ARTICLE pubs.acs.org/IECR
New Approach for Simultaneous Measurement of Gas Absorption and Swelling Tobias M. Fieback*,† and Frieder Dreisbach‡ † ‡
Ruhr-Universit€at Bochum, Thermodynamik, 44801 Bochum, Germany Rubotherm GmbH, Universit€atsstrasse 142, 44799 Bochum, Germany ABSTRACT: For sorption measurements many different methods are applicable, but nearly all of them require a correction of the raw experimental data by a factor including the sample’s volume. This can be determined by a separate volume measurement for samples with constant volumes. If the sample volume is not constant because of swelling effects, the actual volume is usually calculated by suitable equations of state (EOS) for the sample-gas-system (if available) or estimated by optical or spectroscopic sample observation and assumptions about orientation of swelling. The advantage of the new approach presented here is that one measurement leads to both unknown quantities: sample volume and absorption. Not only is the volume measurement for constant sample volumes is obsolete, also the actual volume of swollen samples can be determined with minimal effort. The method can be applied to liquid and solid state samples without optical or spectroscopic sample observation or any assumption about orientation of swelling.
1. INTRODUCTION Measuring gas solubility requires knowledge of the (actual) volume (density respectively) of the sorbent material.17 This quantity is necessary for correcting the raw experimental data for systematic effects affecting the measurement. In gravimetric experiments for example, the buoyancy effect—which is proportional to the volume of the sample material—acting on the sample must be taken into account. In volumetric/manometric measurements, the data treatment must account for the volume occupied by the sample. A similar correction involving the volume (density) of the sorbent material is necessary in all presently applied gas solubility measuring methods. This correction can be performed straightforwardly if the volume of the sample can be measured in a separate experiment (before or after the sorption measurement) and is constant throughout the whole measurement. However, if the sample volume (density) changes—caused by the gas absorption—the data correction is not possible without further assumptions.810 Mainly the following approaches are used for estimation of the (unknown) sample material volume. • Calculation of the sample density using a suitable EOS1113 • Observation of the sample in a view cell and estimation of the volume change14,15 • Quartz crystal microbalances can measure the mass of a sample firmly attached as a thin film to the crystal’s surface. This measurement can be combined with spectroscopic methods for film thickness determination.15,16 The new approach presented here is a measuring method which measures in one single experiment both unknown quantities: sample volume and absorption. The measuring method employs only well-known and established measuring devices for pressure, temperature, and sample mass. Not only the separate volume measurement for constant sample volumes is obsolete, also the actual volume of swollen samples can be determined with r 2011 American Chemical Society
minimal effort. The method can be applied to liquid and solid state samples without optical or spectroscopic sample observation or any assumption about orientation of swelling.
2. MEASURING METHOD For gas ad- or absorption measurements the gravimetric17 and volumetric/manometric18 measuring methods are well-established. In the former, the mass of the sample material is weighed directly with a high resolution balance. The latter measures the change of fluid (gas phase) pressure which is caused by the sorption of the fluid on/in the sample in a confined volume. The combination of both methods is known to provide additional experimental information. This allows measuring gas phase/solid or gas phase/liquid sorption systems with an additional degree of freedom. Thus, using this method the sorption of binary mixtures (total sorption and individual sorption of each component of the mixture) can be measured without further analysis.19 A schematic drawing of a measuring instrument for combined gravimetric/manomentric measurements is presented in Figure 1. In the shown minimum configuration, it consists of • a dosing tank with calibrated volume VD in which the gas phase mixture (gas, vapor, or supercritical fluid) can be prepared • a measuring cell with calibrated volume VMC in which the sample is located (in a suitable crucible) attached to a balance allowing to measure the mass of the sample and crucible • a circulation pump ensuring that the composition of the gas phase mixture is the same in all parts of the instrument Received: January 13, 2011 Accepted: April 11, 2011 Revised: April 8, 2011 Published: April 11, 2011 7049
dx.doi.org/10.1021/ie200076k | Ind. Eng. Chem. Res. 2011, 50, 7049–7055
Industrial & Engineering Chemistry Research
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the gas density cannot be derived. The volume accessible for the gas phase is the calibrated volume of the instrument minus the volume occupied by the sample (VD þ VMC VS). Thus, the absorption can formally be calculated from eq 3 to be m ¼ VD F ðVD þ VMC VS ÞFG
ð4Þ
The gravimetric measurement of the sample’s mass yields Δm ¼ m þ mS VS FG
Figure 1. Schematic drawing of measuring instrument for combined gravimetric/manometric measurements.
• a thermostat controlling the temperature of all parts of the instrument equipped with suitable temperature sensor(s), and at least one pressure sensor measuring the pressure in the dosing tank (and all connected parts of the instrument depending on valve settings) The measurement starts with evacuated measuring cell and dosing tank. The degassed sample is located in the crucible and its weight is monitored by the balance. In the first step, the gas phase mixture is prepared in the dosing tank. The measuring cell is isolated from the dosing tank and remains evacuated. The mass of gaseous mixture prepared in the dosing tank (with calibrated volume VD) can be calculated from the measured dosing pressure (P*), temperature (T), and known composition of the binary mixture (w*, 1 w* 2 = 1 w*) 1 {For the sake of simplicity, the mass based concentration w1 of the gas mixture’s component 1 is used in this paper. It can be converted into the molar concentration y1 using the molar masses M1 and M2 of the gas mixtures components by w1 = y1[M1/(y1M1 þ (1 y1)M2)]} by using a suitable thermal equation of state (F* = f(P*, T, w1*)) according to20 m ¼ V D F
ð1Þ
The total mass of gaseous mixture can be divided into the partial masses of the two mixture components with the known gas dosing composition w*: 1 mi ¼ wi m ¼ wi VD F, i ¼ 1, 2
m ¼ m þ mG
The balance reading (Δm) represents the mass of degassed sample (mS) plus the mass of gas absorbed in the sample (m) minus the buoyancy effect acting on the sample. The buoyancy is proportional to the volume of the sample (VS) and the (unknown) density of the gas phase (FG). This equation can be rearranged for the absorption: m ¼ Δm mS þ VS FG
ð3Þ
requires that the dosed gaseous mixture (m*) must be either absorbed in the sample (m) or still be in the gas phase (mG). This mass of the gas phase can formally be calculated by multiplying the gas phase density (FG) with the volume accessible for the gas. However, since the gas phase mixture composition is unknown
ð6Þ
Combining eqs 4 and 6 allows determining the density of the gas phase mixture. [Alternatively to this calculation of the gas phase density, gravimetric instruments equipped with magnetic suspension balance allow measuring the gas phase density with the sinker.20 The measured density can then be used as reference for checking the accuracy of the calculation shown here.] FG ¼
VD F ðΔm mS Þ VD þ VMC
ð7Þ
The density of a binary gas phase mixture at known pressure and temperature is an explicit function of the mixture’s composition, as long as the molar masses of the mixture components are different (M1 6¼ M2). Thus the gas phase mixture density can be used for calculation of the mixture’s composition by applying a suitable thermal equation of state20 (FG = f(P, T,w1): w1 ¼ f ðFG Þ
ð8Þ
Knowing the mixture’s composition in absorption equilibrium allows performing the gas phase material balance (eq 3) for each of the two components and, thus, determining the individual absorption for each component of the binary mixture: mi ¼ mi mGi
ð2Þ
When the mixture in the dosing tank is prepared, the connecting valves between the dosing tank and the measuring cell are opened and the gas phase is circulated in the instrument until the sorption equilibrium is reached. In the equilibrium, the balance reading (Δm), pressure (P), and temperature (T) are measured. The gas mixture composition (w1, w2 = 1 w1) is not separately measured and, thus, unknown. It will be different from the dosing composition, since sorption processes are usually selective. The manometric material balance of the gas phase
ð5Þ
¼ wi VD F wi ðVD þ VMC VS Þ 3 FG , i ¼ 1, 2
ð9Þ
The above-described data handling procedure can easily be extended to measurements with more than one dosing step. For performing a measurement at increasing pressures the measuring cell is isolated again from the dosing volume after the equilibrium data are recorded. Then a new gas phase mixture at (higher) pressure is prepared in the dosing tank and expanded into the measuring cell. The above formalism will in this case be extended taking into account the gas phase mixture which is still present in the measuring cell from the last measuring point. Note that for this measurement fully characterizing the sorption of a binary mixture no concentration measurement for the gas phase is necessary. Knowing the dosing composition of the mixture and combining the manometric and gravimetric measurement method in one experiment is sufficient. However, it is significant to note also that the volume of the sorbent material (VS) needs to be known for performing the material balances (eq 9). Usually the sample volume can be 7050
dx.doi.org/10.1021/ie200076k |Ind. Eng. Chem. Res. 2011, 50, 7049–7055
Industrial & Engineering Chemistry Research
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Figure 2. Flow schematics of the employed measuring instrument for combined gravimetric/manometric measurements.
determined in a separate measurement. For this volume determination, a reference experiment with an inert gas (no ad- or absorption) is performed. This experiment yields the volume of the unloaded sorbent material.
3. NOVEL MEASURING PRINCIPLE If the sample material changes its volume during the sorption process, the data treatment shown above—and also the data treatment of sorption experiments with pure fluids—is not correct. In the case of swelling sorbent materials, the actual volume of the material has to be used in the data treatment process. If the combined gravimetric/manometric method is applied in a different way, it is possible to measure in one single experiment the sorption and the (actual) volume of the sample. For that a binary gas phase mixture consisting of the absorbing fluid (for example CO2) and an inert fluid which is not—or in a negligible amount—absorbed (for example He, Ar, N2) is used. The combined gravimetric/manometric measuring method provides the necessary additional experimental information which allows simultaneous measurment of the volume of the sample and the sorption of the measuring gas. Let us assume that component 1 is the nonabsorbing inert fluid and component 2 is absorbing. In this case the absorption of component 1 is per definition negligible (m1 = 0). Under this assumption, the componentwise material balances (eq 9) lead to 0 ¼ m1 mG1 ¼ w1 VD F w1 ðVD þ VMC VS ÞFG
ð10Þ
m2 ¼ m2 mG2 ¼ ð1 w1 ÞVD F ð1 w1 ÞðVD þ VMC VS ÞFG ð11Þ Using eq 10 the actual volume of the sorbent material—being in absorption equilibrium with gas phase mixture’s component 2— can be determined: ! w1 F VS ¼ VMC VD 1 ð12Þ w 1 FG
The manometric/gravimetric sorption measurement using a binary mixture of an inert and an absorbing fluid leads simultaneously to the absorbed mass (m2) and the volume of the sorbent material (VS). Trivially described, this method combines the sorption and the reference experiment in one measurement by using a mixture of an absorbing fluid and an inert reference fluid. We suggested using Helium for reference gas, other gases with negligible absorption in the sample material may be used alternatively. Thus, the results of the measurements are excess quantities which do belong to the chosen, nonabsorbing reference gas.
4. MEASUREMENTS Typical swelling sorbent materials with high scientific and technical relevance are polymers2128 or ionic liquids.2932 The novel measuring principle is applicable for both, solid, or liquid sorbent materials. Particularly PMMACO2 systems have been investigated intensively and many results have been published.13,5,9,23 Measurements using the same system were performed in this work to prove the new measuring principle. Helium was chosen as a nonabsorbing gas phase component. Polymethylmethacrylate (PMMA) pellets, supplied from R€ohm/Evonik “Plexiglas 6N”, carbon dioxide (99,99% purity), and helium (99,999% purity) both supplied from Linde were used for our measurements. The measuring instrument employed for these measurements is shown in Figure 2 and is described with its technical details in ref 33. Its main components are • Temperature measurement in different parts of the instrument by means of calibrated Pt100 resistance thermometers with an accuracy of (0.03 °C. • Pressure measurement of the gas phase by means of a cascade of three different pressure sensors with the following measuring ranges and accuracies: (P2) Vac 20 MPa, ( 0.04% full scale, (P3) Vac 1 MPa, ( 0.04% full scale, (P4) Vac 0.035 MPa, ( 0.07% full scale. The employed pressure senor is chosen depending on the pressure in the instrument. 7051
dx.doi.org/10.1021/ie200076k |Ind. Eng. Chem. Res. 2011, 50, 7049–7055
Industrial & Engineering Chemistry Research
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Figure 3. Experimental results for weight increase of polymethylmethacrylate in pure He at 58.8 °C and 3 MPa.
• A magnetic suspension balance (MSB) with high pressure measuring cell. The MSB is used to measure the mass of the polymer sample with an accuracy of (0.04 mg. Simultaneously the MSB measures the density of the gas phase34 with an accuracy of (0.01 kg/m3. The volume of the MSB with measuring cell was calibrated prior to the measurements (VMC = 186.0558 ( 0.2791 cm3). • Two dosing tanks with calibrated volumes (VS1 = 70.73300 ( 0.12025 cm3, VS2 = 36.25280 ( 0.06163 cm3) for preparing the gas phase mixture. For mixture preparation, each dosing tank is filled with one pure component of the mixture (CO2 and He). The mass of each component of the gaseous mixture can be calculated by applying a suitable thermal equation of state20,35 for each pure component from the known volumes and measured pressure and temperature data. After filling, the pure components are mixed, and thus, a binary mixture with exactly known composition is generated. The above-mentioned, calibrated volumes of the instrument are used in the formalism (eqs 7, 11, and 12) for calculating the absorption of CO2 and the volume of the sample. The volume of the dosing tank used in the equations (VD) is calculated from the calibrated volumes of the instrument’s dosing tanks (VS1, VS2): VD ¼ VS1 þ VS2
ð13Þ
The measuring accuracies which are realized with this instrument in these measurements are Δm/m e 0.02 mg/g for the
absorbed mass, ΔF/F e 0.01 kg/m3 for the gas phase density, and Δw/w e 0.01 for the CO2 concentration in the gas phase mixture. For performing the measurement, the PMMA sample is filled in the crucible of the MSB, the messuring cell is closed and leak tested. The PMMA sample was degassed in vacuum for two days at 90 °C. The sample mass was 2.64745 g measured with MSB after degassing. After this pretreatment, the measuring temperature was adjusted to 58.8 °C and the measuring cell volume was isolated by closing the connection valves V2 and V11. In a first experiment, the assumed inert behavior of He toward the PMMA sample was verified. Thus, a sorption exerpiment was perfromed by continuously measuring the mass of the PMMA sample for 65 h in pure He at 3 MPa. In Figure 3, the results of this measurement are shown as weight increase of PMMA versus time. The ratio of the balance resolution to the sample mass for this experiment is
