110th Anniversary: New Volumetric Frequency Response System for

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110th Anniversary: New Volumetric Frequency Response System for Determining Mass Transfer Mechanisms in Microporous Adsorbents Mohammad I Hossain, C.E. Holland, Armin D. Ebner, and James Anthony Ritter Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b02422 • Publication Date (Web): 22 Aug 2019 Downloaded from pubs.acs.org on August 23, 2019

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Industrial & Engineering Chemistry Research

110th Anniversary: New Volumetric Frequency Response System for Determining Mass Transfer Mechanisms in Microporous Adsorbents

Mohammad I. Hossain, Charles E. Holland, Armin D. Ebner and James A. Ritter*

Department of Chemical Engineering Swearingen Engineering Center University of South Carolina Columbia, SC 29208

A revised research article submitted to the Special Issue of I&EC Research 110th Anniversary of I&EC Research for consideration for publication.

July 2019

*Address

all correspondence to J. A. Ritter at [email protected].

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract A new volumetric frequency response (VFR) system was developed for studying the mass transfer characteristics of gases in microporous adsorbents. For this VFR system, the differential pressure response from a small perturbation in volume was measured in a closed system after equilibrium was established for a gas adsorbate-adsorbent pair at constant temperature and pressure. It operates over a wide range of frequencies from 10-5 to 10 Hz; it operates from atmospheric pressure down to vacuum pressures of 100 torr; and it operates at temperatures from 5 to 80 oC. The sample chamber holds up to 100 g of adsorbent. These operating ranges make this new VFR system capable of measuring mass transfer characteristics of adsorbate-adsorbent systems at conditions relevant to many commercial separation processes using a relatively large volume of adsorbent in a unique packed bed arrangement. The apparatus and procedure were described in detail, including the use of runs with different gases and different porous and nonporous solid beads and pellets to fully characterize the system in terms of its dynamic behavior especially at high frequencies and in terms of various volumes required in the analyses. It was shown how to analyze these baseline runs to correct for gas compression heating and pressure drop effects in the high frequency region of the pressure change amplitude response curves, and to determine intensity (or amplitude ratio) and phase shift (or lag) response curves from which fundamental thermodynamic and kinetic information for an adsorbate-adsorbent pair could be extracted. To demonstrate the utility of this new VFR system, experiments were carried out with CO2 in 13X zeolite beads at 25 oC and 100, 200 and 760 torr using 32 frequencies at each pressure. Slopes of this isotherm estimated from the intensity response curves at low frequency showed very good agreement with those measured independently. The mass transfer time constant estimated from the maximum in the phase lag response curve also agreed well with that reported in the literature. Unique features of the intensity and phase lag response curves were revealed.

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Introduction To design and predict the performance of adsorption-based separation processes, like pressure swing adsorption (PSA) or vacuum swing adsorption (VSA), understanding and characterizing the dynamic behavior of gas adsorbate-adsorbent systems is important. In general, the kinetics or mass transfer rate of adsorption and desorption of a pure gas in a microporous adsorbent can be controlled by a single mechanism, like micropore diffusion, macropore diffusion or macropore advection, or any combination of these mechanisms.1 In recent decades, frequency response (FR) methods2-36 have proven to be one of the best macroscopic techniques for investigating the kinetic behavior of gas adsorbate-adsorbent systems due to their ability to discriminate among different rate limiting mechanisms. In FR systems, a system that is initially in equilibrium is subjected to a continuous perturbation, typically in the form of a sinusoidal function, of one physical variable, i.e., pressure, volume or concentration.2 The system then produces a periodic response with the same frequency of the perturbed variable but with a different amplitude and phase angle that reflects unique thermodynamic and kinetic characteristics of the system. The response curve measured over a wide range of frequencies can then be analyzed to possibly determine one or more mechanisms associated with kinetic processes taking place within the microporous adsorbent. One common frequency response technique involves a closed, batch system in which the volume of the system is perturbed periodically to induce a periodic change in system pressure. This volumetric frequency response (VFR) technique was pioneered by Naphtali and Polinski3 and later used by various other researchers. Yasuda used VFR to study the diffusion of gases in zeolites4,5 and for catalytic reaction processes.6 Sun and coworkers measured intracrystaline diffusion of various hydrocarbons in silicate7 and NaX zeolite.8 Rees and coworkers also used VFR with a square-wave perturbation to study diffusion and adsorption



kinetics of gases in silicate-19,10 and various zeolites.11-15 In addition, substantial work on frequency response theory and the development of mass transfer models to interpret frequency response data has been done by Yasuda,16 Jordi and Do,17,18 Sun et al.,19 and Wang and LeVan.2 Besides VFR, another type of widely used frequency response is a flow-through technique that involves perturbation of variables like inlet flow rate,20 inlet stream concentration,21-27 or pressure.28-30 In recent years, LeVan and coworkers used a combined frequency response technique using volumetric and flow through experiments to study pure gas mass transfer rates in adsorbents,31 or combinations of pressure-swing and concentrationswing frequency response experiments to study mass transfer rates for both pure and mixed gases in various adsorbents.25,32 Most recently, Wang et al.34 used pressure swing frequency response to study the mass transfer mechanism of ethane in ZIF-8 material and verified the results against VFR. The objective of this work is to introduce a unique VFR system based largely on the simple schematic in the work of Reyes,35 with some ideas taken from Tuner et al.36 This is a closed, batch system wherein the differential pressure response from a small perturbation in volume is measured after equilibrium is established for a gas adsorbate-adsorbent pair at constant temperature and pressure using a relatively large volume of adsorbent. A detailed description of the apparatus, its operating procedure, including the use of baseline runs with different gases and different porous and nonporous solid beads and pellets that fully characterize the system in terms of its dynamic behavior especially at high frequencies and in terms of various volumes required in analyses, are provided. A detailed procedure for analyzing the experimental data to achieve the final frequency response functions in terms of intensity and phase lag response curves for a gas adsorbate-adsorbent pair, are also provided. To demonstrate the utility of this new VFR system, several experiments are carried out with CO2 in 13X zeolite beads at 25 oC with the corresponding results analyzed in terms of intensity and


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phase lag response curves. Experiment Volumetric Frequency Response (VFR) Apparatus A schematic of the volumetric frequency response (VFR) system is shown in Figure 1. It was designed and constructed in-house. This VFR system comprises six sections: a computer and data acquisition section running National Instruments hardware and software; an electronics section including motor drives for modulation and frequency control; a pressure, volume and temperature (PVT) section that includes the sample chamber and pressure transducers; a temperature control section that includes a constant temperature bath and a large ballast tank; a vacuum pumping station section; and a gas delivery section. A photograph of the entire VFR system is shown in Figure 2 (top), along with a closer view of the electronics and PVT sections, the two most important sections (bottom). Major components of this system include the Servo Drive Motor (Motor Automation Direct, USA Model SVL-204B), 9:1 Speed Reducer (Shimpo Driver Inc., Model VRAFC09P0701902T 00), AC Servo Drive (Automation Direct, USA, Model SVA-2040L), AC Servo Driver Interface (Automation Direct, USA, Model ZL-RTB50), Linear Variable Differential Transducer (TE Connectivity, Model DC-EC-250), Linear Encoder (US Digital, Model PE-250-1-I-D-L), DP Transducer (Omegadyne Inc., + 2.5 kPa, Model MMDDB10WBIV10P2C0T2A2CEPS with a response time of 1 ms), Absolute Pressure Transducer (MKS, 1,000 torr, Model 628A13TEE), Absolute Encoder (US Digital, Model A2-A-B-E-MD), Metal Bellows Assembly (Standard Bellows Company, Basic Part Number 103-55), Temperature Controller (Omega Engineering Inc., Model CNi1643-C24), 13 Liter Refrigerated Circulating Bath (VWR North America, Model 1157P), Turbo Molecular Drag Pump (Adixen Drytel 1025 w/ Diaphragm Vacuum Pump AMD 1), and Ionization Gauge Controller (Granville-Phillips, Model 350). Many of these components are visible in Figure 2.



This VFR system comprises three different zones in terms of volume (Figure 1): a) the working volume is shown in dark gray, b) the reference volume is shown in light gray, and c) the external volume is shown in white, which simply connects the system with vacuum or feed gas. Except for the immersed components, all parts containing the working and reference volumes are thermally insulated to reduce the effects of any temperature variation in the laboratory. The working volume includes a large sample chamber, a thermocouple in the sample chamber for temperature measurement, and a metal bellows that contracts and expands via a shaft for working volume modulation. The shaft connected to the metal bellows is driven by the servo motor system via an eccentric sheave which causes the working volume to vary sinusoidally. The position of the bellows is determined by the linear variable differential transducer (LVDT) along with a linear encoder, which measure the change in working volume. The reference volume includes a two-liter ballast tank that is immersed within the water chamber of the constant temperature bath for temperature and thus pressure stabilization within the reference volume at the operating temperature. The pressure of the sample is measured by the absolute pressure transducer located in the reference volume. The differential pressure transducer is located between the reference and working volumes to follow the differential pressure change between these volumes. Data acquisition and control of the VFR system is accomplished with an in-house developed National Instruments LabVIEW program. The control system operates all the electronics, including the servo drive motor for volume modulation at each frequency and switching between frequencies. Connectivity between the different zones is controlled via air actuated valves V1 through V4 (SS-BNV51-C, Swagelok normally closed BN series bellows valves with ¼” female VCR fittings, and SS-BN8FR8-C, Swagelok normally closed BN series bellows valves with ½” female VCR fittings). All the connections in the PVT section are stainless steel CF high vacuum piping and fittings. The outputs from the LDVT, pressure


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transducers and thermocouple are recorded and saved in LabView files for subsequent analysis in Excel. VFR Procedure Two different procedures were developed and utilized for this VFR system. The first and most involved procedure was developed for determining mass transfer rates and mechanisms of gas adsorbate-adsorbent pairs in microporous adsorbents. This procedure operated the system at different pressures and temperatures with the gas adsorbate-adsorbent pair of interest and also in helium with the same adsorbent over the entire frequency range. The second and less involved procedure was developed for characterizing the system in terms of its dynamic response and for determining various volumes within the working volume of the system. This procedure utilized different gases with an empty sample chamber, and with the sample chamber filled with porous and non-porous solids. For this procedure the system usually operated at just one pressure and temperature, but still over the entire frequency range. However, in some cases only one low frequency was required for the analysis. Each of these procedures is described in detail below. VFR Procedure: Adsorbent Activation The adsorbent was placed in the sample chamber in between two layers of glass beads to ensure thermal homogeneity. The system was then evacuated and thermally regenerated by keeping valves V1, V2 and V4 open with valve V3 closed (Figure 1). During sample activation the bath was removed, and the container was heated to the regeneration temperature via aluminum concentric sleeves wrapped with rigid electric band heaters connected to a Variac. Activation was typically carried out for a period of hours or even days at the regeneration temperature until the pressure at the vacuum pump was stable for a few hours at less than 1.5×10-5 torr; this, of course, depended on the type of adsorbent. Then, the system was allowed to cool, the heaters and sleeves were removed and the sample chamber was fully immersed in



the water jacketed beaker that was set at the target working temperature using the constant temperature bath. VFR Procedure: Adsorbent Equilibration Once the working volume was cooled to the working temperature, valve V4 was closed and the working gas was allowed into the working and reference volumes via valve V3 to pressurize the system to the target working pressure. A needle valve was used (not shown) to control the flow of the working gas into the system. Once at the target working pressure, the shaft connecting the bellows to the servo drive motor was moved to a position where the bellows was at the midpoint. Valve V2 was then closed and the system was allowed to equilibrate at the target working temperature and pressure for another several hours or even days, again depending on the adsorbent. Once the system was in equilibrium, valve V1 was closed to isolate the working volume from the reference volume. At this point, with the differential pressure Pd between these two volumes reading zero, the sample and the system were ready for a run through the frequency spectrum. VFR Procedure: Frequency Spectrum Runs A run through the frequency spectrum was carried out as follows. Once the system was at equilibrium, the adsorbent was subjected to volume modulation at each frequency using a predefined set of 32 frequencies between 5.0×10-5 and 10 Hz. Ten cycles were typically run at each frequency to ensure the latter cycles achieved sinusoidal periodic behavior. This was a fully automated step where the LabView program took over and ran uninterrupted from the lowest to the highest frequency. Of course, the lower frequencies took days to run 10 cycles at each frequency, while the higher frequencies finished in fractions of a second. For a subsequent run with the same working gas, no activation was needed. Instead, the sample chamber remained inside the water jacketed beaker. Valves V1 and V2 were opened and, depending on the new target working temperature and pressure, gas was removed from or


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fed into the working and reference volumes via valves V4 or V3, respectively. The shaft connecting the bellows to the servo drive motor was again moved to position the bellows to the midpoint. Once the system was in equilibrium at the new target working pressure and temperature, valve V2 was closed and the sample and system were again ready for a run through the frequency spectrum. VFR Procedure: System Characterization A series of experiments were carried out to fully characterize the dynamic response of the system especially in the high frequency range. These experiments involved determining the response from different solid media sizes and different solid media porosities and shapes [2 or 3 mm glass beads, stainless steel beads (6.35 mm diameter), 13X zeolite beads (8-12 mesh, Grace Davison) or carbon molecular sieve (CMS 3K-172, Shirasagi, Japan)] at different temperatures and pressures, and for gases of different molecular sizes and structures [O2, N2, Ar, He, H2, CH4 (all UHP Grade, Airgas) or CO2 (Bone Dry Grade, Airgas)]. They were carried out over the entire frequency range. In these secondary procedural runs, evacuation, gas filling and equilibration were carried out like that described for the first procedure with the sample chamber always immersed in the jacketed water bath. VFR Procedure: Empty (VE), Displaced (V) and Excluded Volume (VEX) Determinations Three unique volumes within the working volume were required for subsequent data analyses with this VFR system. These are the empty volume VE, change in working volume V and excluded volume VEX when the adsorbent was in the sample chamber. Three experimental runs were carried out for this purpose, each over the entire frequency range but at one temperature and pressure (750 torr and 25 oC). For VE, O2 was used with an empty sample chamber. For V, O2 was used with 528 stainless steel (SS) beads of known solid volume VSS in the sample chamber. Any gas could have been used to determine these volumes. For VEX, helium was necessarily used with 13X in the sample chamber. In these secondary procedural 9 ACS Paragon Plus Environment


runs, evacuation, gas filling and equilibration were carried out like that described for the first procedure with the sample chamber always immersed in the water jacketed beaker. VFR Procedure: Quantitative System Operation For the experiments conducted with 13X, a 120 cm3 sample chamber was loaded with three layers of materials: a top layer with 46.3 g of 3.0 mm glass beads, a center layer with 39.8 g of 13X beads and a bottom layer with 46.3 g of 3.0 mm glass beads. The sample was regenerated under vacuum (1.5×10-5 torr) at 350 oC for 40 h. For experiments conducted with CO2, 32 frequencies were used starting from 7×10-5 Hz and ending with 9.25 Hz at three different pressures of 100, 200 and 750 torr at 25 oC. For experiments conducted with He in 13X, the same 32 frequencies were used but just at 750 torr and 25 oC. For experiments conducted with He in CMS, the 120 cm3 sample chamber was loaded with enough adsorbent to fill it, with the actual amount being inconsequential. The sample was regenerated under vacuum (1.5×10-5 torr) at 150 oC for 40 h. The same 32 frequencies were used but just at 760 torr and 25 oC. For all other experiments conducted with an empty sample chamber or filled with glass or SS beads, the volume occupied by the solid media was determined by its size, density and/or number of beads added to the chamber. Either the same 32 frequencies were used or a smaller subset starting at some higher frequency but ending at 9.25 Hz was used. Typically, these experiments were carried out 750 torr and 25 oC, unless the effect of temperature (25, 40 and 55 oC) or pressure (200, 400 and 750 torr) was being studied during system characterization. Theory and Analysis Response Variables The analysis developed for this VFR system uses the amplitude ratio and the phase lag between the input and output variables as two independent responses to represent the frequency response of the adsorbate-adsorbent pair. As mentioned earlier, the input and output variables


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are, respectively, the change in the working volume and the corresponding change in its pressure relative to that at equilibrium when the shaft is at its midpoint. The amplitude ratio between the change in the working volume V and the change in pressure P relative to that of the absolute equilibrium pressure Po (which is also the pressure of the reference volume) is conveniently expressed in terms of the following function:  P V  I  o  1 V EX P 

(1)

with the phase lag function evaluated directly as,

   P  

(2)

VEX is the excluded volume of the system defined as V EX  Vo  V g , p

(3)

Vo is the average value of the working volume V that is external to the pellets, and Vg,p is the macropore volume, i.e.,

V g , p  ma

p p

(4)

ma is the mass of the adsorbent, p is the pellet porosity and p is the pellet density.  P and   are the phase angles corresponding to the output and input variables, respectively. V is given by

V  V g ,i  VEXT  Vo  V sin( 2ft )

(5)

VEXT is the fraction of the working volume that varies with time and is not occupied by the region within the sample chamber containing just adsorbent, while Vg,i is the fraction of the working volume occupied by the region in the sample chamber containing just adsorbent that corresponds to interparticle volume

Vg ,i  ma

1  b     p  1   b 

(6)



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b is the bed interparticle porosity. The intensity function I defined by eq 1 physically represents the ratio between the working capacities of the adsorbed and gas phases. Thus, it tends to decrease as the frequency of the input function increases. This function also approaches zero at very high frequencies where the adsorbent behaves like a solid that cannot be penetrated, i.e., a solid wall. Analysis of Experimental Sinusoidal Response Curves This VFR system produces experimental sinusoidal response curves at each frequency, in terms of the shaft displacement  from the LDVT and the differential pressure Pd from the differential pressure transducer. These curves are fitted respectively to the following functions:

   os   sin(2ft    )

(7)

Pd  Pd ,os  P sin( 2ft   P )

(8)

where f is the frequency, t is the time, os and Pd,os are the corresponding offsets, and  and

P are the corresponding amplitudes. From the fitting at a given frequency f, the amplitudes  and P, and the phase lag P -  are extracted. For each frequency f the system provides a response expressed in terms of the two functions in eqs 1 and 2. However, the change in working volume V and the excluded volume VEX require additional experimental evaluation and analyses, as described below. Analyses of Empty (VE), Displaced (V) and Excluded (VEX) Volumes If Po,E and PE are respectively the equilibrium absolute pressure and the amplitude of the pressure change when the system is empty, and Po,SS and PSS are respectively the absolute equilibrium pressure and the amplitude of the pressure change when the system contains only stainless steel beads of known volume Vss then V and VE are given by V  VE - VSS PSS /Po,SS

(9)

VE  VSS /(1 - Z E )

(10) 12 ACS Paragon Plus Environment

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with Z E  Po,SS /Po, E PE /PSS 

(11)

When system contains the adsorbent and possibly some inert material of known volume VI , and if Po,He and PHe are respectively the equilibrium absolute pressure and the amplitude of the pressure outside the bed volume when using helium as the working gas, then the excluded volume of the system is given by V EX  VSS /(1 - Z He )

(12)

Z He  Po,SS /Po, He PHe /PSS 

(13)

with

Analyses of Skeletal Density and Isotherm Slope The skeletal density of the material S and the slope of the adsorbate-adsorbent isotherm are obtained as follows. The skeletal density is evaluated via the following expression

 S  ma / Vs

(14)

where Vs is the skeletal volume given by Vs  V E  V EX  V I

(15)

The slope of the gas adsorbate-adsorbent isotherm is given by q P

 eq

V I q  EX P ma RT

(16)

where I is the intensity given in eq 1 but only at frequencies low enough to ensure that the sample operates under local equilibrium. Results and Discussion Several sets of experiments were carried out with this VFR system. Some were done with the sample chamber empty, some were done with it filled with glass or stainless steel beads, and some were done with it filled with adsorbent. Several different gases were also used, depending on what was in the sample chamber. The results from these experiments are 13 ACS Paragon Plus Environment


discussed in turn beginning with those that characterized the system and revealed some interesting features that had to be accounted for in the analyses and ending with those that produced intensity and phase lag functions, from which thermodynamic and kinetic information about the CO2-13X system was obtained. It is noteworthy that the RTD located in the adsorbent bed did not sense any significant changes in temperature throughout any of these frequency response experimental runs; thus, no temperature trends are reported. VFR System Characterization Figure 3 shows the pressure change amplitude response curve for three runs: one with O2 in stainless steel (SS) beads in the sample chamber, one with O2 in an empty sample chamber, and one with He with 13X in the sample chamber. An interesting feature appeared in the high frequency range for all three runs. In fact, this feature appeared in every run, no matter the conditions, as shown later. The two runs carried out with O2 began to exhibit a significant upward deviation at about 0.04 and 0.06 Hz, with that for He beginning to exhibit it at about 2 Hz. As shown by Bourdin et al,37,38 this feature of increasing pressure at higher frequencies was due to a combination of issues that include mainly gas compression heating taking place in the working volume outside the adsorbent bed and pressure drop taking place along the adsorbent bed. These results showed that 1) this system dynamic at high frequencies might depend on system parameters such as gas properties, pressure, temperature, and size, shape and porosity of the solid, and 2) if it did depend on some of these parameters, then this system dynamic must be accounted for in the analyses associated with determining the intensity function, using a methodology similar to that of Yasuda.4 So, all these parameters were studied in a series of experiments; the results are shown in Figures 4 to 8. Figure 4 shows the effect of the solid material size on the pressure change amplitude response curve. These experiments used identical spherical glass beads but with different diameters of 2 mm and 3 mm in CO2 at 400 torr and 25 oC to study this effect. The pressure


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change amplitude response curves essentially overlapped with each other, indicating there was no effect of the size of the solid material over the entire frequency range. These results clearly showed that pressure drop along the adsorbent bed did not play any role on the results over the range of frequencies analyzed. The increase of the amplitudes at the higher frequencies was consistent with the theory behind gas compression heating,37,38 because it is a phenomenon that takes place away from the adsorbent bed and therefore not subject to packed bed properties. An interesting feature consistently observed in both runs, i.e., a slight shoulder between 10-2 Hz and 10-3 Hz, might also be due to gas compression heating. Figure 5 shows the effect of the solid material porosity and shape on the pressure change amplitude response curve. These experiments used spherical, nonporous, 3 mm glass beads and cylindrical, porous, CMS pellets in helium at 750 torr and 25 oC. The sample chamber was filled with just the respective solid in each case. The top graph in Figure 5 shows the original response curves of both runs, while the bottom graph in Figure 5 shows the response curves forced to overlay with each other at low frequencies by simple scaling to better observe any differences at high frequencies. These scaled pressure change amplitude response curves essentially overlapped with each other, indicating there was no effect of solid material porosity and shape over the entire frequency range. Likewise, these results again showed that pressure drop along the adsorbent bed did not play any role over the range of frequencies analyzed and that the increases of the amplitude at higher frequencies were associated with gas compression heating. Figure 6 shows the effect of the absolute pressure on the pressure change amplitude response curve. These experiments used 3 mm glass beads in O2 at three different pressures of 200, 400 and 750 torr at 25 oC. The top graph in Figure 6 shows the original response curves of all three runs, while the bottom graph in Figure 6 shows the response curves forced to overlay with each other at low frequencies by simple scaling to better observe any differences at high



frequencies. These scaled pressure change amplitude response curves did not overlap with each other, departing more from each other with increasing pressure and thus indicating there was an effect of pressure at high frequencies, which was consistent with gas compression heating. Figure 7 shows the effect of temperature on the pressure change amplitude response curve. These experiments used 3 mm glass beads in O2 at 400 torr at three different temperatures of 25, 40 and 55 oC. The top graph in Figure 7 shows the original response curves of all three runs, while the bottom graph in Figure 7 shows the response curves forced to overlay with each other at low frequencies by simple scaling to better observe any differences at high frequencies. These scaled pressure change amplitude response curves essentially overlapped with each other, while showing a very slight reduction with increasing temperature over the entire frequency range that was deemed negligible. As before this effect was consistent with gas compression heating, with the observed differences resulting from the increased gas conductivities at higher temperatures. Figure 8 shows the effect of different gases on the pressure change amplitude response curve. These experiments used 3 mm glass beads in O2, N2, Ar, CO2, He, H2 or CH4 at 750 torr and 30 oC. All the response curves exhibited essentially the same response at low frequencies, so scaling was not needed. However, significant differences between the response curves were exhibited at high frequencies, indicating a marked effect of gas molecular size and structure. Several interesting trends were gleaned from these results. First, the high frequency feature began at lower frequencies with higher molecular weight gases. From lower to higher frequencies it began in the following order: CO2 < Ar < O2 ~ N2 < CH4

110th Anniversary: New Volumetric Frequency Response System for

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