Peculiarities of β-pinene autoxidation

Article abstract of DOI:10.1002/cssc.201100266

The thermal oxidation of the renewable olefin β-pinene with molecular oxygen was experimentally and computationally investigated. Peroxyl radicals abstract weakly bonded allylic hydrogen atoms from the substrate, yielding allylic hydroperoxides (i.e., myrtenyl and pinocarvyl hydroperoxide). In addition, peroxyl radicals add to the C=C bond of the substrate to form an epoxide. It was found that a relatively high peroxyl radical concentration, together with the high rate of peroxyl cross-reactions, make radical-radical reactions surprisingly important for this particular substrate. Approximately 60% of these peroxyl cross-reactions lead to termination (radical destruction), keeping a radical chain length of approximately 4 at 10% conversion. Numerical simulation of the reaction-based on the proposed reaction mechanism and known or predicted rate constants-demonstrate the importance of peroxyl cross-reactions for the formation of alkoxyl radicals, which are the precursor of alcohol and ketone products. Copyright

Full text of DOI:10.1002/cssc.201100266

DOI: 10.1002/cssc.201100266
Peculiarities of b-Pinene Autoxidation
Ulrich Neuenschwander, Emanuel Meier, and Ive Hermans*[a]
The thermal oxidation of the renewable olefin b-pinene with
molecular oxygen was experimentally and computationally in-
vestigated. Peroxyl radicals abstract weakly bonded allylic hy-
drogen atoms from the substrate, yielding allylic hydroperox-
ides (i.e., myrtenyl and pinocarvyl hydroperoxide). In addition,
peroxyl radicals add to the C=C bond of the substrate to form
an epoxide. It was found that a relatively high peroxyl radical
concentration, together with the high rate of peroxyl cross-re-
actions, make radical–radical reactions surprisingly important
for this particular substrate. Approximately 60% of these per-
oxyl cross-reactions lead to termination (radical destruction),
keeping a radical chain length of approximately 4 at 10% con-
version. Numerical simulation of the reaction—based on the
proposed reaction mechanism and known or predicted rate
constants—demonstrate the importance of peroxyl cross-reac-
tions for the formation of alkoxyl radicals, which are the pre-
cursor of alcohol and ketone products.
Introduction
Terpenic isomers are therefore cheaply available renewable
resources that can be used for a wide range of applications. a-
Pinene is, for instance, converted into a-pinene oxide, which is
a precursor for all synthetic sandalwood fragrances.[4] b-Pinene
is a substrate for the synthesis of insecticides,[5] menthol and
fragrance products such as camphor. Both isomers, as well as
their oxidised derivatives, are desired in perfumery due to their
woody pine odour.[6] a-Pinene can be found in both enantio-
meric forms in different turpentine types. b-Pinene from tur-
pentine sources is usually found in enantiopure (ꢀ) form
(enantiomeric excess (ee)>95%).[7] The other enantiomer,
(+)-b-pinene, prevails in citrus fruit oil.[8]
a-/b-Pinene as renewable resources
a- and b-pinene (Scheme 1) are two chief constituents of tur-
pentine oil, which can be obtained by the distillation of pine
tree resins or as a by-product of the kraft pulping process.[1]
In the kraft or sulfate process, wood chips are heated to
150–1808C in an aqueous digestion mix (NaOH, Na2S, Na2CO3
and small quantities of Na2SO4, Na2SO3 and Na2S2O3) in large
pressure vessels at 7–13 bar for several hours.[1] Crude sulfate
turpentine is condensed from the waste gas from the digester
and is separated from the water. It still contains 5–15 wt%
sulfur compounds (e.g., MeSH, Me2S). These can be oxidised
with NaOCl solution at about 608C to give the less volatile sul-
fonic acids, sulfoxides or sulfones, which can be effectively sep-
arated by washing with water or by distillation. The yield of re-
fined sulfate turpentine is approximately 10 kg per ton of pulp
for pine trees. The location and date of the wood harvest, as
well as the length of the storage period before processing, all
affect the yield and the composition of the product. Typical
American turpentine oil contains 60% a- and 30% b-pinene.
The world production of sulfate turpentine reached 6ꢀ
105 tons per year in 2008,[2] making up two-thirds of the total
turpentine production. Production has more than doubled
since 1990. Moreover, if bio-refineries[3] make it to the industrial
market, a significant increase in turpentine availability can be
anticipated.
A publication by Widmark and Blohm in 1957 reported the
autoxidation rates of different monoterpenes (e.g., D3-carene,
a-pinene, b-pinene and (+)-limonene) at room temperature in
air, but not the product distribution.[9] Recently, we reported
the mechanism of the oxyfunctionalisation of a-pinene.[10,11]
a-Pinene autoxidation
The autoxidation of a-pinene was previously studied and
found to be propagated by four different peroxyl radicals,
C
C
C
namely, verbenyl (R(a)OO ), pinocarvyl (R(b)OO ), pinenyl (R(c)OO )
[10]
C
and myrtenyl peroxyl radical (R(d)OO ). These radicals abstract
weakly bonded a-hydrogen atoms in the substrate, yielding
the corresponding hydroperoxide and a resonance-stabilised
alkyl radical. Hydrogen abstraction can occur both at the a and
[a] U. Neuenschwander, E. Meier, Prof. Dr. I. Hermans
Department of Chemistry and Applied Biosciences
ETH Zurich
Wolfgang-Pauli-Strasse 10, 8093 Zurich (Switzerland)
E-mail: ive.hermans@chem.ethz.ch
Homepage: http://www.hermans.ethz.ch
Scheme 1. Structure of the two regional isomers a- and b-pinene. The four
different oxidation sites are denoted a–d.
Supporting Information for this article is available on the WWW under
http://dx.doi.org/10.1002/cssc.201100266.
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1613

I. Hermans et al.
responsible for the oxidation of b-pinene as that described for
a-pinene.
Results and Discussion
Scheme 2. The two resonance-stabilised radicals formed upon abstraction of
an H atom from the a (left) and d sites (right) of a-pinene and the Mulliken
atomic spin densities of the most relevant atoms (UB3LYP/6-
311+ +G(df,pd)//UB3LYP/6-31G(d,p)-level).
Overall observations
b-Pinene oxidation was studied at 363 K (i.e., 908C) in a
bubble column reactor under 1 bar of pure O2 as described in
the Experimental and Computational Section. Figure 1 shows
the evolution of b-pinene conversion as a function of time:
d sites of a-pinene (Scheme 1); in both cases producing reso-
nance-stabilised radicals (Scheme 2).
O2 addition to these two allyl radicals generates the four
C
R(x)OO peroxyl radicals. Competing with the hydrogen abstrac-
tion reaction is the addition of the peroxyl radicals to the C=C
double bond in the substrate (Scheme 3). The adduct inter-
mediate (AI) can eliminate an alkoxyl radical to form an epox-
ide or it can react with O2 and ultimately yield a dialkyl perox-
ide (Scheme 3). At moderate oxygen pressures, epoxide forma-
tion is kinetically favoured.[11]
Figure 1. Time evolution of b-pinene conversion at 363 K.
after a short induction period of approximately 10 min, the
conversion increases in an almost quadratic way. This is in
stark contrast with the situation observed during cyclohexane
oxidation,[16] but similar to the behaviour observed during the
autoxidation of ethylbenzene[17] and a-pinene.[10] The main
reason for this difference in kinetic behaviour between the dif-
ferent substrates is the fact that ethylbenzene and a-pinene
oxidation do not produce products that can accelerate the for-
mation of radicals (chain initiation), in contrast to cyclohexa-
none during cyclohexane oxidation.[18]
Scheme 3. Addition of peroxyl radicals to a-pinene; formation of pinene
oxide.
The alkoxyl radicals formed in the epoxidation step are con-
verted into alcohols and ketones upon reaction with the sub-
strate and O2, respectively. This explains the 1:1 ratio between
the epoxide and the sum of alcohol and ketone up to 10%
conversion. At higher conversions, more alcohol and ketone is
formed than estimated from this 1:1 relation, due to the co-ox-
idation of the hydroperoxide, yielding additional alcohol and
ketone upon abstraction of the a-hydrogen atom.
Scheme 4 summarises the main products of b-pinene autoxi-
dation as identified by GC and GC–MS (see the Supporting In-
formation).
Many of these products are valuable ingredients for the fine-
chemical industry. Myrtenol, for instance, is used as a beverage
preservative, a flavour ingredient, a fragrance,[6] and can serve
as an insect pheromone in insect traps by attracting pine bark
beetles.[5] Myrtenal is also used in the perfume industry, for in-
stance, as a deodorant constituent, and can form an interest-
ing ligand scaffold. Substituted or oxidised pinocarveol deriva-
tives are promising fragrance compounds. Hydroperoxides can
be reduced, for instance, with sodium sulphite, to increase the
yield of the corresponding alcohol. b-Pinene oxide (bPO) can
be rearranged into useful products such as perilla alcohol.[19]
Figures 2 and 3 show the evolution of the most important
products as a function of the sum of products, up to approxi-
mately 20% conversion. Similar to the situation with a-pinene
oxidation, the product distribution is much less conversion de-
At increasing oxygen pressure, a significant decrease in ep-
oxide selectivity was observed.[11] Indeed, AI can be trapped
with O2, preventing the formation of epoxide (Scheme 3). Asso-
ciated with this is an increase in the reaction rate, due to en-
hanced initiation by the dialkyl peroxide produced. Also due
to kinetic competition, ketone formation is favoured at higher
O2 pressures.[11]
Although a lot of work has been carried out in the field of
catalytic oxidation of b-pinene,[12–15] a fundamental study on
the radical-propagated autoxidation mechanism is lacking. The
goal of this contribution is to verify if a similar mechanism is
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Peculiarities of b-Pinene Autoxidation
Figure 3. Evolution of the pinocarvyl products (b-site oxidation products in
Scheme 1) versus the sum of the products. The selectivity is reported at
10% conversion (i.e., Si[producti]=630 mm).
Scheme 4. Main products of b-pinene oxidation.
Figure 4. Correlation between the epoxide and the sum of alcohol and
ketone concentrations during a- (a) and b-pinene (b) oxidation in the con-
version range of 0–10%.
fore, it can be concluded that a different mechanism is respon-
sible for the formation of alcohols and ketones.
Peroxyl radical chemistry: Input from quantum chemical cal-
culations
Numerical simulations of b-pinene oxidation show that the
most abundant radicals in the system are peroxyl radicals (see
below). It is therefore instructive to investigate how these in-
termediates react with the substrate. For computational sim-
plicity, a smaller model radical, namely, ethylperoxyl, was used.
Abstraction of one of the two hydrogen atoms in the acti-
vated b position (Scheme 1, right) has slightly different barri-
ers, that is, 10.7 and 13.0 kcalmolꢀ1, depending on the orienta-
tion of the hydrogen atoms towards the dimethyl bridge
Figure 2. Evolution of the myrtenyl products (d-site oxidation products in
Scheme 1) and bPO versus the sum of the products. The selectivity is report-
ed at 10% conversion (i.e., Si[producti]=630 mm).
pendent than for cyclohexane autoxidation, meaning that con-
secutive over-oxidation is less important. The most remarkable
over-oxidation products are pinocarveol oxide and myrtenol
oxide, stemming from consecutive epoxidation of pinocarveol
and myrtenol, respectively (the observed selectivities are zero
up to 3% conversion).[20]
(UB3LYP/6-311+ +G(df,pd)//UB3LYP/6-31G(d,p)
level
of
theory). The slightly lower barrier, in comparison with a-pinene
(i.e., 12.5 kcalmolꢀ1), can be attributed to the 2.9 kcalmolꢀ1
lower stability of the b-pinene isomer. Based on a typical pre-
s
factor per hydrogen atom (i.e., 3.25ꢀ108 mꢀ1 ꢀ1), one can thus
An interesting observation is the relatively low epoxide yield
(9%), compared with a-pinene oxidation (34%).[10] Another
striking observation is that [alcohol]+[ketone]@[epoxide],
whereas during a-pinene oxidation, the amount of epoxide is
equal to the amount of alcohol plus ketone (Figure 4). There-
estimate a rate constant for hydrogen abstraction of kabs(363 K)
ꢁ120mꢀ1
s
ꢀ1. The resonance-stabilised radical is shown on the
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I. Hermans et al.
right-hand side in Scheme 2, together with the Mulliken
atomic spin densities of the most relevant atoms. Addition of
O2 to this resonance-stabilised radical yields pinocarvyl peroxyl
effect,[24] these findings provided strong experimental evidence
for the Russell rearrangement[27] of the tetroxide, leading to
termination [Reaction (2)]. Recently, Peeters et al. proposed a
mechanism to explain the formation of singlet oxygen, via a
five-membered, cyclic transition state.[28]
C
C
(R(b)ꢀOO ) and myrtenyl peroxyl (R(d)ꢀOO ) radicals. From the
observed myrtenyl to pinocarvyl ratio of about 1.3, one can
conclude that addition of O2 to the d site is slightly favoured
over the b site, which is in agreement with the slightly higher
spin density at the d site C atom (see Scheme 2). Note that ab-
straction at the tertiary bridgehead position is strongly disfav-
oured, since that would lead to an sp2 centre at the bridge-
head. The calculated energy barrier is 17.6 kcalmolꢀ1, which is
too high to be of any importance at moderate temperatures.
The barrier for the addition of a peroxyl radical to the C=C
double bond of b-pinene was computationally predicted to be
13.0 or 13.6 kcalmolꢀ1, depending on how the C=C bond was
approached. Note that addition to the less-substituted end of
the b-pinene double bond is favoured (the d site, Scheme 1),
due to the higher stability of the resulting radical.[21] Combin-
ing the predicted barriers with a typical pre-factor of 2ꢀ
108 mꢀ1 sꢀ1 (for example, determined for the addition of the
methylperoxyl radical to propylene[22]) results in an addition
rate constant, kadd, of 4.3mꢀ1 sꢀ1. Subsequent unimolecular re-
lease of an alkoxyl radical and the corresponding epoxide is
much faster and not rate determining (computed barrier of
7.0 kcalmolꢀ1).
1
ð2Þ
ROOOOR ! Q¼O þ ROH þ O2
Not only is Reaction (2) possible, but scission of an OꢀO
bond can also occur. According to Ghigo et al.,[29] this leads to
a loose complex, consisting of triplet oxygen and two alkoxyl
radicals [Reaction (3)]. Hasson et al. described the complex
C
rather as alkoxyl and trioxyl radicals, with ROOO decaying into
3
[30]
C
O2 and RO .
3
3
C
C
ð3Þ
ROOOOR ! fRO þ RO g . . . O2
When considering the orientation of the two alkoxyl radicals,
they must have parallel spins, due to spin-conservation.[31]
Thus, they form a “spin-down” triplet opposite to the “spin-up”
triplet of oxygen. Thermodynamic arguments prohibit the for-
mation of singlet oxygen in that step (1O2 formation must be
coupled to an exothermic reaction to be feasible).
Whether 3O2 is loosely bound to the nascent alkoxyl radi-
cal(s) from Reaction (3), or whether they are kept together by a
solvent cage, has not yet been unambiguously proven, howev-
er, that does not qualitatively change the further outcome of
the reaction. The fate of the nascent radicals can be threefold.
Indeed, the first possibility is a mutual reaction between the
two radicals, yielding electronically excited ketone [Reac-
tion (4)]:
The ratio of the predicted rate constant for hydrogen ab-
straction (120mꢀ1 sꢀ1) over that for addition (4.3mꢀ1 sꢀ1) is
much larger for b-pinene than for a-pinene (16.6 versus 2.3);
this explains the significantly lower epoxide yield observed for
b-pinene.
The source of alcohol and ketone
3
3
C
C
ROOOOR ! fRO þ RO g . . . O2
ð4Þ
3
3
One remarkable difference between the oxidation of a- and b-
! Q¼O þ ROH þ O2
pinene is that a large fraction of the peroxyl radicals produced
C
during b-pinene are primary peroxyl radicals (e.g., R(d)-OO )
Notice that Reaction (4) leads to termination (i.e., a net de-
crease in radicals) and can, in principle, be monitored through
rather than secondary ones. The cross-reaction between pri-
mary peroxyl radicals is known to be significantly faster than
the chemiluminescence of the excited ketone.[32]
for secondary peroxyl radicals (6ꢀ108 versus 4ꢀ107 mꢀ1
s
ꢀ1).[23]
Alternatively, O2 can react with one of the two RO radicals,
3
C
C C
yielding ketone, RO and HO2 [Reaction (5)]:
Given the typical radical concentrations during autoxidations
of about 10ꢀ7 m, relative to hydrogen abstraction (120mꢀ1 sꢀ1
and C=C addition (4.3mꢀ1 ꢀ1), such mutual cross-reactions
cannot be neglected. Therefore, this cross-reaction needs to be
carefully evaluated.
)
3
3
C
C
ROOOOR ! fRO þ RO g . . . O2
s
ð5Þ
C
C
! Q¼O þ RO þ HO2
When two peroxyl radicals react, they initially form a short-
lived tetroxide ROOOOR intermediate [Reaction (1)], which is
stabilised by 16 kcalmolꢀ1.[24]
Yet another possibility is the diffusive separation of the two
3
radicals prior to a mutual reaction or reaction with O2 [Reac-
tion (6)]:[33]
3
3
C
C
ROO þ ROO ! ROOOOR
ð1Þ
C
3
C
ROOOOR ! fRO þ RO g þ O2
ð6Þ
2
2
C
C
! RO þ RO þ O2
Ingold and Howard observed that tetroxides arising from
primary and secondary peroxyls eliminated both singlet and
triplet oxygen, whereas tetroxides arising from tertiary peroxyls
eliminated only triplet oxygen.[25] The structural influence on
the singlet oxygen yield was confirmed by Mendenhall and
Niu, who reported values of 0 (tertiary) and 4–13% (primary,
secondary).[26] Together with the observed kinetic isotope
Ab initio estimation of all involved branching fractions is cur-
rently prohibited and still an ongoing challenge for quantum
chemistry.[29,28,34] The branching fractions reported in Scheme 5
are the result of numerical simulation (see below) of the exper-
imentally observed product distribution of b-pinene. The re-
ported values are in agreement with the quantitative struc-
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Peculiarities of b-Pinene Autoxidation
work,[10] the addition of aldehydes increases selectivity towards
the epoxide. In the present case, an initial addition of 3 mol%
myrtenal does indeed increase the epoxide selectivity from 6
to 9% at 2% conversion. This stems from the fact that the a-
hydrogen atom of an aldehyde can be easily abstracted; the
activation energy for abstraction was determined to be only
9 kcalmolꢀ1. With a typical pre-factor of 2ꢀ108 mꢀ1 sꢀ1 for this
bimolecular reaction, the rate constant becomes 763mꢀ1 sꢀ1 at
363 K, that is, 6 times faster than hydrogen abstraction from b-
pinene. This implies that for a hypothetical aldehyde yield of
14 mol%, an equal amount of peroxyl radicals would react
with the substrate and the aldehyde. Subsequently, the acyl
radical will be converted into an acyl peroxyl radical upon O2
addition. Such acyl peroxyl radicals can directly epoxidise C=C
bonds, similar to other peroxyl radicals, much faster (namely,
rate-determining addition barrier only 2.5 kcalmolꢀ1).[37] Alter-
natively, the acyl peroxyl radical can abstract an allylic hydro-
gen atom from the substrate and yield a peracid (computed
barrier of 3 kcalmolꢀ1).[38] Such peracids are known epoxidation
agents, too (so-called Prilezhaev mechanism).[39] Both channels
thus lead to a secondary contribution to the bPO yield (see
Scheme 6).
Scheme 5. Reaction channels in the cross-reactions of peroxyl radicals.
ture–activity relationship (QSAR) suggested by Capouet et al.
(i.e., (50ꢂ20)% non-terminating cross-reactions for primary
peroxyl radicals).[35]
Interestingly, trace amounts of nopinone were detected in
the product mixture. This is indeed a fingerprint for the occur-
According to this mechanism, sizeable amounts of myrtenic
acid and peracid are formed, which is in agreement with the
experimental observations that 1) there is a small myrtenic
acid peak in the chromatogram and 2) this peak increases by
about 20% upon reduction of the sample with phosphine.
1
rence of O2, since the latter can, among other things, add to
b-pinene to form a dioxetane that releases formaldehyde and
1
nopinone.[36] The Schenck O2 addition product predominantly
formed is indistinguishable from the autoxidation product
R(d)OOH.
Modelling shows that the cross-reaction of peroxyl radicals
is indeed the dominant source of alkoxyl radicals during the
autoxidation of b-pinene. These alkoxyl radicals are converted
into alcohols and ketones upon reaction with the substrate,
the hydroperoxide and O2, respectively [Reactions (7)–(9)],
analogous to the situation with a-pinene.
C
HO2 chemistry
C
Considerable amounts of HO2 radicals are produced during
the autoxidation of b-pinene, for instance, in Reactions (5) and
C
C
(9). These HO2 radicals equilibrate with ROO radicals, accord-
ing to Reaction (10). The forward and reverse rate constants
for Reaction (10) can be estimated to be 1.8ꢀ104 and 3ꢀ
103 mꢀ1
s
ꢀ1, respectively.[40]
C
C
RO þ RH ! ROH þ R
ð7Þ
ð8Þ
ð9Þ
C
C
RO þ ROOH ! ROH þ ROO
C
C
HO2 þ ROOH Ð H2O2 þ ROO
ð10Þ
C
C
RO þ O2 ! Q¼O þ HO2
C
Alternatively, HO2 can also abstract hydrogen atoms from
the substrate [Reaction (11)], or add to the C=C bond of the
substrate and yield an epoxide [Reaction (12)].
The formation of epoxide
Interestingly, epoxide selectivity
increases from 5% at 1% con-
version to approximately 10% at
20% conversion. This implies
that, in addition to the primary
epoxidation mechanism (analo-
gous to the reactions shown in
Scheme 3), there is also a secon-
dary source of epoxide. Indeed,
C
the addition of ROO to b-pinene
with subsequent epoxide forma-
tion is not fast enough to ex-
plain the observed bPO selectivi-
ty. As known from previous Scheme 6. Co-oxidation of myrtenal and the secondary contribution to the epoxide formation.
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I. Hermans et al.
C
C
0.5) kcalmolꢀ1.[45] Also taking this effect into consideration, one
can estimate an initiation barrier of (22ꢂ3) kcalmolꢀ1, that is,
significantly lower than in the case of cyclohexanone ((27ꢂ
1) kcalmolꢀ1).[18] This result confirms the higher efficiency of
the bimolecular initiation mechanism over the unimolecular
decomposition mechanism: the latter facing a barrier of rough-
ly 40 kcalmolꢀ1 (homolytic hydroperoxide cleavage). In princi-
ple, since the substrate is an olefin, OH transfer from ROOH to
the double bond (instead of H transfer from the substrate to
ROOH) needs to be considered as an alternative initiation
mechanism. However, evaluating such a reaction on the struc-
ture- and spin-contamination-corrected CBS-QB3 level, the cor-
responding barrier amounts to (28ꢂ3) kcalmolꢀ1, such that
OH transfer can have only a minor influence on the total initia-
tion at moderate temperatures, as encountered in this study.
Unfortunately, bimolecular initiation is very demanding to
describe from a computational point of view because spin and
dynamic effects will play an important role. For instance, intrin-
sic reaction coordinate (IRC) analysis of the reaction suggests
that the located transition state would connect not only to al-
koxyl, water and allyl, but further on to two closed-shell alco-
hol products. However, IRC analysis follows the energetically
steepest descent path, but neglects entropic effects, as well as
potential solvent (cage) effects. More work is required to com-
putationally describe this reaction in detail, preferably by using
multi-reference methods to accurately describe state mixing.[46]
HO2 þ RH ! H2O2 þ R
ð11Þ
ð12Þ
C
C
HO2 þ RH ! bPO þ OH
C
However, HO2 radicals also play a role in determining the
overall radical concentration because they can terminate in a
diffusion-controlled manner, according to Reactions (13) and
(14).[41,42]
C
C
HO2 þ HO2 ! H2O2 þ O2
ð13Þ
ð14Þ
C
C
HO2 þ ROO ! O2 þ ROOH
Modelling shows that the H2O2 concentration steadily grows
up to 6 mm at 20% conversion, that is, low and difficult to
quantify in the complex reaction mixture.
Over-oxidation of the hydroperoxides
Myrtenyl and pinocarvyl hydroperoxides have weakly bonded
a-hydrogen atoms that can be abstracted by peroxyl and hy-
droperoxyl radicals, yielding additional ketone [Reactions (15)
and (16)].[43]
C
C
HO2 þ ROOH ! H2O2 þ Q¼O þ OH
ð15Þ
ð16Þ
C
C
ROO þ ROOH ! ROOH þ Q¼O þ OH
C
In principle, the OH radical released in this step can trigger
an activated cage reaction, producing some additional alco-
hol.[44] However, for activated substrates, such as ethylben-
zene[17] and a-pinene,[10,11] and hence, also b-pinene, the impor-
tance of this alcohol production channel can be neglected in
first approximation.
Kinetic modelling
A kinetic model was set up in Matlab by using the ODE15s
solver for stiff ordinary differential equations (ODEs). The initial
conditions for solving the ODEs were obtained from experi-
mental data. Initial estimations of the rate constants were de-
termined either from quantum chemical predictions or from
known rate constants reported in the literature. To reduce the
complexity, and due to limited available kinetic data, regioiso-
meric products were lumped together, similar to a recent
study on atmospheric limonene oxidation.[47] This assumption
Chain initiation
It was found that during the autoxidation of cyclohexane radi-
cals were formed in the bimolecular reaction of cyclohexyl hy-
droperoxide and cyclohexanone.[18] In this reaction, the OH rad-
ical, breaking away from the hydroperoxide, abstracts a weakly
bonded a-hydrogen atom from the ketone, producing a reso-
nance-stabilised ketonyl radical, water and an alkoxyl radical. A
similar initiation should take place in the autoxidation of b-
pinene, since a resonance-stabilised allyl radical can be formed
[Reaction (17)].
C
implies that both radical sites in the R radical are equivalent
and means, for instance, that ROH stands for myrtenol plus pi-
nocarveol. Note that this also implies that the myrtenyl and pi-
nocarvyl peroxyl radicals are assumed to react similarly. Al-
though this is a good approximation for hydrogen abstraction
and C=C addition, it might be too simplified for the peroxyl
cross-reactions. On the other hand, this is an elegant way of
keeping the complexity under control, while, at the same time,
(approximately) taking into account the effect of cross-reac-
C
C
ROOH þ RH ! RO þ H2O þ R
ð17Þ
The barrier of the analogous reaction between propene and
methyl hydroperoxide was computationally predicted to be
22.7 kcalmolꢀ1 at the CBS-QB3 level of theory. This value can
be isodesmically extrapolated to b-pinene, based on the differ-
ence in the DFT barrier of 6.9 kcalmolꢀ1 between b-pinene and
propene (UB3LYP/6-311+ +G(df,pd)//UB3LYP/6-31G(d,p) level
of theory). However, the transition state of Reaction (17)
should be considered as a singlet diradical. Although an ad-
vanced level of theory, CBS-QB3 systematically overestimates
the energy in the computation of open-shell singlets by (5.8ꢂ
tions between R(b)ꢀOO and R(d)ꢀOO radicals.[35] Table 1 summa-
rises the different reactions taken into account, together with
the corresponding rate constants.
C
C
Based on this model, the evolution of hydroperoxides, epox-
ide, alcohols and ketones can be described rather accurately
(see Figures 5 and 6). The small deviations (<30%) are proba-
bly due to simplifications made in the model, as well as experi-
mental errors.
Interesting numbers that can be extracted from this model-
ling are, for instance, radical concentrations, for example,
1618
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ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ChemSusChem 2011, 4, 1613 – 1621

Peculiarities of b-Pinene Autoxidation
Table 1. Overview of the different reactions implemented in the kinetic modelling, together with the corresponding rate constants.
Reaction
k kinetic model [mꢀ1sꢀ1
]
Reference reaction
see text
k reference [mꢀ1sꢀ1
]
Ref.
1.6ꢀ10ꢀ5
80
5.0ꢀ106
1.5ꢀ1010
2ꢀ109
7.6
2.0ꢀ109
1.2ꢀ107
128
1.7ꢀ10ꢀ5
120
5.0ꢀ106
1.5ꢀ1010
2ꢀ109
7.6
2.0ꢀ109
1.2ꢀ107
126
[48]
[48]
[10]
[49]
[50]
[51]
C
C
ROOH+RH!RO +H2O+R
C
C
C
ROO +RH!ROOH+R
CH3CH2OO +bP
[a]
C
C
RO +RH!ROH+R
a-pinene substrate
[a]
C
C
C
RO +ROOH!ROH+ROO
tBuO +tBuOOH
OH +RH!H2O+R
(C2H5)2C=CH2 +OH·
[a]
C
[a]
C
C
C
HO2 +RH!H2O+R
HO2 +bP
[a]
C
C
O2 +R !ROO
diffusion controlled
[a]
C
C
C
RO +O2!Q=O+HO2
O2 +n-C4H9O
[52]
[48]
[48]
[48]
[48]
[48]
[51]
[23]
[48]
[41]
C
C
C
ROO +ROOH!ROOH+Q=O+ OH
EtOO +R(b)ꢀOOH
C
C
C
ROO +Q(d)=O!ROOH+Q (d)=O
572
EtOO +Q(d)=O
763
HO2 +ROOH!H2O2 +ROO
1.8ꢀ104
3ꢀ103
6
HO2 +CH3OOH
1.8ꢀ104
3ꢀ103
4.3
[a]
C
C
C
C
[a]
C
C
ROO +H2O2!ROOH+HO2
CH3OO +H2O2
C
C
C
C
ROO +RH!bPO+RO
EtOO +bP!bPO+EtO
[a]
C
C
C
HO2 +RH!bPO+HO
17
CH3CH=CH2 +HO2
17
2ROO !termination+propagation
3.9ꢀ108
1.3ꢀ109
8.8ꢀ109
2n-C4H9O2
6ꢀ108
1.3ꢀ109
9.8ꢀ109
C
C
[a]
C
C
2HO2 !H2O2 +O2
2HO2
C
C
C
C
HO2 +ROO !O2 +ROOH
HO2 +n-C4H9O2
[a] Reactions with low sensitivity (perturbation of the rate constants with 20% did not induce a significant change in the product–time curves, and hence
could, not be optimised with the experimental data; for these reactions the reference values were used).
ꢀ7
[ROO ]=3ꢀ10 m and [RO ]=1.5ꢀ10ꢀ14 m at 10% conversion.
It also shows that hydrogen abstraction from b-pinene (1.5ꢀ
10ꢀ4 msꢀ1) and the bimolecular peroxyl cross-reaction (8.0ꢀ
C
C
10ꢀ5 msꢀ1) are both important ROO channels, leading to prod-
C
C
ucts. Initiation Reaction (17) and the ROO cross-reactions, sum-
C
marised in Scheme 5, are the most important RO sources; ep-
oxidation of b-pinene, according to the mechanism in
C
Scheme 3, is only a minor source of RO radicals. More results
from the modelling study can be found in the Supporting In-
formation.
Chain length
The chain length, n (i.e., the ratio of the rate of chain propaga-
tion and the rate of chain termination), is given by Equa-
tion (1); knon-term and kterm refer to the rate constants of the non-
terminating and terminating cross-reactions, respectively, of
the combined peroxyl radicals. Figure 7 shows the evolution of
n as a function of conversion.
Figure 5. Evolution of the hydroperoxides (i.e., R(b)ꢀOOH plus R(d) ꢀOOH)
and b-pinene oxide (bPO) as a function of time; solid line is the result of a
numerical simulation (see text).
2
Rprop ðkabs þ kaddÞ½ROOꢃꢄ½RHꢄ þ knonꢀterm½ROOꢃꢄ
ð1Þ
v ¼
¼
2
kterm½ROOꢃꢄ
Rterm
The ratio of mono- over biradical propagation reactions in
Figure 7 shows that peroxyl hydrogen abstractions and addi-
tions are only responsible for the formation of 60% of prod-
ucts.
Temperature dependence
The effect of the temperature on the reaction rate at 2% con-
version is summarised in the Arrhenius plot given in Figure 8.
The experimentally observed activation energy is (21ꢂ
2) kcalmolꢀ1 and the Arrhenius pre-factor is 3ꢀ108 mꢀ1 sꢀ1.
Based on quasi-steady-state analysis, it can be shown that the
Figure 6. Evolution of the alcohols (i.e., R(b) ꢀOH plus R(d) ꢀOH) and the car-
bonyl compounds (i.e., Q(b)=O plus Q(d) =O) as a function of time; solid line
is the result of a numerical simulation (see text).
experimentally observed activation energy equals Eprop +(Einit
/
ChemSusChem 2011, 4, 1613 – 1621
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1619

I. Hermans et al.
the peroxyl radicals, which was much more important for b-
pinene than for a-pinene, was the cross-reaction of two perox-
yl radicals. Numerical simulation of the reaction revealed that
approximately 60% of the cross-reactions led to chain termina-
tion, compensating for the chain-initiation reaction between a
hydroperoxide product and the RH substrate. However, 40% of
the peroxyl cross-reactions did not lead to the destruction of
radicals and actually contributed to chain propagation. Hence,
b-pinene oxidation was characterised by mono- and biradical
chain propagations; the ratio between these channels was ap-
proximately 2:1 at 10% conversion. This behaviour deviated
from that of cyclohexane, for which the reaction was dominat-
ed by monoradical propagations.[16] The importance of these
biradical cross-reactions is not only clear from modelling, but
also from the formation of nopinone, which is a product that
is an indicator of singlet oxygen, produced in a small fraction
(i.e., 10%) in the cross-reaction of the peroxyl radicals. Alkoxyl
radical concentrations increased were about 10ꢀ14 m and were
predominantly formed in the biradical cross-reactions of perox-
Figure 7. Evolution of chain length n (a) and the ratio of mono- over biradi-
cal propagation reactions (b) as a function of the b-pinene conversion.
C
yl radicals. RO radicals are the precursors of the observed alco-
hols and carbonyl products. Co-oxidation of myrtenal, which is
a primary aldehyde product, causes the formation of additional
b-pinene oxide.
Experimental Section
The experiments were performed in a glass 10 mL bubble column
reactor equipped with
a
condenser. O2 was bubbled
(100 NmLminꢀ1) through 250 mm pores of a bubbler to ensure fast
gas–liquid mass transfer. The temperature was controlled by a
thermostat, equipped with an immersion heater and thermocouple
(standard run at (363ꢂ2) K). The reactor was heated to the reac-
tion temperature under a flow of N2 (inert conditions); subsequent-
ly the gas flow was changed to O2 to start the reaction. Caution!
This is potentially dangerous and appropriate safety measures
should be taken. Samples (ꢂ250 mL each) were withdrawn from
the reactor and analysed by GC (HP6890; HP-5 column, 30 m/
0.32 mm/0.25 mm; flame ionization detector). n-Nonane (Sigma Al-
drich, >99%) was added to the (ꢀ)-b-pinene substrate (Sigma Al-
drich, 99%) and used as an inert internal standard (1 mol%). The
hydroperoxide yields were determined by double injection, with
and without reduction of the reaction mixture by trimethylphos-
phine (Sigma Aldrich, 1m in toluene). From the obtained augmen-
tation in alcohol content, the corresponding hydroperoxide yield
was determined. Products were identified by GC–MS, using split in-
jection (Tinject =2508C) and cool-on-column injection (Tinject =508C),
to verify the thermal stability of the products. No difference in
product distribution could be observed. Products were additionally
characterised by their Kovats indices (see the Supporting Informa-
tion).
Figure 8. Arrhenius plot of the uncatalysed b-pinene autoxidation. The loga-
rithm of the reaction rate at 2% conversion is shown for 333, 343, 353, 363
and 373 K (correlation coefficient=0.997).
2)ꢀ(Ecross/2).[53] The barrier of the radical cross-reaction can be
assumed to be very small (Ecross ꢅ2 kcalmolꢀ1). The relevant
propagation barrier is the thermally averaged barrier for hydro-
gen abstraction and peroxyl radical addition (Eprop ꢁ11 kcal
molꢀ1). The initiation barrier [namely, Reaction (17)] was esti-
mated to be 22 kcalmolꢀ1 (see above). Putting all these values
together, one expects, according to the proposed mechanism,
an apparent activation energy of (21ꢂ4) kcalmolꢀ1, which is in
excellent agreement with experimental results.
Conclusion
The radical chain autoxidation of b-pinene was compared with
previous results for the isomer a-pinene. Resonance-stabilised
alkyl radicals were generated upon abstraction of an allylic hy-
Quantum chemical calculations were performed with Gaussian 09
software[54] at the UB3LYP/6-311+ +G(df,pd)//UB3LYP/6-31G(d,p)
level of theory.[55] Earlier, this method was validated against several
benchmark levels of theory (namely, G2M, G3 and CBS-QB3) for hy-
drogen-abstraction reactions by peroxyl radicals.[16] The reported
relative energies of the stationary points on the potential energy
surfaces (namely, the energy barriers Eb and reaction energies DE)
were corrected for zero-point energy (ZPE) differences.
C
drogen atom. Addition of O2 to these R radicals yielded myr-
tenyl and pinocarvyl peroxyl radicals. These radicals did not
only abstract hydrogen atoms, regenerating the alkyl radicals,
but also added to the C=C double bond; a reaction that ulti-
mately led to epoxide and alkoxyl radicals. Another reaction of
1620
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ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ChemSusChem 2011, 4, 1613 – 1621

Peculiarities of b-Pinene Autoxidation
[34] T. S. Dibble, Atmos. Environ. 2008, 42, 5837.
[35] M. Capouet, J. Peeters, B. Noziꢄre, J.-F. Mꢂller, Atmos. Chem. Phys. 2004,
4, 2285.
Acknowledgements
Financial support of the ETH Zurich is kindly acknowledged. E.M.
is grateful for the Schweizerische Gesellschaft der Verfahrens- und
ChemieingenieurInnen Thesis Award 2011.
[36] D. R. Kearns, Chem. Rev. 1971, 71, 395.
[37] Experimental values for similar substrates range from 4 to 6 kcalmolꢀ1
,
see: R. R. Diaz, K. Selby, D. J. Waddington, J. Chem. Soc. Perkin Trans. 2
1977, 360.
[38] The subsequent destructive cage reaction (peracid+allyl radical, giving
acyloxyl radical and alcohol) faces an activation energy of 9.9 kcalmolꢀ1
.
Keywords: autoxidation
renewable resources · singlet oxygen
·
kinetics
·
radical reactions
·
In comparison with the unactivated cage reaction in cyclohexane au-
toxidation (CyOOH+alkyl radical, giving alkoxyl radical and alcohol), for
which the barrier is 6.8 kcalmolꢀ1 and the cage efficiency is 5%,[16] one
can exclude the contribution of such a cage reaction in the present
case.
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Received: May 25, 2011
Published online on September 7, 2011
ChemSusChem 2011, 4, 1613 – 1621
ꢁ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemsuschem.org
1621