Reactive Extrusion of Polypropylene with Pulsed Peroxide Addition

The results from this analysis have shown that such reactive extrusion operations are ... control strategies would be required for large operating win...
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Ind. Eng. Chem. Res. 1997, 36, 1067-1075

1067

Reactive Extrusion of Polypropylene with Pulsed Peroxide Addition: Process and Control Aspects Steven B. Dickson, Costas Tzoganakis,* and Hector Budman Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Controlled-rheology polypropylenes (CRPPs) have been produced by using pulsed peroxide addition during reactive extrusion of a commodity resin. It has been shown that, in contrast with processes involving continuous peroxide addition, it is possible to independently vary the weight-average molecular weight (M h w) and polydispersity (PDI). The effects of peroxide pulse characteristics on the product molecular weight characteristics have been investigated using the rheological properties of the CRPPs produced, and it has been found that the pulse width, amplitude, and period provide extra degrees of freedom for controlling M h w and PDI. A simple kinetic model has been employed for process simulation, and model predictions have been used to rationalize the control options through a relative gain array (RGA) analysis of the process. The results from this analysis have shown that such reactive extrusion operations are highly nonlinear and that multivariable control strategies would be required for large operating windows. 1. Introduction Polypropylene (PP) is a partially crystalline thermoplastic polymer with numerous applications in the fiber spinning, injection molding, and film extrusion industries. Its molecular weight characteristics are generally influenced by the polymerization conditions used in production. The conventional polymerization process is carried out in an inert hydrocarbon medium at moderate pressures and temperatures using Ziegler-Natta catalyst systems. Commercial polypropylene resins produced this way have relatively high weight-average molecular weights (M h w) and broad molecular weight distributions (MWD), with high polydispersity (PDI) values attributed to the broad distribution of active sites on the catalyst (Gaylord and Mark, 1959). Since MWD determines the flow characteristics and performance in processing, grades with varying M h w and MWD are used in the plethora of polypropylene end-uses. M h w and PDI are difficult parameters to control, especially when Ziegler-Natta catalysts are used. Controlling these properties necessitates the use of chain transfer agents and manipulation of polymerization conditions. Modification of PP melt flow characteristics can be accomplished economically and efficiently in a postreactor stage involving reactive extrusion of commodity PP grades in the presence of organic peroxides (Steinkamp and Grail, 1975; Baba et al., 1975). Such reactive extrusion operations are widely used in industry for the production of modified polypropylenes with tailor-made molecular properties, and they generally lead to removal of the high molecular weight tail and narrowing of the molecular weight distribution. Polypropylene materials produced this way are called “controlled-rheology polypropylenes” (CRPPs), and they generally exhibit reduced viscosity and elasticity. Although CRPPs have been commercially available for a long time, fundamental studies on PP degradation have been reported in the literature only in the last 10 years. During this time period, numerous experimental and modeling studies have been published addressing the production of CRPP (Fritz and Sto¨hrer, 1986; * Author to whom correspondence should be addressed. Phone: 519-885-1211 (ext. 3442). FAX: 519-746-4979. Email: [email protected]. S0888-5885(96)00288-6 CCC: $14.00

Suwanda et al., 1988a,b; Tzoganakis et al., 1988a,b, 1989; Ryu et al., 1992; Triacca et al., 1993; Krell et al., 1994; Tzoganakis 1994; Huang et al., 1995; Barakos et al., 1996). The issues addressed in these studies include the development of deterministic and stochastic kinetic models, experiments in batch mixers, single-screw and twin-screw extruders, MWD and rheological property measurements, residence time distribution (RTD) measurements, and development of correlations between rheological and molecular characteristics. In these studies, the peroxide is either premixed with the polymer or injected in the feed throat or along the extruder. The common element in all these operations is the steady peroxide addition rate. Controlled degradation of PP is achieved through free radical reactions initiated by peroxide radicals produced from the peroxide decomposition (Tzoganakis et al., 1988a). Peroxide radicals abstract tertiary hydrogen atoms from the PP backbone with subsequent chain cleavage through a β-scission mechanism. Due to the random nature of the abstraction reaction, peroxide radicals preferentially react with longer chains, leading to a simultaneous reduction of M h w and PDI. As a result, the breadth of the MWD and the polymer M h w cannot be controlled independently. This presents a process limitation since many times average M h w and PDI have opposing effects on processing properties. For example, it is well-known that in PP fiber production, at a given draw ratio, tenacity decreases with decreasing M h w and increases with decreasing PDI. Also, elongation at a given draw ratio increases with decreasing M h w and decreases with decreasing PDI. Therefore, it is crucial to be able to independently control these two parameters in a reactive extrusion process. This can be achieved to some extent by adding the peroxide to the extruder in a periodic fashion as described in a relatively recent patent (Davison, 1986). In such a process, the peroxide is added in a cyclic fashion and the cycle time is selected to guarantee that the polymer mixed with peroxide and the polymer not containing peroxide do not mix before the peroxide decomposes and initiates chain scission. As illustrated later in the paper, this is a function of (i) peroxide feed location, (ii) peroxide decomposition time, and (iii) the mixing characteristics of the extruder. By varying the peroxide addition rate, degraded material © 1997 American Chemical Society

1068 Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997

Figure 1. Polypropylene degradation reaction scheme used in the kinetic model.

is blended in situ with virgin PP fed to the extruder, thus retaining to a certain extent the high molecular weight end of the MWD. Depending on the peroxide feeding policy, it is possible to produce grades of similar M h w and varying PDI using relatively low peroxide concentrations. In this work, a model is developed to provide insight into the relationship between peroxide feeding conditions, pulse amplitude and frequency, and molecular weight characteristics and to quantitatively show that independent control of average M h w and PDI is possible. Rheological data obtained from a series of experiments carried out on a twin-screw extruder are used to validate model predictions and to highlight the effects of the feeding parameters on the product M h w and PDI. Finally, relative gain array analysis of model predictions is employed to study the interactions between manipulated (pulse amplitude and frequency) and controlled variables (M h w and PDI) and to identify the best pairs in a process control scheme. 2. Kinetic Model Several mathematical models have been developed to simulate the molecular weight changes occurring during peroxide-promoted degradation reactions (Suwanda et al., 1988b; Tzoganakis et al., 1988a; Ryu et al., 1992; Triacca et al., 1993). Although several free radical reactions may be potentially involved, the models developed have been primarily based on kinetic mechanisms involving the following main free-radical reactions: peroxide decomposition, hydrogen abstraction and chain scission, and termination by disproportionation. This mechanism is shown in Figure 1. The common assumptions in these models were those of the stationary-state hypothesis for radicals and of equal reactivity of all carbon-carbon bonds along the polymer backbone. Under these assumptions, these models contained as adjustable parameters the efficiency and the rate constant of the peroxide decomposition reaction. Suwanda et al. (1988b) were able to develop an analytical solution which could predict the entire MWD of the degraded polymer. Triacca et al. (1993) developed a model capable of predicting the MWD with the degree of chain scission being the sole parameter. Tzoganakis et al. (1988a), based on the method of moments and using a closure method, developed models which could predict the changes in the average molecular weights. All groups have reported good agreement between the MWD simulation results and experimental measurements by size exclusion chromatography (SEC). It has been pointed out (Ryu et al., 1992) that under the assumptions used, these models are valid for systems with uniformly distributed peroxide. Therefore, their predictive capabilities may be limited in macrosegregated systems where the stationary-state hypothesis for radical concentration is violated. Finally, Monte Carlo

Figure 2. Model predictions of the time evolution of MWD using a 0.05 wt % initial peroxide concentration.

techniques have been used (Huang et al., 1995) to develop a stochastic model for peroxide degradation of PP without employing the stationary-state hypothesis for polymer radicals. Although this last model gives similar predictions with the previously developed deterministic ones, it may be used successfully for the estimation of the chain scission rate constant. The kinetic model employed in the this work is the one developed by Suwanda et al. (1988b), and it involves the reaction scheme shown in Figure 1. According to this model, the MWD may be calculated from the following equations:

[Pn]2 ) -

λ3 (λ2[Pn]1 + λ3) exp(λ1λ2(t2 - t1)) λ2 λ2

(1)

where

λ1 )

2fkd[I]m0 Fp

λ2 ) 1 - n

(2) (3)

∞

λ3 ) 2

∑

[Pr]

(4)

r)n-1

[I] ) [I]0 exp(-kdt)

(5)

where [Pn]1 and [Pn]2 are the concentrations of the polymer with chain length n at times t1 and t2 respectively, [I] and [I]0 are the peroxide concentrations at time t and time t ) 0, respectively, f and kd are the peroxide decomposition efficiency and rate constant, m0 is the monomer molecular weight, and Fp is the polymer density. This model has been successfully employed in the past to simulate the evolution of the MWD during controlleddegradation reactions, and Figure 2 shows typical model predictions for the change of MWD in time at a peroxide level of 0.05 wt % using decomposition data for the 2,5bis(tert-butylperoxy)hexane peroxide (Tzoganakis et al., 1988a). Under a constant peroxide feeding rate, simultaneous reduction of the average weights and PDI is achieved as shown in Figure 3. Thus, with constant peroxide addition, no independent control of these two variables is feasible. Tzoganakis et al. (1988a) found the viscosity to be correlated to M h w, while Yoo (1993)

Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 1069

τ

Figure 4. Illustration of peroxide pulses and term definitions.

unreacted) of the polymer, the period (T) of the pulses has to be shorter than the average residence time of the mixture in the extruder. In the following discussion, the results will be presented for different pulse periods and amplitudes. The “pulse parameter” used to describe the peroxide pulsing is defined as

R)

pulse duration τ ) cycle period T

(6)

and the values of R tested ranged between 0.1 and 0.9. Using this parameter, the molecular weight distribution of the product has been calculated as the weighted average of the degraded and the undegraded materials as

[Pn]product ) R[Pn]degraded + (1 - R)[Pn]undegraded Figure 3. Model predictions of the effect of peroxide concentration on the average molecular weights and polydispersity.

obtained a correlation between the PDI to the elastic and viscous moduli G′ and G′′. Consequently, it is highly desirable to control independently the PDI and M h w since this will provide greater flexibility for controlling the elastic and viscous properties of the product. Additional degrees of freedom for independent control of M h w and PDI can be provided by using a periodic peroxide feeding policy (Davison, 1986). Adding the peroxide in this fashion allows for degradation of a small part of the feed and its subsequent mixing with the undegraded fraction of the feed. To understand the methodology used in the computations for this peroxide addition policy, let us consider Figure 4, which illustrates the concept of peroxide pulsing used in this study. During the pulse, peroxide is being injected into the system, thus degrading the polymer according to the reaction scheme shown in Figure 1. Following this reaction step, the degraded material is mixed with the virgin polymer being fed to the extruder. The degree of mixing depends on the screw configuration used as well as on the operating conditions. For the purpose of the present simulations, it is assumed that the reacted polymer is completely mixed with the virgin one. This assumption may not be valid for twin-screw extruders since they exhibit RTDs closer to plug-flow rather than to well mixed systems. However, this assumption may be relaxed later on by incorporating the actual RTD of the extruder, and it is only being used here to illustrate the feasibility of independent M h w and PDI control. To guarantee mixing of the two fractions (reacted and

(7)

Another parameter used is the average peroxide concentration, which can be calculated using the pulse amplitude and the pulse parameter (R) as

av concentration )

1 T

∫0T I(t) dt ) R(pulse amplitude) (8)

where I(t) represents the peroxide pulse concentration profile. The effect of peroxide pulsing on the MWD is illustrated in Figure 5 for certain combinations of pulse amplitudes and R values. These simulation results seem to indicate that peroxide pulsing provides an additional degree of freedom which could be potentially used for decoupling M h w and PDI control. To demonstrate this concept further, extensive simulation runs were performed under varying peroxide feeding conditions and the results are summarized in Figures 6-10. The effects of the pulse parameter and average peroxide concentration on the final average molecular weights are shown in Figures 6-8. First of all, it should be pointed out that the pulse amplitude varies along all curves presented. A maximum pulse amplitude of 2.5 wt % was used in the simulations, and it corresponds to the end point of all these curves. As expected, pulsing has a negligible effect on the number-average molecular weight M h n as indicated by the overlapping of all curves in Figure 6. However, M h w seems to be significantly affected by the value of R. It can be observed in Figure 7 that for a given average concentration, increasing R (moving toward continuous peroxide addition) leads to lower M h w values. Also, it can be seen that changes in

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Figure 6. Effects of R and average peroxide concentration on model predicted M h n.

Figure 7. Effects of R and average peroxide concentration on model predicted M h w.

Figure 5. Model predictions of MWD using pulsed peroxide addition. (a) Pulse amplitude ) 0.05 wt %, R ) 0.2; (b) pulse amplitude ) 0.05 wt %, R ) 0.8, (c) pulse amplitude ) 1.5 wt %, R ) 0.2.

R values have a more pronounced effect at lower levels of this pulse parameter. Similar trends are observed for M h z in Figure 8; however, the impact of mixing between degraded and virgin material is more obvious. The minimum observed on the curves corresponding to values of R other than unity can be explained in terms of the relative effects of the average concentration on the second and third moments of the MWD. Figure 9 illustrates the effects of average peroxide concentration and R on PDI. It can be seen that for a given average

Figure 8. Effects of R and average peroxide concentration on model predicted M h z.

concentration, decreasing R results in broader MWDs. In addition, for low values of R and relatively high peroxide concentrations, the PDI of the product exceeds that of the virgin material. This is expected since the mixing process contributes to partial preservation of the high molecular weight end of the distribution, while at the same time the molecular weight range is extended to lower values of molecular weight generated during

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Figure 11. Schematic diagram of the reactive extrusion process.

Figure 9. Effects of R and average peroxide concentration on model-predicted PDI.

Figure 12. Extruder configuration used in the experiments.

Figure 10. Effects of R and average peroxide concentration on the interdependence between model predicted M h w and PDI. Symbols represent the results from the RGA analysis discussed in section 5. Dotted lines indicate the different average peroxide concentrations used as follows: (5) 0.1, (4) 0.2, (3) 0.5, (2) 1, (1) 1.5 wt %.

scission. As mentioned previously, the main motivation in injecting the peroxide in the form of pulses is to add degrees of freedom for independent control of M h w and PDI by simultaneous manipulation of pulse amplitude and R. To demonstrate this point, PDI is plotted against M h w in Figure 10. The dotted lines are used to indicate the different average peroxide concentrations involved in the simulations. It can be clearly seen that independent control of M h w and PDI is feasible by proper selection of pulse amplitude and R. In order to study the interactions between manipulated and controlled variables, the relative gain array (RGA) measure was used. The symbols in Figure 10 correspond to the RGA results and are discussed later in this article to rationalize control strategies. 3. Experimental Section Reactive extrusion experiments were carried out on a pilot-scale twin-screw extruder to test the model predictions, to collect rheological data for materials produced under pulsed peroxide addition, and to quantify the interactions between manipulated and controlled variables.

Materials. The polypropylene used in the experiments was KF6100 from Montell Canada, with a melt index of 3.00. 2,5-Dimethyl-2,5-bis(tert-butylperoxy)hexane (Lupersol-101) from Elf Atochem was used as the peroxide in a solution form. Methanol was used as the solvent in the preparation of the peroxide solutions added to the system. Equipment. A Leistritz 34-mm twin-screw extruder equipped with a K-Tron LWFD5-200 loss-in-weight solids feeder and a Berlyn PEL-4 pelletizer was used in all experiments. An intermeshing co-rotating screw configuration was employed, and a metering pump (Fluid Metering Inc., QSY-2) was used along with a solenoid valve (three-way Asco solenoid valve) to inject the peroxide stream into the extruder. A process schematic diagram is given in Figure 11, and the extruder configuration used in the experiments is shown in Figure 12. A Dynisco PT462E-3.5CB-6/18 pressure transducer was used to monitor the die pressure, and data acquisition was done using a 486 IBM compatible personal computer through an Optomux interface (OPTO22 A/D converter with AC422 serial link). A computer code written in C was employed for on-line data acquisition and for controlling the solenoid valve in the pulsedaddition operating mode. A Kayeness Galaxy V capillary rheometer was used to measure the melt flow index (MFI) of the samples collected, and their linear viscoelastic properties were measured using a Rheometrics 605 mechanical spectrometer using a parallel plate configuration. Procedures. Polymer was fed to the extruder at a rate of 40 g/min, and the screw speed used was 40 rpm. Peroxide injection was tested at two locations: the feed port and an open port located at the fifth barrel zone (see Figure 11). In the feed port injection case, the peroxide solution dropped directly on the polymer pellets

1072 Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 Table 1. Experimental Conditions, Experimental Data, and Model Predictions expt

injection location

pulse amplitude, wt %

R

1 (virgin PP) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

feed feed feed melt melt feed melt feed melt melt feed melt feed melt feed feed feed

0.005 0.05 1.66 1.66 1.66 0.86 0.86 0.86 0.86 0.86 0.26 0.26 0.26 0.26 0.04 0.04 0.04

1 0.1 0.19 0.19 0.19 0.06 0.06 0.06 0.06 0.06 0.23 0.23 0.23 0.23 0.15 0.15 blend

cycle period, s ∞ 10 20 20 40 20 20 40 40 60 20 20 40 40 20 40

as they entered the extruder channel, while in the open port case the solution was added directly to the polymer melt in the intermeshing region. Pelletized samples collected from all experiments were analyzed in terms of their linear viscoelastic properties, using frequency sweep tests on the mechanical spectrometer. A parallel disk (25 mm diameter, disk gap of 2 mm) configuration was used at 20% strain and 230 °C. The MFI of the samples collected was performed according to the ASTM method D 1238-86 (230 °C, 2.16 kg) on the capillary rheometer. Polydispersity Measures. The polydispersity (PDI) of the materials produced was estimated by using data from linear viscoelastic measurements and correlations between a rheological measure of PDI and PDI measured by size exclusion chromatography (SEC). SEC analysis was not carried out since the equipment was not available at the time of the experiments. In any case, if process control is desired, the implementation will be done through rheological measurements since SEC measurements cannot be obtained on-line. The rheological measure of PDI used was the “modulus separation (modsep)” (Yoo, 1993), which is defined as follows:

modsep )

frequency at G′ ) 1000 Pa frequency at G′′ ) 1000 Pa

(9)

This parameter has been successfully used as a rheological polydispersity measure in the past, and Yoo (1993) has developed the following good correlation between SEC polydispersity data and modsep:

modsep ) 5.795 09 - 0.463 89

M hw M hn

(10)

A similar correlation has been proposed by Tzoganakis (1994), and it is listed below:

modsep ) 5.439 - 0.329

M hw M hn

(11)

Equations 10 and 11 have been used in this work to assess the effect of pulsed peroxide addition on the polydispersity of the materials produced. 4. Results and Discussion Several experiments were performed to investigate the effect of pulsed peroxide addition on the molecular

MFI, g/10 min 3.0 3.7 4.0 195 234 15.6 10.8 14.6 10.5 17.6 11.0 17.4 9.6 4.2 3.7 4.6

modsep 3.2 3.8 3.6 4.4 3.8 3.7 4.4 2.9 3.6 3.2 3.0 4.1 3.1 3.6 3.4 3.2 3.3 3.4

normalized PDI data using eq 10 using eq 11 1.0 0.77 0.85 0.54 0.77 0.81 0.54 1.12 0.85 1.00 1.08 0.65 1.04 0.85 0.92 1.00 0.96 0.92

1.0 0.73 0.82 0.46 0.73 0.78 0.46 1.13 0.82 1.00 1.09 0.60 1.04 0.82 0.91 1.00 0.95 0.91

normalized PDI pred 1.0 0.97 0.97 1.23 1.23 1.23 1.03 1.03 1.03 1.03 1.03 0.92 0.92 0.92 0.92 0.96 0.96 0.96

Figure 13. Comparison of experimental storage modulus (G′) data for experiments 1, 4, and 12.

weight characteristics of the CRPPs produced. More specifically, experiments were carried out to study (i) the effect of pulse parameter R and pulse amplitude on the PDI and M h w, (ii) the effect of peroxide addition location on the molecular weight characteristics, and (iii) the level of mixing along the extruder. It was anticipated that the reacted and unreacted polymer under pulsed peroxide injection do not mix completely, as assumed in the batch model. Also, the level of mixing should encompass mixing of polymer fed with peroxide and polymer fed without peroxide before the reaction occurs. Consequently, differences between the experimental data and model predictions may be related to the incomplete longitudinal mixing occurring in the extruder. The experimental conditions for the runs conducted are summarized in Table 1, and it should be noted that the same combinations of pulse amplitude and pulse parameter R were tested for different cycle times (20, 40, and 60 s) and for both feed and melt injection situations. Typical curves for the storage and loss moduli measured with the mechanical spectrometer are given in Figures 13 and 14 for experiments 1 and 4 and experiment 12, respectively. The experimental results are presented along with model predictions in Table 1. The MFIs of all samples were measured as described earlier, while the modseps are determined from linear viscoelastic data and the PDIs are estimated using the

Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 1073

Figure 14. Comparison of experimental loss modulus (G′′) data for experiments 1, 4, and 12.

correlations presented in the previous section. PDI values reported in this table were normalized with the PDI of the starting material (experiment 1) to better visualize the trends in both experimental data and model predictions. The results presented in this section are subject to experimental error due mainly to the following two reasons: (i) For a specific set of experimental conditions, the samples were randomly collected from a container of pelletized material produced over time during the experimental run. Therefore, the measured properties are expected to be an average over time. (ii) The polydispersity was inferred from correlations with G′ and G′′ as explained above. There is some uncertainty in these correlations which cannot be completely assessed at the present. Despite the expected experimental error, the results show clear trends from which several important conclusions may be drawn. Comparison of experiments 2 (continuous peroxide addition) and 3, which correspond to the same average peroxide concentration, suggests that peroxide pulsing leads to a slightly broader MWD while maintaining approximately the same M h w (as indicated by the similar MFI values). However, it should be kept in mind that the difference in PDIs is relatively small. This may be attributed to the low peroxide concentration used as well as to possible pulse averaging (experiment 3) since the peroxide was injected at the feed port where the reaction does not occur until the solid PP pellets start to melt. For the rest of the experiments, it can be seen that the PDI of the degraded PP is similar or exceeds that of the starting material in some cases (experiments 8, 10, 11, and 13) and that in all of them, the peroxide pulses were added in the melt. Comparing experimental runs that differ only at the peroxide injection location (experiments 4 and 5, 7 and 8, 9 and 10, 12 and 13, and 14 and 15), it can be observed that melt peroxide injection results in consistently higher PDI values. This trend may be again attributed to the averaging of peroxide pulses when injected at the feed port. Also, examination of the MFI results for the same experiments indicates that the melt injected cases exhibit lower MFI values, which suggest higher M h w. This trend can be explained if we recall that peroxide pulsing contributes to partial retaining of the high molecular weight tail of the MWD. It must be pointed out that

experiments 4 and 5 show an opposite trend in the MFI data. However, one should keep in mind that experimental MFI measurements at that high level are very difficult and perhaps inaccurate when using the testing method outlined in the Experimental Section. The effect of the cycle period on PDI can be examined by considering experiments 7 and 9 as well as 12 and 14. In both pairs, the cycle period of the second run was twice as long as that of the first one. Since the pulse amplitude and pulse parameter remain constant within each pair of runs, the average peroxide concentration is constant. In turn, this would lead to materials with similar M h w. This seems to be true, since runs in each pair have similar MFI values. It is interesting to note that by changing the cycle period, the PDI may be varied while maintaining a constant MFI and, therefore, M h w. In section 2 of this article, we tested via simulation the interdependence of PDI and M h w with two input variables, namely, the pulse amplitude and the pulse parameter R. Here, experimental data indicate that the cycle period may be used as a third input/variable or degree of freedom to achieve multivariable process control. It appears that longer cycle periods enhance the effect of peroxide pulsing and, consequently, the PDI values obtained are closer to the model predictions as compared with the PDI values obtained with shorter cycle times. Some indication about mixing in the extruder can be obtained by considering experiments 16-18. Experiment 18 involved degradation of PP under continuous peroxide addition (0.04 wt %) and subsequent mixing with virgin material according to the R value in experiments 16 and 17. This was done to test the complete mixing assumption used in the model, and it appears that mixing conditions were similar in all three cases, as indicated by the comparable MFI and PDI results. It must be pointed out, however, that mixing could change with the amount of peroxide added to the system, as residence time distribution measurements have shown (Tzoganakis et al., 1989). In general, the model used seems capable of predicting the trends in the data. However, due to the assumption of complete mixing between polymer fed with and without peroxide before reaction occurs or between degraded and undegraded PP fractions after reaction starts, the model cannot properly account for the effect of injection location (feed vs melt) as well as for the effect of cycle period (short vs long). Currently, a dispersion model is being employed in simulations to evaluate the effect of pulse characteristics on polymer mixing in the extruder. 5. Control Considerations The use of the batch kinetic model allowed for a basic examination of the possible effects of the pulsed injection of peroxide. By looking at a variety of cases and applying the RGA analysis technique (Seborg et al., 1989), the interactions between the controlled variables, M h w and PDI, and the manipulated variables, peroxide pulse amplitude and R, may be quantified. The RGA method (Seborg et al., 1989) is a systematic approach for the analysis of multivariable process control problems. This approach requires only steady-state information and provides two items of information: (i) a measure of process interactions (ii) a recommendation concerning the most effective pairing of controlled and manipulated variables if one wishes to design a simple control strategy consisting of single-input-single-output

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Severe interaction was observed for cases 1-6, 8, 9, 12, and 15. For example, for case 9,

Table 2. Relative Gain Array Analysis Case Studies case study

pulse amplitude, wt %

R

1, 2, 3 4, 5, 6 7, 8, 9 10, 11, 12 13, 14, 15 16, 17, 18 19, 20, 21 22, 23, 24 25, 26, 27

0.05 0.10 0.15 0.20 0.30 0.40 0.50 1.00 1.50

0.10, 0.45, 0.80 0.10, 0.45, 0.80 0.10, 0.45, 0.80 0.10, 0.45, 0.80 0.10, 0.45, 0.80 0.10, 0.45, 0.80 0.10, 0.45, 0.80 0.10, 0.45, 0.80 0.10, 0.45, 0.80

controllers. The RGA method is based on the concept of the relative gain. Consider a process with n controlled variables and n manipulated variables. The relative gain between a controlled variable, ci, and a manipulated variable, mj, is defined to be the dimensionless ratio of two steady-state gains:

(∂ci/∂mj)m open-loop gain ) λij ) (∂ci/∂mj)c closed-loop gain

[λ1 - λ 11

11

1 - λ11 λ11

]

(12)

(13)

where

λ11 )

1 K12K21 1K11K22

(14)

and Kij is the steady-state gain between input j and output i. The following convention was used for the inputs and outputs: m1, m2, c1, and c2 represent R, pulse amplitude, M h w, and PDI, respectively. The RGA provides useful information if one wishes to design a simple control strategy consisting of single input and single output controllers. In general, the best pairing is the one for which the corresponding relative gain is closer to one. Negative relative gains indicate that due to interaction, the corresponding steady-state gain changes sign as all single control loops are being closed. RGA calculations were conducted for several cases summarized in Table 2, and the required steadystate gains were calculated from model predictions. From the RGA analysis, two distinct operating regions are observed: one at low average peroxide concentration (marked with circles in Figure 10) and the other at high average concentrations (marked with triangles in Figure 10). In the first region, which includes cases 1-12, 14, 15, 18, and 21, the RGA reveals that the preferable pairing is pulse amplitude controlling M h w and R controlling the PDI. For example, the RGA for case 7 is

RGA )

0.89 [0.11 0.89 0.11 ]

2.56 [-1.59 2.56 -1.56 ]

(15)

(16)

The negative relative gains indicate that two singleinput-single-output controllers designed for this system will have opposing control action. The RGA analysis in the high peroxide region, which includes cases 13, 16, 17, 19, 20, and 22-27, reveals that the preferable pairing is the pulse amplitude controlling the PDI and R controlling M h w, which is the opposite of the result obtained for the low peroxide concentration region. For example, the RGA for case 13 is

RGA )

In eq 12, the symbol (∂ci/∂mj)m denotes a partial derivative that is evaluated with all of the manipulated variables except mj held constant. Thus, this term is the open-loop gain between ci and mj. Similarly, (∂ci/ ∂mj)c is evaluated with all of the controlled variables except ci held constant. This situation could be achieved in practice by adjusting the other manipulated variables using PID controllers. Thus, (∂ci/∂mj)c can be interpreted as a closed-loop gain that indicates the effect of mj on ci when all of the other feedback control loops are closed. For the two-input-two-output case addressed in this work, the RGA is given by

RGA )

RGA )

0.24 [0.76 0.24 0.76 ]

(17)

Severe interaction is observed for some cases in the high peroxide concentration region, and this interaction increases with increasing R. For example, the RGA for case 16

RGA )

1.3 [-0.3 1.3 -0.3 ]

(18)

shows more interaction as compared to case 13 above. The very distinct behavior of the system around different operating conditions, reflected by the different RGA results, suggests that the system is highly nonlinear. Therefore, if one wishes to control this system along a large window of operation, two single controllers will not provide efficient regulation and a multivariable nonlinear control strategy will be required. The RGA results and the trends presented in Figure 10 are physically justifiable if the difference between the MWDs of the degraded and undegraded fractions is considered. In the low peroxide concentration region, the average concentration is relatively low and, therefore, the MWDs of the two fractions should be close to each other. Therefore, the PDI of the mixed material will depend on the pulse parameter R which controls the mixing according to eq 7. In the second region, high average concentrations are achieved by high pulse amplitudes. This means that the MWDs of the degraded and undegraded PP fractions are further apart. Therefore, the PDI of the final product is more sensitive to the pulse amplitude than to the pulse parameter R. In addition to the strong process interaction, an additional obstacle to control the process is the difficulty to measure polymer properties on-line. During the course of this work, an attempt was made to infer the molecular weight average and the polydispersity from the die pressure and the extrudate die swell, respectively. Tzoganakis et al. (1988b) found an empirical relationship between the die pressure and the weight average molecular weight. In the same work, it was shown that for different peroxide concentrations, the extrudate swell could be used to infer changes in polydispersity. In this work, a laser micrometer (Lasermike Model 101-100 single-axis scanner) was used to monitor the swell. Whereas noise in the die pressure measurement was successfully filtered with a first order filter, we were unsuccessful to filter the die swell measurement noise. The main source of this noise was the strand oscillations induced by the pelletizer takeup mechanism. The lack of a suitable sensor to infer the polydispersity impeded us to achieve closed-loop

Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 1075

control of the process. We are currently testing an online wedge rheometer which will measure changes in polydispersity based on the signal from four pressure transducers located along a die of variable cross section. 6. Concluding Remarks Controlled-rheology polypropylenes have been produced by using pulsed peroxide addition during reactive extrusion of a commodity resin, and it has been shown that, in contrast with processes involving continuous peroxide addition, it is possible to independently vary M h w and PDI. The present work expands on similar reports in the patent literature and, furthermore, quantifies the effects of various parameters on the molecular weight characteristics of CRPP grades produced under intermittent peroxide addition. More specifically, it has been shown that pulse amplitude, pulse period, and pulse parameter R can be manipulated to control the average molecular weight and polydispersity. In addition, a simple kinetic model has been employed for process simulation, and model predictions have been used to rationalize control options through a relative gain array analysis of the process. The results of this analysis indicate that (i) at low peroxide concentrations, the pulse amplitude should be used to control M h w and R should be used to control the PDI and (ii) at high peroxide concentrations, the pulse amplitude should be used to control PDI and R should be used to control M h w. Also, the results from the relative gain analysis suggest that the process is highly nonlinear and that a multivariable control strategy would be required to control such processes for large operating windows. Finally, the need for models accounting for polymer mixing effects has been identified and additional simulation efforts are under way using a dispersion model. Acknowledgment Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and from the Ontario Center for Materials Research (OCMR) is gratefully acknowledged. Literature Cited Babba, K.; Shiota, T.; Murakami, K.; One, K. Method for producing a modified crystalline propylene polymer. U.S. Patent 3,887,534, Sumitomo Chemical Co., 1975. Barakos, G.; Mitsoulis, E.; Tzoganakis, C.; Kajiwara, T. Rheological Characterization of Controlled-Rheology Polypropylenes Using Integral Constitutive Equations. J. Appl. Polym. Sci. 1996, 59, 543.

Davison, S. Controlled degradation or cracking of alpha-olefin polymers. U.S. Patent 4,578,430, Shell Oil Company, 1986. Fritz, H. G.; Sto¨hrer, B. Polymer Compounding Process for Controlled Peroxide-Degradation of Polypropylene. Int. Polym. Proc. 1986, 1, 31. Gaylord, N. G.; Mark, H. F. Linear and Stereoregular Addition Polymers; Interscience: New York, 1959. Huang, C.; Tzoganakis, C.; Duever, T. A. Monte Carlo Simulation of Peroxide Initiated Degradation of Polypropylene. Polym. React. Eng. 1995, 3, 43. Krell, M. J.; Brandolin, A.; Valle´s, E. M. Controlled Rheology Polypropylenes. An Improved Model with Experimental Validation for the Single Screw Extruder Process. Polym. React. Eng. 1994, 2, 389. Ryu, S. H.; Gogos, C. G.; Xanthos, M. Parameters Affecting Process Efficiency of Peroxide-Initiated Controlled Degradation of Polypropylene. Adv. Polym. Technol. 1992, 11, 121. Seborg, D. E.; Edgar, T. F.; Mellichamp, D. A. Process Dynamics and Control; John Wiley & Sons: New York, 1989. Steinkamp, R. A.; Grail, T. J. Polymers with improved properties and process therefore. U.S. Patent 3,862,265, Exxon Research & Engineering, 1975. Suwanda, D.; Lew, R.; Balke, S. T. Reactive Extrusion of Polypropylene I: Controlled Degradation. J. Appl. Polym. Sci. 1988a, 35, 1019. Suwanda, D.; Lew, R.; Balke, S. T. Reactive Extrusion of Polypropylene II: Degradation Kinetic Modelling. J. Appl. Polym. Sci. 1988b, 35, 1033. Triacca, V. J.; Gloor, P. E.; Zhu, S.; Hrymak, A. N.; Hamielec, A. E. Free Radical Degradation of Polypropylene: Random Chain Scission. Polym. Eng. Sci. 1993, 33, 445. Tzoganakis, C. A Rheological Evaluation of Linear and Branched Controlled-Rheology Polypropylene. Can. J. Chem. Eng. 1994, 72, 749. Tzoganakis, C.; Vlachopoulos, J.; Hamielec, A. E. Production of Controlled-Rheology Polypropylene Resins by Peroxide Promoted Degradation During Extrusion. Polym. Eng. Sci. 1988a, 28, 170. Tzoganakis, C.; Vlachopoulos, J.; Hamielec, A. E. Modelling of the Peroxide Degradation of Polypropylene. Int. Polym. Proc. 1988b, 3, 141. Tzoganakis, C.; Tang, Y.; Vlachopoulos, J.; Hamielec, A. E. Measurements of Residence Time Distributions for the Peroxide Degradation of Polypropylene in a Single-Screw Plasticating Extruder. J. Appl. Polym. Sci. 1989, 37, 681. Yoo, H. J. Use of Rheology in Polypropylene Resin Design. SPE ANTEC 1993, 39, 3037.

Received for review May 23, 1996 Revised manuscript received August 16, 1996 Accepted August 16, 1996X IE960288U

X Abstract published in Advance ACS Abstracts, February 15, 1997.