- Email: [email protected]
Complex linear polycondensation—I Semi-batch reactor
Chemical Engineering
Science,1972,
Vol. 27, pp. 2219-2232.
Pergamon
Press.
Printed in Great Britain
Complex linear polycondensation - I Semi-batch reactor J. W. AULT? and D. A. MELLICHAMP Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, California, U.S.A. (Receioed 6 July 1971; accepted 14 January 1972) Abstract-A kinetic model which takes into account the presence of zero and monofunctional as well as bifunctional species was shown to correlate experimental ester interchange reaction data from the literature. In a second study, the two-stage production of poly(ethylene terephthalate) in a well-stirred semi-batch reactor was simulated. Zero and monofunctional species present in the product from the “monomerization” stage, which ordinarily result in “end-capping” in the second stage, were shown to lead to a higher molecular weight product under certain conditions of the relative reaction rates. INTRODUCTION
engineering standpoint, the most useful polymer property is the number average degree of polymerization due to the fact that most other polymer properties are primarily functions of the number average molecular weight. Hence, efforts to model reversible polycondensing systems have been directed at obtaining simple but rigorous relations to compute the degree of polymerization. As an example Mellichamp [ 11 showed that the polymerization of poly(ethylene terephthalate) can be modeled by a set of equations for the three forms of by-product species (speaking loosely: the endgroup quantities) if an idealized reaction mixture containing only bifunctional species is assumed. Unfortunately, many important industrial polycondensation processes involve mixtures of different functionality species, e.g. the two-stage production of poly(ethylene terephthalate) from dimethyl terephthalate (DMT) and ethylene glycol. In the first stage, DMT is exchanged with ethylene glycol to form his+ hydroxyethyl terephthalate (the monomer of poly(ethylene terephthalate)) and methanol which is continually removed from the reacting mixture. The “monomer” is condensed in the second stage with the continuous removal of the ethylene glycol formed [2]. Several papers in the FROM
AN
literature[2,3] report that it is essential to drive the ester interchange reaction (first stage) to completion before proceeding with the polymerization reaction (second stage). This is to insure that the methoxy groups are minimized in order that limitation in chain growth during polymerization not occur. In actual industrial practice, this supposition frequently is not observed[4]. The product of the ester interchange stage may contain as much as lo-25 percent of non-transesterified methoxy groups which take part in the reactions of the polymerization stage. The polymer obtained is of satisfactory high molecular weight [4]. Reacting systems of this type involve molecules of zero functionality (DMT and its higher oligomers), monofunctionality (methanol, the singly substituted mixed ester and its higher oligomers), and bifunctionality (ethylene glycol, the monomer and its higher oligomers). Four distinct reaction mechanisms are involved simultaneously (ester interchange, transesterification, polymerization, and rearrangement). This series of complex polycondensation reactions can be conveniently exprssed in terms of an alphabetic sequence of three letters, if only linear polycondensation products are considered. Conforming to the notation used by Ault [5] A is used to designate a free ethylene
?Present address: Chevron Oil Field Research, La Habra, California, U.S.A.
2219
J. W. AULT
and D. A. MELLICHAMP
glycol species (HOCH2CH20H), an end-group ethylene glycol ester unit (HOCH,CH20-), or an internal ethylene glycol ester unit (-OCH,CH,O-). The terephthalyl unit (-OCQCO-) is designated by B. C is introduced to represent free methanol (CH,OH) or the end methanol ester group (CHIO-). There are no internal methanol species.
Ester Interchange
Transesterification
(2) ...AT+CT...~...AI...+C~ T Polymerization
Ester Interchange ...AT+AT...~...AI...+AF. v
A+CBC * ABC+C A+ABC *ABA+C A + CBABA * ABABA + C
Transesterification ABC + CBC * CBABC + C ABA + CBC 13 ABABC + C ABABC +ABC F? ABABABC + C
(1) Polymerization ABC+ABC ABC+ABA ABA+ABABC
* CBABC+A ti ABABC+A * ABABABC+A
The Rearrangement reactions collapse exactly to zero. The end-group quantities -AF represents all “free” A species, AT represents all “terminal” A species, AI represents all “internal” A species, and C, and CT represent all “free” and “terminal” C species respectively - represent molar quantities or concentrations which may be converted to dimensionless quantities. It is the objective of this study to simulate the two-stage production of linear poly(ethylene terephthalate) in a semi-batch reactor. The collapsed rate expression model will be employed in an attempt to resolve the conflicting points of view concerning completion of reaction at the end of the tist stage. In a preliminary study, the usefulness of the collapsed model in correlating rate data available in the literature will be demonstrated. REACTION
Rearrangement ABC+ABABC G CBABC+ABA ABABC+ CBABC * CBABABC+ABC ABABA +ABABC * CBABABA +ABA
Ault further showed that the individual kinetic rate expressions describing the reactions of species of mixed functionality can be collapsed to a set of three (pseudo) second-order reversible rate expressions which can be used to compute five essential end-group quantities.
MODEL FOR A SEMI-BATCH REACTOR
The collapsed material balance equations required to describe ester interchange, transesterification, and polymerization occurring simultaneously in a semi-batch reactor were derived by Ault. In order to make the equations applicable to a varying reaction volume, as in the case of the semi-batch reactor simulated in this study, it is necessary to define the volume of the reacting medium. V = V,,-(Mass
Out)/pO.
(3)
Equation (3) implies that the liquid mass density is a constant equal to the initial density, po.
2220
Complex linearpolycondensation- 1
In many liquid reacting systems this is the case. Defining a dimensionless reactor volume as
v=;=l-Ih$;;i&
programmed reactor and the dimensionless pressure as II(e). Then Q as a function of reaction time becomes
Q(e) = QVL n(N).
(4)
0
the dimensionless material balance equations for a varying volume in a semi-batch reactor become
dAF_ 1 ---B(~E-~,)-Q$&~(A,)
The total mass leaving the semi-batch reactor Simply the tOtd mass Of methai’iO1, CF, and ethylene glycol, AF , taken overhead by Q.
iS
(5) Mass Out = (Initial Moles)
d0
~=@zE+RT)-QX(CF)
(6)
==+(RE-2Rp-RT) de
(7)
dG_ -d8
(8)
d0
1 $R”+R,)
X
RE = f+Cd, P
reversible
-A+] E
x,=
l-t&&
2A
(16)
The initial conditions required for Eqs. (5)-(9) are quite simply computed from the definition of the end-group quantities. (Ault [5] gives details.)
collapsed
(10) NUMERICAL VALUES EQUILIBRIUM
(12) The volatile species (AF and CF) and the species (AT, CT, and A,) are dimensionless molar quantities. 0, the dimensionless reaction time, is defined as k&(O) t, where 5 (0) is the initial molar density. The dimensionless instantaneous vapor overhead flow rate, Q, is normally adjusted so as to maintain a programmed pressure in the reactor This can be accomplished by defining the dimensionless equilibrium reactor pressure as (13)
FOR THE RATE CONSTANTS
AND
The literature contains few studies of the production of poly(ethylene terephthalate) under conditions which would lead to important simultaneous contributions from ester interchange, transesterification and polymerization reaction mechanisms[5,6]. Most reported rate studies have been conducted by chemists under conditions to permit simple analysis for only one rate parameter at a time. For example, studies have dealt with monomerization under conditions of excess glycol, “eliminating” the polymerization reactions. Or, similarly, the experimental procedure in polymerization studies usually is to start with “pure” monomer (bis-fl-hydroxyethyl terephthalate), thus, eliminating the ester interchange and transesterification reactions. Consequently, it is very difficult to determine a
2221 CESVol.27No.12-H
+#M(AF)X(AF)} de. F
The number average degree of polymerization, X,, is, in terms OfAT, CT and AI.
(11)
II, = X(C,) +#X(A,)
M(CF)X(CF)
(1%
(9) where the second-order rate expressions are
(14)
J. W. AULT and D. A. MELLICHAMP
set of rate and equilibrium constants obtained under similar conditions of temperature, catalyst types and concentrations, reactor type, etc. The following paragraphs furnish a brief enumeration of rate and equilibrium data, derived from what appear to be the most reliable sources and adjusted where necessary to fit a reasonably consistent set of assumptions. A complete review of the literature pertaining to the experimental studies of the ester interchange, transesterification, and polymerization reactions of ethylene glycol and dimethyl terephthalate is given by Ault [5]. Neglecting the reverse reactions, Fontana [7] experimentally determined the forward ester interchange rate constant, kE, for the reaction of dimethyl terephthalate and ethylene glycol. A differential rate data analysis revealed a third-order reaction mechanism for the ester interchange reaction: one order each with respect to hydroxyl group, methoxy group, and catalyst. With the assumptions that the glycol -OH was twice as reactive as the polymer -OH and the assumption that the methoxy groups on DMT and half-transesterified DMT were equally reactive, Fontana[7] concluded that the ratio of the forward rate constants for transesterification and ester interchange reactions (kr/&) was approximately O-5. With a relation for kT in terms of kE, he was able to fit his experimental data to a one-parameter model instead of the more diacult two-parameter kinetic model. The reversible polycondensation of bis-Phydroxyethyl terephthalate without catalysts was studied by Challa[8], while the catalyzed reversible polymerization reaction was investigated by Stevenson and Nettleton[9]. Their results indicated that the polymerization reaction followed second-order kinetics. Others have reported first-order kinetics [5]. Equilibrium studies on the polymerization reaction reveal a spectrum of values for &. Fontana[7] found Kp to be approximately 0.5 and sensibly independent of temperature or degree of polymerization. Stevenson and Nettleton[9] calculated an average value of
0.36 with a standard deviation of +0-l 1. The strict application of Flory’s principle of equal reactivity to the polymerization of bis-phydroxyethyl terephthalate indicates that Kp should be unity[6,7, 101. Challa[l l] challenged Flory’s principle of equal reactivity because his results revealed that Kp increased from O-4 at a degree of polymerization of 1.7-l. 1 at a degree of polymerization of 6.2. The ester interchange equilibrium for the reaction of dimethyl terephthalate and ethylene glycol in the presence of a zinc acetate catalyst was also studied by Challa[ 121. At low extents of reaction, he reported KE to be approximately O-3 and relatively insensitive to temperature variations. In the same study, Challa computed Kp to be 0.4. This evidence tends to suggest that KE and Kp are of the same order of magThe transesterification equilibrium nitude. constant, KT, is related to KE and Kp by [ I21 KT= KE.KP. Since the collapsed rate expressions [5] describing ester interchange, transesterification, and polymerization reactions were based on Flory’s principle of equal reactivity and since there appear to be substantial disagreements among experimental workers in the field, the numerical results presented in this study are predominantly based on the ester interchange and polymerization equilibrium constants being approximately unity and invariant with temperature and degree of polymerization. Table 1 summarizes the more reliable rate constants reported in the literature. Specific ratios of rate constants used in numerical studies have been taken from these values; where specific conclusions might be subject to errors in these values, a range of rate ratios has been used. Unquestionably, more thorough kinetic studies will be required before the production of poly(ethylene terephthalate) can be modeled in an absolute sense. In this regard, it is of course unfortunate that much of the data already obtained are, simply, not available in the open literature.
2222
Complex linear polycondensation Table 1. Second-order Reaction
rate constants from the literature Rate constant //mole-min
Catalyst
Ester interchange dimethyl terephthalate with ethylene glycol
Energy kcal/mole
Reference
15
I71
kp = 3.2 x lo+
23
t81
@ 262°C k, = 2.5 x 1O-3 @ 231°C
29
191
ks = 3.0 x 1O-3
zinc acetate
@ 180°C* k,/k,
Polymerization bis-P-hydroxyethyl terephthalate bis-P-hydroxyethyl terephthalate
- I
no catalyst antimony trioxide
= 0.5
*Fontana’s original rate constants were based on a third order rate expression (one order with respect to catalyst concentration). Here the catalyst concentration was included in k,+ ESTER
EXCHANGE IN A SEMI-BATCH REACTOR
s=-&(RE+RT)
For the ester exchange of dimethyl terephthalate and ethylene glycol, Fontana[7] postulated that third-order rate expressions for RE and RT (one order each with respect to hydroxy group, methoxy group, and catalyst concentration) along with a constant ratio of kT/kEequal to O-5 were appropriate. A differential analysis of his data was used to arrive at a thirdorder forward rate constant, kE, of 5.0 (l./mole)*min-’ at 180°C. In order to demonstrate the applicability of the reaction model presented in this study, Eqs. (5)-(g) were modified to describe third-order ester interchange and transesterification reactionst occurring simultaneously in a variable volume, semi-batch reactor at constant temperature.
(20) (21)
where RT
=
+,AT-F)
T
E
RE = 2CIYqF-+. E
(22) (23)
The dimensionless reactor volume can be computed in the same manner as discussed earlier. In terms of the third-order forward rate constant, k,, the dimensionless time, 8, is now defined as 8 E +j! * (Catalyst amount in moles) *t(O) *t. 0
~=&R,-Q~X(A,) d0
dC,_
~-pd&+&)
1
@=+(RE-RT) d6
P* (AF) F
-QX(C,)
(17)
(18) (1%
tThe second-order expressions with catalyst concentration included in the forward rate constants appear to be equally appropriate and might just as well have been used in this study. However, we have chosen to test Fontana’s original assumptions.
Fontana’s experimental apparatus consisted of a stirred reactor (a standard 11. three-necked flask equipped with a thermowell, stirrer, and takeoff column). The column comprised 20 theoretical plates in order to insure the maximum recovery of ethylene glycol from the overhead vapor flow. With complete recycle of the unreacted ethylene glycol, it is possible to assume that the rate of the polymerization zero. Table 2 reaction, Rp, is approximately lists Fontana’s experimental results. Also
2223
J. W. AULT and D. A. MELLICHAMP Table 2. Initial conditions for ester interchange simulation of Fontana’s experimental data (Run 10 of Ref. 7) Time min. 0
5 10 15 20 28 35 43 50 60
Reactor Pressure mm Hg 738 738 700 620 504 379 310 240 240 240
Moles CH,OH formed o-035 0.172 O-296 0.426 0.504 O-620 0.677 O-721 0.762 0.813
Reaction Temperature = 180°C. p* (CF) = 25 atm,p* (AF) = 0.625 atm. Initial Charge = O-5mole DMT and one mole ethylene glycol. Catalyst = 0.0199 g of Zn(OA&-2H,O. /IF(O) = 06439, C,(O) = O-6439,&(0) = 0.0228. C,(O) =0.0228,/t,(O) = 0.
A
Fontona
-This ---
included are the initial conditions required for the semi-batch material balance equations. A Lagrange quadratic interpolation formula was used to generate the programmed reactor pressure, II (f3), corresponding to the reactor pressure measured by Fontana (Table 2). Since ethylene glycol is only removed through reaction (Q(P*(A~)/J)*(C~))X(A~) = 0), the methanol concentration in the liquid bulk can be computed directly from the reactor pressure, II (0). Rearranging Eq. (13), the dimensionless methanol molar concentration becomes
(24) where, (&+A*)/2 = the dimensionless moles of polymer. Solution of Eqs. (17)-(24) was accomplished by means of a fourth-order Runge-Kutta routine with variable step integration. Using the catalyst amount, initial volume, initial molar density, and kE value from Fontana’s experiment, the factor relating real time to dimensionless time was O-02777 mirP.
I 0
work Constant
pressure
I
I
I
I
0.4
0.6
I.2
I.6
DimensIonless
Fig.
data
reaction
time
1. Comparison of computed results with Fontana experimental data (kr/& = 4).
Figure 1 demonstrates the closeness of the fit to Fontana’s data for methanol production obtained with the reactor model. A numerical solution of the model equations also was obtained for the case of constant pressure operation. The moles of methanol formed, also shown in Fig. 1, differ significantly from the decreasing reactor pressure simulation results only at large reaction times (t > 40 min). This result indicates that adequate rates for the ester interchange reaction can be obtained by operating the experimental semi-batch reactor at constant pressure in the initial region. The trouble and expense of experimental vacuum systems can be eliminated in the ester exchange reactor. The effect of varying the equilibrium constants, & and KT, from the assumed values is shown in Table 3. The production of methanol as a function of dimensionless reaction time, 8, is not affected by order of magnitude variations
2224
Complex linear polycondensation - I Table 3. The effect of varying KE and KT on the ester interchange and transesterification reactions (kT/kE= if). Dimensionless time e 0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Moles of methanol formed K*=l KT=l 0.14920 O-24673 040022 0.51545 060402 0.67332 0.72846 0.77284 0.80884
K,=lOOO KT= 1000 0.14939 O-24694 040169 0.51753 060626 0.67547 0.73034 o-77443 0.81025
a two-parameter search would be required to fix the values of k, and kE precisely. The dimensionless reactor volume, P, calculated from Eq. (4) decreased by approximately 15 percent in the simulations presented here. This volume decrease corresponds to a 12 percent increase in catalyst concentration. Variation in catalyst activity, which Fontana did not investigate, might cancel this increase in catalyst concentration. Davies[6] points out that polycondensation kinetics are best described through second-order rate expressions. The results obtained from the simulated runs of this study indicate that Fontana’s experimental methanol data might be presented effectively by two second-order rate expressions (one order with respect to hydroxyl and methoxy group) with the catalyst concentration effect included with the rate constants, kE and kT.
in KE and KT. The results of Table 3 indicate that, conducting the methanol withdrawal rate with the reactor pressures of Table 2, the reverse reactions can be neglected. Fontana claims that his experiments were operated with rapid methanol take-off so as to minimize the reverse reactions. OPTIMIZATION OF THE TWO-STAGE Several runs were made with the model in PRODUCTION OF POLY(ETHYLENE TEREPHTHALATE) which the ratio of the forward rate constants for transesterification and ester interchange The production of poly(ethylene terephthalate) was varied (k,lk,=O-1, O-25, O-5, and 1). is typically carried out in a two-stage reactor Table 4 lists the sum of the square of the error [2,3, 131. The objective of the first stage is to between the methanol production of Fontana’s convert dimethyl terephthalate (DMT) through work and the calculated results obtained in this ester exchange with ethylene glycol (EG) to the study for each value of kT/kEinvestigated. The monomer of poly(ethylene terephthalate), results of Table 4 illustrate that the data of his+-hydroxyethyl terephthalate. In the second Fontana are best correlated by a ratio of kTlkE stage the pressure is reduced in order to drive equal to 0.5 (in comparison to all other values off the excess ethylene glycol. As mentioned investigated) when the value of kE is taken earlier in this paper, the literature[2,3] reports to be 5-O (l./mole)2min_, at 180°C. Obviously, that it is essential to carry the ester exchange reactions to completion, i.e. convert all of the Table 4. Effect of varying the forward CT species to A, before proceeding to the rate constant ratio k,/k, on the ester second stage. It is believed that small amounts transesterification interchange and reactions of the CT species will effectively “kill” the reactions of the second stage reactor. Petukhov kdk, {f (Error)*de} x lo4 [4] states that in practice this “end-capping” effect is not observed. The methoxy groups 0.1 32.775 (C, groups) take part in the polycondensation 0.25 13999 reactions, and a polyester with sufficiently high 0.5 3.040 1.0 20,876 molecular weight is obtained. Only when the ester exchange reactor product contains large Error = moles CH,OH produced this amounts of CT does the end-capping effect study-moles CH,OH produced Ref. [7]. appear. 0, = 1.65 (60 min). 2225
J. W. AULT and D A. MELLICHAMP
In order to investigate the end-capping effect, the operation of a two-stage varying volume semi-batch reactor was simulated by the collapsed rate expressions (Eqs. 4-16). By varying the amount of CT in the reacting charge to the second stage reactor, plots of degree of polymerization (X,) were obtained versus CT initially present. A fourth-order Runge-Kutta routine with variable step integration was used to solve Eqs. (4)-( 16) for the case of two moles of ethylene glycol reacting with one mole of dimethyl terephthalate in a two-stage semibatch reactor with one stage operated at constant pressure (complete reflux of unreacted glycol) and the pressure reduced exponentially in the second stage (no reflux of ethylene glycol). Equilibrium constants (&, KE, and KT) equal to unity were used for these simulations. First stage. Typical reaction temperatures in the first stage reactor are in the range 150220°C [ 131. Currently in the production of poly(ethylene terephthalate) it is the practice to employ mixed catalysts, one component, usually a metal acetate [ 141, which is active during the ester interchange step and another component (antimony trioxide [ 151), which becomes active in the polymerization stage. At 220°C the ratio of Fontana’s[7] forward rate constant for ester interchange, kE, to the forward rate constant for polymerization, kp, from the work of Stevenson and Nettleton[8] is approximately 8 (see Table 1). This value for kE/kp might be considered the most reliable value available from data currently in the open literature. However, in order to investigate more than one value of kElkp and kTlkp, the first stage was simulated with both kElkp = 8 (kT/kp = 4) and also kElkp = 4 (kT/kp = 1). These latter values correspond to the situation where the transesterification and polymerization reactions have the same forward rate constants (kT/kp = 1). Since during the first stage of operation the ethylene glycol is only depleted through reaction, the methanol concentration can be computed directly from the reactor pressure (Eq. 24). The initial conditions for the ester interchange reactor (first stage simulations) are
Table 5. Initial and operating conditions for simulations of first stage Reaction temperature: 220°C Equilibrium constants: K, = KE = KT = 1 Forward rate constant ratios: +$~+g,+ P P
F
P
Vapor pressures of volatile specie& p* (C,) = 60 atm,p* (AF) = 2.5 atm Dimensionless
Constant Reactor Pressure:
II, = II (13)= *(A,) Dimensionless
(0) = O-0267
initial molar quantities:
Total initial moles = 3 CT(O)=&(O) = 2/3 AT(O) = A,(O) = C,(O) = 0 Reflux: Complete reflux of the unreacted ethylene glycol and no reflux of the methanol produced tThe pure component vapor pressures were obtained from Ref. [ 161.
(p* (C,), p* (AF))
listed in Table 5. The operating reactor pressure corresponding to a dimensionless pressure of O-0267 is approximately 1.6 atm. Figure 2 depicts the dimensionless molar concentration profiles vs. dimensionless reac-
0.5 --
---
-
0
I
Dimensmnless
k/k,=& kE/kp=4,
k/k,=4 kT/kp= I
3
2
reaction
time
Fig. 2. &, AT, A,, and C, vs. 0 for first stage simulations.
2226
Complex linear polycondensation
tion time, 8, for ethylene glycol &), hydroxyl groups (AT), m,ethoxy groups (C,), and internal ester links (AI) during the simulation of the first stage production of poly(ethylene terephthalate). If the ester interchange reaction were the only reaction occurring in this stage, the glycol depletion would be the same as the methoxy group depletion. However, after a dimensionless reaction time of approximately O-25 (kE/kp = 4, k,/k, = 1) the transesterification and polymerization reactions begin to become important. The maximum obtained in the AT profile at 8 equal to 0.5 is the direct result of this change in reaction rate magnitude, the transesterification and polymerization reactions begin depleting the hydroxyl groups causing the reverse trend in the curve of AT vs. 0 in Fig. 2. The results for kE/kp = 8, kT/kp = 4 are similar with the exception of a shift to the left in Fig. 2. Equilibrium conditions are reached sooner in this case. In terms of dimensional reaction time, t, the dimensionless time is defined as 0 = kp *
- I
The amount of C, removed during the course of reaction in the first stage was determined by material balance on the C, in solution and the amount of C, reacted. The results of the first stage simulations (Fig. 3) indicate that the maximum amount of CH,OH that can be recovered is approximately 99.3 percent of the theoretical total. Thus, even at equilibrium,
Initial Moles . t VII
I
*
0.02
For the cases presented in Fig. 2, k, is approximately O-002 1. mole-‘mm-’ (see Table l), and the initial reactor volume, V,, is approximately O-3 1. Thus, a dimensionless time of 0.5 corresponds roughly to 25 min of actual reaction time. Since the results of Fig. 2 indicate that equilibrium conditions are reached after 125 min (8 = 2.5)) the design engineer may conclude that the total reaction time required for this first step in the production of poly(ethylene terephthalene) from DMT and EG should be between 25 and 125 min. In order to narrow this range of operating time to a more select group of reaction times, it is helpful to observe the change in the percent total possible methanol removed from the first-stage semi-batch reactor as a function of reaction time. % Methanol removed =
C, Removed . 1oo. CT(O)
004
I
I
I
I
0.06
0.1
0.2
0.4
Dimensionless
reaction
I
I
I
I
06
I
2
4
time
Fig. 3. Percent total methanol removed during first stage.
there exists in the polymer melt a small fraction of unconverted methoxy groups. According to Petukhov [4], a substantially much higher amount of methoxy groups must be present before an end-capping effect appears in the second stage. The degree of polymerization, X,, given by Eq. (16), increased to a value of 1.98 at equilibrium conditions in the first stage simulations. This value of X, confirms the results reported in the literature, i.e. the ester exchange product is mainly comprised of dimer and trimer oligomers with hydroxy and methoxy end-groups [2,13]. The total reacting liquid volume decreased by 25 percent during the course of the ester interchange step. Employing the usual assumption of a constant volume reactor during the simulations would have introduced considerable error in the final semi-batch reactor results.
2227
J. W. AULT
and D. A. MELLICHAMP
Second stage. Poly(ethylene terephthalate) is formed when the product from the first stage reactor is heated to 270-285°C with continuous evacuation to low pressures (2-1 mm Hg) [2, 13,151. The high temperature is required in order to maintain the polyester product in molten form. The growth of the polymer molecules is accompanied by a substantial increase in the fluid viscosity. Extreme diffusional resistances are encountered by the evolving glycol and methanol species if the polymer is allowed to solidify partially. Low pressures are necessary in order to drive the transesterification and polymerization reactions to completion yielding internal ester linkages and the by-product C, and& species.
At 275°C kE/kp (Fontana[71 and Stevenson and Nettleton [9]) is approximately 4,. indicating that the energies of activation for the three reactions are practically equal. In all runs a total second stage dimensionless reaction time (0,) of 20 was used. Twenty dimensionless time units correspond to approximately 70 min of actual reaction time. To reproduce a typical pressure draw-down cycle, an exponential decrease in dimensionless reactor pressure (from the initial equilibrium pressure to a final pressure equivalent to 2 mm Hg absolute) was made during the first half of the reactor cycle (0,/2 = 10). During the final half of the cycle the operating pressure was maintained constant at m (0,).
40) = T,(O)exp {-[me(O)-d&II (Ulo)) 0 s 8 s t&!/2 (25)
AT+& * AI+CF AT+AT G A,+AF.
T(O) = .rr(&) In order to verify or disprove Petukhov’s observations, the second stage production of poly(ethylene terephthalate) from ethylene glycol and dimethyl terephthalate was simulated by Eqs. (4)-(16). A set of starting conditions corresponding to successively longer operating times (0,) for the first stage, i.e. decreasing concentration of the end-capping CT species, was chosen. Preliminary tests indicated that endcapping effects were sensitive to variations in k,/k, (and relatively independent of changes in kE/kp). To evaluate the end-capping sensitivity to the transesterification rate constant, the second stage reactor simulations were performed for three separate cases: (1) kE/kp = 1 (kE/kp = l/4, (2) k,lk, = 4 (k,/k, = l), and (3) kElkp = 8 (kT/kp = 4). The simulation with kE/kp = 8 (kT/kp = 4) or kE/kp = 4 (kT/kp = 1) in both the first and second stages represents a reacting system in which equal energies of activation for the ester interchange, transesterification, and polymerization reactions are observed. The simulation with kE/kp = 4 (kT/kp = 1) in the first stage and k,/k, = 1 (kT/kp = l/4) in the second stage represents the case of unequal activation energies (polymerization reaction greater than both ester interchange and transesterification reactions).
&?I2-==c 8 c 8,.
(26)
Ault [5] summarizes the initial and operating conditions for the second stage simulations. Also, the details of the numerical solution of Eqs. (4)(16) are given in [5]. For the case most likely to give end-capping (kE/kp = 1 and kdk, = l/4), the number average degree of polymerization, X,, obtained in the second stage is shown in Fig. 4 as a function of dimensionless reaction time with the mole fraction methoxy groups (C,) in initial feed as a parameter. Included in Fig. 4 is the curve for X, corresponding to the ideal case of “pure monomer” (C, = 0) fed to the second stage. Substantial decrease in the degree of polymerization is observed when the product from the ester exchange reactor contains a methoxy end-group mole fraction greater than approximately O-02. When the initial charge to the polymerization stage contains a CT mole fraction greater than about O-10, the polymer growth is effectively “killed”. The effect of higher ester interchange and transesterification rate constant ratios, k,/k, and kTlkp, upon the number average degree of polymerization, X,, is illustrated in Figs. 5 and 6. Here the unreacted methoxy groups have a
2228
Complex
linear polycondensation-
I
XC,)(O)
8,
I
0.425
025
I
0.55
0.05
2
0.270
0.50
2
0.45
0.10
3
0.24
0.25
4
0.60
0.025
X(C,)(O)
---
0
Dimensionless
.
I
0
I
2
IO
5
Dimensionless
reaction
time
stage
I
I
I
I
2
5
IO
20
Dimensionless
reaction
time
time
in
second
stage
20
in second
Fig. 4. The effect of the methoxy groups on degree of polymerization (,4,/k, = 1, kT/k, = 0.
I
reaction
Fig. 6. The effect of the methoxy groups on degree of polymerization (kE/kp = 8, b/kp = 4).
I
I
8,
in second
I
stage
Fig. 5. The effect of the methoxy groups on degree of polymerization (kE/kp = 4, b/k, = I).
greater chance to react with ethylene glycol before it is drawn off at the low reactor pressures (II(O) - 10e4). At low glycol concentrations the CT end-groups are essentially consumed only by the transesterification reaction. If the polymerization reaction is faster than the transesteri-
fication reaction, as is the case in Fig. 4, the hydroxyl end-groups (AT) disappear before they have the opportunity to react with the methoxy groups. On the other hand, with k,/kp = 8 and kT/kp = 4, an actual increase in the degree of polymerization is possible (as shown in Fig. 6). From these results, it is evident that a polymerization catalyst in the second stage reactor should enhance the transesterification reactions as well as the polymerization reactions. Figure 7 indicates that a moderately high molecular weight polyester results from the second stage reactor (0, = 20) if the ester exchange step is concluded in approximately 100 min (0, = 2) when the key transesterification rate constant is relatively small (kT/kp = 0.25). When the transesterification rate is of the same order of magnitude as the polymerization rate the first stage reaction time can be reduced by about 50 per cent (0, = 1) with no degradation in degree of polymerization of the product from the second stage. Finally, with a transesterification rate four times higher than the polymerization rate (kT/kp = 4) the first stage reaction time can be reduced by a factor of ten (0, = O-2) with no overall degradation in performance. Or, by a further reduction in first stage reaction time (to 8, = 0.0% an approximate 30 per cent enhancement in degree of polymerization from the second stage would be observed. 2229
J. W. AULT and D. A. MELLICHAMP 70,
attempt to eliminate the zero functional species (terephthalic acid and its higher oligomers). The product of the first stage is polymerized in a single subsequent stage without end-capping effects occurring. Furthermore, additional references in the patent literature describe the deliberate introduction of zero functional species to enhance the degree of polymerization in commercial reactors. A more complete study of the enhancement effect will be given in the sequel after the model (with difFusiona effects included) is developed to describe reaction at high degrees of polymerization.
I
0.02
I 0.04
Dimensionless
I 0.1
02
reaction
0
kE/kp=8,
kT/,kp-4
A
kE/kp=4.
kT/kp= I
0.4
time
I I
in first
I 2
I 4
CONCLUSIONS
stage
Fig. 7. Degree of polymerization in product from second stage as function of reaction time in first stage.
These differences represent significant productivity increases; however, they are based on a two-stage, semi-batch model which can only be applied to small well-stirred reactors or to thin film reactors. Most commercial reactors, although designed to enhance stirring and the continuous formation of thin films as much as possible, actually are severely difhrsion-limited in the final stages of reaction (X, > 20). In such a reactor the end-capping effect would be much less likely to occur (even with a relatively low transesterification rate). The unreacted terminal methoxy groups would have considerably more time to react with terminal -OH groups (which deplete more slowly because of the relatively low glycol diffusion rate). Hence, Petukhov[4], who based his conclusions on evidence obtained from an actual industrial process, probably is correct in stating that end-capping is only observed at high CT levels. Mellichamp [ 171 reports that in the direct esterification of terephthalic acid with ethylene glycol, for example, the first stage can be operated at very high temperatures in order to increase reaction rates and yield a high degree of polymerization (on the order of 6-20), making no
1. After a review of the literature it is evident that more thorough kinetics studies on the ester interchange, transesterification, and polymerization reactions are necessary before the two stage production of poly(ethylene terephthalate) can be modeled in an absolute sense. 2. The semi-batch reactor model presented in this study can be used to correlate kinetic rate data. It is possible, through preliminary theoretical investigations, to minimize the complexity of experiments and the analysis of results in determining polycondensation kinetic parameters. 3. In a two-stage process utilizing a wellstirred semi-batch reactor end-capping can occur in the second stage if the relative ratio of the transesterification reaction rate constant to the polymerization rate constant is less than unity. However, at values greater than one, substantially higher concentrations of end-capping reactants (C,) can be depleted effectively. Hence, the monomerization stage can be operated at holding times significantly less than required to obtain complete conversion to monomer, with a resulting increase in productivity.
2230
NOTATION A
molecular unit in the ABABAB. . . polymer chain, or total dimensionless molar concentration of A units
Complex linear polycondensation
AF dimensionless
molar concentration of “Free A” AI dimensionless molar concentration of “Internal A” AT dimensionless molar concentration of “Terminal A” B molecular unit in the ABABAB. . . polymer chain, or total dimensionless molar concentration of B units molecular unit in the CBABAB. . . c polymer chain, or total dimensionless molar concentration of C units molar concentration of CF dimensionless “Free C ” dimensionless molar concentration of C, “Terminal C” ester interchange reaction equilibrium & constant polymerization reaction equilibrium KP constant reaction equilibrium KT transesterification constant molecular weight of AF M(A,) molecular weight of C, M(C,) volumetric flowrate of CF and AF reQ0 moved from the reactor Q dimensionless volumetric flowrate of Q”P* (CF) ” R RE RP RT T
V
volume of reacting mass initial volume of reacting mass P dimensionless volume of reacting mass mole fraction of AF in liquid X(A,) mole fraction of CF in liquid X (C,) mole fraction of CT in liquid X( C,) X, number average degree of polymerization (chain length) kE second- or third-order forward ester interchange rate constant? kP second-order forward polymerization rate constant? kT second- or third-order forward transesterification rate constant! p* (AF) pure component vapor pressure of species AF at reaction temperature, V,
T p* (C,)
pure component vapor pressure of species CF at reaction temperature, T t
dimensional time
Greek symbols
dimensionless reaction time total dimensionless reaction time in first stage total dimensionless reaction time in second stage dimensionless equilibrium pressure dimensionless reactor pressure molar density of reactants equilibrium pressure reactor pressure mass density of initial reacting mixture
andAF’ RTk,(V,,[(O))’
gas constant dimensionless reaction rate for collapsed ester interchange reactions dimensionless reaction rate for collapsed polymerization reactions dimensionless reaction rate for collapsed transesterification reactions absolute reaction temperature
- I
tAll rate constants reactants.
expressed
in terms of monofunctional
REFERENCES
[ll MELLICHAMP D. A., Chem. Engng Sci. 1969 24 125. I21Anon., Brit. Chem. Engng 14 BCE Process Scan 1969. 131 FORNEY R. C., McCUNE L. K., PIERCE N. C. and TOMPSON R. Y., Chem. Engng Prog. 1966 62 88. B. V., The Technology of Polyester Fibres. MacMillan, New York 1963. 141 PETUKHOV [51 AULT J. W., Ph.D. Dissertation, University of California, Santa Barbara, California 1971. 161 DAVIES T., High Polymers, Vol. XIX, Chapt. VII. Interscience Publishers, New York 1964. [7j FONTANA C. M., J. Polymer Sci.: Part A-I, 1968 6 2343. 181 CHALLA G.. Makromolekulare Chem. 1960 38 125. ,9j STEVENSON R. W. and NETTLETON H. R., J. Polymer Sci.: Part A-I 1968 6 889. [lo] ABRAHAM W. H., Chem. Engng Sci. 1970 25 33 1.
2231
J. W. AULT and D. A. MELLICHAMP [ 1 l] CHALLA G., Makromolekulare Chem. 1960 38 105. [121 CHALLA G., Recueil trau. Chim. Pays-Bas 1960 79 90. [13] GOODMAN I. and RHYS J. A., PO&esters, Vol. I, Saturated Polymers. Elsevier New York 1965. 1141 FLETCHER N., British Patent 2.998.412. Auuust 29 1961. il5] TURNER G. MI, U.S. Patent 3,161,710, December 15 1964. [I 61 PERRY J. H., ChemicalEngineers’ Handbook, 4th Ed. McGraw-Hill, New York 1963. [17] MELLICHAMP D. A., U.S. Patent 3,496,146, February 17 1970. Resume - Les auteurs montrent qu’un modble cinttique, tenant compte de la presence de composes de fonction zero, un et deux, correspond aux donnees dune reaction experimentale d’echange d’esther de la litterature. Dans une seconde etude, les auteurs ont simule la production en deux phases de terephtalate de polyethylene dans un reacteur-agitateur a charges discontinues. Les composes de fonction zero et un presents dans le produit resultant de la phase de “monomerisation” et qui d’ordinaire occasionnent un arr&t dans la chaine du polymere dans la seconde phase, menaient a un produit de poids moliculaire superieur, dans certaines conditions des taux relatifs de reaction. Zusammenfassung- Es wurde dargelegt, dass mit Hilfe eines kinetischen Modells, das die Anwesenheit null- und monofunktioneller sowie bifunktioneller Species beriicksichtigt, die experimentellen Esteraustauschreaktionsdaten aus der Literatur in Korrelation gebracht werden konnen. In einer zweiten Untersuchung wurde die zweistufige Herstellung von Poly(athylen terephthalat) in einem gut gertihrten Halbchargenreaktor swinliest. Es wurde gezeigt, dass die aus der “Monomerisation” Stufe herrilhrenden null- und monofunktionellen Species in dem Produkt, die normalerweise in der zweiten Stufe Anlass zur “Endverkappung” geben, unter gewissen Bedingungen der relativen Reaktionsgeschwindigkeiten zu einem hiihermolekularen Produkt fiihren.
2232
Science,1972,
Vol. 27, pp. 2219-2232.
Pergamon
Press.
Printed in Great Britain
Complex linear polycondensation - I Semi-batch reactor J. W. AULT? and D. A. MELLICHAMP Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, California, U.S.A. (Receioed 6 July 1971; accepted 14 January 1972) Abstract-A kinetic model which takes into account the presence of zero and monofunctional as well as bifunctional species was shown to correlate experimental ester interchange reaction data from the literature. In a second study, the two-stage production of poly(ethylene terephthalate) in a well-stirred semi-batch reactor was simulated. Zero and monofunctional species present in the product from the “monomerization” stage, which ordinarily result in “end-capping” in the second stage, were shown to lead to a higher molecular weight product under certain conditions of the relative reaction rates. INTRODUCTION
engineering standpoint, the most useful polymer property is the number average degree of polymerization due to the fact that most other polymer properties are primarily functions of the number average molecular weight. Hence, efforts to model reversible polycondensing systems have been directed at obtaining simple but rigorous relations to compute the degree of polymerization. As an example Mellichamp [ 11 showed that the polymerization of poly(ethylene terephthalate) can be modeled by a set of equations for the three forms of by-product species (speaking loosely: the endgroup quantities) if an idealized reaction mixture containing only bifunctional species is assumed. Unfortunately, many important industrial polycondensation processes involve mixtures of different functionality species, e.g. the two-stage production of poly(ethylene terephthalate) from dimethyl terephthalate (DMT) and ethylene glycol. In the first stage, DMT is exchanged with ethylene glycol to form his+ hydroxyethyl terephthalate (the monomer of poly(ethylene terephthalate)) and methanol which is continually removed from the reacting mixture. The “monomer” is condensed in the second stage with the continuous removal of the ethylene glycol formed [2]. Several papers in the FROM
AN
literature[2,3] report that it is essential to drive the ester interchange reaction (first stage) to completion before proceeding with the polymerization reaction (second stage). This is to insure that the methoxy groups are minimized in order that limitation in chain growth during polymerization not occur. In actual industrial practice, this supposition frequently is not observed[4]. The product of the ester interchange stage may contain as much as lo-25 percent of non-transesterified methoxy groups which take part in the reactions of the polymerization stage. The polymer obtained is of satisfactory high molecular weight [4]. Reacting systems of this type involve molecules of zero functionality (DMT and its higher oligomers), monofunctionality (methanol, the singly substituted mixed ester and its higher oligomers), and bifunctionality (ethylene glycol, the monomer and its higher oligomers). Four distinct reaction mechanisms are involved simultaneously (ester interchange, transesterification, polymerization, and rearrangement). This series of complex polycondensation reactions can be conveniently exprssed in terms of an alphabetic sequence of three letters, if only linear polycondensation products are considered. Conforming to the notation used by Ault [5] A is used to designate a free ethylene
?Present address: Chevron Oil Field Research, La Habra, California, U.S.A.
2219
J. W. AULT
and D. A. MELLICHAMP
glycol species (HOCH2CH20H), an end-group ethylene glycol ester unit (HOCH,CH20-), or an internal ethylene glycol ester unit (-OCH,CH,O-). The terephthalyl unit (-OCQCO-) is designated by B. C is introduced to represent free methanol (CH,OH) or the end methanol ester group (CHIO-). There are no internal methanol species.
Ester Interchange
Transesterification
(2) ...AT+CT...~...AI...+C~ T Polymerization
Ester Interchange ...AT+AT...~...AI...+AF. v
A+CBC * ABC+C A+ABC *ABA+C A + CBABA * ABABA + C
Transesterification ABC + CBC * CBABC + C ABA + CBC 13 ABABC + C ABABC +ABC F? ABABABC + C
(1) Polymerization ABC+ABC ABC+ABA ABA+ABABC
* CBABC+A ti ABABC+A * ABABABC+A
The Rearrangement reactions collapse exactly to zero. The end-group quantities -AF represents all “free” A species, AT represents all “terminal” A species, AI represents all “internal” A species, and C, and CT represent all “free” and “terminal” C species respectively - represent molar quantities or concentrations which may be converted to dimensionless quantities. It is the objective of this study to simulate the two-stage production of linear poly(ethylene terephthalate) in a semi-batch reactor. The collapsed rate expression model will be employed in an attempt to resolve the conflicting points of view concerning completion of reaction at the end of the tist stage. In a preliminary study, the usefulness of the collapsed model in correlating rate data available in the literature will be demonstrated. REACTION
Rearrangement ABC+ABABC G CBABC+ABA ABABC+ CBABC * CBABABC+ABC ABABA +ABABC * CBABABA +ABA
Ault further showed that the individual kinetic rate expressions describing the reactions of species of mixed functionality can be collapsed to a set of three (pseudo) second-order reversible rate expressions which can be used to compute five essential end-group quantities.
MODEL FOR A SEMI-BATCH REACTOR
The collapsed material balance equations required to describe ester interchange, transesterification, and polymerization occurring simultaneously in a semi-batch reactor were derived by Ault. In order to make the equations applicable to a varying reaction volume, as in the case of the semi-batch reactor simulated in this study, it is necessary to define the volume of the reacting medium. V = V,,-(Mass
Out)/pO.
(3)
Equation (3) implies that the liquid mass density is a constant equal to the initial density, po.
2220
Complex linearpolycondensation- 1
In many liquid reacting systems this is the case. Defining a dimensionless reactor volume as
v=;=l-Ih$;;i&
programmed reactor and the dimensionless pressure as II(e). Then Q as a function of reaction time becomes
Q(e) = QVL n(N).
(4)
0
the dimensionless material balance equations for a varying volume in a semi-batch reactor become
dAF_ 1 ---B(~E-~,)-Q$&~(A,)
The total mass leaving the semi-batch reactor Simply the tOtd mass Of methai’iO1, CF, and ethylene glycol, AF , taken overhead by Q.
iS
(5) Mass Out = (Initial Moles)
d0
~=@zE+RT)-QX(CF)
(6)
==+(RE-2Rp-RT) de
(7)
dG_ -d8
(8)
d0
1 $R”+R,)
X
RE = f+Cd, P
reversible
-A+] E
x,=
l-t&&
2A
(16)
The initial conditions required for Eqs. (5)-(9) are quite simply computed from the definition of the end-group quantities. (Ault [5] gives details.)
collapsed
(10) NUMERICAL VALUES EQUILIBRIUM
(12) The volatile species (AF and CF) and the species (AT, CT, and A,) are dimensionless molar quantities. 0, the dimensionless reaction time, is defined as k&(O) t, where 5 (0) is the initial molar density. The dimensionless instantaneous vapor overhead flow rate, Q, is normally adjusted so as to maintain a programmed pressure in the reactor This can be accomplished by defining the dimensionless equilibrium reactor pressure as (13)
FOR THE RATE CONSTANTS
AND
The literature contains few studies of the production of poly(ethylene terephthalate) under conditions which would lead to important simultaneous contributions from ester interchange, transesterification and polymerization reaction mechanisms[5,6]. Most reported rate studies have been conducted by chemists under conditions to permit simple analysis for only one rate parameter at a time. For example, studies have dealt with monomerization under conditions of excess glycol, “eliminating” the polymerization reactions. Or, similarly, the experimental procedure in polymerization studies usually is to start with “pure” monomer (bis-fl-hydroxyethyl terephthalate), thus, eliminating the ester interchange and transesterification reactions. Consequently, it is very difficult to determine a
2221 CESVol.27No.12-H
+#M(AF)X(AF)} de. F
The number average degree of polymerization, X,, is, in terms OfAT, CT and AI.
(11)
II, = X(C,) +#X(A,)
M(CF)X(CF)
(1%
(9) where the second-order rate expressions are
(14)
J. W. AULT and D. A. MELLICHAMP
set of rate and equilibrium constants obtained under similar conditions of temperature, catalyst types and concentrations, reactor type, etc. The following paragraphs furnish a brief enumeration of rate and equilibrium data, derived from what appear to be the most reliable sources and adjusted where necessary to fit a reasonably consistent set of assumptions. A complete review of the literature pertaining to the experimental studies of the ester interchange, transesterification, and polymerization reactions of ethylene glycol and dimethyl terephthalate is given by Ault [5]. Neglecting the reverse reactions, Fontana [7] experimentally determined the forward ester interchange rate constant, kE, for the reaction of dimethyl terephthalate and ethylene glycol. A differential rate data analysis revealed a third-order reaction mechanism for the ester interchange reaction: one order each with respect to hydroxyl group, methoxy group, and catalyst. With the assumptions that the glycol -OH was twice as reactive as the polymer -OH and the assumption that the methoxy groups on DMT and half-transesterified DMT were equally reactive, Fontana[7] concluded that the ratio of the forward rate constants for transesterification and ester interchange reactions (kr/&) was approximately O-5. With a relation for kT in terms of kE, he was able to fit his experimental data to a one-parameter model instead of the more diacult two-parameter kinetic model. The reversible polycondensation of bis-Phydroxyethyl terephthalate without catalysts was studied by Challa[8], while the catalyzed reversible polymerization reaction was investigated by Stevenson and Nettleton[9]. Their results indicated that the polymerization reaction followed second-order kinetics. Others have reported first-order kinetics [5]. Equilibrium studies on the polymerization reaction reveal a spectrum of values for &. Fontana[7] found Kp to be approximately 0.5 and sensibly independent of temperature or degree of polymerization. Stevenson and Nettleton[9] calculated an average value of
0.36 with a standard deviation of +0-l 1. The strict application of Flory’s principle of equal reactivity to the polymerization of bis-phydroxyethyl terephthalate indicates that Kp should be unity[6,7, 101. Challa[l l] challenged Flory’s principle of equal reactivity because his results revealed that Kp increased from O-4 at a degree of polymerization of 1.7-l. 1 at a degree of polymerization of 6.2. The ester interchange equilibrium for the reaction of dimethyl terephthalate and ethylene glycol in the presence of a zinc acetate catalyst was also studied by Challa[ 121. At low extents of reaction, he reported KE to be approximately O-3 and relatively insensitive to temperature variations. In the same study, Challa computed Kp to be 0.4. This evidence tends to suggest that KE and Kp are of the same order of magThe transesterification equilibrium nitude. constant, KT, is related to KE and Kp by [ I21 KT= KE.KP. Since the collapsed rate expressions [5] describing ester interchange, transesterification, and polymerization reactions were based on Flory’s principle of equal reactivity and since there appear to be substantial disagreements among experimental workers in the field, the numerical results presented in this study are predominantly based on the ester interchange and polymerization equilibrium constants being approximately unity and invariant with temperature and degree of polymerization. Table 1 summarizes the more reliable rate constants reported in the literature. Specific ratios of rate constants used in numerical studies have been taken from these values; where specific conclusions might be subject to errors in these values, a range of rate ratios has been used. Unquestionably, more thorough kinetic studies will be required before the production of poly(ethylene terephthalate) can be modeled in an absolute sense. In this regard, it is of course unfortunate that much of the data already obtained are, simply, not available in the open literature.
2222
Complex linear polycondensation Table 1. Second-order Reaction
rate constants from the literature Rate constant //mole-min
Catalyst
Ester interchange dimethyl terephthalate with ethylene glycol
Energy kcal/mole
Reference
15
I71
kp = 3.2 x lo+
23
t81
@ 262°C k, = 2.5 x 1O-3 @ 231°C
29
191
ks = 3.0 x 1O-3
zinc acetate
@ 180°C* k,/k,
Polymerization bis-P-hydroxyethyl terephthalate bis-P-hydroxyethyl terephthalate
- I
no catalyst antimony trioxide
= 0.5
*Fontana’s original rate constants were based on a third order rate expression (one order with respect to catalyst concentration). Here the catalyst concentration was included in k,+ ESTER
EXCHANGE IN A SEMI-BATCH REACTOR
s=-&(RE+RT)
For the ester exchange of dimethyl terephthalate and ethylene glycol, Fontana[7] postulated that third-order rate expressions for RE and RT (one order each with respect to hydroxy group, methoxy group, and catalyst concentration) along with a constant ratio of kT/kEequal to O-5 were appropriate. A differential analysis of his data was used to arrive at a thirdorder forward rate constant, kE, of 5.0 (l./mole)*min-’ at 180°C. In order to demonstrate the applicability of the reaction model presented in this study, Eqs. (5)-(g) were modified to describe third-order ester interchange and transesterification reactionst occurring simultaneously in a variable volume, semi-batch reactor at constant temperature.
(20) (21)
where RT
=
+,AT-F)
T
E
RE = 2CIYqF-+. E
(22) (23)
The dimensionless reactor volume can be computed in the same manner as discussed earlier. In terms of the third-order forward rate constant, k,, the dimensionless time, 8, is now defined as 8 E +j! * (Catalyst amount in moles) *t(O) *t. 0
~=&R,-Q~X(A,) d0
dC,_
~-pd&+&)
1
@=+(RE-RT) d6
P* (AF) F
-QX(C,)
(17)
(18) (1%
tThe second-order expressions with catalyst concentration included in the forward rate constants appear to be equally appropriate and might just as well have been used in this study. However, we have chosen to test Fontana’s original assumptions.
Fontana’s experimental apparatus consisted of a stirred reactor (a standard 11. three-necked flask equipped with a thermowell, stirrer, and takeoff column). The column comprised 20 theoretical plates in order to insure the maximum recovery of ethylene glycol from the overhead vapor flow. With complete recycle of the unreacted ethylene glycol, it is possible to assume that the rate of the polymerization zero. Table 2 reaction, Rp, is approximately lists Fontana’s experimental results. Also
2223
J. W. AULT and D. A. MELLICHAMP Table 2. Initial conditions for ester interchange simulation of Fontana’s experimental data (Run 10 of Ref. 7) Time min. 0
5 10 15 20 28 35 43 50 60
Reactor Pressure mm Hg 738 738 700 620 504 379 310 240 240 240
Moles CH,OH formed o-035 0.172 O-296 0.426 0.504 O-620 0.677 O-721 0.762 0.813
Reaction Temperature = 180°C. p* (CF) = 25 atm,p* (AF) = 0.625 atm. Initial Charge = O-5mole DMT and one mole ethylene glycol. Catalyst = 0.0199 g of Zn(OA&-2H,O. /IF(O) = 06439, C,(O) = O-6439,&(0) = 0.0228. C,(O) =0.0228,/t,(O) = 0.
A
Fontona
-This ---
included are the initial conditions required for the semi-batch material balance equations. A Lagrange quadratic interpolation formula was used to generate the programmed reactor pressure, II (f3), corresponding to the reactor pressure measured by Fontana (Table 2). Since ethylene glycol is only removed through reaction (Q(P*(A~)/J)*(C~))X(A~) = 0), the methanol concentration in the liquid bulk can be computed directly from the reactor pressure, II (0). Rearranging Eq. (13), the dimensionless methanol molar concentration becomes
(24) where, (&+A*)/2 = the dimensionless moles of polymer. Solution of Eqs. (17)-(24) was accomplished by means of a fourth-order Runge-Kutta routine with variable step integration. Using the catalyst amount, initial volume, initial molar density, and kE value from Fontana’s experiment, the factor relating real time to dimensionless time was O-02777 mirP.
I 0
work Constant
pressure
I
I
I
I
0.4
0.6
I.2
I.6
DimensIonless
Fig.
data
reaction
time
1. Comparison of computed results with Fontana experimental data (kr/& = 4).
Figure 1 demonstrates the closeness of the fit to Fontana’s data for methanol production obtained with the reactor model. A numerical solution of the model equations also was obtained for the case of constant pressure operation. The moles of methanol formed, also shown in Fig. 1, differ significantly from the decreasing reactor pressure simulation results only at large reaction times (t > 40 min). This result indicates that adequate rates for the ester interchange reaction can be obtained by operating the experimental semi-batch reactor at constant pressure in the initial region. The trouble and expense of experimental vacuum systems can be eliminated in the ester exchange reactor. The effect of varying the equilibrium constants, & and KT, from the assumed values is shown in Table 3. The production of methanol as a function of dimensionless reaction time, 8, is not affected by order of magnitude variations
2224
Complex linear polycondensation - I Table 3. The effect of varying KE and KT on the ester interchange and transesterification reactions (kT/kE= if). Dimensionless time e 0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Moles of methanol formed K*=l KT=l 0.14920 O-24673 040022 0.51545 060402 0.67332 0.72846 0.77284 0.80884
K,=lOOO KT= 1000 0.14939 O-24694 040169 0.51753 060626 0.67547 0.73034 o-77443 0.81025
a two-parameter search would be required to fix the values of k, and kE precisely. The dimensionless reactor volume, P, calculated from Eq. (4) decreased by approximately 15 percent in the simulations presented here. This volume decrease corresponds to a 12 percent increase in catalyst concentration. Variation in catalyst activity, which Fontana did not investigate, might cancel this increase in catalyst concentration. Davies[6] points out that polycondensation kinetics are best described through second-order rate expressions. The results obtained from the simulated runs of this study indicate that Fontana’s experimental methanol data might be presented effectively by two second-order rate expressions (one order with respect to hydroxyl and methoxy group) with the catalyst concentration effect included with the rate constants, kE and kT.
in KE and KT. The results of Table 3 indicate that, conducting the methanol withdrawal rate with the reactor pressures of Table 2, the reverse reactions can be neglected. Fontana claims that his experiments were operated with rapid methanol take-off so as to minimize the reverse reactions. OPTIMIZATION OF THE TWO-STAGE Several runs were made with the model in PRODUCTION OF POLY(ETHYLENE TEREPHTHALATE) which the ratio of the forward rate constants for transesterification and ester interchange The production of poly(ethylene terephthalate) was varied (k,lk,=O-1, O-25, O-5, and 1). is typically carried out in a two-stage reactor Table 4 lists the sum of the square of the error [2,3, 131. The objective of the first stage is to between the methanol production of Fontana’s convert dimethyl terephthalate (DMT) through work and the calculated results obtained in this ester exchange with ethylene glycol (EG) to the study for each value of kT/kEinvestigated. The monomer of poly(ethylene terephthalate), results of Table 4 illustrate that the data of his+-hydroxyethyl terephthalate. In the second Fontana are best correlated by a ratio of kTlkE stage the pressure is reduced in order to drive equal to 0.5 (in comparison to all other values off the excess ethylene glycol. As mentioned investigated) when the value of kE is taken earlier in this paper, the literature[2,3] reports to be 5-O (l./mole)2min_, at 180°C. Obviously, that it is essential to carry the ester exchange reactions to completion, i.e. convert all of the Table 4. Effect of varying the forward CT species to A, before proceeding to the rate constant ratio k,/k, on the ester second stage. It is believed that small amounts transesterification interchange and reactions of the CT species will effectively “kill” the reactions of the second stage reactor. Petukhov kdk, {f (Error)*de} x lo4 [4] states that in practice this “end-capping” effect is not observed. The methoxy groups 0.1 32.775 (C, groups) take part in the polycondensation 0.25 13999 reactions, and a polyester with sufficiently high 0.5 3.040 1.0 20,876 molecular weight is obtained. Only when the ester exchange reactor product contains large Error = moles CH,OH produced this amounts of CT does the end-capping effect study-moles CH,OH produced Ref. [7]. appear. 0, = 1.65 (60 min). 2225
J. W. AULT and D A. MELLICHAMP
In order to investigate the end-capping effect, the operation of a two-stage varying volume semi-batch reactor was simulated by the collapsed rate expressions (Eqs. 4-16). By varying the amount of CT in the reacting charge to the second stage reactor, plots of degree of polymerization (X,) were obtained versus CT initially present. A fourth-order Runge-Kutta routine with variable step integration was used to solve Eqs. (4)-( 16) for the case of two moles of ethylene glycol reacting with one mole of dimethyl terephthalate in a two-stage semibatch reactor with one stage operated at constant pressure (complete reflux of unreacted glycol) and the pressure reduced exponentially in the second stage (no reflux of ethylene glycol). Equilibrium constants (&, KE, and KT) equal to unity were used for these simulations. First stage. Typical reaction temperatures in the first stage reactor are in the range 150220°C [ 131. Currently in the production of poly(ethylene terephthalate) it is the practice to employ mixed catalysts, one component, usually a metal acetate [ 141, which is active during the ester interchange step and another component (antimony trioxide [ 151), which becomes active in the polymerization stage. At 220°C the ratio of Fontana’s[7] forward rate constant for ester interchange, kE, to the forward rate constant for polymerization, kp, from the work of Stevenson and Nettleton[8] is approximately 8 (see Table 1). This value for kE/kp might be considered the most reliable value available from data currently in the open literature. However, in order to investigate more than one value of kElkp and kTlkp, the first stage was simulated with both kElkp = 8 (kT/kp = 4) and also kElkp = 4 (kT/kp = 1). These latter values correspond to the situation where the transesterification and polymerization reactions have the same forward rate constants (kT/kp = 1). Since during the first stage of operation the ethylene glycol is only depleted through reaction, the methanol concentration can be computed directly from the reactor pressure (Eq. 24). The initial conditions for the ester interchange reactor (first stage simulations) are
Table 5. Initial and operating conditions for simulations of first stage Reaction temperature: 220°C Equilibrium constants: K, = KE = KT = 1 Forward rate constant ratios: +$~+g,+ P P
F
P
Vapor pressures of volatile specie& p* (C,) = 60 atm,p* (AF) = 2.5 atm Dimensionless
Constant Reactor Pressure:
II, = II (13)= *(A,) Dimensionless
(0) = O-0267
initial molar quantities:
Total initial moles = 3 CT(O)=&(O) = 2/3 AT(O) = A,(O) = C,(O) = 0 Reflux: Complete reflux of the unreacted ethylene glycol and no reflux of the methanol produced tThe pure component vapor pressures were obtained from Ref. [ 161.
(p* (C,), p* (AF))
listed in Table 5. The operating reactor pressure corresponding to a dimensionless pressure of O-0267 is approximately 1.6 atm. Figure 2 depicts the dimensionless molar concentration profiles vs. dimensionless reac-
0.5 --
---
-
0
I
Dimensmnless
k/k,=& kE/kp=4,
k/k,=4 kT/kp= I
3
2
reaction
time
Fig. 2. &, AT, A,, and C, vs. 0 for first stage simulations.
2226
Complex linear polycondensation
tion time, 8, for ethylene glycol &), hydroxyl groups (AT), m,ethoxy groups (C,), and internal ester links (AI) during the simulation of the first stage production of poly(ethylene terephthalate). If the ester interchange reaction were the only reaction occurring in this stage, the glycol depletion would be the same as the methoxy group depletion. However, after a dimensionless reaction time of approximately O-25 (kE/kp = 4, k,/k, = 1) the transesterification and polymerization reactions begin to become important. The maximum obtained in the AT profile at 8 equal to 0.5 is the direct result of this change in reaction rate magnitude, the transesterification and polymerization reactions begin depleting the hydroxyl groups causing the reverse trend in the curve of AT vs. 0 in Fig. 2. The results for kE/kp = 8, kT/kp = 4 are similar with the exception of a shift to the left in Fig. 2. Equilibrium conditions are reached sooner in this case. In terms of dimensional reaction time, t, the dimensionless time is defined as 0 = kp *
- I
The amount of C, removed during the course of reaction in the first stage was determined by material balance on the C, in solution and the amount of C, reacted. The results of the first stage simulations (Fig. 3) indicate that the maximum amount of CH,OH that can be recovered is approximately 99.3 percent of the theoretical total. Thus, even at equilibrium,
Initial Moles . t VII
I
*
0.02
For the cases presented in Fig. 2, k, is approximately O-002 1. mole-‘mm-’ (see Table l), and the initial reactor volume, V,, is approximately O-3 1. Thus, a dimensionless time of 0.5 corresponds roughly to 25 min of actual reaction time. Since the results of Fig. 2 indicate that equilibrium conditions are reached after 125 min (8 = 2.5)) the design engineer may conclude that the total reaction time required for this first step in the production of poly(ethylene terephthalene) from DMT and EG should be between 25 and 125 min. In order to narrow this range of operating time to a more select group of reaction times, it is helpful to observe the change in the percent total possible methanol removed from the first-stage semi-batch reactor as a function of reaction time. % Methanol removed =
C, Removed . 1oo. CT(O)
004
I
I
I
I
0.06
0.1
0.2
0.4
Dimensionless
reaction
I
I
I
I
06
I
2
4
time
Fig. 3. Percent total methanol removed during first stage.
there exists in the polymer melt a small fraction of unconverted methoxy groups. According to Petukhov [4], a substantially much higher amount of methoxy groups must be present before an end-capping effect appears in the second stage. The degree of polymerization, X,, given by Eq. (16), increased to a value of 1.98 at equilibrium conditions in the first stage simulations. This value of X, confirms the results reported in the literature, i.e. the ester exchange product is mainly comprised of dimer and trimer oligomers with hydroxy and methoxy end-groups [2,13]. The total reacting liquid volume decreased by 25 percent during the course of the ester interchange step. Employing the usual assumption of a constant volume reactor during the simulations would have introduced considerable error in the final semi-batch reactor results.
2227
J. W. AULT
and D. A. MELLICHAMP
Second stage. Poly(ethylene terephthalate) is formed when the product from the first stage reactor is heated to 270-285°C with continuous evacuation to low pressures (2-1 mm Hg) [2, 13,151. The high temperature is required in order to maintain the polyester product in molten form. The growth of the polymer molecules is accompanied by a substantial increase in the fluid viscosity. Extreme diffusional resistances are encountered by the evolving glycol and methanol species if the polymer is allowed to solidify partially. Low pressures are necessary in order to drive the transesterification and polymerization reactions to completion yielding internal ester linkages and the by-product C, and& species.
At 275°C kE/kp (Fontana[71 and Stevenson and Nettleton [9]) is approximately 4,. indicating that the energies of activation for the three reactions are practically equal. In all runs a total second stage dimensionless reaction time (0,) of 20 was used. Twenty dimensionless time units correspond to approximately 70 min of actual reaction time. To reproduce a typical pressure draw-down cycle, an exponential decrease in dimensionless reactor pressure (from the initial equilibrium pressure to a final pressure equivalent to 2 mm Hg absolute) was made during the first half of the reactor cycle (0,/2 = 10). During the final half of the cycle the operating pressure was maintained constant at m (0,).
40) = T,(O)exp {-[me(O)-d&II (Ulo)) 0 s 8 s t&!/2 (25)
AT+& * AI+CF AT+AT G A,+AF.
T(O) = .rr(&) In order to verify or disprove Petukhov’s observations, the second stage production of poly(ethylene terephthalate) from ethylene glycol and dimethyl terephthalate was simulated by Eqs. (4)-(16). A set of starting conditions corresponding to successively longer operating times (0,) for the first stage, i.e. decreasing concentration of the end-capping CT species, was chosen. Preliminary tests indicated that endcapping effects were sensitive to variations in k,/k, (and relatively independent of changes in kE/kp). To evaluate the end-capping sensitivity to the transesterification rate constant, the second stage reactor simulations were performed for three separate cases: (1) kE/kp = 1 (kE/kp = l/4, (2) k,lk, = 4 (k,/k, = l), and (3) kElkp = 8 (kT/kp = 4). The simulation with kE/kp = 8 (kT/kp = 4) or kE/kp = 4 (kT/kp = 1) in both the first and second stages represents a reacting system in which equal energies of activation for the ester interchange, transesterification, and polymerization reactions are observed. The simulation with kE/kp = 4 (kT/kp = 1) in the first stage and k,/k, = 1 (kT/kp = l/4) in the second stage represents the case of unequal activation energies (polymerization reaction greater than both ester interchange and transesterification reactions).
&?I2-==c 8 c 8,.
(26)
Ault [5] summarizes the initial and operating conditions for the second stage simulations. Also, the details of the numerical solution of Eqs. (4)(16) are given in [5]. For the case most likely to give end-capping (kE/kp = 1 and kdk, = l/4), the number average degree of polymerization, X,, obtained in the second stage is shown in Fig. 4 as a function of dimensionless reaction time with the mole fraction methoxy groups (C,) in initial feed as a parameter. Included in Fig. 4 is the curve for X, corresponding to the ideal case of “pure monomer” (C, = 0) fed to the second stage. Substantial decrease in the degree of polymerization is observed when the product from the ester exchange reactor contains a methoxy end-group mole fraction greater than approximately O-02. When the initial charge to the polymerization stage contains a CT mole fraction greater than about O-10, the polymer growth is effectively “killed”. The effect of higher ester interchange and transesterification rate constant ratios, k,/k, and kTlkp, upon the number average degree of polymerization, X,, is illustrated in Figs. 5 and 6. Here the unreacted methoxy groups have a
2228
Complex
linear polycondensation-
I
XC,)(O)
8,
I
0.425
025
I
0.55
0.05
2
0.270
0.50
2
0.45
0.10
3
0.24
0.25
4
0.60
0.025
X(C,)(O)
---
0
Dimensionless
.
I
0
I
2
IO
5
Dimensionless
reaction
time
stage
I
I
I
I
2
5
IO
20
Dimensionless
reaction
time
time
in
second
stage
20
in second
Fig. 4. The effect of the methoxy groups on degree of polymerization (,4,/k, = 1, kT/k, = 0.
I
reaction
Fig. 6. The effect of the methoxy groups on degree of polymerization (kE/kp = 8, b/kp = 4).
I
I
8,
in second
I
stage
Fig. 5. The effect of the methoxy groups on degree of polymerization (kE/kp = 4, b/k, = I).
greater chance to react with ethylene glycol before it is drawn off at the low reactor pressures (II(O) - 10e4). At low glycol concentrations the CT end-groups are essentially consumed only by the transesterification reaction. If the polymerization reaction is faster than the transesteri-
fication reaction, as is the case in Fig. 4, the hydroxyl end-groups (AT) disappear before they have the opportunity to react with the methoxy groups. On the other hand, with k,/kp = 8 and kT/kp = 4, an actual increase in the degree of polymerization is possible (as shown in Fig. 6). From these results, it is evident that a polymerization catalyst in the second stage reactor should enhance the transesterification reactions as well as the polymerization reactions. Figure 7 indicates that a moderately high molecular weight polyester results from the second stage reactor (0, = 20) if the ester exchange step is concluded in approximately 100 min (0, = 2) when the key transesterification rate constant is relatively small (kT/kp = 0.25). When the transesterification rate is of the same order of magnitude as the polymerization rate the first stage reaction time can be reduced by about 50 per cent (0, = 1) with no degradation in degree of polymerization of the product from the second stage. Finally, with a transesterification rate four times higher than the polymerization rate (kT/kp = 4) the first stage reaction time can be reduced by a factor of ten (0, = O-2) with no overall degradation in performance. Or, by a further reduction in first stage reaction time (to 8, = 0.0% an approximate 30 per cent enhancement in degree of polymerization from the second stage would be observed. 2229
J. W. AULT and D. A. MELLICHAMP 70,
attempt to eliminate the zero functional species (terephthalic acid and its higher oligomers). The product of the first stage is polymerized in a single subsequent stage without end-capping effects occurring. Furthermore, additional references in the patent literature describe the deliberate introduction of zero functional species to enhance the degree of polymerization in commercial reactors. A more complete study of the enhancement effect will be given in the sequel after the model (with difFusiona effects included) is developed to describe reaction at high degrees of polymerization.
I
0.02
I 0.04
Dimensionless
I 0.1
02
reaction
0
kE/kp=8,
kT/,kp-4
A
kE/kp=4.
kT/kp= I
0.4
time
I I
in first
I 2
I 4
CONCLUSIONS
stage
Fig. 7. Degree of polymerization in product from second stage as function of reaction time in first stage.
These differences represent significant productivity increases; however, they are based on a two-stage, semi-batch model which can only be applied to small well-stirred reactors or to thin film reactors. Most commercial reactors, although designed to enhance stirring and the continuous formation of thin films as much as possible, actually are severely difhrsion-limited in the final stages of reaction (X, > 20). In such a reactor the end-capping effect would be much less likely to occur (even with a relatively low transesterification rate). The unreacted terminal methoxy groups would have considerably more time to react with terminal -OH groups (which deplete more slowly because of the relatively low glycol diffusion rate). Hence, Petukhov[4], who based his conclusions on evidence obtained from an actual industrial process, probably is correct in stating that end-capping is only observed at high CT levels. Mellichamp [ 171 reports that in the direct esterification of terephthalic acid with ethylene glycol, for example, the first stage can be operated at very high temperatures in order to increase reaction rates and yield a high degree of polymerization (on the order of 6-20), making no
1. After a review of the literature it is evident that more thorough kinetics studies on the ester interchange, transesterification, and polymerization reactions are necessary before the two stage production of poly(ethylene terephthalate) can be modeled in an absolute sense. 2. The semi-batch reactor model presented in this study can be used to correlate kinetic rate data. It is possible, through preliminary theoretical investigations, to minimize the complexity of experiments and the analysis of results in determining polycondensation kinetic parameters. 3. In a two-stage process utilizing a wellstirred semi-batch reactor end-capping can occur in the second stage if the relative ratio of the transesterification reaction rate constant to the polymerization rate constant is less than unity. However, at values greater than one, substantially higher concentrations of end-capping reactants (C,) can be depleted effectively. Hence, the monomerization stage can be operated at holding times significantly less than required to obtain complete conversion to monomer, with a resulting increase in productivity.
2230
NOTATION A
molecular unit in the ABABAB. . . polymer chain, or total dimensionless molar concentration of A units
Complex linear polycondensation
AF dimensionless
molar concentration of “Free A” AI dimensionless molar concentration of “Internal A” AT dimensionless molar concentration of “Terminal A” B molecular unit in the ABABAB. . . polymer chain, or total dimensionless molar concentration of B units molecular unit in the CBABAB. . . c polymer chain, or total dimensionless molar concentration of C units molar concentration of CF dimensionless “Free C ” dimensionless molar concentration of C, “Terminal C” ester interchange reaction equilibrium & constant polymerization reaction equilibrium KP constant reaction equilibrium KT transesterification constant molecular weight of AF M(A,) molecular weight of C, M(C,) volumetric flowrate of CF and AF reQ0 moved from the reactor Q dimensionless volumetric flowrate of Q”P* (CF) ” R RE RP RT T
V
volume of reacting mass initial volume of reacting mass P dimensionless volume of reacting mass mole fraction of AF in liquid X(A,) mole fraction of CF in liquid X (C,) mole fraction of CT in liquid X( C,) X, number average degree of polymerization (chain length) kE second- or third-order forward ester interchange rate constant? kP second-order forward polymerization rate constant? kT second- or third-order forward transesterification rate constant! p* (AF) pure component vapor pressure of species AF at reaction temperature, V,
T p* (C,)
pure component vapor pressure of species CF at reaction temperature, T t
dimensional time
Greek symbols
dimensionless reaction time total dimensionless reaction time in first stage total dimensionless reaction time in second stage dimensionless equilibrium pressure dimensionless reactor pressure molar density of reactants equilibrium pressure reactor pressure mass density of initial reacting mixture
andAF’ RTk,(V,,[(O))’
gas constant dimensionless reaction rate for collapsed ester interchange reactions dimensionless reaction rate for collapsed polymerization reactions dimensionless reaction rate for collapsed transesterification reactions absolute reaction temperature
- I
tAll rate constants reactants.
expressed
in terms of monofunctional
REFERENCES
[ll MELLICHAMP D. A., Chem. Engng Sci. 1969 24 125. I21Anon., Brit. Chem. Engng 14 BCE Process Scan 1969. 131 FORNEY R. C., McCUNE L. K., PIERCE N. C. and TOMPSON R. Y., Chem. Engng Prog. 1966 62 88. B. V., The Technology of Polyester Fibres. MacMillan, New York 1963. 141 PETUKHOV [51 AULT J. W., Ph.D. Dissertation, University of California, Santa Barbara, California 1971. 161 DAVIES T., High Polymers, Vol. XIX, Chapt. VII. Interscience Publishers, New York 1964. [7j FONTANA C. M., J. Polymer Sci.: Part A-I, 1968 6 2343. 181 CHALLA G.. Makromolekulare Chem. 1960 38 125. ,9j STEVENSON R. W. and NETTLETON H. R., J. Polymer Sci.: Part A-I 1968 6 889. [lo] ABRAHAM W. H., Chem. Engng Sci. 1970 25 33 1.
2231
J. W. AULT and D. A. MELLICHAMP [ 1 l] CHALLA G., Makromolekulare Chem. 1960 38 105. [121 CHALLA G., Recueil trau. Chim. Pays-Bas 1960 79 90. [13] GOODMAN I. and RHYS J. A., PO&esters, Vol. I, Saturated Polymers. Elsevier New York 1965. 1141 FLETCHER N., British Patent 2.998.412. Auuust 29 1961. il5] TURNER G. MI, U.S. Patent 3,161,710, December 15 1964. [I 61 PERRY J. H., ChemicalEngineers’ Handbook, 4th Ed. McGraw-Hill, New York 1963. [17] MELLICHAMP D. A., U.S. Patent 3,496,146, February 17 1970. Resume - Les auteurs montrent qu’un modble cinttique, tenant compte de la presence de composes de fonction zero, un et deux, correspond aux donnees dune reaction experimentale d’echange d’esther de la litterature. Dans une seconde etude, les auteurs ont simule la production en deux phases de terephtalate de polyethylene dans un reacteur-agitateur a charges discontinues. Les composes de fonction zero et un presents dans le produit resultant de la phase de “monomerisation” et qui d’ordinaire occasionnent un arr&t dans la chaine du polymere dans la seconde phase, menaient a un produit de poids moliculaire superieur, dans certaines conditions des taux relatifs de reaction. Zusammenfassung- Es wurde dargelegt, dass mit Hilfe eines kinetischen Modells, das die Anwesenheit null- und monofunktioneller sowie bifunktioneller Species beriicksichtigt, die experimentellen Esteraustauschreaktionsdaten aus der Literatur in Korrelation gebracht werden konnen. In einer zweiten Untersuchung wurde die zweistufige Herstellung von Poly(athylen terephthalat) in einem gut gertihrten Halbchargenreaktor swinliest. Es wurde gezeigt, dass die aus der “Monomerisation” Stufe herrilhrenden null- und monofunktionellen Species in dem Produkt, die normalerweise in der zweiten Stufe Anlass zur “Endverkappung” geben, unter gewissen Bedingungen der relativen Reaktionsgeschwindigkeiten zu einem hiihermolekularen Produkt fiihren.
2232