117
Ind. Eng. Chem. Prod. Res. Dev. 1980, 19, 117-125
Poly(ethylene terephthalate) Formation. Mechanistic and Kinetic Aspects of the Direct Esterification Process Herbert K. Reimschuessel Allied C,bemical Corporation, Morristown, New Jersey 07960
The prirncipal equilibrium reactions entailed in the formation of poly(ethy1ene terephthalate) by direct esterification of terephthalic acid with ethylene glycol are (1) esterification-hydrolysis, (2) polycondensation-glycolysis, and (3) transesterification-acidolysis. The reactive species in these reactions are carboxyl groups, glycol hydroxyl groups, and the moieties of P-hydroxyethyl carboxylate, glycol dicarboxylate, and bis(terephtha1ate). For the formulation of a convenient kinetic scheme both the extent of esterification (pE)and the extent of polycondensation ( p c ) have been introduced. These parameters are related to the extent of reaction p by the relationship p = pEpc. For a given initial composition the system is completely defined by these two quantities and the fractional conversion
of terephthalic acid (7). The corresponding kinetic and thermodynamic parameters were estimated from appropriate model reactions.
Introduction Commerical polymerization processes for the manufacture of poly(ethy1ene terephthalate) entail either transesterification of dimethyl terephthalate or direct esterification of terephthalic acid with ethylene glycol. The latter process is a rather recent development. Although poly(ethy1ene terephthalate) is produced commercially by either route in large-scale operations both by continuous and discontinuous processes, information on reaction mechanisms is still inconclusive and significant quantitative data on polymerization equilibria and reaction rates are either inadequate or not available at all, particularly with respect to the direct esterification procem. Therefore, this study was conducted to establish for this process a representative mechanistic scheme and to develop data and information suitable for process description and design. Generally, the system considered appears to be characterized by two principal types of equilibria that entail both esterification-hydro1 ysis
i
-C-OH
+
K
HO-
-C-O-
+
HZO
(I.)
and condensation-glycolysis
reactions. Published reports by Ishikawa et al. (19591, Challa (1960), Sumoto and Hasegawa (1965), Mareg (1969), Kemkes (1969), Kodaira et al. (1971), Krumpole and Mdek (1973), and Rod et id. (1976) indicate that this general mechanistic aspect has been well recognized; however, most of the corresponding studies were based upon rather simplified concepts and imodels. It also has been realized that a rigorous analysis of the formation of poly(ethy1ene terephthalate) is complicated by a series of complex side reactions which occur to considerable extents already during the early stages of the polymerization process. These side reactions are indicated by the formation of carboxyl groups, acetaldehyde, vinyl ester groups, water, diethylene glycol, and cyclic oligomers (Buxbaum, 1968). Of particular concern with respect to kinetic studies are those reactions that result in elimination or generation of functional groups entailed in the esterification and condensation equilibrium reactions. They are principally 0196-4321/80/1219-0117$01.00/0
pyrolysis reactions involving both terminal 2-hydroxyethyl ester groups according to eq 3, and internal diester moieties according to eq 4. (3) n
CH,CHO
r
1
For the reaction entailing the terminal 2-hydroxyethyl ester group (eq 3) Buxbaum suggested a seven-membered ring as a transition state, but it is much more likely that the reaction proceeds via the here postulated five-membered cyclic ortho ester type intermediate. Such a mechanism is well supported by studies on 2-hydroxyethyl esters as reported by Hine et al. (1973). The formation of acetyaldehyde from the 1,3-dioxolane moiety is then readily explained via the intermediate formation of ethylene oxide. Using mass spectrometric thermal analysis Kanazashi et al. (1970) identified ethylene oxide as a main thermal decomposition product of poly(ethy1ene terephthalate). Furthermore, the formation of diethylene glycol and concomitant production of water may be interpreted as the result of an interaction of glycol with the five-membered ortho ester intermediate according to eq 5. 0
L
This mechanism is quite compatible with experimental findings reported by Hovenkamp and Munting (1970). In addition, a part of the ethylene oxide formed according to eq 3 may easily react with either free glycol or a terminal 2-hydroxyethyl group to form the corresponding ether structure r
@ 1980 American Chemical Society
1
118
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 1, 1980
Table I. Equilibrium Reactions
20 r 18
'E&
n
3
e 12L g-
G
"
g 10r
,L
It is not the purpose of this paper to elucidate and discuss comprehensively and in detail the secondary reactions encountered in the production of poly(ethy1ene terephthalate). The ones referred to here are examples of those that may seriously impede an adequate determination of kinetic and thermodynamic parameters for the primary reactions of this polymerization process and thus complicate the elucidation of the reaction mechanism. It was therefore considered reasonable to obtain information on the reaction mechanism and the principal thermodynamic and kinetic quantities from studies on appropriate model compounds. Two model systems were employed: one for the study of the reaction of ethylene glycol with an aromatic carboxyl group, the other to investigate the reactions entailed in the esterification of terephthalic acid. Ethylene Glycol-Benzoic Acid Model System This system has been employed previously as a model for the condensation-glycolysis equilibrium (eq 2) by Hashimoto and Hiraoka (1968) and by Hovenkamp (1971) with respect to the effect of various substituents in p substituted benzoic acids and the influence of different types of metal catalyst, respectively. Neither of these studies considered the two esterification-hydrolysis equilibria 6 and 7 -COOH
+
1
0
I1
-C-O(CH2)z@H
+
+
HO(CH21zOH Z Z -C-O(CH,),OH
HOOC-
n
-C-O(CH2)2-OC-
K
(6)
H20
i-
H*0
(7)
which become operative when water or excess carboxyl groups are present. Thus the process of formation of glycol esters by direct esterification of carboxylic acids with glycol may be represented by a mechanism entailing the three equilibrium reactions of the type shown in Table I for the system benzoic acid-ethylene glycol. According to the definitions of the equilibrium constants as presented in Table I, KHt refers to the hydrolysis-esterification equilibrium entailing the 2-hydroxyethyl ester moiety, KHirepresents the equilibrium involving the internal diester group, and K , pertains to the condensation equilibrium. These three equilibrium constants are interrelated by the relationship K, = KHt/KHi
(11)
The rate constants and kE(2) refer to reactions entailing the first and second glycol hydroxyl group, respectively, whereas k , is related to the glycolysis reaction. In analogy to the corresponding equilibrium constants, k~~ and k H '
_LPL20
10
75
-4r
L 50
[C3Oh]xl0
I
60
L - i _ E _
'0
60
90
(Mdg
Figure 1. Relationship between the rate constant and the carboxylic acid concentration.
are the rate constants for the hydrolysis of the terminal and internal ester moieties, and k , pertains to the condensation reaction. From the mechanism depicted in Table I it follows that the total process is characterized by two independent reactions for which the following two rate equations may be written. d[B1/dt = KHi[wl(k,(,,Kc[(E,)B1+ 2kE(Z)[(Ed)B])[Bl(2kE(l)[Gl+ kE(Z)[(Et)BI)(12) d[G1 /dt = K,[(E,)Bl(kE(l,KHi[wl+ kg[(Et)Bl]2[Gl(kE(l)[B]+ 2kg[(Ed)R11 (13) Furthermore, the five chemical species in this system are interrelated by the following three independent stoichiometrical reactionships [WI = [Wol + ([Bo1 -
PI)
[(Et)g] = [(E~)B]O - ([Bo] - [Bl) + GO)
(14) [GI)
(15)
[ ( E ~ ) B=I [ ( E ~ ) B + ] o ([Bo] - [BI) - ([Go] - [GI)
(16)
-
where the subscript 0 denotes initial concentrations. Thus, eq 1 2 and 13 may readily be rewritten in terms of the particular initial concentrations and the respective concentrations of benzoic acid and glycol. Employing procedures and conditions that will be reported elsewhere (Reimschuesselet al., 1979) experimental data have been obtained and evaluated. It was found that (a) all reactions were catalyzed by carboxyl groups (linear relationships such as shown in Figure 1 for the hydrolysis of ethanediol dibenzoate were indicated for the dependence of k on the concentration of carboxyl groups), and (b) antimony triacetate catalyzed the condensation reaction but did not affect the esterification reactions as can be seen in Figure 2. These findings appear to justify representation of the individual rate constants in eq 12 and 13 by the following relationships
k , = kgO
kE(1)
=
kE(ljO + kE(l)CIBl
(17)
kE(2)
=
kE(2)O + kE(2)C[Bl
(18)
+ k,"[B] + kgm[Sb]+ k,'"[B][Sb]
(19)
where the superscripts 0, c, m, and cm denote the rate constants for the uncatalyzed reactions (O), reactions catalyzed by carboxyl groups (c), reactions catalyzed by the metal catalyst (m), and reactions entailing interactions
119
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 1, 1980 1.8
I
1.7
1.6 15 14
13
-
12-
g 5
/
1.1 -
10.
7
2
.9'
5
.8-
7 6. 541
3
L
50
1 ha
n e ( V I,,
L '50
230
2 60
Figure 2. Effect of antimony of the esterification of benzoic acid with ethanediol at 202 O C . [Sb(00CH3)3]:0 , 0; m, 1.64 X 10" mol g-': A, 3.28 x lo4 mol/g
' \UTES
Figure 4. Hydrolysis of ethanediol dibenzoate 0 = 202 "C; "C; 0 = 226 "C; [(EJO] = [Wo].
X =
215
'11 - r 5
IINU-E>
Figure 3. Hydrolysis of' ethanediol monobenzoate: solid symbols = 226 "C; open symbols == 202 "C; 0 , O = glycol; . , 0 = benzoic acid; [(EJoI = W o l .
Figure 5. Condensation of ethanediol monobenzoate at 202 "C; (concentration of antimony triacetate: o = 0; A = 1.09 x lo4; x = 2.1'7 X lo4; 0 = 4.41 X lo4 molig).
Table 11. Kinetic and Thermodynamic Parametersa A S , cal
hE(')o hE(!)' 1 2 ~ ( ~
h ~ j ti! g
kgc hgrn hgCm K', KH'
A 2.55 x 1 0 - 5 8.672 X l o 5 ) : 8.426 X 10' ~7.564 ) X 10' 5.038 X 10" 3 . 3 2 5 x 106 4.071 X 10'* 3.60 X 10:
E , cal (mol).'
(mol K)-I
A H , cal (mol).'
o
20.63 X i o 3 29.71 X l o 3 10.31 X l o 3 49.16 X l o 3 21.86 X l o 3 27.60 X l o 3 -19.21 -9122 10.80 5666
h," (kg m o l - ' mirt-I); k t C (kg' mol-' m i n - I ) ; K , (di. mensionless).
between the carboxyl groups and the metal (antimony) catalyst (cm). Assuming that (1) the rate constants depend on the temperature according to the Arrhenius equation: k = A exp(-E/RT), and (2) for the temperature range considered entropy and enthalpy changes are constant in accordance with the thermodynamic equation
a nonlinear regression procedure-a discription of which is presented elsewhere (Reimschuessel et al., 1979)-was
C"
lu6C
f
1II
I"" 1
4c
d l
4rTES
Figure 6. Condensation of ethanediol monobenzoate a t 215 "C; (concentration of antimony triacetate: 0 = 0; X = 1.25 X lo4; 0 = 1.96 X 10" mol/g).
employed and resulted in the set of parameters listed in Table 11. Using these parameters the rate equations were integrated. Since the kinetic system comprising eq 12 through 19 is nonlinear, the Runge-Kutta integration scheme was employed. The results are shown in Figures 3 through 7 together with the experimental data (symbols). The very good agreement between calculated and experimental data indicates that the process of formation of ethanediol benzoates is adequately represented by the mechanism depicted in Table 1.
120
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 1, 1980 I
Table IV. Values of Equilibrium Constants a t 230 "C
reactions, respectively. Related to the transesterification reaction is the rate constant k T , whereas k A is the rate constant for the acidolysis reaction. Substituting kE(21), kE(22)7 kT, and K E ( Z Z ) by IZHiKE(21), kHiKTKE(21),kAKTt and K T K E ( ~respectively, ~), the following three rate equations may be formulated from the mechanism shown in Table 111. . 0
330
bSC
901:
120C
.
1500
l80C
2100
2400
2700
30W
'WNUTES
Figure 7. Condensation of ethanediol monobenzoate at 226 "C; 0 = (concentration of antimony triacetate: 0 = 0; X = 7.46 X 1.26 X 10- mol/g). Table 111. Equilibrium Reactions and Equilibrium Constants
Terephthalic Acid-2-(2-Methoxyethoxy) Ethanol Model System The process of esterification of terephthalic acid with 2-(2-methoxyethoxy) ethanol was considered another appropriate model reaction for the formation of poly(ethy1ene terephthalate) and has been investigated. Details on experimentation and evaluation will be reported elsewhere (Reimschuessel and DeBona, 1979). It was found that this process is characterized by the three equilibrium reactions shown in Table 111. There are, as can be seen, two esterification-hydrolysis equilibria entailing the reactions of the two terephthalic acid carboxyl groups; the third reaction is a transesterification-acidolysis equilibrium involving two terminal terephthalic acid moieties. The products of these three interrelated equilibria are terephthalic acid, its monoester and diester, water, and the particular alcohol which is in this case the 242-methoxyethoxy) ethanol. The three equilibrium constants are interrelated by the relationship where KE(21) refers to the esterification-hydrolysis equilibrium entailing the second hydroxyl group of the glycol and the first carboxyl group of the terephthalic acid, whereas KE(22)represents the equilibrium involving the second function of either of the two reactants. KT has been assigned to the third reaction, which is a transesterification-acidolysis equilibrium. The rate constants k,,,,), kE(z2), and k~~ refer to the corresponding esterification reactions and the hydrolysis
2V1) d[Hl/dt = ~ H ~ ( ~ K E ( ~ ) [-T[Wl([Hl ][DI KTKE(21)[Hl[Dl~ + 2kA(4[Tl[F] - KT[H12) (24) d[Fl /dt = ~ H ~ ( K T K E ( X[Dl ) [ H-I 2[Fl [WI) + ~A(KT[H]' - 4[TI[Fl) (25) d[Tl/dt = k~'([Hl[Wl- ~ K E ( ~ ~ ) [ T I+ [DI) k~(&[Hl' - 4[Tl[FI) (26) d[H]/dt = - d[F]/dt - d[T]/dt The five chemical species of this system are interrelated by the following stoichiometrical relationships (27) [Fl = [Flo + ([TI, - [TI) - ([HI - [HI,) = [Wl = [Wlo + ([HI - [HI01 + 2([Fl [Wlo + 2([Tlo - [TI) - ([HI - [HI,) (28) [Dl = [Dlo - ([HI - [HI,) - 2([Fl - [Flo) = [Dlo - 2([Tlo - [TI) + ([HI - [HI,) (29) where the subscript 0 denotes initial concentrations. The system considered here is characterized by the two equilibrium constants KT and KE(21) and the two rate constants IZHl and k A . As shown elsewhere (Reimschuessel and DeBona, 1979),values for these quantities were obtained for a temperature of 230 "C. The values for the equilibrium constants are listed in Table IV. The value for KE(21) is the same as the one found for KE(2),the equilibrium constant pertaining to the reaction 9 of the benzoic acid-ethylene glycol system. It was also found that the experimental value for the rate constant kHi in the present system was the same as that observed in the benzoic acid-glycol system. Employing the kinetic and thermodynamic parameters (Table 11) determined for the latter system, kHi was found to be represented by relationship 30.
k~~ = K H ' @ E (+ Z ~~E(,)'([H]+ [TI))
(30)
Here the catalytic active concentration of carboxyl groups is equal to ([HI + [TI), whereas the total concentration of carboxyl groups is equal to the sum ([HI + 2[T]). Obviously a t a given instance only one of the two carboxyl groups of the terephthalic acid is entailed in the catalysis of the reaction. The value for kHi is 5.48 X (min)-l. The rate constant kA, related to reaction 22, was found to depend upon the composition of the reaction mixture. It was found to increase as the concentration of terephthalic acid increased. As can be seen in Figure 8, a linear relationship is indicated between k A and the ratio [T]/[H] and may be represented by the equation k A = k~' + k ~ ~ ( [ l ' ] / [ H ]=) 9.58 X + 4.36 X 10-4([Tl/[Hl (31) The corresponding reaction is obviously subject of electrophilic catalysis entailing ionized carboxylic groups. Since more than one type of carboxylic group is present,
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 1, 1980
Table V.
121
Equilibrium Constants-Comparison with Published Experimental Values
K, ( K , ) this work
Chegolya
468 487 496 507 51 7 527 535 47 3-523
1.15 0.78 0.66 0.54 0.45 0.38 0.34
0.59' 0.50' 0.51'; 0.75b 0.49' 0.48' 0.47' 1.10d 0.61-0.46d
' 2-hydroxyethylbenzoate.
(K,)
(KH1)-l
this work
Chegolya
this work
Chegol ya
1.13 1.46 2.17
1 . 4 9 ; 2.40* 1.42; 2.60*
3.67 2.35 1.26
0.72; 1.20 0.95; 1.49
423 453 503 Initial system:
(Ic*)
(KHt)-'
temp, K
...
...
' Bis(2-hydroxyethyl terephthalate).
oligo-PET.
PET.
101kA x
13
gL.I_LLLLIII__LL 1
0 01
0 02
I
1
'
I
0 03
'
1
1
004
'
'
'
'
I
1
'
'
l
0 05
I
1
l
,
0 06
l
0°'
l
I
t
(&)
Figure 8. Relationship between k A and terephthalic acid concentration.
F H
T
0
100 200 300 400 500 600 700 ROO Minutes
0O 1
2
0
0
0
b C
; C
TL
d
100 200 300 400 500 600 700 Minutes
Figure 9. Esterification of terephthalic acid with 2,2-(2-methoxyethoxy) ethanol at 230 [TI, = 0.279 mol/kg; [F] = 0.279 - [TI - [HI, [D] = 7.382 + 2[T] [HI, [W] = 0.558 - 2[T] - [HI; [W], = 0; [HI, = 0.
Figure 10. Esterification of mono-2-(2-methoxyethoxy)ethyl terephthalate with 2-(2-methoxyethoxy)ethanolat 203 O C : [HI, = 0.266 mol/kg; [F] - 0.266 - [HI - [TI; [Dl = 7.464 + 2[Tl + [HI; [Wl = 0.532 - 2[T] - [HI; [TI, = 0.
the reaction system is characterized by an effective dissociation constant (&.) that changes as the relative concentrations of the individual carboxylic groups change. In the present system there are three dissociation constants, one related to the carboxylic group of the mono-2-(2methoxyethoxy)ethyl terephthalate (KH),and two that carboxylic pertain to the first and the second (KTc2)) group of the terephthalic acid. The system, comprising eq 24-31 is nonlinear and was thus integrated numerically using again the RungeKutta variable step integration routine. The results are shown in Figures 9, 10, arid 11, where the solid lines are the
calculated values and the symbols the experimental data. Though a rather good agreement between experimental and calculated data is evident, it would be interesting to compare the here-developed equilibrium and rate constants with corresponding published values. However, most of the reported data were often-as in the case of the extensive work of Bonatz et al. (1973) and a study by Schumann (1971)-related to so-called "effective" rate constants, that means, to quantities that combined contributions of both chemical reaction and mass transfer. They are therefore useless for a comparison with the present data that relate solely to chemical reactions. Some
