Ind. Eng. Chem. Res. 2009, 48, 7117–7124
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Solubility and Diffusivity of Carbon Dioxide in Solid-State Isotactic Polypropylene by the Pressure-Decay Method Da-chao Li, Tao Liu,* Ling Zhao,* and Wei-kang Yuan State Key Laboratory of Chemical Engineering, East China UniVersity of Science and Technology, Shanghai 200237, P.R. China
The solubility and diffusivity of carbon dioxide (CO2) in the solid-state isotactic polypropylene (iPP) were studied by using the pressure-decay method at temperatures of 373.15, 398.15, and 423.15 K and pressures ranging from 1 to 15 MPa. The solubilities of CO2 in the solid-state and amorphous regions of iPP were both obtained. They increased almost linearly with increasing pressure and decreased with increasing temperature. The Sanchez-Lacombe equation of state (S-L EOS) correlated the solubility in the amorphous regions of the solid-state iPP within 3% average relative deviation in conjunction with a temperature-dependent interaction parameter. The diffusion coefficient of CO2 in the solid-state iPP showed a weak concentration dependence and had an order of magnitude of 10-10-10-9 m2/s in the solid-state iPP. 1. Introduction Supercritical carbon dioxide (scCO2) has many unique properties such as nonflammable, nontoxic, relatively inexpensive, and relatively easy to reach a supercritical state (critical temperature, 31.1 °C, and critical pressure, 7.38 MPa). As a supercritical fluid, it is capable of dissolving apolar or not exceedingly polar compounds and plasticizing and/or swelling polymer matrices in the solid state. Moreover, the density of scCO2 is easily tuned from gas-like to liquid-like by changing temperature or pressure, so its solvation ability can be strengthened greatly. This provides a possibility to control the degree of plasticization/swelling of polymers and partition the monomers between the plasticized/swollen polymer phase and the scCO2 fluid phase. Therefore, scCO2 has been increasingly considered and used as a promising alternative to organic and other toxic or harmful solvents for applications in solid-state polymer processing, such as grafting, foaming, and impregnation of additives.1-4 The so-called “solid state” means that the processing temperature is chosen to be below the melting temperature of the polymer. Solubility and diffusivity of CO2 are two critical thermodynamic parameters that establish intrinsic gas transport characteristics and are needed for designing and optimizing the polymer processing in the solid state. For example, in foaming applications, both solubility and diffusivity of CO2 in the polymer matrix play important roles on the cell formation in polymer foams and subsequently affect the product properties.4-6 Solubility and diffusivity of CO2 in different polymers had been widely studied.2 Those polymers include poly(methyl methacrylate),7,8 polystyrene,9,10 low-density polyethylene, and high-density polyethylene,10-13 poly(ethylene terephthalate),14,15 polypropylene,10,13,16-18 and so on. Three methods are commonly used for measuring the solubilities and diffusivities of gases in polymers, that is, pressure-decay method,13,19 frequency modulation method,20 and magnetic suspension balance (MSB) method.21-23 The diffusivity of gases in polymers could be conducted by the pressure-decay method and MSB method. The MSB method has a good sensitivity and requires just a small amount of polymer sample during an experiment. * To whom correspondence should be addressed. Tel.: +86-2164253175. Fax: +86-21-64253528. E-mail:
[email protected] (T.L.),
[email protected] (L.Z.).
However, the gas solubility should be corrected by considering gas buoyancy acting on the polymer volume, and the exorbitant price also restricts the popularization of the MSB method. Although the apparatus for the pressure-decay method is simple and the operation is very easy, there is a greater possibility of leakage and the initial gas density is hard to measure. Davis et al.24 developed a new pressure-decay method which utilized elements of the gravimetric method. This technique has few possibilities of leakage, and the initial gas density can be easily gravimetrically determined. Isotactic polypropylene (iPP) can be foamed and used in products such as heat insulators and support materials. In solidstate foaming applications, CO2 solubility and diffusivity in iPP play important roles on the nature of the functional materials and affect the products performance. However, for the case of iPP, the solubility and diffusivity of CO2 have only been reported over a limited range of conditions,10,13,16-18 and most of them are limited to the case of molten iPP. Lei et al.16 carefully studied the solubility of CO2 in polypropylene at temperatures from 313.2 to 483.7 K and pressures up to 25 MPa by using a MSB method. Literature about solubility of CO2 in the solidstate iPP is very limited. Manika and co-workers17 described the interaction of compressed CO2 with iPP and measured the solubility and diffusivity of CO2 in solid-state iPP at a temperature of 323.2 K and relatively low pressure (no more than 200 psi) by using a high-pressure electrobalance. In this work, the solubility and diffusivity of CO2 in the solidstate iPP were studied by using the pressure-decay method24 at 373.15, 398.15, and 423.15 K and pressures ranging from 1 to 15 MPa. The crystallinity of the iPP before and after solubility measurements was tested by the differential scanning calorimetry (DSC). The solubility in the amorphous regions was then calculated by deducting the mass of crystal regions. The Sanchez-Lacombe equation of state (S-L EOS) was used to correlate the experimental data of solubility of CO2 in the amorphous regions in conjunction with a temperature-dependent interaction parameter. The diffusion coefficient of CO2 in the solid-state iPP was determined so as to minimize the difference between the experimental mass uptake and the Fick’s model correlation.
10.1021/ie8019483 CCC: $40.75 2009 American Chemical Society Published on Web 06/23/2009
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Figure 2. Scheme of CO2 diffusion into iPP cylinder. Figure 1. Schematic diagram of pressure-decay experiment.
2. Experimental Section 2.1. Materials. iPP pellets (Y1600) with an average diameter of 3 to 4 mm were supplied by Shanghai Petrochemical Company. The mass-average and number-average molar masses of the iPP were 197 000 and 42 000 g/mol, respectively, which were measured by gel permeation chromatography (PL-GPC220, Polymer Lab, U.S.A.) at 150 °C with 1,2,4-trichlorobenzene as a solvent. Its melting temperature and crystallinity, Tm and wcry, were 168.6 °C and 47.1% in nitrogen at ambient pressure. The CO2 was supplied by Air Product Co. with a purity of 99.5% and was used as received. The argon was purchased from Shanghai Chenggong Industry Gases Corp. with a purity of 99.9% and was also used as received. 2.2. Apparatus and Experimental Procedure. A schematic diagram of the pressure-decay method for studying the solubility and diffusivity of CO2 in solid-state iPP is shown in Figure 1. A high-pressure vessel made in stainless steel with internal volume of about 120 cm3 and inner diameter of 38 mm was used as the sample chamber. The entire apparatus was placed in a temperature-controlled forced-convection air bath. The temperature of the latter was controlled with an accuracy of (0.5 °C. The titanium capsule was a small cylinder about 10 cm long and 2 cm in diameter, with an internal volume of about 12 mL. The capsule and Valve 2 could be dismantled from the system as a union, and the combined weight of them was less than 195 g. This allowed the capsule unit to be weighed on a high-precision (0.0001 g) Sartorius analytical balance. The system pressure was measured by a 3051S pressure transducer of Emerson Beijing Instrument Co., at an accuracy of (5 kPa. The pressure data were collected by a data acquisition system at a time interval of 1 s. After the sample was loaded in the sample chamber, a vacuum was applied for 24 h to desorb the iPP (usually 50 g) of any impurities. The headspace volume was required to convert gas density data into mass uptake data. This volume was measured by a headspace-determination experiment, which was conducted by expansion of argon from the titanium capsule into the sample chamber. Argon is an inert gas with very low permeability coefficient in polymers.25 The capsule weights gave the mass of argon, the pressure could be measured, and the temperature was set at 40 °C which was a bit higher than the room temperature. The eight-parameter Benedict-Webb-Rubin (BWR) equation of state26 was used to measure the headspace volume from this information. A solubility experiment was conducted by detaching and filling the titanium capsule with the desired mass of the CO2. The gas-filled capsule was connected to the sample chamber, Valve 1 was opened, and a vacuum was
applied for 24 h again to desorb the iPP (usually 50 g) of argon and any other impurities before the measurement with CO2. After the sample was sufficiently desorbed, Valve 1 was closed, and the data acquisition system was started. The experiment began with the opening of Valve 2, allowing the contents of the capsule to fill the headspace of the apparatus. With the sorption of CO2 into the PP, the pressure in the system was decreased until equilibrium was reached. From the equilibrium pressure of CO2, the density of CO2 in the headspace was obtained from the BWR equation of state. Then, the mass of CO2 in the headspace could be obtained. Since the total mass of CO2 was determined earlier by weighting the titanium capsule, the solubility of CO2 in solid-state iPP at the pressure was subsequently calculated by subtracting the mass of CO2 in the headspace from the total amount in the titanium capsule. For diffusivity measurement, in the literature, the polymer was melted and molded to be a plane sheet, whose flank was sealed to satisfy a single-sided diffusion. In this work, as shown in Figure 2, an iPP cylinder with 32 mm in diameter and 70 mm in height was extruded and placed in the center of the high pressure vessel. The crystallinity of the iPP cylinder was the same as that of the virgin iPP. Both ends of the cylinder were sealed by aluminum films with iPP grafted maleic anhydride as the adhesive to make sure CO2 could just diffuse through the flank of the cylinder. The reason why we chose a cylinder rather than a plane sheet was that it was easy to extrude a cylinder without an air bubble inside, which inevitably existed in the tablet forming process. Before measurement, a vacuum was also applied at 80 °C for 3 days to desorb the iPP cylinder of any impurities. In general, the dissolved CO2 will induce swelling of the polymer and change the specific volume of the polymer. Therefore, strictly speaking, since the swelling occurs during the diffusivity measurement, Fick’s second law cannot describe the diffusion process when the swelling effect is large. In this work, the stepwise change in pressure was controlled small enough, namely, smaller than 1 MPa, to ensure the swelling small. Thus, the mutual diffusion coefficient could be treated as a constant parameter during the measurement. The way to control the stepwise change in pressure was to reload the titanium capsule with desired mass of CO2 so that the variation in pressure could be controlled accurately. 2.3. Thermophysical Properties of the iPP. Michaels and Bixler27 have shown that CO2 is insoluble in the crystalline domain. If the crystallinity of the iPP was known, the solubility of CO2 in the amorphous regions of the iPP could be calculated. Thermophysical properties of the solid-state iPP were measured using differential scanning calorimeter (DSC) of type NETZSCH DSC204 HP under ambient nitrogen. The sample was heated
Ind. Eng. Chem. Res., Vol. 48, No. 15, 2009 Table 1. BWR Parameters for CO2 and Argon parameters of BWR
CO2
A, (l/mol) × atm A0, (l/mol)2 × atm B, (l/mol)2 B0, l/mol c, (l/mol)3 × K2 × atm C0, (l/mol)2 × K2 × atm a, (l/mol)3 γ, (l/mol)2 3
Table 2. Characteristic Parameters for S-L EOS substance T*, K P*, MPa F*, kg/m3 Mi, g/mol
Ar -1
1.36814 × 10 2.73742 4.1293 × 10-3 4.99101 × 10-2 1.49180 × 104 1.38567 × 105 8.47 × 10-5 5.934 × 10-3
-2
2.88358 × 10 8.23417 × 10-1 2.15289 × 10-3 2.2282597 × 10-2 7.982437 × 102 1.314125 × 104 3.558895 × 10-5 2.3382711 × 10-3
up to 200 °C at a rate of 10 °C/min. The following equation was used to calculate the crystallinity (mass fraction), wcry, of the iPP: wcry ) ∆H/∆Hm0 × 100%
(1)
where ∆H was the enthalpy of crystallization per gram of sample and ∆Hm0 the enthalpy of crystallization per gram of 100% crystalline iPP. The latter was 209 J/g.28 A quantitative relationship between CO2 induced melting temperature depression of the iPP and its pressure indicated that the melting point of iPP was above 423.15 K when the pressure was below 15 MPa.3 Moreover, the melting behaviors of the CO2-induced crystallized iPP (annealed at 423.15 K and 10 MPa CO2 for 30 min) were tested under 12 and 14 MPa CO2 by the high pressure DSC (NETZSCH DSC 204 HP, Germany). The starting points of the melting peaks were 427.8 and 427.0 K, respectively, indicating that the iPP sample should remain in the solid state at all the experiment conditions in this work. 3. Data Analysis 3.1. Calculation of Solubility. The densities of CO2 and argon in the headspace of the autoclave were calculated by BWR equation of state as shown in eq 2:
(
P ) RTF + B0RT - A0 -
C0
7119
)
F2 + (bRT - a)F3 + T2 cF3 aRF6 + 2 [(1 + γF2) exp(-γF2)] T
CO2 iPP
300 692
630 297.5
1515 882.8
P, MPa ref
36 303-589 0-200 13
the interaction parameter, k12, in S-L EOS showed strong temperature dependence. In this work, the S-L EOS was chosen to correlate and predict the solubility of CO2 in the amorphous regions of the solid-state iPP. The S-L EOS is given by 1 P˜ ) -F˜ 2 - T˜ ln(1 - F˜ ) + 1 - F˜ r
[
P , P˜ ) P*
F˜ )
F , F*
(
T T˜ ) , T*
)]
and r )
(3) MP* RT*F*
where M is the molecular weight and P*, F*, and T* are the characteristic parameters of the S-L EOS. The mixing rules of the S-L EOS are shown by eqs 4-10 as follows: P* )
∑ ∑ φ φ P* i j ij
i
T* ) P*
∑ i
φi0T*i P*i
φi0
1 ) r
∑r
ri0 )
MiP*i RT*i F*i
i
(5)
(6)
(7)
0 i
(8)
(φiP*i /T*i )
∑ (φ P*/T*) j j
(2)
(4)
j
P*ij ) (1 - kij)(P*i P*j )0.5
φi0 )
where P was the pressure, T the absolute temperature, and F the molar density. The parameters A0, B0, C0, a, b, c, R, and γ were the empirical constants for a given gas, and R is the gas constant. Those parameters for CO2 and argon are given in Table 1.29 The headspace volume (Vheadspace), which was used to calculate the residual CO2 mass in conjunction with CO2 density, could be determined easily by the mass and density of argon. The residual CO2 mass was subtracted from the total CO2 mass to obtain the absorbed mass. Thereafter the solubility of CO2 in the solid-state iPP was obtained. As iPP was a semicrystalline polymer and CO2 was insoluble in the crystalline domain,3,26 the solubility in the amorphous regions of the solid-state iPP was calculated by deducting the mass of crystal regions. 3.2. Correlation of Solubility with and without Swelling Correction. Three thermodynamic models, that is, the S-L EOS,30,31 Simha-Somcynsky (S-S) EOS,32 and perturbed chain statistical associating fluid theory (PC-SAFT) EOS,33,34 are commonly used to investigate the fluid phase equilibria for the CO2/polymer system, where the theoretical solubility is typically determined quantitatively. Although the S-L EOS’s validity had not been verified to date, Li et al.35 predicted the theoretical solubility and swollen volume for a PP/CO2 mixture system by S-L EOS, as well as S-S EOS and PC-SAFT EOS, and found
44 197000
T, K
(9)
j
j
φi )
(wi /F*i )
∑ (w /F*) j
(10)
j
j
P*, Mi, and F*i are where wi is the mass fraction, T*, i i characteristic parameters of component i in the pure state. The values of T*i and P*i as well as F*i for CO2 and iPP are listed in Table 2. These characteristic parameters of S-L EOS for iPP were developed by Sato et al.,13 which were suitable for molten and completely amorphous regions of solid-state PP and solidstate PP with crystal regions at relatively low pressure ( 0
at r ) 0, t > 0
(20) (21)
where C was the concentration of CO2 in iPP, R the radius of cylinder, and D the diffusion coefficient of CO2 in polymer, which was treated as being independent of the gas concentration during gas dissolution. The appropriate solution of the diffusion equation had been given by Crank:37 Mt )1M∞
∞
+ R) ∑ 4 +4R(1 4R + R q
2
2
n)0
[ ]
exp
n
-Dqn2t R2
(22)
where Mt and M∞ were the mass of absorbed gas in the polymer at t ) t and t ) ∞, respectively. They qn values are the positive and nonzero roots of RqnJ0(qn) + 2J1(qn) ) 0
(23)
G
µ1 µ1 ) RT RT
(14)
Application of S-L EOS to calculate the µ1P and µ1G yielded
(
(17)
∂C 1∂ ∂C ) rD ∂t r ∂r ∂r
where mCO2 was the total mass of CO2, FCO2 the density of CO2 at the experiment condition, mpolymer the mass of the solid-state iPP sample, and Vpolymer the volume of iPP sample at the condition of the headspace-determination experiment (40 °C and about 1.5 MPa). We defined Sw, the swelling degree, as the ratio between the polymer volume after CO2 dissolution and that determined in headspace-determination experiment, which could be calculated by
)
r10T*1 P*2 µ1P ) ln φ1 + 1 - 0 φ2 + RT r2 T*2 P*1 r10FT*1 φ22[P*1 + P*2 - 2(1 - k12)(P*1 × P*2 )0.5] + P*1 F*T PF*T*1 FT*1 F* F + + - 1 ln 1 r10 + F*T P*1 FT F F*
(
) (
) F 1 ln( ) F* ] r 0
(
)(
where J0(qn) and J1(qn) are the Bessel function of the first kind of order zero and Bessel function of the first order, respectively, and R ) A/πR2 the ratio of the volumes of solution and iPP cylinder. In this case, there was a partition factor, K, between CO2 concentrations in the cylinder and in the solution at equilibrium, so that R ) Vsolution/(VcylinderK). In our experiment, R was about 4, and the qn values were obtained from the literature.37 4. Results and Discussion
(15)
1
[
∂C ) D(∇2C) ∂t
mCO2 - (Vheadspace - Vpolymer × Sw) × FCO2 mpolymer(1 - wcry) (12)
[
3.3. Diffusion Coefficient Measurement. Assuming that the diffusion could be expressed by Fick’s second law
)
PF*1 T*1 F1T*1 F1 µ1G F*1 1 ) r10 + + - 1 ln 1 + 0 ln RT F*1 T P*1 F1T F1 F*1 r1 F1 (16) F*1
( )]
where subscripts 1 and 2 stood for CO2 and iPP phases, respectively. Thus, the swelling degree of the solid-state iPP/ CO2 system would be theoretically calculated by eqs 3 and 12-14.
4.1. Solubility of CO2 in the Solid-State iPP without Swelling Correction. Experimental solubility of CO2 in the solidstate iPP at temperatures 373.15, 398.15, and 423.15 K and pressures up to 15 MPa are illustrated in Figure 3. Repeated experiments showed that the relative deviation for CO2 pressure measurement was no more than (10 kPa, so that the deviation for the solubility was no more than (5%. Figure 3 showed that the solubility of CO2 increased almost linearly with increasing pressure and decreased with increasing temperature. Results were consistent with Henry’s law. Most literature7-12,16-18 focused on the solubility of CO2 in the molten polymers gave the similar trend. But Sato et al.13 found the solubility of nitrogen in molten PP or high-density polyethylene (HDPE) increased with increasing temperature. Although the solubility of CO2 in molten iPP has been carefully studied, reports about that in the
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Table 4. Experimental Solubility of CO2 in the Amorphous Regions of the Solid-State iPP without and with Swelling Correction
T, K
P, MPa
SCO2 without swelling correction (g CO2/kg amorphous iPP)
373.15
2.93 3.81 4.89 5.52 6.31 7.44 8.48 9.08 9.57 10.06 10.73 11.76 12.55
24.69 33.24 42.55 51.44 56.67 65.21 72.91 78.64 82.45 88.18 92.91 100.08 108.62
1.37 1.81 2.24 2.42 2.59 2.93 3.24 3.46 3.69 3.97 4.07 4.35 4.51
26.18 35.85 46.82 56.74 63.31 74.40 84.89 92.61 98.42 106.55 113.47 125.03 136.99
398.15
2.95 4.12 5.66 5.98 6.92 8.10 10.07 10.60 12.19 12.23 13.41 13.90
22.49 32.82 43.87 46.95 53.39 59.52 77.16 77.64 91.44 93.66 100.54 101.46
1.23 1.73 2.02 2.27 2.56 2.93 3.46 3.95 4.23 4.36 4.51 4.62
23.73 35.30 47.99 51.88 59.94 70.53 90.97 94.43 112.84 113.81 126.28 133.06
423.15
4.39 5.30 6.35 7.46 8.12 8.50 9.27 10.75 12.52 13.62 14.96
28.83 34.02 41.99 48.14 55.33 55.52 63.41 67.87 78.49 92.09 100.10
1.51 1.93 2.36 2.54 2.84 3.12 3.37 3.66 3.91 4.19 4.53
31.16 37.68 47.47 55.23 62.08 63.67 70.58 83.70 98.94 116.48 129.81
Figure 3. Solubility of CO2 in the solid-state iPP at 373.15, 398.15, and 423.15 K without swelling and crystallinity corrections. Table 3. Crystallinity of the Solid-State iPP Treated in CO2 T, K
P, MPa
wcry, wt %
virgin
average wcry, wt % 47.1
373.15
2.93 11.94
47.0 47.6
47.3
398.15
ambient N2 4.12 8.12 12.91
49.6 49.2 49.9 50.3
49.8, about 2.4% increase
423.15
ambient N2 3.47 9.27 15.59
53.3 52.5 54.3 54.6
53.9 about 6.5% increase
solid-state iPP are very limited. The solubility measured in Manika’s work17 at 323.2 K and relatively lower pressure (no more than 200 psi) also followed Henry’s law. Lei et al.16 measured the solubility of CO2 in the solid-state PP at temperatures of 372 and 392 K and pressures of 5 and 10 MPa by using the MSB method, which are also shown and compared in Figure 3. The solubility measured in this work was higher than that in Lei’s work, which should be due to the difference of iPP used. In this work, the iPP used had mass-average molar mass of 197 000 g/mol and original crystallinity of 47.1%, while that in Lei’s work had mass-average molar mass of 985 000 g/mol and crystallinity of 62%. However, in Lei’s work, the solubility of CO2 in solid-state PP increased with temperature at the given pressure. An increase in CO2 solubility with decreasing temperature is in agreement with results presented in the literature for many gas-polymer systems38 and can be thermodynamically understood based on the concept of activity. 4.2. Correlation of Solubility in the Amorphous Region of the iPP without Swelling Correction. S-L EOS derived from the lattice fluid model is based on a “mean field” approximation. It is only suitable for amorphous polymers, so the correlation should be performed on the solubility of CO2 in the amorphous regions. Much literature39-41 had indicated that the amorphous regions of polymers could be induced crystallization by thermal or CO2 treatments when the operating temperature was between Tg (glass transition temperature) and Tm (melting temperature) of the polymer along with the thermal treatment or adsorption of CO2. Before calculation, the crystallinity of iPP samples treated at 373.15, 398.15, and 423.15 K and different pressures of CO2 were tested by DSC and listed in Table 3. Compared to the virgin iPP, the iPP treated at 373.15 K remained unchanged, at 398.15 K increased about 2.4%, and at 423.15 K increased 6.5% in crystallinity. Moreover, the increase of iPP crystallinity was basically unaffected by CO2 pressure.
Sw, %
SCO2 with swelling correction (g CO2/kg amorphous iPP)
Experimental solubilities of CO2 in the amorphous regions of the solid-state iPP without swelling correction at temperatures of 373.15, 398.15, and 423.15 K and pressures up to 15 MPa are shown in Table 4 and Figure 4. The solubility data were correlated using the S-L EOS without swelling correction, and the binary interaction parameter was obtained:
Figure 4. Solubility of CO2 in the amorphous regions of the solid-state polypropylene: experimental results (symbols) and calculation results (lines) via S-L EOS with k12 ) -7.40 × 10-4 × T + 0.261.
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k12 ) -7.4 × 10-4 × T + 0.261 The calculation results are also shown in Figure 4. The S-L EOS could correlate solubility within 2.0%, 1.7%, and 2.9% in the average relative deviations at 373.15, 398.15, and 423.15 K, respectively. Li et al.35 also found that the interaction parameter, k12, in S-L EOS for a molten PP/CO2 mixture system showed strong temperature dependence: k12 decreased as the temperature increased. 4.3. Correlation of Solubility in the Amorphous Regions of the iPP with Swelling Correction. The solubility data were also correlated using the S-L EOS with swelling correction. As a result of the swelling of CO2, the expansion of iPP would decrease Vheadspace and had an effect on the solubility measurement by the pressure-decay method. Experimental solubilities of CO2 in the amorphous regions of the solid-state iPP at temperatures of 373.15, 398.15, and 423.15 K and pressures up to 15 MPa with swelling correction are shown in Table 4 and Figure 5. The solubility data were also correlated using the S-L EOS with swelling correction, and the binary interaction parameter was obtained:
Figure 5. Solubility of CO2 in the amorphous regions of the solid-state polypropylene with swelling correction: experimental results (symbols) and calculation results (lines) via S-L EOS with k12 ) -6.08 × 10-4 × T + 0.215.
k12 ) -6.08 × 10-4 × T + 0.215. The S-L EOS could correlate solubility within 1.7%, 1.1%, and 1.4% in the average relative deviations at 373.15, 398.15, and 423.15 K, respectively. As shown in Table 4, although the values of Sw were small, the corresponding effect on the solubility measurements was large and significant. Solubilities determined without swelling correction were 5.2-23.7% smaller than the swelling corrected ones. More importantly, the sorption isotherm without swelling correction was concave to the pressure axis in Figure 4, which was a typical behavior observed for glassy polymers, and a three-parameter dual-mode sorption isotherm model42 had been widely used to describe the gas sorption, whereas the sorption isotherm in Figure 5, swelling corrected, was convex to the pressure axis, as observed for the dissolution of vapors in polymers above their glass transition temperature and was historically described by using the Flory-Huggins equation.43 In the case of iPP, reported Tg values range from -30 to 20 °C,25 and a concave sorption curve should be observed. Therefore, the swelling correction is very important in the iPP/ CO2 system, which not only influences the measured solubility on the valves but also determines whether the trend of the solubility curve is right. Moreover, at a given pressure, a higher temperature resulted in a lower swelling degree. A higher temperature would increase the free volume and specific volume of iPP while decreasing the solubility of CO2 in iPP matrix. Judging from the simulation results as shown in Table 4, the diffusion of CO2 out of the polymer matrix increased more compared to the increased free volume of polymer at a higher temperature, leading to a reduction of swelling degree. Li et al.44 measured the volume swelling ratio of a PP/CO2 solution at 180, 200, and 220 °C and pressures up to 30 MPa and also found that the swelling degree increased with increasing CO2 pressure or decreasing temperature. 4.4. Diffusion Coefficient of CO2 in the Solid-State iPP. Mutual diffusion coefficients of CO2 in the solid-state iPP were measured at temperatures of 373.15, 398.15, and 423.15 K. They were determined by measuring pressure-time curves which could be converted into mass uptake curves. Figure 6 compares the experimental mass uptake curve to the theoretical model,
Figure 6. Sorption profiles for CO2 in solid-state iPP samples obtained by the step change in pressure from 4.5 to 5.5 MPa at different temperatures.
Figure 7. Mutual diffusion coefficient of CO2 as a function of CO2 mass fraction in iPP at different temperatures.
that is, eq 22. The diffusion coefficient was determined so as to minimize the difference between the experimental mass uptake and the model correlation. The mutual diffusion coefficient of CO2 in the solid-state iPP as a function of CO2 mass fraction during sorption is shown in Figure 7. These diffusion coefficients increased with increasing temperature and showed a weak CO2 concentration dependence. The diffusion coefficients of the solid-state iPP/CO2 system at the three temperatures had an order of magnitude of 10-10-10-9
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m /s. As illustrated in Figure 7, it was noted that those values were a magnitude higher than those measured at 50 °C by Manika et al.17 while 5-6 times lower than those obtained at 200 °C by Surat et al.10 Temperature showed a strong effect on diffusion coefficient. The diffusion coefficient increased with increasing the temperature. Moreover, our measurements were carried out for the solid-state iPP/CO2 system. Aparting from lower temperature, less mobility of polymer molecules in solidstate iPP than that in the molten-state is another main factor that decreases the diffusion coefficient of CO2 in this case. Moreover, we could see from Figure 7 that at the same temperature, the diffusion coefficient increases slightly with increasing CO2 pressure. For the adjacent points, the change of CO2 pressure was small and the change of swelling degree caused by CO2 pressure variation could be ignored. However, the whole trend showed that the swelling degree increased with increasing CO2 mass fraction in iPP (as showed in Table 4). The increase in swelling degree would lead to the increase in the specific volume of polymer, which finally resulted in the increase of diffusion coefficient. 5. Conclusions The solubility of CO2 in the solid-state iPP was measured with a pressure-decay method at temperatures of 373.15, 398.15, and 423.15 K and pressures ranging from 1 to 15 MPa. The crystallinity of the iPP before and after solubility measurements was tested by DSC. Along with the swelling correction by the S-L EOS, the solubility of CO2 in the amorphous regions of the iPP was obtained. Both the solubility in the iPP and the in amorphous regions of the iPP increased almost linearly with increasing CO2 pressure and decreased with increasing temperature. The S-L EOS correlated the solubility in the amorphous regions of the solid-state iPP within 3% average relative deviation in conjunction with a temperature-dependent interaction parameter. iPP cylinders with two ends sealed were used to study the mutual diffusion coefficient of CO2 in it at the three temperatures and pressures up to 7.5 MPa. During the pressure-decay measurement, the stepwise change in pressure was controlled small enough so that the mutual diffusion coefficient could be obtained through minimizing the difference between the experimental mass uptake and the Fick’s model correlation. The diffusion coefficient of CO2 showed a weak concentration dependence and had an order of magnitude of 10-10-10-9 m2/s in the solid-state iPP at the three temperatures. The reasons why the diffusion coefficient of CO2 in the solidstate iPP is lower than that of molten state are due to the lower temperature and less mobility of polymer molecules in the solidstate iPP. Acknowledgment The authors are grateful to the National Science Foundation of China (50703011), Shanghai Rising-Star Program (08QA1402200), Shanghai Shuguang Project (08SG28), Program for Changjiang Scholars and Innovative Research Team in University, and the 111 Project (B08021). Professor Lei Z.G., Beijing University of Chemical Technology, is thanked for making a useful discussion with us on the manuscript about the parameters of S-L EOS for iPP. Literature Cited (1) Khan, V. A. Solubility of gases in molten polymers at high pressures. Dissertation for the Doctoral Degree, Wayne State University, Detroit, MI, 1998.
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ReceiVed for reView December 17, 2008 ReVised manuscript receiVed May 31, 2009 Accepted June 5, 2009 IE8019483
