Ind. Eng. Chem. Res. 2003, 42, 1557-1562
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A Static Sorption Technique for Vapor Solubility Measurements John E. Palamara, Peter K. Davis, Uthaiporn Suriyapraphadilok, Ronald P. Danner, J. Larry Duda,* Ronald J. Kitzhoffer,† and John M. Zielinski† The Center for the Study of Polymer-Solvent Systems, Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802-4400
A new experimental technique has been developed to measure the solubility of gases and vapors in polymers and other sorbents at elevated pressures. The technique involves measuring the total weight of a vessel containing the sorbent material pressurized with a vapor, assessing the amount of vapor in the headspace of the vessel with an appropriate equation of state, and evaluating the total amount of vapor in (on) the sorbent material by the difference. Adsorption isotherms for carbon dioxide and nitrogen on an activated carbon were measured with the static sorption technique. These data were found to agree well with data taken with a standard volumetric technique. Sorption data obtained using this method for carbon dioxide in poly(vinyl acetate) and propylene in poly(propylene) compare well with data acquired by established techniques. The group-contribution lattice-fluid theory equation of state was used to predict solubility in these systems, and the Panayiotou-Vera equation of state was applied to correlate the solubility data. Introduction Many experimental techniques1 have been developed to measure the uptake of gases by adsorbents and absorbents. The volumetric approach2 developed by Emmett and Brunauer in 1934 is one of the oldest and most widely used experimental techniques. The term “volumetric” arises from the use of a mercury manometer to determine the volume of gas taken up by the sample. It is still common to find gas uptake reported in units of volume of gas at STP, arising from the value measured with these early volumetric methods. Because glass was used in the construction of these manometers, data could only be obtained at lower pressures. Mercury displacement has since been widely replaced by modern pressure transducers capable of operating at much higher pressures. The volumetric, or now more appropriately, pressure decay technique was originally used to study gas sorption in polymers by Newitt and Weale in 1948 who used the technique to study the solubility of gases in poly(styrene).3 In the 1960s pressure decay was extended to measure the kinetics of gas uptake in polymers, namely, the diffusion coefficient, as well as the solubility.4,5 The precision of pressure decay can be greatly increased if a differential pressure transducer is used to monitor the pressure difference between a reference chamber and a chamber in which sorption occurs. This differential pressure decay technique was first introduced by Schlosser6 in 1959 to measure the Brunauer-Emmett-Teller surface areas of powders and porous materials. Differential pressure decay was refined in later years by Haul and Du¨mbgen7 and first used to study polymers in 1976 by Koros and Paul.8 Instead of using a pressure transducer to measure gas sorption, Brantley et al.9 demonstrated that an IR sensor could be used to analyze the gas concen* To whom correspondence should be addressed. E-mail:
[email protected]. Phone: (814) 865-1640. Fax: (814) 865-7846. † Present address: Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, PA 18195-1501.
tration directly. This method can also be applied to measure multicomponent gas sorption by a sorbent.10 Instead of relying on a change in volume, pressure, or concentration to measure the amount of sorption, gravimetric techniques directly measure the mass uptake of a sample. Gravimetric techniques are especially useful when studying the sorption of a condensable vapor. In 1926 McBain and Bakr11 introduced a balance that employed a quartz spring as the measuring device in a glass chamber. Gravimetric techniques capable of operating at high pressures became more popular with the advent of the electronic microbalance. An electronic microbalance is a special analytical balance which can be used in severe pressure-temperature conditions by measuring the relative weight of a sample and a reference mass.12 Another type of balance used for highpressure sorption measurements is the magnetic suspension balance. This is a relatively new concept in which a sorbent is placed in a sample bucket that is suspended by a magnet inside a gas chamber. The strength of the magnetic field is monitored from outside of the pressure vessel to obtain weight uptake measurements, thereby isolating the sensitive load cell away from harsh experimental conditions. This technique has been used to study both adsorption13 and absorption14 to high pressures and temperatures and is gaining in popularity. The oscillating quartz crystal microbalance was first used to measure gas sorption in polymers by Bonner and Cheng in 1975.15 In this technique, a crystal is coated with the sample of interest. The coated crystal is then exposed to the gas, the resulting frequency of the resonating crystal is monitored during the sorption process, and the mass uptake is calculated based on this signal. Like the methods just described, the approach used in this study makes use of a gravimetric measurement. Unlike the other gravimetric techniques, where the mass of the sample is monitored from inside of a pressurized vessel, in the static sorption technique the entire pressure vessel is weighed before and after the experiment to determine the amount of gas uptake. This
10.1021/ie0207414 CCC: $25.00 © 2003 American Chemical Society Published on Web 02/11/2003
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Figure 1. Schematic of the experimental apparatus.
allows solubility measurements to be conducted at high pressures at much less cost and a lower degree of complexity than currently practiced methods. Description of the Technique The following protocol is employed to measure the amount of vapor uptake of an absorbent or adsorbent material with the static sorption technique: Step 1. Attach a capsule (consisting of a valve connected to a small pressure cell) of a predetermined volume to the pressurization system as shown in Figure 1. Open the valve and evacuate the capsule. Upon evacuation, close the valve, remove the capsule from the system, and measure the total weight of the evacuated capsule with an analytical balance. Step 2. Load the material to be studied into the capsule. Reattach the capsule to the system and open the valve to the vacuum pump so that the headspace in the capsule is evacuated, and the sorbent material is degassed, usually at an elevated temperature to expedite the process. The capsule is then closed and detached from the vacuum line. The total weight of the capsule is again recorded. The difference between the total weight recorded in step 2 and the total weight recorded in step 1 is the weight of the material. Step 3. Connect the capsule to the source containing the vapor to be studied and bring the capsule to the experimental temperature of interest. The source could be a gas cylinder or another device such as a saturator. Open the valve to enable the vapor to fill the capsule and diffuse into the sorbent at the desired temperature. Step 4. While the valve is open, the pressure of the system is maintained at a constant value. The vapor is sorbed until the sorbent reaches saturation and the system reaches equilibrium. When equilibrium is reached and the sorption process is complete, the valve is then closed. Step 5. After the valve is closed, remove the capsule from the temperature control unit. Record the final weight of the capsule. To ensure that the sorption process was complete, the capsule can be reattached to the system and held at the same pressure. At some later time, the capsule is detached and reweighed. If the mass is found to be the same, the sorption process is complete. Step 6. The difference between the total weight after step 5 and the weight recorded in step 2 is the total weight of the vapor molecules in the capsule. These vapor molecules are partitioned between the headspace of the vessel and the sorbent. The goal is to find the number of volatile molecules that reside in the sorbent phase. To obtain this value, the volume of the headspace must be determined using information about the density of the material. In the case of polymer sorption, this volume changes because the polymer phase swells. As described below, the group-contribution lattice-fluid
theory equation of state (GCLF-EOS) has been used to estimate the swelling of the polymer phase. A suitable equation of state is then chosen for the vapor phase in order to estimate the density of the vapor in the headspace. If an equation of state is not available for the vapor, the density can be assessed directly by repeating the above experiment with an empty capsule. Using the density of the vapor in the headspace and information about the volume of the headspace, one is able to calculate the contribution of the vapor phase to the total weight of the vapor. This value is then subtracted from the total amount of volatile molecules obtained in the final total weight. The resulting quantity is the amount of vapor ad/absorbed by the sorbent material. There are a few important points to emphasize regarding the use of this technique. First, the capsule does not need to be weighed at the experimental temperature. After the capsule has been sealed and detached from the pressurization system, it will return to ambient temperature, and the partitioning of gas between the sample and headspace will change inside of the capsule. The total mass within the closed capsule, however, is unaffected by this temperature change. In effect, closing the valve freezes the measurement in time. Second, this technique is less sensitive to leaks than conventional techniques, provided a leak does not occur after the valve on the capsule is closed and before the weight measurement. During a pressure decay experiment, for instance, any leak would be interpreted as uptake by the sample because this method relies upon knowing the total amount of vapor in the system at all times. During an experiment conducted with the static sorption technique, the pressurization system must only be maintained at a constant pressure, making small leaks tolerable. Last, the pressure transducer itself does not need to be held at the experimental temperature, thereby widening the range of operating temperatures. Experimental Section Apparatus. The weight of the cell and attached valve is critical because commercially available analytical balances sensitive enough to perform these measurements have low maximum load capacities. In this study, the cell and attached valve weighed approximately 190 g. The maximum allowable working pressure of the capsule is 3000 psia, at 250 °C. The temperature and pressure rating of the valve are the current constraints of the operating conditions for the system. A solid aluminum block with internal heaters and temperature sensors is used to control the temperature of the capsule. The heating block contains cylindrical channels that hold the capsule but allow access to operate the valve. A vacuum line connects the system to a vacuum pump, and the vapor is supplied using a gas cylinder and pressure regulator or a solvent saturator. A schematic of the experimental setup is provided in Figure 1. The balance used to measure the mass of the capsule is an Ohaus Analytical Plus electronic balance. This balance has a maximum capacity of 210 g and an accuracy of (0.1 mg. Materials. An activated carbon was selected for an initial adsorption study with the static sorption technique. A sample of coconut char derived Calgon PSC carbon was provided by Air Products and Chemicals, Inc., for this purpose. This sample was activated under
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vacuum for 12 h at 140 °C before the sorption experiment was conducted. For a study of polymer solubility with this technique, poly(vinyl acetate) (PVAc) and atactic poly(propylene) (PP) were obtained from the Aldrich Chemical Co. and The Dow Chemical Co., respectively. All samples were degassed for at least 12 h prior to beginning the sorption measurements. Approximately 1-4 g of material was used for a sample in each experiment. Carbon dioxide (>99.8% purity), ultrahigh-purity (UHP) nitrogen, and propylene (>99.5% purity) were obtained from Valley National Gases Corp. Sorption Measurements. Before sorption measurements can be conducted with the static sorption capsule, the volume of the empty capsule must be determined. This is accomplished by first measuring the weight of the evacuated capsule. The capsule is then filled with a well-behaved gas to a known pressure and temperature and then weighed a second time. To obtain the volume of the capsule from these weight measurements, an appropriate equation of state is used to predict the density of the vapor. The volume is the difference in weight divided by the density. Nitrogen was used instead of helium, for instance, because the higher molecular weight of nitrogen will yield a larger weight change, increasing the accuracy of the measurement. A heavier gas such as argon may produce even better results. The procedure outlined previously is followed in conducting a sorption experiment. Typically the experiment is done in steps. Following each equilibrium point, the pressure was increased to the next target pressure. After each pressure step, the valve was closed, the capsule detached, and total weight of the capsule recorded. The following equation was used to obtain the mass of vapor sorbed by the sample:
Mgs ) Mtot - Mevac - FgVhs
(1)
where Mgs is the mass of vapor in/on the sorbent, Mtot is the total mass of the capsule and its contents after a sorption step, Mevac is the mass of the evacuated cell and the degassed sample, and the product of the density of the vapor, Fg, and the volume of the headspace, Vhs, is the mass of the gas in the vapor phase. For the case of adsorption, the headspace volume could be assumed to remain constant because adsorbents do not swell. Mtot and Mevac are measured directly from the balance readings, and Vhs is obtained from subtracting the volume taken up by the sample from the total volume of the capsule. There are two methods by which Fg may be obtained. The density of the vapor phase may be predicted with an equation of state, or, alternatively, an empty capsule of known volume can be filled with the same gas at the same pressure and then weighed. In the calculations conducted in this work, the densities of the gases were predicted with the BWR equation of state.16 The calculation of the amount of gas absorbed by any material that changes dimensions upon sorption such as a polymer is more complex than that in the case of simple adsorption. Because swelling of the absorbent phase reduces the headspace volume, Vhs in eq 1 cannot be assumed to be a constant. Often, a separate experiment must be conducted to measure the swelling of the polymer phase. In this work, an equation of state was used to predict the density of the polymer phase. The Panayiotou-Vera17 equation of state along with GCLFEOS was used to predict the density of the polymer
phase in an iterative calculation to determine the best estimate of Vhs. Lattice models have been widely used to correlate the solubility of solvents in polymers. Panayiotou and Vera developed a lattice-fluid model based on the partition function derived by Guggenheim. Because of its unique mathematical and statistical methods for describing a fluid on a lattice, the equation of state can be used for polymer-solvent systems. The equation of state takes the form
( )
(
)
v˜ + q/r - 1 P ˜ v˜ z θ2 ) ln + ln v˜ - 1 2 v˜ T ˜ T ˜
(2)
P ˜, T ˜ , and v˜ are the reduced pressure, temperature, and molar volume, respectively. The parameters z, q, r, and θ contain information about the number of lattice sites occupied by each molecule and how these sites interact with one another. The chemical potential of species i in a mixture (µi) is calculated by
(
) ( )
δi (1 - θi)ri -µi 1 1 ) ln + ln(qi) + ln + qiθ + + RT σi θi T ˜i T ˜ θ2 1 (ri - qi) - zqi ln(Γii) (3) 2 T ˜ In this equation Γii is a factor which accounts for the nonrandom mixing of the molecules, δi is a dimensionless flexibility parameter, and σi is a dimensionless symmetry parameter. To solve the equation of state and the chemical potential, it is necessary to determine the pure-component parameters, vi* and ii, and a binary interaction parameter, kij, which is used to calculate the interaction energy between two unlike molecules. The value of kij contributes to P ˜, T ˜ , and v˜ because these parameters scale with the interaction energy of the system. In this work, the hard-core volume (vi*) and interaction energy (ii) parameters are obtained from the group-contribution techniques of Lee and Danner:18
ii )
(i) Θ(i) ∑k ∑ k Θm xekkemm m
Θ(i) k
n(i) k Qk
)
v i* )
∑n
(4)
(5)
n(i) n Qn
∑k n(i)k Rk
ij ) (iijj)1/2(1 - kij)
(6) (7)
The Θ parameters in these equations are group surface fractions, Qk, ekk, and Rk are individual group parameters, and nk is the number of groups in the molecule. These equations are solved with a standard IMSL subroutine. The GCLF-EOS has been shown to be accurate in predicting the PVT behavior of polymers and polymer-solvent mixtures over a wide range of temperatures and pressures.19 Results and Discussion Figure 2 shows the volumes of the capsules, measured by filling the capsules with nitrogen and weighing the
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Figure 2. Volume measurements for capsule 1 at 40 °C (0) and 60 °C (9) and capsule 2 at 40 °C (3) and 60 °C (1) taken by filling capsule with nitrogen and measuring the total weight. The solid lines are the average volumes.
vessel. The results are plotted against the pressure used for each measurement. The BWR equation of state was used to determine the density of nitrogen in the capsules. Volume measurements on the capsules yield an average of 12.54 cm3 for capsule 1 and 12.10 cm3 for capsule 2. Excellent repeatability was found in the volume measurements taken at different temperatures and pressures. This finding also validates the effectiveness of the temperature control block because temperature gradients within the capsules would result in errors in the volume measurements. The error bars in Figure 2 are the result of a propagation of error analysis on this method to obtain the volume of the capsules. Smaller errors are incurred when the volume of the capsules is measured at higher gas density. This indicates that volume measurements with a denser, well-behaved gas, such as argon, would give even more accurate volume measurements. The results of the adsorption study on activated carbon at 30 °C are presented in Figure 3. Adsorption is the simplest case where Vhs in eq 1 is considered to be constant. This value was determined by measuring the amount of material loaded and using the known helium density of the carbon to directly calculate the headspace volume. The carbon dioxide and nitrogen adsorption data show good agreement with the data obtained with a standard pressure decay technique. To examine reproducibility in the practice of this technique, a second set of data was taken on carbon dioxide with a different capsule and a different temperature control system. The data compare well with the previous result. An error analysis performed on this system has shown that the error in the data was not greater than 5% for any of the data points. Solubility data for carbon dioxide in PVAc at 40 °C are shown in Figure 4. The carbon dioxide-PVAc solubility data are plotted as a function of pressure, along with the values obtained if swelling is neglected in the calculation. Data collected on the same system by Sato et al.20 using a magnetic suspension balance, and Takishima et al.21 with an absolute pressure decay technique, are also plotted in Figure 4 for further comparison. In addition, the prediction of carbon dioxide
Figure 3. Adsorption isotherms for CO2 and N2 on a Calgon PSC carbon at 30 °C. Data taken with the static sorption technique [CO2 (1); N2 (9)] are compared to data obtained with a standard pressure decay technique [CO2 (3); N2 (0)]. Another CO2 experiment (+) was run using a different capsule and a different heating block to show reproducibility.
Figure 4. Solubility of CO2 in PVAc at 40 °C. Comparison of the results obtained with the static sorption technique (b) to data taken with a magnetic suspension balance (3)20 and a pressure decay apparatus (0).21 The result of ignoring swelling in the polymer phase (O) is also shown. The dashed line is a prediction of the solubility using the GCLF-EOS, while the solid line is a correlation of the data using the Panayiotou-Vera equation of state.
solubility in PVAc using the GCLF-EOS is shown. The influence of the swelling of the polymer phase on the measured solubilities was found to increase with increasing pressure. There are two contributions to this effect: (1) the loss of headspace volume due to increases and (2) the gas density in the headspace increases. In conducting these experiments, the weight of the carbon dioxide in the headspace is appreciably larger than that absorbed in the polymer. Although this condition is acceptable provided the volume of the headspace is accurately known, minimizing the volume of the headspace and its overall contribution to the total weight will reduce the error in the solubility measurement. The error bars appearing in Figure 4 show the results of a
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Figure 5. Solubility of propylene in the amorphous fraction of PP at 50 °C. Data taken with the static sorption technique (b) on atactic PP containing no crystals are compared to data taken with a magnetic suspension balance (3)22 on a PP sample with a crystallinity of 33%. The result of ignoring swelling in the polymer phase (O) is also shown. The dashed line is a prediction of the solubility using the GCLF-EOS, while the solid line is a correlation of the data using the Panayiotou-Vera equation of state.
propagation of error analysis on the measurement of solubility. Although the error in the prediction of the swelling of the polymer phase was conservatively assumed to be 20%, the overall error in the solubility measurement was reasonable. At these higher solubilities, the leading contributors to error besides the density of the polymer phase are the temperature control/ measurement and the pressure measurement. When measuring the solubility in systems with much less capacity (
