Pressure and temperature dependence of the decomposition rate of aliphatic tert-butyl peroxyesters

Full text of DOI:10.1524/zpch.2000.214.5.583

Zeitschrift für Physikalische Chemie, 214, 5, 583Ϫ607 (2000)
by Oldenbourg Wissenschaftsverlag, München
Pressure and Temperature Dependence
of the Decomposition Rate
of Aliphatic tert-butyl Peroxyesters
By Michael Buback* and Johannes Sandmann
Institut für Physikalische Chemie der Universität Göttingen, Tammannstraße 6,
D-37077 Göttingen, Germany
Dedicated to Prof. Dr. Dr. h. c. mult. H. Gg. Wagner
on the occasion of his 70th birthday
(Received January 31, 2000; accepted February 8, 2000)
Peroxides / Chemical Kinetics / Spectroscopy, Infrared / High Pressure
The thermal decomposition in solution of n-heptane of several aliphatic tert-butyl peroxy-
esters RC(O)OOTB: TB peroxypropionate, TB peroxy-n-butyrate, TB peroxy-iso-buty-
rate, TB peroxy-2-methylbutyrate, TB peroxy-2-ethylhexanoate, TB peroxy-3,5,5-tri-
methylhexanoate, and TB peroxy-neo-decanoate has been investigated at pressures up to
2500 bar and temperatures up to 185°C. The experiments were carried out in a tubular
reactor at residence times up to 140 s. Peroxide concentration was monitored via quanti-
tative FT-IR spectroscopic analysis of the pressurized medium under continuous flow
conditions. For each peroxide first-order decomposition kinetics were observed over sev-
eral half-lives. The type of carbon atom (in the R moiety) that is in A-position to the
carbonyl group controls decomposition kinetics. The observed first-order rate coefficient,
kobs, is smallest in situations where this particular C-atom is primary and is largest when
it is tertiary. The “primary” TB peroxyesters are associated with the higher activation
energies, around 145 kJ molϪ1. The activation energies, EA, of the “tertiary” and “second-
ary” TB peroxyesters are around 120 und 130 kJ molϪ1, respectively, with the individual
EA’s being proportional to the stability of the particular free-radical species Rᠨ. The acti-
vation volumes, ∆V϶obs, of the “secondary” and “tertiary” TB peroxyesters are in the
narrow range 3.0Ϯ1.5 cm3 molϪ1. ∆Vo϶bs of the “primary” TB peroxyesters is above
Ϫ1
10 cm3 mol and, in addition, is slightly pressure-dependent. Both observations demon-
strate that the “primary” aliphatic TB peroxyesters decompose via single-bond scission
with this result being supported by modelling dissociation dynamics in the compressed
fluid state. The “secondary” and “tertiary” TB peroxyesters decompose via concerted
two-bond scission associated with the immediate formation of CO2. These results are
fully consistent with evidence from the literature and from our preceding detailed study
into TB peroxyacetate and TB peroxypivalate dissociation kinetics. The mode of primary
bond dissociation, via single-bond or via concerted two-bond scission, largely affects
the initiation efficiency of TB peroxyesters in free-radical polymerization. For each TB
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

584
M. Buback and J. Sandmann
peroxyester, rate expressions for kobs(p,T) are presented. This data for decomposition in
compressed n-heptane should be highly suitable for simulation and optimization of techni-
cal high-pressure polymerization processes.
1. Introduction
Industrial polymerizations are carried out within extended ranges of tem-
perature and pressure, up to 300°C and 3000 bar. To model such processes,
the relevant rate coefficients should be precisely known as a function of p
and T. In addition to this application-oriented interest, peroxyester de-
composition kinetics are of fundamental relevance with respect to the detail-
ed understanding of the mechanism of unimolecular processes. In a preced-
ing paper [1], the thermal decomposition of tert-butyl peroxyacetate (TBPA)
and of tert-butyl peroxypivalate (TBPP) has been studied in n-heptane solu-
tion at pressures up to 2500 bar and at temperatures between 120 and 190°C
for TBPA and between 110 to 145°C for TBPP. These two peroxyesters
differ considerably in the size of the observed first-order decomposition rate
coefficient, kobs, and in pressure and temperature dependence of kobs. The
experimental data indicate that TBPA and TBPP are the archetypes of ther-
mal peroxyester decomposition via single-bond and via concerted two-bond
scission, respectively. Scheme 1 illustrates the two decomposition pathways,
(a) for single-bond scission and (b) for concerted two-bond scission. De-
composition via (a) produces an acyloxy and an alkoxy radical in the pri-
mary step. Cage recombination of these two species restores the peroxyester
which may decompose into primary free radicals within a subsequent de-
composition step. Mechanism (b) immediately yields carbon dioxide, the
tert-butoxy radical, and an alkyl radical Rᠨ. Cage recombination after a
primary decomposition event according to mechanism (b) produces an ether
which, under typical polymerization conditions, is not capable of producing
free radicals by another dissociation step. As a consequence, mechanisms
(a) and (b) should be associated with quite different efficiencies of free-
radical production. Primary dissociation dynamics thus, in addition to pro-
viding fundamental mechanistic evidence, has important consequences for
the optimal design of technical polymerization processes. It should also be
Scheme 1. Reaction scheme for the thermal decomposition of tert-butyl peroxyesters: via
one-bond scission (a) or concerted two-bond scission (b); in a successive reaction step,
the tert-butoxy radical, that is formed in both pathways, may decompose to acetone and
to a methyl free radical (or abstract a hydrogen atom and react to tert-butanol).
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
585
noted that, depending on whether decomposition mechanisms (a) or (b) ap-
ply, oxygen-centred or carbon- and oxygen-centred free radicals, are pro-
duced in the primary step. These two types of radicals differ in hydrogen-
abstraction activity which, in actual polymerizations, may result in different
microstructures of the polymeric products.
The difference in decomposition pattern of TBPA and TBPP is assigned
to the type of carbon atom in the A-position of the “acid side” of the tert-
butyl peroxyester. With TBPP, the tertiary carbon atom in A-position to the
carbonyl moiety induces two-bond scission, as a relatively stable free rad-
ical is formed with the steric crowding at the tertiary carbon atom being
considerably reduced compared to the situation in TBPP or in the hypotheti-
cal (CH3)3C-COO free-radical species. With TBPA no significant steric
crowding occurs at the A-carbon-position. Moreover, the rather unstable
CH3 free radical would be produced by mechanism (b). Thus the primary
dissociation event in thermal TBPA decomposition takes place as a single-
bond scission. These arguments are fully supported by the experimental
material contained in the previous paper and in the relevant literature
[1Ϫ11].
After having established the distinct difference in decomposition be-
havior of TBPA and TBPP, it appeared worthwhile to study the dissociation
kinetics of a series of aliphatic tert-butyl peroxyesters RC(O)OOTB and to
compare the results with the TBPA (R ϭ CH3) and TBPP (R ϭ (CH3)3)
data. Moreover, quantitative information about decomposition kinetics of
RC(O)OOTB compounds is of considerable application-oriented interest.
The kobs values for TBPA and TBPP at p and T conditions that are typical
for the high-pressure ethene polymerization differ by about two orders of
magnitude. Tert-butyl peroxyesters of intermediate decomposition rate are
required as initiators for situations in between the ones where TBPP and
TBPA are optimal and also for use within further extended p and T ranges.
The tert-butyl peroxyesters that have been selected for the present study are
listed in Table 1 with the size of the alkyl group R increasing from top to
bottom. TBPA and TBPP which have already been studied in detail [1] are
also included in Table 1. The peroxides, TBPA, TBPProp, TBPnB, and
TBPN have in common that the carbon atom in A-position to the carbonyl
group is a primary one. These peroxides in what follows will be referred to
as “primary” TB peroxyesters. In TBPiB, TBPMB, and TBPO this particu-
lar carbon atom is secondary and is tertiary in TBPP and TBPD. These two
groups of peroxides will be referred to as “secondary” and “tertiary” TB
peroxyesters, respectively.
Among the tert-butyl peroxyesters in Table 1, TBPD, TBPiB, TBPO,
TBPN (together with TBPA and TBPP) are frequently used as initiators in
technical polymerizations. The entire set of peroxides was kindly provided
in high purity (see Table 1) by AKZO NOBEL. Among them, TBPnB and
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

586
M. Buback and J. Sandmann
Table 1. Structures of the aliphatic tert-butyl peroxyesters selected for this study; also
given in the table are the purities of these materials.
RC(O)OOTB
R ϭ
Name
Abbre-
viation
Purity/
wt/%
CH3
tert-butyl peroxyacetate*
TBPA
94.6
CH2-CH3
CH2-CH2-CH3
CH(CH3)2
CH(CH3)(C2H5)
C(CH3)3
CH(C2H5)(C4H9)
CH2-CH(CH3)-CH2-
C(CH3)3
tert-butyl peroxypropionate
tert-butyl peroxy-n-butanoate
tert-butyl peroxy-iso-butanoate
tert-butyl peroxy-2-methylbutanoate
tert-butyl peroxypivalate*
TBPProp 95.7
TBPnB
TBPiB
TBPMB
TBPP
98.0
97.6
97.5
99.0
98.7
tert-butyl peroxy-2-ethylhexanoate
TBPO
tert-butyl peroxy-3,5,5-trimethylhexanoate
TBPN
TBPD
97.8
96.8
C(CH3)R1R2;
R1 ϩ R2 ϭ C7H16 tert-butyl peroxy-neo-decanoate
* Decomposition kinetics of compounds marked with an asterisk were already pre-
sented in [1].
TBPMB were specially made for this study to allow for a systematic investi-
gation into the dependence of decomposition kinetics on the type of sub-
stituent R.
Literature data on decomposition rate coefficients of the peroxides in
Table 1 (with the exception of TBPA and TBPP) are scarce. For TBPnB
and TBPMB no single piece of kinetic information was found in the open
literature. For TBPO and TBPN one half-life value is reported which allows
to estimate one rate coefficient for each of these two peroxides [12]. For
Ϫ1
TBPProp, an activation enthalpy of ∆H϶ ϭ 148 kJ mol was given by
Koenig [3] for decomposition in ethyl benzene. The corresponding value
for decomposition in cumene reported by Pryor and Smith [5] is ∆H϶
139 kJ mol .
ϭ
Ϫ1
Only for TBPiB and TBPD slightly extended data sets are available.
Most of this data, however, refers to fairly low temperatures and to ambient
pressure. Kinetic data for the high-pressure high-temperature decomposition
of TBPD in iso-dodecane have been provided by the Luft group [13, 14].
Ϫ1
The activation energy is reported to be close to 100 kJ mol and the mea-
sured activation volume is around 6 cm3 molϪ1 with these parameters, how-
ever, being derived from a relatively small number of experiments. For
TBPiB, rate coefficients as a function of pressure have been measured by
Neuman and Pankratz [15] in cumene solution at 90°C. The activation vol-
Ϫ1
ume is reported to be slightly pressure-dependent: ∆V϶obs ϭ 1.6 cm3 mol
at 1000 bar and 3.2 cm3 molϪ1 at 5000 bar. A linear fit of the data set yields
∆V϶obs ϭ 2.7 cm3 mol . Bartlett and Gortler [16] observed ∆H϶ to be sol-
Ϫ1
Ϫ1
Ϫ1
vent dependent: 133 kJ mol in cumene and 141 kJ mol in chloroben-
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
587
zene solution. Koenig and Huntington [17] studied secondary deuterium
isotope effects in TBPiB decomposition. The observed strong effect was
interpreted as an indication of decomposition via concerted two-bond scis-
sion.
In view of the enormous technical and also fundamental mechanistic
interest in accurate decomposition rate data of tert-butyl peroxyesters, rate
coefficients for a series of compounds RC(O)OOTB have been quantita-
tively studied at pressures up to 2500 bar and temperatures up to a maxi-
mum of 185°C. The reactions were carried out in dilute solution of n-
heptane under continuous operating conditions with the peroxide concen-
tration being monitored by online Fourier transform IR spectroscopy. In
addition to providing accurate rate coefficients for modelling purposes, the
present paper aims at deriving evidence about the decomposition mechan-
ism.
2. Experimental section
The experiments were carried out under turbulent flow conditions in a con-
tinuously operated tubular reactor of 10 m length and 0.5 mm internal diam-
eter that has already been detailed [1, 18]. Peroxide decomposition was IR-
spectroscopically monitored, via the carbonyl fundamental mode, using a
Bruker IFS 88 instrument equipped with a globar light source, a silicon-
coated CaF2 beam splitter, and a liquid-nitrogen-cooled MCT detector. The
IR spectra were taken in an optical high-pressure flow-through cell main-
tained at 50 °C. The cell is positioned directly behind the tubular reactor.
Pressure is measured within Ϯ15 bar and temperature to better than
Ϯ0.5°C.
The peroxides were synthesized at the AKZO NOBEL Research Center
Deventer in high purity. They were used as obtained as was the solvent n-
heptane (Ͼ99%, Merck). The solutions were freshly prepared and air-liber-
ated prior to each experiment. The initial peroxide concentration was always
1.0 · 10Ϫ2 M which is sufficiently low to exclude induced decomposition.
Details about the experimental set-up and procedure are given elsewhere
[18].
3. Results
The measurement of the decomposition rate coefficient of a peroxide at a
given pressure p and temperature T consists of recording IR spectra of the
reaction solution for different tubular reactor residence times. Between 5
and 10 flow rates, corresponding to different residence times of the turbu-
lent medium, were chosen for deriving a single rate coefficient. The spectra
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

588
M. Buback and J. Sandmann
Fig. 1. Carbonyl region of the infrared absorbance spectrum measured during TBPProp
decomposition at 175°C and 500 bar in n-heptane solution; initial peroxide concentration:
1.0 · 10Ϫ2 M; optical path length: 1 mm; the arrows indicate the direction of spectral
change with increasing residence time.
are taken immediately behind the tubular reactor in a separate cell at pres-
sure p and at 50°C. The lower temperature is chosen to prevent peroxide
decomposition behind the tubular reactor.
Illustrated in Fig. 1 is a spectral series collected during the decompo-
sition of TBPProp at 500 bar and 175°C. The absorbance spectra are taken
at residence times up to 140 s. The arrows indicate the direction of spectral
change with residence time t. The intense carbonyl fundamental mode of
TBPProp at around 1788 cmϪ1 decreases toward larger residence (reaction)
Ϫ1
times. The absorption close to 1722 cm is due to acetone that is formed
via β-scission of the intermediate tert-butoxy free radical. The major frac-
tion of the intermediate tert-butoxy free radicals abstracts hydrogen from
the solvent to give tert-butanol that is easily identified by the associated IR
Ϫ1
absorption around 3620 cm (not shown in Fig. 1). Alkanes and alkenes
which are also produced, via combination and disproportionation reactions
of alkyl free radicals (from decarboxylation and also from β-scission of
intermediate alkoxy free radicals) can not be quantitatively measured by IR
spectroscopy in solutions of n-heptane. The concentrations of these species
are accessible from gas chromatographic analysis carried out on product
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
589
Table 2. Maximum wavenumber of the carbonyl fundamental mode of the tert-butyl
peroxyesters at p ϭ 500 bar and T ϭ 50°C.
Peroxide
TBPD TBPP TBPO TBPMB TBPiB TBPN TBPnB TBPProp TBPA
[1] [20] [1]
Ϫ1
ν
max/cm
1772.5 1775.0 1780.0 1782.0 1784.0 1783.5 1786.5 1787.5 1790.0
˜
mixtures after complete peroxide decomposition. The results of such GC
analyses which contain a wealth of additional kinetic information will be
presented in a forthcoming paper [19]. Trends in product distribution are
also reflected in the IR. The quality of this spectroscopic information, how-
ever, can not compete with the quantitative evidence from GC studies.
Whereas the GC method allows for measuring product concentrations after
complete peroxide decomposition, the IR method is perfectly suited for the
online kinetic analysis of peroxide decay. The carbonyl mode of the per-
oxide is measured under stationary conditions of flow rate, pressure, and
temperature. It should be noted that monitoring the peroxide decay rather
than detecting product concentrations significantly enhances the quality of
decomposition rate measurement.
The spectral series of peroxide carbonyl absorbance look rather similar
for the components in Table 1. The band maximum positions, which are
slightly different for the individual peroxides, are listed in Table 2 with the
entries referring to 500 bar and 50°C. The maximum wavenumber de-
creases from “primary” to “secondary” and to “tertiary” peroxyesters.
The peroxide concentration is deduced from the absorbance spectra by
either taking the integral over the high-wavenumber half-band, between the
Ϫ1
peak maximum and 1840 cm , or by inspection of the integrated ab-
Ϫ1
sorbance of the narrow wavenumber region at Ϯ5.0 cm around the car-
bonyl peak maximum. At the fairly low peroxide concentrations employed
within the present study and with a non-polar solvent being used, Beer-
Lambert’s law is valid and peroxide concentration is proportional to each
of the above-mentioned integrated absorbance measures. Relative peroxide
concentrations, ct/co, (with ct referring to the stationary concentration at
residence time t and co to the initial peroxide concentration at t ϭ 0) obtain-
ed from the two types of integrated absorbance measures, are in excellent
agreement. The ct/co data that will be presented in the subsequent text are
Ϫ1
derived from the narrow absorbance range at Ϯ5.0 cm around the peak
maximum. A more detailed description of the procedure used for deriving
rate coefficients of peroxide decomposition is given in [18c, 18d].
In Fig. 2, for decomposition reactions of TBPProp at 500 bar and tem-
peratures between 150 and 185°C, the logarithm of relative peroxide con-
centration, ln (ct/co), is plotted vs. residence (reaction) time t. The extent
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

590
M. Buback and J. Sandmann
Fig. 2. Time dependence of relative peroxyester concentration, ln (ct/co), of TBPProp de-
composition in n-heptane solution at 500 bar and temperatures between 150 and 185°C.
of peroxide conversion per residence time interval largely increases with
decomposition temperature. At 150°C less than 50 per cent are decomposed
(50% conversion correspond to ln (ct/co) ϭ Ϫ0.69) whereas at 185°C the
residence time of 37.5 s exceeds four decomposition half-lives. ln (ct/co) vs.
t data at constant p and T closely fit to a straight line which demonstrates
that decomposition kinetics is adequately described by a first-order rate law.
The slope to each of these lines directly yields the observed (overall) first-
order rate coefficient, kobs
:
d c
ϭ Ϫkobs · c
d t
(1)
where c is the time-dependent peroxide concentration.
Plots of the same quality as in Fig. 2 are obtained for each of the per-
oxides listed in Table 1. The first-order decomposition rate coefficients, kobs,
derived from the straight line ln (ct/co) vs. t plots are summarized in Ta-
bles 3Ϫ5. Given in Table 3 are the rate coefficients for TBPD at 2000 bar
and temperature variation. Decomposition rate coefficients of TBPProp,
TBPnB, TBPN, TBPiB, TBPMB, and TBPO at constant pressure, but tem-
perature variation are given in Table 4. The TBPnB data have been deter-
mined by Nelke within her Diploma Thesis [20]. kobs data at pressure vari-
ation, but constant decomposition temperature are summarized in Table 5
for the seven peroxides of the present study. As can be seen from the entries
in Tables 3Ϫ5, kobs is strongly enhanced toward increasing temperature and
weakly diminished toward higher pressure. The precision of kobs is estimated
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
591
Table 3. First-order rate coefficients, kobs, for the decomposition of TBPD in n-heptane
solution at 2000 bar.
Ϫ1
kobs · 103/s
T/°C
TBPD
2000 bar
95
100
105
110
115
120
3.20
5.26
9.21
14.8
22.9
35.9
Table 4. First-order rate coefficients, kobs, for the thermal decomposition of tert-butyl
peroxyesters in n-heptane solution at constant pressure and temperature variation.
Ϫ1
kobs · 103/s
TBPO
TBPMB
TBPiB
TBPN
TBPnB
TBPProp
500 bar
T/°C
1000 bar 2000 bar 2000 bar 2000 bar 500 bar
125
130
135
140
145
150
155
160
165
170
175
180
185
4.08
6.65
10.9
17.2
26.8
41.2
63.6
3.29
8.58
6.15
9.77
14.5
13.9
2.00
3.18
5.36
9.27
1.98
3.39
5.49
9.00
24.2
36.8
57.0
87.8
20.7
32.8
50.7
3.47
5.65
8.88
13.8
22.6
33.6
50.3
76.4
14.3
13.7
22.1
22.4
32.9
49.7
32.9
to be better than Ϯ10%. Within each series of experiments, on the same
peroxide at either constant temperature or constant pressure, the precision
should be even higher, probably close to Ϯ5%.
Presented in Fig. 3 are Arrhenius plots of kobs (at experimental pressures
in the range 500 to 2000 bar) including the literature data [1] for TBPP and
TBPA (which are fitted by dashed lines). The open symbols refer to “pri-
mary” TB peroxyesters, the filled symbols to “secondary” and the grey
symbols to “tertiary” TB peroxyesters.
For each peroxide, the kobs values measured at a constant pressure close-
ly fit onto a straight line. Some kind of family behavior is seen within each
of the three groups, “primary”, “secondary”, and “tertiary” TB peroxyesters.
The “primary” peroxyesters TBPA, TBPProp, TBPN, and TBPnB almost
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

592
M. Buback and J. Sandmann
Table 5. First-order rate coefficients, kobs, for the thermal decomposition of tert-butyl
peroxyesters in n-heptane solution at constant temperature and pressure variation.
Ϫ1
kobs · 103/s
TBPD
110°C
TBPO
145°C
TBPMB TBPiB
TBPN
165°C
TBPnB TBPProp
p/bar
150°C
145°C
170°C
170°C
100
200
250
31.1
30.2
25.0
24.2
17.2
28.3
15.0
19.1
24.1
350
400
500
600
750
29.9
28.5
17.2
17.1
16.6
16.6
15.6
26.3
26.1
25.2
24.1
23.2
14.9
14.8
14.0
14.0
13.5
18.1
16.2
22.3
19.6
18.7
16.8
14.6
22.3
20.3
800
28.2
27.7
1000
1250
1500
1750
2000
2500
15.3
14.5
14.1
13.6
13.0
19.7
18.5
17.5
16.7
15.7
26.6
24.6
23.3
Fig. 3. Temperature dependence of kobs for tert-butyl peroxyesters at constant pressure
(500, 1000 or 2000 bar); the grey symbols refer to “tertiary”, the filled ones to “second-
ary”, and the open symbols to “primary” TB peroxyesters; the dashed lines, for TBPA
and TBPP, were calculated from the k(p,T) relations given in [1].
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
593
Table 6. Pre-exponential factor, A, and activation energy, EA, of the decomposition rate
coefficient, kobs, of tert-butyl peroxyesters in n-heptane solution; the reaction pressure
and the temperature range of the experiments are listed.
Ϫ1
Ϫ1
Peroxide
Pressure/bar
Temperature
range/°C
A · 10Ϫ14/s
EA/kJ mol
TBPD
TBPP [1]
2000
2000
95Ϫ120
110Ϫ145
1.22
6.10
116.8Ϯ3.3
125.4Ϯ3.9
TBPO
TBPMB
TBPiB
1000
2000
2000
125Ϫ155
135Ϫ165
130Ϫ160
4.10
4.84
4.03
129.6Ϯ1.0
132.1Ϯ3.2
131.9Ϯ3.0
TBPN
TBPnB
TBPProp
TBPA [1]
2000
500
500
145Ϫ170
145Ϫ180
150Ϫ185
120Ϫ190
56.9
147.7Ϯ2.4
144.8Ϯ2.9
142.3Ϯ1.9
150.4Ϯ1.7
25.3
12.9
70.5
2000
coincide on the scale used for Fig. 3. (It should, however, be noted that the
TBPN data are for 2000 bar, whereas the other three peroxides were studied
Ϫ1
at 500 bar.) From linear regression of the ln kobs vs. T data, the activation
energy, EA, and the pre-exponential factor, A, are obtained. Both Arrhenius
parameters are listed for the entire set of TB peroxyesters in Table 6. The
activation energy increases from “tertiary” to “secondary” and to “primary”
TB peroxyesters. The pre-exponential is distinctly lower with the “tertiary”
and “secondary” peroxyesters than with the “primary” TB peroxyesters.
Literature data of activation energy are available for TBPProp [3, 5], for
TBPiB [15, 16], and for TBPD [13, 14]. Actually, in most cases activation
enthalpies, ∆H϶, have been reported which are converted into activation
energies, EA, according to the relation: EA ϭ ∆H϶ ϩ RT. The following
comparison is made with EA referring to ambient pressure (see Eq. (3), be-
low).
EA for TBPProp decomposition in ethyl benzene solution has been re-
Ϫ1
ported by Koenig [3] to be 150 kJ mol . The corresponding value for de-
Ϫ1
composition in cumene, as given by Pryor and Smith [5], is 142 kJ mol .
The latter value is in perfect agreement with the ambient pressure EA value
Ϫ1
from the present investigation: 141.8Ϯ1.9 kJ mol . Also for TBPiB, the
Ϫ1
literature value for decomposition in cumene: 135 kJ mol , reported by
Bartlett und Gortler [16], is very close to the corresponding number from
Ϫ1
the present study: 131.4Ϯ3.0 kJ mol . For the TBPD decomposition in
Ϫ1
Ϫ1
iso-dodecane, activation energies of 103 kJ mol [14] and of 97 kJ mol
[13] have been determined by the Luft group. These values were estimated
by the authors to be accurate within Ϯ6%. Thus no satisfactory agreement
Ϫ1
with the number from the present investigation: 116.4Ϯ3.3 kJ mol is
obtained.
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

594
M. Buback and J. Sandmann
Fig. 4. Pressure dependence of kobs for tert-butyl peroxyesters at constant temperature
(between 110 and 170°C); the grey symbols refer to “tertiary”, the filled ones to “second-
ary”, and the open symbols to “primary” TB peroxyesters.
Plotted in Fig. 4 is the pressure dependence of ln kobs for the TB per-
oxyesters at the actual experimental temperatures. The ln kobs values are of
similar size as quite different experimental temperatures have been selected,
higher ones for the “primary” TB peroxyesters: TBPProp, TBPN, and
TBPnB and a lower temperature for the “tertiary” peroxyester TBPD. Two
observations are particularly noteworthy: (i) The pressure dependence of
kobs is much stronger for the “primary” than for the “secondary” and “ter-
tiary” TB peroxyesters and (ii) a slight curvature is seen on the ln kobs vs. p
plots of experimental data measured for the “primary” TB peroxyesters
whereas linear ln kobs vs. p relations are obtained for the “secondary” and
“tertiary” TB peroxyesters. As a consequence, a weakly pressure-dependent
activation volume, ∆V ϶obs, is obtained for the “primary” TB peroxyesters
whereas ∆V϶obs is independent of pressure with the “secondary” and “ter-
tiary” TB peroxyesters. ∆V ϶obs is determined according to Eq. (2):
∂ ln kobs
∆V ϶obs
RT
ϭ Ϫ
.
(2)
ͩ ͪ
∂p
T
In case of straight-line ln kobs vs. p behavior, ∆V϶obs is directly obtained from
the slope of the fitted line. The pressure-dependent activation volumes of
the “primary” TB peroxyesters are deduced from the first derivative of
ln kobs vs. p data fitted to a quadratic polynomial. The resulting activation
volumes are listed in Table 7. The data for TBPN and for TBPnB are given
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
595
Table 7. Activation volume, ∆V϶obs, of the decomposition rate coefficient, kobs, of tert-
butyl peroxyesters in n-heptane solution; the reaction temperature and the pressure range
of the experiments are listed; for easier comparison of pressure-dependent and pressure-
independent activation volumes, ∆V϶obs at 1000 bar is given for all peroxides.
Ϫ1
Peroxide
T/°C
Pressure
∆V϶obs/cm3 mol
∆V϶obs
range/bar
(1000 bar)/
Ϫ1
cm3 mol
TBPD
TBPP [1]
110
125
250Ϫ2000
100Ϫ2500
1.7 Ϯ0.6
3.0 Ϯ0.9
1.7
3.0
TBPO
TBPMB
TBPiB
145
150
145
250Ϫ2000
100Ϫ2500
200Ϫ2000
3.6 Ϯ1.1
4.0 Ϯ1.1
2.2 Ϯ0.9
3.6
4.0
2.2
TBPN
TBPnB
TBPProp
TBPA [1]
165
170
170
168
250Ϫ2000
200Ϫ2000
100Ϫ2000
100Ϫ2000
(14.5Ϫ5.78 · 10Ϫ3 · p/bar)
(13.6Ϫ3.19 · 10Ϫ3 · p/bar)
(11.4Ϫ2.47 · 10Ϫ3 · p/bar)
(20.5Ϫ2.74 · 10Ϫ3 · p/bar)
8.7
10.4
8.9
18.2
in italics to indicate the appreciable scatter of the underlying kobs data (see
Fig. 4) which prevents an accurate determination of ∆V϶obs (p). ∆V o϶bs for
TBPA has been obtained as the mean value from four series of experiments,
at 120, 150, 165, and 170°C [1]. To allow for some immediate comparison
of pressure-dependent and pressure-independent activation volume data,
∆V϶obs has been calculated for a common reference pressure of 1000 bar.
This ∆V϶obs (1000 bar) data are presented in the last column of Table 7. The
values for the “primary” TB peroxyesters clearly exceed the corresponding
numbers measured for the “secondary” and “tertiary” TB peroxyesters.
Literature data for ∆V϶obs have been reported for TBPD [13, 14] and for
TBPiB [15] only. The ∆V϶obs value given by Luft et al. for decomposition
Ϫ1
of TBPD in iso-dodecane is 6.1 cm3 mol [13]. From tabulated TBPD
decomposition rate coefficients (also in iso-dodecane) provided by the same
Ϫ1
Ϫ1
group [14], activation volumes of 5.2 cm3 mol , 7.1 cm3 mol , and
6.1 cm3 molϪ1 have been determined for 100, 130, and 200°C, respectively.
The authors estimate their activation volumes to be accurate within Ϯ30%.
Comparison with the entry in Table 7 shows that the literature values are
slightly above the corresponding data of the present investigation. It can not
be ruled out that this discrepancy is due to the difference in solvent, al-
though it is not overly likely that the minor solvent variation, iso-dodecane
vs. n-heptane, may lead to a significant difference in ∆V϶obs. For TBPiB
decomposition in cumene solution at 90°C, Neuman and Pankratz [15] re-
port ∆Vo϶bs to be 1.6 cm3 molϪ1 at around 1000 bar and 3.2 cm3 molϪ1 in the
pressure range 3000 to 5000 bar. The pressure-independent ∆V϶obs value of
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

596
M. Buback and J. Sandmann
Ϫ1
2.2Ϯ0.9 cm3 mol determined for experiments in n-heptane at 145°C
within the present study thus is fully consistent with the Neuman and
Pankratz numbers.
4. Discussion
Linear correlations of the logarithm of peroxide concentration vs. reaction
(or residence) time, as in Fig. 2, have been observed for each of the per-
oxides listed in Table 1 at each set of decomposition temperature and pres-
sure conditions. Thus first-order kinetics apply over extended conversion
ranges and no indication of induced decomposition is seen at the low (ini-
tial) peroxide concentrations of 1.0 · 10Ϫ2 M. As this concentration is well
above peroxide contents used in free-radical polymerization, the obtained
rate coefficients should be well suited for modelling thermal peroxyester
decomposition during polymerization of non-polar monomers such as eth-
ene.
Because of the strong application-oriented interest in such decompo-
sition data, the observed rate coefficients, kobs, will first be fitted to suitable
rate expressions that allow for estimates of peroxide decomposition rate in
hydrocarbon solution at arbitrary p and T conditions within the range of
the underlying experiments and perhaps even at some modest extrapolation
beyond this p and T region.
The Arrhenius relation, k ϭ A exp (ϪEA/RT), should be well suited for
this purpose. To fit the k(p,T) data, an Arrhenius expression has been used
in which (i) the pre-exponential factor is assumed to be independent of p
and T, (ii) the activation energy, EA, is a pressure-dependent quantity, and
(iii) the activation volume is independent of temperature, but may vary with
pressure. It is the curvature on some of the ln kobs vs. p correlations (Fig. 4)
which suggests a pressure-dependent activation volume. With the assump-
tions (i) to (iii) being taken into account, the expression for kobs(p,T) reads:
C2 ϩ p/bar (C3 Ϫ C4 · p/bar)
k(p,T)/sϪ1 ϭ C1 · exp Ϫ
.
(3)
ͩ
ͪ
T/K
In Table 8, the constants, C1 to C4, are listed for each TB peroxyester.
The format of Eq. (3) is such that, via the dimensionless constants C1 to C4,
Ϫ1
the decomposition rate coefficient kobs (in s ) may be estimated for speci-
fied p (in bar) and T (in K) conditions (out of the range of the underlying
experiments which is indicated by the last two columns in Table 8). The
physical meaning behind the constants is: C1 pre-exponential factor; C2
activation energy at zero pressure divided by Avogadro’s constant, (EA
(0 bar) ϭ EA (at pressure p) Ϫ p · ∆V϶obs); C3 temperature-independent
activation volume divided by R; and C4 pressure dependence of ∆V o϶bs
.
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
597
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

598
M. Buback and J. Sandmann
Depending on the type of peroxide, one out of two procedures has been
applied for deriving the coefficients. For the peroxides which show no
pressure dependence of ∆Vo϶bs, that is at C4 ϭ 0, the coefficients C1, C2, and
C3 were deduced from the experimentally obtained pre-exponential and the
activation energy (given in Table 6), and from the activation volume
(Table 7), respectively. For the other peroxides, which are the “primary”
ones, the coefficients have been found by least squares fitting of the entire
set of experimental rate coefficients to Eq. (3). The number of data points,
N, subjected to analysis is listed for each peroxide, as are (|∆k|/k)max, the
maximum deviation, in per cent, between measured and calculated de-
composition rate coefficients, and (|∆k|/k)av the mean value of deviation for
the entire set of N data points. For none of the seven peroxides of the
present investigation the maximum deviation exceeds 11% or the averaged
deviation exceeds 6%. For the three “primary” TB peroxyesters: TBPN,
TBPnB, and TBPProp, (|∆k|/k)av is even as low as 2%.
The rate expressions obtained by fitting the experimental data to Eq. (3)
allow to estimate kobs for the p and T conditions of literature studies and thus
to compare absolute kobs data. (The temperature and pressure dependence of
kobs has already been compared in the preceding section.) Unfortunately,
rate data for the pressure and temperature range as in the present study have
only been reported for TBPD [14]. Comparison with the TBPiB data pro-
vided by Neuman und Pankratz [15] requires some extrapolation beyond
the temperature range of the present study.
The TBPD data by Mehrling et al. [14] are given for 100, 130, and
200°C at both ambient pressure and 3000 bar. From this literature data, via
Eq. (2), kobs values for 2000 bar are estimated. Comparing this data with kobs
values calculated from Eq. (3) shows that the rate coefficients of the present
study (Eq. (3)) are clearly above the literature values, by 50% at 100°C, by
68% at 130°C, and by 86% at 200°C. The discrepancy increases toward
higher temperature because of the lower activation energy associated with
the literature data (see above).
To afford for a comparison with the TBPiB literature data, Eq. (3) has
been applied at 40 °C below the temperature range of the underlying experi-
ments. The Neuman und Pankratz data for decomposition in cumene [15]
are by about 41% above the data estimated via Eq. (3). The Bartlett und
Gortler data [16], also for decomposition of TBPiB in cumene, are by ap-
proximately 33% higher than the data from Eq. (3). In view of the fact that
some extrapolation goes into this comparison and because of cumene and
n-heptane being clearly dissimilar solvents, a difference in kobs of 40% is
not unusual. It should be remembered that kobs of diacyl peroxides, upon
variation of the solvent, increases by a factor of six in going from n-heptane
to acetonitrile [21]. In these systematic studies kobs was seen to be distinctly
larger in the aromatic solvent toluene than in n-heptane.
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
599
Decomposition rate data estimated from Eq. (3) should be well suited
for modelling high-pressure ethene polymerizations (to yield LDPE), as the
solvent medium (compressed n-heptane at fairly high temperature) is not
too dissimilar from a molecular surrounding as is occurring in ethene Ϫ
polyethylene mixtures during LDPE production.
5. Temperature dependence of kobs
The activation energy should provide insight into the decomposition mech-
anism. The majority of studies carried out so far, was concerned with TBPA
and with TBPP. The results reported by Bartlett and Hiatt [4], Pryor and
Smith [5, 8], and Koenig et al. [6, 7] provide convincing evidence that tert-
butyl peroxyacetate (TBPA) decomposes via single-bond scission whereas
tert-butyl peroxypivalate (TBPP) undergoes concerted two-bond scission.
The preceding detailed spectroscopic analysis of decomposition kinetics of
these two peroxides fully supports the view that TBPA and TBPP may be
considered as the archetypes of thermal peroxyester decomposition via sin-
gle-bond and concerted two-bond scission, respectively.
To identify the type of bond scission of other aliphatic TB peroxyesters,
it appears recommendable to investigate the kinetics by means of a Polanyi
plot. This type of analysis assumes a proportionality of activation energy
and of reaction heat for (similar) transformations carried out within homolo-
gous series [22]. The decomposition kinetics within the series of aliphatic
TB peroxyesters in Table 1 should be perfectly suited for such an analysis.
The procedure has already been tested for the decomposition of a variety
of TB peroxyesters, RC(O)OOTB, by Engel et al. [23]. Following the Evans
and Polanyi suggestion, they plotted experimental (decomposition) acti-
vation energy, EA, vs. BDE(RϪH), the associated RϪH bond dissociation
energy. The BDE(RϪH) serves as a measure of the stability of the free
radical Rᠨ. The Polanyi plot tells whether and to which extent EA reflects
the stability of Rᠨ. A linear EA vs. BDE(RϪH) correlation with slope unity
indicates that the stability of Rᠨ significantly influences the rate determining
step which in turn strongly suggests a concerted two-bond scission mecha-
nism. In case of single-bond scission, on the other hand, the species Rᠨ
would not show up during the primary dissociation event and EA should be
more or less independent of BDE(RϪH). For the decomposition rate coef-
ficient of an extended series of azoalkanes, Engel et al. obtained an approxi-
mately linear EA vs. BDE(RϪH) plot with slope unity, whereas the slope
fitted to the TB peroxyester kobs data was distinctly different from unity and
close to 0.5 [23]. Engel et al. assumed that polar effects play some role in
case of the TB peroxyesters thus preventing a one-to-one correlation of EA
and BDE(RϪH). Because of their pronounced similarity, the TB peroxyes-
ters of the present investigation should be much better suited for a Polanyi
plot analysis than the compounds used by Engel et al.
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

600
M. Buback and J. Sandmann
Fig. 5. Activation energy, EA, of the decomposition rate coefficient, kobs, for tert-butyl
peroxyesters, R-CO-OO-TB, plotted vs. the bond dissociation energy of the associated
alkane, BDE(RϪH); (᭺) EA from this study (᭹) EA from Ref. [1]; the activation energies
refer to zero pressure.
The RϪH bond dissociation energy was deduced as the enthalpy of the
reaction
∆rH
RϪH –→ Rᠨ ϩ Hᠨ
using the Benson procedure [24] for estimating the standard heat of forma-
tion of Rᠨ and RϪH. The standard heat of formation of Hᠨ was taken from
Cox and Pilcher [25]. It should be noted that such estimates of BDE(RϪ
H) are restricted to materials in the dilute gaseous phase. The error associ-
ated with applying this data to reactions in hydrocarbon solution should,
however, be small as BDE(RϪH) is determined by the same procedure for
the entire set of compounds that go into the Polanyi plot. The activation
energy that is used in the Polanyi plot refers to zero pressure.
Fig. 5 shows the EA vs. BDE(RϪH) plot for the aliphatic TB peroxy-
esters of the present work (open circles) together with the data for TBPA
and TBPP from the preceding study (full circles) [1]. The line in Fig. 5 is
constructed by passing a straight line with slope unity through the data point
for TBPMB which is one of the “secondary” TB peroxyesters. Fig. 5 con-
tains several interesting pieces of information: (i) With the exception of
TBPA, the entire set of aliphatic TB peroxyesters closely fits to a linear EA
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
601
vs. BDE(RϪH) correlation with slope unity; (ii) Considering only the
TBPA and TBPP data yields a correlation with a slope close to 0.5 which
is in agreement with the number given by Engel et al. [23]; (iii) Fitting a
straight line only through the data points of the “primary” TB peroxyesters:
TBPA, TBPProp, TBPN, and TBPnB yields a line with the slope being
close to zero.
That the “tertiary” and “secondary” TB peroxyesters are nicely fitted by
a straight line with slope unity indicates that the stability of free radicals
Rᠨ significantly contributes to the rate determining step and thus suggests
concerted two-bond scission in these peroxides. As TBPA is not expected
to show this type of behavior, it is by no means surprising that the full line
does not pass through the TBPA point. No clear conclusion about the type
of bond scission of the “primary” TB peroxyesters: TBPProp, TBPN, and
TBPnB can be drawn from Fig. 5. The data for these three peroxides may
be fitted either by the full line, which may be interpreted as an indication
of concerted two-bond scission, or by a more or less horizontal line through
the entire set of “primary” TB peroxyesters including TBPA, which would
indicate single-bond scission with a small or even negligible influence of
the substituent Rᠨ. In order to elucidate whether the decomposition mecha-
nism of the peroxides TBPProp, TBPN, and TBPnB is closer to TBPA or
to the “secondary” and “tertiary” TB peroxyesters, the pressure dependence
of kobs will now be addressed in some more detail.
6. Pressure dependence of kobs
The application of high pressure toward identifying the mechanism of per-
oxide decomposition has been pioneered by Neuman et al. [9, 10, 15]. Acti-
vation volumes of about 4 cm3 mol have been assigned [9] to concerted
Ϫ1
Ϫ1
two-bond scission and numbers around 10 cm3 mol to single-bond scis-
sion. Neuman and Amrich [10] explained the larger value of ∆V϶obs in case
of single-bond scission by additional contributions (to ∆V϶obs) resulting from
the pressure dependence of out-of-cage diffusion of the geminate free rad-
icals. Inspection of the entries in Table 7 indicates that, according to this
criterion, the “secondary” and “tertiary” TB peroxyesters decompose via
two-bond scission whereas single-bond scission occurs with all “primary”
TB peroxyesters.
The significant difference in pressure dependence of ∆V϶obs is illustrated
in Fig. 6 by plotting ln [(kobs/kobs (2000 bar)] as a function of pressure. Rela-
tive kobs is plotted, as kobs (p) data for identical temperature are not available
for the different TB peroxyesters. The similarity in pressure dependence of
kobs/kobs (2000 bar) for the “tertiary” peroxide, TBPD, and the “secondary”
peroxide, TBPiB, suggests that both compounds decompose by the same
mechanism. This result is in perfect agreement with the evidence from the
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

602
M. Buback and J. Sandmann
Fig. 6. Pressure dependence of relative (with respect to the 2000 bar value) rate coef-
ficients for TBPProp at 170°C, TBPiB at 145°C, and TBPD at 110°C.
Polanyi plot (Fig. 5), that the “tertiary” and “secondary” peroxides decom-
pose by concerted two-bond scission. The activation volumes for the entire
set of “secondary” and “tertiary” peroxides (Table 7) are in the range
Ϫ1
∆V϶obs ϭ 3.0Ϯ1.5 cm3 mol . Such values are considered to be character-
istic for decomposition via two-bond scission. From the Polanyi plot (Fig. 5)
the decomposition mode of the “primary” peroxides TBPN, TBPnB, and
TBPProp could not be safely established. The activation volumes of these
compounds are clearly above ∆V϶obs of the “secondary” and “tertiary” per-
oxyesters which is indicative of a difference in decomposition mechanism.
The activation volumes of TBPN, TBPnB, and TBPProp are, however,
smaller than ∆V ϶obs of TBPA (Table 7). This discrepancy may, at least partly,
be due to the fact that, in a strict sense, TBPA is no “primary” TB peroxy-
ester. Another argument for an identical decomposition mechanism, via sin-
gle-bond scission, of TBPA and of TBPN, TBPnB, and TBPProp is pro-
vided by the curvature of the ln kobs vs. p correlation of these four peroxides.
This curvature is rather weak and is difficult to be safely established within
the limits of experimental accuracy. It needs, however, to be noted that for
each of the “primary” TB peroxyesters studied so far, the same type of
curvature is seen. Toward lower pressure, the kobs data deviate from a more
or less linear pressure dependence of ln kobs (at high p) in such a way that
kobs is (additionally) enhanced. This tendency is consistent with decompo-
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
603
Scheme 2. Decomposition mechanism via one-bond scission for “primary” tert-butyl per-
oxyesters in solution; the individual reaction steps of homolytic bond cleavage (kdiss), in-
cage recombination (krec), decarboxylation of the acyloxy free radical (k2), and out-of-
cage diffusion (kdiff) are depicted.
sition occurring via single-bond scission. Upon lowering the pressure, out-
of-cage diffusion of the geminate free radicals is favoured which results in
an (additional) enhancement of kobs, with respect to the situation where out-
of-cage diffusion is hindered. It should be made clear that out-of-cage dif-
fusion upon lowering the pressure is also favoured with peroxides under-
going concerted two-bond scission. However, as the carbonyl mode consti-
tutes the experimental probe of decomposition kinetics in the IR-based
study, radical-radical cage recombination after release of CO2 is not reflect-
ed in the spectroscopic analysis.
In addition to such qualitative arguments, the relationship between sin-
gle-bond scission and the curvature of the ln kobs vs. p plots may be demon-
strated by modelling approaches based on Eq. (4), which has first been used
by Neuman and Amrich for representation of peroxide decomposition via
single-bond scission [10].
k
diff ϩ k2
kobs ϭ kdiss
(4)
ͩ ͪ
k
diff ϩ k2 ϩ krec
kdiss, krec, kdiff, and k2 are the rate coefficients of peroxide bond dissociation,
of recombination of the resulting two primary free radicals, of out-of-cage
diffusion (of at least one) of these primary radicals, and of decarboxylation
of the acyloxy radical, respectively. The assignment of the coefficients to
the individual processes during peroxide decomposition via single-bond
scission is visualized in Scheme 2.
Information about the size and the pressure dependence of the individual
k’s is not available. It is assumed that kdiss does not contribute to the curva-
ture of the ln kobs vs. p plots. Thus the term in brackets (Eq. (4)) will primar-
ily be investigated. k2 of the acyloxy free radicals, CH3C(O)O and
C2H5C(O)O, has been reported by Pryor et al. to be 1.6 · 109 sϪ1 [26]. These
authors also suggest that kdiff should be slightly above k2. According to
Braun et al. [27], krec should exceed both kdiff and k2 by at least one order
of magnitude. Even less information is available on the activation volumes.
∆V϶(k2) has been chosen to be 2.5 cm3 molϪ1 which corresponds to 50 per
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

604
M. Buback and J. Sandmann
Fig. 7. Pressure dependence of the term ln (kdiff ϩ k2)/(kdiff ϩ k2 ϩ krec)] contained in
Eq. (4); the rate coefficients and activation volumes used for estimating the data points
are listed in the figure; the full line is obtained by fitting the data to a quadratic poly-
nomial whereas the dashed line illustrates a straight-line fit.
cent of the activation volume associated with single-bond scission, for
which ∆V϶ (kdiss) ϭ 5 cm3 mol appears to be a reasonable value. The
Ϫ1
pressure dependence of ∆V ϶ (kdiff) is assumed to be 20 cm3 mol . The
Ϫ1
activation volume of the in-cage recombination process should be rather
small: ∆V϶ (krec) ϭ Ϫ1 cm3 mol is considered to be an adequate value.
Ϫ1
Via these rate coefficients and activation volumes, Eq. (4) allows for an
estimate of the pressure dependence of ln [(kdiff ϩ k2)/(kdiff ϩ k2 ϩ krec)].
The resulting plot is shown in Fig. 7. A clear curvature is seen on the calcu-
lated data (open circles). The dashed line refers to a straight-line fit. The
activation volume (for 150°C) associated with the full line through the cal-
Ϫ3
Ϫ1
culated data is: ∆V϶ ϭ (13.4Ϫ2.0 · 10 p/bar) cm3 mol . To afford for a
comparison with experimental ∆V ϶obs, the activation volume for kdiss, ∆V϶
(kdiss) ϭ 5 cm3 mol , has to be added, which yields as the modelled (via
Ϫ1
Eq. (4) activation volume: ∆V ϶ ϭ (18.4Ϫ2.0 · 10 p/bar) cm3 mol . This
result is remarkably close to ∆V϶obs derived as the mean value from the
TBPA decomposition experiments at 120, 150, 165, and 170°C (see Table 7
Ϫ3
Ϫ1
Ϫ3
Ϫ1
and Ref. [1]): ∆V϶obs ϭ (20.5Ϫ2.7 · 10 p/bar) cm3 mol (It should be
noted that the pressure-dependent term (to ∆V϶obs) of the individual iso-
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
605
thermal experimental runs [1] varies between Ϫ1.61 · 10Ϫ3 p/bar (at 120°C)
Ϫ3
and Ϫ3.88 · 10 p/bar (at 170°C) without any clear trend with tempera-
ture).
∆V϶obs measured for the other “primary” peroxyesters is below the TBPA
value (Table 7). The pressure-dependence of ∆Vo϶bs is not easily and reliably
identified, which is particularly true for the TBPN and TBPnB data. The kobs
values for TBPProp should be better suited for an analysis of the pressure
dependence of ∆V϶obs. The curvature of the ln kobs vs. p data of TBPProp
turns out to be very close to (or perhaps slightly below) the TBPA case
(Table 7). In view of the significant number of not precisely known coef-
ficients and parameters that go into estimates via Eq. (4) it appears un-
reasonable to fit the kobs(p) data measured for TBPProp to Eq. (4) with
the intention of deriving rate coefficients of the individual steps. It should,
however, be mentioned that even minor variation of only a single rate coef-
ficient in Eq. (4) is sufficient to reproduce the trend in ∆V϶obs that is seen in
going from TBPA to TBPProp. Upon reducing kdiff by a factor of two, to
account for a reduction in diffusivity in case of a larger RC(O)O moiety,
Eq. (4) yields as the modelled activation volume: ∆V϶obs ϭ (15.6Ϫ1.7
Ϫ3
Ϫ1
· 10 p/bar) cm3 mol . Reduction of kdiff by a factor of three (to
kdiff ϭ 8.0 · 108 s ) yields ∆Vo϶bs ϭ (13.8Ϫ1.4 · 10 p/bar) cm3 mol
Ϫ1
Ϫ3
Ϫ1
which is fairly close in zero-pressure activation volume to the experimental
values of TBPProp and also of the other “primary” peroxyesters: TBPN
and TBPnB (Table 7). The observed ∆V ϶obs values of the “primary” TB per-
oxyesters thus may be semi-quantitatively understood in terms of the model
for single-bond scission underlying Eq. (4). Further improvement of the ex-
perimental method, with an extension of the studies toward significantly
enhanced pressures, and the availability of information on the individual
rate coefficients contained in Eq. (4) from independent sources are, how-
ever, required for a quantitative analysis.
7. Concluding remarks
The kinetic study provides rate coefficients, kobs, of decomposition in n-
heptane within wide ranges of pressure and temperature for a fairly large
number of aliphatic TB alkyl peroxyesters. The rate data should be particu-
larly well suited for the modelling of high-pressure ethene polymerization.
The decomposition mechanism, via concerted two-bond scission or via sin-
gle-bond scission, may be identified from an inspection of both the tempera-
ture and the pressure dependence of kobs. It appears interesting to look for
situations in which both mechanisms occur to significant extents as parallel
processes. Also of interest is the highly time-resolved measurement of CO2
evolution subsequent to applying ps laser pulses [28].
The investigations into thermal decomposition of peroxyesters will be
extended to measuring kobs for series of alkyl peroxyesters where the tert-
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

606
M. Buback and J. Sandmann
butyl moiety is replaced by tert-amyl, by 1,1,3,3-tetramethylpropyl, or by
1,1,3,3-tetramethylbutyl groups. In addition, the aliphatic peroxyesters will
be applied as initiators in ethene high-pressure polymerization to investigate
whether and to which extent the mechanistic differences in unimolecular
decomposition mechanism, single-bond scission vs. concerted two-bond
scission, translate into differences in initiator efficiency. Part of these stud-
ies is already underway.
Acknowledgements
The authors are grateful to the Deutsche Forschungsgemeinschaft for finan-
cial support of this study within the Sonderforschungsbereich 357 (“Mole-
kulare Mechanismen unimolekularer Prozesse”). The intense cooperation
enjoyed with AKZO NOBEL, in particular with Dr. B. Fischer, Dr. J. Meij-
er, Dr. A. van Swieten, and R. Gerritsen, is gratefully acknowledged, as is
the synthesis and provision of the peroxide samples.
References
1. M. Buback, S. Klingbeil, J. Sandmann, M.-B. Sderra, H. P. Vögele, H. Wackerbarth
and L. Wittkowski, Z. Phys. Chem. 210 (1999) 199.
2. Y. Sawaki, in Organic Peroxides, ed. W. Ando, John Wiley and Sons, New York
(1992) 425.
3. T. Koenig, in Free Radicals, Vol. I, ed. J. K. Kochi, Wiley-Interscience, New York
(1973) 113.
4. P. D. Bartlett and R. R. Hiatt, J. Am. Chem. Soc. 80 (1970) 1398.
5. W. Pryor and K. Smith, Int. J. Chem. Kin. 3 (1971) 387.
6. T. Koenig and R. Wolf, J. Am. Chem. Soc. 89 (1967) 2948.
7. T. Koenig, J. Huntington and R. Cruthoff, J. Am. Chem. Soc. 92 (1970) 5413.
8. W. A. Pryor and K. Smith, J. Am. Chem. Soc. 92 (1970) 5403.
9. R. C. Neuman and J. V. Behar, J. Am. Chem. Soc. 91 (1969) 6024.
10. R. C. Neuman and M. J. Amrich, J. Am. Chem. Soc. 94 (1972) 2730.
11. C. Rüchardt, Angew. Chem. 82 (1970) 845.
12. H. Seidl and G. Luft, J. Macromol. Sci.-Chem. A15 (1981) 1.
13. G. Luft, P. Mehrling and H. Seidl, Angew. Makromol. Chem. 73 (1978) 95.
14. P. Mehrling, G. Luft, B. Giese and H. Seidl, Chem. Ber. 118 (1985) 240.
15. R. C. Neuman, Jr. and R. P. Pankratz, J. Am. Chem. Soc. 95 (1973) 8372.
16. P. D. Barlett and L. B. Gortler, J. Am. Chem. Soc. 85 (1963) 1864.
17. T. Koenig and J. Huntington, J. Am. Chem. Soc. 96 (1974) 594.
18. a) M. Buback and H. Lendle, Z. Naturforsch., Part A 34a (1979) 1482;
b) M. Buback and S. Klingbeil, Chem. Ing. Tech. 67 (1995) 493;
c) M. Buback and C. Hinton, in High-pressure Techniques in Chemistry and Physics:
A Practical Approach, eds. W. B. Holzapfel, N. S. Isaacs, Oxford University Press,
Oxford, New York, Tokyo (1997) 151;
d) M. Buback and C. Hinton, Z. Phys. Chem. 193 (1996) 61.
19. M. Buback, D. Nelke and H. P. Vögele, to be published.
20. D. Nelke, Diploma Thesis, Göttingen (1998).
21. M. Buback and C. Hinton, Z. Phys. Chem. 199 (1997) 229.
22. M. G. Evans and M. Polanyi, Trans. Faraday Soc. 34 (1938) 11.
23. P. S. Engel, A. I. Dalton and L. Shen, J. Org. Chem. 39 (1974) 384.
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM

Pressure and Temperature Dependence of the Decomposition Rate . ..
607
24. S. W. Benson, Thermochemical Kinetics, 2nd Edition, Wiley Interscience Publi-
cations, John Wiley and Sons, New York, London, Sydney, Toronto (1976).
25. J. D. Cox and G. Bilcher, Thermochemistry of Organic and Organometallic Com-
pounds, Academic Press, London, New York (1970).
26. W. A. Pryor, E. H. Morkved and H. T. Bickley, J. Org. Chem. 37 (1972) 1999.
27. W. Braun, L. Rajbenbach and F. R. Eirich, J. Phys. Chem. 66 (1962) 1591.
28. J. Aschenbrücker, M. Buback, N. P. Ernsting, J. Schroeder and U. Steegmüller, Ber.
Bunsenges. Phys. Chem. 102 (1998) 965.
Brought to you by | provisional account
Unauthenticated
Download Date | 6/25/15 4:48 PM