Ind. Eng. Chem. Res. 2009, 48, 6633–6640
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MATERIALS AND INTERFACES Effects of Branching on the Pressure-Volume-Temperature Behaviors of PP/CO2 Solutions Y. G. Li and C. B. Park* Department of Mechanical and Industrial Engineering, Microcellular Plastics Manufacturing Laboratory, UniVersity of Toronto, Canada M5S 3G8
The pressure-volume-temperature (PVT) properties of polymer/gas solutions are characterized by determining their volume dilation at a known temperature and pressure. This paper presents the results of an experiment that measured the volume swelling of linear and branched polypropylene (PP) with CO2 using a new PVT measurement apparatus. The swellings and specific volumes for linear and branched PP/CO2 are compared. The swelling mechanism that occurred due to CO2 dissolution, and the effects of the branched structure on volume swelling are investigated and discussed. Due to its entangled branch structure, the branched PP underwent a lesser degree of volume swelling than did the linear PP. Introduction In thermoplastic foam processing, it is desirable to produce a fine-celled structure since polymeric foams with a small cell size and more uniform cell distribution are known to exhibit better mechanical properties1-6 The most commonly used materials for thermoplastic foam production are polystyrene (PS) and polyethylene (PE); however, since PS and PE have limited physical properties,7 they yield foamed products that exhibit restricted usefulness. Polypropylene (PP) foams, on the other hand, display different functional characteristics and cost less to manufacture. For instance, PP foams offer high rigidity and stiffness for static loads; they also have better impact properties than PS foams and boast a higher strength than PE foams.7 In addition, PP foams typically perform better than PE and PS at high temperatures because they possess a higher heat deflection temperature.8 As such, PP foams have been widely adopted recently as an alternative to thermoplastic foams. Despite their interesting properties, however, linear PP materials are commonly known to have very poor foamability due to their low melt strength,9 which makes them more difficult to foam in comparison to other plastics. If the melt strength is too low, as in the case of linear PP, the cell walls separating the bubbles will be too weak to bear the extensional force during foaming process and will thus be susceptible to coalescence and rupture. Therefore, it is necessary to submit PP resins to branching prior to foaming applications. Several technologies have been developed to blend a long chain branched structure into the backbone of PP molecules. The incorporation of a branched structure serves to increase the viscosity of the melt, which in turn increases the foamability and thermoformability of PP.10 In order to enhance PP foamabilty, researchers have conducted extensive investigations on the effects of branching on various PP melt properties, such as melt strength, strain hardening, and extensional viscosity. To date, however, no studies have explored the effects of branched PP on the pressure-volume-temperature (PVT) behaviors in the context of gas dissolution. Some experimental results have indicated that branched PP is more effective in the development * To whom correspondence should be addressed. E-mail: park@ mie.utoronto.ca.
of low-density foam because of its enhanced melt strength, which reduces the degree of cell coalescence and prevents gas loss during the foaming process. Moreover, long chain branching has been found to affect both the rheological and mechanical properties of PP melts.11,12 Gotsis et al.,11 for example, observed that branched PP displayed a distinct pattern of strain hardening in contrast to linear PP, which exhibited none whatsoever. They concluded that strain hardening is desirable because it enhances the melt strength of branched PP considerably. It has also been shown that the zero shear viscosity and elasticity of branched PP also increase as the number of branches per molecule increases.11 In addition, Gotsis et al.12 found that the melt strength and elasticity of branched PP increased with the increases of the number of branches per molecule in comparison with linear PP. Overall, the degree of long chain branching appears to affect the fluidity, elasticity, strain hardening, and melt strength of polymer melts. On the other hand, branching can have a negative impact on PP resin properties. For instance, it can lead to a decrease in the critical stress and an increase in the incidence of melt fractures in the PP resin.13 It also yields an increase in the PP critical temperature (Tc), which can limit the expansion ratio of PP foam.14 Furthermore, the solubility of a blowing agent may decrease because of the decreased specific volume of the branched structure. These adverse effects indicate that there is likely an optimal degree of branching for a foamable PP resin; however, since the decrease in the specific volume of PP/CO2 solutions due to branching as well as the dissolution of CO2 has not been accurately quantified to date, the ideal degree of branching cannot yet be assessed. In our previous studies, the specific volume (i.e., the PVT behaviors) of PP/CO2 solutions were described by using equations of state (EOS).15 The validity of all the EOS has not yet been verified experimentally; a more accurate evaluation of the PVT data in situ based on actual measurements is required. Since the PVT behaviours of a polymer/gas solution are intimately related to viscosity, solubility, and surface tension16 and because it is expected that a branched structure would also affect the PVT behaviors, the purpose of this paper is to study the effect of long chain
10.1021/ie8015279 CCC: $40.75 2009 American Chemical Society Published on Web 06/10/2009
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branching on the volume swelling behaviours of a PP/CO2 solution that is subjected to high temperatures and pressures. Theoretical Background When gas dissolves into a molten polymer in a polymer/gas solution system, the polymer swells or dilates due to gas dissolution. The amount of polymer swelling or dilation is characterized by its PVT properties, which can be obtained by measuring the equilibrium state volume of a polymer/gas solution at a given temperature and pressure. Zoller et al.17-19 and Sato et al.20 have both used a bellowtype dilatometer to measure the density of pure polymer in a polymer/gas solution in which the polymer sample and liquid mercury were confined to the dilator. Zollar et al. described the measurement procedures in detail and used this method to build a PVT database for various pure polymers. Nevertheless, this type of dilatometer is not capable of measuring the PVT properties of polymer/gas solutions. Attempts have been made to measure polymer swelling under high-pressure gas conditions21-32 and record the corresponding dimensional changes undergone by the polymer sample. Briscoe et al.31 developed a vibrating reed technique to determine the solubility of gases in organic polymers in hydrostatic gas pressure media. They studied the sorption of N2 and He into poly(tetraflouroethylene) (PTFE), up to a maximum pressure of 7400 psi but at a low temperature range of 0-70 °C. Ender22 used the coil of a linear variable differential transformer (LVDT) to measure the volume swelling of various elastomers under high pressures in CO2 at relatively low temperatures. Foster et al.23 used a cylinder piston-type method in a compressible chamber to acquire the PVT data by multiplying the crosssectional area with the linear displacement of the piston. Park et al.24 measured the PVT properties of polymer/CO2 solutions using a foaming extruder and a positive-displacement gear pump mounted on the extruder. The major drawback of the latter method is that it requires a limited range of extrusion processing conditions in order to calculate the PVT data. Ham et al.26 presented a method of measuring polymer swelling by determining the changes in length of a thin polymer film; however, their samples experienced warpage, which limited their application and resulted in an inaccurate length measurement. Wissinger et al.,25 Hirose et al.,29 and Fleming et al.28 presented a method of measuring polymer swelling by determining the changes in length of a thin polymer film; however, their samples experienced warpage, which limited their application and resulted in an inaccurate length measurement. Moreover, their approach only proved to be valid for calculating the isotropic swelling. Pope et al.30 later modified the approach to be able to used in the case for nonisotropic swelling. In general, most of the methods described above only operate successfully at fairly low temperatures (i.e., 25-100 °C). Pantoula et al.32 used optical method to determine the volume change and combined it with the magnetic suspension balance (MSB) method to determine the swelling of glassy polymers (poly(methyl methacrylate) (PMMA) and PS) due to CO2 sorption at temperatures from ambient to 132 °C and pressures up to 400 bar. Funami et al.33 developed a new method of directly measuring the densities of two polymer melt-CO2 single-phase solutions, poly(ethylene glycol) (PEG)-CO2 and polyethylene (PE)-CO2, at high pressure and temperature using MSB. A thin disk-shaped platinum plate was submerged in the polymer-CO2 single-phase solution in the MSB high-pressure cell. The weight of the plate was measured while keeping temperature and CO2 pressure in the sorption cell at a specified level. Since the buoyancy force
exerted on the plate by the polymer/CO2 solution reduced the apparent weight of the plate, the density of the polymer/CO2 mixture could be calculated by subtracting the true weight of the plate from its measured weight. However, this density measuring method has some limitations on applicable polymers. When the plate is moving up and down in the polymer melt during the position changeover operation, a dragging force is generated. Therefore, the readout could not be guaranteed when the viscosity of polymer melt is high. A method based on the axialsymmetric drop shap analysis (ADSA) technique commonly used in surface tension measurement was also used to measure the swelling of CO2-induced PMMA swelling over temperatures of 40-200 °C and pressures up to 100 bar in the work of Liu et al.34 A recent attempt was made to calculate the surface tension and density simultaneously using surface tension ADSA-P method35,36 to study the PS/N2 solution at pressure up to 500 psi and 200 °C. The limitation is that the ADSA method cannot handle asymmetry PS drop shape due to its high viscosity and elasticity even at low temperature. The results are not accurate in the low temperature range, and in addition, the operating pressure is low. Due to the difficulty of conducting empirical measurements, the theoretical EOSs, such as the Sanchez and Lacombe (SL) EOS,37-39 the Simha and Somcynsky (SS) EOS,15,40 and the statistical associating fluid theory (SAFT),41,42 which are all based on statistical thermodynamic theory, have been used extensively to predict the volume swelling of polymers due to gas dissolution. The EOSs were originally developed and applied to describe the PVT behaviors of polymerical liquids and their mixtures. The SL EOS and the SS EOS are the most widely used EOSs, but currently, the SAFT EOS is gaining popularity. Nonetheless, due to a lack of experimentally measured data with respect to volume swelling, the validity of these theories for polymer/gas mixtures has not yet been verified. Recently, our research team developed a new apparatus to measure the volume swelling of polymers directly. The details of the system construction and methodology have been outlined in our previous publication.16 On the basis of the measured PVT data using this apparatus, the volume swelling ratio Sw was defined as follows: Sw )
V(T,P,teq) V(T,P,tini)
)
V(T,P,teq)
(1)
msampleνpure polymer
where V(T, P, teq) is the measured equilibrium polymer/gas solution volume at temperature T, pressure P, and equilibrium time teq. V(T, P, tini) is the volume of the pure PP sample without any gas at temperature T and hydraulic pressure P. The mass of the initial pure polymer sample is denoted as msample, which is determined and weighed using a precision Meledo Mettlo microbalance. The specific volume of the initial pure sample is νpure polymer and can be calculated using the Tait equation. The Tait equation is an isothermal compressibility fitting model rather than a true equation of state. It reliably calculates the specific volume of a pure polymer at different temperatures and pressures using particular PVT data measured from a bellow-type dilatometer.18 The equation has various forms and coefficients depending on the grade of the polymer sample used. The original form of the Tait equation is shown in eq 2:
{
[
ν(P, T) ) ν(0, T) 1 - 0.0894 ln 1 +
P B(T)
]}
(2)
where the zero-pressure isotherm is ν(0, T) ) ν0 + ν1T
(3)
Ind. Eng. Chem. Res., Vol. 48, No. 14, 2009 Table 1 coefficients
a1
a2
a3
a4
linear PP branched PP
7.46 × 106 6.485 × 106
6.45 × 109 5.733 × 109
1.06 × 102 1.221 × 102
9.86 × 107 1.146 × 108
and the B(T) is B(T) ) B0e-B1T
(4)
where ν0, ν1, and B0 are constants. The latter are determined based on the empirical fitted data for each different material grade. The following equation is a version of the Tait equation applied in the Moldflow PVT model for the specific grade of PP used in the current study. The specific volume υ is in units of cubic meters per kilogram; the pressure, P, is in Pascal; and temperature, T, is in degrees Celsius. νpp )
a3T a1 + a2 + P a4 + P
(5)
The coefficients of eq 5 for both linear and branched PP are listed in Table 1. The specific volume υ is expressed in units of cubic meters per kilogram, pressure P is in Pascal, and temperature T is in degrees Celsius. Using our new measurement method, the specific volume of the final polymer/gas mixture could be determined precisely with the following eq 6: υpolymer/gas mixture )
V(T,P,teq) msample + mgas(T,P,teq)
(6)
Therefore, by combining eqs 1 and 6, the specific volume of the polymer/gas mixture at equilibrium can be expressed as υpolymer/gas mixture )
Sw*νpure polymer (1 + Sapp)
(7)
where Sapp is the apparent solubility measured in the magnetic suspension balance,15 and Sw is the swelling ratio. The volume swelling ratio from eq 1, the swollen volume, can be rearranged in terms of the volume swelling ratio and the initial polymer sample volume as Vswollen ) V(T, P, tini)(Sw - 1)
(8)
Thus, the final specific volume of the polymer/gas mixtures can be determined with eq 9: υpolymer/gas mixture )
(1 + Sapp
Sw*νpure polymer + Fgasνpure polymer(Sw - 1)) (9)
Table 1 lists the coefficients of the Tait equation (5) for both linear and branched PP as mentioned before. Experimental Details Experimental Setup. Figure 1 shows a schematic of the PVT measurement apparatus used in this study to measure the PVT properties of the PP/CO2 solutions. A detailed description of this relatively new system can be found in our previous publication.16 As such, only a brief outline of the system is given in this paper. Experiment Material. Linear PP (DM 55, Borealis,); branched PP (Daploy WB130 HMS, Borealis,), and carbon dioxide (Coleman grade, 99.99% purity, BOC Canada) were used in this study. Table 2 summarizes some of the typical properties of both PP resins.
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Experimental Procedure. First, polymer samples were selected from pellets of both linear and branched PP, and weighed using a precision Toledo microbalance. The selected PP samples were attached to the droplet rod to form a sessile drop for each experiment. Second, the volume of each sessile drop was measured in the CO2 chamber at three different temperatures: 180, 200, and 220 °C. At each temperature, the pressure of CO2 in the chamber was varied from 6.9 (1000) to 31.0 MPa (4500 psi) in 3.4 MPa (500 psi) increments. Each pressure level was maintained for over 1 h to ensure the equilibrium condition was reached for the PP/CO2 solution. Equilibrium was considered to have been achieved when the polymer sample was totally saturated with supercritical CO2, or, in other words, when the total volume of the PP/CO2 solution no longer fluctuated. Third, the volume of the polymer/CO2 sessile drop was calculated from its profile based on the axialsymmetric drop shap analysis (ADSA) theory,43 and the volume swelling was determined using eq 1. Results and Discussion Determination of the Swelling Ratio of Linear and Branched PP/CO2 Solutions. As depicted in eq 1, the swelling ratio is the quotient of the total PP/CO2 mixture volume at an equilibrium state divided by the initial pure polymer volume. In our study, the final volume was experimentally measured. The initial pure polymer volume was determined using the polymer’s density information, which was ascertained with the Tait equation and by measuring the initial sample weight with a microbalance. Figures 2 and 3 show the volume swelling of linear PP/CO2 and branched PP/CO2 solutions at different temperatures and pressures, respectively. As discussed above, the increasing solubility of CO215 at a higher pressure causes more CO2 to dissolve into the PP matrix, inducing more volume swelling. The results indicated that when the pressure was increased at each individual temperature, the volume swelling ratio increased for both linear and branched PP/CO2 mixtures. When we began to increase the pressure from its initial low level, the effect of gas dissolution on the volume change dominated over that of hydraulic pressure; the net result was that the increase in volume swelling obeyed a more linear trend. As the pressure was raised further, however, the volume swelling for both materials increased at a slower pace. The rate of the volume increase (i.e., the slope of the volume swelling curve) became smaller, and a concave downward increase was observed (see Figures 2 and 3). These results signaled that, in addition to the effects of hydraulic pressure, the polymer chain structure and chain entanglement of both the linear and branched PPs restrained the indefinite swelling of the polymer matrix at higher pressure levels. Therefore, the overall effect of the gas dissolution was weakened. The effects of chain entanglement on the volume swelling of a linear PP/CO2 mixture have been postulated briefly in our previous publication.16 The same phenomena were also observed in the case of the branched PP/CO2 vis-a`-vis volume swelling in this study. We observed that the chain entanglement that occurred with both the linear and the branched PP had similar effects on the volume swelling as the branched structure did. Figures 2 and 3 indicate that the polymer matrix did not dilate indefinitely as the temperature and pressure continued to increase. In other words, this suggests that there is an upper limit on the polymer’s volume expansion potential because of the constraint posed by the polymer chain entanglement. Wissinger et al.25 reported similar volume swelling and sorption
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Figure 1. Schematic of the PVT system. Table 2 property
melt flow rate (MFR; g/10 min)
molecular weight Mw (g/mol)
Mw/Mn
melting point (Tm)
degree of crystallinity (%)
linear PP branched PP
2.8 2.1
481750 654039
4.5 5.34
162-166°C 162-166°C
27.8 29.7
behaviours in PC/CO2 and PMMA/CO2 systems; they began to level off at around 80 atm and eventually reached their respective limits at lower temperatures of approximately 35 and 32.7 °C. Similar results were also yielded when the pressure
Figure 2. Linear PP/CO2 volume swelling. Reprinted with permission from ref 16. Copyright 2008 Elsevier.
Figure 3. Branched PP/CO2 volume swelling.
was in the range of 70-100 atm. Although the effects of entanglement on viscosity and elasticity,44 intrinsic brittleness and toughness,45 and the deformation mechanism46,47 have been reported, it nonetheless remains important to investigate how entanglement limits the volume swelling of polymer melts in future studies. Moreover, Bonavoglia et al.48 have studied the sorption and swelling of semicrystalline polymers in supercritical CO2 at temperature from 40 to 80 °C and pressure up to 200 bar, and they have divided the experimental curves into three different regions and claimed that in the low pressure region the gas sorbs without significant dilation of the polymer matrix and sorption occurs together with significant swelling as pressure increases but in the last region of even higher pressure the swelling becomes negligible. Figure 4 compares the volume swelling values for linear and branched PP/CO2 at three individual temperatures, respectively. The results suggest that the branched PP/CO2 mixture generally underwent less volume swelling than the linear PP/CO2 mixture. We surmised that this was due to more branching within the polymer chain structure itself, as well as the likelihood that the branched PP exhibited a greater polymer chain entanglement density. The effect of the branching structure promoted strain hardening, which resulted in a melt strength increase. On the one hand, an increase in melt strength can lead to an augmentation in the zero-shear viscosity and a reduction in fluidity. The reduction in fluidity in turn restrains the mobility of the polymer chains and thereby limits the polymer matrix’s ability to undergo swelling. On the other hand, a temperature increase can also help increase the chain mobility of both linear and branched PP. Although the potential increase to the melt strength and strain hardening generated by the branched structures could be counterbalanced to some extent by the increase in temperature from 180 to 200 to 220 °C, the linear PP would still exhibit a significantly higher volume swelling than the branched PP at all pressures. Determination of the Specific Density of a PP/CO2 System. The dissolution of CO2 within the PP matrix allows for an accurate measurement of the volume swelling within the PP/
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Figure 4. Comparison of linear and branched PP/CO2 volume swelling.
Figure 5. Comparison of linear and branched PP/CO2 specific volume.
CO2 solution. Using this value, one can acquire even more precise CO2 solubility information with an MSB and a buoyancy compensation calculation. Equipped with accurately compensated solubility information, which yields the amount of CO2 gas dissolved in the PP matrix, it is then straightforward to determine the density information for the PP/CO2 solution at
high temperatures and pressures using a previously derived equation (see eq 12 in ref 16). In the following discussion, the volume swelling refers to the net volume swelling which takes into the consideration of the isothermal compressibility due to hydraulic effect. Figure 5 compares the specific volume of PP/CO2 at different saturation
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Figure 6. Linear PP/CO2 volume swelling: experimental vs EOS predictions. Reprinted from ref 16. Copyright 2008 Elsevier.
Figure 7. Branched PP/CO2 volume swelling: experimental vs EOS predictions.
pressures and temperatures. As shown in Figure 5a and b, at 180 and 200 °C and pressures up to 2500 psi, the specific volume values for both the linear and the PP/CO2 mixtures exhibited a slight increase. The latter suggests that, at lower pressure levels, the volume increase due to gas sorption is higher than the volume decrease caused by the hydrostatic effect and the increased volume due to the net volume swelling also prevailed over the weight increase due to CO2 dissolution. As illustrated by Figure 5, when the volume swelling showed signs of decreasing or leveling off after the pressure had surpassed 2500 psi, the effects of the dissolved CO2 on the weight of the solution began to dominate over the volume swelling, indicating that the specific volume
had started to decrease. With the increases in operating pressure, the hydrostatic effect becomes progressively more pronounced, thereby reducing the net volume increase due to gas sorption, and the specific volume would start to decrease eventually. Moreover, the decrease in the specific volume also contributed to an increase in the CO2 density as a function of the increased pressure. As the temperature reached 220 °C, the swelling continued to rise as the pressure increased but was nonetheless becoming significantly less pronounced for both the linear and branched PP/CO2 mixtures in comparison to those exhibited at 180 and 200 °C due to the fact that for a given operating pressure, the amount of gas absorbed by the polymer decreases with increasing temperature. Hence, the dissolution of CO2
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initially counterbalanced the greater part of the increase to the mixture’s volume, while the resultant specific volumes remained unchanged and even decreased slightly for the branched and linear PP/CO2, respectively. Once the swelling started to level off after the pressure reached 3000 psi, however, the mass of dissolved CO2 became dominant, and the specific volume for both the linear and branched PP/CO2 started to decrease, as shown in Figure 5c. Moreover, Figure 5a-c reveals the branched PP/CO2 solution to have had a lower specific volume at all three temperatures and at all pressures. Since the volume swelling of the branched PP/CO2 solution was smaller than that of the linear one at all temperatures and pressure and because it was more difficult for CO2 to penetrate the branched PP matrix due to its branched structure, the specific volume of branched PP/CO2 was smaller than that of the linear PP/CO2 solutions. Ascertaining the density information for polymer/gas mixtures is especially useful for conducting the surface tension calculation of the supercritical fluid CO2 in the PP matrix since the density difference across the gas and polymer/gas solution phase boundary is typically one of the input parameters. Comparison with the EOS-Based Swelling Ratio. The new PVT measurement technology deployed in this study was also significant insofar as it enabled a comparison between the experimentally measured volume swelling data and the theoretically predicted swelling data postulated by the SS and SL EOSs.20 Figures 6 and 7 show a three-way comparison among the swelling ratios obtained from the SS EOS, the SL EOS, and the experiments for both linear and branched PP at 180, 200, and 220 °C, respectively. The materials used in the experiment were the same as those used for the EOS predictions, and the temperature and pressure parameter settings were similar as well. At all three temperatures, both the SS and SL EOSs predicted that the volume swelling would increase as the pressure increased. The SL EOS yielded a concave upward increasing trend while SS EOS demonstrated a more linear increase. As observed from the experimental results, the volume swelling ratio increased and then started to level off across a pressure range of 2500-3000 psi. Moreover, there appeared to be an upper limit with regard to the volume swelling regardless of the pressure value. Since these EOSs have been developed mainly for neat polymers and blends, however, some modifications would need to be introduced in future studies to accommodate the polymer/gas mixture behaviors. Summary This study measured the PVT data of both linear and branched PP/CO2 solutions at 180, 200, and 220 °C across a pressure range of 1000-4500 psi using a new PVT measurement apparatus. The effects of branching structures on PVT behaviors were examined by comparing the volume swelling results for linear and branched PP/CO2 mixtures. In general, the volume swelling was found to increase as the pressure was increased, and the volume swelling decreased as the temperature was increased. We surmised that, due to its branched structure, branched PP exhibited less swelling in comparison to linear PP. In addition to branching, polymer chain entanglement also contributed to a curbing of the volume expansion once the CO2 gas filled the initial free volume for both mixtures at higher pressures. The specific volume of the branched PP/CO2 solution was smaller than that of the linear PP/CO2 solution. Unlike the swelling predictions based on the SS and SL EOSs, the volume increase
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eventually leveled off and reached an upper limit as the pressure increased indefinitely. Acknowledgment We would like to thank AUTO21 and the Consortium for Cellular and Micro-Cellular Plastics (CCMCP) for their financial support.44 Literature Cited (1) Collias, D. I.; Baird, D. G. Tensile Toughness of Microcellular Foams of Polystyrene, Styrene-Acrylonitrile Copolymer, and Polycarbonate, and the Effect of Dissolved Gas on the Tensile Toughness of the Same Polymer Matrices and Microcellular Foams. Polym. Eng. Sci. 1995, 35, 1167. (2) Collias, D. I.; Baird, D. G. Impact Behavior of Microcellular Foams of Polystyrene and Styrene-Acrylonitrile Copolymer, and Single-EdgeNotched Tensile Toughness of Microcellular Foams of Polystyrene, StyreneAcrylonitrile Copolymer, and Polycarbonate. Polym. Eng. Sci. 1995, 35, 1178. (3) Collias, D. I.; Baird, D. G.; Borggreve, R. J. M. Impact Toughening of Polycarbonate by Microcellular Foaming. Polymer 1994, 35, 3978. (4) Doroudiani, S.; Park, C. B.; Kortschot, M. T. Processing and Characterization of Microcellular Foamed High Density Polyethylene/ Isotactic Polypropylene Blends. Polym. Eng. Sci. 1998, 38, 1205. (5) Matuana, L. M.; Park, C. B.; Balatinecz, J. Structures and Mechanical Properties of Microcellular Foamed Polyvinyl Chloride. J. Cellul. Polym. 1998, 17, 1. (6) Seeler, K. A. V. K. Tension-Tension Fatigue of Microcellular Polycarbonate: Initial Results. J. Reinforced. Plast. Comp. 1993, 12, 359. (7) Leaversuch, R. D. Quantum Probes New Polyolefin Technology. Modern Plast. 1990, 19. (8) Park, C. B.; Cheung, L. K. A Study of Cell Nucleation in the Extrusion of Polypropylene Foams. Polym. Eng. Sci. 1997, 37, 1. (9) Naguib, H. E.; Park, C. B.; Panzer, U.; Reichelt, N. Strategies for Achieving Ultra Low-density Polypropylene Foams. Polym. Eng. Sci. 2002, 42, 1481. (10) Weng, W.; Markel, E. J.; Dekmezian, A. H. Synthesis of LongChain Branched Propylene Polymers via Macromonomer Incorporation. Macromol. Rapid Commun. 2001, 22, 1488. (11) Gotsis, A. D.; Zeevenhoven, B. L. F. Effect of Long Branches on the Rheology of Polypropylene. J. Rheol. 2004, 48, 895. (12) Gotsis, A. D.; Zeevenhoven, B. L. F. The Effect of Long Chain Branching on the Processability of Polypropylene in Thermoforming. Polym. Eng. Sci. 2004, 44, 973. (13) Naguib, H. E.; Park, C. B.; Song, S.-W. Effect of Supercritical Gas on Crystallization of Linear and Branched Polypropylene with Foaming Additives. Ind. Eng. Chem. Res. 2005, 44, 6685. (14) Naguib, H. E.; Park, C. B.; Rechelt, N. Fundamental Foaming Mechanisms Governing Volume Expansion of Extruded PP Foams. J. Appl. Polym. Sci. 2004, 91, 2661. (15) Li, G.; Wang, J.; Park, C. B.; Simha, R. Measurement of Gas Solubility in Linear/Branched PP Melts. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 2497. (16) Li, Y. G.; Park, C. B.; Li, H. B.; Wang, J. Measurement of the PVT Property of PP/CO2 Solution. Fluid Phase Equilib. 2008, 270, 15. (17) Zoller, P. The Pressure-Volume-Temperature Properties of Three Well-Characterized Low-Density Polyethylenes. J. Appl. Polym. Sci. 1979, 23, 1051. (18) Zoller, P.; Bolli, P.; Pahud, V.; Ackermann, H. Apparatus for Measuring Pressure-volume-temperature Relationships of Polymers to 350 °C and 2200 kg/cm2. ReV. Sci. Instrum. 1976, 47, 948. (19) Zoller, P.; Walsh, D. Standard Pressure-Volume-Temperature Data for Polymers; Technomic Publishing: Lancaster, PA, 1995. (20) Sato, Y.; Yamasaki, Y.; Takishima, S.; Masuoka, H. Precise Measurement of the PVT of Polypropylene and Polycarbonate up to 330 °C and 200 MPa. J. Appl. Polym. Sci. 1997, 66, 141. (21) Buckley, D.; Berger, J. M.; Poller, D. The Swelling of Polymer Systems in Solvents. I. Method for Obtaining Complete Swelling-Time Curves. J. Polym. Sci. 1962, 56, 163. (22) Ender, D. H. Elastomeric Seals. CHEMTECH 1986, 16, 52. (23) Foster, G. N.; Waldman, N.; Grisly, R. Pressure-volume-temperature Behavior of Polypropylene Polymer Engineering & Science. J. Polym. Eng. Sci. 1996, 6, 131. (24) Park, S. S.; Park., C. B.; Ladin, D.; E., N. H.; Tzoganakis, C. Development of a Dilatometer for Measurement of the PVT Properties of
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ReceiVed for reView October 9, 2008 ReVised manuscript receiVed February 26, 2009 Accepted April 13, 2009 IE8015279
