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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

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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

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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

1292 V. V. Krongauz et al.

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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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