik@catalysis.nsk.su
Received January 16, 2009
Abstract—The most important information concerning thermal conversions of vegetable terpenes
ꢀpinene, ꢀpinene, turpentine, and cisꢀverbenol) in supercritical lower alcohols is systematized. The kinetꢀ
(
α
β
ics of selected reactions is reported and is compared with the kinetics of the same reactions in the gas and liqꢀ
uid phases. Thermodynamic calculations of the phase states and kinetic parameters are presented for a numꢀ
ber of multicomponent multiphase systems containing terpenes and lower alcohols. The effect of the superꢀ
critical solvent pressure on the rate and selectivity of the selected reactions is reported.
DOI: 10.1134/S0023158410020035
INTRODUCTION
90%
β
ꢀpinene. Biosynthesis in plants produces both
β
ꢀpinene enatiomers. As a rule, one of them is much
more abundant.
the synthesis of
Heatꢀinduced chemical conversions of (mono)terꢀ
penic compounds of vegetable origin are of considerꢀ
able practical interest for they are used in the synthesis
of С –С alkylated benzenes, various monooxygenꢀ
ated and polyoxygenated compounds for medicinal
applications (active components of pharmaceuticals,
aromatherapy), diene and triene compounds (semiꢀ
βꢀPinene is the starting chemical for
β
ꢀmyrcene, an important component
of natural and synthetic perfume compositions [18,
9, 26] and a convenient synthetic precursor of more
7
10
1
valuable fragrance compounds and some carotenoids.
Verbenol is a bicyclic C terpenoid belonging to the
10
products for fine organic synthesis), and monomers to family of monohydroxy derivatives of ꢀpinene. Verꢀ
α
be polymerized or oligomerized. For example, the benol has cis and trans isomers, and either can exist as
noncatalytic thermolysis of the bicyclic monoterpenic two enantiomers, all having the pleasant odor of camꢀ
hydrocarbons
components of turpentine, yields limonene and components of the aggregation pheromones of bark
ꢀmyrcene, which are used in the production of cosꢀ beetles (Ips sp and Dendroctonus sp ) and occur in the
metics, perfumery, and household chemicals.
essential oils of some plants. At the same time they can
be synthesized by the catalytic allylic oxidation of
α
ꢀ
and
ꢀpinene, which are the main phor. In nature, the verbenol isomers are the main
β
β
.
.
α
ꢀ
α
ꢀPinene is among the most abundant monoterꢀ
pinene. They are employed in the preparation of artiꢀ
ficial perfume compositions and in the synthesis of
other compounds in demand, such as citral, piperꢀ
itenol isomers, and vitamin A.
penic hydrocarbons in nature [1]. Its industrial sources
are various kinds of turpentine from softwood. Biosynꢀ
thesis in plants produces both ꢀpinene enantiomers,
α
one of them being usually dominant. Pinene is a conꢀ
venient starting chemical for producing fragrance
compounds and perfume compositions [2–5] and a
valuable semiproduct for the pharmaceutical industry
2, 5]. For example, the thermal isomerization of
pinene in the gas phase [6–19] or in the liquid phase
11, 12, 15, 16, 20–25] yields mixture of monocyclic
and acyclic compounds, such as limonene, allooꢀ
cimene and pyronene isomers, and substituted cycloꢀ
hexenes. This mixture is typically dominated by the
Purified sulfate turpentine is obtained by processing
crude turpentine, which is a byꢀproduct of sulfate celꢀ
lulose production. It is a volatile monoterpene mixture
consisting of
phene, tricyclene,
nolene, ꢀphellandrene, and a number of other comꢀ
pounds. In addition, sulfate turpentine contains sulꢀ
furꢀcontaining compounds (up to 0.05% sulfur).
These compounds markedly limit the area of its appliꢀ
cation because they have unsuitable organoleptic
[
α
ꢀ
3
α
ꢀpinene,
β
ꢀpinene,
Δ
ꢀcarene, camꢀ
β
ꢀmyrcene,
α
ꢀterpinene, terpiꢀ
[
β
monocyclic C diene limonene.
10
β
ꢀPinene is a monoterpenic bicyclic hydrocarbon properties and poison the catalysts used in its processꢀ
present in turpentines and the essential oils of plants. ing. Nevertheless, since sulfate turpentine contains a
The turpentine of some coniferous trees contains up to large proportion of ꢀpinene (up to 80%) and other
α
162

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
163
unsaturated hydrocarbons with bridged cyclic strucꢀ
Now we will proceed with a detailed presentation
tures, it is viewed as a convenient and cheap raw mateꢀ of our studies of the heatꢀinduced conversions of
rial for obtaining a variety of valuable products [27– monoterpenic and terpenic compounds in supercritiꢀ
3
4]. It is largely used as a solvent for varnishes and oil cal fluids as solvents [40–48]. It seems pertinent to
paints and is a valuable starting chemical for producꢀ begin with systematically describing our experimental
ing synthetic camphor, a compound possessing a variꢀ procedures, data analysis and processing techniques,
ety of pharmaceutical properties.
Turpentine oil is obtained by processing pine oleoꢀ We will report the phase states of alcohol–water–
resin. It is a transparent volatile liquid with a specific pinene mixtures (liquid–vapor, liquid–liquid, or liqꢀ
odor, containing no precipitate or water. The total
uid–liquid–vapor) studied by methods of nonideal
and
ꢀpinene content of turpentine oil is at least 60%. thermodynamics in wide composition, temperature,
and reaction scheme and kinetic model construction.
α
ꢀ
α
ꢀ
β
Turpentine oil is used as a raw material in organic synꢀ and pressure ranges—data that can be interesting and
thesis and as a solvent. It is the starting chemical in the significant from the practical standpoint.
synthesis of camphor, a substance having manifold
medicinal properties.
EXPERIMENTAL PROCEDURES
The chemical conversions of the above monoterꢀ
AND CHEMICAL ANALYSIS OF REACTION
penic compounds are very diverse and have been careꢀ
PRODUCTS
fully investigated. In particular, the thermal isomerizaꢀ
The following terpenes were used in our experiꢀ
ments: (+)ꢀ ꢀpinene (>98%, Aldrich), (–)ꢀ ꢀpinene
99%, Fluka), (+)ꢀlimonene ( 99%, Aldrich), (S)ꢀ
cisꢀverbenol (95%, Aldrich). Sulfate turpentine was a
commercial product consisting of ꢀpinene (76–
0%), camphene (1.2%), ꢀpinene (4.1%), 3ꢀcarene
tion of
α
ꢀ and ꢀpinenes has been studied in detail.
β
α
β
This reaction is usually carried out at a reduced or
atmospheric pressure in the gas or liquid phase. The
(
≥
≥
gasꢀphase thermal isomerization of ꢀpinene is conꢀ
α
α
ducted at 220–450°С [13–15, 18, 19], and the liquidꢀ
phase process is performed at 180–257°С and the corꢀ
responding saturation pressures [16, 23]. The reaction
8
β
(
(
10.8%), limonene (3%), and other compounds
0.9%).
mixture residence time necessary for 90–95%
α
ꢀ
pinene conversion may be as along as tens of hours.
The thermal isomerization of terpenes in supercritꢀ
This long residence time hampers wide commercialꢀ ical solvents was studied using a laboratory setup with
3
ization of terpene isomerization technologies both in a tubular flow reactor ~7 cm in volume. The reaction
the synthesis of polyunsaturated aliphatic compounds temperature and pressure were varied between 530 and
and in the production of the most important arenes.
The thermal isomerization rate of terpene comꢀ
pounds can be increased by using a catalyst [35] or a
new, more favorable reaction medium. Supercritical
solvents seem to be the most promising for this purꢀ
pose. Supercritical fluids have already been recognized
as attractive media for some organic reactions, ensurꢀ
ing a multifold increase in the reaction arte and selecꢀ
tivity control [36–38].
700 K and between 80 and 300 atm, respectively.
Depending on the solvent, the reaction mixture was
fed into the reactor as one or two liquid streams. In the
latter case, one feed was a solution of a monoterpene
in an alcohol and the other was distilled water. These
independent liquid feeds were mixed at the reactor
inlet.
The residence time (
reactor volume (Vr) to the flow rate of the reaction
mixture (Qmix) under the inlet conditions (T0
Qmix, was ~70–140 s.
The reaction mixture leaving the reactor was
τ
), defined as the ratio of the
,
P0), =
τ
Among the supercritical solvents suitable for chemꢀ
Vr
/
ical reactions, water, CO , alcohols, and some lower
2
saturated and unsaturated hydrocarbons have received
greatest attention. In some cases, preference is given to cooled and, after separation into gas and liquid phases,
supercritical water (SCW) and CO . At the same time, was analyzed. The composition of the reaction prodꢀ
2
lower alcohols are conventional solvents for organic ucts was determined by GCꢀMS on a Hewlett Packard
reactions, including those conducted under supercritꢀ 5890/II gas chromatograph coupled with an HP MSD
ical conditions. Owing to their high solvating power, in 5971 quadrupole mass spectrometer as the detector.
combination with comparatively small values of critiꢀ An HPꢀ5 quartz column (length of 30 m, inner diamꢀ
cal parameters (for ethanol, the critical temperature is eter of 0.25 mm, stationary phase: biphenyl (5%)–
Tcr = 516.2 K and the critical pressure is Pcr = 63 atm), dimethylsiloxane (95%) copolymer, film thickness of
lower alcohols are finding increasing application as 0.25
supercritical solvents.
μ
m) was used in these measurements. The carrier
gas was helium (1 ml/min). The injection port temperꢀ
An analysis of the literature demonstrates that the ature was 280°С. The oven temperature was proꢀ
thermal isomerization of monoterpenic compounds in grammed as follows: 50°С (2 min), 50–200°С
supercritical solvents was not studied earlier. There (4°С/min), 200–300°С (20°С/min), and 300°С
have been only sparse reports on the catalytic hydrogeꢀ (20 min). The ionizing electron energy was 70 eV.
nation of
α
ꢀpinene in supercritical CO [39–41] and
Qualitative analyses of reaction products were carꢀ
2
on the synthesis of esters (esterification reactions) of ried out by comparing the retention (Kovats) indexes
terpenic alcohols [38].
and complete mass spectra of components with the
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

1
64
ANIKEEV et al.
corresponding data for pure compounds (if available) Mathematical Description of the Experimental Reactor
and with mass spectrometric data from the NIST Mass
The mathematical model of a plugꢀflow reactor is
Spectral Library (190825 compounds), Wiley Registry
represented as the set of ordinary differential equaꢀ
of Mass Spectral Data (621600 compounds), and the
tions
catalogue by Tkachev [49]. The percentages of mixꢀ
NR
ture components were derived from chromatographic
peak areas without using correction coefficients.
dCi
dτ
=
z jiR
j
C
(
)
(1)
(2)
∑
j =1
The enantiomer composition of the initial comꢀ
pounds and thermolysis products was determined by
GCꢀMS on an Agilent 6890 gas chromatograph with a
subject to the initial conditions
0
0
i
τ = 0 : C = C ; C = 0, i = 2,..., NS.
1
1
5975 Inert quadrupole massꢀselective detector. Mixꢀ
0
tures were separated under the following conditions: Here, Ci designates the inlet component concentraꢀ
30ꢀmꢀlong capillary column; inner diameter of tions (g mol/l), NS is the number of components, NR is
0
.25 mm; CycloSilꢀB chiral stationary phase with a the number of chemical reactions included in the conꢀ
film thickness of 0.25 m; helium (1 ml/min) as the
carrier gas; injection port temperature of 250°С; interꢀ
face temperature of 250°С; ion source temperature of
μ
version network, and z ji designates the jth row and ith
column of the stoichiometric matrix corresponding to
the accepted reaction network.
2
1
30°С; temperature programming: 50°С (2 min), 50–
80°С (2°С/min), 180–220°С (5°С/min), 220°С
A preliminary analysis demonstrated that all of the
reactions are monomolecular and obey the firstꢀorder
rate law. By equivalent transformations through the
introduction of the dimensionless concentrations
(
20 min); ionizing electron energy of 70 eV; mass
scanning range of 29–500 amu. The cathode was
switched on 3.5 min after sample injection. The samꢀ
ple size was 0.2 μl.
0
y = C /C , the set of equations (1) in this particular
i
i
1
case can be represented as
NR
dyi
dτ
=
( )
z R y ,
MATHEMATICAL METHODS OF DATA
PROCESSING AND KINETIC SIMULATION
∑
j =1
0
ji
j
(3)
0
τ = 0 : y = 1, y = 0, i = 2,..., N ,
1
i
S
As a rule, kinetic studies of complex reactions in
plugꢀflow reactors result in the establishment of a relaꢀ
tionship between the composition of the reaction mixꢀ
ture and the residence time under isothermic and isoꢀ
baric conditions at a given feed composition. The
resulting integral composition–residence time curves
are sufficiently informative to postulate some interꢀ
conversion network and to formulate primary hypothꢀ
eses concerning the form of the kinetic functions to be
fitted to the observed rates of particular reactions.
Subsequent processing of the experimental data is perꢀ
formed to determine the numerical values of constants
in the rate equations. In order to establish the temperꢀ
where Ri designates the firstꢀorder reaction rates.
Note that, for reactions of fractional and higher
0
orders, the rightꢀhand side of Eq. (3) will contain C1
or an equivalent quantity, namely, the molar volume of
the initial mixture.
The rate constants k j in Eq. (3) are represented
according to the Arrhenius law:
E j
⎛
⎞
⎟
k = k exp −
.
(3a)
j
j0
⎜
⎝
RT ⎠
The set of equations (3) was used in the identificaꢀ
ature dependences of these constants, it is necessary to tion of parameters of the kinetic model.
obtain several composition–residence time isotherms
at high and low temperatures. A drawback of this
Identification of the Kinetic Model
approach is that experimental limitations do not allow
the residence time (flow rate) at each particular temꢀ
perature point to be varied in a sufficiently wide range.
As a consequence, it is difficult to record complete
composition–residence time curves both at comparaꢀ
tively low and at comparatively high temperatures. For
this reason, we varied the reaction temperature at a
fixed residence time and pressure in most kinetic
experiments. Data processing demonstrated that the
resulting composition–temperature relationships are
informative for the reaction scheme chosen, affording
correct temperatureꢀdependent kinetic constant data.
The identification problem includes determination
of the unknown rate constants and activation energies
ensuring the best fit between experimental and calcuꢀ
lated data. For this purpose, we formulate an objective
function to be minimized with respect to its parameꢀ
ters:
Nexp
T
exp
calc
Q =
(yk − yk
p
( )
)
∑
k =1
(4)
−
1
exp
calc
×
Wk (yk − yk p ⎯ ⎯→ min p ,
( )
( )
)
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
Component concentration, %
165
exp
where yk is the NSꢀdimensional column vector conꢀ
1
00
sisting of experimental
measured in the th run, yk is the vector of calcuꢀ
lated concentrations obtained by integrating the set of
differential equations (3) between 0 and (s) at the
temperature of the th run Tk Wk is the weight unit
matrix, and is the NPꢀdimensional column vector of
sought parameters:
ith component concentrations
calc
k
1
80
60
40
α
ꢀPinene
τ
2
k
( ),
3
p
3
'
0
1
0
2
0
N
2
'
p = ⎡k ,k ,..., k ,E ,E ,..., E ⎤
.
(5)
Limonene
1
2
N
20
⎣
⎦
1
'
Objective function (4) was minimized by Gauss
and Marquardt’s classical iteration method [50] with
modifications [51] making the iterative procedure
much more rapid, reducing the size of the confidence
region, and thereby enhancing the statistical validity of
the constants. The component concentrations were
calculated in each iteration step by numerical integraꢀ
tion of the set of differential equations (3) at current
values of the constants.
5
0
100
150
200
250
300
Residence time, s
Fig. 1.
(1
–3
)
α
ꢀPinene and (
1
'–
3
'
) limonene concentraꢀ
tions in the products of
critical alcohols ((
α
ꢀpinene isomerization in superꢀ
) methanol, ( ) ethanol, and ( ) 1ꢀproꢀ
panol) as a function of the residence time (300°С
00 atm).
1
2
3
,
1
Solving the identification problem was followed by
an a posteriori analysis of the statistical validity of the
results [52, 53].
fested in the dynamics of accumulation of the totality
of minor products and in the limonene concentration
dynamics. The largest amounts of byꢀproducts are
observed in ꢀpinene isomerization in supercritical 1ꢀ
α
KINETICS OF THE THERMAL
ISOMERIZATION OF MONOTERPENIC
COMPOUNDS IN SUPERCRITICAL SOLVENTS
propanol. The maximum attainable limonene conꢀ
centration in this solvent is the lowest among the alcoꢀ
hols examined.
α
ꢀPinene Isomerization in Supercritical Lower Alcohols
No compounds indicating alcohol decomposition
Lower alcohols are widespread solvents for many were detected among the reaction products. Thereꢀ
organic compounds and have a high solvating power, fore, all of the alcohols are thermally stable in the temꢀ
particularly toward polar molecules, with which they perature and pressure ranges examined.
form hydrogen bonds. They have comparatively low
Although ꢀpinene proved much more reactive in
α
critical parameters and are thermally stable in their 1ꢀpropanol, we chose supercritical ethanol as the solꢀ
vicinity. In view of this, they are of interest as superꢀ vent for subsequent kinetic studies of monoterpene
critical solvents for chemical reactions. In our investiꢀ isomerization.
gation of ꢀpinene isomerization, we chose the lower
α
alcohols methanol, ethanol, and 1ꢀpropanol as superꢀ
critical solvents.
α
ꢀPinene Isomerization in Supercritical Ethanol
Figure 1 plots the
and the yield of the main product, limonene (curves
α
ꢀpinene conversion (curves
1
–
3
)
The experimental data concerning the thermal
1
'– isomerization of
ꢀpinene (Table 1) were obtained in
α
3'), as a function of the residence time for the reactions two series of experiments. The first series demonꢀ
carried out in supercritical methanol, ethanol, and 1ꢀ strated how the composition of the reaction mixture
propanol at a constant temperature and pressure. varies over the temperature range of 560–660 K at a
Here, the residence time was used as the independent constant pressure of
variable because the problem was to carry out a comꢀ dence time of
parative analysis of the ꢀpinene reactivities in differꢀ ments was carried out to elucidate the effect of the
ꢀpinene conversion
rate at a constant temperature of 600 K and a constant
ꢀpinene in residence time of = 70 s.
Figure 2 shows the temperature dependence of the
reaction mixture composition in thermal ꢀpinene
P
= 120 atm and a constant resiꢀ
τ
= 70 s. The second series of experiꢀ
α
ent supercritical solvents at a constant temperature reaction medium pressure on the
and pressure.
α
It was found that the reactivity of
α
τ
supercritical alcohols increases with an increasing
number of CH groups in the alcohol molecule, the
chemical composition of the reaction products is solꢀ
ventꢀindependent, and none of the supercritical alcoꢀ
α
isomerization at a constant pressure (points) based on
the data presented in Table 1. Our experimental data
and an analysis of the literature [13, 14, 16, 23] suggest
hols reacts with
ucts.
α
ꢀpinene or its isomerization prodꢀ
that the main routes of
α
ꢀpinene isomerization in
The slight difference between the selectivities of the supercritical alcohols can be represented as Scheme 1,
reaction in different alcohols is most clearly maniꢀ which is similar to the scheme of ꢀpinene isomerizaꢀ
α
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

1
66
ANIKEEV et al.
Table 1. Experimental data on the thermal isomerization of αꢀpinene in supercritical ethanol at a constant residence time
of τ = 70 s
Reaction mixture composition normalized to the initial αꢀpinene concentration, %
T, K
P, atm
4
E,6Zꢀallooꢀ 4E,6Eꢀallooꢀ
(
α
+ β)ꢀpyꢀ
α
ꢀpinene
limonene
other products
cimene
cimene
ronene
561
581
601
621
641
661
600
120
82.8
60.4
32.1
5.6
11.5
23.0
37.4
52.5
49.0
48.1
28.2
37.4
45.7
48.3
49.3
52.2
2.6
10.3
18.3
21.9
21.4
11.5
14.0
18.3
20.7
24.2
25.7
20.3
2.1
5.0
0.2
0.8
2.1
0.8
0.5
0.7
0.7
4.3
7.9
0.8
0.7
1.0
0.7
1.2
2.0
9.4
13.1
10.5
5.6
6.2
13.8
26.0
1.4
1.0
0.9
90
49.4
32.1
16.1
10.4
6.4
6.2
120
150
180
210
270
9.4
2.1
13.2
12.2
12.7
16.5
3.3
4.2
4.7
5.7
3.3
tion in the gas or liquid phase [13, 14, 16, 23]. The rate fact that the concentration ratio of these two isomers
of each step obeys a firstꢀorder rate equation.
in the reaction products (Table 1) is nearly the same,
approximately 2, at all experimental temperatures.
These reversible reactions are rapid, and this is why the
rate constants of steps 4 and 5 cannot be identified.
This provides good reason to simplify the model: these
The occurrence of reversible conversions between
the
4E,6Zꢀ
and
4E,6Eꢀalloocimenes is proved by the
isomers are taken to be a single component (
4E,6Zꢀ
x
1
,
00
y
, %
and ,6 ꢀalloocimenes), and the concentration of
4E E
this component is taken to be equal to the sum of the
isomer concentrations.
1
80
60
40
20
The minimization of the objective function (4) for
the model based on the complete network of ꢀpinene
α
thermal isomerization reactions (Scheme 1) enabled
us to calculate kinetic parameters (rate constants and
activation energies) and their confidence intervals. In
spite of the good agreement between the experimental
and calculated data, all parameters of the kinetic
model (except for routes 1 and 2 in Scheme 1) contain
large uncertainties. This is evident from their wide
confidence intervals corresponding to the 95% confiꢀ
dence level, which far exceed the rate constant estiꢀ
mates in some cases. Obviously, the experimental data
are indifferent to these routes.
2
3
4
5
Based on these considerations, we suggest a simpliꢀ
fied reaction network (Scheme 2). The results of the
identification of this model as calculated constants
and their confidence intervals are presented in Table 2.
Figure 2 demonstrates that the experimental and calꢀ
culated data in this case are in good agreement.
5
40
580
620
660
, K
T
Fig. 2.
yields as a function of temperature (
ꢀpinene, ( ) limonene, ( ) 4
ꢀalloocimene, and ( ) pyronene isomers. The points
α
ꢀPinene conversion and isomerization product
= 120 atm, = 70 s):
,6 ꢀalloocimene, (
P
E
τ
(
4
1
E
)
,6
α
2
3
Z
4)
E
5
Although the rate constant k40 has a wide confiꢀ
dence interval, route 4 in Scheme 2 was not excluded
represent experimental data, and the solid lines represent
calculated data.
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
167
R1
α
ꢀPinene
Limonene
R2
R3
R4
R5
R6
+
4E,6
EꢀAlloocimene
4E,6ZꢀAlloocimene
α
ꢀPyronene
βꢀPyronene
R7 R8
Other products
The other products include the dimerization
and polymerization products of alloocimenes,
4+2]ꢀcycloaddition products, etc.
[
Scheme 1. Complete scheme of
αꢀpinene thermal isomerization routes.
R1
α
ꢀPinene
Limonene
R2
R4
R3
Other products
,6
4
E
E
ꢀ
and
4
E,6
ZꢀAlloocimenes
α
and βꢀPyronenes
Scheme 2. Simplified scheme of αꢀpinene thermal isomerization routes.
from the model, because doing this would break the the activation energy of route 2 is higher than that of
balance in the system.
route 1: E > E (see Eq. (6)).
2
1
Selectivity of the reaction. Figure 3 plots the temꢀ
perature dependences of the reaction selectivities with
respect to the main products. Here, selectivity is an
integral quantity defined as the ratio of the isomerizaꢀ
tion product yield to the amount of converted
k1
k1 + k2
S =
Li
(6)
k exp
(
−E /RT
)
1
0
1
=
.
k10 exp
(
−E /RT
1
)
+ k exp
20
(
−E /RT
2
)
α
ꢀpinene under given conditions. As in the case of the
gasꢀ or liquidꢀphase thermal isomerization, the main
product of ꢀpinene conversion in supercritical ethaꢀ
nol is limonene. The limonene selectivity of the reacꢀ
As a consequence, raising the reaction temperature is
favorable for route 2 (Scheme 2), increasing the yield
of the alloocimene isomers. As the temperature is furꢀ
α
ther increased, the overall
α
ꢀpinene conversion begins
tion decreases with increasing temperature because to be dominated by the reactions yielding pyronene
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

1
68
ANIKEEV et al.
Table 2. Estimates of the kinetic constants of the reactions in
Scheme 2 and their statistical characteristics
α
ꢀPinene Isomerization in WaterꢀContaining
Supercritical Ethanol
Interest in the thermal isomerization of ꢀpinene
α
Kinetic constants and their confidence intervals
in supercritical ethanol–water mixtures (in our study,
monoterpene isomerization was carried out in ethanol
containing ~5% water) stems from the desire to underꢀ
stand the effect of water on the reaction mechanism
and on the selectivity and rate of the overall converꢀ
sion. This is explained by the fact that water in the
region of its critical parameters (SCW) is strongly disꢀ
sociated [54, 55] and can show the properties of an
acid or base catalyst. This is favorable for a variety of
chemical reactions [36, 37]. However, as was found
experimentally, use of pure SCW as a solvent in the
rate constant, s–1
activation energy, kJ/mol
k10 8.51E+07
2.73E+09
±
±
±
±
1.38E+07
E1
118.0
137.0
129.0
74.3
±
±
±
±
8.07
9.21
31.0
60.6
k20
4.99E+08
6.15E+07
1.37E+03
E2
k30 1.08E+08
k40 1.23E+03
Standard error
E3
E4
0.97%
thermal isomerization of ꢀpinene causes deep strucꢀ
α
tural rearrangements of the terpene into 60 identified
products because of the high reactivity of SCW. The
carbon backbones of the products vary between С6 and
isomers and other byꢀproducts, thus reducing the total
alloocimene selectivity.
С40 and are dominated by C (monoterpenic comꢀ
For convenient comparison between the
isomerization rate in supercritical ethanol with the
same data for the gas and liquid phases from the literꢀ
α
ꢀpinene
10
pounds). The main
α
ꢀpinene conversion product
under these conditions is limonene, whose yield does
not exceed 20–25%. Bringing the solvent (water) into
the subcritical region effects limonene hydration into
ature, we will consider the overall rate of
isomerization via all routes. As follows from Fig. 4, the
overall rate of ꢀpinene isomerization in supercritical
α
ꢀpinene
the monoterpene alcohol ꢀterpineol (~20–25%).
α
α
ethanol is well above the rates of isomerization in the
gas and liquid phase. At the same time, the observed
Experimental data on the thermal isomerization of
ꢀpinene in supercritical ethanol–water mixtures are
α
activation energies of these reactions are approxiꢀ presented in Fig. 5 (points) as the dependence of the
mately equal, and this fact should be taken into conꢀ mole fractions of reaction products (limonene, allooꢀ
sideration when comparing the activation energies of cimene isomers, pyronenes, and the total fraction of
isomerization of other monoterpenic compounds other products) on the water content of the feed under
(
β
ꢀpinene, verbenol, and turpentine) in supercritical fixed conditions. It follows from these dependences
ethanol under equal conditions. Such a comparison that, in spite of the high water concentration in ethaꢀ
would provide a better understanding of the common nol, the distribution of
ꢀpinene isomerization prodꢀ
α
and specific features of the reactions of structurally ucts is the same as in the case of thermal isomerization
similar compounds in supercritical solvents and would in pure supercritical ethanol (Table 1). Furthermore,
demonstrate the potential of solvents for selectivity as the water concentration in the reaction mixture is
and reaction rate control.
raised, the limonene yield increases from 57 to 69%,
−
1 −1
Selectivity, %
ln
2
w
[mol l s ]
6
4
2
0
0
2
4
6
8
1
1
3
−
−
−
−
0
2
0
3
−
10
4
2
−
−
12
0
5
40
580
620
660
, K
14
1
T
.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
000/
1
T
Fig. 3. Product selectivities as a function of temperature:
Fig. 4. Arrhenius plot of the overall rate of the thermal
isomerization of ꢀpinene ( ) in supercritical ethanol,
) in the liquid phase [16], and ( ) in the gas phase [18, 19].
(1
) limonene, (
2) 4E,6
Z
ꢀ and 4
E
,6
E
ꢀalloocimenes, (
3)
α
1
(α
+
β
)ꢀpyronenes, and (
4
) other products.
(2
3
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
log(Kw) [(gꢀion/kg)2]
169
Density, g/cm3
Product yield, mol %
7
6
5
4
3
2
1
0
0
0
0
0
0
0
1
.0
.8
2
1
1
2
8
4
1
0
0.6
.4
2
0
3
0.2
0
4
10
00
2
400
600
, K
800
1000
0
10
20
30
40
50
60
T
Water content of the mixture, vol %
Fig. 5. Yields of organic products as a function of the water
content of the reaction mixture: ( ) limonene, ( ) 4 ,6
and 4 ,6 ꢀalloocimenes, ( ) pyronenes, and ( ) other
products. The concentrations are normalized to the initial
ꢀpinene concentration in the solution. = 657 K;
30 atm.
Fig. 6. Negative logarithm of the water ion product and
water density as a function of temperature at = 230 atm.
1
2
E
Z
ꢀ
P
E
E
3
4
α
T
P =
perature range of 273–1273 K and in the pressure
range of 1–10000 atm:
2
logK = Q1
(
T
)
+ Q2
(
T
2
)
logρw,
w
the yield of alloocimene isomers remains almost
unchanged, and the pyronene concentration
decreases markedly, possibly because of the increasing
yield of other products. As the water concentration in
3
Q = A + B/T + C/T + D/T ,
1
(7)
2
Q = E + F/T + G/T .
2
2
the reaction mixture is lowered, the qualitative and Here, Kw is expressed in units of (gꢀion/kg) and the
3
quantitative compositions of the
tion products tend to those typical of isomerization in coefficients of Eq. (7) are as follows [55]:
pure supercritical ethanol. Therefore, the increase in
the limonene yield with an increase in the water conꢀ
centration in the supercritical solvent can be due to the
increasing contribution from the ionic mechanism of
α
ꢀpinene isomerizaꢀ water density
ρ
is expressed in units of g/cm . The
w
105 K2
;
A
= –4.098;
B
= –3245.2 K;
= –3.984
107 K3
= –1262.3 K;
C
E
= 2.2362
= 13.957;
= 8.5641
105 K2
×
D
F
×
;
G
×
.
αꢀpinene isomerization.
Figure 6 plots the temperature dependence of the
ion product and density of water at = 230 atm as calꢀ
culated via Eq. (7). The density of water was calculated
according to NIST standards [58]. It is clear from
Fig. 6 that the water ion product increases by 3 orders
of magnitude as the temperature is raised from 300 to
Р
Indeed, as was noted above, as the density of the
supercritical medium increases in the critical region of
+
water parameters, the
Н ion concentration grows
considerably owing to the increasing degree of ionizaꢀ
tion of water [54, 55]. This imparts water the properꢀ
ties of an acid catalyst and can thus increase the reacꢀ
tion rate [56, 57]. In order to obtain a quantitative estiꢀ
mate of the degree of ionization of water in a
supercritical water–ethanol mixture (and, accordꢀ
6
00 K. As water reaches its critical point and passes
into the supercritical state in the 600–700 K interval,
Kw decreases sharply because of the water density
decreasing in this temperature range.
Because isomerization was performed in water–
alcohol mixtures (solutions), in the calculation of Kw
+
–
ingly, the
Н and ОН concentrations), it is necessary
to correctly calculate the ionization constants of subꢀ
critical and supercritical water as a function of temperꢀ
ature, pressure (density), and the fraction of water in
the twoꢀcomponent supercritical solvent.
via Eq. (7) the density of pure water,
w, was replaced
with the “density of water in the mixture,” ρ
w, m i x :
ρ
3
ρ
= ρ C [gH2O/cmmix]
,
(8)
w, mix
w
w
As a rule, the degree of ionization of water is charꢀ
+
−
where Cw is the volume faction of water in the solution
acterized by the ion product Kw
=[H ]×[OH ]. Under
3
3
normal conditions, logKw = –14. As the temperature
(
сmH O/сmmix ). Although the definition of the “denꢀ
2
3
is raised to 800°С at a density of 1 g/cm , the water ion sity of water in the mixture” ( w, mix) in terms of Eq. (8)
ρ
product increases by 6 orders of magnitude and the H+ is somewhat arbitrary, it accounts well for the variation
concentration increases by 3 orders of magnitude [54]. of Kw with the water concentration in the solution.
In this study, Kw was calculated using the empirical
equation suggested in [55], which is valid in the temꢀ ionic mechanisms (routes
Scheme 3 depicts the most likely freeꢀradical and
and , respectively) of ꢀ
А
В
α
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

170
ANIKEEV et al.
A
B
~
H•
1, 5]ꢀshift
•
H+
–H+
Limonene
[
H+
•
Limonene
Biradical
α
ꢀPinene
2ꢀPinanyl cation
Scheme 3. Freeꢀradical (route
A) and ionic (route
B
) mechanisms of ꢀpinene isomerization.
α
pinene isomerization. The first step of route
an intermediate biradical with a ꢀmenthane strucꢀ K3, respectively:
ture, which then turns into limonene, formally via the
A yields reversible reactions with equilibrium constants K2 and
p
+
+
i
[
[
LH ]
PH ]
[L][H ]
[LH ]
[
1,5] shift of the
H
atom.
K =
2
, K =
.
(12)
+
3
+
The key step of the ionic mechanism (route
В) is
the formation of a pinaneꢀtype carbocation, which, The reactions of mechanism (9) are supplemented
according to the literature [5], forms readily from the with the solution electroneutrality equation
α
ꢀpinene molecule as a result of electrophilic attack
+
+
+
–
+
by an
rearrangement into a
which then yields limonene.
Н
ion. The resulting cation undergoes skeletal
[H ] + [PH ] + [LH ] = [OH ],
(13)
pꢀmenthaneꢀtype carbocation,
–
+
where [OH ] = K /[H ].
w
Schematically, the elementary steps of the ionic After determining the cation concentrations [AH+
]
+
mechanism can be represented as
and [BH ] from Eq. (12) and substituting these conꢀ
centrations into Eq. (13), the latter can be solved for
+
+
+
[
H ] as
(
I) P + H
PH ;
(9)
+
+
+
+
+
(
II) PH
LH ; (III) LH
L + H ,
⎡H ⎤ = K /Denom
,
(14)
(15)
w
⎣
⎦
where
P
= ꢀpinene, L
= limonene, and PH+ and
LH are the respective intermediate cations. In
water–acid solutions, the first step is usually rateꢀlimꢀ
iting. In addition, step I is likely irreversible: in the
α
[
L]⎛ 1
⎞
+
Denom = 1 +
+ 1
.
⎜
⎟
⎠
K3 ⎝K
2
The expression for the reaction rate (11) with Eq. (14)
taken into account can be written as
presence of an acid,
rearrangements never leaving the pinane backbone
intact. By contrast, the ꢀmenthane backbone of
α
ꢀpinene undergoes rapid skeletal
p
R1B = k y1 K / Denom
.
(16)
1B
w
limonene remains practically unchanged under the
same conditions.
Equation (16) demonstrates that, in principle,
limonene accumulation in the reaction products can
decrease the limonene formation rate R1B (because of
the increase in the Denom value due to the growth of
the limonene concentration [L]). In fact, this does not
take place, because the absolute values of the
limonene concentration in the supercritical solution
Within the simplified scheme of
sions (Scheme 2), with the two possible
α
ꢀpinene converꢀ
ꢀpinene
α
isomerization mechanisms (Scheme 3) taken into
consideration, the overall limonene formation rate is
representable as
are small (
≤
0.05 wt %). Accordingly, the second term
R = R + R1B,
(10)
1
1A
of Eq. (15) is much smaller than unity and Denom
≈1.
As a consequence, the rate of limonene formation via
the ionic mechanism, R1B, is directly proportional
where R1A = k [y ] is the reaction rate for route
А
and
1A
1
y1 is the mole fraction of
α
ꢀpinene in the solution.
to K w
.
Under the assumption that the rateꢀlimiting step of
route
route
B
B
is step I of mechanism (9), the reaction rate for
is
It would be logical to assume that, in the presence
of water, the ionic mechanism can take place for the
other products of thermal
α
ꢀpinene isomerization. If
+
this is the case, the rates of the other reactions appearꢀ
R = k [y ]×[H ]
,
(11)
1
B
1B
1
+
ing in Scheme 2 will also depend on the
Н concentraꢀ
where [H+] is the H+ ion concentration in the soluꢀ tion and will be proportional to K w (firstꢀorder with
+
tion. Steps II and III of mechanism (9) are taken to be respect to H ).
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
ꢀpinene conversions Table 3. Rate constant data
171
The mathematical model of
α
according to Scheme 2 is the following set of ordinary
differential equations:
Constant
Units
Value
dy1
k1A
k2A
k3A
k4A
s–1
(8.9
(6.8
(1.7
(3.9
(5.9
(1.1
(4.0
(3.8
±
±
±
±
±
±
±
±
1.5)
1.1)
0.3)
0.8)
2.9)
0.5)
1.6)
0.3)
1.74
×
10–2
=
=
=
=
=
−
(
k1 + k2 y1
)
dτ
dy2
dτ
dy3
dτ
dy4
dτ
dy5
dτ
10–2
10–2
×
×
×
×
×
×
×
k y
1
1
10–3
k y −
2
(
k3 + k4
)
y3
(17)
(18)
1
kg (gꢀion s)–1
10+8
k1B
k2B
10+8
k3y3
10+7
k3B
k4B
10+6
k y ,
4
3
Standard deviation between the experiꢀ
mental and calculated data, %
0
τ
= 0: y1
=
y1
,
y2
y3 y4
= = = y5 = 0.
The subscripts i in yi (mole fractions) correspond to
the component numbers in Scheme 2.
Since the reaction rate for all routes in Scheme 2 is
zero when there is no water in supercritical ethanol
calc
which is based on yij calculation by integrating the
set of equations (17), because the objective function
formulated in terms of integrals in (21) is a quadratic
function of unknown parameters. Due to this circumꢀ
stance, the size of the confidence region of the paramꢀ
eters is much smaller and, accordingly, their statistical
validity is higher. The objective function in the implicit
method, which uses the numerical or analytical soluꢀ
(
under conditions such that limonene forms largely
via the freeꢀradical mechanism), the overall rate conꢀ
stants k j in model (17) are represented as
+
k = k + k [H ]
,
j
= 1–4.
(19)
j
jA
jB
In order to verify the above assumptions, we deterꢀ
mined the numerical values of the parameters of
model (17) using experimental data. The problem was
solved by minimizing the objective function
calc
tion of the set of equations (17) in yij calculation, is
strongly nonlinear with respect to the sought parameꢀ
ters. As a consequence, the confidence region size is
much larger and, accordingly, the statistical validity of
the parameters is lower.
Nexp NS
2
exp
calc
S =
yij − yij
⎯ ⎯→ min
.
(20)
∑∑
j =1 i =1
(
)
The calculated rate constants are listed in Table 3.
Clearly, the values of all rate constants are wellꢀcondiꢀ
tioned, with acceptable confidence intervals. The
standard deviation between the experimental and calꢀ
culated data is below 2%. The fit between the experiꢀ
mental and calculated data is illustrated by Fig. 7,
which plots the yields of the main reaction products
versus the H+ concentration in the supercritical
water–alcohol solvent. Here, the solid lines represent
the calculated values obtained by integrating the set of
equations (17) and the points represent experimental
data. It is clear from Fig. 7 that the model with these
calculated rate constants is in good agreement with the
experimental data.
Here, NS = 5 is the number of components and
Nexp = 8 is the number of experiments carried out at
various water concentrations in the twoꢀcomponent
water–alcohol supercritical solvent. The parameters
of these experiments are constant values of temperaꢀ
ture, pressure, and residence time, as well as
+
Н
conꢀ
centrations calculated using the above procedure for
the preset water concentration in each particular
experiment. The minimization problem was solved by
the combined, direct/indirect, gradient method [59].
The essence of this method is that calculated concenꢀ
calc
tration values (yij ) are found as the integrals of the
The limonene, alloocimene, and byꢀproduct forꢀ
mation reactions turned out to be the most sensitive to
concentration in the solvent. While the allooꢀ
cimene yield decreases with increasing [
of limonene and byꢀproducts rise. For example, the
limonene yield can increase by 10–15% as the water
rightꢀhand sides of Eq. (17):
+
τ
the
Н
calc
0
i
+
+
Н ], the yields
yij = y + Φ y, k,[H ] dτ
.
(21)
i
(
)
∫
0
+
Here, Ф (y, k, [H ]) stands for the corresponding concentration in the supercritical water–ethanol mixꢀ
i
rightꢀhand sides of the differential equations (17). The ture is raised from 0 to 60 vol %. However, taking into
integrals in expression (21) were calculated by the account the results of thermal ꢀpinene isomerization
α
method described in [59]. This method proved more in pure SCW (discussed above), it can be deduced that,
reliable than the implicit method suggested in [60], upon further increase in the water concentration (and,
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

172
ANIKEEV et al.
Product yield, mol %
Concentration, %
100
70
60
50
40
30
20
10
1
8
0
0
1
2
6
2
40
3
20
4
3
5
0
0.2 0.4 0.6 0.8 1.0 1.2 1.4
+
4
E10
,
gꢀion/kg
0
H
2
80
320
360
400
440
, °C
T
+
Fig. 7. Yields of main products as a function of the H ion
Fig. 8. Concentrations of
products as a function of temperature (
70 s): ( ꢀpinene, ( ꢀmyrcene, ( ) limonene, (
menthaꢀ1(7),8ꢀdiene, and ( ) other products. The solid
lines represent the data calculated using the model, and the
points represent experimental data.
β
ꢀpinene and its isomerization
concentration in the supercritical water–ethanol solvent
P
= 120 atm,
τ
=
(
T
= 657 K,
P
= 230 atm,
τ
= 70 s): (
1
) limonene,
) other products.
The solid lines represent calculated data, and the points
represent experimental data.
1)
β
2)
β
3
4) pꢀ
(
2) alloocimenes, (
3
) pyronenes, and (
4
5
accordingly, the Н+ concentration) in the reaction cyclic and acyclic compounds with the general forꢀ
mixture, the limonene yield will stop increasing and mula С Н16. Here, the products of ꢀpinene converꢀ
will begin to decline and other compounds will domiꢀ sion are the same as in the thermal isomerization of
β
10
β
ꢀ
nate the conversion products.
pinene in the gas or liquid phase [8, 18, 19, 26, 61, 62].
The identity of the products of ꢀpinene conversion in
supercritical ethanol and the products of thermal
pinene isomerization in the gas phase suggests that the
ꢀpinene thermolysis mechanism in supercritical ethꢀ
anol and in the gas phase is the same (Scheme 4). This
mechanism includes the formation of the intermediate
biradical I, which then either turns into limonene and
β
One of the most important results of this study is
that it verified the assumption that, in the presence of
water, the electrophilic (ionic) mechanism of thermal
β
ꢀ
β
αꢀpinene isomerization can be “switched on” to join
+
the radical mechanism. The electrophiles are
whose concentration increases dramatically in the
critical region owing to the increasing degree of ionꢀ
Н ions,
p
ꢀmenthaꢀ1(7),8ꢀdiene or transforms into biradical
II, finally yielding ꢀmyrcene.
It was demonstrated that, under our experimental
conditions, the main ꢀpinene conversion routes are
ization of the Н О molecules.
2
β
Isomerization of
β
ꢀPinene and the
αꢀ +
β
ꢀPinene
β
Mixture in Supercritical Ethanol
the following reactions:
β
ꢀPinene is an isomer of αꢀpinene. The molecules
R1
1
2
3
4
. βꢀpinene ⎯ ⎯→ limonene,
of both compounds have the same carbon backbone
and differ only in the position of the C=C bond. In the
gas phase,
mal rearrangement, whose main product is
ꢀmyrcene. It is interesting to compare the reactivities
R2
. βꢀpinene ⎯ ⎯→ βꢀmyrcene,
(22)
β
ꢀpinene, like
α
ꢀpinene, undergoes therꢀ
R3
. βꢀpinene ⎯ ⎯→ pꢀmenthaꢀ1(7),8ꢀdiene,
R4
. βꢀmyrcene ⎯ ⎯→ other products.
β
of these pinenes and the kinetics of their conversion in
supercritical ethanol under equal conditions.
The main reaction of
anol is the thermal opening of the bicyclic pinane sysꢀ
ꢀmyrcene, whose maximum
ꢀpinene conversion and thermolꢀ yield (72%) is reached at 400°С (Table 4). As the temꢀ
ysis selectivity in supercritical ethanol at = 120 atm perature is further raised, the yield of this product
and = 70 s. Experiments demonstrated that the decreases markedly and the yields of other products,
pinene conversion in supercritical ethanol is over 99% mainly oligomers with unidentified structures,
even at 410°С (Fig. 8). The main reaction of ꢀpinene increase sharply. These temperature dependences of
in supercritical ethanol is its thermolysis, as in the case the accumulation of unidentified products and of the
of ꢀpinene [42, 43], which yields a mixture of monoꢀ ꢀmyrcene yield suggest that the main contribution to
β
ꢀpinene in supercritical ethꢀ
We studied the effect of temperature in the 280– tem yielding acyclic
20°С range on the
β
4
β
P
τ
β
ꢀ
β
α
β
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
173
•
•
Δ
+
•
•
(1
S)ꢀ(ꢀ)ꢀβꢀPinene
Biradical
I
(S)ꢀ(ꢀ)ꢀLimonene пꢀMenthaꢀ1(7),8ꢀdiene
Biradical II
βꢀMyrcene
Scheme 4. Mechanism of the thermal isomerization of
βꢀpinene in supercritical ethanol.
the formation of the unidentified products is from stants obtained by identification of this model are staꢀ
reactions of ꢀmyrcene, such as [4+2]ꢀcycloaddition tistically reliable. The numerical values of the rate
β
[
63] and polymerization [64].
constants of the reactions appearing in scheme (22)
are listed in Table 5. Figure 8 presents a comparison
between the calculated and experimental data, demꢀ
onstrating that the accepted kinetic model is in good
agreement with the experimental data.
The enantiomer composition of the products
resulting from the thermolysis of
pinene alone in supercritical ethanol [47] indicates
that there is a single possible route for limonene formꢀ
α
ꢀpinene or
β
ꢀ
ing directly from
ꢀpinene and ꢀmyrcene cannot be limonene precurꢀ
sors in ꢀpinene thermolysis. In addition, the conservaꢀ the same data for gasꢀphase isomerization [18, 19, 26,
tion of the initial enantiomer purity of ꢀpinene during 62] (Fig. 9) indicates that the gasꢀphase reaction is iniꢀ
β
ꢀpinene.
p
ꢀMenthaꢀ1(7),8ꢀdiene,
A comparison between the specific overall rate of
α
β
β
ꢀpinene isomerization in supercritical ethanol and
β
β
its thermolysis rules out the occurrence of reversible tiated at lower temperatures than the reaction in
steps for reactions 2 and 3 in the reaction scheme (22). supercritical ethanol. In addition, the specific rate of
There is no reversibility in the
reaction as well, as is indicated by the fact that even several orders of magnitude higher than that observed
traces of ꢀpinene were not observed in limonene in the gas phase and the activation energy of the reacꢀ
thermolysis in supercritical ethanol [43]. It is, thereꢀ tion in supercritical ethanol at = 120 atm far
fore, possible to substantially reduce the number of exceeds that of the gasꢀphase reaction at atm in
elementary reactions in the kinetic model. all of the three cases considered.
βꢀpinene
limonene
β
ꢀpinene isomerization in supercritical ethanol is
β
P
P
≤
1
The ꢀpinene thermal conversion scheme (22) was Isomerization of the ꢀ +
β
α
β
ꢀpinene mixture in
used as the basis for the kinetic model. The rate conꢀ supercritical ethanol. The products of the cothermolyꢀ
Table 4. Outcomes of βꢀpinene isomerization in supercritical ethanol as a function of temperature (residence time of 70 s, P =
1
20 atm, C0 = 1 mol/l)
Temperature, С
°
Component, %
280
300
320
340
360
380
400
420
β
ꢀ
Pinene
±)ꢀLimonene
Myrcene
Menthaꢀ1(7),8ꢀdiene
Other products
100.0
–
100.0
–
99.7
–
93.6
1.6
3.5
1.0
0.3
77.6
5.8
25.8
10.0
56.4
6.2
1.9
13.3
71.9
7.5
0.6
14.7
61.6
7.3
(
βꢀ
–
–
0.1
–
11.5
4.6
pꢀ
–
–
–
–
0.2
0.5
1.6
5.4
15.8
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

174
ANIKEEV et al.
Table 5. Calculated parameters of the kinetic model of the thermal conversions of βꢀpinene
Thermolysis in the vapor phase
Thermolysis in supercritical ethanol
at P = 1 atm
at P = 120 atm
Reaction
–
1
–1
k0 (s )
Ea
(
kJ/mol
)
k0 (s )
Ea
(kJ/mol
)
βꢀPinene
βꢀPinene
βꢀPinene
βꢀMyrcene
β
ꢀ
myrcene
limonene
Menthadiene
other products
5147.0
±
±
±
±
97.0
77.6
76.8
82.2
75.1
±
±
±
±
1.78
(1.31
(2.07
(2.64
(2.32
±
0.27)
0.43)
0.60)
0.87)
×
×
×
×
1020
1019
1014
108
276.1
275.3
215.3
15.76
±
±
±
±
16.7
17.5
19.2
3.28
564.6
605.2
581.5
42.5
99.3
40.2
7.36
16.15
6.95
±
±
±
p
ꢀ
Standard error
1.11%
1.08%
sis of the equimolar
only of the compounds that result from the indepenꢀ experimental conditions,
dent thermolysis of individual ꢀpinene [42, 46] and undergo thermolysis independently, even though they
ꢀpinene [47] in supercritical ethanol. The reaction yield the same products, namely, limonene and a
mixture contained no compounds that could have group of compounds that were given the common
resulted from the interaction between ꢀ and ꢀpinene name of “other products.” The good agreement
α
ꢀ +
β
ꢀpinene mixture consist pinene. This is further evidence that, under the given
α
ꢀpinene and ꢀpinene
β
α
β
α
β
thermolysis products or from the interaction of these between the experimental data and the corresponding
products with either pinene. For this reason, in the calculated data for all reaction participants (Figs. 10,
mathematical description of the cothermolysis of the 11) is evidence that the parameters of the kinetic
equimolar
scheme (22) and the
in supercritical ethanol (Scheme 2) were left as the
basis of the kinetic scheme. Accordingly, the general
scheme of heatꢀinduced reactions of the
pinene mixture in supercritical ethanol can be repreꢀ
sented as Scheme 5.
α
ꢀ +
β
ꢀpinene mixture, routes 1–4 of model were calculated correctly.
α
ꢀpinene thermolysis reactions
Note that, in addition to the reactions appearing in
Scheme 5, the reversible prototropic isomerization
reaction
α
ꢀpinene
β
ꢀpinene was included in the
α
ꢀ +
β
ꢀ
kinetic model of the overall cothermolysis process.
This reaction could occur in supercritical ethanol
under the thermal conditions of our experiment, as
The thermolysis rate constants of
β
ꢀpinene nixed was suggested by earlier results [65, 66]. However,
with ꢀpinene, obtained by identification of the
α
kinetic model based on Scheme 5, coincide, within
the confidence interval, with the rate constants
Concentration, %
derived from experimental data for individual
β
ꢀ
60
2
−
, mol l s
1
−
1
50
ln
2
w
0
2
4
6
8
40
1
1
3
–
–
–
–
2
30
4
3
20
4
10
–10
–
12
0
280
1
.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
1000/
320
360
400
440
T
Temperature, °С
Fig. 10. Comparison between experimental and calculated
data: ( ꢀpinene, ( ꢀpinene, ( ) limonene, and
ꢀmyrcene. The lines represent the data calculated using
the model, and the points represent experimental data.
Fig. 9.
ꢀpinene in supercritical ethanol compared to (
ature data: ( ) [18, 19], ( ) [62], and ( ) [26].
(
1
) Specific overall rate of thermal isomerization of
1)
α
2)
β
3
β
2–4) literꢀ
(4)
β
2
3
4
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
175
R3
4
1
5
7
R2
R1
R5
R6
R7
3
2
6
R8
R4
Other products
1
2
3
4
5
6
7
,
βꢀPinene
, Limonene
,
,
,
,
,
β
ꢀMyrcene
п
α
ꢀ
Menthadiene
ꢀPinene
Alloocimene
Pyronenes
Scheme 5. General scheme of the thermal isomerization of ꢀ and ꢀpinenes.
α
β
model identification did not confirm the occurrence
α
ꢀpinene concentration (~5.0 mol/l) allows one to
of the forward or back reaction; therefore, under the draw analogies and make comparisons between the
given experimental conditions, the interconversion of thermal isomerization of turpentine and that of pure
α
ꢀpinene and
than their conversion into other products. This inferꢀ supercritical solvents. At the same time, the difference
ence is corroborated by the following experimental between the ꢀpinene concentrations in turpentine
data. Firstly, ꢀpinene thermolysis does not yield and in the related systems, the presence of other terpeꢀ
ꢀmyrcene, the main product of ꢀpinene thermolyꢀ nes in turpentine capable of isomerization, and the
sis. Secondly, the limonene resulting from ꢀpinene absence of ethanol as a specific reaction medium can
thermolysis has the same enantiomer purity as the iniꢀ have a serious effect on the thermal isomerization proꢀ
tial ꢀpinene. This means that the ꢀpinene cess.
ꢀpinene reaction does not occur during thermolysis,
β
ꢀpinene proceeds much more slowly
α
ꢀpinene under various conditions, including in
α
α
β
β
β
β
β
α
The sulfate turpentine used as the starting reactant
since ꢀpinene would turn into racemic limonene
α
in this study contained 75–80% ꢀpinene 1.2–1.5%
camphene, 3–5% ꢀpinene, 11–14% 3ꢀcarene, 2–4%
limonene, and other compounds. The sulfur content
of sulfate turpentine was about 0.03–0.05%.
α
(
dipentene) [47], which would reduce the enantiomer
β
purity of the limonene resulting from enantiomerically
homogeneous ꢀpinene.
β
Note also the fact that
β
ꢀpinene conversion starts at
ꢀpinene thermolysis and its
From both scientific and practical standpoints, it is
pertinent to study the thermal isomerization of turꢀ
pentine without a solvent, but under conditions simiꢀ
higher temperatures than
α
rate increases more rapidly with increasing temperaꢀ
ture. Among the basic reactions involving ꢀpinene
and ꢀpinene (Tables 2, 5), those of ꢀpinene are
characterized by higher activation energies and preexꢀ
ponential factors. This can clearly be seen from the
plots presented in Fig. 10 and from the dependences of
α
lar to the ꢀpinene isomerization conditions in superꢀ
α
β
β
critical ethanol (comparable residence times, temperꢀ
atures, and pressures). From the standpoint of
science, it is interesting to compare the activation rate
and rates of chemical reactions and to study the effect
of pressure. For practical purposes, it is significant to
estimate the yield of the desired products—limonene
and alloocimenes—from turpentine isomerization
without a solvent and to compare it to the yield of these
the overall rates of thermal
isomerizations (Figs. 4, 9).
α
ꢀpinene and ꢀpinene
β
Thermolysis of Sulfate Turpentine at High Pressures
As was mentioned above,
products from
ꢀpinene is the main ethanol under identical conditions. This comparison
component (up to 80%) f sulfate turpentine. The high would be more correct and informative if the phase
α
ꢀpinene isomerization in supercritical
α
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

176
ANIKEEV et al.
lations because no experimental data were available
Concentration, %
2
2
1
1
4
0
6
2
8
for most of the monoterpenes (Table 6). Table 6 lists
the boiling points of some of the terpenes, which will
be useful in the discussion of the results presented
below.
2
The Tcr and Pcr values for limonene, 3ꢀcarene,
alloocimenes, and some other monoterpenes (Table 6)
were calculated using Joback’s group contribution
methods [67]. The results of these calculations demꢀ
onstrate that the critical parameters of ꢀpinene and
α
other monoterpenes that are either turpentine compoꢀ
nents or turpentine thermolysis products are similar:
1
Tcr
under the sulfate turpentine thermolysis conditions
= 533–693 K, = 40–280 atm; see Table 7), in the
≈
615–655 K and Pcr
≈
24–29 atm. Therefore,
4
0
3
(
T
P
absence of any solvent, the reaction mixture can be
either in the subcritical (liquidꢀlike fluid) state or in
the supercritical state, depending on the reaction temꢀ
perature.
2
80 300 320 340 360 380 400 420 440
Temperature, °С
Fig. 11. Comparison between experimental and calculated
data: ( ) alloocimenes, ( ) pyronenes, and ( ꢀmenthaꢀ
dienes. The lines represent the data calculated using the
model, and the points represent experimental data.
Main thermolysis products of sulfate turpentine.
The most important experimental data for sulfate turꢀ
pentine thermolysis at high pressures are presented in
Table 7. These data were obtained from two series of
experiments. In one of them, the thermolysis temperꢀ
1
2
3) p
compositions of turpentine and its thermolysis prodꢀ ature was varied at a fixed pressure; in the other, the
thermolysis pressure was varied at a constant temperaꢀ
ucts under the experimental conditions were deterꢀ
ture. The residence time of the reaction mixture in
mined. To do this, it is necessary to know the critical
these two experimental series was the same. Most of
parameters of the individual components of the multiꢀ
the volatile products resulting from turpentine converꢀ
component mixture of monoterpenes in sulfate turꢀ
sion were identified in each experiment. These prodꢀ
pentine and those of the anticipated thermolysis prodꢀ
ucts accounted for at least 94–95 wt % of the total
ucts. The necessary critical data were gained by calcuꢀ product yield. A quantitative analysis of the reaction
Table 6. Calculated critical temperature, pressures, and molar volumes for some monoterpene hydrocarbons, water, and ethanol
present in reaction mixtures in turpentine thermolysis in supercritical solvents
3
Component
Tboil, K (1 atm
)
Tcr, K
Pcr, atm
Vcr, cm /mol
α
ꢀ
Pinene
445.9
440.9
445.9
448.6
425.7
440.6
440.6
446.8
456.5
448.7
450.9
460.5
455.8
373.2
351.5
632.5
623.7
632.5
646.0
615.2
642.8
642.8
638.2
642.0
646.0
639.5
639.5
654.8
647.3
516.2
28.9
28.5
28.5
27.6
23.9
24.7
24.7
27.6
28.1
27.2
27.1
27.1
29.0
217.6
63.0
484.5
482.5
484.5
496.5
539.5
537.5
537.5
497.5
498.5
496.5
494.5
495.5
490.5
56.0
βꢀPinene
3ꢀ
Carene
Limonen
Myrcene
βꢀ
4E
,6Zꢀ
Alloocimene
4E
,6EꢀAlloocimene
α
ꢀ
Pyronene
βꢀPyronene
Silvestrene
Phellandrene
Menthaꢀ1(6),4ꢀdiene
,5,5ꢀTrimethylcycloheptaꢀ1,3ꢀdiene
α
ꢀ
m
ꢀ
1
Water
Ethanol
167.0
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
177
Table 7. Products resulting from the thermal isomerization of sulfate turpentine
Allooꢀ
cimenes
Other
products
α
ꢀPinene
Limonene
3ꢀCarene
Pyronenes
Turpentine
, К
80.0
1.3
11.0
0.0
0.0
7.7 (0.0)
entry
Т
Р, atm
1
2
3
4
5
6
7
8
9
533
555
573
597
614
634
653
673
693
120
77.5
66.4
49.4
10.4
1.0
3.0
7.8
11.3
10.7
11.5
12.1
11.0
8.9
0.0
0.0
0.0
0.1
0.3
2.2
5.2
8.4
11.7
9.3
4.7
8.2 (0.6)
15.0 (8.8)
17.0 (9.8)
20.0 (12.1)
26.4 (18.1)
43.7 (36.2)
50.7 (42.6)
62.6 (50.5)
79.1 (60.1)
17.3
40.3
45.5
34.1
30.2
23.2
13.7
4.5
15.0
10.9
4.7
0.2
0.0
7.4
0.0
0.0
4.9
0.0
0.0
2.5
0.0
Turpentine
76.3
2.6
13.6
0.0
0.0
7.5
10
11
12
13
14
15
16
17
18
593
40
70
16.9
15.2
15.2
11.7
14.0
11.7
12.6
12.2
12.4
30.6
32.4
32.3
34.3
32.4
35.6
34.3
33.9
35.1
12.3
12.2
12.4
12.4
12.5
12.5
12.4
12.8
12.4
21.4
22.4
19.9
23.0
23.4
21.4
20.1
21.5
21.1
2.1
2.1
2.3
2.7
2.6
2.6
2.5
2.6
2.5
16.8
15.6
17.9
16.0
15.2
16.2
18.0
17.2
16.6
100
130
160
190
220
250
280
products demonstrated that the main thermolysis conversion rates. In sulfate turpentine at
products of sulfate turpentine are limonene and allooꢀ = 70 s, = 120 atm), the 3ꢀcarene conversion is
cimene and pyronene isomers, as in the case of over 50%, much higher than the conversion of pure
T = 673 K
(
τ
P
α
ꢀ
pinene thermolysis. Among the volatile compounds 3ꢀcarene at
belonging to the group of “other products,” we identiꢀ
fied diꢀ and monoalkylbenzenes (with methyl, ethyl,
isopropyl, and isopropenyl substituents), trimethylcyꢀ
T
= 753 K (
τ
= 60 s,
P 1 atm).
≈
The percentages of nonvolatile reaction products
included in the group of “other products” were estiꢀ
mated versus an internal standard (menthol) and were
calculated as the difference between the total weight
percent of volatiles in the initial sulfate turpentine and
the total weight percent of the volatiles that remained
in the reaction mixture after thermolysis. Since the
amount of the gaseous products of pyrolysis in our
cloheptadienes, pꢀ and
mꢀtrimethylcycloheptatrienes
(
terpinenes, terpinolene, phellandrenes), dimethylocꢀ
tadienes (except alloocimenes), unreacted turpentine
monoterpenes (camphene, fenchene, tricyclene), and
C –C compounds.
12
20
The formation of each of the identified volatile experiments was small (as determined visually when
products can be explained in the framework of the sampling the products for analysis), we assumed that
freeꢀradical mechanisms of thermolysis of the correꢀ the decrease in the amount of volatile compounds in
sponding monoterpenic hydrocarbons, such as the the reaction mixtures is due solely to the formation of
familiar freeꢀradical mechanisms of the thermal oligomers that are nonvolatile under the GCꢀMS conꢀ
isomerization of
α
ꢀ and
β
ꢀpinene [41, 47], limonene ditions. The thusꢀobtained quantitative data characꢀ
[
68], and 3ꢀcarene [69–72].
terizing the component composition of the reaction
mixtures seem to us quite reliable.
A comparison between the thermolysis of
ꢀcarene—the second most abundant component of
3
Note the following specific features of ꢀpinene
α
sulfate turpentine—alone in the gas phase at atmoꢀ conversion in supercritical ethanol (Fig. 2) and the
spheric pressure [70–72] and the thermolysis of conversion of ꢀpinene as a component of sulfate turꢀ
ꢀcarene in turpentine reveals a difference between the pentine at 120 atm (Figs. 12, 13). Firstly, in ꢀpinene
α
3
α
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

1
78
ANIKEEV et al.
Concentration, %
Concentration, %
8
7
6
5
4
3
2
1
0
0
0
0
0
0
0
0
80
70
6
0
0
1
5
3
2
40
3
2
1
0
0
1
2
0
0
3
5
25 550 575 600 625 650 675 700
T, K
0
5
25 550 575 600 625 650 675 700
, K
T
Fig. 12. Concentrations (mol %) of
α
ꢀpinene as a turpenꢀ
Fig. 13. Concentrations (mol %) of turpentine thermolysis
products as a function of temperature ( = 120 atm,
70 s): ( ) pyronenes, ( ) 3ꢀcarene, and ( ) other products.
The solid lines represent the data calculated using the
kinetic model, and the points represent experimental data.
tine component and its thermolysis products as a function
P
3
τ
=
of temperature (
P
= 120 atm,
τ
= 70 s): (
1)
α
ꢀpinene,
1
2
(2) limonene, and (
3) alloocimenes. The solid lines repreꢀ
sent the data calculated using the model, and the points
represent experimental data.
α
ꢀpinene (reactions 1, 2, and 4 in Scheme 6) were
isomerization in supercritical ethanol, the limonene
and alloocimene concentrations reach their maxima
used as the basis of the kinetic model. At the same
time, the set of reactions included in Scheme 6 differs
from that used in the kinetic model of ꢀpinene therꢀ
molysis in supercritical ethanol (Schemes 1, 2). Since
the limonene and pyronene concentrations as a funcꢀ
tion of temperature pass through a maximum, the
at complete
in turpentine, these concentrations reach their maxꢀ
ima at a lower ꢀpinene conversion of 90–92%. Secꢀ
ondly, while the concentration of pyronenes in
ꢀpinene isomerization in supercritical ethanol
α
ꢀpinene conversion; in the same process
α
α
α
reactions limonene
pyronene “other products” (5), and 3ꢀcarene
other products” (6) were included in the kinetic
model for sulfate turpentine. Another distinction
between this model and the model of ꢀpinene isomerꢀ
ization in supercritical ethanol is the absence of the
alloocimenes “other products” route in the former.
“other products” (3),
increases steadily throughout the temperature range
examined, the pyronene concentration in the therꢀ
molysis of sulfate turpentine passes through a maxiꢀ
mum. Thirdly, the greatest difference between these
reactions is in the formation rate of “other products,”
whose concentration increases sharply owing to the
“
α
thermolysis of the products of
in turpentine.
αꢀpinene isomerization
This route was omitted for the reason that preliminary
data processing based on identification of the complete
This behavior of the reaction participants suggests kinetic model gave statistically unreliable values of the
that the monoterpenic compounds in supercritical activation energy
ethanol are thermally more stable than the same comꢀ alloocimenes
pounds in the absence of a supercritical solvent. Note
E
and preexponential factor for the
“other products” reaction.
Experimental data with the above sulfate turpenꢀ
tine thermolysis reactions taken into account were
processed using the plugꢀflow reactor model in the
form of a set of ordinary differential equations with
firstꢀorder rate equations for each route (Scheme 6).
The calculated preexponential factors, activation
energies, and their statistical characteristics are listed
in Table 8. Figures 12 and 13 illustrate the good agreeꢀ
ment between the experimental data (points) and the
calculated data (lines). The only exception is the disꢀ
crepancy between the experimental and theoretical
temperature dependences of the “other products”
concentration (Fig. 13). A possible cause of this disꢀ
the low conversion of 3ꢀcarene and its insignificant
contribution to the yield of “other products.”
Another result of sulfate turpentine thermolysis
that is in agreement with earlier data [34] is the formaꢀ
tion of oligomers (>C –C ) nonvolatile under the
25
30
GCꢀMS conditions, whose amount can be up to
0 wt % of the total amount of thermolysis products
6
(
Table 7, entry 9).
Turpentine thermolysis kinetics. From the experiꢀ
mental data presented in Table 7, we derived a kinetic
model for sulfate turpentine thermolysis. The reaction
routes of this model are shown in Scheme 6.
Since the main component of sulfate turpentine is crepancy is disregard of the exact stoichiometry of
ꢀpinene, the reactions characteristic of individual reactions 3, 5, and 6 in Scheme 6.
α
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
179
3
Other products
1
6
5
Limonene
2
α
ꢀPinene
4
3ꢀCarene
Pyronenes
Alloocimenes
Scheme 6. Sulfate turpentine thermolysis routes.
Calculation of the overall reaction rate. To begin a where y0 and
comparison between the observed rates of
thermolysis in turpentine (Table 8) and the same data uct at a given temperature and pressure, respectively,
and are the rate constant of reactions 1 and 2
y
(
T
,
P
) are the
α
ꢀpinene concentrations
α
ꢀpinene (mole fractions) in the feed and in the reaction prodꢀ
for
α
ꢀpinene thermolysis in supercritical ethanol, it is and
k
1
k
2
in Scheme 6 (Table 8).
necessary to find appropriate comparison parameters.
The preferable ones are rate constants and activation
energies. However, it would not be quite correct to
The effect of the reaction medium temperature.
Consider ln
k
as a function of 1000/
T
for the
α
ꢀpinene
) and in
). At a given
ꢀpinene converꢀ
version in turpentine, taking it to be the sum of the sion in turpentine is larger than the same rate constant
rates of the two main reactions, namely,
ꢀpinene in supercritical ethanol, and the activation energy of
conversions into limonene and alloocimene isomers the reaction in turpentine is higher than that of the
reaction in supercritical ethanol:
Σ
directly compare k0 and
in different kinetic models. For this reason, we introꢀ supercritical ethanol (Fig. 14, curve
duce the concept of the overall rate of ꢀpinene conꢀ pressure, the overall rate constant of
E for the same reactions, but conversions in turpentine (Fig. 14, curve
1
2
α
α
α
E
(
reactions 1 and 2 in Scheme 6). For firstꢀorder reacꢀ
tions in a plugꢀflow reactor, the overall rate constant of
ꢀpinene conversion in turpentine can be calculated
11
In turpentine ,
kΣ0 = 2.69 ×10 1/s
:
α
via the equation
E = 149.4 kJ/mol
.
7
In supercritical ethanol
:
kΣ0 = 5.46 ×10 1/s
,
ln(y /y(T,P))
0
k (T,P) =
Σ
, k = k + k2,
(23)
Σ
1
E
= 113.3 kJ/mol.
τ
Table 8. Estimates of kinetic constants and their statistical characteristics
Reaction
k0, s–1
E, kJ/mol
1
2
1012
1011
109
100
3
.85
.03
×
×
±
±
±
±
±
±
1.08
×
×
×
×
×
×
163.0
151.0
503.0
117.0
302.0
209.0
±
±
±
±
±
±
4.11
4.59
1.54
13.9
430.0
49.4
α
ꢀ
ꢀ
Pinene
Pinene
limonene
1011
1
3.16
1.19
6.41
3.29
3.34
α
alloocimenes
other products
3
102
1
.25
×
Limonene
Alloocimenes
4
107
106
7
.21
×
pyronenes
5
1021
1021
1.31
×
×
Pyronenes
other products
other products
6
1014
1013
1.15
3ꢀCarene
Standard deviation: 3.0%
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

180
ANIKEEV et al.
α
ꢀpinene concentration was 50 times lower than in
ln
k
Σ
turpentine. Unfortunately, the available data are insufꢀ
ficient to make certain whether the [TS] ordering is
–
2
3
4
5
6
7
due to the lower initial
solvent effect.
α
ꢀpinene concentration or the
–
–
–
–
#
#
1
Despite the marked differences in ΔH and ΔS
,
#
2
the temperatureꢀaveraged values of ΔG for the reacꢀ
tions of ꢀpinene in turpentine and in supercritical
α
ethanol are similar. This fact may indicate that the
thermolysis mechanism (and [TS] structure) of
α
ꢀpinene changes only slightly on passing from one
–
–
reaction medium to another. Using the familiar therꢀ
modynamic relationship between the equilibrium
#
eq
8
1
constant
K
and the Gibbs energy of a reaction,
.5
1.6
1.7
1.8
1.9
000/
1
T
#
⎛
ΔG
(
T
)
⎞
⎟,
#
eq
K
= exp⎜−
(24)
Fig. 14. Arrhenius plots of ln
tine and (
k
versus 1000/
) supercritical ethanol.
T
: (
1
) turpenꢀ
= 70 s.
RT
Σ
⎝
⎠
2
P
= 120 atm;
τ
it can be demonstrated that, for the
α
ꢀpinene
[TS]
#
reaction, the
are larger than those for supercritical ethanol
Fig. 15). The larger value of the equilibrium constant
K
(T) values for the turpentine medium
eq
In order to explain this difference between the
kinetic parameters of the reactions, we will find the
(
#
#
#
activation parameters ΔH
,
ΔS , and ΔG of the
ꢀpinene [TS] reaction using transition state theꢀ
#
eq
K
means that the equilibrium [TS] concentration in
α
turpentine is higher than that in supercritical ethanol,
and this may be responsible for the higher overall
pinene conversion rate in turpentine.
ory [73] and experimental values of the activation
α
ꢀ
energy and rate constant kΣ0. The calculated values of
the sought quantities, averaged over the temperature
range of 533–693 K, are listed in Table 9.
HeatꢀInduced Conversions of cisꢀVerbenol
in Supercritical Ethanol
#
#
Here, ΔH and ΔS have the meaning of the
enthalpy of activation and entropy of activation averꢀ
aged over the temperature range examined. Accordꢀ
A comparison between the reactivities of
α
ꢀ and
β
ꢀpinene in their thermal isomerization reactions,
#
ingly, ΔG is the averaged activation energy calculated
measurement of reaction rates, and determination of
the corresponding activation energies would make it
possible to establish a correlation between the strucꢀ
ture and chemical properties of these structurally simꢀ
ilar compounds. Additional information for establishꢀ
ing this structure–properties correlation can be gained
by investigating the thermal isomerization of related
compounds having the same carbon backbone, but
different functional groups. One of the pinene relatives
#
#
#
as ΔG (T) = ΔH − T ΔS . It is clear from Table 9 that
the entropy of activation is negative for both systems,
implying that the [TS] structure is more ordered than
the structure of the initial ꢀpinene molecule. This
ordering is likely due to the loss of the rotational
degree of freedom by one CH3 group or more. The
absolute value of the entropy of activation of [TS] in
α
#
supercritical ethanol is much higher than the ΔS of is cisꢀverbenol, derivative having an OH group in the
TS] in turpentine. This possibly means that [TS] is allyl position at the Cꢀ4 atom. This OH group is cis to
[
more ordered in supercritical ethanol, in which the the gemꢀdimethyl fragment of cyclobutane. It is,
Table 9. Mean values of the activation parameters of the transition state
#
#
#*
System
ΔH
,
kJ/mol
ΔS
,
J/(mol K)
ΔG
, kJ/mol
α
ꢀ
ꢀ
Pinene in turpentine
144.4
116.9
–40.3
–96.2
169.0 (165.4–172.6)
175.6 (166.9–184.3)
α
Pinene in supercritical ethanol
Note: T = 533–693 K, P = 120 atm, τ = 70 s.
The numbers in parentheses are the minimum and maximum values.
*
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
181
#
K
Conversion, %
100
eq
−
13
13
13
14
14
14
1.5
1.3
1.0
7.5
5.0
2.5
×
×
×
×
×
×
10
−
−
−
−
−
10
10
10
10
10
80
60
40
1
2
20
0
0
5
525 550 575 600 625 650 675 700
T, K
40
580
620
660
700
740
, K
T
Fig. 16. cisꢀVerbenol conversion as a function of temperꢀ
ature. = 120 atm; = 70 s. The points represent experꢀ
imental data, and the solid line is the result of data proꢀ
cessing.
#
eq
Fig. 15. Equilibrium constant
ature: ( ) turpentine and ( ) supercritical ethanol.
atm; = 70 s.
K
as a function of temperꢀ
P
τ
1
2
P
= 120
τ
therefore, interesting to study and understand the the product mixture. However, the GC data for trans
ꢀ
effect of this heterofunctionality on the conversion isopiperitenol available from an earlier publication
routes and thermal isomerization energetics of cisꢀverꢀ
benol.
[
75] and the chromatograms and mass spectra of
transꢀisopiperitenol kindly presented on our request
There have been only a few studies of the thermal by Rodney Croteau, one of the authors of this publicaꢀ
isomerization of cisꢀverbenol in the gas and liquid tion, enabled us to identify this compound among the
phases [3, 4, 74]. According to these studies, the main
products of this reaction are isopiperitenol (no inforꢀ
mation about whether cis or trans) and cis/transꢀcitral
isomers, which likely result from the successive openꢀ
ing of the fourꢀ and sixꢀmembered rings of the bicyclic
pinane structure. It was noted that small amounts of
heavy and light hydrocarbons were present in the reacꢀ
tion mixture.
products of verbenol isomerization in supercritical
ethanol. In Table 11, the mole fraction of transꢀisopiꢀ
peritenol and the sum of the mole fractions of cis
ꢀ
isopiperitenol and piperitenol are presented in sepaꢀ
rate rows.
Experimental data demonstrate that conducting
cis
nol affords a significant increase in the reaction rate
transꢀverbenol conꢀ
/transꢀverbenol isomerization in supercritical ethaꢀ
For further investigation of the reactions of terpeꢀ
nes in supercritical solvents, the thermal isomerization and ensures almost complete cis
/
of verbenol was carried out in supercritical ethanol at version at a comparatively low temperature of 380
°
C
various temperatures and a constant pressure. As a (in gasꢀphase isomerization, no noticeable verbenol
result, we determined the verbenol conversion as a
function of the reaction temperature (Fig. 16). The
identified initial compounds and reaction products are
listed in Table 10. Analysis demonstrated that the iniꢀ
tial verbenol contained 92.6% cisꢀverbenol, 4.7%
transꢀverbenol, about 1.4% verbenene, and 0.4% verꢀ
benone. cisꢀCitral, transꢀcitral, and isogeranial were
reliably identified in the reaction products, and this
confirmed the results of an earlier [74]. According to
that work, the main verbenol isomerization product is
isopiperitenol, whose amount is 60–70 vol %. Unforꢀ
tunately, Maksimchuk et al. [74] did not identify the
piperitenol isomers (transꢀ and cisꢀisopiperitenol) and
referred to them as a single compound—isopiperꢀ
itenol. In the studies reported here, the unavailability
of pure cisꢀ and transꢀisopiperitenols and piperitenol
conversion is observed at this temperature [74]). The
yield (selectivity) of the desired product—cisꢀ and
transꢀcitrals—increases from 8% in the gas phase [74]
to 38% in supercritical ethanol.
Note the temperature dependence of the mole
fractions of reactants (Table 10). On the one hand, the
complete cisꢀ or transꢀverbenol conversion point coinꢀ
cides with the cisꢀ and transꢀcitral peak; on the other
hand, it is accompanied by the formation of large
amounts of light an heavy hydrocarbons, which likely
result from the pyrolysis of the citrals, transꢀ and cis
ꢀ
isopiperitenols, and piperitenol. It is, therefore, diffiꢀ
cult to explain why the concentrations of transꢀ and
cisꢀisopiperitenols and piperitenol begin to decrease
and lack of the corresponding retention index data did when verbenol is still present in the reaction mixture.
not allow us to reliably identify these compounds in For this reason, we had to augment the reaction netꢀ
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

182
ANIKEEV et al.
Table 10. Experimental data on the thermal isomerization of verbenol in supercritical ethanol
Temperature
340 361
93.45 88.02 74.72 45.62 10.61
, С
°
Entry
Compound
278
300
321
381
400
419
438
1
2
3
4
5
6
7
8
9
cisꢀVerbenol
0.83
0.16
0.00
0.00
0.00
0.00
0.00
0.00
5.64
7.74
transꢀVerbenol
3.79
0.40
0.07
0.12
3.41
1.63
0.57
0.70
2.69
1.35
0.70
Neral (cisꢀcitral)
4.58 10.43 15.61 16.12 15.24 11.83
Geranial (transꢀcitral)
Isogeranial
2.08
2.16
0.97
7.05 16.21 20.12 19.61 15.36
4.72
2.87
7.24
5.31
7.51
6.19
7.88
6.53
7.64
2.96
6.42 3.42
Isocyclocitral
0.00 0.25
6.40
4.87
2.11
6.36
1.44
1.53
transꢀIsopiperitenol
cisꢀIsopiperitenol and piperitenol
Other compounds
0.83 2.37 5.84 12.17 16.33 11.85
0.34
1.00
0.00
1.09
1.96
0.00
2.77
5.68
6.75
4.01
4.19 10.11 20.86 27.75 33.49 40.85 36.58
0.00 0.00 0.38 5.46 6.65 12.16 37.29
10
Resins and nonvolatile components
Table 11. Compositions of azeotropic mixtures at various pressures (initial mixture composition, mol %: αꢀpinene, 10; ethanol,
1
0; water, 80)
Liquid 1
pinene
Liquid 2
pinene
Vapor
Paz, atm
Taz, K
α
ꢀ
ethanol
α
ꢀ
ethanol
α
ꢀpinene
ethanol
1
5
352.4
402.8
430.6
463.2
502.0
528.0
548.4
0.00
0.00
0.00
0.00
0.02
0.07
0.18
0.53
1.19
1.62
2.11
2.55
2.73
2.82
45.23
40.39
36.53
30.87
22.80
17.08
12.80
43.37
36.79
32.24
26.47
19.55
15.19
12.04
5.05
5.49
5.84
6.30
6.81
7.02
6.99
54.34
43.58
37.36
30.23
22.32
17.51
14.01
1
2
4
6
8
0
0
0
0
0
work with the conversion of transꢀ and cisꢀisopiperꢀ supercritical solvent changes the properties of the actiꢀ
itenols, and piperitenol into “other products”:
vated complex and thus shifts the equilibrium in the
reversible step of the reaction toward the final product.
1.
2.
3.
4.
5.
6.
cisꢀVerbenol
cisꢀVerbenol
cisꢀVerbenol
cisꢀVerbenol
cisꢀCitral
cisꢀcitral.
transꢀisopiperitenol.
cisꢀisopiperitenol + piperitenol.
isogeranial.
EFFECT OF PRESSURE ON THE RATE
OF THERMAL ISOMERIZATION
OF MONOTERPENIC COMPOUNDS
IN SUPERCRITICAL ALCOHOLS
“other products.”
cis/transꢀIsopiperitenol + piperitenol
“other
products.”
A specific feature of many organic reactions n
supercritical fluids is that their rate or rate constant
depends strongly on pressure [37, 76–78]. The effect
of pressure on the rate constant is typical of reactions
The apparent overall activation energy determined
by Maksimchuk et al. [74], 96.7 kJ/mol, differs greatly
from the value obtained in this study, 157 kJ/mol.
As follows from the results of this work, the activaꢀ in aqueous solutions. For reactions in supercritical
tion energy of thermal isomerization of monoterpenic solvents, an increase in pressure (density of the
compounds (such as
βꢀpinene; see Scheme 4) in medium) can lead both to an increase in the reaction
supercritical alcohols is also higher than the activation rate [37, 79–84] and to a slowdown of the reaction [79,
energy of thermal isomerization of these compounds 85–88] or cause the reaction rate to pass through an
in the gas or liquid phase at atmospheric pressure. A extremum [79, 89]. In any case, the effect of pressure
possible cause of this significant difference is that the on the rate constant can be explained in terms of the
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
183
x
,
y, %
Selectivity, %
100
60
1
1
8
6
4
2
0
0
0
2
4
0
2
2
0
0
3
3
4
8
0
120
160
200
240
280
, atm
0
P
5
4
Fig. 18. Product selectivities of the reaction as a function
of pressure: ( ) limonene, ( ) alloocimene isomers,
) pyronene isomers, and ( ) other products. T = 600 K;
= 70 s. The points represent experimental data, and the
lines represent calculated data.
0
1
2
8
0
120 160 200 240 260
, atm
(
3
4
P
τ
Fig. 17.
ization products (
between experimental data (points) and calculated data
lines). T = 600 K; = 70 s.
α
ꢀPinene conversion (
x) and the yield of isomerꢀ
y) as a function of pressure: a comparison
allel reactions and because the activation energies of
these reactions differ by ~19 kJ/mol (Table 2).
(
τ
The reaction rates as a function of pressure for
specific interaction of the solvent with the solute molꢀ routes 1 and 2 at a constant experimental temperature
ecules, the properties and nature of the supercritical of T0 = 600 K are written as
solvent, or the interaction of the solute molecules or
#
#
clusters with the solvent.
R1
(
T0,P
)
= k1
(
T0,P
)
y
R2
(
T0,P
)
= k2
(
T0,P
)
y
, (25)
Experiments on the thermal isomerization of
pinene in supercritical ethanol also demonstrated that
the pressure of the reaction medium exerts a signifiꢀ
α
ꢀ
#
where
y
is the dimensionless equilibrium concentraꢀ
tion of [TS]i; i = 1, 2.
cant effect on the rate of parallel reactions of
α
ꢀpinene
The pressure dependence of the apparent rate conꢀ
(
Fig. 17). At the same time, pressure variation does not stants can be expressed as the following equation [90]:
produce any appreciable effect on the selectivity of the
reaction (Fig. 18).
∂ ⎛ ki, app
(
T
,P
)
⎞
0
ln
⎜
P ⎝
⎟
⎠
∂
ki
(
T0,P
)
The effect of the solvent pressure (density) on the
0
(
26)
#
apparent rate constants of thermal
α
ꢀpinene isomerꢀ
∂lnΦA1
1
⎛
⎜
∂lnΦ ⎞ −ΔV
TS
− =
⎟
=
, i = 1,2,
ization was explained and quantitatively described
using transition state theory [73]. According to this
theory, as the reaction moves along the reaction coorꢀ
dinate, it surmounts a potential energy barrier, whose
peak corresponds to the maximum potential energy of
the activated complex, or the transition state [TS]
between the molecule of reactant A and the molecule
of product B (for monomolecular reactions): A
RT ⎝ ∂P
∂P
⎠
RT
where ki, app is the apparent rate constant of route 1
or 2. The numerical values of k1
(
T0,P0
)
and k2
(
T0,P0
)
(
T0 = 600 K, P0 = 120 atm) are derived from the above
experimental data (Table 1).
The fugacity coefficients Ф = Ф
(
y,T,P
)
in
i
i
[
TS]
and is the most rapid in the overall reaction A
Applying the postulates of transition state theory to the components, and the molar composition of the mixꢀ
thermal isomerization of
ꢀpinene (Scheme 2), we ture. The numerical value of the volume of activation
which is equal to the difference between the partial
B. Here, the [TS] formation step is reversible Eq. (26) are functions of temperature, pressure, critiꢀ
B. cal parameters and other properties of the individual
α
(
can represent this process as the following two reacꢀ
molar volumes of the activated complex and the reacꢀ
tions: ꢀpinene [TS]1 limonene (route 1) and
α
#
α
ꢀpinene [TS]2
alloocimenes (route 2). The tant, ΔV = V −VA) depends on the internal properꢀ
introduction of two structurally different activated
complexes, [TS]1 [TS]2, is quite appropriate because
TS
ties of the system, on the properties of the reactant,
and on the external factors determined by the solvent.
≠
#
of the formation of two different isomers via two parꢀ The ΔV value can be both positive and negative.
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

184
ANIKEEV et al.
−
k [s ]
1
of equations (3). The apparent rate constants in
Eq. (3) are now functions of pressure:
ln
Σ
−
−
−
−
−
−
−
−
−
−
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
#
⎛ ΔV
(
P
)
⎞
1
2
ki, app = ki
(
T0,P0
exp −
P − P0 ⎟
.
(30)
)
(
)
⎜
RT
⎝
⎠
Solving the inverse problem yielded the following valꢀ
ues of the sought coefficients of expression (29):
b0 = −1974.63 ± 136.85
,
b1 = 13.15 ± 0.91
,
b2 = −0.022 ± 0.002
.
It is clear from experimental data (Fig. 17) that
pressure has a significant effect only on the rate conꢀ
stants of routes 1 and 2 in Scheme 2, raising the yields
of limonene and alloocimenes. Although the yields of
pyronenes and “other products” are seemingly presꢀ
sureꢀindependent, the pressureꢀinduced increase in
the concentration of alloocimenes—precursors of
pyronenes and “other products”—must certainly
change the concentrations of the latter.
0
50 100 150 200 250 300
, atm
P
Fig. 19. ln
and (2) supercritical ethanol (T = 600 K).
k
versus pressure: (
1
) turpentine (
T = 593 K)
Σ
#
Integration of Eq. (26) between P0 and
20 atm) yields the apparent rate constants as a funcꢀ
tion of pressure in the following form:
P
(
P0
=
The calculated
values are negative over the
ΔV
1
pressure range examined; therefore, the rate constants
grow with increasing pressure. The most rapid
increase of the constants is observed in the 90–
20 atm range, in the nearest vicinity of the critical
pressure of the solvent (ethanol).
The model suggested here is in good agreement with
the experimental data indicating the constancy of the
ꢀpinene isomerization selectivity (Fig. 18). This folꢀ
lows immediately from the model because the presꢀ
sureꢀinduced increase in the rate constants of the reacꢀ
lnki, app
(
T0,P
)
1
P
(27)
1
RT
#
=
lnki
(
T0,P0
)
−
ΔV
(
P
)
dP i = 1,2.
∫
P0
α
Solving the parameter identification problem using a
pressureꢀdependent data array. Sine there is no explicit
#
ΔV
(
P
)
relationship, it seems impossible to use tions in the
α
ꢀpinene
limonene and ꢀpinene
α
Eq. (27) in the determination of the apparent rate alloocimenes routes does not change the rate constant
constants. The problem can be solved by using the ratio k T,P /k T,P), the quantity determining the
(
)
(
1
2
meanꢀvalue theorem, dividing the continuous integraꢀ
selectivity of the reaction.
tion interval in Eq. (27) into discrete intervals P1
– ,
P0
with the
P0. intervals. This
will bring Eq. (27) to the following form:
#
P2
–
P0, …, Pk
–
P0 and replacing ΔV
P
( )
Effect of Pressure on the Turpentine Isomerization Rate
#
mean integral values ΔVk in the Pk
–
Above, we discussed the reactions of ꢀpinene in
α
sulfate turpentine at a constant pressure of 120 atm
and variable temperature (based on the experimental
data presented in Table 7), compared them with the
lnki, app
(
T0,Pk
)
= ln ki
(
T0,P0
)
Pk
#
k
#
k
ꢀ
ꢀ
(28) reactions of
α
ꢀpinene in supercritical ethanol, sugꢀ
ΔV
ΔV
−
dP = lnki
(
T0,P
)
−
(
Pk − P
0
.
)
0
gested a kinetic model, and determined its parameters.
Here we will process the experimental data presented
in Table 7 to elucidate the effect of pressure on the rate
∫
P0
RT
RT
#
The mean integral value ΔVk in the
k
th interval and selectivity of thermolysis of
ꢀpinene as a compoꢀ
α
remains a function of pressure, so the dependence of nent of sulfate turpentine. For this purpose, we will
#
again use the overall rate constant of
sion ( ) in turpentine calculated via Eq. (23) for the
data listed in the second part of Table 7.
Figure 19 plots the ln versus pressure depenꢀ
b2, and b3 are the dence derived from experimental data for
unknown parameters of the model. To determine these thermolysis in turpentine along with the same depenꢀ
coefficients, we solved the inverse problem for the dence for ꢀpinene isomerization in supercritical ethꢀ
reaction routes presented in Scheme 2 by minimizing anol. The fact that the rate constant of ꢀpinene
α
ꢀpinene converꢀ
ΔVk on
Р in each interval is representable as a quaꢀ
dratic polynomial,
k
Σ
#
k
2
ΔV = b + b P + b P
,
(29)
0
1
2
k
Σ
in which the coefficients b1
,
α
ꢀpinene
α
α
the objective function (4) and calculated the compoꢀ isomerization in supercritical ethanol increases with
nent concentrations by numerically integrating the set increasing pressure was explained in terms of transiꢀ
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
185
tion state theory, in which the pressure dependence of
the rate constant is determined by the sign of the volꢀ
−
k [s ]
1
ln
Σ
−
−
−
3.5
4.0
4.5
#
1
ume of activation, ΔV , according to Eq. (26).
Experimental pressureꢀdependent ln ln k data
Σ
#
allow the ΔV value to be determined using Eq. (26).
2
Since the dependence of ln ln k on
Р for the reaction
Σ
#
of ꢀpinene in turpentine (Fig. 19) is linear, the ΔV
α
value of this reaction is pressureꢀindependent. In this
case, integration of Eq. (26) in which ki, app is replaced
−
5.0
5.5
with
k
yields the expression
Σ
#
−
ΔV
ln k = ln k −
P
,
(31)
Σ
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Density, g/cm
RT
where ln k0 is the rate constant at
The pressure dependence of ln k for
3
Р
= 0.
Fig. 20. ln
turpentine (
00 K).
k as a function of the density of the solution: (1)
T = 593 K) and (2) supercritical ethanol (T =
α
ꢀpinene
Σ
Σ
isomerization in supercritical ethanol (Fig. 19) is nonꢀ
6
#
linear, clearly indicating that the ΔV value of this
reaction is pressureꢀdependent. The linear fit for
experimental data for
α
ꢀpinene in turpentine,
[TS] concentration, and this will inevitably accelerate
the reaction. If the density stops growing as the presꢀ
(32) sure is further raised, as in the case of supercritical fluꢀ
ln k = −3.8305 + 0.000758P
Σ
,
ids in the critical region, the pressure effect on the rate
constant will decrease.
and the polynomial fit for
ethanol,
α
ꢀpinene in supercritical
ꢀ
5
2
ln k = −7.2495 + 0.02632P − 4.919 ×10 P (33)
Σ
Effect of Pressure on the αꢀPinene Isomerization Rate
#
in WaterꢀContaining Supercritical Ethanol:
The Ionic Mechanism of the Reaction
make it possible to calculate the corresponding ΔV
values via Eq. (31). For
α
ꢀpinene thermolysis in turpenꢀ
#
3
As was demonstrated above, the water ionic prodꢀ
tine, Eqs. (31) and (32) lead to ΔV = –37 cm /mol.
#
uct K increases in proportion to water density,
w
For
α
ꢀpinene in supercritical ethanol, ΔV is also
according to relationship (7), bringing about an
negative and depends linearly on pressure, varying
+
increase in the H concentration. This causes an
3
between –858 and –36 cm /mol in the pressure range
increase in the reaction rate. An increase in pressure in
of 90–270 atm. It is this variation of the volume of
activation that causes the reaction rate to increase with
increasing pressure.
the supercritical ethanol + water + ꢀpinene system
α
leads to an increase in the density of the supercritical
medium according to its equation of state and,
accordingly, to an increase in the ion concentration.
The difference between the
α
ꢀpinene isomerizaꢀ
tion rates in turpentine and supercritical ethanol is
Although ethanol contains only 4–5% water, the presꢀ
+
clearly illustrated by the dependence of ln k on the sureꢀinduced increase in the H concentration speeds
Σ
density of the medium (Fig. 20). The latter was calcuꢀ up the reaction via the ionic mechanism of
lated using the Peng–Robinson equation [91]. It folꢀ isomerization, as follows from Eq. (16).
α
ꢀpinene
lows from Fig. 19 that the density of
component of turpentine is higher than the density of
ꢀpinene in supercritical ethanol throughout the presꢀ
α
ꢀpinene as a
THERMODYNAMICS OF MONOTERPENE
MIXTURES IN SOLVENTS
α
sure range and varies insignificantly with pressure.
No chemical reaction can be examined separately
The
α
ꢀpinene–water and
α
ꢀpinene–ethanol–
from the medium in which it occurs. For many reacꢀ water systems under normal conditions belong to the
tions in gaseous and liquid solvents and supercritical class of immiscible or separating liquids. There are no
media, it is to be expected that, as the pressure is experimental data concerning phase equilibria in these
raised, the reaction rate and the position of the equiꢀ systems at high temperatures and pressures up to the
librium will alter because of the changes in the characꢀ critical region. At the same time, kinetic and mechaꢀ
ter and intensity of intermolecular interactions nistic studies of monoterpene isomerization in superꢀ
between the solute and the solvent. Depending on the critical solvents need knowledge of critical parameters
properties of the solvent and solute, an increase in the and the way they vary with the composition of the
solvent pressure or density can increase the solvation reaction mixture. This is the reason why we used therꢀ
number, the frequency of molecular collisions, and the modynamic simulation as the main tool in our study of
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

186
ANIKEEV et al.
the phase state of twoꢀ and threeꢀcomponent systems
and in the calculation of critical parameters.
F2
(
T,P
)
≡ Det
(
M2
)
= 0
.
(39)
The elements of the matrix M1 in Eq. (38) are the
first derivatives of the natural logarithms of the fugacꢀ
ities of components with respect to the umber of their
moles calculated at a constant pressure and temperaꢀ
ture:
Equation of state. Under subcritical and supercritꢀ
ical conditions, the reaction system cannot be
described in terms of ideal gas or ideal solution laws,
which assume that the mixture components are enerꢀ
getically independent. In view of this, the state of reacꢀ
tion mixtures is calculated using twoꢀparameter cubic
equations of state, such as the Redlich–Kwong–
Soave, Peng–Robinson, and Patel–Teja equations. In
our study, the phase states and the thermodynamic and
thermophysical properties of multicomponent mixꢀ
tures were calculated using the Redlich–Kwong–
Soave (RKS) equation of state [91]:
⎧
⎫
∂
ln fi
M =
i =1, 2, …, N; j = 1, 2, …, N, (40)
1
⎨
⎩
⎬
∂
nj ⎭T, P
is the number of components in the mixture.
T,P,y
, which
where
N
The fugacity of the components, fi
(
)
is a function of temperature, pressure, and the molar
composition of the mixture (vector ), is conventionꢀ
y
RT
Vm − bm Vm
am
(
T
)
ally calculated using cubic equations of state.
The matrix M2 in Eq. (39) is obtained from the matrix
M1 by replacing any of its rows with the row vector
P =
−
,
(34)
(
Vm + bm
)
whereVm is the molar volume of the mixture (l/(g mol)).
The coefficients am and bm for a mixture with a given
molar composition vector y are defined as follows:
[
∂F /∂n , ∂F /∂n ,..., ∂F /∂n
]
.
(41)
Equation (38) defines a spinodal line (sp) in the
plane. It is monovariant and, for any mixture
composition, has a set of solutions in terms of the
interdependent pair of values Tsp Psp) to Psp Tsp) satisꢀ
1
1
1
2
1
N
Т⎯Р
Ns
Ns
Ns
Ns
am =
y y a , b =
y y b
,
(35)
∑ ∑
j =1 i =1
i
j
ij
m
∑ ∑
j =1 i =1
i
j
ij
(
(
fying Eq. (38). The criterion of spinodal stability
(StCrit) or spinodal instability of a mixture of a given
composition is the value of function (38) at an arbiꢀ
trary temperature and pressure. If StCrit < 0, the mixꢀ
ture is considered to be spinodally stable. Conversely,
if StCrit > 0, the mixture is considered to be spinodally
unstable.
The critical point of a mixture, (Tmix,cr, Pmix,cr), is a
singular point in the spinodal curve, simultaneously
satisfying Eqs. (38) and (39).
2
2
i, cr
aii = αi
(
T
)
0.42748R T /Pi, cr)
,
(
(36)
b = 0.08664RT /P ,
ii
i, cr i, cr
aij =
(
1 − kij
)
a a , b =
(
1 − cij )(bii + bjj
)
/2
,
(37)
ii jj
ij
2
α
(
T
)
= ⎡1 + d
i
(
1 − T/Ti, cr ⎦
)
,
⎤
i
⎣
2
i
d = 0.480 + 1.574ω − 0.176ω
.
i
i
Here, Ti,cr and Pi,cr are, respectively, the critical temꢀ
perature and critical pressure of the th component of
the mixture. The parameter i, called the acentric facꢀ
For solving the above mathematical problem, we
suggested an equivalent form of the critical phase
equations (38) and (39) [95], which substantially simꢀ
plified numerical calculations. The problem was
solved by the homotopy method.
i
ω
tor, can be found in thermochemical handbooks, and
kij and cij are binary interaction coefficients. The accuꢀ
racy of the calculation of the phase diagrams and critꢀ
ical parameters of complex depends strongly on
whether kij and cij in Eq. (37) are correctly chosen or
calculated using experimental data available on binary
equilibria. In view of this, we earlier suggested a kij and
cij determination procedure [92] taking into account
the temperature and pressure dependences of these
coefficients. When there were no necessary experiꢀ
mental data, the binary interaction coefficients were
taken to be zero in most cases.
Model for Calculating Gas–Liquid, Liquid–Liquid,
and Gas–Liquid–Liquid Phase Boundaries
In the calculation of the phase boundaries separatꢀ
ing homogeneous fields, gas–liquid and liquid–liquid
twoꢀphase fields, and gas–liquid–liquid threeꢀphase
fields, we used familiar thermodynamic models of
monovariant binodal lines [96], also known as tangent
plane equations [97]. In the general case, at a fixed
composition of one of the phases, each temperature
and pressure make a pair of interdependent values
minimizing the function
Calculating the Critical Point for a Multicomponent
Mixture of a Given Composition
ΔG
)
≡
F
(
x,T,P
A mixture of a given composition is in the critical
state when its temperature Tmix,cr and pressure Pmix,cr
are such that the following conditions are satisfied
simultaneously [93, 94]:
εRT
N
1
RT
=
xi
[
ln x + lnΦ
(
x,T,P
)
(42)
∑
i =1
i
i
F1
(
T,P
)
≡ Det
(
M1
)
= 0
,
(38)
−ln z − lnΦi
(
z,T,P → min
)
]
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
187
under the constraint
The
α
ꢀpinene–water binary system is a hetꢀ
ꢀpinene and water are
eroazeotropic system because
α
N
practically immiscible under normal conditions. If the
temperature and pressure increase, the liquid phases
will dissolve in one another and their components will
pass into the vapor phase. Once the critical parameters
have been reached, the twoꢀphase system will become
a homogeneous system.
xi = 1
,
(43)
is
∑
i =1
where
the vector of mole fractions of the components formꢀ
ing in infinitely small amounts ( ) in the new equilibꢀ
rium phase, is the vector of the mole fractions of the
components in the initial mixture of a given composiꢀ
x,T,P z,T,P
tion, and Фi and Фi are the correspondꢀ
Δ
G
is the Gibbs energy of phase transition,
х
ε
The above models are quite appropriate for calcuꢀ
lating the phase states of reaction mixtures containing
z
α
ꢀpinene, water, and ꢀpinene thermolysis products,
α
(
)
(
)
such as limonene, alloocimenes, and pyronenes. The
phase diagrams of systems containing these reaction
products will be very similar, both quantitatively and
ing fugacity coefficients calculated using an equation
of state. Equation (42) subject to constraint (43) is
monovariant: at a given
dentTb pairs satisfying Eqs. (42) and (43).
Obviously, the following condition should be satisfied parameters of
z, there are only interdepenꢀ
qualitatively, to the diagrams calculated for the
pinene–water system. This is confirmed by the critical
ꢀpinene and some other monoterpenes
α
ꢀ
(
Pb
)
or Pb
Tb
( )
α
at the minimum points of Eq. (42):
calculated from structural data using group contribuꢀ
tion methods [67].
Figure 21 presents the calculated phase diagrams of
the binary mixture at 20 and 50 atm. Either diagram
det hx > 0 det hz > 0
[
]
[
]
,
(44)
where hx and hz are symmetrical matrices with the
has five characteristic fields: L–L, L–V1, L–V2, Liq,
elements
and Va p . The limiting points of the abscissa axis in the
diagrams represent the pure compounds: 0, water;
2
2
⎧
⎫
⎧
, h = ⎨
⎩
⎫
∂
F ⎬
∂ F
∂z ∂z
1
00,
α
ꢀpinene. This kind of phase diagram is typical of
hx =
⎬,
⎭
⎨
∂
⎩
z
(
45) heteroazeotropic systems.
xi∂x
j
i
j
⎭
The lines L1 and L2 in Figs. 21a and 21b represent
the compositions of the two coexisting equilibrium liqꢀ
i = 1,2,…, N, j = 1,2,…, N.
In the case of a system having three equilibrium uid phases as a function of temperature. The horizonꢀ
phases, e.g., a gas phase and two immiscible liquid tal dashed lines indicate the boiling temperatures of
phases, the properties of the vapor can be derived from the azeotropic mixtures, Taz, at a given pressure (e.g.,
the properties of any of the two liquid phases using the Taz = 478.4 K at
P = 20 atm). At any pressure, Taz is
phase equilibrium condition for this system:
below the boiling point of the more volatile compoꢀ
nent (water, 486.1 K at 20 atm). The calculated boiling
(46) temperature of the ꢀpinene–water azeotropic mixꢀ
(
l1
)
(
l2
)
( )
v
fi = fi = fi
.
α
ture at 1 atm and the only experimental boiling temꢀ
perature value reported for the turpentine–water mixꢀ
ture (367.7 K) [99] (turpentine contains 60–80%
To do this, it is necessary to calculate the equilibrium
between the two liquid phases at a given overall comꢀ
position of the heterogeneous liquid mixture. Division
into two liquid phases is done by a standard flash
method [98]. Next, using models (42) at a fixed presꢀ
sure and a fixed composition of the liquid phase (in our
α
ꢀpinene) are in good agreement, which is evidence in
favor of the thermodynamic model used here. Points
, 2, and 3 in the horizontal lines in Figs. 21a and 21b
1
represent the compositions of the three phases of the
heteroazeotrope. The end points indicate the compoꢀ
sitions of the two liquid phases, and the interior point
represents the vapor composition.
case, the
tion and temperature satisfying conditions (42) and
43) are calculated.
α
ꢀpineneꢀrich phase), the vapor composiꢀ
(
In the liquid L1, which is a water–
ture, the ꢀpinene concentration is nearly zero
<0.001%); accordingly, the line L1 almost coincides
�Pinene–water system. Twoꢀcomponent liquid– with the ordinate axis. By contrast, the liquid conꢀ
liquid–vapor systems have one degree of freedom. sists of ꢀpinene containing a considerable concentraꢀ
This means that a separating heterogeneous mixture at tion of dissolved water.
a fixed pressure will evaporate at a constant temperaꢀ In the field in Figs. 21 and 21b, any mixture
α
ꢀpinene mixꢀ
α
Calculation Results and Discussion
(
α
L
2
α
L–L
ture and the composition of its phases will not change separates only into two liquid phases, whose composiꢀ
until one of the liquid phases disappears. Such systems tions are given by the curves L1 and L2. The field Liq is
are called heteroazeotropic [91, 97], with coordinates the field of homogeneous liquid solutions; in the fields
Taz and Paz, where Paz is the vapor pressure over the
L–V1 and L–V2, the mixture separates only into a
immiscible liquids, which is equal to the total pressure, vapor and a liquid. In the field Va p , the mixture is
and Taz is the boiling temperature of the azeotropic entirely in the vapor state. The twoꢀphase liquid–
mixture.
vapor equilibrium fields L–V1 and L–V2 originate
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

188
ANIKEEV et al.
T
, K
T
, K
650
Taz, К
00
6
6
5
5
4
4
3
3
50
(a)
6
Vap
98
00
50
00
50
00
50
600
550
500
450
400
350
80
550
500
60
L–V1
L–V2
40
Liq
1
2
3
20
L–L
L2
L1
4
50
00
10
5
3
100
00
00
0
20
40
60
80
4
6
6
5
5
4
4
3
3
50
00
50
(b)
650
600
550
500
450
400
350
1
Vap
350
0
20
40
60
80
100
L–V1
V
2
–
L
α
ꢀPinene content, mol %
Liq
L2
00 1 2
3
Fig. 22. Boiling temperature of azeotropic
α
ꢀpinene–
water mixtures as a function of their equilibrium composiꢀ
tion. Points (from left to right) represent the compositions
50
of the phases L1, V, and L2.
00
50
00
L
1
L–L
and pressure are progressively increased, the composiꢀ
tions and properties of the vapor and the second liquid
phase come closer to each other. Above 98.3 atm, the
threeꢀphase heteroazeotropic phenomena are not
observed any longer and the mixture separates into to
fluid phases with nearly equal compositions.
300
0
20
40
60
80
100
[αꢀpinene], mol %
Fig. 21.
P
erozeotrope phases: (
details, see main text.
T–X
diagrams of the
= 50 atm. Compositions of the hetꢀ
) liquid phases; ( ) vapor. For
α
ꢀpinene–water system: (a)
= 20 atm; (b)
P
1,
3
2
The complete critical curve calculated via the
above procedure for the
shown in Fig. 23 in the Tmix,cr
curve ). The points and at the ends of this curve
indicate the critical parameters of pure water and pure
ꢀpinene, respectively. In going from the point to
the point along critical curve or in the opposite
α
ꢀpinene–water system is
–
Pmix,cr coordinates
(
1
A
B
from the boiling point of the azeotrope. Because the
boiling point of the azeotrope is very close to that of
water, the field
The curve branches bounding the field
the bubbleꢀpoint and dewꢀpoint branches of the binꢀ
odal calculated using the model defined by Eqs. (42)
α
A
L–V1 is very narrow.
B
1
L–V2 are
direction, the compositions of the binary mixture do
not change. Note the anomalous shape of this curve,
which has a temperature minimum. Line
2 in Fig. 23
and (43). Below the critical pressure of
Fig. 21a), these branches converge at the boiling
α
ꢀpinene
represents, on the plane, the coordinates of
threeꢀphase twoꢀcomponent azeotropic mixtures
indicated in Fig. 22. This line ends at the minimum
T–P
(
point of pure
α
ꢀpinene (for example the boiling point
= 20 atm is 602.1 K). Above the critꢀ
ꢀpinene (Fig. 21b), the binodal
of
α
ꢀpinene at P
point of the critical curve
Tmix,cr = 574.9 K and Pmix,cr = 98.3 atm. The correꢀ
sponding ꢀpinene content is 15%. As was mentioned
1, whose coordinates are
ical pressure of
branches meet at the critical point of the mixture of
the given composition.
The calculated sequence of azeotropic lines (boilꢀ
ing temperatures) at various pressures is shown in
Fig. 22. The point indicate the compositions of the
three phases— 1
points in Figs. 21a and 21b at a given pressure.
As the pressure is raised at a constant temperature, the ethanol–water system differs from the
α
α
above the azeotropic phenomena disappear as the repꢀ
resentative point comes fairly close to the critical
parameters of the mixture and the twoꢀphase equilibꢀ
rium disappears at the critical point.
L , V, and L2—corresponding to
1
,
2,
3
α
ꢀPinene–ethanol–water system. The
α
ꢀpinene–
ꢀpinene–
α
α
ꢀpinene solubility in the aqueous phase changes water system in that, in its water–ethanol and
insignificantly (left line), in contrast with the water pinene–ethanol binary constituents, the components
solubility in ꢀpinene (right line). As the temperature are unlimitedly soluble in each other, forming homoꢀ
α
ꢀ
α
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
189
geneous liquid solutions. Therefore, behavior of this
ternary system will depend considerably on the
P
, atm
A
water/(
α
ꢀpinene + ethanol) and
α
ꢀpinene/ethanol
200
ratios in the solution.
1
Fixing the ratio between two components in a
threeꢀcomponent heteroazeotropic system reduces
the number of degrees of freedom. As a consequence
this system becomes monovariant, like a binary sysꢀ
tem, and its phase equilibria can be calculated using
the procedure described above for the binary system.
Calculating the phase equilibria in the ternary system
1
60
20
1
8
0
examined, we fixed the ratio of the
α
ꢀpinene and ethꢀ
anol contents at ꢀpinene/ethanol = 1.
q
=
α
4
0
0
2
1
Figures 24a–24d display the
P
–T
diagrams calcuꢀ
B
lated for ꢀpinene–ethanol–water mixtures with varꢀ
ious water contents (80, 70, 50, and 50%, respecꢀ
tively). Lines and ' in these figures represent the
α
350 400 450 500 550 600 650
, K
T
1
1
bubbleꢀpoint and dewꢀpoint branches of the binodal.
The apex points of the lines are the critical points of
the mixtures of the given compositions. In the field
Fig. 23.
(
1
) Critical curve for ꢀpinene–water mixtures
α
and (2) the threeꢀphase equilibrium curve in the Р–Т
plane.
bounded by lines
vapor and a homogeneous liquid. To the right of line
', the mixture is in the vapor state. The field of liquid
phases is to the left of line
1 and 1', the mixture separates into a
1
increase. The azeotropic phenomena disappear only
in mixtures containing more than 90% ( ꢀpinene +
1.
α
ethanol) because water becomes completely soluble in
the organic fraction.
Calculation of phase equilibria to the left of the
bubbleꢀpoint branch of the binodal (Figs. 24a–24d,
The discrete Taz and Paz values calculated for fixed
pressures in the system are represented by open circles
at the bubbleꢀpoint branches of the binodals
(
Figs. 24a–24d, curves
each curve, with the coordinates ( end
limiting points of azeotropy in the given mixture.
Above this point (in line ) and up to the critical point,
1
). The upper open circle in
line
tical boundary (straight line
the point (Tend Pend)) into two subfields—
The field is the place of equilibrium between two
immiscible liquid phases. In the field , bounded by
line and by the upper branch of the binodal, the mixꢀ
1
) demonstrated that this field is divided by a verꢀ
, which originates from
and
T
,
Pend), is the
2
,
L
–L
L.
1
L–L
the mixture of the given overall composition is a
homogeneous solution in equilibrium with its vapor at
its boiling temperature.
L
2
ture is a homogenous, singleꢀphase liquid.
Note the following specific features of the calculaꢀ
tion of the bubbleꢀpoint branch of the binodal in the
case of separating threeꢀcomponent liquid mixture
These phase relations in the ternary system are
valid for the case of
q = 1 in the organic faction. In the
limiting cases of q → ∞ and q → 0, the ternary system
(
in the case of the existence of azeotropic states). In
appears as the
binary systems.
α
ꢀpinene–water and water–ethanol
the calculation of each point of the binodal for such
systems, the initial mixture, represented as a hypoꢀ
thetical homogeneous liquid, is spinodally unstable;
that is, StCrit < 0. This means that the chosen phase of
the given composition cannot exist as a stable homoꢀ
geneous liquid. This problem is solved by dividing the
initial mixture into two liquid phases. Next, the equiꢀ
librium vapor composition is derived from the compoꢀ
sition of one of the liquid phases using Eq. (46). The
The compositions of the equilibrium phases at the
azeotropic points at selected pressures are listed in Table
1
1. It follows from these data that liquid
phase containing a minor amount of ethanol and
almost no ꢀpinene. In the organic phase (liquid ), the
amount of the ꢀpinene + ethanol fraction at low
1" is an aqueous
α
2
α
temperatures and pressures is much larger than the
amount of water. The vapor phase is enriched with
ethanol at low pressures and with water at higher presꢀ
sures. The composition of the organic phase tends to
the vapor composition as the pressure is raised.
resulting Taz
the boiling temperature of the azeotrope at the presꢀ
sure Paz
(Paz) or Paz(Taz) values define the locus of
.
A comparison of the plots in Figs. 24a–24d demꢀ
onstrates that, as the water content of the mixture
decreases, Tend and Pend decrease and the twoꢀphase
Thus, the above approaches and computational
procedures provide means to determine the phase
state of binary and ternary mixtures of the
water and ꢀpinene–ethanol–water types, to find the
ꢀpinene + ethanol heteroazeotropic state existence conditions, and to
fraction in the mixture decreases, Pend and Tend determine the critical parameters of such mixtures in
α
ꢀpinene–
vapor–liquid equilibrium field between lines
broadens. As the proportion of the
1
and
1
'
α
α
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

1
90
ANIKEEV et al.
P, atm
1
20
120
100
80
(a)
(b)
2
2
1
00
8
6
4
2
0
0
0
1
60
1
L–L
V
L–L
V
40
1'
1'
0
20
0
0
3
50 400 450 500 550 600
350 400 450 500 550 600
1
20
00
120
(c)
(d)
1
100
80
2
2
8
6
4
2
0
0
0
60
L–L
V
L–L
V
40
1
1'
1
0
20
0
1'
0
3
50 400 450 500 550 600
350 400 450 500 550 600
, K
T
Fig. 24.
P–T
diagrams for
α
ꢀpinene–ethanol–water mixtures: (a) 80, (b) 70, (c) 60, and (d) 50% water; (
1,
1
') bubbleꢀpoint and
dewꢀpoint branches of the binodal. The points at curve apices are the critical points of the mixtures;
calculated for fixed pressures in the system.
+
, discrete (Taz Paz) values
,
order to optimize the reaction conditions for organic important of our results is that the thermal isomerizaꢀ
compounds in the subcritical and supercritical regions tion of terpenes in supercritical media (lower alcohols)
and mixture separation conditions in wide temperaꢀ
ture, pressure, and composition ranges.
proceeds more rapidly than the same reactions in the
gas or liquid phase and is equally selective toward the
Certainly, before performing a kinetic study of any desired products.
of the above reactions in the supercritical solvent, we
The kinetic studies and thermodynamic calculaꢀ
tions of the phase states and critical parameters of
which this reaction takes pace. It is these calculations selected multicomponent multiphase terpeneꢀconꢀ
that enabled us to correctly choose the initial compoꢀ taining systems enabled provided a deeper insight into
sitions of the reaction mixtures and reaction temperaꢀ the mechanism of isomerization of the terpenic comꢀ
calculated the phase state of the complex reaction
mixture in order to elucidate the conditions under
tures and pressures and to correctly represent the reacꢀ
tion routes and kinetic model equations.
pounds and into the role of the supercritical solvent in
the multifold increase in the reaction rate relative to
the rates observed for the same compounds in the gas
or liquid phase. It was demonstrated that raising the
pressure of the supercritical solvent markedly
increases the rates of the reactions examined.
CONCLUSIONS
In this work, we systematized our basic results in
the field of heatꢀinduced conversions of terpenic comꢀ
The chemical reactions of the above terpenes in
tine, cisꢀverbenol) in supercritical fluid solvents, supercritical fluid solvents can serve as a basis for
pounds of vegetable origin (
α
ꢀ and ꢀpinenes, turpenꢀ
β
mainly in supercritical lower alcohols. The most advanced, highꢀperformance technologies for obtainꢀ
KINETICS AND CATALYSIS Vol. 51
No. 2
2010

KINETICS OF THERMAL CONVERSIONS OF MONOTERPENIC COMPOUNDS
191
ing a wide variety of practically significant organic 24. Savich, T.R. and Goldblatt, L.A., J. Am. Chem. Soc.
compounds, medicines, and fragrance substances.
,
,
1
945, vol. 67, no. 11, p. 2027.
5. Hawkins, J.E. and Hunt, H.G., J. Am. Chem. Soc.
951, vol. 73, no. 11, p. 5379.
2
2
1
REFERENCES
6. Kolicheski, M.B., Cocco, L.C., Mitchell, D.A., and
Kaminski, M., J. Anal. Appl. Pyrolysis, 2007, vol. 80,
p. 92.
1
2
3
4
5
6
7
8
9
. Simonsen, J., The Terpenes, Cambridge: Cambridge
Univ. Press, 1957, vol. 2.
. Osadchii, S.A. and Tolstikov, G.A., Khim. Interes. Ust. 27. Dorsky J., in Perfumes: Art, Science, and Technology
,
Razv., 1997, no. 5, p. 79.
Müller, P.M. and Lamparsky, D., Eds., London:
Elsevier Applied Science, 1991, p. 399.
. Il’ina, I.I., Maksimchuk, N.V., and Semikolenov, V.A.,
Ross. Khim. Zh, 2004, vol. 48, no. 3, p. 38.
28. Bryulyakov, Yu.E., Gorlovskii, S.I., and Shadrin, A.B.,
Kompleksn. Ispol’z. Miner. Syr’ya, 1988, no. 2, p. 21.
. Simakova, I.L. and Semikolenov, V.A., Khim. Interes.
Ust. Razv., 2003, vol. 11, no. 1, p. 271.
2
9. Sun, J.ꢀH. and Zeng, T., Linchan Huaxue Yu Gongye
005, vol. 25, p. 43.
,
2
. Erman, W.E., Chemistry of the Monoterpenes: An Encyꢀ
clopedic Handbook, New York: Marcel Dekker, 1985.
3
0. Summers, H.B., Hedrick, G.W., Magne, F.C., and
Mayne, R.Y., Ind. Eng. Chem., 1959, vol. 51, p. 549.
. Arbuzow, B.A., Ber. Deut. Chem. Ges., 1934, vol. 67,
p. 563.
3
1. Johansson, A., Biomass, 1982, vol. 2, p. 103.
3
2. Yumruta
ša, R., Alma, M.H., Özcan H., and Kaška, Ö.,
. Charlton, R.W. and Day, A.R., Ind. Eng. Chem., 1937,
vol. 29, p. 92.
Fuel, 2008, vol. 87, p. 252.
3
3. Afre, R.A., Soga, T., Jimbo, T., Kumar, M., Ando, Y.,
Sharon, M., Somani, P.R., and Umeno, M.,
Microporous Mesoporous Mater., 2006, vol. 96, p. 184.
. Goldblatt, L.A. and Palkin, S., J. Am. Chem. Soc., 1941,
vol. 63, no. 12, p. 3517.
. Nikitin, V.M., Zh. Obshch. Khim., 1946, vol. 16, no. 7,
p. 1041.
34. Radbil’, A.B., Khim. Rastit. Syr’ya, 2005, no. 1, p. 5.
3
5. Conceicao Cruz Costa, M., Johnstone, R.A.W., and
Whittaker, D., J. Mol. Catal. A: Chem., 1996, vol. 104,
p. 251.
1
1
1
1
1
1
0. Burwell, R.L., J. Am. Chem. Soc., 1951, vol. 73, no. 9,
p. 4461.
1. Bochwic, B. and Kapuscinski, J., Rocz. Chem., 1967,
36. Chemical Synthesis Using Supercritical Fluids, Jessop, P.G.
vol. 41, no. 10, p. 1767.
and Leitner, W., Eds., Weinheim: WileyꢀVCH, 1999.
2. Fuguitt, R.E. and Hawkins, J.E., J. Am. Chem. Soc.
947, vol. 69, no. 2, p. 319.
,
3
7. Anikeev, V.I. and Ermakova, A., Zh. Fiz. Khim., 2003,
vol. 77, no. 2, p. 265 [Russ. J. Phys. Chem. (Engl.
Transl.), vol. 77, no. 2, p. 211].
1
3. Crowley, K.J. and Traynor, S.G., Tetrahedron, 1978,
vol. 34, no. 18, p. 2783.
38. Ikushima, Y., Adv. Colloid Interface Sci., 1997, vols. 71–
4. Gajewski, J.J. and Hawkins, C.M., J. Am. Chem. Soc.
986, vol. 108, no. 4, p. 838.
,
72, p. 259.
1
3
9. Chouchi, D., Gourgouillon, D., Courel, M., Vital, J.,
and Nunes da Ponte, M., Ind. Eng. Chem. Res., 2001,
vol. 40, p. 2551.
5. Garist, I.V., PetrovaꢀKuminskaya, S.V., Roganov, G.N.,
Filippenko, Z.A., and Stolyarova, L.G., Zh. Fiz. Khim.
000, vol. 74, no. 3, p. 397 [Russ. J. Phys. Chem. (Engl.
Transl.), vol. 74, no. 3, p. 327].
,
2
40. Milewska, A., Banet, OsumaA.M., Fonseca, I.M., and
Numes da Ponte, M., Green Chem., 2005, p. 726.
1
1
1
6. Gajewski, J.J., Kuchuk, I., Hawkins, C., and Stine, R.,
4
1. BogelꢀLukasik, E., BogelꢀLukasik, R., Kriaa, K., Fonꢀ
seca, I., Tarasenko, Y., and Nunes da Ponte, M.,
J. Supercrit. Fluids, 2008, vol. 45, p. 225.
Tetrahedron, 2002, vol. 58, no. 34, p. 6943.
7. Riistama, K. and Harva, O., Finn. Chem. Lett., 1974,
no. 4, p. 132.
42. Anikeev, V.I., Ermakova, A., Chibiryaev, A.M.,
8. Stolle, A., Brauns, C., Nuchter, M., Ondruschka, B.,
Kozhevnikov, I.V., and Mikenin, P.E., Zh. Fiz. Khim.
2007, vol. 81, no. 5, p. 825 [Russ. J. Phys. Chem. (Engl.
Transl.), vol. 81, no. 5, p. 711].
,
Bonrath, W., and Findeisen, M., Eur. J. Org. Chem.
,
2006, no. 15, p. 3317.
1
9. Stolle, A., Ondruschka, B., and Bonrath, W., Eur. J. 43. Chibiryaev, A.M., Anikeev, V.I., Ermakova, A., Mikeꢀ
Org. Chem., 2007, no. 14, p. 2310.
nin, P.E., Kozhevnikov, I.V., and Sal’nikova, O.I., Izv.
Akad. Nauk, Ser. Khim., 2006, no. 6, p. 951.
2
0. Smith, D.F., J. Am. Chem. Soc., 1927, vol. 49, p. 43.
1. Conant, J.B. and Carlson, G.H., J. Am. Chem. Soc.
4
4. Ermakova, A., Chibiryaev, A.M., Mikenin, P.E.,
2
,
,
,
Sal’nikova, O.I., and Anikeev, V.I., Zh. Fiz. Khim.
008, vol. 82, no. 1, p. 71 [Russ. J. Phys. Chem. (Engl.
Transl.), vol. 82, no. 1, p. 62].
,
1
929, vol. 51, p. 3464.
2. Thurber, F.H. and Johnson, C.H., J. Am. Chem. Soc.
930, vol. 52, p. 786.
3. Fuguitt, R.E. and Hawkins, J.E., J. Am. Chem. Soc.
945, vol. 67, p. 242.
2
2
2
1
4
5. Yermakova, A., Chibiryaev, A.M., Kozhevnikov, I.V.,
and Anikeev, V.I., J. Supercrit. Fluids, 2008, vol. 45,
p. 74.
1
KINETICS AND CATALYSIS Vol. 51
No. 2
2010