Chemical Kinetics of a two component phase segregated system. A simple rate model

9 1997 Elsevier Science B. V. All rights reserved. Dynamics of Surfaces and Reaction Kinetics in Heterogeneous Catalysis G.F. Froment and K.C. Waugh, editors

Chemical Kinetics of a two component system. A simple rate model

495

phase segregated

Amir A. AI-Haddad* and Johnson Mathew Chemical Engineering Department Kuwait U n i v e r s i t y - PO Box 5969 Safat 13060- Kuwait 1. ABSTRACT Considerable research has been performed on polymeric systems that exhibit liquid crystalline or mesomorphic behavior. The principal reason for this effort was that these materials might be developed as ultrahigh strength materials. Jackson and Kuhfuss from Tennessee Eastman demonstrated that liquid crystalline behavior existed in copolymers based on poly(ethylene terephthalate) (PET) and para-hydroxy benzoic acid (ABA). However, intricate details pertaining to the polyesterification kinetics have remained unexamined. Transesterification reactions between poly(ethylene terephthalate) PET, and acetoxybenzoic acid (ABA) were conducted using the melt polymerization technique to understand the transesterification kinetics of a phase segregated system. The transesterification kinetics of two compositions PET 20 / 80 (ABA) and PET10 / 90 (ABA) have been studied at 260, 275, 290 and 305~ using dibutyl tinoxide (0.1 mole percent) as a catalyst. Homopolymerization of acetoxy benzoic acid was also studied at similar temperatures and catalyst concentration. In the present experimental work moles of acetic acid found experimentally is computed using a standard procedure. The rate constant k is determined. The role of the catalyst is also evaluated. Keywords:Copolymerization kinetics, transesterification reactions, melt polycondensations. 2. I N T R O D U C T I O N Aromatic polyesters undoubtedly represent the most important class of thermotropic nematics. 1-5 Fully aromatic rod-like homopolymers such as poly(poxybenzoate) or poly (p-phenylene terephthalate) melt at temperatures which are too high to form a stable nematic mesophase. 4 However if the regular chemical structure of the homopolymer is disrupted, the melting temperature is reduced and it is possible to obtain thermotropic nematics. 1"5

*Author for correspondence e-mail:[email protected] Fax #: (965) 483-9498

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497 Copolyesters of poly(ethylene terephthalate) and 4-acetoxybenzoic acid (PET / oxybenzoate) were synthesized by Jackson et al. through high temperature melt transesterification. H o w e v e r i n t r i c a t e d e t a i l s p e r t a i n i n g to t h e polyesterification kinetics have remained unexamined. In this system, insertion of 4-oxybenzoate moieties, with stiff rod like conformations, into flexible PET chains fosters the development of thermotropic character within a definite range of copolyester composition. Optical and electron microscopy examinations, 6 coupled with data from x-ray and conventional electron microscopy, endorse the existence of ordered domains or lamellar 4-oxybenzoate blocks in the PET 20 / 80 ABA copolyester. The c o o l i n g of a n a n n e a l e d m e l t is k n o w n to t r i g g e r a b i p h a s i c s t r u c t u r e . 6 The foregoing discussion clearly shows t h a t while there is information available on the structure property aspects of PET / ABA systems, but there is a total lack of kinetic information. This work is an a t t e m p t at formulating a plausible phase segregated kinetic model for the PET 20 / 80 ABA and PET 10 / 90 ABA melt copolyesterification reaction. There is no published literature on the melt polyesterification kinetics of a phase segregated two component system like PET / 80 ABA and PET / 90 ABA. Here we explore the kinetics of a two component system wherein many parallel reactions take place simultaneously. Precipitation has been observed during the synthesis of these polymers. 3. E X P E R I M E N T A L 3.1. M a t e r i a l s

4-acetoxybenzoic acid was prepared by sodium hydroxide catalyzed reaction of 4-hydroxybenzoic acid with .acetic anhydride and was recrystallized using methanol. The yield was around 70% and had a melting point of 184~ Poly(ethylene t e r e p h t h a l a t e ) (1800 ~m), of intrinsic viscosity 0.62 (Aldrich chemical company), was used as received. 3.2. R e a c t o r

A 250 ml glass reactor as shown in Figure 1 was used for the melt transesterification kinetic investigations. 3.3. P r e p a r a t i o n o f C o p o l y e s t e r s

Polyesterification kinetics were investigated for i

.

iiiii-

ABA homopolymerization PET / 80 ABA and PET / 90 ABA.

P E T m e l t e d a r o u n d 260~ and degraded around 326~ on k e e p i n g isothermally for 20 minutes. The reaction temperatures chosen were 260, 275, 290 and 305~ A dry nitrogen b l a n k e t was m a i n t a i n e d t h r o u g h o u t the experiments to prevent oxidative degradations. The rate of byproduct evolution (acetic acid) was monitored as a function of time. Sodium acetate (0.1 mole

498 percent) was used as catalyst for the melt transesterification reactions. This h a s h i t h e r t o not been e v a l u a t e d as a catalyst for the s y n t h e s i s of P E T / ABA systems.

4. R E S U L T S A N D D I S C U S S I O N In our earlier study 7 it was observed t h a t second order kinetics was valid for polyesterification of ABA. It is assumed t h a t in the present analysis the s a m e m e c h a n i s m is valid for homopolyesterification. For t r e a t i n g the second reaction it was a s s u m e d t h a t the 4-acetoxybenzoic acid (ABA) monomers approach a P E T homopolyester, followed by a reaction. This also can be t r e a t e d as a second order reaction between a P E T segment and an ABA oligomer. In the h o m o p o l y e s t e r i f i c a t i o n of ABA 7 a tacit a s s u m p t i o n was m a d e t h a t oligomers upto D P = 5 were in the melt.

4.1. Kinetics and M e c h a n i s m The reactions which occur w h e n PET and 4-acetoxybenzoic acid are h e a t e d together or m a i n t a i n e d isothermally at t e m p e r a t u r e s of crystalline P E T m a y be depicted below. 0

II

~

3

0

II

II -OH+

~

o

0

/

H

O

~

II

__-_~

3

o OH+CH

(A)

COOH 3

Oligomer 2

II -OCH C H O 2 2

+CH

- C

---

OH

3

PET

Oligomer

0

+ CH 3 C O O H

Copolymer

Scheme

1

(B)

499 There are m a n y possible ways by which acetic acid can be g e n e r a t e d t h r o u g h route (A), like the d i m e r reacting with a n o t h e r monomer or t r i m e r or t e t r a m e r or other h i g h e r oligomers. W h e n a reactive polymer like P E T is incorporated into this reaction the kinetics becomes even more complicated. Considering reaction A, one finds t h a t for the formation of an even or an odd oligomer w i t h a n y n u m b e r of r e p e a t units, two different functional groups i.e. O II

m C O O H or - O - C - C H

3 r e m a i n as end groups.

Thus one can note the existance of m a n y variables (rate c o n s t a n t s ) for t h e s e independent reactions. It is difficult to solve these m a n y variables analytically. Hence the following a s s u m p t i o n s are m a d e to simplify the kinetic picture.

_

34-

Major p a r t of the ABA homopolymerization reaction leads to the formation of oligomers (dimers). A dimer of ABA can react with P E T molecule. Since dimers are a s s u m e d to be the major p a r t during the initial stages of the reaction, f u r t h e r reaction of ABA can only be with a P E T molecule. Processes exist wherein higher oligomers of ABA are formed, but their rate of reaction is a s s u m e d to be too slow for the generation of acetic acid a n d hence of no consequence in the m a s s balance of ABA. Hence the above two reactions (A & B) are given prime importance.

If Z denotes the d i m e r formed by ABA reaction the following steps are a s s u m e d for the polymerization reaction X -+" X (a-x) (a-x)

kl

)Z-+-HA z x

(I) Z + (x-y)

P

k2 > Z P + H A

(p-y)

y

(y)

where X, Z, P, ZP, HA, a, x, z, p and y denotes ABA, dimer of ABA, poly(ethylene t e r e p h t h a l a t e ) , copolymer, acetic acid, initial concentration of ABA, n u m b e r of moles of ABA converted, initial concentration of dimer, initial concentration of P E T segments and n u m b e r of moles of P E T segments converted. Rate of dimer formation can be given as dx dt

-dX ~=kl(a-x

)2

dt

(1)

From m a s s balance we have

or

x =z +y z -- x - y

(2a) (2b)

Rate of copolymer formation is V~

l~g]

"-__.e_~= ---.__.__v_r= k2 z ( p - y) dt

dt

(3)

500 wi

•dp

dt

dt

-__e_,=

= k2 ( x - y ) ( p - y)

(4)

Total r a t e of acetic acid p r o d u c t i o n can be given by the algebraic s u m of e q u a t i o n s 1 and 4 as d(HA.__...~)= d(x + y) = kl (a - x) 2 + k 2 (x - y) ( p - y) dt

(5)

dt

A s s u m e r a t e of (z) is r a t e controlling step and the incorporation of d i m e r (z) into the polymer is fast so t h a t the concentration of (z) at any time is very small, t h u s production of (z) can be set equal to zero. Thus dz

d ( x - y)

dt

dt

= k 1 (a

- x) 2 - k 2 (x - y) ( p - y) = 0

(6)

T h u s equation (5) can be given as d(HA_____~)= 2 k I (a - x) 2

(7)

dt

Now, we take into account t h a t the reacting system is n o n h o m o g e n e o u s a n d s e p a r a t e s into two different phases i.e. a polymer rich (PET) and poor p h a s e w i t h c o n c e n t r a t i o n s d' a n d d". It is a s s u m e d t h a t the reactions proceed in both the p h a s e s by the scheme shown in (I). Consider a new distribution coefficient (k) which is r e p r e s e n t e d as C'

K .

.

.

C"

m' v'

(8)

.

m" v"

w h e r e m' and m" are the corresponding masses and v ' / v " are two p h a s e volumes r e p r e s e n t e d by 7It is noted t h a t m

m'= ~ m and m" = ~ I+TK 1+~ 1 7K

(9)

For both the p h a s e s we a s s u m e equation to be valid. d(nA) 1

= 2 k I (a'-x' )e

Thus (10)

dt

for the second p h a s e we have d(HA)

1

d(HA)'

1

d(HA)"

dt

1+- 1 7

dt

1 + ~,

dt

(11)

501 Equation (7) can be replaced by d(HA----~) I I += 2dkl t

T(1 x+ 7-)K) K2) 2 1 (a 1-

(12)

where the notations like a, x and HA have similar meaning to that in equation (7). For K = 1 i.e. no phase segregation, equation (12) reduces to equation (7). The new term I1 + T(1-K2_) (1 + 7 K) 2 J1 is an additional term to replace the rate constant kl which is affected by phase separation. Let the new term obtained be represented 1 by kl. Solution of equation (12) under condition of equation (6) and solution of equation (9) and (10) leads to 2a 1 =l+k]at 2a-y-x 1-P

(13)

Figure 2 shows experimental data points for the catalyzed ABA homopolymer system at different temperatures and fitting curves according to equation 13. This figure also indicates t h a t the reaction rate model is adequate. Rate constants and activation energies are listed in Table 1. It is obvious that the catalyst sodium acetate plays a very marginal role. Arrhenius plots for catalyzed and uncatalyzed ABA homopolyesterification reaction is indicated in Figure 3. Kinetics in systems comprising 80 to 90% of ABA were also studied and evaluated according to equation 13 both for uncatalyzed and catalyzed reactions. 1 The quantity is taken as the average degree of polymerization. Number (l-p) of reactions were carried out between 260 - 305~ in steps of 15~ interval. Typical examples are presented in Figure 4 and 5. It is obvious that the experimental data points can be modelled by equation 13. The rate constants for different reactions are given in Table 1. Figure 6 and 7 depicts a typical Arrhenius plot for uncatalyzed and catalyzed PET20 / ABA 80 and PET 10 / ABA 90 composition. Table 1 reveals that no remarkable changes in rate constants and activation energies occur with rising ABA content. Figures 4 and 5 shows slight periodic deviations of experimental d a t a points from the s t r a i g h t line for higher temperatures. This could reflect periodic phase dissolutions and phase separations during the course of the reactions. 5. C O N C L U S I O N Kinetics of a two component system, PET and ABA in which phase separation occurs has been investigated. To retain simplicity of the analysis few assumptions were made. A generalized scheme in which acetic acid is produced through two channels is considered valid for PET rich and poor phase. Kinetically both these reactions were assumed and shown to be of second order with respect to reactants. Steady state approximation has been considered. Parameters were chosen such that the least squares deviation between moles of

Table

tg~

1

t,9

Rate constants from second order plots of ABA and PET / ABA systems

System

Composition

ABA 100

PET / ABA

20 / 80

PET / ABA

10/90

Temperature oC

Uncatalysed rate constant Lit mol 1 sec -1

Catalysed rate constant Lit mo1-1 sec 1

260 275 290 305

0.0118 0.029 0.070 0.082

0.023 0.038 0.080 0.098

260 275 290 305

0.002 0.010 0.018 0.029

0.004 0.029 0.038 0.032

260 275 290 305

0.006 0.018 0.030 0.038

0.01 0.029 0.04 0.055

Uncatalysed EOA (Kcal / mol)

Catalysed EOA (Kcal / mol)

17.1 +_3

15.8 +_2

18.2 +_3

8.8 +_3

19.6 +_4

10.1 +_3

503 19

17 [] A o

15

15

"-"

11

I

--

9

1 0

4

8

12

16

20

TIIME(min)

Fig.2. S e c o n d - o r d e r p l o t i l l u s t r a t i n g t h e effect of t e m p e r a t u r e for s o d i u m a c e t a t e (0.1 mol% c o n c e n t r a t i o n ) c a t a l y z e d r e a c t i o n s for ABA

260~ 275~ 290~ 305~

504

9 (cat)

[] (uncat)

-2

t2

-3

-4--

-6

~

~

!

t

~

l

~

~.

"

~

i

0.00177 0.00178 0.00179 0.0018 0.00181 0.00182 0.00183 0.00184 0.00185 0.00186 0.00187 lfr

Fig. 3. Arrhenius plots for u n c a t a l y s e d and catalyzed ABA reactions

e-t.-

~

I

0

*#

~

OZ.,

O8

:3

--4

b

ot

Po

Ob

03

i

7 J . m

[ !

FO

FO ! !

pO

1/(1-P) r'd !

cb

13

9

o

po

~n 0

U~ 0

~ u~ Po po Po ~" o to --4 m

II

I

I

L~

o L~

0

el'-

~0

e-F~

I

ee-

0

0

Crl

E

j~

PO 9

GO

-

I

i

0 0

1

I

I

.

i

n

i

i

I

~ i

o~ i

PO

-~ 9

1/(1-P) I

I

l

l

i

~

5 ' 0 to -.4 @ ~. t.n 0 t.~ o

loo.o

l

o~

PO ~ I

c)J 9

OX

L/I

597

-e4 I, u..rdct~T 9

_2.6l

Cs

-2-8

-5"0 y c'"

-3"2

-3-4

0

-3"6

-3"8 O 1

0-00175

l

1

1

0"00179

1

0-00183

I

1

O.00157

1/T

Fig. 6. A r r h e n i u s plots for u n c a t a l y z e d a n d c a t a l y z e d P E T 20 / 80 ABA

508

-0.5

9 (eat)

[]

(uncat)

-1

-1.5

-2

-2.5

-3

-3.5

-4

-4.5

i

~

'

0.00172 0.00174 0.00176 0.00178

;

0.0018

!

I

1

0.00182 0.00184 0.00186 0.00188

1/T

Fig. 7. A r r h e n i u s p l o t s for u n c a t a l y z e d a n d c a t a l y z e d P E T 10 / 90 A B A r e a c t i o n s

509 acetic acid produced and theoretically predicted is a minimum.

Plots of

1

(l-p) versus time were found to generate linear fits. The kinetic order for the dimerization steps is determined independently. The polymerization catalyst is found to play a very marginal role. ACKNOWI~DGEMENT The authors would like to acknowledge the generous funding from the research administration of Kuwait University under project number EC 065 without which this work could not be initiated. REFERENCES

1-

Preston, J. Angew, Makromol. Chemie 1982, 109 / 110, 1.

2-

Dobb, M.G. and McIntyre, J.E. Adv. Polym. Sci. 1984, 60 / 61, 61.

_

McFarlane, F.E., Nicely, V.A and Davis, T.G. Contemporary topics in polymer science, Vol. 2 (Eds. E.M. Pearce and J.R. Schae'fgen), Plenum Press, New York, London, 1976, p. 109.

4-

Jackson, W.J., Jr. Br Polym. J. 1980, 12, 154.

5-

Jin, J.I., Antoun, S., Ober, C. and Lenz, R.N. Br. Polym. J. 1980, 12, 132.

6-

Zachariades, A.E., Economy, J., Hogan, A . J . J . Appl. Polym Sci. 1982, 27, 2009.

_

Mathew, J., Bahulekar, R.V., Ghadge, R.S., Rajan, C.R., Ponrathnam, S., and Prasad, S.D. Macromolecules, 1992, 25, 7338.