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8/18/2019 Cumene 2014
1/15
Kinetics of catalyst-free thermal and photo-oxidation of cumene
Vadim V. Krongauz •
John F. O’Connell •
Michael T. K. Ling
Received: 9 September 2013 / Accepted: 27 November 2013 / Published online: 13 December 2013
Akadémiai Kiadó, Budapest, Hungary 2013
Abstract Kinetics of thermal and photo-oxidation of
cumene in the absence of catalyst was studied using high-pressure differential scanning calorimetry and low-pressure
photocalorimetry. Kinetics of oxidation was followed by
cumene hydroperoxide (CHP), acetophenone, and phenol
formation. The amount of CHP formed was deduced from
the total heat of reaction of thermal degradation of CHP at
453 K and using a new gas chromatographic method. CHP
solution in cumene oxidized at 453 K and 680 psi of
oxygen reproducibly with the heat of reaction linearly
dependent on peroxide concentration in cumene. It was
confirmed that cumene thermal oxidation was slow at
\453 K, but at C453 K could occur explosively. Autoca-
talysis by CHP during thermo-oxidation was confirmed.
Apparent activation energy of the photo-oxidation of
cumene was found to be E a = 22.3 kJ mol-1. The value
corresponds to radical chain process of the cumene
autoxidation. Under assumption of pseudo-first order
reaction, the rate constant of CHP formation was found to
change from k CHP & 0.76 s-1 during the first 4 h of photo-
oxidation to k CHP & 0.2 s-1 at the later stages at
2.0 W cm-2 of UV exposure dose. It was established that
the initial presence of the CHP in cumene does not change
the photo-oxidation kinetics, but shifts the kinetic curve to
earlier time. Finite difference method was employed to
numerically model kinetics of cumene oxidation. The
result indicated higher than expected thermal and photo-
stability of both, cumene and CHP.
Keywords Cumene Thermal autoxidation
Photo-oxidation Kinetics Activation energy Rate constants Kinetic modeling
Introduction
Reactions with oxygen at high temperature or in the pre-
sence of ultraviolet light lead to a number of well-known
phenomena such as fire, darkening of the paints, degrada-
tion of tires, and so on. Oxidation which accelerates as it
proceeds was termed ‘‘auto-oxidation’’ or ‘‘autoxidation’’
[1, 2].
Saturated hydrocarbons oxidize through a chain of rad-
ical reactions forming peroxides, alcohols, ketones, and
eventually carbon dioxide and water [1–3]. Usually the rate
of room temperature oxidation in the absence of light or
catalyst is low, and after several months of storage only
fraction of the percent of peroxides or other products would
form. Low rate of oxidation is stipulated by low probability
of radicals formation in liquid saturated hydrocarbons.
Unsaturated hydrocarbons may react with oxygen faster,
forming peroxides and epoxides. In the presence of cata-
lyst, heat or ultraviolet light oxidation of hydrocarbons may
and often does proceed explosively due to fast formation of
radicals and consequent exothermic chain reactions.
1-Methylethyl benzene (cumene) is an alkyl-aromatic
compound boiling at 152 C. The oxidation of cumene is
an important industrial process. It proceeds through for-
mation of (2-hydroperoxypropan-2-yl) benzene [cumene
hydroperoxide (CHP)] (boiling at &125 C), which con-
sequently converts to phenol, acetophenone, acetone,
cyclohexanone, caprolactam, and other essential com-
pounds (Scheme 1) [4]. The catalytic CHP formation and
conversion process was developed and patented by the
V. V. Krongauz (&) J. F. O’Connell M. T. K. LingBaxter Healthcare Corp., Rt. 120 & Wilson Rd., RLT-14, Round
Lake, IL 60073, USA
e-mail: vadim_krongauz@baxter.com
1 3
J Therm Anal Calorim (2014) 116:1285–1299
DOI 10.1007/s10973-013-3577-2
8/18/2019 Cumene 2014
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group of Sergeyev, USSR [5–9] and almost simultaneously
by Hock, Germany [10]. Because of its industrial impor-
tance, the kinetics of catalytic oxidation of cumene was
extensively studied [11–57].
The mechanism of thermal oxidation of cumene can be
constructed by the analogy with other hydrocarbonsoxidation
mechanisms [1–3, 11–51]. The most comprehensive reaction
mechanism was constructed and examined by Opeida et al.[16, 17], Denisov and coworkers [3, 11, 29, 30, 34], Thomas
and Tolman [27], and Somma et al. [46].
Majority of cumene oxidation studies were conducted in
the presence of catalyst. The rate constants of reaction of
cumene with oxygen in the absence of catalyst or photo-
initiator was deduced by Ikawa et al. [13], for the reaction
RH ? R•, to be 2.70 9 10-9 L s-1 mol-1 at 100 C and
by Denisov and coworkers [29], for the reaction 2RH ?
O2 ? 2R•? H2O2, to be 2.51 9 10
-9 L2 mol-2 s-1 at
90 C. Other hydrocarbons react with oxygen in the
absence of catalyst at rates of the same order of magnitude
[30, 31]. The experimental and theoretical analysis of hydrocarbon oxidation mechanism by Denisov and
coworkers [29, 30] was most scrupulous and comprehen-
sive and was accepted as classic. In our kinetic scheme of
oxidation mechanism, we followed Denisov’s approach
and considered that cumene oxidation initiation occurred
by tri-molecular reaction rather than that by Russell’s
bimolecular one, RH ? O2 ? R•? HO2
• [31]. The rate of
cumene reaction with oxygen sited by Denisov was
&2.51 9 10-9 L2 mol-2 s-1 at 90 C. Russell obtained
indene autoxidation initiation rate constant of
1.55 9 10-9 L s-1 mol-1 at 50 C. We estimated the
reaction rate of hydrocarbons with oxygen initiating
cumene oxidation to be &6 9 10-11 L s-1 mol-1 at
25 C using Russell’s value of activation energy of
104.6 kJ mol-1 and pre-exponential factor of 108 s-1 [1].
The overall activation energy of cumene oxidative degra-dation was reported to be E a = 144.21 kJ mol
-1 with
apparent frequency factor, A = 1014.63 s-1 [33].
CHP is an intermediate in cumene oxidation. It is
unstable at high temperature as other peroxides. Thermal
degradation kinetics of CHP was studied in detail in the
past to insure control of ‘‘cumene process’’ and safety of
production [32–41]. The rates of thermal degradation of
CHP at room temperature were relatively low. It occurred
with apparent activation energy, E a = 97.2 kJ mol-1 [39].
Other recent work on CHP decomposition reported higher
activation energy, E a = 120.6 kJ mol-1 and extraordi-
narily large frequency factor, A = 1030.2 s-1 [37]. Sincefrequency factor should be close to a frequency of
molecular vibrations, 1013 s-1 [52–56], we believe that
activation energy of 120.6 kJ mol-1 could be erroneous as
well. However, in all the reviewed studies a very slow
oxidation of cumene or degradation of CHP at temperatures
\150 C was reported [34, 37, 39].
Photochemical initiation of cumene oxidation was stud-
ied in the past by many researchers starting with Hock and
Lang [10] and Melville and Richards [43]. In these inves-
tigations, photoinitiators were added to accelerate the photo-
oxidation [43, 57]. However, even in the absence of initia-
tors, hydrocarbons eventually oxidize at room temperature
in the dark or under ambient fluorescent illumination com-
monly used in the laboratories and warehouses [58].
Therefore, in the present work we monitored the kinetics
of cumene oxidation in the absence of initiators and com-
pared it with the previously published data [1–3, 11–51].
Oxygen concentration in cumene was estimated using
available data to be &0.01 mol L-1 [60]. Photoactivation
rates were estimated from the experimental data as well
[61, 62]. In addition to experimental measurements, the
kinetics of cumene oxidation was modeled numerically by
a finite difference method [59] using our results and
previously published information on oxidation kinetics
[1–3, 10–51].
Experimental
Materials
Cumene used in most experiments was 99.9 % pure (PHR
1210-3X1.2 mL, Fluka Analytical); CHP was 89.0 ± 0.1 %
CH3
CH3
+ O O
CH3
CH3
O
O
CH3
CH3
O
O
+
CH3
CH3
C
CH3
CH3
CH3
CH3
O
OH
+
OH
+ CH3 CH3
O
CH3 O
+
Scheme 1 Simplified cumene oxidation reaction scheme
1286 V. V. Krongauz et al.
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pure in cumene (Cat. No. 213942, MP Biomedicals, LLC).
Toluene, acetophenone, and hexane were ReagentPlus,
99 % pure grade (Sigma-Aldrich).
Equipment
Du Pont Instruments 910 Differential Scanning Calorimeter
(DSC) with high-pressure cell or with Photo-DSC attach-ment custom made by the authors was used for calorimetric
kinetic measurements. OmniCure 2000 light source and
OmniCure R2000 radiometer (Lumen Dynamics) were used
for photoexcitation. Two-output split optical fiber was used
to illuminate the reference and the sample pans of Du Pont
910 DSC simultaneously. Cary 4000 (Varian) spectropho-
tometer was used to measure absorption spectra. Emission
spectra were measured using a fiberoptic spectrophotometer
USB4000 (Ocean Optics Inc.).
All the chromatographic separations were conducted
using Varian CP-3800 gas chromatograph (GC) equipped
with 30 m long Supelcowax 10 capillary column.
Analytical procedures
DSC and photo-DSC were conducted using the 5–10 mg of
cumene or CHP placed in aluminum crimping cover
(SSC000E032, TA Instruments). The isothermal conditions
with initial equilibration at 20 C min-1 were used in DSC
experiments.
The GC method of cumene and cumene peroxide ana-
lysis was developed and implemented using 30 m capillary
Supelcowax 10 column with flame ionization detector
(FID) (Table 1). Toluene was used as an internal standard.
The samples of cumene and CHP were diluted with hexane
prior to the GC analysis. The reagent and product amounts
were obtained using calibration curves and interpolated to
the original concentrations in cumene.
Computations
Solution of the stiff system of differential equations
describing cumene oxidation reaction kinetics [1–3, 11–51]
was conducted using Kaps-Rentrop finite differences
method [59]. Ordinary differential equations solver routine
in PSI Plot version 10.5, (Poly Software International Inc.)
was used.
Results and discussion
Thermal oxidation
Commercial interest in cumene oxidation products led to
extensive search for the improved oxidation rate and yield,
accompanied by high purity of the products. Absence of
substantial work on cumene thermal oxidation in the
absence of catalyst was discussed in the Introduction. We
observed that in the absence of catalysts, cumene is highly
resistant to thermal degradation. Thus, no reaction of
99.9 % pure cumene with oxygen was detected by high-
pressure DSC at temperatures up to 180 C at 680 psi O2pressure. We did not monitor oxidation at higher temper-
atures, since even smallest amounts of CHP forming at
temperature[180 C led to explosions of various intensity.
To evaluate the extent of cumene peroxide initiation of
explosive chain oxidation, we analyzed its stability. Like
cumene, cumene peroxide reaction with oxygen was almost
undetectable by high-pressure DSC at temperatures
\150 C and 680 psi of oxygen. At 180 C, the degrada-
tion of &10 mg 80 % CHP in cumene occurred with an
audible and destructive explosion (Fig. 1).
Relatively pure cumene was more resistant to oxidation
at 180 C than CHP solutions in cumene (Figs. 1, 2). The
exothermic oxidation of CHP solution in cumene was
examined (Figs. 1, 2). The dependence of the enthalpy of
thermo-oxidation of CHP solution in cumene on CHP
concentration was remarkably linear (Fig. 3). After a cal-
ibration of DSC response (peak area), we were able to
detect as little as 40 ppm of CHP in cumene (Figs. 2, 3).
Overall the oxidation of up to 2 % solutions of CHP in
cumene at 180 C was less violent than might have been
expected considering reported autocatalytic effect of CHP
radicals [1–3]. The initial slope of each curve of heat flow
dependence on time of isothermal heating (from the end of
heating at &1.5 min to peak inflection point) and the slope
of the peaks after first peak inflection point increased with
Table 1 GLC analysis method parameters
Function/equipment Value/setting
Injection volume 10 lL, liquid injection
Cleaning cycle Two pre-injection and post-injection
flushes with hexane
Two pre-injection and post-injection
flushes with MEK Oven temperature regime Hold at 40 C for 5 min
Increase temperature to 150 C
at 5 C min-1
Injector temperature 200 C
FID temperature 300 C
Carrier gas Helium
Make-up gas Nitrogen, 27 mL min-1
Helium carrier flow rate 3.0 mL min-1
Hydrogen flow rate 35 mL min-1
Air flow rate 300 mL min-1
Conditions Split flow
Kinetics of thermal and photo-oxidation of cumene 1287
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the CHP concentration (Figs. 2, 4). The slope of the DSC-
detected heat emission curves (Fig. 2) was considered
proportional to an overall rate of thermo-oxidation. Then,
the rate of heat emission increased with the CHP concen-
tration increase (Fig. 4). The higher slope of the early
portion of DSC trace may indicate autocatalysis of the
cumene oxidation by CHP. The duration of the initial low
slope, or rate of oxidation reaction, before the peak (Fig. 4)was analogous to the induction period of oxidation reac-
tions. With the increase of the CHP concentration duration
of initial region possibly indicating autocatalysis (Fig. 4).
At 180 C and 680 psi of O2 80 % CHP solution in cumene
reacted highly energetically (Fig. 1). It was not clear to
what extent the heat emission kinetics was stipulated by the
cumene oxidation initiated by CHP and to what extent it
was determined by the reactions of CHP only. Indeed, once
the radical chain reaction of cumene oxidation is initiated it
could be expected to yield similar overall reaction heat
(peak size). This was not observed (Figs. 1, 2). High-
pressure DSC experiments could not separate contributions
of different species and processes to overall oxidation
reaction exotherms. Therefore, we conducted kinetic
modeling of cumene autoxidation in the presence of CHP
to assist with the data interpretation.
Analysis of cumene oxidation products
CHP concentration dependence of the heat of CHP thermo-
oxidation reaction in solution (Fig. 3) can be and was used
by us for quantitative detection of CHP in cumene by DSC
1
11
21
31
41
51
61
71
81
91
0.1 1 10
H e a
t f l o w
/ m W
E x o
t h e r m →
Time/min
CHP at 100 °C
CHP at 125 °C
CHP at 150 °C
CHP at 180 °C
Fig. 1 Typical high pressure, 680 psi of O2, DSC-monitored results
of oxidation of 80 % cumene hydroperoxide solution in cumene at
different temperatures. Exothermic direction was positive in the used
position of sample and standard in DSC cell. Vertical line at 180 C
indicated explosive combustion at 180 C
0
10
20
30
40
50
0 10 20 30 40
H e a t f l o w / m W
E x o t h e r m
→
Time/min
CHP in Cumene (mass%) Heat of Reaction at 180 °C
0.4 7.54 J/g0.68 42.47 J/g1.0 112.37 J/g2.0 323.56 J/g
Fig. 2 Examples of DSC-monitored oxidation of cumene hydroper-
oxide solutions in cumene at 180 C, and 680 psi of O2. Peak height
increased with increase of CHP concentration in cumene
y = 196.83x – 83.466R ² = 0.9964
0
50
100
150
200
250
300
350
400
0 0.5 1 1.5 2 2.5
H e a t r e l e a s e d / J
g – 1
CHP concentration/mass%
Fig. 3 Dependence of enthalpy of oxidation of cumene hydroper-
oxide solution in cumene at 180 C and 680 psi of O2 on CHP
concentration
heat emission ratey = 9.0147x – 2.2665
heat emission ratey = 1.6507x + 0.8287
inflection point
y = –1.331ln(x ) + 3.775
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0
2
4
6
8
10
12
14
16
18
20
0 0.5 1 1.5 2 2.5
I n f l e c t i o n p o i n t t i m e / m i n
R a
t e o f
h e a
t e m
i s s
i o n
/ m W
m i n –
1
Cumene hydroperoxide concentration/mass%
Fig. 4 Dependence of the initial rate of heat emission before peak
inflection point ( filled square), the initial rate of heat emission after
inflection ( filled circle), and the first inflection point time ( filled
triangle) during the oxidation of solution of CHP in cumene at 180 C
and 680 psi on CHP concentration
1288 V. V. Krongauz et al.
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as an alternative to other methods of CHP analysis.
Remarkably, the oxidation rates in slow and fast autoxi-
dation regions were linearly dependent on CHP concen-
tration as well (Fig. 4). This proportionality can be used for
CHP concentration analysis as well.
Species differentiation is difficult by classical high-
pressure DSC. To detect a broad range of CHP and cumene
concentrations as well as reaction products, we developed agas chromatographic (GC) technique giving a good reso-
lution and sensitivity (Fig. 5). Under the GC conditions
described above, the retention time of phenol was
26.6 min, retention of CHP was 21.6 min, of cumene
6.3 min, and of toluene standard 2.6 min (Fig. 5). An equal
GC response to cumene and CHP could not be assumed to
simplify the CHP concentration determination from a
chromatogram (Fig. 5). Thus, the main difficulty in CHP
analysis by both, high-pressure DSC and by GC methods
arose from the absence of high-purity standard. The best
commercial standard found was only 89.0 ± 0.1 % purity
CHP solution in cumene (MP Biomedicals). The GCresponse to CHP concentration was almost linear over a
wide range of CHP concentrations based on this standard
dilution (Fig. 6).
Photo-oxidation, monitored by photo-DSC
According to the First Law of Photochemistry, Grotthuss–
Draper law, only the light absorbed by the molecules may
lead to chemical reaction [62]. The absorption spectra of
both cumene and CHP (Fig. 7) have practically no overlap
with the emission spectra of regular household fluorescent
lamps (Fig. 8). Yet, we detected a substantial yield of CHP
upon exposure of 99.9 % pure cumene to the light sources
with only a weak emission in UV-region. This indicated a
branching, autocatalytic radical chain mechanism of photo-
oxidation leading to high CHP yield (Scheme 1).
According to the Second Law of Photochemistry, Stark–
Einstein Law, the rate of photochemical reaction increases
with the light intensity increase [62]. The light intensity
dependence of cumene photo-oxidation kinetics was
obtained using OmniCure 2000 light source, not filtered,
continuous illumination, and Du Pont 910 DSC, 30 C
isothermal conditions, ambient air pressure (Figs. 9, 10).
The illumination of the sample and reference thermo-
couples in Du Pont 910 DSC through split glass fiber light
guide produced a consistent initial drop in the heat flow
even in the absence of any samples in the pan. The same
drop was observed when water was placed in the sample
pan as well. No heating of empty or water-filled sample
and reference pans was observed.
Two distinct regions in photo-oxidation of cumene were
observed. First region was a few seconds wide, fast process
starting immediately after the light exposure started, the
second region was slow, lasting up to several hours. The
rate of the reaction was obtained as a slope of the linear fit
to the ascending region of the heat release curve (Figs. 9,
10). The reaction rates in both fast and slow regions of
photo-oxidation increased with the light intensity increase
as Stark–Einstein law predicted, confirming the occurrence
of photochemical reaction (Fig. 10). The fast, early portion
of the heat emission kinetics curve (first few seconds afterillumination start) could be attributed to the photoinitiation
of the radical reaction of cumene oxidation, while the
slower, later one could be attributed to chain propagation.
Enthalpy of cumene photo-oxidation reaction was
deduced from the heat flow kinetics for the entire process,
starting from the moment when the light exposure began,
and separately for the slower portion of the process starting
–0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 5 10 15 20 25 30
R e s p o n s e
/ v o
l t s
Time/min
Toluene
Cumene
Acetophenone
CumeneHydroperoxide
↙
Phenol
↙
Fig. 5 A typical chromatogram of cumene photo-oxidation productswith toluene internal standard added. Retention times: t toluene &
2.6 min, t cumene & 6.3 min, t acetophenone & 19.0 min, t CHP &
21.6 min, and t phenol & 26.6 min
y = 2.9799x R ² = 0.9956
y = 3.5897x R ² = 0.9942
y = –0.3817x 2 + 1.4579x
0
0.5
1
1.5
2
2.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
C o n c e n t r a t i o
n i n h e x a n e / m g m L –
1
Normalized analyte peak height/volts
– Cumene
– Acetophenone
– Cumene Hydroperoxide
Fig. 6 Example of GC calibration: dependence of the analyte peak
height normalized to toluene internal standard peak height on the
analyte concentration in hexane: filled triangle cumene hydroperox-
ide, open square acetophenone, and filled circle cumene
Kinetics of thermal and photo-oxidation of cumene 1289
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from the bend on heat flow curve (Fig. 9). The total
enthalpy of the cumene photo-oxidation reaction and
enthalpy of the slower, later process passed through a
maximum as the light intensity increased (Fig. 11). Such
behavior was observed in the past in radical polymerization
reactions. The heat effect of a complex reaction is a sum of
all enthalpies of the elementary steps. Thus, it was
observed by Alfrey and Lewis that exothermicity of co-
polymerization reaction depends on relative monomer
concentration and passes through the maximum at certain
monomer ratio [63, 64]. Krongauz observed that in the
absence of oxygen photo-induced radical processes were
overall less exothermic than in the presence of oxygen. He
supported his explanation for the observed lower enthalpy
of oxygen-free radical photopolymerization by showing
that the sum of enthalpies of elementary radical reactions
was higher in the presence of oxygen [65–67] (Table 2). At
high intensity of initiating light oxygen diffusion into the
liquid layer where photo-activated radical processes occur
could become slower than the rate of generation of radicals
and the chain reaction propagation rate as was established
by Norrish, Smith, Medvedev and Trommsdorff [65–69],
while higher radical concentration lead to faster oxygen
scavenging. As a result, low contribution of radical reac-
tions with oxygen would reduce overall exothermicity of
cumene photo-oxidation at high light intensity (Fig. 11)
[65–69]. Further analysis and kinetic modeling are needed
to confirm the interpretation of this behavior of cumene
photo-oxidation reaction enthalpy. The observed maximum
1
10001
20001
30001
40001
50001
300 350 400 450 500 550 600 650 700
R e l a t i v e e m i s s i o n i n t e n s i t y
Wavelength/nm
incandescentfluorescent
mercuryUV–lightsource
Fig. 7 Emission spectra of various light sources used (measured
using Ocean Optics USB 4000)
–0.1
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
230 240 250 260 270 280 290 300
O p
t i c a
l d e n s
i t y
Wavelength/nm
100 % hexane
100 % cumene
80 % CHP in cumene
Fig. 8 Absorption spectra of hexane, cumene, and 80 % solution of
CHP in cumene (measured using Varian Cary 4000)
–15
–5
5
15
25
35
400 4000
H e a
t f l o w / m
W
E x o
t h e r m →
Time/s
0.5 W cm–2 1 W cm–2 2 W cm–2
3 Wcm–2 4 W cm–2 5 W cm–2
Fig. 9 Dependence of DSC-detected cumene photo-oxidation
kinetics on light intensity: OmniCure 2000 light source, full spectrum:
continuous illumination, isothermal DSC regime at 30 C. Sharp
initial drop in a heat flow was due to slight difference in intensity of
light exposure of the sample and the standard in photo-DSC. High
initial heat release rate was attributed to photoinitiation of chain
oxidation of cumene. The arrows on the graph point to examples of the end of the fast initiation and the beginning of the slower chain
propagation process
Light intensity/W cm–20 1 2 3 4 5
H e a
t e m
i s s
i o n r a
t e / m W
s –
1
0.0001
0.001
0.01
0.1
1
10Reaction Rate Light Intensity Dependence
Fitting Model:
y = a *x^ b + c
a = 0.00194807206
b = 1.85336283
c = 0.00122442427
Fitting Model:
y = a *x^ b + c
a = 0.57841212
b = 0.8257315
c = –0.081943607
short–time slope
long–time initial slope
Fig. 10 Dependence of DSC-detected cumene photo-oxidation rate
on light intensity: OmniCure 2000 light source, full spectrum,
continuous illumination, isothermal DSC regime at 30 C. The top
curve ( filled triangle) represents early, chain initiation events, lower
curve ( filled circle) corresponds to the initial portion of the later chain
propagation process
1290 V. V. Krongauz et al.
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in the dependence of the enthalpy of cumene photo-oxi-
dation on light intensity was not reported previously
(Fig. 11).
Photo-oxidation threshold energy
To the best of our knowledge, the activation energy of
cumene photo-oxidation in the absence of catalyst was notreported previously. Temperature dependence of cumene
photo-oxidation kinetics was monitored at temperatures
between 30 and 100 C under isothermal photo-DSC
regime at initiating light intensity of 2.0 W cm-2 (Fig. 12).
The slope of a linear fit (PSI Plot) to the initial regions of
the kinetic curves (virtually first few points) (Fig. 12)
yielded the rates of cumene photo-oxidation. The fast
photoinitiation process rate showed no temperature
dependence, confirming it as a region of initiation, where
the radicals are generated by light absorption and covalent
bond cleavage (Fig. 12). Indeed, the energy required to
cleave the carbon–carbon and carbon–hydrogen covalent
bonds far exceeds thermal energy at temperatures between
30 and 100 C. However, the diffusion controlled chain
propagation and termination reactions are sensitive even to
minor temperature variations [75].
The activation energy of cumene photo-oxidation was
found using the Arrhenius–Eyring equation:
k ¼ AeE a
RT ;
where k is a rate constant, A is a frequency factor, usually
A & 1013 s-1, R = 8.31 J mol-1 K -1, T is absolute tem-
perature and E a is an activation energy. The activation
energy of photo-oxidation was obtained using Arrhenius–
Eyring plot of the natural logarithm of the photo-oxidation
rate dependence on the inverse absolute temperature. The
slope of the linear fit to the experimental heat flow curve
(in the slower kinetic region starting from the inflection
point) yielded the activation energy of cumene photo-oxi-
dation to be E a & 22.3 kJ mol-1 (Fig. 13). The value of
E a & 22.3 kJ mol-1 is close to that of reactions of
hydrogen abstraction from hydrocarbons by radicals, which
is also &20 ± 5 kJ mol-1 for most systems [1, 3, 70, 71].
For example, Bamford and Dewar reported activation
energy of &18 kJ mol-1 for tetraline photo-initiated
autoxidation [72].
Activation energy value of E a & 22.3 kJ mol-1 indi-
cated that the slower portion of the DSC-detected heat flow
kinetic curves (Figs. 9, 12) corresponded to the radical
chain propagation and termination reactions, while fast,
temperature-invariant portion corresponded to direct light-
hydrocarbon interaction.
Photo-oxidation, monitored by GC
The peroxide-free cumene (99.9 % pure analytical standard
grade) and solvent grade cumene (99 % pure grade) were
exposed in 1 9 1 cm quartz cell continuously to
2.0 W cm-2 broad-spectrum light from OmniCure 2000
(Fig. 7). The kinetics of CHP formation upon cumene
photolysis was monitored using GC analysis of the cumene
and its photo-oxidation products (Fig. 5). It was observed
0
1000
2000
3000
4000
5000
6000
7000
8000
0 1 2 3 4 5 6 S p e c
i f i c
t o t a l e n
t h a
l p y o
f r e a c
t i o n
/ J g –
1
Illumination light power/W cm–2
Fig. 11 Dependence of DSC-detected heat of the reaction of cumene
photo-oxidation on light intensity (OmniCure 2000 light source, full
spectrum continuous illumination, isothermal DSC regime at 30 C):
filled triangle total enthalpy of photo-oxidation reaction; filled circle
enthalpy of photo-oxidation excluding the fast initiation region
Table 2 Radical reactions enthalpy [65–67]
Radical reactions in oxygen Specific total
enthalpy/kJ mol-1Radical reactions
without oxygen
Specific total
enthalpy/kJ mol-1
RCH2•? O2 ? ROO
• 121.3 R• ? R• ? R2 100–330
RCH2OO• $ [RCH–O–O–HH•]*
$ •RCHOOH•-14.6 R• ? H2C=CR1 ?
•R–CH2C–R1 8–80
•RCHOOH• ? RCHO• ? OH• 238.5 R• ? HR1 ? RH ? R1• 8–80
2RCHO•? RCHOOHCR 154.8
2RCHO• ? RCO ? RCOH 334.7
RCHO• ? R1•? RCHOR1 188.3
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that the CHP formation kinetics were different for cumene
of different purity (Fig. 14). However, after some amount
of CHP was formed in 99.9 % pure cumene, the kinetics of
CHP production followed the same kinetic path regardless
the original CHP concentration (Fig. 15).
Under the assumption of pseudo-first order kinetics, i.e.,
Concentration = C oekt , it was found that during the first
4 h of exposure to 2.00 W cm-2 broad-spectrum UV light
CHP formation occurred with the rate constant
k CHP & 0.76 s-1, while the rate constant of CHP forma-
tion after 4 h was &0.2 s-1 (Figs. 14, 15, data). Initial
concentration, C o, obtained by the regression fitting of the
data was 0.01 % for first 4 h of reaction and 0.1 % for later
processes. Since the initial purity of cumene was 99.9 %,
the initial value of 0.01 % was plausible.
The difference in the apparent rate constants is a result
of gross simplification of the complex chain mechanism of
hydrocarbon oxidation. Nevertheless, the extraction of
apparent overall rate constant and apparent activation
energy allows a straightforward estimate of the reaction
rate and comparison of oxidation stability of various
compounds, becoming almost traditional in the literature
[1–3, 33, 39, 45].
The rate constants for reactions occurring under the
exposure to light of different intensity could be obtained
from the rate constants at 2.00 W cm-2 light dose,
–10
–5
0
5
10
15
20
25
0 200 400 600 800 1000 1200
H e a
t f l o w
/ m W
E x o
t h e r m
Time/s
30 °C 50 °C 65 °C
75 °C 90 °C
↑
Fig. 12 Dependence of DSC-detected cumene photo-oxidation
kinetics on temperature. OmniCure 2000 light source, full spectrum,
continuous illumination light intensity was 2.00 W cm-2 in all the
measurements. Sharp initial drop in a heat flow was due to slight
difference in intensity of light exposure of the sample and the
standard in photo-DSC. High initial heat release rate was attributed to
photoinitiation of chain oxidation of cumene. The arrows on the
graph point to examples of the end of the fast initiation and the
beginning of the slower chain propagation process
T –1 /K
–1
0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034
L n
( R a
t e )
–5.0
–4.5
–4.0
–3.5
–3.0
Fitting Model: y = a *x + b
a = –2684.25 b = 4.021
Activation energy, E a = 22.3 kJ/mol
Fig. 13 Dependence of DSC-detected cumene photo-oxidation rate
(slow portion of the process, chain propagation) on inverse temper-
ature. OmniCure 2000 light source, full spectrum, continuous
illumination light intensity was 2.00 W cm-2 in all the measurements
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 5 10 15
C o n c e n t r a t i o n o f C
H P i n c u m e n e / m a s s %
Time of exposure to 2.0W cm–2 of UV/hour
Fig. 14 Kinetics of cumene hydroperoxide formation upon UV
exposure of cumene: filled circle analytical grade, 99.9 % pure
cumene; filled triangle solvent grade, 99 % pure cumene
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 5 10 15 C
o n c e n
t r a
t i o n o
f C H P i n c u m e n e
/ m a s s %
Time of exposure to 2.0W cm–2 of UV/hour
Fig. 15 Superimposed kinetics of CHP formation upon UV exposure
of 99 % pure cumene and of 99.9 % pure cumene: filled circle
analytical grade, 99.9 % pure cumene; filled triangle solvent grade,
99 % pure cumene data shifted in time
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considering that the radical production rate constant con-
tains a square root of light intensity, I 0.5 [62, 75].
According to the published data [12], acetophenone is
a product of CHP decomposition. We detected formation
of around 10-2 % of acetophenone during light exposure
of cumene (Fig. 16, top). It was observed that when CHP
is initially present in cumene, like in the reagent grade
solvent, the acetophenone was also present as an impu-rity, and slowly decayed under the light exposure
(Fig. 16, top). However, when 99.9 % cumene analytical
standard was exposed to light, acetophenone concentra-
tion steadily increased with time of light exposure and
kinetics of its accumulation resembled the one expected
for the secondary products of cumene oxidation (Fig. 16,
top). Similarly, phenol was present as an impurity in the
reagent grade, 99 % pure, cumene, and decayed upon the
light exposure, however formed upon UV exposure of
99.9 % pure analytical cumene standard (Fig. 16, bot-
tom). It appeared that phenol photo-degraded faster than
acetophenone (Fig. 16), which may explain its lowerconcentration in the UV-exposed cumene. The kinetic
modeling of cumene oxidation qualitatively confirmed
the low concentrations of forming phenol and
acetophenone.
Kinetic modeling
We modeled formal kinetics of cumene autoxidation using
Gulbert and Waage’s Law of Mass Action [61, 73, 74].
According to the Mass Action Law, the rate of reaction is
proportional to the product of reactants concentrations.
Thus, for the reaction aA ? bB ? cC, where A, B, and C
are reactants and product, and a, b, c are the corresponding
stoichiometric coefficients, the Law of Mass Action would
take a form:
1
a
d½ A
dt ¼
1
b
d½ B
dt ¼
1
c
d½C
dt ¼ k ½ A x½ B y;
where t is time, x and y are the reaction order with respect
to the reagents A and B present in concentrations [ A] and
[ B], respectively [61]. A series of differential equations
describing the rates of elementary steps of a complex
reaction are integrated to obtain dependence of the
reagent and product concentrations on time of reaction.
We used Kaps–Rentrop finite differences methods of
numeric integration of a series of stiff differential equa-
tions [59].
The series of elementary reactions involved in hydro-
carbons oxidation are usually abbreviated to a few reactions
which influence the rate of products formation the most. In
published cumene oxidation process studies, the reaction
scheme varied from one author to another [1–3, 10–51].
We compiled the results of the previously published
investigations of cumene oxidation to construct a reason-
ably comprehensive reaction scheme [1–3, 11–51]
(Table 3). As in the cited publications, more elementary
reactions could be added, but we believed that the reaction
scheme was realistic and in agreement with the published
models [1–3, 10–51]. Some reactions, for example,
decomposition of dicumyl peroxide (P in the equations)
[37] were not included in our reaction scheme (Table 3).
The rate constants used in the computations were shown in
the last column of Table 3.
It was assumed that viscosity of cumene was low
enough to insure that mixing of the reagents was much
faster than the elementary reactions rates, i.e., kinetics in
‘‘perfectly stirred’’ reactor was considered. This assump-
tion is contrary to the experimental dependence of reaction
enthalpy on the UV light intensity (Fig. 11). However, at
2.00 W cm-2 of UV dose and low temperature thermal
oxidation, formal kinetics with no diffusion rate controlling
step was applicable.
Oxygen solubility in non-polar hydrocarbon liquids
varies from 10-2–10-3 mol L-1 [60]. We used constant
0.00
0.01
0.02
0.03
0.04
0.05
0 5 10 15 C o n c e n
t r a t i o n o
f a c e
t o p
h e n o n e
i n
c u
m e n e
/ m a s s
%
UV exposure time/hour
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 5 10 15 C o n c e n
t r a
t i o n
o f p
h e n o
l i n c u m e n e
/ m
a s s
%
UV exposure time/hour
Fig. 16 Top kinetics of acetophenone formation upon UV exposure
of analytic, 99.9 % pure, cumene ( filled circle) and reagent grade,
99 % pure, cumene containing initially[5 % cumene peroxide ( filled
square). Bottom kinetics of phenol formation upon UV exposure of
analytic, 99.9 % pure, cumene ( filled diamond ) and reagent grade,
99 % pure, cumene containing initially[5 % cumene peroxide ( filled
triangle)
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oxygen concentration of 10-2 mol L-1 in all the compu-
tations. Light intensity up to 5.0 J s-1 cm-2 was used in
OmniCure 2000 Hg lamp illumination. The absorbed
photons corresponded to the wavelengths B405 nm (see
above). The number of photons emitted by OmniCure 2000
light source at this wavelength would be of
O(1019) s-1 cm-2. Considering that the area of the DSC
pan was &0.25 cm2 and assuming absorbance of 0.1 and a
Table 3 Mechanism of cumene oxidation (R is Cumyl) used in thermo-oxidation modeling
Reaction Rate const Rate constant value Temperature/ C References Constants used
in calculations
2RH ? O2 ? 2R•? H2O2 k 1(Denisov) 0.25 9 10
-8 L2 s-1 mol-2 90 [29, 30] 2 9 10-8 L2 s-1 mol-2
1.52 9 10-8 L2 s-1 mol-2 120
2.61 9 10-8 L2 s-1 mol-2 130
5.66 9 10-8
L2
s-1
mol-2
140R• ? O2 ? ROO
•k 2 1 9 10
9 L s-1 mol-1 35 [42] 1 9 105 L s-1 mol-1
1 9 105 L s-1 mol-1 85 [16, 17]
4 9 105 L s-1 mol-1 65 [11]
1 9 107 L s-1 mol-1 Any [3, 46]
ROO• ? RH ? ROOH ? R• k 3 1.0 L s-1 mol-1 65 [11] 1.0 L s-1 mol-1
1.2 L s-1 mol-1 110 [34]
1.7 L s-1 mol-1 85 [16]
1.035 L s-1 mol-1 65 [17]
0.31 L s-1 mol-1 50 [43]
0.56 L s-1 mol-1 65 [43]
0.64 L s-1 mol-1 57 [27]
ROO• ? ROO• ? 2RO• ? O2 k 4 5.4 9 104 L s-1 mol-1 85 [16, 17] 2 9 104 L s-1 mol-1
12.8 9 104 L s-1 mol-1 50 [43]
3.3 9 104 L s-1 mol-1 65, 57 [27, 43]
1.6 9 104 L s-1 mol-1 30 [11]
1. 9 108 L s-1 mol-1 25–65 [11]
0.87 9 104 L s-1 mol-1 25 [45]
3.05 9 104 L s-1 mol-1 65 [45]
RO• ? RH ? ROH ? R• k 5 [4 9 105 L s-1 mol-1 65 [11] 1.0 L s-1 mol-1
11 L s-1 mol-1 66 [17]
0.64 L s-1 mol-1 57 [27]
ROOH ? RO• ? HO• k 6 3.5 9 10-6 s-1 100 Computed
using [33, 44]
1 9 10-6 s-1
7.1 9 10-9 s-1 100 Computed using [39]
1.4 s-1 100 Computed using [41]
HO• ? RH ? H2O ? R•
k 7 0.64 L s-1 mol-1 57 [27] 1.0 L s-1 mol-1
R• ? R• ? R2 k 8 3.3 9 104 L s-1 mol-1 65, 57 [16, 17, 27, 43] 3.3 9 104 L s-1 mol-1
RO•? RO
•? ROOR k 9
R• ? RO• ? ROR k 10
R• ? ROO• ? ROOR k 11
R•? HO
•? ROH k 12
RO• ? HO• ? ROOH k 13
RO• ? ROO• ? ROR ? O2 k 14
HO• ? HO• ? H2O2 k 15
HO
•
? ROO
•?
ROH ? O2 k 16H2O2 ? HO
•? HO• k 17 1 9 10
-12 to 10-19 s-1 25 Computed
using [47–51]
1 9 10-12 s-1
RO•? ROOH ?
ROH ? ROO•k 18 1. 9 10
6 L s-1 mol-1 25 [16, 17, 27] 1. 9 106 L s-1 mol-1
12 L s-1 mol-1 1.0 L s-1 mol-1
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In simulated thermal oxidation at 30 C, the computed
cumene disappearance rate increased with initial CHP
concentration increase, and the computed yield of the
secondary products increased as well (Fig. 19, top). When
much faster photo-oxidation initiation was modeled, com-
puted autocatalytic effect of CHP on the kinetics of cumene
disappearance was substantially weaker than in the case of
thermal oxidation process (Fig. 19, bottom). Indeed, fastinitiation rate and fast cumene radicals formation used in
photo-oxidation model, lead to very weak influence of
secondary radicals forming during CHP degradation on
cumene disappearance. However, CHP and secondary
species were sensitive to the change in initial CHP con-
centration (Fig. 19, bottom). Our experimental data
showed strong dependence of CHP yield during cumene
photolysis on the initial CHP concentration (Figs. 14, 15).
It appears that computed CHP yield was similarly sensitive
to initial CHP concentration (Fig. 19). Naturally, at long
reaction times some of the formed CHP would decay, as
was shown by classic consequent reactions shape of thecomputed data plots (Fig. 19). The secondary products
formation computed using cumene photo-oxidation model
showed the CHP catalysis comparable to that computed for
the thermal process (Fig. 19, top vs. bottom).
The modeling of formal reaction kinetics depends on the
choice of the elementary reactions, and the values of the
corresponding rate constants. Kinetic model is helpful in
prediction and illustration of the relative yields and relative
kinetics of reactions, when experimental data are difficult or
dangerous to obtain, like the data of cumene autoxidation at
high cumene conversion, or high temperature. It appears that
theselected kinetic scheme and the rate constants presented in
Table 3 provided a reasonably comprehensive kinetic model
and can be used to visualize cumene autoxidation, under both
thermal and photoinitiation in the absence of initiators or
catalysts. It appears that k 18 = 1.0 L s-1 mol-1 or
k 18 = 12.0 L s-1 mol-1 [27] could be reasonably chosen.
Use of a higher rate constant of k 18 = 1 9 106 L s-1 mol-1
did not lead to physically impossible computational results.
However, similar rates of CHP and cumene reactions with
radicals [27] appear more realistic.
Conclusions
The initiator and catalyst-free cumene autoxidation under
thermal and photochemical initiation leading to formation
of unstable peroxides was monitored and the mechanism of
this chain process was numerically modeled.
Two methods of cumene peroxide concentration moni-
toring were developed and used. One method was based on
monitoring, by DSC, the heat of CHP solution oxidation,
which was proportional to the peroxide concentration
(Figs. 2, 3). Another technique used capillary gas chro-
matography (Figs. 4, 5). The GC technique was used to
detect cumene, CHP and the products of CHP degradation,
phenol and acetophenone. GC was used for point-by-point
discrete kinetic monitoring (Figs. 14, 15, 16).
Kinetics of cumene autoxidation was monitored con-
tinuously by reaction heat emission rate using high-pres-
sure DSC and low-pressure photo-DSC.Thermal catalyst-free autoxidation of cumene in the
absence of initiator or catalyst was found to be insignificant
at room temperature and 680 psi O2 pressure, and explo-
sive at temperatures near and above 180 C. Autocatalysis
of cumene catalyst-free autoxidation by CHP, especially at
180 C, was confirmed.
Activation energy of the photo-oxidation of cumene was
found by photo-DSC method to be E a = 22.3 kJ mol-1
(Figs. 12, 13). The value was consistent with the radical chain
process, which constituted most of the autoxidation of
cumene. Under assumption of pseudo-first order reaction, the
rate constant of CHP formation upon exposure to2.00 W cm-2 broad-spectrum UV activation was found to
change from k CHP & 0.76 s-1 at the early stage of photo-
oxidation (0–4 h) to k CHP & 0.2 s-1at the later stages. The
rate constants under other light intensity could be obtained
using photoinitiation rate proportionality to the square root of
activation light intensity [75]. It was established that the initial
presence of CHP in cumene does not change the photo-oxi-
dation kinetics, but shifts the kinetic curve to the earlier times,
consistent with autocatalysis by the CHP (Figs. 14, 15).
It was observed that the total heat of photo-oxidation
reaction dependence on activating light intensity passed
through a maximum (Fig. 11). The observed behavior was
attributed to the decreasing contribution of the enthalpy of
reactions between the radicals and oxygen as concentration
of radicals and the radicals reactions rates increased with
the light intensity increase.
A formal kinetic model of cumene autoxidation was
developed and kinetics was computed under various
assumptions using finite difference method (Table 3;
Figs. 17–19). The sensitivity of the computations results to
rate of CHP degradation was found and evaluated. The
kinetic scheme (Table 3) gave good semi-quantitative
agreement with the experimentally obtained kinetics of
cumene autoxidation.
Kinetics of thermal and photo-oxidation reactions was
extensively studied in the past [1–3, 11–57]. However, the
mechanism and kinetics of these reactions was not con-
clusively established due to experimental difficulties in
monitoring intermediate species. This lack of detailed
experimental information on the hydrocarbons oxidation
intermediates and kinetics lead, for example, to recent
attempt to re-evaluate the intermediates in chain oxidation
of hydrocarbons using molecular modeling [76]. Most of
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the earlier work on cumene oxidation kinetics and mech-
anism was conducted in the presence of catalysts or initi-
ators, while majority of recent investigations concentrated
on the second stage of cumene oxidation, i.e., on the
decomposition kinetics of CHP [41, 77–79]. Therefore, we
re-visited the initiator and catalyst-free thermal and photo-
induced cumene autoxidation. Once the reaction was star-
ted, the radical process occurred as expected with theformation of CHP. The yield of the secondary products of
autoxidation, such as phenol and acetophenone, was two
orders of magnitude lower than that of CHP, significantly
lower than observed in catalyzed processes [11–51]. Due to
the renewed interest in the hydrocarbons oxidation mech-
anism in general [76] and cumene oxidation in particular,
more experimental work focused on the direct observation
of transient species is expected.
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