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Materials Science and Engineering A 454–455 (2007) 221–226

Study on reactive extrusion processes of block copolymer

Lili Wu a, Yuxi Jia a,b,∗, Sheng Sun a, Guofang Zhang a,Guoqun Zhao a, Lijia An b,∗∗

a School of Materials Science and Engineering, Shandong University, Jinan 250061, Chinab State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry,

Chinese Academy of Sciences, Changchun 130022, China

Received 1 August 2006; received in revised form 2 November 2006; accepted 29 November 2006

bstract

The anionic copolymerization process of styrene–butadiene (S/B) block copolymer in a closely intermeshing co-rotating twin screw extruderith butyl-lithium initiator was studied. According to the anionic copolymerization mechanism and the reactive extrusion characteristics, theathematical models of monomer conversion, average molecular weight and fluid viscosity during the anionic copolymerization of S/B were

onstructed, and then the reactive extrusion process was simulated by means of the finite volume method and the uncoupled semi-implicit iterativelgorithm. Finally, the influence of the feeding mixture composition on conversion was discussed. The simulated results were nearly in agreementith the experimental results. 2006 Elsevier B.V. All rights reserved.

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eywords: Reactive extrusion; Copolymerization; Numerical simulation; Block

. Introduction

In recent years, the styrene/butadiene block copolymer haseen developed rapidly. As the typical representation, thetyrene–butadiene rubber has become the biggest kind of generalynthetic rubber and has been applied in many fields.

The reactive extrusion process is a new type of polymerrocessing technology. Using twin screw extruders as reac-ors, the reactive extrusion for polymerization can realize anntegrated process of the chemical reaction and the continuousxtrusion.

At present, there are many investigations into the reactivextrusion process of copolymerization [1–12], but most of whichere concentrated on the graft copolymerization and most ofhich were experimental studies. There are complex interac-

ions among such phenomena as fluid flow, heat transfer andhemical reaction during the reactive extrusion process, whichause the theoretical research to be very difficult.

∗ Corresponding author at: School of Materials Science and Engineering,handong University, Jinan 250061, China. Tel.: +86 531 88395811;ax: +86 531 88395811.∗∗ Corresponding author.

E-mail addresses: jia yuxi@sdu.edu.cn (Y. Jia), ljan@ciac.jl.cn (L. An).

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921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2006.11.154

lymer

In this paper, the numerical simulation of the reactive extru-ion process for the block copolymerization of S/B in co-rotatingwin screw extruders was carried out via the finite volume

ethod, and the evolutions of the key variables were numeri-ally analyzed, then the influence of styrene content on reactivextrusion processes was discussed.

. Construction of mathematical models

.1. Analysis of the reaction mechanism

The reactive extrusion for the anionic copolymerization oftyrene–butadiene is a new synthesis method and its mechanisms different from that of the anionic solution copolymerization.

When the anionic copolymerization of S/B is conducted in aonventional tank reactor, the butadiene monomer tends to poly-erize first because the reactivity ratio of butadiene is much

igher than that of styrene, and the styrene monomer cannotolymerize until most of the butadiene monomer has been con-umed [13].

In an extruder reactor, the barrel temperature is much higherhan the boiling point of the butadiene monomer (−4 ◦C).ccordingly, most of the butadiene monomer is vaporized

mmediately after being fed into the extruder. The butadiene

2 Engineering A 454–455 (2007) 221–226

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2

rtlmt

st

⎧⎪⎨⎪⎩

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Table 1Main input data related to the twin screw extruder [12]

Parameters Numerical values

Nominal diameter of screws (mm) 35Centerline distance of screws (mm) 30RNL

t⎧⎨⎩

o

X

w

m

M

m

TM

P

DDMMIIIFAFAATTTCVV

22 L. Wu et al. / Materials Science and

onomer in gas phase occupies the unfilled part of the extrudernd only little can keep in the liquid phase and copolymerize withhe styrene monomer. Therefore, as the initiator is added, thetyrene polymerization follows after the complete consumptionf little liquid butadiene monomer. Only when the melt viscosityncreases to a certain extent with the polymerization of styrene,he number of the gaseous butadiene monomer will decrease,art of butadiene will gradually diffuse into the polymer meltnd polymerize immediately because of its high reactivity ratio11,12].

.2. Construction of the kinetic model of copolymerization

On the basis of the copolymerization mechanism, the wholeeactive extrusion process can be divided into two periods. Inhe first period, the extent of polymerization of butadiene is veryittle, and then only the styrene monomer is assumed to poly-

erize. In the second period, the butadiene monomer adds tohe macromolecular chains.

In the first period, there is only the homopolymerization oftyrene. The conversions of the two types of monomers, respec-ively, are [14]

X1(I, J) = 1 − 1 − X1(I − 1, J)

1 + Ap1c

1/2i e−Ep1/(RT (I,J)) �t

X2(I, J) = 0

(1)

here X(I,J) denotes the monomer conversion in the Ith timetep on the Jth space point, X(I − 1,J) the monomer conver-ion in the (I − 1)th time step on the Jth space point, Ap therequency factor for chain propagation, ci the concentration of

ctive centers, Ep the activation energy for chain propagation,the general gas constant, T the fluid temperature, �t the time

tep and the subscripts 1 and 2 denote styrene and butadiene,espectively.

M

able 2ain input data related to the material and process [12,18,19]

arameters

ensity of styrene (kg m−3)ensity of butadiene (kg m−3)olecular weight of styrene (g mol−1)olecular weight of butadiene (g mol−1)

nitial concentration of styrene (mol m−3)nitial concentration of butadiene (mol m−3)nitial concentration of butyl-lithium (mol m−3)requency factor for chain propagation reaction of styrene homopolymerization ((L mctivation energy for chain propagation reaction of styrene homopolymerization (kJrequency factor for chain propagation reaction of butadiene homopolymerization (Lctivation energy for chain propagation reaction of butadiene homopolymerization (ctivation energy for fluid flow (J mol−1)he time constant in Carreau equation (s)he non-Newtonian index in Carreau equationhe infinite shear viscosity in Carreau equation (Pa s)ritical molecular weight for entanglement effects (g mol−1)elocity of fluid flow in the entrance of the model (m s−1)elocity of fluid flow on the wall of the model (m s−1)

atio of screw length to diameter 40umber of thread starts 2ead of screws (mm) 30

In the second period, the butadiene monomer polymerizes,he conversions of the two types of monomers, respectively, are

X1(I, J) = 1

X2(I, J) = 1 − 1 − X2(I − 1, J)

1 + Ap2ci e−Ep2 /(RT (I,J)) �t

(2)

In the whole copolymerization process, the total conversionf S/B mixture is

(I, J) = 1 −

cm1,0(I, J)[1 − X1(I, J)]

+cm2,0(I, J)[1 − X2(I, J)]

cm1,0(I, J) + cm2,0(I, J)(3)

here cm,0 denotes the initial monomer concentration.The numerical calculation equation of the weight-average

olecular weight of the polymer is

w(I, J)= cm1,0(I, J)X1(I, J)MM1 +cm2,0(I, J)X2(I, J)MM2

ci(4)

where MM denotes the molecular weight of monomer.The numerical calculation equation of the weight-average

olecular weight of fluids is

2 2

eqw(I, J) =

Mw (I, J)ci + cm1,0(I, J)MM1[1 − X1(I, J)]

+ cm2,0(I, J)M2M1

[1 − X2(I, J)]

MM1cm1,0(I, J) + MM2cm2,0(I, J)(5)

Numerical values

906621.1104.1554.096368.983065.860.8504

ol−1)1/2 s−1) 1.1289 × 106

mol−1) 5.907 × 104

mol−1 s−1) 9.3 × 104

kJ mol−1) 2.88 × 104

9500030.4500380000.00380.0057

L. Wu et al. / Materials Science and Eng

F

2

c

i

η

wtoMv

The numerical calculation equation of the apparent viscosityis [16]

ig. 1. Evolution of barrel temperature along the axial direction of the extruder.

η

Fig. 2. Flow chart of num

ineering A 454–455 (2007) 221–226 223

.3. Construction of chemorheological model

The apparent viscosity of fluids is influenced by monomeronversion, temperature and shear rate.

The numerical calculation equation of the zero shear viscositys [15]

0(I, J) ={

K1 eEη/(RT (I,J))c(I, J)Mw(I, J) φMw(I, J) ≤ Mc

K2 eEη/(RT (I,J))c5.4(I, J)M3.4w (I, J) φMw(I, J) > Mc

(6)

here K1 and K2 are the constants for the given polymer, Eη

he activation energy for fluid flow, c the mass concentrationf macromolecular chains, φ the polymer volume fraction andc is the critical molecular weight for entanglement effects in

iscosity.

(I, J) = η∞ + [η0(I, J) − η∞]{1 + [λγ̇(I, J)]2}(n−1)/2(7)

erical simulation.

2 Engineering A 454–455 (2007) 221–226

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3

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4

4e

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4

The evolutions of such variables as the weight-averagemolecular weight and the apparent viscosity of the fluid alongthe axial direction of the extruder are shown in Figs. 4 and 5,respectively.

24 L. Wu et al. / Materials Science and

here �∞ denotes the infinite shear viscosity, � the time con-tant, γ̇ the shear rate and n is the non-Newtonian index.

.4. Initial and boundary conditions

In the experiment, the reactor is a closely intermeshing co-otating twin screw extruder, the S/B mixture and the initiator areed at the different axial position of the extruder separately [12].nd so the simulated zone is the reaction zone whose length

s 600 mm (the feeding port of initiator is at the axial position00 mm and the die is at the axial position 1000 mm).

The input data related to the twin screw extruder are shown inable 1 [12]. By means of the construction method of the reactorodel [17], the equivalent length and radius of the reactor model

re calculated, and then quadrilateral mesh is used to make thisodel discrete. The number of the nodes in the axial direction

f the model is 9030 and the number of the nodes in the radialirection is 30.

According to the experimental conditions, the main inputata related to the material and process are listed in Table 212,18,19]. The evolution of the barrel temperature along thexial direction of the extruder is shown in Fig. 1 [12]. In thisaper, the temperatures of the nodes with the same length ofcrews are assumed to be identical and equal to the temperaturef the corresponding location in the barrel. The inlet velocity isalculated by the feeding rate, and the velocity of the wall ofhe reactor model is determined according to the screw speed asell as the degree of the wall slip. The abscissa title L in Figs.and 3–6 denote the extruder length.

. Numerical simulation methods

By means of the finite volume method [20] and the uncoupledemi-implicit iterative algorithm, the conservation equations ofomentum and mass, the numerical computation expressions

f the monomer conversion, the average molecular weight andhe fluid viscosity were numerically solved. The detailed flowhart of the numerical simulation is shown in Fig. 2.

. Results and discussion

.1. Monomer conversion and its comparison withxperiment

The comparison between our simulated conversion and thexperimental results in ref. [12] is shown in Fig. 3 (“–�–.003231 m” represents the nodes whose distance to the center-ine of the reactor model is 0.003231 m, which is close to the wallf the model; “–�– 0.001864 m” represents the nodes whoseistance to the centerline of the model is 0.001864 m; “–�–.000621 m” represents the nodes whose distance to the center-ine of the model is 0.000621 m, which is near the centerline ofhe model).

It can be seen that the simulated results are nearly in agree-ent with the experimental results, which demonstrates the

alidity of the models that we have built. In general, the simu-ated results of the monomer conversion are appreciably higher

Fa

ig. 3. Comparison between our simulated conversion and the experimentalesults.

han the experimental results, and at the axial length 0.82 m ofhe extruder, the curves of the simulated results are not smooth.he reasons for the above phenomena are analyzed as follows:

1) In the simulation, it is assumed that the materials are mixedwell. But in real processes, it is hard to fulfill the condi-tion, so the experimental results are less than our simulatedresults.

2) The butadiene monomer cannot react until the styrenemonomer has been completely consumed in our simulation.Therefore, when the styrene monomer fully polymerizes,the butadiene monomer starts to rapidly react, correspond-ingly the curves are not smooth.

.2. Evolutions of other key variables

ig. 4. Evolution of the weight-average molecular weight of the fluid along thexial direction of the extruder.

L. Wu et al. / Materials Science and Engineering A 454–455 (2007) 221–226 225

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ig. 5. Evolution of apparent viscosity along the axial direction of the extruder.

It can be seen from Fig. 4 that with the increase of theuid flow length, the weight-average molecular weight of theuid gradually increases. The reason is that the weight-averageolecular weight of the fluid is the increasing function of theonomer conversion, which can be concluded from Eqs. (4) and

5).The temperature and weight-average molecular weight cor-

esponding to the turning point on the apparent viscosity curvere listed in Table 3 when R = 0.001864 m.

It can be seen from Fig. 5 and Table 3 that with the increasef the fluid flow length, the evolution of the fluid viscositys complex. The reason is that the zero shear viscosity is thencreasing function of the weight-average molecular weight andhe decreasing function of the temperature (Eq. (6)), and thepparent viscosity is the increasing function of the zero sheariscosity and the decreasing function of the shear rate (Eq.7)). When the fluid flow length varies from 0.74 to 0.82 m,he increase of the weight-average molecular weight of theuid is slow, but the fluid temperature increases rapidly, so thepparent viscosity decreases. When the fluid flow length variesrom 0.82 to 0.88 m, the butadiene monomer rapidly polymer-zes, the weight-average molecular weight of the fluid rapidlyncreases, whose influence on the apparent viscosity exceedshat of the increasing temperature. So the apparent viscosityncreases. When the fluid flow length varies from 0.88 to 1.0 m,he increase of the weight-average molecular weight becomeslow, the influence of the increasing temperature on the appar-

nt viscosity becomes obvious, resulting in the decrease of thepparent viscosity.

On the nodes with the same axial length of screws and theifferent radial distance, the values of the variables are different.

able 3emperature and weight-average molecular weight corresponding to the turningoint on the apparent viscosity curve (R = 0.001864 m)

(m) T (K) Meqw (g mol−1) η (×106 Pa s)

.74 393.6 516419.7 11.9

.82 410.7 625445.1 7.14

.88 422.7 869350.3 14.1

.00 442.7 949918.6 5.26

aoed

6

Scmiw

Fig. 6. Influence of styrene content on monomer conversion.

he reasons are presented as follows. According to the reactorodel in our simulation, the velocity of the fluid near the modelall is faster than the velocity in the inner. Therefore, with the

ncrease of the distance to the centerline, the residence timef the fluid decreases, and then the monomer conversion, theeight-average molecular weight and the apparent viscosity of

he fluid decrease.

. Influence of feeding mixture composition ononversion

The influence of the feeding mixture composition on theonomer conversion can be seen from Fig. 6 (“s” denotes the

imulated result and “e” denotes the experimental result). It cane seen that with the decrease of the content of the styreneonomer, the conversions at the same axial position of the

xtruder decrease and the polymerization zone moves towardshe die. The reasons are analyzed as follows.

With the same feeding rate and the same ratio of the initiatoro the styrene, because the density of styrene is higher than thatf butadiene, the velocity of fluid flow in the entrance and theoncentration of the butadiene monomer under the condition oftyrene content 0.61 are higher than those under the conditionf styrene content 0.82. With the increase of the velocity of fluidow in the entrance, the residence time of the fluid decreases,nd then the total conversion decreases. So with the decreasef the styrene concentration and the increase of the butadi-ne concentration in the feeding mixture, the total conversionecreases.

. Summary

The numerical simulation of the anionic copolymerization of/B in closely intermeshing co-rotating twin screw extruders was

arried out, and the evolutions of monomer conversion, averageolecular weight and fluid viscosity were obtained, and then the

nfluence of the feeding mixture composition on the conversionas discussed. The conversion increases with the increase of

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26 L. Wu et al. / Materials Science and

he content of styrene monomer. The simulated results and thexperimental results nearly show a correspondence.

In practice, a twin screw extruder often consists of consid-rable forward conveying screw elements, one or two reverseonveying screw elements, and a die. So the structure of a twincrew extruder is complex, and it is not always fully filled. Theore precise three-dimensional reactor model should be built.The butadiene monomer is in gas phase in extruders, it con-

inuously diffuses into the polymer melt and then polymerizes.he kinetic model of block copolymerization constructed in thisaper is simple, which can show the trend of the complex reac-ion, but is not very precise. So the more complicated kineticquation of copolymerization should be studied by means of theiffusion theory.

cknowledgements

This work was supported by the National Natural Scienceoundation of China (50573079, 50390096, 50425517 and0340420392) and the Special Funds for Major State Basicesearch Projects (2003CB615601).

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