Optimization of the Polymer Foam Process by the Residence Time

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Optimization of the Polymer Foam Process by the Residence Time Distribution Approach Mathieu Larochette,† Didier Graebling,*,†,‡ Djamel Nasri,† and Fre´de´ric Le´onardi† UniVersite´ de Pau et des Pays de l’Adour, IPREM/EPCP UMR 5254, 2 AVenue Angot, 64053 Pau Cedex 9, France, and INRIA Bordeaux-Sud-OuestsE´quipe Projet Concha

In this work, we used the residence time distribution to study the polystyrene foaming during an extrusion process. The extruder associated with a gear pump is simply and quantitatively described by three continuously stirred tank reactors with recycling loops and one plug-flow reactor. The blowing agent used is CO2 and is obtained by thermal decomposition of a chemical blowing agent (CBA). This approach allows the optimization of the density of the foam in accordance with the CBA kinetic of decomposition. 1. Introduction The residence time distribution (RTD) is a theoretical frame for studying complex flow networks and is perfectly adequate for describing the polymer flow through an extruder. For reactive extrusion processes where the reaction time is of the same order of the mean residence time, the RTD is of interest, since the length of time that the material remains in the extruder should be closely coupled to the reaction kinetics. The RTD approach has been proven for its efficiency to simulate the single screw extruder1-3 or the twin-screw extruder.6-20 In this paper, we have studied the processing of polystyrene foam by extrusion in a single screw extruder coupled with a gear pump. The basic principle of foaming is to mix a blowing agent into a polymer melt and induce a thermodynamic instability through a temperature or pressure change to nucleate bubbles of the blowing agent. After nucleation, the bubble growth is controlled by reducing the temperature lower than the glass transition temperature of the polymer.21 The blowing agent used is CO2 and is obtained by thermal decomposition of an organic molecule called chemical blowing agent (CBA). To obtain an optimal foam, that is, lower density, the process parameters of the extruder must be adapted to the CBA kinetic of decomposition. 2. Theoretical Background

hydrofluorocarbons or HFCs because they show zero ozone depletion potential. Unfortunately, these agents are known as greenhouse gases (The Kyoto Protocol24). Actually, the polymers are foamed by carbon dioxide often under supercritical conditions.25-31 The gas can be produced by thermal decomposition of an organic or inorganic unstable compound called chemical blowing agent. This thermal decomposition can be endothermic or exothermic. Endothermic chemical agents contain acid and carbonate components treated to provide stable mixtures and generate carbon dioxide on decomposing.32 Azodicarbonamide exothermic agents generate nitrogen gas on decomposition.33-35 These chemical blowing agents produce three to five times more gas than endothermics.36 Since 2004, the use of these agents as blowing agent has been banned in Europe. 2.2. Residence Time Distribution. Suppose that an inlet particle concentration Ci(t) is applied to the reactor.37-39 Then we want to calculate the outlet particle concentration Co(t). The particles are conveyed by a fluid flowing at a volumetric flow rate Q. It is assumed that particles do not interact which each other. The number of particles that enter the reactor in the time interval (t′,t′ + dt′) and leave the reactor in the time interval (t,t + dt) is QCi(t′)f(t - t′) dt dt′. The total outflow during the time interval (t,t + dt) is QCo(t) dt, and thus QCo(t) dt ) Q dt

2.1. Polymer Foam. The polymeric foams with closed cell structures exhibit low densities, high impact strengh, and excellent thermal and phonic insulation. The foam applications such as foam building insulation, packaging, and automotive industries can be explained by these properties.22 Many polymers such as polyolefins, polyurethane, and polystyrene can be foamed. In the case of polystyrene, extrusion is the main process for obtaining large sheets of foam-board insulation. The expandable bead molding is the typical technique used for packaging. Traditionally, the most commonly used foam blowing agents were chlorofluorocarbons or CFCs. However, the use of these molecules was banned because of their implication as “ozone depleting substances” (The Montreal Protocol23). Therefore, since the early 1990s, these have been mostly replaced by * To whom correspondence should be addressed. E-mail: [email protected]. † Universite´ de Pau et des Pays de l’Adour. ‡ INRIA Bordeaux-Sud-Ouest.

{

∫

t

-∞

Ci(t') f (t - t') dt'

Co(t) )

w

Co(t) )

∫ ∫

t

-∞ ∞ 0

Ci(t') f (t - t') dt'

(1)

Ci(t - t') f (t') dt'

where f(t) is the residence time density function and it represents the density of probability expressed as probability per unit time. This function depends on the characteristics of the system. In the Laplace domain, eq 1 becomes L {Co(t)} ) L {Ci(t)} × L { f (t)} w L { f (t)} )

L {Co(t)} L {Ci(t)} (2)

The function L {f (t)} is known as the transfer function of the reactor. If the inlet signal is a Dirac delta function, the outlet response of the system is identical to the residence time density function. The cumulative residence time distribution F(t) and the spacetime of the reactor jt are defined by the following equations:

10.1021/ie800836j CCC: $40.75  2009 American Chemical Society Published on Web 04/08/2009

Ind. Eng. Chem. Res., Vol. 48, No. 10, 2009

F(t) )

∫ f (t') dt' t

0

jt )

∫

∞

0

t'f (t') dt' )

V Q

(3)

where V is the volume of the reactor and Q its volumetric flow rate. In the special case of the steady flow of fluid with a constant density, the space-time is equal to the mean residence time. In this article, we use a statistic theory instead of a physical model to relate the overall residence time distribution in a single extruder to those in appropriately divided elements. We represent a single extruder by association of elementary tanks: CSTR and/ or PFR. The better compromise between simplicity and precision is obtained by the association of three identical CSTRs with recycling and one PFR in series (Figure 1). The average in all experiments of the root-mean-square deviation is 1.5 × 10-3 for two identical CSTRs and 0.4 × 10-3 for three identical CSTRs. Q is the volumetric flow rate passing through the system and q is the recycling volumetric flow rate between two CSTRs. We define the recycling parameter R as the ratio q/Q. The recycling flow define by the parameter R is due, for example, to the back pressure existing in the extruder. The residence time density function of the three identical CSTRs with recycling loops is given by the following equation:

f(t) )

j j e (-2 + e-βt/t + eβt/t ) 4Rtj

(4)

with β)

1 +2R2R

where jt is the mean residence time of one CSTR. The addition of the PFR implies a simple time shift. The residence time density function of the extruder is given by the following equation: j j

f(t) )

j j j j e-(t-t 0)/t (-2 + e-β(t-t 0)/t + eβ(t-t 0)/t )Υ(t - jt 0) 4Rtj

(5)

where jt0 is the mean residence time of the PFR or the latency period and Υ(t) is the Heaviside step function. Without recycling, eq 5 becomes (t - jt 0)2

j j

(6) e-(t-t 0)/t Υ(t - jt 0) 2tj3 In Figure 2, we show the behavior of the system given by eq 5 for differents values of R and jt. The relationship between jt the mean residence time of one CSTR, jt0 the mean residence time of PFR, and jtx the mean residence time of the extruder is f0(t) ) lim f (t) ) Rf0

jt x )

Figure 1. The RTD vision of extruder.

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-t/tj

∫

∞

0

tf(t) dt ) (3 + 4R)tj + jt 0 ) jt c + jt 0

(7)

where jtc represents the mean residence time of the three CSTRs with recycling. The mean residence time of PFR jt0 was determinated directly from the measurements. For each experiment, the model parameters jt and R were determined by a nonlinear least-squares method with Scilab (numerical computational package developed by INRIA). In all cases, the standard deviation is less than 10-3. The theoretical and experimental mean residence times jtx were calculated with the eq 7: direct integration for the experimental time and model parameters for the theoretical time. To compare the different results, we used the dimensionless residence time density function defined by φ(τ) ) jtx f (t) with τ ) t/tjx. For our model of extruder describe by eq 5, the dimensionless residence time density function is given by the following relationship: φ(τ) )

λe-λ(τ-τ0) (-2 + e-βλ(τ - τ0) + eβλ(τ - τ0))Υ(τ - τ0) (8) 4R

Figure 2. Theoretical RTD for 3 CSTRs in series with recycling loop and in series with a PFR (eq 5). Residence time density function vs time: jt0 ) 25 s and (A) jt ) 3 s, (B) R ) 1.

Figure 3. CBA thermal decomposition: apparatus.

Figure 4. CBA thermal decomposition: volume of CO2 vs time. Experimental data (symbol) and kinetic model (dash line).

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Figure 5. CBA thermal decomposition: kinetic parameters vs reciprocal temperature.

3. Experimental Section

Figure 6. Working domain in extrusion: gear pump rotation speeds np vs screw rotation speeds nx at 180 and 220 °C.

Figure 7. Pressure vs screw rotation speeds nx at 190 °C for the extrusion line with and without gear pump.

where λ ) κ/(1 - τ0), κ ) 3 + 4R is a recycling parameter, and τ0 ) jt0/tjx is a dimensionless latency period.

3.1. Products. The polystyrene PS 1450N was supplied by Total Petrochemicals with 1050 kg/m3 as density. Carbon dioxide is produced by thermal decomposition of an endothermic chemical blowing agent Tracel NCS 175 from Tramaco. The thermal decomposition of this agent is obtained in the temperature range of 135-220 °C. The tracer used for RTD measurements is a blue dye for polystyrene referenced M120442 SPC from Elian. 3.2. CBA Kinetic of Decomposition Measurement. The kinetic experiments was carried out on a tailor-made system (Figure 3). For each temperature, the release volume of CO2 produced by thermal decomposition of 100 mg of CBA was measured as a function of time. All results are given for the normal pressure, 1.013105 Pa. The thermal decomposition of AIBN (azo-bis-isobutyronitrile) was used to validate our experimental approach.48 3.3. Process. We used a single Thermo Haake Rheomex 252p extruder with a length to diameter ratio of 25:1. A gear pump MSDP 090/039 supplied by Xaloy (1.2 cm3/rpm), was mounted between the die and the end of the extruder. The mixing capacity of gear pumps is very limited. The polymer melt is passed through a capillary die, diameter of 2 mm and length of 12 mm, before cooling with four computer fans. The cold extrudate is analyzed by the RTD system. To control the outflow speed of the extrudate a pelletizer Varicut (Thermo Haake) is modified and is used as a speed control pull system. This speed is adjusted to maintain the extrudate diameter equal to the die diameter. 3.4. RTD Measurement. Many in-line methods have been proposed in the literature for RTD measurement40-47 An optical method based on light transmittance was chosen for our experiments. The RTD is measured by transit experiments by injecting a small quantity of an inert tracer at the feel hopper of the extruder. The dye concentration evolution is analyzed continuously in real time. A cold white light is used as light source. The transmitted light intensity is quantified by a photodiode supplied by Vishay Telefunken. An electronic module amplifies and converts the photodiode current in a voltage signal compatible with the analog to digital converter. The signal obtained is directly sent to a computer from the data acquisition system, ADC 212 Pico Technology.

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Figure 8. Experimental and theoretical RTD for a single extruder with pump np ) 26, 30, and 35 rpm and without pump at 190 °C. Screw rotation speeds: nx ) 70 and 75 rpm.

The RTD measurements were realized without the foaming agent and 100 mg of blue dye was used for each experiment. For all measurements, the extrudate diameter is the same. In this case, the light transmittance is directly proportional to the dye concentration in the polymer extrudate. We consider that if the inlet signal is a Dirac delta function, the outlet response of the system is identical to the residence time density function. The transmitted light intensity, that is, the concentration, is normalized such that the area under each curve is equal to unity. 4. Results and Discussion 4.1. CBA Kinetic of Decomposition. The CBA decomposition was studied by thermal gravimetry analysis, TA 2950, in the temperature range of 100- 300 °C for three heating rates: 10, 15

and 20 °C/min. This blowing agent is characterized by two domains of temperature 135-170 °C and 190-230 °C. The observed weight loss remained relatively constant for each heating rate, 15% for the first domain and 17% for the second. The residual weight of the samples is due to a mineral compound. The rate of decomposition was influenced only by the temperature of the sample (Figure 4). The CO2 release volume is given by the following equation: VCO2 ) V∞(1 - exp(-k(t - t0))),

∀ t g t0

(9)

where V∞, t0, and k are, respectively, the total volume of CO2, the inhibition time, and the kinetic constant associated to the decomposition.

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{

t0 k120f150 k150f200

(

3 ) 4.82 × 10-7 exp 8.14 × 10 T 99.7 × 103 ) 24.9 × 109 exp T 3 21.2 × 10 ) 5.4 exp T

(

(

)

)

)

(s) (s-1) (10) (s-1)

The total volume of CO2 variation is given by the following hyperbolic function of temperature: V∞ ) 32.01 -

Figure 9. jtx vs screw rotation speeds at 190 °C for the extrusion line with and without gear pump: comparison between the experimental data and the RTD model.

Figure 5 shows the thermal behavior of these parameters. The thermal variation of the kinetic constant clearly shows the two domains of temperature decomposition. The thermo-dependence of the inhibition time and the kinetic constant is given by Arrhenius’ law:

8.72 × 103 T

(mL/100 mg of CBA)

(11)

The temperature in the extruder was set to a temperature range of 190-200 °C. In this case, the time to obtain the total decomposition of CBA is 150 s. 4.2. Residence Time Distribution Analysis. The gear pump mounted between the extruder and the die was used to increase the pressure gradient in the extruder. Usually, gear pumps are solely used to generate pressure ahead of the die. In this case, the pressure differential across the pump is positive. To increase the mean residence time, the melt pump was mounted to obtain a negative pressure differential. The appropriate gear pump lubrication is obtained when the operating pressure is higher than 1 MPa. To limit the polymer leak, the maximum operating pressure is fixed at 35 MPa. The range of pressure necessary for an accurate working

Figure 10. t0, jtc, jt and R vs screw rotation speeds at 190 °C for the extrusion line with and without gear pump.

Ind. Eng. Chem. Res., Vol. 48, No. 10, 2009

Figure 11. Experimental and theoretical RTD (eq 8) for a single extruder with pump np ) 26, 30, and 35 rpm and without pump at 190 °C: dimensionless residence time density function vs dimensionless time. Table 1. Density of Foams Vs Process Parameters expt no. CBA (%m) nx (rpm) np (rpm) P (MPa) jtx (s) F (kg/m3) 0 1 2 3

0 0.5 0.5 0.5

60 80 55 55

26

8.8 8.4 8.1 13

129 90 135 160

915 790 721 615

of the pump strongly limits the domain of screw rotation speed explored (Figure 6). Moreover, the domain size decreases dramatically with decreasing temperature of extrusion. In our experiments, the variation of the pressure gradient with the screw rotating speed is similar for all melt pump flow rates studied (Figure 7). The curves are shifted toward the screw rotating speed axis. The residence time density function are shown for the two configurations of the extrusion line: without and with gear pump, and for different gear pump rotation speeds (Figure 8). The RTD model (eq 5) is in perfect agreement with the experimental data. The comparison between experimental data and the model confirms that the RTD approach is able to describe simply and quantitatively the extrusion process for two configurations: with and without gear pump. The results in terms of mean residence times jtx show the efficiency of the pump (Figure 9). We see that the mean residence time decreases with increasing screw rotation speed. The presence of the pump implies mean residence time increasing due to the back flow in the extruder. The mean value of this growth is approximately 20 s. The analysis of the three characteristic parameters of the residence time density function curve: jt0, jt, and R is not obvious (Figure 10). For the same configuration of the extrusion line, we observe a decrease in the latency period jt0 and in the mean

Figure 12. Foam extrudates vs process parameters given in Table 1.

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residence time jt. Without pump, we observe an increase in the recycling parameter R with the screw rotating speed of the extruder. However, this curve presents clearly a maximum near 80 rpm with the pump. The two curves of the latency period are quasi-parallel and the gap between these curves is close to 20 s. This value is very similar to the observed increase in time on the mean residence time of the extruder. The principal effect of the pump is to increase the latency period of the extrusion line. The variation of the CSTRs times jtc with the screw rotation speed corroborated this remark. The values obtained on the line for the two configurations are similar. The mean residence time is defined by the ratio volume of the reactor and its flow rate. In the case of CSTRs with recycling loops the flow rate in the reactor is the sum of the volumetric flow rate Q and the recycling volumetric flow rate q. Thus, the variation of jt can be explained by the increase in the flow rate while the volume of the reactor, that is, extruder, is constant. The effect of the back flow due to the pressure gradient is clearly shown by the variation of the recycling parameter R. An increase in screw rotation speed implies an increase of the volumetric flow rate Q in the extruder but too an increase of the recycling volumetric flow rate q. This study shows that the characteristic parameters of the residence time density function curve do not depend on the rotation speed of the gear pump. The main effect of the gear pump is to increase the pressure range in the extruder: 7-9 to 14-23 MPa. We suppose that the back flow in the extruder increases with the increasing pressure. An increase of the back flow implies an increase of the shear rate in the extruder. All these results can be explained if we take into account that the polymer melt is a pseudoplastic liquid. The dimensionless residence time density function φ(τ) versus dimensionless time τ are given in Figure 11. The experimental curve was obtained directly with the value of the experimental mean residence time of the line jtx. The theoretical curves are given by eq 8. They were obtained by fitting the experimental data using a nonlinear least-squares method. For each configuration of our extrusion line, these curves were unique. We found τ0 ) 0.5 s and R ) 2.5 without pump and τ0 ) 0.55 s and R ) 1.2 with the pump. This representation shows clearly the effect of the pump on the dimensionless latency time τ0. With the foam, the bubbles prevented any light transmission and so the RTD measurements become impossible with our system. The density of the foam provides another way to find the adequate process parameters. The density can be calculated with the mass, the dimensions of the extrudate, and the kinetic parameters. The foams were prepared with 0.5 wt % in chemical blowing agent. At 200 °C the total release volume of CO2 given by eq 11 is 65.88 mL/100 g of polystyrene. With 1050 kg/m3 as value of polystyrene density, the value of optimal foam density is 620 kg/m3. Table 1 shows the relationship between the density of the foam and the process parameters. The density

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values given in this table are the five samples average. The low value obtained for the polystyrene is due to the presence of small bubbles in the extrudate. The pressure at the inlet of the gear pump was descreased in the presence of the foaming agent. This effect is due to the solubility of CO2 in the polymer matrix and the viscosity is a function of this solubility.21,49,50 Lowest foam density was only obtained at 55 rpm with the gear pump at 26 rpm. This value, 615 kg/m3, is close to the optimal foam density. The mean residence time of the extrusion line is higher than the time to obtain the total decomposition of CBA. In the absence of the pump, the mean residence time of the line is lower than the chemical time and the density foams are too high. The mean residence time of the extrusion line is the critical parameter (Figure 12). 5. Conclusions The results obtained confirm that the residence time distribution theory is able to describe simply and quantitatively an extrusion process. An association of three continuoustly stirred tank reactors with recycling loops and one plug-flow reactor was sufficient. In this case, the extrusion line without and with a gear pump could be described by three parameters: jt0, the delay time or the mean residence time of the PFR; jt, the mean residence time of each CSTR; and, R, the recycling flow between the CSTR. In presence of the CBA, the formation of the bubbles does not allow the RTD measurements on the extrudate. A determination of the foam density shows the importance of the correlation between the chemical time associated to the blowing agent and the mean residence time of the extrusion line. Acknowledgment The authors are pleased to acknowledge the Communauté d’Agglomération Pau-Pyrénées and the Knauf Insulation Company for a financial contribution to this research. Literature Cited (1) Pinto, G.; Tadmor, Z. Mixing and residence time distribution in melt screw extruders. Polym. Eng. Sci. 1970, 10, 279. (2) Bigg, D.; Middleman, S. Mixing in a screw extruder. A model for residence time distribution and strain. Ind. Eng. Chem. Fundam. 1974, 13, 66. (3) Kembłowski, Z.; S¸ek, J. Residence time distribution in a real single screw extruder. Polym. Eng. Sci. 1981, 21, 1194. (4) Yeh, A.-I.; Jaw, Y.-M. Modeling residence time distributions for single screw extrusion process. J. Food Eng. 1998, 35, 211. (5) Yeh, A.-I.; Jaw, Y.-M. Predicting residence time distributions in a single screw extruder from operating conditions. J. Food Eng. 1999, 39, 81. (6) Chen, L.; Pan, Z.; Hu, G.-H. Residence time distribution in screw extruders. AIChE J. 1993, 39, 1455. (7) Chen, L.; Hu, G.-H. Applications of a statistical theory in residence time distributions. AIChE J. 1993, 39, 1558. (8) Jager, T.; Santbulte, P.; van Zuilichem, D. J. Residence time distribution in kneading extruders. J. Food Eng. 1995, 24, 285. (9) Gao, J.; Walsh, G. C.; Bigio, D.; Briber, R. M.; Wetzel, M. D. Residence-time distribution model for twin-screw extruders. AIChE J. 1999, 45, 2541. (10) Shearer, G.; Tzoganakis, C. Relationship between local residence time and distributive mixing in sections of a twin-screw extruder. Polym. Eng. Sci. 2001, 41, 2206. (11) Unlu, E.; Faller, J. F. RTD in twin-screw food extrusion. J. Food Eng. 2002, 53, 115. (12) Yichong, G.; Fuhua, Z. Study of the different flow patterns in the melting section of a co-rotating twin-screw extruder. Polym. Eng. Sci. 2003, 43, 306.

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ReceiVed for reView May 26, 2008 ReVised manuscript receiVed March 12, 2009 Accepted March 24, 2009 IE800836J