Role of Processing Temperature in Polystyrene and Polycarbonate

Ind. Eng. Chem. Res. 2007, 46, 7107-7116

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Role of Processing Temperature in Polystyrene and Polycarbonate Foaming with Carbon Dioxide Anson Wong, Siu N. Leung, Gary Y. G. Li, and Chul B. Park* Department of Mechanical and Industrial Engineering, UniVersity of Toronto, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8

This paper examines the effect of processing temperature on polystyrene (PS)/CO2 and polycarbonate (PC)/ CO2 polymeric foaming systems. Using in situ visualization data from batch foaming experiments, plastic foam characteristics including cell density and average cell size at different processing temperatures were analyzed. These results were compared with those generated by computer simulation, and satisfactory agreements between the two were observed. It was found that the maximum cell densities in the PS/CO2 foaming system were higher at lower processing temperatures. For processing temperatures above the melting temperature of PC, a similar, but less significant, relationship between the maximum cell densities and temperature was observed for the PC/CO2 system. Introduction Foamed plastics with a high cell density and uniform cell size offer superior mechanical properties such as higher toughness and specific tensile strength, as well as better thermal and acoustic insulation properties, when compared to their solid counterparts.1-3 In the past, the effects of the processing temperature on the cell density have been studied carefully and systematically by a number of researchers using foam extrusion systems. While many of these studies have led to valuable insights on the effect of processing temperature on polymeric foaming behavior, the final conclusions seem to vary from one study to another, and so a general consensus on this subject seems to be lacking. For example, Park et al.4 and Xu et al.5 conducted foaming of high-impact polystyrene (HIPS) and polystyrene (PS), respectively, with carbon dioxide (CO2), using an extrusion foaming line, and it was found that the effect of processing temperature on cell density was minimal. A similar trend was observed by Naguib et al.6 in their study of polypropylene (PP) foaming with butane. On the other hand, in a study conducted by Lee et al.7 to investigate polycarbonate (PC) foaming with CO2, it was observed that cell density decreased with increasing temperature. The processing temperature can affect the polymeric foaming behavior in many different ways. For example, as the processing temperature varies, the viscosity of a polymer-gas solution changes, which subsequently leads to a change in the shear force that is acted on the polymer-gas solution during an extrusion foaming process. It has been shown by Lee8 and Chen et al.9 that a shear force can enhance cell nucleation significantly. Furthermore, the gas diffusivity through a polymer-gas solution, which is known to be a function of temperature, affects cell growth and, ultimately, the final cell density.3 At the same time, other temperature-dependent parameters, such as the surface tension and the melt strength of a polymer-gas solution, also affect cell nucleation and cell density in different ways. Because of the different, and often competitive, effects of processing temperature on these parameters, it is difficult to understand the overall impact of temperature variation on the foaming behavior. Therefore, it is desirable, as the first endeavor, to * To whom correspondence should be addressed. Tel.: 416-9783053. Fax: 416-978-0947. E-mail: [email protected].

Figure 1. Schematic of the batch foaming visualization system.10 Table 1. Experimental Conditions for Foaming Experiments and Computer Simulations polymer PS

PC

gas content (wt %) [Psat (MPa)]

processing temperature [Tsys (°C)]

5.0% (12.1) 5.0% (12.5) 5.0% (12.9) 5.0% (13.4) 5.0% (14.7) 5.0% (15.1) 5.0% (15.5) 5.0% (15.9)

140 160 180 200 240 260 280 300

investigate individually how the temperature influences each of these parameters during a foaming process and the impact of such changes on the foaming behavior. However, this is difficult to achieve through experiments using foam extrusion systems, since many of the relevant parameters vary at the same time during such processes and foam characterization is typically undertaken after the foam has been extruded from the die. The objective of this study is to re-examine the effect of temperature on PS and PC foaming with CO2 using a different approach. This study consists of two main branches. The first branch involves carrying out PS/CO2 and PC/CO2 foaming experiments using the batch foaming visualization system developed by Guo et al.10 The advantages of conducting this study are 2-fold: (1) The foaming process is captured in situ; hence, it is possible to probe the temperature effect at different

10.1021/ie070551z CCC: $37.00 © 2007 American Chemical Society Published on Web 10/02/2007

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Figure 3. Sessile drop coordinate system definition.

mately, the study will help to optimize the processing conditions of various foaming processes and to facilitate the development of materials with improved foamability. Experimental Section

Figure 2. (a) Numerical simulation algorithm of cell-nucleation process and (b) numerical simulation algorithm of bubble growth process.

stages of foaming (i.e., cell growth and cell coalescence). (2) It is a static batch foaming process; hence, it is possible to minimize the effect of shear to simplify this analysis. One might argue that, by suppressing shear, the true mechanics of foaming would not be revealed. Nevertheless, this study could serve as the first step in investigating the fundamental effects of temperature on foaming behavior. The second branch of this study involves using a numerical simulation tool developed by Leung et al.11,12 to simulate the same foaming processes. The foaming visualization data could be used to verify the validity of the computer model or to provide a basis to improve the model and the theory behind the phenomena. The aim of this study is to establish a better understanding of the role of processing temperature in polymeric foaming processes. Ulti-

Experimental Materials. The polymers used for the foaming experiments were PS (Styron PS685D, Dow Chemical Ltd.) and PC (Makrolon 3158, Bayer MaterialScience). The melt flow indices (MFIs) of PS and PC are 1.5 and 6.5 g/(10 min), respectively. The densities of PS and PC are 1.04 and 1.2 g/cm3, respectively. The blowing agent used was CO2 (i.e., 99% pure, BOC Canada Ltd.). Experimental MethodologysBatch Foaming Experiments. Figure 1 shows a schematic of the batch foaming visualization system developed by Guo et al.10 The batch foaming visualization system consists of a high-temperature, high-pressure chamber in which a small plastic sample is enclosed for each foaming experiment. The temperature and pressure inside the chamber are precisely controlled by an electric heater with proportional-integral-derivative (PID) feedback control and a metered stream of gas supply via a syringe pump, respectively. The chamber is equipped with a set of two sapphire windows to allow for visualization of the plastic sample. An optical system, which consists of a high-speed camera coupled with a high magnification zoom lens and an optic fiber transmissive light source, is installed to allow for bright field observation and video recording of the plastic sample during the foaming process. A computer system is integrated into the system to control the opening of the gas exit valve of the chamber and to trigger the high-speed camera and the pressure transducer to record data. To carry out a foaming experiment, a thin diskshaped plastic sample that is 200 µm in thickness is placed inside the chamber. The chamber is then maintained at the designated temperature and pressure for 30 min to allow the blowing agent to be completely dissolved into the sample. Finally, the blowing agent is released from the chamber by opening the gas exit valve. The rapid pressure drop inside the chamber causes foaming to occur in the plastic sample. The foaming process is captured in situ by the high-speed camera, and the pressure drop profile is recorded via the readings of the pressure transducer. By adjusting the resistance of the gas exit path, different pressure drop rates can be obtained. Foaming experiments of PS and PC were conducted at different temperatures (i.e., 140, 160, 180, and 200 °C for PS and 240, 260, 280, and 300 °C for PC), while keeping the CO2 gas content fixed at 5 wt % and the pressure drop rate fixed at -47 MPa/s (refer to Table 1). The rationale behind fixing the latter two experimental parameters was to isolate the effect of temperature on the polymeric foaming processes. The

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Figure 4. Batch foaming visualization data sample taken from PS/CO2 foaming experiments.

Figure 5. Surface tension vs temperature.

Figure 6. CO2 diffusivity vs temperature.

CO2 gas content was kept the same in each case by using the corresponding saturation pressure at each temperature, which was obtained from the solubility studies of the PS/CO2 system and the PC/CO2 system by Li and co-workers.13,14 Note that the PC/CO2 solubility data at temperatures above 240 °C is not available; therefore, this data was extrapolated from the solubility data being measured at temperatures below 240 °C and used to estimate the solubility at the higher temperatures. Furthermore, in their PC/CO2 solubility study,13 Li et al. demonstrated that there would be CO2-induced crystallization of PC at a low processing temperature (i.e., 160 °C). Crystals in the PC/CO2 solution may act as heterogeneous nucleating agents or may

Figure 7. Zero shear viscosity vs temperature.

Figure 8. Relaxation time vs temperature.

generate a stress field, which could affect the foaming behavior. Liao et al.15 demonstrated that the Tm of PC decreases with increasing CO2 gas content. Therefore, the temperature range of the PC/CO2 system was chosen to be above the melting temperature (Tm) of PC at ambient conditions (i.e., Tm ) 220 °C) to ensure that there would be no crystallization of PC in all experimental cases; this allows the effect of temperature on the foaming behavior to be isolated. Each foaming experiment was carried out three times to test the repeatability of the results. The resulting in situ visualization data were analyzed to obtain the cell density and cell-growth profiles at each experimental condition.

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Figure 9. (a, b, c, d) Nb,unfoam vs time graphs for each temperature for the PS/CO2 system (experiment vs simulation).

Theoretical Framework The numerical foaming simulation tool was based on the modified nucleation theory and the bubble growth simulation model developed by Leung and co-workers.11,12 The overall simulation algorithms for cell nucleation and cell growth are illustrated in parts a and b of Figure 2, respectively. The computer simulation of the cell-nucleation process determined the cell-population density with respect to the unfoamed polymer volume, Nb,unfoam. This was calculated by integrating the total cell-nucleation rate over time as follows,

Nb,unfoam(t) )

∫0 [Jhom(t′) + AhetJhet(t′)] dt t

x

Whom )

(

)

Whom 2γlg exp πm kBTsys 16πγlg3

3(Pbub,cr - Psys)2

Jhet )

∫β Fβ(β)N2/3 Q(θc,β)

(1)

where Jhom(t′) and Jhet(t′) are the homogeneous nucleation rate (i.e., number of bubbles per unit volume of polymer melt) and the heterogeneous nucleation rate (i.e., number of bubbles per unit surface area of heterogeneous nucleation agents), respectively; Ahet is the total surface area of the heterogeneous nucleating sites per unit volume of the polymer-gas solution; and t and t′ are the time of the current simulation step and the time at which bubbles are nucleated, respectively. Jhom(t′) can be calculated using the following equations,11,16

Jhom ) N

where N is the number of gas molecules per unit volume; γlg is the surface tension at the liquid-gas interface; m is the molecular mass of the gas; Whom is the free energy barrier to initiate homogeneous nucleation; kB is the Boltzmann constant; Tsys is the processing temperature; Pbub,cr is the pressure in a critical bubble; and Psys is the system pressure. Jhet(t′) can also be computed using the following equations,11,16

(2)

(3)

x

2γlg πmF(θc,β)

×

(

exp -

Whet )

16πγlg3F(θc,β) 3(Pbub,cr - Psys)2

)

Whet dβ (4) kBTsys (5)

where Whet is the free energy barrier to initiate heterogeneous nucleation; F is the ratio of the volume of the heterogeneously nucleated bubble to the volume of a spherical bubble having the same radius; and Q is the ratio of the surface area of the liquid-gas interface of the heterogeneously nucleated bubble to the surface area of a spherical bubble with the same radius. Using simple geometry, F and Q were determined to be functions of θc and β, where θc is the contact angle (i.e., the angle between the bubble surface and the solid surface measured in the liquid phase) and β is the semiconical angle of a nucleating site. Also, it was noted that Fβ is the probability


Figure 10. (a, b, c, d) Nb,unfoam vs time graphs for each temperature for the PC/CO2 system (experiment vs simulation).

Figure 11. Average cell size for (a) PS/CO2 and (b) PC/CO2 (experiment only).

density function of β. The expressions of F and Q are shown below:

F(θc,β) )

[

]

cos θc cos2(θc - β) 1 2 - 2 sin(θc - β) + 4 sin β Q(θc,β) )

1 - sin(θc - β) 2

(6)

(7)

The bubble-growth simulation was based on the cell model presented by Amon and Denson.17 In the simulation, each bubble was assumed to be surrounded by a finite shell of viscoelastic

fluid with a limited gas concentration. Also, it was assumed that the bubbles were evenly distributed in the polymer-gas solution. The complete set of governing equations for the bubble-growth process (i.e., mass balance equation, momentum equation, constitutive equations, and diffusion equations) and the simulation algorithm are described in detail in ref 12 and illustrated in Figure 2b. The values of Pbub,cr, for both the PS/CO2 and PC/CO2 systems were determined using the Sanchez-Lacombe equation of state (SL EOS) and the thermodynamic equilibrium condition that requires the chemical potential of CO2 in gas and liquid phases to be equal.18 The SL EOS

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Figure 12. Maximum cell density for (a) PS/CO2 and (b) PC/CO2 (experiment vs simulation).

Figure 13. (a, b, c, d) Cell-nucleation rate vs time graphs for the PS/CO2 system (experiment vs simulation).

and the thermodynamic equilibrium condition are listed below,

FR2 + PR + TR[ln(1 - FR) + (1 - 1/r)FR] ) 0

(8)

µG,bub(Tsys, Pbub,cr) ) µG,sol(Tsys, Psys, C)

(9)

where PR, TR, and FR are the reduced pressure, temperature, and density of the polymer-gas solution, respectively; r is the number of lattice sites occupied by a mer; µG,bub is the chemical potential of the gas inside the critical bubble; and µG,sol is the chemical potential of the gas in the polymer-gas solution; and C is the dissolved gas content.

Computer simulation was conducted using the same experimental conditions as the batch foaming experiments summarized in Table 1. For the simulation, the values of θc for both foaming systems were estimated using a method that is detailed in ref 19. The viscosity data of the PS/CO2 solutions were taken from the study by Lee et al.20 For the PC/CO2 solutions, the viscosity of pure PC at each temperature was first measured using a dynamic stress rotational rheometer (i.e., SR-200, Rheometrics Scientific). Because of the plasticization effect of CO2, the viscosity of the PC/CO2 solution would be lower than that of the pure PC. Therefore, a reduction factor derived by Gendron and Daigneault21 was applied to the pure PC viscosity data to


Figure 14. (a, b, c, d) Cell-nucleation rate vs time graphs for the PC/CO2 system (experiment vs simulation).

estimate the viscosity of the PC/CO2 solution. The temperature dependence of gas diffusivity (D) for both PS/CO2 and PC/ CO2 systems was assumed to obey the Arrhenius relationship,22

(

D ) D0 exp -

)

Ea RGTsys

(10)

where D0 is the pre-exponential factor; Ea is the activation energy for the gas diffusion; RG is the universal gas constant; and Tsys is the temperature in the absolute scale. The values of D0 and Ea were determined by the diffusivity data at two different temperatures. For the PS/CO2 case, the diffusivity data were obtained from ref 23. For PC/CO2, they were derived from the sorption measurement using the approach detailed in ref 24. The relaxation times, λ, of the polymer-gas solution were unavailable for both foaming systems, so the values for pure polymer were used. In order to simulate the randomness of the surface geometries of the nucleating sites, the nucleating sites were assumed to be conical with a β that followed a uniform Fβ from 0° to 90°. The γlg data for the PS/CO2 system were obtained from the experimentally measured data by Park et al.25 On the other hand, the γlg data for the PC/CO2 system were derived in this study. Because of the unavailability of the γlg data on the PC/CO2 system, careful measurements on this parameter were made to improve the validity of the PC/CO2 simulations. There are various methods and approaches to measure the surface tension. Among them, the sessile drop method based on the axialsymmetric drop shape analysis (ADSA) was used, which is one of the most popular and efficient methods to obtain the surface

tension data.26-28 The Young-Laplace capillary equation, as shown as eq 11, is the basis of the surface tension measurement.29 It shows the relationship between the radii curvature and the pressure difference across a curved interface,

∆P ) γlg

(

1 1 + R1 R2

)

(11)

where γlg is the surface tension, R1 and R2 represent the two principle radii of curvature, and ∆P is the pressure difference across the interface. From Figure 3, the Young-Laplace equation could be expressed as a set of the following first-order differential equations:

dx ) cos φ ds

(12)

dz ) sin φ ds

(13)

sin φ dφ ) 2 + χz ds x

(14)

χ, the shape parameter, is defined as

χ ) ∆FgR02/γlg

(15)

where R0 is the radius of curvature at the origin of the (x, z) coordinate system, g is the gravitational acceleration, and ∆F is the density difference between the polymer-gas solution and the gas phases. The overall method to determine γlg is outlined

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as follows: (1) Obtain the (x, z) coordinates of the boundary profile of a sessile drop in equilibrium with the blowing agent using the captured images from the pressure-volume-temperature (pvT) visualization system developed by Li et al.30 (2) Starting from an initial estimate of the γlg and the empirically derived parameters, calculate a sessile drop profile from eqs 11-15.26,31 (3) Compare this theoretically determined sessile drop profile with the ones measured from the images taken by the pressure-volume-temperature (pvT) visualization system. Update the former in an iterative process until the best fit between the two is obtained. (4) From the updated sessile drop profile, determine the surface tension value using the YoungLaplace equation. The detailed numerical method can be found in refs 26 and 31. Because of the limitations of the pressurevolume-temperature (pvT) measurement system, the surface tension data was only measured up to 260 °C. Consequently, the γlg data at higher temperatures were obtained by extrapolating the data that were obtained at and below 260 °C. Results and Discussion A series of the visualization data from the foaming experiments is shown in Figure 4. A summary of the material parameters for the PS/CO2 and PC/CO2 systems is depicted in Figures 5-8. From the PS/CO2 and PC/CO2 foaming visualization data, the cell density and the cell size were measured and analyzed. Note that the computer foaming simulation tool does not consider bubble-to-bubble interactions. Therefore, comparisons between the experimental and simulation results could only be made in the initial foaming stage when the bubbles are far apart so that their interactions are negligibly small. Parts a-d of Figure 9 depict both the experimentally measured and numerically simulated cell density vs time graphs for each processing temperature of the PS/CO2 foaming systems. In each case, the pressure drop profiles of the system pressure are also included in the plots. Note that, because of the limited optical resolution of the visualization system camera, the smallest bubble that can be observed is approximately 3-5 µm in diameter.12,19 Therefore, the cell density vs time plots are based only on the observable cell densities. To achieve a meaningful comparison between the experimental and simulation data, the computer simulation determined both the nuclei density and the observable (i.e., Rbub g 1.5 µm) bubble density. Both sets of simulation results and experimental results are shown on the same plots. The same set of graphs for the PC/CO2 system is shown in parts a-d of Figure 10. It was noted that the observable cell density increased at earlier times in both foaming systems as the temperature increased, regardless of the approach used (i.e., experimental or simulation). In theory, as temperature increases, the mobility of gas molecules and that of polymer chains increases, which leads to a higher gas diffusivity (refer to Figure 6). Furthermore, the thermal fluctuation would be higher at elevated temperatures, which increases the probability of the gas molecules forming gas clusters larger than the critical size; thus, it will promote the initial nucleation rate. Meanwhile, γlg decreases with increasing temperature (refer to Figure 5), which lowers the free energy barrier for nucleation and, hence, increases the initial nucleation rate further. The result of the higher initial nucleation rate is that more bubbles would be observed at an earlier time. It should be noted that this phenomenon is much more apparent in the PS/CO2 case than in the PC/CO2 case for the same increase in temperature. This could be due to the elevated temperature range used in the latter case, which causes cell nucleation to occur very quickly upon pressure release, even at the lowest temperature being studied

(i.e., 240 °C). For the PC/CO2 case, it is interesting to note that the cell-nucleation processes started much earlier than was predicted by the computer simulations, even after the latter had been adjusted to reflect the observable cell density. One possible reason for this is the error, due to extrapolation, associated with some of the material parameters used in the simulation, notably the surface tension data. The average cell-growth profiles from the PS/CO2 and PC/ CO2 foaming experiments at different temperatures are depicted in parts a and b of Figure 11, respectively. For the PS/CO2 case, it can be observed that cells grow more rapidly at higher temperatures. This could be because gas diffusivity increases, and the viscosity of the gas-polymer solution decreases, as temperature increases (refer to Figures 6 and 7); this in turn promotes gas diffusion into the bubbles and reduces the resistance for cell growth, respectively. Furthermore, it can be observed that the relaxation time is longer for lower temperatures (refer to Figure 8). A longer relaxation time means that the stress in the polymer-gas solution around the bubble will take a longer time to build up, which promotes cell growth initially; however, the maximum value of stress attained in such cases is also higher,32 which restrains the cell-growth rate as stress builds up over time. The net effect of a higher relaxation time can be a lower cell-growth rate at lower temperatures. As a result, the combined effect of a higher gas diffusivity, lower viscosity, and lower relaxation time can lead to a higher cell-growth rate at high temperatures. For the PC/CO2 case, the cell-growth rates at each temperature are similar, which could be due to the low viscosity of the polymer-gas solution at high temperatures. Despite the higher initial nucleation rates at higher temperatures, a slightly lower maximum observable cell density was observed in the PS/CO2 foaming system using both approaches (i.e., experimental vs simulation) (refer to Figure 12a). For the case of the PC/CO2 foaming system, a similar, but less noticeable, trend was observed in the experimental results (see Figure 12b). On the other hand, slightly higher cell densities were predicted at 280 and 300 °C in the computer simulations. As explained previously, this could be attributed to the possible errors in the material parameters used in the simulation, notably the surface tension data, which is a critical parameter of cell nucleation. One reason for the lower maximum cell density at the higher temperatures could be the accelerated gas-depletion rate (-dC/dt) in the polymer-gas solution at the elevated temperatures, which is caused by the higher initial nucleation rate and cell-growth rate in such cases. By simultaneously solving eqs 8 and 9, it can be demonstrated that Pbub,cr increases with both C and Psys.18 Therefore, the higher -dC/dt effectively drives Pbub,cr and, hence, the degree of supersaturation down at faster rates. Consequently, as time progresses, the overall nucleation rate decreases at a higher rate according to eqs 2-5. This implies that, as the temperature increases, cell nucleation is sustained for a shorter period of time. The nucleation rate vs time graphs are depicted in parts a-d of Figure 13 and parts a-d of Figure 14 for the PS/CO2 and the PC/CO2 foaming systems, respectively. In these figures, the experimental nucleation rate is determined from the direct differentiation of the observable cell-density data obtained from the visualization data. In addition, two different nucleation rates from simulations were shown in each of these figures: one models the real nucleation rate, while the other is the predicted rate of generation of bubbles with radii >1.5 µm. From parts a-d of Figure 13, it is obvious that, for the PS/CO2 case, the cell-nucleation process was sustained for a longer period of time as the temperature decreased, regardless of the approach used (i.e., experimental


or simulation). In contrast, from parts a-d of Figure 14, it can be observed that the 240 °C case of the PC/CO2 system seems to deviate from this trend. To be specific, a shorter time-duration of nucleation was observed in the experimental results of the 240 °C case than those at higher temperatures. The reason for this phenomenon has not been fully understood yet, and further investigation will be carried out in the future to clarify this. In addition to the higher gas-depletion rate, the rate of decrease of Ahet is another possible reason for the lower maximum cell density at higher temperatures. As more bubbles were nucleated, Ahet decreased since some of the nucleating sites were occupied by the existing bubbles. At the same time, as the bubbles grew to bigger sizes, Ahet continued to decrease because the expanding bubbles would occupy more surface area on the heterogeneous nucleating sites. As mentioned before, the initial nucleation rate and cell-growth rate increased with temperature. Therefore, the rate of decrease of Ahet was accelerated at elevated temperatures, which ultimately led to a decrease in cell density according to eq 1. Therefore, the combined effect of higher -dC/dt and -dAhet/dt was a slightly lower maximum cell density at higher temperatures for both the PS/CO2 and PC/CO2 systems. Possible Reasons for the Discrepancy between Experimental and Simulated Cell-Density Profiles. Since accurate values for some of the experimental parameters to be used in the simulations could not always be obtained, a discrepancy between the simulation and the foaming experiments is possible. First of all, the surface tension data of PC/CO2 at 280 and 300 °C were obtained by extrapolation, so it is unclear how accurate these values are. Second, the temperature dependence of CO2 diffusivity data for both the PS/CO2 and PC/CO2 foaming systems was assumed to follow the Arrhenius relationship.22 Third, because of the lack of availability of the contact angle (i.e., θc) data, the values of θc for both the PS/CO2 and PC/ CO2 foaming systems were estimated using a fitting analysis that is detailed in ref 19. Fourth, the relaxation times for the polymer-gas solution, λ, were approximated by those of the pure polymers. Therefore, further investigations on γlg, D, θc, and λ are needed to verify and possibly to improve the accuracy of the simulations. In addition, various approximations were used in the cell-nucleation and -growth model. In particular, the cell-nucleation rate was determined by using the average gas concentration of the solution at each time-step. This might not completely reflect the real phenomena and might have an impact on the determination of the cell-nucleation rate and, hence, the estimation of the cell-density profile. Conclusion The effect of temperature on the foaming behavior of the PS/CO2 and PC/CO2 foaming systems was studied carefully by conducting experiments and a computer simulation. It was found that the cell-growth rate increased with temperature because of the higher CO2 diffusivity and the lower viscosity and relaxation time of the polymer-gas solution. Meanwhile, the maximum cell density of both polymeric foaming systems decreased slightly at higher temperatures, which could be due to a combined effect of the higher gas-depletion rate and the faster decrease in the area for heterogeneous nucleation due to the accelerated cell growth and the higher initial nucleation rate. Since there exist competitive effects of processing temperature on the overall cell density and the cell sizes, the ultimate effect might very well depend on the actual change in the relevant parameters addressed in this paper as the temperature varies. Therefore, the temperature might have a more noticeable effect

if a different range of temperature is chosen or if another polymer-gas foaming system is used. Nevertheless, this paper explained some key mechanisms through which the processing temperature affects the polymeric foaming behaviors in general terms. Acknowledgment The authors are grateful to the Consortium of Cellular and Micro-Cellular Plastics (CCMCP), AUTO21, and the Natural Sciences and Engineering Research Council of Canada (NSERC) for the financial support of this project. Nomenclature Ahet ) surface area of nucleating agents per unit volume of polymer melt, m2/m3 C ) dissolved gas concentration, mol/m3 D ) diffusivity, m2/s D0 ) pre-exponential coefficient, m2/s Ea ) activation energy for the gas diffusion, J F ) ratio of the volume of the nucleated bubble to the volume of a spherical bubble with the same radius, dimensionless g ) gravitational acceleration, m/s2 Jhet ) heterogeneous nucleation rate (per unit area of nucleating agent), #/m2‚s Jhom ) homogeneous nucleation rate (per unit volume of polymer), #/m3‚s kB ) Boltzmann constant, m2‚kg/s2‚K m ) molecular mass of gas molecules, kg N ) number density of dissolved gas molecules, #/m3 Nb,unfoam ) cell density with respect to unfoamed volume, #/m3‚ s Pbub,cr ) bubble pressure of a critical bubble, Pa PR ) reduced pressure, dimensionless Psys ) system pressure, Pa ∆P ) pressure difference across the interface of gas and polymer, Pa Q ) ratio of the surface area of the nucleated bubble to the surface area of a spherical bubble with the same radius, dimensionless r ) number of lattice sites occupied by a mer, # R0 ) radius of curvature at the origin of the (x, z) coordinate system, m R1 ) first principle radii of curvature, m R2 ) second principle radii of curvature, m Rbub ) bubble radius, m RG ) universal gas constant, J/K‚mol t ) current time, s t′ ) time at which a bubble is nucleated, s TR ) reduced temperature, dimensionless Tsys ) system temperature, K Tm ) melting temperature, K Whet ) free energy barrier to heterogeneously nucleate a bubble, J Whom ) free energy barrier to homogeneously nucleate a bubble, J Greek Letters β ) semiconical angle of a heterogeneously nucleating site, deg γlg ) surface tension, N/m θc ) contact angle, deg λ ) relaxation time, s µG,bub ) chemical potential of the gas inside the bubble, J/mol

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µG,sol ) chemical potential of the gas in the polymer/gas solution, J/mol FR ) reduced density, dimensionless Fβ ) probability density function of β, dimensionless ∆F ) density difference across the polymer-gas solution and gas phases, g/cm3 φ ) turning angle, deg χ ) shape factor, dimensionless Literature Cited (1) Baldwin, D. F.; Tate, D.; Park, C. B.; Cha, S. W.; Suh, N. P. Microcellular Plastics Processing Technology (1). J. Jpn. Soc. Polym. Proc. 1994, 6, 187. (2) Matuana, L. M.; Park, C. B.; Balatinecz, J. J. Structures and Mechanical Properties of Microcellular Foamed Polyvinyl Chloride. Cell. Polym. 1998, 17, 1. (3) Park, C. B.; Baldwin, D. F.; Suh, N. P. Effect of the Pressure Drop Rate on Cell Nucleation in Continuous Processing of Microcellular Polymers. Polym. Eng. Sci. 1995, 35, 432. (4) Park, C. B.; Behravesh, A. H.; Venter, R. D. Low-Density Microcellular Foam Processing in Extrusion Using CO2. Polym. Eng. Sci. 1998, 38, 1812. (5) Xu, X.; Park, C. B.; Xu, D.; Pop-Iliev, R. Effect of the Die Geometry on Cell Nucleation of PS Foams Blown with CO2. Polym. Eng. Sci. 2003, 43, 1378. (6) Naguib, H. E.; Park, C. B.; Reichelt, N. Fundamental Foaming Mechanisms Governing Volume Expansion of Extruded PP Foams. J. Appl. Polym. Sci. 2004, 91, 2661. (7) Lee, J. W. S.; Wang, K. H.; Park, C. B. Challenge to Manufacturing of Low-Density Microcellular Polycarbonate Foams Using CO2. Ind. Eng. Chem. Res. 2005, 44, 92. (8) Lee, S. T. Shear Effects on Thermoplastic Nucleation. Polym. Eng. Sci. 1993, 33, 418. (9) Chen, L.; Sheth, H.; Wang, X. Effect of Shear Stress and Pressure Drop Rate on Microcellular Foaming Process. J. Cell. Plast. 2001, 37, 353. (10) Guo, Q.; Wang, J.; Park, C. B.; Ohshima, M. A Microcellular Foaming Simulation System with a High-Pressure Drop Rate. Ind. Eng. Chem. Res. 2006, 45, 6153. (11) Leung, S. N.; Park, C. B.; Li, H. Numerical Simulation of Polymeric Foaming Processes Using a Modified Nucleation Theory. Plast., Rubber Compos. Macromol. Eng. 2006, 35, 93. (12) Leung, S. N.; Park, C. B.; Xu, D.; Li, H.; Fenton, R. Computer Simulation of Bubble-Growth Phenomena in Foaming. Ind. Eng. Chem. Res. 2006, 45, 7823. (13) Li, G.; Wang, J.; Park, C. B.; Moulinie, P.; Simha, R. Comparison of the SS-Based and SL-Based Estimation of Gas Solubility. Presented at SPE ANTEC, Chicago, IL, May, 2004; Paper 421. (14) Li, G.; Wang, J.; Park, C. B.; Simha, R. Investigation of the Gas Solubility in Polycarbonate Based on Experiments and Equation-of-State. Presented at PPS-20, Akron, OH, June, 2004; Paper 109. (15) Liao, X.; Wang, J.; Li, G.; He, J. Effect of Supercritical Carbon Dioxide on the Crystallization and Melting Behavior of Linear Bisphenol A Polycarbonate. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 280.

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ReceiVed for reView April 19, 2007 ReVised manuscript receiVed August 2, 2007 Accepted August 6, 2007 IE070551Z

Role of Processing Temperature in Polystyrene and Polycarbonate

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