Multiphase reaction kinetics of epoxidation of polyisobutene

Article abstract of DOI:10.14233/ajchem.2013.14802

The kinetics of epoxidation of polyisobutene by peracetic acid generated in situ from hydrogen peroxide and acetic acid in the presence of solid acid WO3/ZrO2 were studied. The effect of several reaction parameters such as stirring speed, acetic acid-to- double bond molar ratio, temperature and content of catalyst were examined. Dynamic parameters were estimated using nonlinear regression method from the experimental data. A multiphase kinetic model of the epoxidation reaction was developed. There was good agreement between experimental and predicted data and simulation was performed to validate the model.

Full text of DOI:10.14233/ajchem.2013.14802

Asian Journal of Chemistry; Vol. 25, No. 15 (2013), 8493-8497
http://dx.doi.org/10.14233/ajchem.2013.14802
Multiphase Reaction Kinetics of Epoxidation of Polyisobutene
*
MEI LI , GUOMIN XIAO and ZHIMING CHEN
School of Chemistry and Chemical Engineering, Southeast University, Nanjing211189, P.R. China
*Corresponding author: Tel: +86 25 52090611; E-mail: huameitang05@163.com; huameitang13@163.com
(Received: 10 November 2012;
Accepted: 24 August 2013)
AJC-13980
The kinetics of epoxidation of polyisobutene by peracetic acid generated in situ from hydrogen peroxide and acetic acid in the presence
of solid acid WO3/ZrO2 were studied. The effect of several reaction parameters such as stirring speed, acetic acid-to- double bond molar
ratio, temperature and content of catalyst were examined. Dynamic parameters were estimated using nonlinear regression method from
the experimental data. A multiphase kinetic model of the epoxidation reaction was developed. There was good agreement between
experimental and predicted data and simulation was performed to validate the model.
Key Words: Epoxidation, Polyisobutene, Peracetic acid, Kinetics, Model.
did not consider the presence of two immiscible phases. On
the other hand, the kinetic parameters of the reaction considered
as a two-phase liquid-liquid reacting system under the same
reaction conditions were reported13,14.A heterogeneous kinetic
model using acidic ion exchange resins as a catalyst has been
presented15. The model did not consider the presence of liquid-
liquid immiscible phases. Ion exchange resin was prone to
swell in the organic phase, which was neglected by researchers.
In this work, polyisobutene oxide (PIBO) was obtained
in the presence of WO3/ZrO2. There were three phases in the
processes catalyzed by WO3/ZrO2: (1) an aqueous phase
(acetic acid, hydrogen peroxide and water); (2) the organic
phase; (3) an acidic solid catalyst phase.
INTRODUCTION
Chemical modifications are the useful ways to obtain new
polymeric materials. Of the well-known chemical modifications
of materials, epoxidation has been the most promising and
advantageous method. Polyisobutene (PIB) as an important
polymer is widely used as adhesives, sealants, cable insulation
and packing material because of its unique physical properties
such as thermal stability, resistance to weathering and UV light,
excellent gas barrier properties, elasticity1-6. These properties
can be modified by introducing epoxy functional groups into
polymer chains, which can increase the polarity of the final
polymers to expand their applications.
Epoxidation can be carried out by different methods,
depending on feedstock, oxidant, catalyst. In recent years,
much attention has been paid to the use of hydrogen peroxide
as the oxidant because it is relatively low cost, environmentally
friendly and safe7,8. Likewise, the epoxidation of unsaturated
polymers has been attracting much more attention. Nikje and
Mozaffazi9 investigated the epoxidation of hydroxyl-terminated
polybutadiene (HTPB) by using in situ-generated dimethyl-
dioxirane (DMD) as oxidant and tetra-n-butylammonium
bromide as a phase-transfer catalyst. The epoxidation of HTPB
with hydrogen peroxide was investigated in the presence of
phase-transfer catalyst10. Some kinetic concerning the
epoxidation of several oils with peracetic acid generated in
situ under homogeneous catalytic conditions, have been
carried out in previous years11,12. These models were pseudo-
homogeneous and established that the peracetic acid generation
in the epoxidation was always the rate controlling step which
This paper studied the kinetics of the epoxidation of PIB
and the influence of different reaction parameters (temperature
and concentration of acetic acid). Dynamic parameters for the
individual steps were obtained from experimental data. The
objectives of this study were to: (i) propose a mathematical
model for the reaction system; (ii) estimate the model para-
meters and (iii) compare the model predicted with experimental
data.
EXPERIMENTAL
Polyisobutene (PIB: Mn = 1050, content of double bond
= 0.00085 mol/g). Acetic acid (AR Grade), aqueous hydrogen
peroxide (50 wt %) and heptane were obtained from reputed
firms. They were used without further purification.
Catalyst preparation: Zr(OH)4 was prepared by precipita-
tion of the solution of ZrOCl2 with 28 wt % ammonia. Zr(OH)4
was impregnated with the solution of (NH4)6W12O39·xH2O at

8494 Li et al.
Asian J. Chem.
room temperature. After aging for 24 h, the precipitate was
washed with distilled water repeatedly to remove chloride ions
completely and dried at 100 ºC for 5 h. The product was
calcined at 700 ºC in air flow for 4 h.
was first titrated with potassium permanganate and then
peracetic acid was determined iodometrically.
The content of acetic acid was calculated by volumetric
titration, using a solution of sodium hydroxide in the aqueous
phase and potassium hydroxide in the organic phase.
Epoxidation of polyisobutene with peracetic acid gene-
rated in situ: Polyisobutene, WO3/ZrO2 and acetic acid were
placed into the reactor and heated to the reaction temperature
under reflux, using heptane as the diluent of the organic phase.
Then, hydrogen peroxide was added, drop by drop (30 mini-
mums in total) under stirring and the reaction was held for
several hours to achieve reaction completion. Periodically,
samples were taken, centrifuged at 1000 rpm for 10 min and
analyzed.
RESULTS AND DISCUSSION
Epoxidation runs were conducted with the following range
of variables: stirring speed 200-1000 rev/minimums; tempera-
ture (60-80 ºC); acetic acid-to-double bond ratio (mole per
mole) 0.5-1.5; catalyst concentration was expressed as weight
percentage of organic phase in the range of 1 %.
Influence of stirring speed: To investigate the effect of
mass transfer resistance, the reactions were performed carried
out at stirring speeds of 200, 500, 1000 rpm. In these studies,
the following parameters were fixed: temperature of 70 ºC,
reaction time of 3 h and the molar ratio of reagents of PIB/
H2O2/AcOH = 1:5:1.5. Similarly, the amount of catalyst was
0.5 wt % in relation to the PIB. It was found that the highest
yield of PIBO was achieved at stirring speed of 500 rpm
(Table-1).
Phase partition coefficients of acetic acid and peracetic
acid between the aqueous and polymeric phases: Different
contents of acetic acid, H2O, heptane and PIB were placed
into a round-bottom flask, equipped with a reflux condenser.
The mixtures were then stirred (500 rpm) for 3 h and later
standing for another 3 h at 70 ºC until physicochemical equili-
brium was achieved, after which the sample was centrifuged
and analyzed.
Analytical techniques: Iodine value was obtained using
the Hanns’s method in accordance with the Chinese Standard
ZB/B66005.8-1990 by the following equations:
TABLE-1
YIELD OF PIBO AT DIFFERENT STIRRING SPEED
Stirring speed (rpm)
200
500
1000
0.1269(V − V2 )CNa S O
3
1
1
2
2
INae
=
×100×
(1)
Time (min)
120 180
120 180 120 180
m1
2AI
Iodine value (g/100 g)
Iodine conversion (%)
Yield of PIBO
13.5 10.87 11.79 8.32 11. 8 8.52
34.3 47.1 42.7 59.6 42.6 58.6
32.5 44.2 39.6 55.7 39.1 54.9
where INae : iodine number of PIB after epoxidation (mol/
100 g); 0.1269: mass of iodine correspond to 1 cm3 of Na2S2O3
(1 mol/cm3); V1: volume of Na2S2O3 used to titrate blank
sample (cm3); V2: volume of Na2S2O3 used to titrate right
sample (cm3); CNa S O : concentration of Na2S2O3 solution
It can be seen that the oxirane formation rate was not
affected by stirring speeds in the range beyond 500 rpm. Direct
effect of stirring speed on mass transfer process was mainly
the interfacial area of mass transfer. Increased stirring speed
beyond 500 rpm reached the “saturation effect” and may not
result in increased interfacial contact area.
2
2 3
(mol/cm3); m1: mass of sample (g); AI: molecular mass of
iodine (g/mol).
Epoxy number was calculated according to the Chinese
Standard GB/T4612-2008:
Hence, it was assumed that the reaction was free from
mass transfer resistance under the given conditions. However,
all subsequent experiments were performed at a stirring speed
of 600 rpm to ensure that there was no resistance to mass
transfer at interfaces.
100(V4 − V3 )CHClO
4
ENae
=
(2)
100m2
where ENae: epoxy number of epoxy polyisobutylene (PIBO)
(mol/100 g PIBO); V3: volume of HClO4 used to titrate blank
sample (cm3);V4: volume of HClO4 used to titrate right sample
Effect of intra-particle diffusion resistance: There was
a variation in particle sizes ofWO3/ZrO2 to assess the influence
of intra-particle diffusion resistance under otherwise similar
reaction conditions.
(cm3); CHClO : concentration of HClO4 solution (mol/cm3); m2:
4
mass of sample (g).
INbe − INae
The experimental data obtained are presented in Table-2.
The results showed that any of the particle sizes gave practi-
cally same results. Hence, it proved that there was no intra-
particle diffusion resistance on the catalyst (particle size <
0.3 mm).
CIN
=
×100 %
(3)
INbe
where CIN: conversion of PIB; INbe: iodine number of PIB before
epoxidation; INae: iodine number of PIB after epoxidation.
ENae
YEN
=
×100 %
(4)
TABLE-2
EFFECT OF INTRA-PARTICLE
DIFFUSION ON IODINE CONVERSION
ENmax
whereYEN: yield of PIBO; ENae: epoxy number of PIBO after
epoxidation (mol/100 g PIB); ENmax epoxy number of PIBO
calculated from the number of unsaturated bonds.
Particle size (mm)
0.3
0.074
Time (min)
120
11.76
42.8
39.6
240
5.33
74.1
68.5
120
11.58
43.6
40.7
240
5.4
73.7
67.8
The concentrations of peracetic acid and H2O2 were
determined in accordance with the Chinese Standard GB/T
19108-2003. The principle could be summarized as that H2O2
Iodine value (g/100 g)
Iodine conversion (%)
Yield of PIBO

Vol. 25, No. 15 (2013)
Multiphase Reaction Kinetics of Epoxidation of Polyisobutene 8495
k2
Influence of molar ratio of acetic acid to PIB: The
influence of the acetic acid to double bond molar ratio was
investigated at different ratios: 0.5:1, 1:1 and1.5:1. It showed
the effect of acetic acid concentration on yield of the PIBO
(Fig. 1). Increasing the acid concentration was found to increase
a faster reaction rate. It has been observed that at the high
mole ratio of CH3COOH, the stability of the oxirane ring was
poor as the acid promotes the hydrolysis of the epoxide.
AcOOH(org) + PIB
AcOH(org)
PIBO + A(org)
AcOH(aq)
(e)
(f)
Considering our set-up as a well-stirred, ideal isothermal
batch reactor in the slow kinetics regime, where (1) the indivi-
dual volumes of each liquid phase remain nearly constant, (2)
the concentration gradients at three phase interface s were
negligible, (3) degradation of the epoxide ring was neglected.
(4) adsorption and desorption of reactants and products were
fast and were therefore at equilibrium.
80
For the surface reaction controlled peracetic acid forma-
tion, the adsorption and desorption steps are very fast in the
overall conversion process.As such, the surface concentrations
of component may be written as:
0.50 mol
1.00 mol
2.05 mol
60
40
20
0
[AcOH.s]
[AcOOH.s]
KAA
=
KPA =
(5)
[AcOH][s]
[AcOOH][s]
where KAA: adsorption equilibrium constant; KPA: desorption
equilibrium constant.
The total concentration of the sites, Ct expressed as
Ct = [s]+[AcOH.s]+[AcOOH.s]
(6)
where [s] is the concentration of vacant site on the surface.
Substituting the values of [AcOH·s] and [AcOOH·s] into
eqn. 2, gives
0
100
200
300
400
500
Time (min)
Ct
[s] =
Fig. 1. Effect of acetic acid per mole of double bond on yield of PIBO
(7)
1+ KAA[AcOH]+ KPA[AcOOH]
For the surface reaction controlled peracetic acid forma-
tion, the rate of reaction of hydrogen peroxide may be expressed
as:
Kinetic model of the epoxidation reaction:The mechanism
of formation PAA by reacting organic acid with hydrogen
peroxide in aqueous solution was known16. Zhao17 claimed
that the reaction was carried out via a protonated carbonyl
oxygen of acetic acid and this protonated intermediate reacted
with H2O2 to form the PAA and water. According to the above
results, the reacting system has three immiscible phases. The
mechanism for the in situ epoxidation in the presence of solid
catalyst is described as follows:(i) formation of peracetic acid
and decomposition of H2O2 in the aqueous phase in the
presence of a catalyst; (ii) transfer of peracetic acid from the
aqueous phase to the oil phase; (iii) reaction of peracetic acid
in the oil phase to produce epoxide and to release acetic acid;
(iv) transfer of acetic acid from the oil phase back to the
aqueous phase.
d
H2O2
−
dt
Ct (k1KAA[AcOH][H2O2 ]− k−1KPA[AcOOH][H2O])
=
(8)
(1+ KAA[AcOH]+ KPA[AcOOH])
where k1 is the forward rate constant; k-1 is the reverse rate
constant
C1(k1KAA[AcOH][H2O2 ]− k−1KPA[AcOOH][H2O])
R1 =
(1+ KAA[AcOH]+ KPA[AcOOH])
Mass balance for AcOH
In present study, an attempt has been made to develop a model
for the formation of peracetic acid. The classic Langmuir-
Hinselwood-Hougen-Watson (LHHW) model was applied to
the reaction mechanism. WhenWO3/ZrO2 is used as a catalyst,
the reaction proceeds on the active catalyst site as follows: (1)
adsorption of acetic acid on the active catalyst site, (2) surface
chemical reaction between acetic acid and H2O2 and (3)
desorption of the products. Hence, all the rate equation of the
epoxidation reaction was deduced as follows:
aq
AcOH
org
org (9)
=[AcOH]aq Vaq +[AcOH]org
V
AcOH
nHAC = n
+ n
The partition equilibrium of AcOH may be written as
[AcOH]org
ϕAcOH
=
(10)
[AcOH]aq
Eqn. 9 can be recast, as follows:
dnAcOH d[AcOH]aq Vaq
ϕ
AcOHd[AcOH]aq Vorg
dt
=
+
dt
dt
K
AA
AcOH + s
AcOH · s
(a)
(b)
d[AcOH]aq
dt
=
(Vaq + ϕ
k1
org
V )
(11)
(12)
AcOH
AcOH·s + H2O2
AcOOH·s + H2O
k
–
1
Besides:
dnAcOH
dt
K
PA
AcOOH·s
AcOOH + s
(c)
(d)
= (−R1)Vaq + k4[PIB][AcOOH]org Vorg
AcOOH(aq)
AcOOH(org)

8496 Li et al.
Asian J. Chem.
Equivalence between eqns. 7 and 8 rearranging:
TABLE-4
CALCULATED VALUES OF KINETIC
PARAMETERS FOR MODEL
d[AcOH]aq
dt
org
= (Vaq + φ
V
)−1[(−R1)Vaq
AcOH
Temperature (ºC)
Parameters
60
0.047
0.02
70
80
+k4[PIB][AcOOH]org Vorg ]
(13)
k1 (mol-1 L min-1)
k-1 (mol-1 L min-1)
Ct (g mol-1 L min-1)
KAA (dm3 mol-1)
KPA (dm3 mol-1)
R2
0.069
0.034
0.013
4.9
0.13
0.06
0.013
8.02
12.02
0.99
Proceeding in similar fashion as above, the following
expression results:
0.013
2.45



−1
d[AcOH]org
dt
Vaq
4.8
6.05
0.99
=
+ Vorg [(−R1)Vaq

0.97
φAcOH

Rmsd
K2 (mol-1 L min-1)
0.0001206
0.1
0.00004908 0.00009284
0.5 0.91
+k4[PIB][AcOOH]org Vorg ]
(14)
Ct: Concentration of active site per unit mass of catalyst × constant of
surface reaction rate; Rmsd: root-mean-square deviation.
AcOOH was proceeding in similar fashion as above, the
following expression results:
Fourth order Runge-Kutta method was applied for solving
the system of differential eqns. 4, 9-12. Experimental value
and model curves of double bonds and H2O2 at the different
temperature were plotted in Figs. 2 and 3. Figs. 4 and 5
demonstrated the ability of the model with the parameters in
Table-4 to correlate the experimental results.
d[AcOOH]aq
org
V
)−1[R1Vaq
= (Vaq + φ
AcOOH
dt
−k4[PIB][AcOOH]org Vorg ]
(15)
(16)
d[AcOOH]org
dt
Vaq



−1
=
=
+ Vorg [R1aqVaq

φAcOOH

−k4[E][AcOOH]org Vorg ]
[AcOOH]org
[AcOOH]aq
φAcOOH
where
d[PIB]org
dt
= −kr[PIB][AcOOH]org
Phase partition coefficients of acetic acid for each reaction
condition were experimentally determined (Table-3). The
values were based on the molar concentration of AcOH in
each phase (ΦAcOH = CoilAcOH/CaqAcOH). The average value ΦAcOH
(0.006) of the experimental values was lower than that in the
literature Φ (0.035, 0.03)13,18. It could be inferred that the value
some depend on composition of unsaturated hydrocarbons.
Time (min)
TABLE-3
PHASE PARTITION COEFFICIENTS OF AcOH
Fig. 2. Comparison of experimental determined points and predicted model
curves of double bonds vs. time at different temperature
oil
CAcOH
(mol/L)
aq
CAcOH
(mol/L)
PIB/H2O/AcOH
molar ratios
Φ =
CAcOHoil/CAcOH
Try
aq
1
2
3
1/10.3/1.96
1/5.9/0.42
1/13.6/1.7
0.046
0.02
7.11
3.46
5.28
0.0065
0.0058
0.0059
0.031
Table-3 also contained the AcOH values predicted using
UNIFAC, which were very similar to the measured ones. There-
fore, the distribution constant ofAcOH was estimated employing
UNIFAC. The predicted values of peracetic acid was 0.04.
Kinetic modelling results: The surface reaction rate
coefficient, desorption and adsorption equilibrium constant
were estimated by fitting the experimental data using a non-
linear regression (Table-4). The coefficients of determination
of the model were 0.97, 0.99 and 0.99 at 60, 70 and 80 ºC,
respectively.
The kinetic rate constant for the epoxidation of the double
bonds by AcOOH in the organic phase was calculated by
solving the set of simultaneous ODEs using Euler’s numerical
method in MATLAB (Table-4).
Time (min)
Fig. 3. Comparison of experimental determined points and predicted model
curves of H2O2 vs. time at different temperature

Vol. 25, No. 15 (2013)
Multiphase Reaction Kinetics of Epoxidation of Polyisobutene 8497
Conclusion
The kinetics of epoxidation of polyisobutene by peracetic
acid generated in situ from hydrogen peroxide and acetic acid
in the presence of solid acidWO3/ZrO2 were studied. The classic
LHHW model was applied to the reaction mechanism of
peracetic acid. The various constants were evaluated from the
experimental data. A multiphase kinetic model that described
epoxidation was proposed. Comparison of experimental value
and model curves validated the model.
ACKNOWLEDGEMENTS
The Financial support from China National Petroleum
Corporation is greatly appreciated.
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