Ind. Eng. Chem. Res. 2005, 44, 9943-9950
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GENERAL RESEARCH Solubility and Diffusivity of Propylene and Ethylene in Atactic Polypropylene by the Static Sorption Technique John E. Palamara,*,† Kevin A. Mulcahy,‡ Adam T. Jones, Ronald P. Danner, and J. Larry Duda The Center for the Study of Polymer-Solvent Systems, Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802-4400
In this work, the static sorption technique has been extended to measure the diffusivity as well as the solubility of gases in polymers at elevated pressures. This has been accomplished by operating several static sorption capsules in parallel in order to measure the fractional mass uptake of a gas by a polymer with time. Equilibrium and diffusion data of propylene and ethylene in atactic polypropylene have been measured in the temperature range of 25-70 °C. The groupcontribution, lattice-fluid equation of state (GCLF-EoS) was used to correlate the equilibria data with a single value of the binary interaction parameter for each of the systems. The VrentasDuda free-volume theory was employed to describe the propylene and ethylene diffusivity data. The chemical potential gradient used in the free-volume correlation of the diffusivity data was obtained from the GCLF-EoS. Introduction As the number of polymer processing and reaction operations conducted at high pressures has increased in the past half-century, many techniques have been developed to measure the thermodynamics and transport properties of penetrant-polymer properties at high pressures. Pressure decay techniques (both absolute1 and differential2), the Cahn electrobalance,3,4 a highpressure quartz spring balance,5 magnetic suspension balances,6 quartz crystal microbalances,7 and infrared techniques8 have all been developed and used to measure gas sorption by polymers at high pressures. In an earlier work,9 we described the static sorption capsule technique used to determine the solubility of gases and vapors in polymers and other sorbents. This apparatus is less expensive to construct and simpler to operate than many of the aforementioned techniques. In this work, the static sorption technique was modified to measure the diffusivity as well as the solubility of penetrants in polymers. This was accomplished by running several capsule experiments in parallel and stopping them before equilibrium was attained in order to measure the fractional mass uptake as a function of time. Although many experimental techniques have been developed to measure gas transport in polymers at high pressures, experimental diffusivity and solubility data are still in short supply for many polymer-gas systems. * To whom correspondence should be addressed. Tel.: (610) 481-1108. Fax: (610) 481-6578. E-mail:
[email protected]. † Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, PA 18195-1501. ‡ Carpenter Company, 2600 Jefferson Davis Highway, Richmond, VA 23234.
A classic example of this is the limited amount of data that exist for ethylene and propylene in polypropylene. Polypropylene is a commodity polymer produced on a 10 billion pound per year scale in North America alone.10 While mass transfer of the monomers in the reaction process is often an important design consideration in the production of polypropylene and its family of copolymers,11 limited transport and solubility data have appeared in the literature. Ohzono et al.12 measured Henry’s constants for a variety of gases including propylene in molten polypropylene. Sato et al.13 studied the solubility of propylene in samples of polypropylene with varying degrees of crystallinity. Tsuboi et al.14 reported infinitely dilute partition coefficients for ethylene and propylene in semicrystalline polypropylene. Packed bed inverse gas chromatography was used by Sliepcevich et al.15 to obtain partition and diffusion coefficients for ethylene and propylene in semicrystalline polypropylene beads. The limited solubility results from these studies are inconsistent. This may result from the difficulty of studying sorption in semicrystalline polymers. Solubility in semicrystalline polymers is typically reported on the basis of the amorphous content of the polymer, since the crystalline phase of the polymer is assumed impenetrable to the diffusing species. Consequently, accurate measurement of the crystal content of the polymer is of paramount importance. In this study, the diffusion and solubility of propylene and ethylene in atactic polypropylene (a-PP) was measured with the static sorption technique. Because of the absence of stereoregularity in this polymer, a-PP contains no crystals. The solubility of propylene and ethylene was correlated with the group-contribution, latticefluid theory equation of state (GCLF-EoS). The diffusivities of these penetrants as a function of concentration
10.1021/ie050239u CCC: $30.25 © 2005 American Chemical Society Published on Web 11/05/2005
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Ind. Eng. Chem. Res., Vol. 44, No. 26, 2005
Figure 1. Schematic of static sorption apparatus showing the four capsules that were operated in parallel.
and temperature were correlated with the VrentasDuda free-volume theory. Experimental Section Apparatus. A diagram of the experimental apparatus used in this work is shown in Figure 1. The addition of more capsules is the main feature that differentiates this unit from the previous apparatus that was used solely for solubility experiments. Four capsules machined from high-strength aluminum were aligned so they could be operated in parallel. These capsules had an internal volume of ∼5.5 cm3 each and weighed ∼200 g when loaded with the polymer sample. Aluminum was selected as the material of construction because of its low density. All of the weight measurements were taken with an Ohaus Analytical Plus electronic balance that has a maximum capacity of 210 g and an accuracy of (0.1 mg. The pressure transducer used to measure the pressure of the system was a Druck PMP 4010 that has an error of (1.6 psi. The temperature of the capsules was controlled with an aluminum heating block that contained internal heating elements. The capsules resided in four cylindrical channels that were machined into the block. Valves used to open and close the capsules were situated so that they could be operated from outside of the block. Volumes of the empty capsules were measured by filling them with argon, recording the weight change, and determining the volumes based on gas density. Materials. The propylene (>99.5% purity) and ethylene (>99.5% purity) used in this study were purchased from the Valley National Gas Company. a-PP was used as received from The Dow Chemical Company. The polymer samples were made by melting a-PP into small aluminum pans under vacuum. About 1 g of polymer (∼1 cm3) was used in each capsule. The aluminum pans that held the polymer had a volume of about 1 cm3, making the void volume of the capsule (Vc) during the experiment ∼3.5 cm3. Solubility Measurement with the Static Sorption Capsule The static sorption technique has been previously shown to be successful in measuring gas solubility in polymers.9 The technique was extended to measure the diffusivity of gases in polymers as well as the solubility.
The basic experimental technique entails the same steps as described previously: (1) a polymer sample of known weight, mp, was placed in a capsule of known void volume, Vc, and the system was evacuated; (2) the evacuated capsule was detached and the weight of the evacuated capsule and its contents was recorded as Mevac; (3) the capsule containing the degassed polymer was reattached to the apparatus, brought to the experimental temperature, T, and exposed to the gas at a constant pressure, P; (4) at the time of interest, the capsule was sealed, detached from the system, and weighed to obtain the total weight of the capsule with the gas Mtot; and (5) the capsule was reattached and then at a later time reweighed to ensure equilibrium was achieved. The difference between the two methods is that the “time of interest” in this study was some time before the polymer and the gas reached equilibrium such that the rate of mass uptake could be measured. The amount of gas in the polymer, mgp, is given by
[
mgp ) Mtot - Mevac - Vc -
mgp + mp Fl(ωg,T,P)
]
Fg(T,P) (1)
Here, ωg is the weight fraction of gas in the polymer phase, Fg is the density of the gas at the experimental T and P, and Fl is the density of the polymer phase that is a function of T and P and the amount of gas absorbed. The quantity inside of the square brackets in eq 1 is the volume of the capsule not occupied by the polymer solution. Equation 1 cannot be solved explicitly for the mass of gas in the polymer phase since the density of the polymer phase depends on this information. Consequently, an iterative procedure was employed to obtain mgp. The initial value of mgp was calculated by assuming the polymer phase did not swell (i.e., Fl was set equal to the pure polymer density at T and P). The BWR equation of state was used to calculate the density of the gas phase, Fg(T,P). The values of the coefficients in the BWR (Benedict-Webb-Rubin) equation of state given by Canjar et al.16 were used in the calculation of the propylene vapor density. The experiments using ethylene were conducted in the vicinity of its critical point (9.9 °C, 742.1 psia). Because of the sensitivity of ethylene density to the temperature and pressure, an extended form of the BWR equation (13 parameters instead of 9) as suggested by Thomas and Zander17 was used to determine the gas-phase density.
Ind. Eng. Chem. Res., Vol. 44, No. 26, 2005 9945
determined that, for a step change experiment where the concentration of the penetrant is increased and the diffusivity increases as a function of concentration, the following relationship can be used to obtain the concentration at which the diffusivity should be reported:
ω1 ) ω0 + 0.7(ωE - ω0)
Figure 2. Example of dimensionless mass uptake data obtained for the diffusion of propylene in a-PP at 25 °C, over a pressure step from 45.7 to 75.7 psia. The solid line depicts the linear fit used in the regression of the diffusivity.
With the added terms, the equation adequately represented experimental data from the same source to within 0.1%. The density of the polymer phase, Fl(ωg,T,P), was calculated with the GCLF-EoS, as discussed later. Diffusivity Measurement with the Static Sorption Capsule The diffusivity of a gas in a polymer can be determined by the rate of mass uptake after a step change in gas pressure. To measure this, several capsule experiments were operated in parallel and each was halted at a different time prior to equilibrium. If the fractional mass uptake of a penetrant is measured at sufficiently small times (compared to the equilibrium time), the mutual diffusion coefficient, D, is proportional to the fractional uptake versus the square root of time,18 by
[
]
πL2 d(Mt/M∞) D) 4 d(t1/2)
2
(2)
Here, Mt is the weight pickup at time, t, M∞ is the corresponding value when equilibrium is achieved, and L is the thickness of the sample, since only one side of the sample is exposed to the penetrating vapor. The thickness of the sample, L, is taken as the thickness of the sample before the sorption step as determined by its weight, area, and density. Figure 2 shows a sample sorption curve obtained with this technique. Each of the four data points that appear at early times is the result of the fractional mass uptake measured by a capsule. The capsules were reattached, pressurized, and then again removed and weighed after reaching equilibrium. This resulted in the cluster of data points that appear at the end of the curve. If the diffusivity change over the concentration step is significant, the diffusivity measured with this method is an average diffusivity over the concentration range of the step. Vrentas et al.19 analyzed this problem and
(3)
Here, ω1 is the weight fraction at which the diffusivity is reported, ω0 is the weight fraction of the penetrant in the polymer phase before the concentration step, and ωE is the weight fraction of the penetrant at the new equilibrium. The relationship given in eq 3 was reported to contribute
