Znd.
Eng. Chem. Res. 1991,30, 2431-2436
243 1
PROCESS ENGINEERING AND DESIGN
Urethane Polymerization in a Counterrotating Twin-Screw Extruder? Alain Bouillouxf and Christopher W. Macosko* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455
Tom Kotnour Central Research Laboratories/3M, St. Paul, Minnesota 55144
Polyurethane formation in a fully intermeshing, counterrotating twin-screw extruder (Leistritz) has been studied. This polymerization is based on a long polyether poly01 (poly(tetramethy1ene oxide)), a short diol (1,4-butanediol), and a liquid form of an aliphatic diisocyanate (dicyclohexylmethane 4,4’-diisocyanate or hydrogenated MDI). A model previously developed by Stuber was modified to introduce the urethane kinetics and rheology. This model predicts pressure, flow rate, and polymer properties as a function of position along the extruder. The chambers are approximated in a twin-screw extruder as a series of continuous stirred tank reactors connected by leakage flows through the mechanical clearances. When compared with experimental data, the model predicts the proper trends in polymer molecular weight, conversion of isocyanate groups, and extruder pressure generation.
Introduction Reactive extrusion is commonly used to graft polymer chains or polar monomers onto existing polymer backbones. Since extruders can mix and process very viscous polymers and low molecular weight monomers, reactive extrusion can also be a one-step process to polymerize and form thermoplastic polymers. The appropriate monomer($ and initiatods) or catalyst($ are fed to an extruder where the polymerization takes place and produces polymer that can be forced through a die to give a finished article. This is a continuous, bulk polymerization with the extruder providing the mixing and heat control. There are numerous possible advantages in using the extruder as a polymerization reactor. By its nature the extruder is a high-rate, continuous co veyor and an efficient mixer of high-viscosity melts. ontrary to other conventional reactors, an increase in viscosity implies improved conveying capacity. I t allows for a good temperature control by way of heat exchangeethrough the barrel and screw surfaces. Therefore, it is possible to carry polymerization in an extruder reactor to high conversions. Further advantages of the extruder reactor include an easy, well-integrated step of devolatilization, followed by on-line compounding and processing. This can eliminate several solidification-remelting stages. Such integration provides more than just economic saving: it also eliminates polymer degradation in processing and may make ultrahigh molecular weights processable. Illing (1969) reviewed nylon production in a singlescrew-extruder reactor, Gouinlock (1968) used a vented single-screw extruder for polycondensation reactions, and
3
‘Portions presented at the AIChE Annual Meeting, New York, November 1987. Present address: ATOCHEM Research and Development Center, 21470 Serquigny, France.
*
Mack (1972) described the application of twin-screw extruders for the same purpose. Despite the many companies that are doing work in the area of reactive extrusion (Sneller, 1985), very little is published. A single-screwextruder reactor was discussed by Siadat et al. (1979). In this study, the extruder feed was a partially converted polymer mixture. This is required because material is transported down the open channel of the screw by the drag forces at the wall and low-viscosity material will not be dragged down the screw. Another problem with a single-screw extruder is that material will build up on the screw because there are insufficient shear forces to drag the high-conversion polymer into the main flow. Fully intermeshing twin-screw extruders are promising continuous polymerization reactors because the two intermeshing screws can serve as good mixers for even very viscous high-conversion polymerizations. The two screws wipe and refresh the material at the wall frequently, preventing wall buildup and also giving good temperature control of the polymerizing fluid. The two main types of twin-screw extruders are intermeshing and nonintermeshing. In nonintermeshing extruders the two screws do not have flights that extend into the channel of the other screw. Thus nonintermeshing extruders behave like two single-screwextruders with only minor interactions between the two screws. Intermeshing extruders are those in which the flight of one screw fits into the channel of the other screw. A further subdivision of twin-screw extruders is by direction of rotation. Corotating extruders have both screws rotating in the same direction and the material exchanges from screw to screw. With counterrotating screws material is transported through the extruder in the C-shaped chambers mostly independent of the other chambers, except for leakage flows through the mechanical clearances. Our research concentrates on polymerization in a fully intermeshing, self-wiping, counterrotating twin-screw ex-
0888-5885/91/2630-2431$02.50/00 1991 American Chemical Society
2432 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 Qf
Figure 2. Flow interactions between C-shaped chambers in a fully intermeshing counterrotating screw extruder (Jansaen, 1978).
TransDortdirection
Figure 1. C-shaped chambers of an intermeshing counterrotating twin-screw extruder showing the leakage flows in the flight gap (Qf), calender gap (QJ, side gap (Q,), and tetrahedral gap (Qt) (Janssen, 1978).
truder, and all further discussion will deal with this system. This extruder has two screws rotating in a figure eight shaped channel. Figure 1 shows how the two screws interact. This system has two major advantages for reactive extrusion. First, as state above, the tight mechanical clearances give very high resistance to back-mixing. This design also prevents significant polymer buildup on the flights and the long residence times that would result. Below we apply the ideal reactor series model of Jansen (1978; Jansen et al., 1979) to a 34-mm-diameter Leistritz, counterrotating twin screw. We modified this model to introduce urethane kinetics and rheology. Some results are discussed here and compared to experimental data.
Ideal Reactor Approximation Model Models of reactive extrusion are needed to study the effect of operating conditions and equipment parameters on extruder performance and polymerization product. The extruder behavior during polymerization is complex, and such models can be very useful for the understanding of many interactions among the processing variables. One approach to modeling reactive extrusion is the segregated reactor model analyzed in several papers (Siadat et al., 1979; Stuber and Tirrell, 1985). This model is of limited use because it can only predict steady-state exit conditions for a known residence time distribution (RTD). The RTD changes with reaction conditions, and measuring the RTD requires expensive pilot-plant time. The segregated reactor model has many other limitations discussed by Siadat et al. (1979) and Stuber and Tirrell(1985; Stuber, 1986). A second approach, developed by Janssen (1978;Jansen et al., 1979) and adapted by Stuber (1986) for the methyl methacrylate polymerization, approximates the twin-screw extruder as a series of ideal reactors. This model approximates the C-shaped chambers as continuous stirred tank reactors (CSTRs) and the leakage flows (see Figure 1) as CSTR inflows or outflows. The most important feature of this approximation is its ability to predict flow and polymerization properties throughout the extruder. The block flow diagram of this model is shown in Figure 2.
A key to using this model is to understand the leakage flows. Janssen and co-workers have worked extensively analyzing flow in a counterrotating twin-screw extruder.
They have characterized four leakage gaps and the associated flows as shown in Figure 1. The flight gap leakage (Qr) is the flow over the flights of the screws produced by drag and pressure flow. The calender gap leakage (8,) is the flow between the top of one flight and the root of the other screw. The side gap leakage (QJis the flow between the leading edge of one intermeshing flight and the trailing edge of the other flight. The tetrahedron gap leakage (QJ is the pressure-driven flow through the gap created because the flight walls are not perpendicular to the screw channel bottom. Janssen has derived the Newtonian flow equation for each leakage flow (see Janssen (1978) for details) in terms of the pressure and drag driving forces. These rather complex algebraic equations can be rewritten in terms of screw speed N; viscosity 8'; pressures p', p", and pi-2; and three constants related to the geometry, Q3A, Q3B, and QTB. Superscripts i, i-1, and i-2 denote the ith, i-lth and i-2th CSTRs. The three leakages Qt, Q,, and Q, depend on viscosity, pressure, and screw speed in the same way so they can be lumped together as Q3.For the ith CSTR, these leakage equations are as follows:
sg = Qj + s', + Qt
(1)
Si, = (Q3A)N + (Q3B)(pi - P'-~)/v'
(2)
The tetrahedral gap leakage does not depend on N:
Qt = (QTB)(p' - pi-')/?'
(3)
Q3A is a constant that combines all the drag flow terms of the flight, calender, and side gap leakages. Q3B is a constant that combines all the pressure-driven flow terms of the flight, calender, and side gap leakages. QTB is a constant that combines all the pressure-driven flow terms of the tetrahedron gap leakages. With the flow equations connecting the CSTRs, several assumptions are needed to describe the conditions inside the CSTRs. These are as follows: The first assumption is homogeneous C-shaped chambers. Material could be nonhomogeneous due to more converted, more viscous material building up near the wall, but the self-wiping action and the high shear in the extruder should give good mixing. The second assumption is that all chambers are fully filled. The next assumption is uniform extruder configuration. This is the normal setup, but nonuniform conditions could be handled by modifying the dimensions of the leakage flows and the volume of the affected chambers. The last assumption is uniform wall temperature (temperature is constant from the hopper to the die). Nonuniform temperature would be handled in the same manner as a nonuniform configuration. Using the leakage flow equations, eqs 2 and 3, the mass-, component-, and heat-balance equations can be written as follows:
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2433 flow
(5)
mass balance d(Vpi)/dt = Qnp"
+ @;+'pi+'
- Q&tp'
(6)
+ V'(rate)'
(7)
component balance d(v'xi)/dt = Qf,xi-'
+ ,i;"xi+l
- @;,,xi
heat balance d( VpiCPTi)/dt = Qfnpi-lCpTi-l + Q+lpi+lC P Ti+' - Qioutpicp Ti +
VAHpkp(NCO)o+ UR(S - B ) ( ~ T C Y ) ( T- ~ T i~) ~(8)
where superscript i denotes the ith CSTR (with equations appropriately modified near the inlet and outlet), x denotes any component in the reacting stream, and V, R, S, B, and a are dimensions given by Stuber (1986) for the same extruder. Performing a net forward mass flow balance across any cross section (see Figure 2) gives forward mass flow rate = (2NV -
- @;)pi
- @;+lpi+'
(9) Equations 2,3, and 9 are combined and a forward mass flow rate balance is written for every CSTR except the first (where the pressure is fixed by the feed pressure). If the feed pressure, the screw speed, the viscosities, and the extruder constants are known, all the forward mass flow rate balance equations create a matrix that can be solved to give the pressures in all the CSTRs. Knowing the pressure profile, the leakage flows are then known and can be used in the component-balance equation to solve for the polymerization properties. For the reacting flow system the viscosity is changing throughout the extruder, so the pressure- and flow-balance equations must be simultaneously solved with the component- and temperaturebalance equations. During step growth polymerization,viscosity will change with temperature and molecular weight (or conversion). To incorporate these effects into the flow equations, eqs 2, 3, and 9 will be used exactly as is except that the viscosity will be a function of the conversion, and of the temperature as described in the next section. Our approach will use the urethane kinetics and rheology from the following park of this paper to predict flow balances and polymerization properties all along the extruder barrel.
Kinetics and Rheology of the Urethane Model Composition Viscosity is the most important material property in polymer-processing operations involving flow. Thermoplastic melt viscosity is influenced primarily by temperature and shear rate. Reactive systems are complicated by the increase in viscosity due to chemical reaction. In reactive extrusion, since flow is coupled with the chemical reaction, it is essential to obtain viscosity data as a function of reaction and temperature for use in modeling. An expression relating explicitly the viscosity to temperature and the extent of reaction is needed because temperature affects the viscosity rise in two opposing ways. Increasing the temperature will cause the viscosity (7)to decrease at a given conversion but will also raise the reaction rate,
producing an increase in conversion and viscosity. In order to separate these effects, the kinetics must be measured independently. A viscosity-conversion correlation can be constructed by taking isochrones of viscosity and extent of reaction. This simple procedure is explained in detail by Castro and Macosko (1980, 1984). Kinetic Method. Many methods have been used to monitor the kinetics of bulk polymerization reactions. Extensive reviews have been written by Kamal(1973) and Mussati and Macosko (1973). In our study we have used a thermal method, adiabatic temperature rise, based on the high exotherm inherent to the reaction of isocyanate with hydroxyl groups. This technique and how we can use it to obtain kinetic parameters have been described in detail by Macosko (1989). Typically any plastic container over 5-10-cm diameter is sufficient to maintain adiabatic conditions in the center of a high-speed urethane polymerization. A 220-cm3polypropylene cup has worked well in our laboratory. Thermocouples are threaded through the walls of the cup to hold them in a central location. The reacting mixture is prepared by weighing a solution of 1,4-butanediol (BDO) + poly(tetramethy1ene oxide) (PTMO) + catalyst and the corresponding quantity of isocyanate. An homogeneous mixture is obtained by handmixing, which means the mixture was stirred vigorously for approximately 20 s and then poured into the polypropylene cup. The initial temperature of the mixture is 25 "C. Poly01 and BDO readily absorb moisture from ambient air and must be degassed for several hours before handmixing to remove water. The thermocouple signals are recorded on a microcomputer. These temperature versus time profiles can then be fit to various kinetic models. Kinetic Fitting. In the case of the urethane reaction Macosko (1989), Camargo et al. (19831, and Hagar et al. (1981) suggest a simplified kinetic expression d[NCO]/dt = k[Cla[NCOl*[Hlc
(10)
with
k = A exp(-E,/RT)
(11)
where a is the order with respect to catalyst, b + c is the overall order of the reaction, and [C], [NCO], and [HI are the concentrations of the catalyst, isocyanate, and active hydrogen compounds, respectively. This expression is further simplified by introducing the catalyst concentration into the rate constant. Frequently we consider the isocyanate concentration equal to the active hydrogen, [NCO] = [HI, since most polymerizations are run near stoichiometry. Thus the simplest expression used to fit urethane kinetic data is d[NCO]/dt = k[NCO]*
b=2
(12)
The catalyst concentration dependence, which is imbedded in the rate constant obtained for the catalyzed reaction, was obtained by making measurements at several catalyst levels. Combining the data gives an expression that should predict the reaction rate as a function of temperature and catalyst level. This expression is d[NCO]/dt = A ~ X ~ ( E / T ) [ C ] ~ [ N C O ] *(13) with a = 1.1, b = 2, E = -9100 (temperature units, E,/R), A = 7.135 X 10l2(units to give a rate of mol L-' s-l), and [C] and [NCO] are concentrations of catalyst and isocyanate in mol/L. These parameters are in good agreement with the data published by Macosko (1989;Table 2.6) for other urethane
2434 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991
Resrwe mnducers
DK u)
Z 1 P
P
b b
24
*PI-
5 . 2
26
21
pom
28
z9
0
Figure 4. Experimental configuration for fully intermeshing Leistritz counterrotating twin-screw extruder (D= 34 mm, LID = 35).
where 4i is the weight fraction of each component. Temperature dependence is assumed to be of the Arrhenius type: to= I..
0
20
40
eo
80
XI0
120
200
Tima ((I)
Figure 3. Isothermal viscosity rise of a PTMO 1000/BDO/H12MDI system catalyzed with 60 pmol/L DBTDL, 202 "C, 50-mm diameter, 1-mm gap parallel plates.
systems. Sometimes a second rate is added for the slow reaction that occurs without catalyst (Borkent, 1974; Steinle et al., 1980). In our case we have verified that the contribution of the uncatalyzed reaction is negligible, even at high temperature. The parameters above were obtained for 57.3% by weight of hard segment, which is the composition used for the extrusion experiments. The reactivities for the BDO hydroxyl groups and PTMO hydroxyl groups are nearly equal, so eq 13 can be used for a wide range of compositions. Rheology. Isothermal viscosity measurements on catalyzed samples were done with the use of a Rheometrics System Four with parallel-plate geometry, 50-mm-diameter plates and 1-mm gap. The steady shear motor was used, and the shear rate was fixed to 5 s-l. Viscosity was found to be independent of shear rate for this formulation and conversion level. Viscosity samples used with varying temperature (180-192-202 "C) were prepared at room temperature by handmixing using a low concentration of catalyst ([C] = 0.00006 mol/L). Approximately 1.5 mL of the reacting mixture was transferred to the parallel plate, and the viscosity rise as a function of time was obtained. Measurable torque readings were recorded after approximately 10 s. Figure 3 gives an example of the viscosity rise for our system. The final viscosity value in Figure 3 is typical of commercial thermoplastic polyurethanes (e.g., Pellathane product literature, Dow Chemical). Using eq 13 we can transform the viscosity versus time plot into a viscosity versus conversion plot. As shown by Castro and Macosko (1984), plotting reduced viscosity (viscosity divided by the initial viscosity) against extent of reaction, we found that all data fell on a single curve. This means that the viscosity relation can be greatly simplified, since the temperature and extent of reaction effects can be separated. Thus, the general dependence on temperature and conversion becomes dT,C*) = tlO('T3 f(C*) (14) or SAC*) = tl(C*,T)/SO(T) = f(C*) (15) where 7, is the initial viscosity before reaction and C* is the conversion of isocyanate groups; C* = (C, - C)/C,. If we assume linear additivity of the viscosities of the reactants, then 70
= E4iqoi
(16)
A,, exp(E,,/RT)
(17)
with A,, = 0.09876 Pa-s and E , = 16850 cal/(mol K). It was found that an equation of the type (Castro and Macosko, 1980; Macosko, 1989) 7/90
= (C,/(C,- C*))a+@C* (Y = 5.066, /3 = -2, C, = 0.7 (18)
is able to model the experimental data. Parameters for eqs 17 and 18 were obtained for 57.3% by weight of hard segment, which is the composition used in the extrusion experiments. Unlike the kinetic expression, eq 13, the viscosity rise is a function of composition. Thus additional viscosity rise experiments should be done to determine the dependence of A,,, E,,, C,, A, and B in order to apply eq 18 to other hard-segment contents.
Twin-Screw-Extruder Experiments The purpose of the experiments was to study the influence of operating parameters, namely, catalyst concentration, extruder temperature, and screw speed, on molecular weight of the polyurethane produced. We also wanted to create a data base to aid in further development of a model of reactive extrusion. Chemical System. The thermoplastic polyurethane system chosen for this study consists of a polyether soft segment (poly(tetramethy1eneoxide), PTMO 1ooO; Union Carbide). Union Carbide reports a functionality of 2 and a number average molecular weight of 972. The hard segment is based on the chain extender 1,4-butanediol (BDO; GAF Corporation). Dicyclohexylmethane 4,4'-diisocyanate (or hydrogenated MDI) is a liquid cycloaliphatic diisocyanate (Desmodur W, Mobay Chemical Co.). The catalyst dibutyltin dilaurate (DBTDL, T-12; M & T Chemical) was used at concentrations ranging between 0.005 and 0.1% by total weight. Extruder. A 34-mm-diameter, Leistritz self-wiping, fully-intermeshing, twin-screw extruder is used for the study of extrusion of urethane compositions. A barrel length of 1.2 m was used for all the experiments giving a length to diameter ratio of 35. Figure 4 shows the extruder and the associated feed system. The extruder barrel is divided into 10 equal zones (sections). Each zone has individual temperature control with electrical resistance heaters and water jacketed cooling. The screws are segmented into pieces of one-half or one zone long (60 or 120 mm) which are joined together with locking keys to form the full 1,Zm-long screws. The screws for all of the experiments were configured with a pitch means 12-mm advance toward 12-mm-pitch (12" the die per screw revolution) section in zones 0 and 1, an open flight section at the beginning of zone 3 ( 1 0 " long), and a 6-mm-pitch section in zones 2-9. Referring to Figure 1, this screw's configuration corresponds to 18 CSTRs per zone, or 180 CSTRs for the total length of the extruder.
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2435 Table I. Experimental Conditionea run 1 run 2 run 3 run 4 catal, wt 9% of total feed 0.005 0.05 0.05 0.05 temp, "C 200 200 190 200 49 26 screw speed, rpm 26 26 40.2 40.3 76.1 output, g/min 40.1 9.3 5.08 9.3 9.3 residence time, min
run 5 0.05 200 122 189.1 2.05
P
aCompoaition (wt %): 43% PTMO lo00 + 11% BDO + 46% HI2MDI.
Four pressure transducers give the pressure profile for a given set of experimental conditions, and by analyzing the samples coming from two sample ports and from the die (see Figure 4), we get the polymer property profile (mainly molecular weight distribution). Extrusion Experiments. In the study discussed here, a solution of alcohols (PTMO and BDO)containing the catalyst, and the diisocyanate are injected independently into the first zone of the extruder. Only one composition based on 57.3 w t % of hard segment (BDOplus diisocyanate) has been used. The reactive extrusion experiments had many operating variables that could be changed and several operating results that could be observed. For the polymerization, changes were made in the catalyst concentration and the extruder temperature. For the extruder operation, changes were made in the screw speed. The effect of these changes on the throughput, the pressure profile, and the product molecular weight distribution were recorded. The molecular weights of the polymer samples produced in our experiments were measured in a Waters Model 150-Cgel permeation chromatograph (GPC). The solvent used was l-methyl-2-pyrrolidone (NMP) which was run through two Shodex No. A-BOM/S mixed gel columns in series at 85 OC. The GPC was calibrated with polystyrene standards. The extrusion products were collected from the sample ports directly into 20-mL vessels containing a solution of n-butylamine in NMP (1% by weight) in order to quench the reaction. The sampling tube fit into the pressure-transducer port, flush with the barrel interior. The polymer pathway was through an 85-mm-long cylinder that was 3.5 mm in diameter. When we were not sampling, a 85-mm-long solid steel rod was inserted into the port to act as a valve and reduce dead space.
Rssults The polymer products were analyzed for five different runs on the extruder. Table I gives the experimental conditions, and the results of these experiments are listed in Table I1 (weight- and number-average molecular weight). The qualitative trends in Table I1 are reasonable: molecular weight increasea going down the screw (SlS3, exit) and the distribution narrows. Narrowing is expected due to better mixing but the final breadth of the distribution 2 = M,/M, is slightly less than the theoretically expected 2.0 for a well-mixed condensation reaction. This may be due to the GPC calibration based on polystyrene. The M , values are probably more reliable. Molecular weight decreases with decreasing residence time, run 2 vs runs 4 and 5. M , also decreases with catalyst level, run 1 vs 2, and temperature run 2 vs 3. However, the changes in M , are not large. The remarkable result is that these molecular weights are so high even in the second zone of the extruder. Part of the explanation for the high M$s is the sampling method. It takes at least 20 s for a sample to flow out the ports. This is more than the residence time to S2 in run 5. Incomplete mixing in zone 1prevents high conversion
Figure 5. Weight-averagemolecular weight (M,)versus conversion calculated from recursive theory for PTMO 1000/DBO/H12MDI. 1.0-
=
i
I
0.8
-
1
0.6
-
a)
-
i 5
I
5
-
"
WL%DBlDL 0.005
0.2 REACTORS
0.0-
0
1
20
40
I
60
1
"
"
80 100 120 140 160 180 ux)
Figure 6. Model predictions as a function of catalyst concentration and distance down the extruder barrel (200 O C , 26 rpm, 40.2 g/min) for (a) conversion, (b) weight-average molecular weight (Mw),and (c) pressure. There are 18 CST reactors per extruder zone; each zone is 120 mm long.
from S1. Figure 5 indicates the M , values expected for ideal condensation polymerization of these monomers (Macosko, 1989). We see that all extrusion conditions produce conversions of over 975%. Note, however, that near the end of the reaction a small change in conversion has a huge effect on M,. High conversions and M, are also predicted by the CSTR model as indicated in Figure 6. Only when catalyst level is reduced to very low values is the product produced (using a 9-min residence time) below typical polyurethane
2436 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 Table 11. SamDle Molecular Weight Distribution run sample location reactor no. M,, Mw 1
s1 s2 s3 s2 s3 s2 s3
1
1 2 2 3 3 4 4 4 5 5 5
22.5 41 181 41 181 41 181 22.5 41 181 22.5 41 181
s1
s2 s3 s1
S2 s3
5960 33 580 34 950 41 030 44 640 36 490 42 490 8 260 33 230 37 420 3 830 32 220 35 110
10600 57 200 61 350 79 000 91 400 63 230 78 040 27 180 56 330 66 190 9 390 53 970 63 690
Z 1.8 1.7 1.76 2.23 1.77 1.73 1.84 3.3 1.7 1.8 2.45 1.7 1.8
I
106,
a)
' 0
wt% DSTDL
o 005 Expenmental o 05 Expenmental
- 0 005 Predicted ..- 0 05 Predicted
10 3 1
10
0
60
40
120
160
Acknowledgment This work was supported by a postdoctoral fellowship to Alain Bouilloux from ATOChem. Registry No. (PTMO)(BDO)(Desmodur W) (copolymer),
200
Reactors
52292-20-3; PTMO, 25190-06-1; BDO, 110-63-4; Desmodur W, 5124-30-1.
"F 6oo
v)
Conclusion This study explored the Janssen model, which approximates the C-shaped chambers of twin-screw-extruder screws as a series of continuous stirred tank reactors connected by flows through the mechanical clearances. The flow-balance equations of the ideal reactor approximation model are really quite simple, but as shown in our study the model does a reasonable job of predicting reactive extrusion behavior for a urethane polymerization. The set of constants obtained from our kinetics and rheology experiments and from the screw geometry used in a laboratory predicts, without any adjustment, extruder pressure profile and polymer molecular weights in good agreement with reactive extrusion data. The ideal reactor approximation is easy to use because it does not require a measured residence time distribution to predict the results. It predicts polymer properties and extruder pressures all along the extruder barrel, allowing us to visualize the performance of the extruder as a reactor. It should allow us to better utilize current equipment and design equipment better suited to reactive extrusion.
I Wt% b).
DBTDL
0 005 Expenmental
o 05 Expenmental
400
- 0 005 Predicted
e
_._ 0 05 Predicted
Literature Cited Borkent, G. Adv. Urethane Sci. Technol. 1974, 3, 1. Camargo, R. E.; Gonzalez, V. M.; Macosko, C. W. Rubber Chem. Technol. 1983,56, 774. Castro, J. M.; Macosko, C. W. SOC.Plast. Eng., Tech. Pap. 1980,38, 434.
0
0
40
-
I
60
I
I
120
I
I
160
I
200
Reactors
Figure 7. Experimental and predicted values of (a) weight-average molecular weight and (b)pressure as a function of catalyst concentration and position down the barrel. Because of the open flight in zone 3 the theoretical pressure lines were shifted back to zero at this point and calculations continued.
specifications. From conversion and eq 18 viscosity is calculated and used by the model to predict pressure drop. Here catalyst effect is not so simple. High catalyst means high 7 but also more shear heating and thus a somewhat lower pressure rise down the extruder than for intermediate catalyst level. Low catalyst is low enough to reduce significantly viscosity build up and thus pressure. Figure 7 gives a quantitative test of the model. For molecular weight, particularly with the lower catalyst level, the model fits data well. To compare the pressure readings,we modified the model to account for the vent in zone 3. The initial pressures in eqs 2 and 3 were reset to zero at the appropriate CSTR (i = 58) and the calculations continued. There is reasonable agreement between model and experiments.
Castro, J. M.; Macosko, C. W. Polym. Commun. 1984, 25, 82. Gouinlock, E. V. J. Appl. Polym. Sci. 1968, 12, 2403. Hager, S. L.; McRury, T. B.; Gerkin, R. M.; Critchfield, F. E. Urethane block polymers: kinetics of formation and phase development. Urethane Chemistry and Applications; ACS Symposium Series 172; American Chemical Society: Washington, DC, 1981. Illing, G. Mod. Plast. 1969, 46, 70. Janssen, L. P. B. M. Twin-Screw Extrusion; Elsevier: New York, 1978.
Janssen, L. P. B. M.; Hollander, R. W.; Spoor, M. W.; Smith, J. M. AZChE J . 1979,25, 345. Kamal, M. R. Polym. Eng. Sci. 1973,13, 236. Mack, A. Polym. Prepr. (Am. Chem. SOC.,Diu. Polym. Chem.) 1972, 13, 397.
Macosko, C. W. Fundamentals of Reaction Injection Molding; Hanser: Munich, 1989. Mussati, F. G.; Macosko, C. W. Polym. Eng. Sci. 1973,13, 236. Siadat, B.; Malone, M.; Middleman, S. Polym. Eng. Sci. 1979, 19, 786.
Sneller, J. A. Mod. Plast. 1985, 62 (7), 56. Steinle, E. C.; Critchfield, F. E.; Castro, J. M.; Macosko, C. W. J. Appl. Polym. Sci. 1980,25, 2317. Stuber, N. P.; Tirrell, M. Polym. Proc. Eng. 1985, 3, 71. Stuber, N. P. Studies of Continuous Methylmethacrylate Polymerization in a Twin-Screw Extruder. Ph.D. Thesis, University of Minnesota, 1986. Received for review June 10, 1991 Accepted June 25, 1991
