Steady state behavior of a continuous stirred tank reactor for styrene polymerization with bifunctional free radical initiators

Chemical Engineering Science. Vol. 43. No. 4. pp. 965-977. Pnnted in Great Britain.

19X8.

0”09-2509

I(8 s.3 0” +o.oo Pergamon Press plc

STEADY STATE BEHAVIOR OF A CONTINUOUS STIRRED TANK REACTOR FOR STYRENE POLYMERIZATION WITH BIFUNCTIONAL FREE RADICAL INITIATORS KEE JEONG KIM and KYU YONG CHOI* Department of Chemical and Nuclear Engineering and Systems Research Center, University of Maryland, College Park, MD 20742, U.S.A. (Received

3 April

1987;

accepted

24 August

1987)

Abstract-Steady state behavior of a continuous stirred tank reactor is analyzed for styrene polymerization with bifunctional free radical initiators. Compared with polymerization by monofunctional initiators, the bifunctional initiator system produces polymers of significantly high molecular weight at high monomer conversion. This is due to the presence of multiple labile peroxide groups having distinctively different thermal decomposition characteristics. The steady state reactor model analysis indicates that five unique regions of steady state behavior are present in a parameter space with reactor residence time as a bifurcation parameter. It is also shown that a broad range of polymer properties can be obtained by judiciously choosing the reactor operating conditions with the bifunctional initiator.

INTRODUCTION

Over the past few years, many papers have been published on the modeling and control of free radical polymerization reactors. The thrust of current research resides in the development of advanced polymerization technology through improved understanding of the poIymerization kinetics and reactor behavior, and implementation of sophisticated reactor control algorithms in order to tailor polymer properties. In many industrial polymerization processes a variety of initiator systems are practiced to produce polymers of various grades to meet diversified enduse requirements. It is quite surprising, however, that in most of the works reported in the literature only simple monofunctional initiators such as benzoyl peroxide or azobisisobutyronitrile (AIBN) have been considered. Multifunctional initiators are the initiators which contain more than one labile group (e.g. peroxy, perester, azo groups) having distinctively different thermal decomposition characteristics. Although the idea of using multifunctional initiators in free radical polymerization was introduced many years ago, it is only recently that systematic quantitative studies of polymerization kinetics with such multifunctional initiator systems have been performed (O’Driscoll and Bevington, 1985; Choi and Lei, 1987). Moreover, there is a rapidly growing industrial interest in using the multifunctional initiators to produce reactive polymers and polymers of precisely tuned properties more economically. By using properly chosen multifunctional initiators, one can achieve both high monomer conversion and significantly high polymer molecular weight simultaneously. Some multifunctional initiators have also been used for block copolymerization of viny1 monomers via controlled sequential monomer incorporation technique (Gunesin and f

Piirma,

1981; Piirma and Chou,

1979; Waltz

and Heitz,

1978). One of the main attraction of multifunctional initiators is that no major modification of existing polymerization equipment is required and implementation of them into the polymerization processes can be made easily. The use of multifunctional initiators also offers added flexibilities to polymer reactor engineers in optimizing polymerization reactor performance. However, the polymerization kinetics with multifunctional initiators are quite complex and understanding the polymerization characteristics is essential in applying the multifunctional initiators to industrial polymerization processes employing various reactor configurations. In this paper, we shall present a detailed analysis of steady state behavior of a continuous stirred tank reactor for styrene polymerization with bifunctional initiator system which is of the simplest form of the multifunctional initiators. In particular, the effect of bifunctional initiators on the polymer molecular weight properties will be elucidated. POLYMERIZATION

KINETICS

The bifunctional initiator system to be considered in this study is the diperoxyesters of the following structurally

symmetrical

form:

R, COO-OOCXCOO-OOCR1

(1)

where RI and X represent hydrocarbon ligands. The specific initiator system chosen in our numerical simulation study is the diperoxyester studied by Prisyazhnyuk and Ivanchev (1970): CH,

(CH,)&O~OOC[CH,CHCl]COOOOC(CH,),CH,.

(2)

(I) Upon

Author to whom correspondence should be addressed. 965

heating,

the

initiator

decomposes

into

two

966

KEE

radical Zk

species

JEONG KIM

and KYU YONG

CHOI

Table 1. Polymeric species

as follows:

CH3(CH2)6CO0.

Growing polymers

+. OOC[CH,CHCl]COO - OOC(CH2

)hCHs

(3)

P,:

Q.: s,:

(R)

(R’

1

initiation, propagation and termination. As shown in Table 1, six different polymeric species (P,, Q.. S,, T,, Z, and M,) can be defined in accordance with the nature of the end units of the polymer chains. Note that P, , Q. and S, are the growing (or live) polymer radicals with n-monomer units and T., Z, and M, are the dead polymers of n-monomer units. However, Q., T. and Z, species carry undecomposed peroxide groups (-COO-OOCR, ) on the chain ends. Thus, such polymers can be reconverted to active radical species via subsequent thermal decomposition of the peroxides. The decomposition reactions of the primary diperoxyester initiator (I) and the polymeric initiators can be described as following: Z

(4)

ku

Ql-S,+R

(5a)

Qn-&+R kd= z

2k,,

-QQ.+R

kdz Z,-P,, where

kdl

and

+ R

(n2 2)

(5b)

(n3 2)

(6)

(n 3 2)

(7)

kd2 denote

the

decomposition

.

polymers

Inactive

where the primary radical species R’ carries an undecomposed peroxide group which may decompose further during the course of polymerization. It is assumed that the peroxide groups of the same structure in the symmetrical initiator as shown in eq. (I) have the same decomposition rate constants when the ligand between the peroxides is small. If the bridge (i.e. hydrocarbon ligand X) between the peroxide groups is short enough for an inductive effect to be transmitted, the thermal stability of a group will change considerably when the neighbouring group decomposes (Ivanchev, 1979). For the bifunctional initiator shown above, it has been found that the decomposition activation energy of the peroxide group in R’ is quite different from that of the peroxides in the original initiator (I). When monomers are polymerized by the radical species R’, the polymers will carry labile peroxide groups and such polymers are called reactive polymers or polymeric initiators. As will be shown in what follows, quite complex reinitiation, propagation and termination reaction kinetics are resulted due to the existence of the two radical species (R and R’ ) in the polymerization reactor. A mechanism of polymer formation in free radical polymerization initiated by bifunctional initiators is called poly-recombinational polymerization because reactive macromolecules formed in the early stages of polymerization participate in the reaction through re-

%, -R+R

OOCR, COO-OOCR,

rate

T.: Z,,: M,:

constants initiators

R,COSOOC ------COO-OOCR, RICO0 COO-OOCR R,CO C)-----OOCR,

of the two peroxide and in the polymers,

I

groups in the primary respectively. Note that

both the primary initiator (I) and the polymeric species T, have dual functionalities because they contain two undecomposed peroxides of equal activities. Here, it is assumed that cyclization reaction and thermal initiation do not occur. The decomposition of primary radical species R’ is also assumed negligible. According to Ivanchev (1979), the decomposition rate constants of more stable peraxides (i.e. peroxides in Q,, T, and Z,) are independent of polymer chain length. The initiation of polymer chain propagation by the primary radicals takes place as follows: R+ML’t-P, R’+MThe propagation

(8)

k’2 Q1 .

reactions

(9)

are:

k, P, + M-P2. k, P, + M -P,*,

QI+M~Q~ k, Qn+M-Qnt, % S1 + M-S2 S, +M

2b -‘&+I

(1W (n 2 2)

(lob) (IIa)

(n > 2)

(IIb) (12a)

(n 3 2)

(12b)

where the propagation rate constants are also assumed to be independent of polymer chain length. Since S, contains two radicals per molecule, the propagation and the termination reactions involving these polymers occur twice as fast as those involving the other polymeric species. When the termination of growing polymer chains occurs exclusively by combination mechanism (e.g. styrene polymerization), the following termination reactions will take place: P,+P, J’,+

pL’M,+,

Q,&Z,+,

% Pm + S, -P,+m

(n, m 3

1)

(13)

(n,m2 1)

(14)

(n, m 1 1)

(15)

Styrene polymerization

967 n--l

Q. + QmATm+,

(n, m 2 1)

Qn +

(n. m

Sm~Qn+m

4k, S” + sm --s,+m

2

1)

(n, m G= 1).

(17)

above scheme. In eqs (13F(l&), the combination termination rate constants for the different polymeric species are assumed to be identical. In this kinetic scheme, chain transfer reactions have been ignored. With the polymerization mechanism proposed above, batch polymerization kinetics with the bifunctional initiator can be modeled as follows:

dl

and primary

-2k,,

dt=

dR’ ~ dt

= 2f,k,,Z-kki,R’M

(21)

For growing

polymers

k,,RM-kk,MP,

= k,M(P,_,

-kk,P1(P+Q+2S)

(22)

-P,)+k,,Z,-kk,P,(P+Q+2S)

n-1 +2k,

dQ, dt

C m=l

(n 2 2)

P,-,S,

-k,zQ1-ktQl(P+Q+W dt

(24)

--kdZQn+2kd=Tn+k~M(Qn-1-QQn) -kQn(P+Q+W n--l +2k C Qn-,L “=I

dS1 ~ = kd2Ql -2k,MS1 dt dS n= dt

(23)

= ki, R’ M - k, MQ,

dQm -=

dz,_-

--k,,Z,

polymers “$’ m-1

Qn-,,,Q,,,

(n 3 2)

(28)

Pn-mQm (n2 2).

(29)

n-1

dt

For monomers dM p= dt

(27)

+ k,

C #?I=1

and dead polymers

-ki,RM-ki,R’M-kk,M(P+Q+2S) (30)

dMm dt

n--l

k

c

=q,_,

(n > 2)

p”-mpm

(31)

where P, Q, S, T and Z are the total concentrations the corresponding polymeric species, i.e.

P=

1 -=I

P,

Q=cQ.

T=

5 “=2

T,

z=

S =

“=I

1 S, II=,

of

(32)

For primary

c z,. n=2

radicals and live polymeric

species (P.,

Q,

and S,) quasi-steady state approximation will be employed. In order to compute the molecular weight averages of polymers, the following molecular weight moments are used:

fi

where and are the initiator efficiencies which indicate the fraction of primary radicals (R and R’) being involved in chain initiation.

~

-2k,,T,+;

dt

(19)

(20)

dP 2 dt

inactive

(n 2 2).

‘L,

1

= 2f,k,,I-kk,,RM+k,,(Q+2T+Z)

dP, p= dt

C S,_,S, m=1

dT,_-

radicals

dR dt

fi

For temporarily

(18)

Note that various reactive polymeric species (e.g. Q., T,, Z,) containing undecomposed peroxide groups are formed by the combination termination reactions and these species, upon subsequent decomposition and polymerization, will lead to the formation of polymers having extended polymer chain lengths. The termination by primary radicals is assumed negligible in the

For initiator

+2S)+2k,

(16)

kd2Qn+2kpM(S,_,

I,.,

=

c

n=j

nk5.

(25)

-2k,S1(P+Q+2S)

(26)

Q,S(j= 1); T,Z(j= 31 (33)

OD 1: = c nkM, “=l

(34)

where & and Ag denote the kth moment of polymeric species < and dead polymers, respectively. In high conversion free radical polymerization, the termination reactions involving polymeric radicals become diffusion controlled and the termination rate constant decreases considerably with conversion. This phenomenon is referred to as gel effect. Although the gel effect in styrene polymerization is not as strong as in methyl methacrylate polymerization, the gel effect is not quite negligible at high conversion or low solvent volume fraction. In this study, the gel effect correlation suggested by Friis and Hamieiec (1976) for bulk styrene polymerization is used and modified for solution polymerization according to Hamer et al. (1981): gr = $

(n2 2)

C5 = P,

*

= exp [ - 2(BX

+ CX2

+ DX3 )]

where

-S,)-2k,S,(P+Q

E = 2.57 -

5.05 x lo-

C = 9.56-

1.76 x lo-*

D = 3.03+7.85x

1O-3

3 T (K) T (K) T(K)

(35)

968

KEE JEONG KIM

and KYU

and x = x,

(1 -f;i)

is the total concentration of monomer in the presence of solvent with volume fraction off,. ic: denotes the termination rate constant at zero monomer conversion. Figure 1 illustrates the variation in chain termination rate constants predicted by eq. (35) for different temperatures and solvent fractions, respectively. The incorporation of the gel effect correlation into the model improves the model accuracy and increases the model complexity as well. REACTOR

I’% = q(M,-

I’$ = q(Z, ,C,Vg=

M)-

(36)

Vk,M(P+Q+2S)

(37)

- I) - 2VkdI I I’(-An,)k,M(P+Q

pC,q(T,-T)+

+2S)-&A,(T-

T,).

(38)

Here, M is the monomer concentration, Z the initiator concentration, and T the reactor temperature. q denotes the volumetric flow rate of feed and product streams, h, the effective heat transfer coefficient and T, the coolant temperature. Physical properties of the polymer mixture (e.g. p, C,) are assumed constant. In

CHOI

this model the effects of thermal initiation and depolymerization which may occur at very high temperatures are ignored. Due to the presence of active polymeric species (P., Qn , S,) and inactive polymeric species (T,, Z,, M,), the above nonlinear modeling equations become quite complicated. The moment equations for inactive polymers (species M,, T, and 2,) take the following form: d;i$ -=

-;A;

+;k,A;,,

Wa)

dn: dt’=

-ii.:

+ k,k,OA,,,

(39b)

dt’

MODEL

For free radical homopolymerization of styrene with bifunctional initiator in a continuous stirred tank reactor of voIume V, mass and energy balances are represented by the following equations:

YONG

dLid

2= dt’

dA,, A= dt’

-- 1.~“2 + k (jL..,~.., 0

+ jL$,, 1

(39c)

-;i,,+fk&-

2k,, )LT,.o

(40a)

- 2ku A,,

(40b)

1

dR,, dt’

_

dR,, dt’

=

d dt’

di.,o

1 = --%z,,+ e

5

1. = -,x2.1

dt’

-

8

AT., + k~,,iJ,,

-5?.=,2+

k,(J.Q,o~e,~+

A&,,-

%,,4-.2

(41a)

k,A,,,Re,o-kk,,~,,,,

+k,(i.,,&,,

(4k)

+ ~p,l~e.O)- LjLz,, (41 b)

dlz, L= dt’

-b”,.,+k,(i,,~ly.2+22,.,Lp,,

+ jL,,,~.Q.O) (4lc)

- k.,zR,,,

The number average polymer chain length (X,) and the weight average chain length (X,) are defined by

X,=

1

1

iQ2+IS.2+iT.2t~Z,2=~i

A,,,

A,,

(42b) +

+

As.,

+h

+i-=.,

where ij,t represents the kth moment of polymeric species j. The polydispersity index (PD) is a measure of molecular weight distribution broadening and is defined by

1\

50

1

-3

kp,2+

PL+.

(43)

N

The moment eqs (39)-(41) are solved simultaneously with reactor modeling equations.

STEADY

-31 0.0

0.2

0.4 Monomer

0.6 Conversion,

0.6

1.0

X1

Fig. 1. Gel effect correlations for styrene polymerization.

STATE

MODEL

ANALYSIS

The modeling equations are reduced to dimensionless forms by using the following dimensionless variables and parameters:

Styrene

xp=

P+Q+2S (P+Q+2S)/’

969

polymerization

hc4 a = PC, VK(T, )’

1

Q= 2(a2

[-aa,P-aa,+{(a2P+a,)’

- a4)

+4a12ta2-a4)jfl

(51) f

E dl

b=-,

T, -

Y’=RT/’

S=

T

Tf t=t

Da = &c(Tf ),

8’

-;(P+Q)+;

(P+Q)‘+2

2 01

Q

(52)

where

K=-

2bo K(T/)

where

. The subscript f denotes

the feed condition

and (P + Q

+ 2S), is the total concentration of live polymers in the reactor at the feed temperature and concentration conditions [e-g. see eqs (5Ob(52)]. Then, the following dimensionless modeling equations are obtained: dX, -=

dXz --= dt

-xx,+/9

x,+7

dX,

-

(47)

(i) For fixed values of Da and p, use eqs (46) and (47) to obtain:

KDaexp[-&] =

x

=

3.

+KDaexp[-k]

(48)

fiXIs + aDa

(49)

l+aDa

where subscript s denotes the steady state condition. (ii) The dimensionless total live polymer concentration (X,) is computed by solving the following equations which are from the steady state zeroth moment all

eqs of P, Q and S: -a2(P+Q)P+(a3+a4Q+aSP)Q

E 62 *

Ya=RT/.

the results

of steps (i) and (ii) into eq.

F(X,,Da,/J)=

=0 (50)

for

-XX,+Da(l-xX,)X,, (53)

(iv) Vary Da and repeat

steps

(i), (ii) and (iii).

This procedure guarantees that all solutions are found for all admissible values of Da. The mathematical expressions of steady state polymer moments are given in Appendix. The numerical values of physical constants, kinetic parameters and standard reactor operating conditions are listed in Table 2. Note that the monofunctional initiators (Al and A2) are hypothetical ones used for the purpose of comparison with the bifunctional initiator system. The behaviour of the

Table 2. Numerical dard

1

1 +a,B’

aDa (X3 - 6).

Note that tz refers to the dimensionless heat transfer coefficient, /I the dimensionless heat of reaction, and Da the dimensionless mean residence time which can be changed experimentally by varying the reactant flow rate. Because of high degree of nonlinearity and interaction in the modeling equations, some care must be taken in obtaining the steady state solutions. At steady state, the LHS of the modeling eqs (45t(47) vanish and the steady state solutions are computed by the following procedure.

X2r

a5 =

(45) and solve the resulting nonlinear equation the monomer conversion, X, (0 < X, < 1): (44)

dt

RTf

=

(iii) Substitute

-Xz+KDa(l--X,)exp[-*]

dX, -=

1+2a,8’

4 Yr

-X,+Da(l-X,)X,exp[&](45)

dt

2a,a,B

a2a3e a4 =

operating

k,, = 8.90 k,, = 5.59 k, = 1.051 k, = 1.255

x x x x

values of kinetic parameters and stanconditions for styrene polymerization

1O”‘exp (- 23,473/RT), s ’+ 1Ol4 exp (- 30,387/RT), s ’+ 10’ exp (- 7,06O/RT),/l mol st lo9 exp (- 1,6SO/RT), l/mol s:

f;: = 0.23 (i = 1, 2)t (-AH,) = 16.2 kcal/molZ &, = 0.4 kcal/ 1 K: For monofunctional initiators: (Al) k, = 8.90 x 10” exp (- 23,473/RT), f = 0.23 (AZ) k, = 5.59 x lo’=+ exp (- 30,387/RT), f = 0.23 T,- = 300 K, f, = O&1.0,

T, = 303 K, C?=CLlOO

I,

s-’ s- ’

= 0.05 mol/l

TPrisyazhnyuk and Ivanchev (1979). *Brandrup and Immergut (1975).

970

KEE JEONG

monofunctional initiator A2 popular azobisisobutyronitrile RESULTS

AND

is similar (AIBN).

to

KIM

that

and KYU YONG

of

Region Region Region

DISCUSSION

The principal parameters which influence the behavior of the continuous styrene solution polymerization reactors are Da (or Q), a, /? (orfS), y, y, and 6. For given values of the system parameters the steady states may be calculated by solving the steady state nonlinear eqs (45 j(47). In practical situations, one is often interested in knowing the steady state multiplicity pattern existing for a given set of system parameters. With parameters 6, T’ and I, held fixed, the diagram showing the steady state behavior of the reactor has been constructed by using the singularity theory (Balakotaiah and 1984; Luss, Golubitsky and Schaeffer, 1979). Figure 2 is such a diagram in a-8 plane for the bifunctional initiator system. Note that five unique regions of steady state behavior are identified: Region Region

I: II:

Unique steady state Multiple steady state (S-shape

I

0.00 0

20

III: IV:

Isola and unique steady state Isola and multiple steady state

V:

shape curve) Mushroom.

F (XI,

Da, B) = 0

(54a)

~(X,JW)=O

(54b)

I

~(Xd’a.~)=o 1

in which F represents a steady state manifold obtained by combining three modeling eqs (45 j(47) into one by eliminating X2 and X, for fixed value of a. Across the hysteresis variety the number of solutions increases by two for increasing value of a. The criteria for the isola

for

CSTR

model

I

I

I

40

60

60

a

III

1.0 100

I

I 15.6

a I

L

0.422 10.9

11.0

a

11.1

(S-

Here, l-i (l-r ) represents the hysteresis (isola) variety which defines the parameter space at which a continuous change of the parameter causes the appearance or disappearance of hysteresis (isola) type multiplicity. Here, the criteria for the hysteresis variety (i.e. the appearance of multiple steady state) are:

curve)

inadequate

CHOI

11.2

a Fig. 2. Steady state behavior regions for styrene polymerization in a CSTR = 0.01, Ira = 0.025 mol/l.

with

bifunctional

initiator,

6

971

Styrene polymerization

? n c

ii -

972

KEE JEONG KIM

variety

are given

by eqs (54a),

(54b)

and:

For a sequence of a, eqs (54ak(54c) for the hysteresis variety and eqs (54a), (54b) and (54d) for the isola variety have been solved by using the Brown’s method which solves nonlinear simultaneous equations by the modified Newton’s method (Brown, 1969). In regions III and IV, isolated branches (isola) are observed. The existence of isola phenomena has been known for many years in various chemically reacting systems including continuous polymerization reactors (Schmidt at al., 1984). The isola cannot be obtained by simply varying the reactor residence time and special control scheme is required to operate the reactor at such steady state conditions. Since regions IV and V are so small, it will bc practically very difficult to confirm these tiny regions experimentally. This means that most of the reactor behavior will be represented by region I, II and III for practical operating conditions. It is also interesting to observe that unique steady state

and KYU

YONG

CHOI

behavior is never expected in bulk free radical polymerization reactors (i.e. .f. = 0.0). For adiabatic polymerization (i.e. cc= O.O),only type I and 11 steady state profiles will appear. Figure 3(a) and (b) show the similar steady state behavior diagrams for the monofunctional initiator systems Al and A2, respectively. The overall structures of the steady state behavior regions for the bifunctional initiator system and for the monofunctional initiator systems are quite similar. The concentration of peroxide groups in the initiator feed stream is held fixed at the same value for all cases, i.e. I/, = * IfA, = )Z,Az_ The steady state profiles of the reactor state variables (i.e. Xi : monomer conversion, X,: initiator conversion, T: reactor temperature) are illustrated in Fig. 4(a) for these three different

initiator

systems:

Monofunctional initiator (A 1): k,= 8.90x lO”exp(23,473/RT),s-'

I,a,= 0.05mol/l. Monofunctional

initiator

(A2):

k, = 5.59+ 10’4exp(-

30,387/RT),s-l

Z,A2= 0.05mol/l.

l-O-

o.o~ 0.6

Xl

Bifunctional

.-.P.

lF=--4

0.6

(B):

23,473/RT),s-'

krz = 5.59x 1014exp(-

30,387/RT),s-'

If,= 0.025mol/l.

0.4

0.2

initiator

k,, = 8.90x 10" exp(-

i

450

400 T (“K) 350

300_

V

5

10

15

20

9 (hr)

I

I

I

5

10

15

9 (hr)

(al

(

Fig. 4. (a) and (b).

b)

I 20

Styrene polymerization

0.8 0.6 fwj

300

350

x103

T CK)

450

400

2.5-

0.0

0.2

0.4

0.6

0.8

1.0

X1

(hr)

0

(d)

(c) x10-2

0.2 -

G

o,.

‘1 .E-z~~=__~_-_-r__ 0

OO!O 0

(hr) (e)

.LV.-

./--

T

5

10 0

15

cl __ 20

thr)

If)

Fig. 4. (a) Steady state profiles of state variables for three initiator systems: 01= 15, B = 0.5126, 6 = 0.01, I/B = 0.025 mol/l, If~t= If.42 = 0.05 mol/l. (b) Steady state profiles of number average chain length and polydispersity: Q = 15, B = 0.5126, d = 0.01, I/B = 0.025 mol/l, If~t = I~,42= 0.05 mol/l. (c) Steady state profiles of number average chain lengths vs. temperature and monomer conversion (X, ): 01= 15, p = 0.5126, 6 = 0.01, Ifs = 0.025 molfl, If4t = Ifa = 0.05 mol/l. (d) Weight fraction and number average chain length profiles of various inactive polymers: a = 15, ~9= 0.5126, d = 0.01, Ifs = 0.025 mol/l. (e) Weight fraction and number average chain length profiles of various live poiymers: 01= 15, fi = 0.5126, 6 = 0.01, I/B = 0.025 mol/l. (f) Distribution of undecomposed peroxides in various species: Cj = molar concentration of diperoxide in species j, &, = mole fraction of peroxides in species j, LY= 15, fi = 0.5126, d = 0.01, I/B = 0.025 mol/l.

974

KEE JEONG KIM and KYU

0.2

-

320

0

6

200

20

15

10

5

YONG

CHOI

-

0

I

I

I

5

10

15

e

(hr)

20

(hr)

(a)

Note that the steady state for the bifunctional initiator the middle of those for the itiator systems. However, the ties such as number average

profiles of X1, X, and T (B) are approximately in two monofunctional inmolecular weight properchain length (X, ) and

polydispersity (X,/X,) for the bifunctional initiator system are quite different from those for the monofunctional initiator systems as shown in Fig. 4(b). At high monomer conversions, itiator system produces polymers

molecular weight than those obtained by the monofunctional initiators. The potydispersity is slightly higher for the bifunctional initiator system than for the monofunctional initiator systems due to the presence of various polymeric species of different chain lengths. The variations of X N with steady state temperature and monomer conversion are more clearly illustrated in Fig. 4(c). The highest conversion is obtainable by

0.8 0.8 fwj 0.4

using the “slow” initiator (initiator A2) at high temperatures and long residence time; however, both high monomer conversion and high molecular weight of

0.0

polymers are obtained by using the bifunctional initiator (B) at shorter residence time. The high molecular weight obtained by use of the bifunctional initiator is due to the extended lifetime of peroxide groups which reside in various polymeric species such as Q., T. and 2,.

1.0 c 0 -22.0

fwi 0.4 0.2

@-----\

-

I

/

NH /

I 0.0

the bifunctional inof significantly higher

A-w 0

L----T

‘,=

Figure polymers

..-._

4(d) illustrates the X, of various inactive and their weight fractions in the polymer.

.’

5

10

8 (b)

(hr)

15

20

Fig. 5. (a) Steady state profiles of state variables for varying 01values: /I = 0.5126,6 = 0.01, Ire = 9.025 mol/l, a; A = 15.0, B = 19.9, C = 22.0. (b) Weight fraction profiles of inactive polymers for varing a values: fi = 0.5126, 8 = 0.01, ffB = 0.025 mol/l.

Styrene

Note that as steady state reaction temperature creases [e.g. upper solution branch, Fig 4(a)], decomposition

of the peroxide

groups

polymerization

inthe

in T, and Z,-

type polymers is increased and more P, or Q.-type polymers are produced [cf. eqs (6) and (711. When the growth of these live polymeric radicals is terminated, polymers of much higher molecular weight are obtained. It is also interesting to note in Fig. 4(b) and (d) that when the concentrations of T,- and Z,-type polymers are low, polydispersity is lowered due to the reduced heterogeneity of the polymer chain length distribution. The numerical calculation indicates that the concentrations of live polymers (Pm, Q. and S,) are order of magnitude lower than those of inactive polymers as shown in Fig. 4(e). This means that the overall polymer molecular weight is determined predominantly by the dead or inactive polymers. Figure 4(d) also shows that Z--type polymer is a predominant species when the reactor is operated with residence time shorter than 12 h. But the monomer conversion obtainable is only below 2O’j/, [Fig. 4(a)]. The molar concentration (Cj) and the mole fraction ( fmj) of undecomposed peroxide groups in the primary initiator and various polymeric species are shown in Fig. 4(f). In the middle steady state branch (i.e. t) = 2212 h) where the monomer conversion is about 20-70 74,. the undecomposed peroxides reside mostly in T,- and Z.-type polymers. However, as monomer conversion and reactor temperature increase (i.e. upper solution branch), the concentrations of peroxides in those inactive polymers decrease sharply by thermal decomposition and, as a result, the polymer molecular weight increases. If the production of polymers containing high concentration of peroxide is desired, the reactor should be operated at the middle steady state. Such reactor conditions may be practically important, if free radical block copolymerization is performed in a series of CSTRs operating at different polymerization conditions in order to minimize the formation of homopolymers. A special stabilizing control is of course required to operate the reactor at such steady states. The steady state reactor behavior for three different values of a (dimensionless heat transfer coefficient) with the bifunctional

initiator

is shown

regions of steady state behavior of the polymerization reactor are present. Compared with monofunctional initiator systems, the bifunctional initiators provide higher monomer conversion and polymers of higher molecular weight. This implies that wide range of reactor operating conditions can be used to produce polymers of high molecular weight more effectively with bifunctional initiators. Our simulations also show that CSTRs can be used to produce reactive polymers containing undecomposed peroxide groups. Analysis of steady state stability and transient reactor behavior will be reported in our forthcoming paper. Acknowleduemenrs-This research was sunnorted bv the Systems Research Center at the Universi;; of Ma&land through SRC Fellowship to Kim. Authors are also indebted to the Computer Science Center of the University of Maryland for computing time.

NOTATION

AC

CP Da Ed 2 St h, AH, I ZJ Ifs

z,a,

If.42

(b). As predicted in Fig. 2, the S-shaped steady state curves become more exaggerated as a increases for fixed value of /3 and isola begins to appear with further

peroxide residence

groups increase with time (e.g. 0 > 10 h).

a

at

long

M MJ M”

reactor p,

PD CONCLUDING

REMARKS

In this paper, the steady state characteristics of styrene polymerization in a CSTR with bifunctional initiators have been investigated. For the diperoxyester initiator system considered in this study, six different

heat transfer area, cm2 heat capacity of reaction Damkohler number

mixture,

cal/mol

Q" 4 R R’

K

decomposition activation energy, cal/mol activation energy of propagation, cal/mol solvent volume fraction gel effect correlation factor, k,/k,, heat transfer coefficient, Cal/cm’ s K heat of reaction, cal/mol initiator concentration, molfl initiator concentration in feed, mol/l feed concentration of bifunctional initiator, mol/l feed concentration of monofunctional A 1, mol/l feed concentration of monofunctional A2, mol/l initiator decomposition rate constant, initiation rate constant, l/m01 s propagation rate constant, l/m01 s combination termination rate constant, combination termination rate constant conversion, l/m01 s

in Fig. 5(a) and

increase in a. Figure 5(b) illustrates that polymer composition also changes significantly with variation in a. Note that the weight fractions of inactive polymers (T., Z, -type) which contain undecomposed

975

polymeric species are identified according to their end groups. The polymeric species carrying undecomposed peroxides on chain ends can reinitiate the propagation and, as a result, overall lifetime of radicals is extended and the molecular weight of polymer can be significantly increased. It is also shown that five unique

initiator initiator s-i

1 /mol s at zero

monomer concentration, mol/l feed monomer concentration, mol/l dead polymer concentration of n monomer units, mol/l live polymer concentration of n monomer units, mol/l polydispersity concentration of live polymer species defined in Table 1, mol/l volumetric feed flow rate, l/s primary radical concentration mol/l concentration of primary radicals containing

976

undecomposed

T T, TlT, t t’ V X1 XZ X3 x, X, XW

Greek

*U A;

group,

mol/l

CHOW

initiators of radical polymerization and block copolymerization. Polymer Sci. USSR 12, 514524. Schmidt, A. D., Clinch, A. B. and Ray, W. H., 1984, The polymerization continuous behavior of dynamic reactors--III. An experimental study of multiple steady states in solution polymerization. Chem. Engng Sci. 39, 419432. Waltz, R. and Heitz, W., 1978, Preparation of (AB),-type block copolymers by use of polyazoesters. J. Polymer Sci.: Polymer Chem. Edn 16, 1808-1814.

APPENDIX: STEADY STATE POLYMER MOMENTS Inactive polymers Zeroth moment. 2;

dimensionless total live polymer concentration number average polymer chain length weight average polymer chain length concentration fined in Table

Z,

P

peroxide

concentration of live polymer species defined in Table 1, mol/l temperature, K coolant temperature K feed temperature, K concentration of inactive polymer species defined in Table 1, mol/l dimensionless time time, s reactor volume, cm3 monomer conversion initiator conversion dimensionless temperature

S”

; Y Yl 6

andKuuYo~~

KEEJEONGKIM

of inactive 1, mol/l

polymer

species

de-

letters

a

(A.1)

ok, f’Q Az.o = 1 + Ok,,

(A.3

Sk,Q’ T,” = 2(l + 28k,*)’

(A.3)

First moments.

dimensionless heat transfer coefficient dimensionless heat of reaction dimensionless propagation activation energy dimensionless decomposition activation energy dimensionless coolant temperature density of reaction mixture, mol/l kth moment of polymer species < kth moment of dead polymer

A: = t)k,Pi,,

Balakotaiah, V. and Lass, D., 1984, Global analysis of the multiplicity features on multi-reaction lumped parameter systems. Chem. Engng Sci. 39, 865-881. Brandrup, J. and Immergut, E. H., 1975, Polymer Handbook, 2nd edn. Wiley, New York. Brown, K. M., 1969, A quadratically convergent Newton-like method based upon Gaussian elimination. SIAM .I. Analysis

(A.6) Second moment. 1: = ok, (PA p.z + j.lp,, )

a2.2

WW,,,

(A.7)

/‘Q.I + pAQ.Z f QAp.2)

=

1 + ok,,

(A.8)

(A.9) Live polymers First moments.

6, 56G569.

Choi, K. Y. and Lei, G. D., 1987, Modeling of free radical polymerization of styrene by bifunctional initiators with peroxide groups of unequal thermal stabilities. A.I.Ch.E. J. (in press). Friis, N. and Hamielec, A. E., 1976, Gel effect in emulsion polymerization of vinyl monomers. ACS Symp. Ser. 24, 82-91. Golubitsky, M. and Schaeffer, D., 1979, A theory for im perfect bifurcation via singularity theory. Commun. Pure appl. Math. 32, 21-98. Gun&n, B. S. and Piirma, I., 1981, Block copolymers obtained by free radical mechanism-II. Butyl acrylate and methyl methacrylate. J. appl. Polymer Sci. 26, 3103-3115. Hamer, J. W., Akramov T. A. and Ray W. H., 1981. The dynamic behavior of continuous polymerization reactors--II. Chem. Engng Sci. 36, 1897-1914. Ivanchev, S. S., 1979, New views on initiation of radical polymerization in homogeneous and heterogeneous systems. Review. Polymer Sci. USSR 20, 2157-2181. O’Driscoll, K. F. and Bevington, J. C., 1985, The effect of multifunctional initiators on molecular weight in free radical polymerization. Euro. Polymer J. 21, 1039-1043. Piirma, 1. and Chou, L. P. H., 1979, Block copolymers obtained by free radical mechanism--I. Methyl methacrylate and styrene. J. appl. Polymer Sci. 24, 2051-2070. Prisyazhnyuk, A. I. and Ivanchev, S. S., 1970, Diperoxides with differing thermal stabilities of the peroxide groups as

(A.4) (A.5)

REFERENCES

Numerical

= ;Bk,P’

a p.1=

(~I+~I~Q,,)

(A.lO)

Cl

d, IQ.1 = -e, i,,, Second

as.2

=

(A.1 1)

k,,M,(l

-XX,)S+fk,,,ibQ.,

(A.12)

k,U’+Q)

moments.

k,M,U

(az + bzaQ.z)

a p.z=

-

‘Q.Z=

-e,

(A.13)

C2

dz

(A.14)

- X,)Ws,l

=

+ S) + 2k&,, + +k.+> 1 Q,2 k(P

+

Q)

(A.15)

where a, = 2fkk,,I,(l-Xz)+kpM,(l +k,,(Q+2T+Z)+ k,, P b, =p+p

f’+Q

@krka P

1 + ok.,,

-X,)P Zk,M,(l

-X,)SP

f’+Q

(A.16) (A.17)