does not penetrate into the adsorbed film. On the other hand, experimental determination of the position of the GDS is a significant practical problem with static volumetric and gravimetric methods because it is not possible to measure the volume of material adsorbed that is required to carry out any correction for the loss of free gas volume. The excess amount of material adsorbed must approach zero as the density of the bulk phase approaches that of the adsorbed phase, and this phenomenon is the source of the observed maxima in the experimental adsorption isotherms for supercritical f l ~ i d s measured ~-~ by static methods. However, the total amount adsorbed could also display a maximum at intermediate pressures if multilayer adsorption occurred, Le., if the volume of the stationary phase increased with increasing mobile-phase pressure to a maximum and then decreased at higher pressures due to the exfoliation of the outermost layers of the adsorbed film by a bulk phase of increasing density (solvent strength). Thus, the origin of the maxima in chromatographically measured isotherms is uncertain's because the observed maxima could be due to experimental measurement of excess adsorption which must display a maximum, multilayer adsorption, or possibly both causes. The objective of the present investigation was to establish exactly which type of adsorption data can be obtained by tracer pulse chromatographic experiments. Relatively simple systems were investigated at low temperatures rather than supercritical fluids at high pressures in order to elucidate the mechanisms in well-defined model systems. However, the interpretation of low-temperature adsorption processes provides valuable information for the investigation of highpressure adsorption.
EXPERI MENTAL SECT I ON The experimental procedure used for the determination of gas-solid adsorption isotherms was mass spectrometric tracer pulse ~ h r o m a t o g r a p h y . ~This J ~ is a chromatographic tracer pulse technique in which I3C,*H, or '*O-labeled tracer probes are used with a mass-specific detection system. The technique has been employed extensively to measure adsorption and partition isotherms of sub- and supercritical COZ in both packed and capillary SFC columns.14 In order to distinguish between total and excess adsorption experimentally, systems which display significant uptake of adsorbate are required. Measurable adsorption can be induced by performing the experiments at either very high pressures or very low temperatures. Operation at low temperatures is preferable experimentally because no high-pressure pumps are required. For this reason, all of the reported experiments were carried out with the analytical column immersed in a bath of liquid nitrogen (77 K) or dry ice (195 K). The solid support was silica gel with a measured" surface area of 480 m2/g, an average pore size of 6 nm, and a pore volume of 0.75 mL/g. The silica gel, 0.5-1.0 g, was packed in '/g-in.-o.d. copper tubing. A schematic diagram of the instrumentation is shown in Figure 1. The basic instrument was a Hewlett-Packard 597 1 (15) Roth, M. J . Microcolumn Sep. 1991, 3, 173-184. (16) Parcher, J. F.; Selim, M. I . Anal. Chem. 1979, 51, 2154-2156 (17) Song, H.; Parcher, J. F. Anal. Chem. 1990, 62, 2313-2317.
Sample
sample in
Adsorbable
.......................
Flgure 1. Schematic diagram of the tracer pulse instrumentation.
l
9mP
arm
lm,
0 Iujnjection
1
2
m
m
m
m
Retention Time (min) Flgure 2. Chromatogram illustrating the simultaneous pre- and postcolumn injection of helium-3, neon, argon, and carbon dioxide isotopic tracers.
mass-specific detector system with a 5890 Series I1 gas chromatograph. Gas sampling valves (GSVs), flow controllers, pressure transducers, and analytical column were all added to the basic instrumentation, but these were located external to thecommercial instrumentation. Flow regulators wereused to control the flow rate and the composition of the carrier gas. The pressure transducers monitored the gas pressure at the column inlet and outlet. The gas sampling valves 1 and 2 were used for pre- and postcolumn injection of the isotopic adsorption and dead-time probes, and GSV 3 was used to isolate the analytical column for nonequilibrium experiments. Simultaneous pre- and postcolumn injection allowed the accurate determination of only the void volume between GSV 1 and GSV 2. Thus, the large, extracolumn volume of the lines, injection port, and GC capillary column were eliminated and the uncertainties of the split ratio and the source pressure in the mass spectrometer were also avoided. The isotopic tracers were 3He, 15N2 ( m / z = 30), 1 3 C 0 1 8 0( m / z = 47), C13CH32H3( m / z = 34), and C3H52H3( m / z = 47). A typical chromatogram for a dual-injection experiment is shown in Figure 2. The same sample mixture was injected simultaneously at GSV 1 and GSV 2. The capillary column of the GC/MS system was maintained at a sufficiently high temperature that none of the solutes were retained and all components injected via GSV 2 eluted together in the first peak. The sample components injected via GSV 1 passed through the analytical column in which the solutes were retained by interaction with the stationary phase but the 3He dead-time probe was not. The dead time of the analytical column is marked as At,,, in Figure 2, and the corrected retention time of the isotopic tracer is marked as A ~ R * .The measured void volume V,, was calculated from Atm by the equation Vm = F,At,, where Fc Analytical Chemistry, Vol. 66, No. 18, September 15, 1994
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C
Table 1. Isotope Effect of the Tracer Pulse Probe Samples isotope factor t R (natural)/tR (iso) adsorbate
1.05 0.985 0.999 0.992
is the volume flow rate of the binary carrier gas at column conditions. The use of a measured time difference rather than an absolute time from injection for the calculation of V,,, significantly decreased the uncertainty of the measurements. In the experiments involving the retention of isotopic tracers, there were slight differences between the retention of the light and heavy isotopic species. Thus, a correction was required to obtain the retention time of the natural solute from that of the heavy isotope that could be distinguished by the mass spectrometer. This isotope effect was measured from the relative retention times of the isotopic species on the silica gel with nothing adsorbed. The results in the form of the ratio of the retention time of the natural isotope to that of the heavy isotope are given in Table 1. All of the adsorption data were corrected for this effect; however, in no case was the correction greater than 5%. Nonequilibrium adsorption of C02, C2H6, and C3H8 on silica gel at 77 K was measured by initially equilibrating the gas-solid system at 195 K and subsequently measuring the amount of material adsorbed at that temperature by tracer pulse chromatography. The column was then isolated via GSV 3, cooled to 77 K, and allowed to reach steady state in a closed system in which all of the adsorbate condensed onto the silica gel surface. The carrier gas was then changed to pure helium and the analytical column was returned to the flow path by resetting GSV 3 to its original configuration. The amount of material adsorbed at 77 K was calculated from the amount adsorbed at 195 K plus the amount present in the gas phase when the column was isolated. In each case, the melting temperature of the adsorbate was above 77 K and the vapor pressure of the pure adsorbate was less than 1 mTorr at 77 K (as estimated by extrapolation of liquid-phase data). The void volume was subsequently measured with the 3He dead-time probe. Theoretical and Operational Definitions of Total and Excess Adsorption. The IUPAC definitionlCl2 of Gibbs surface excess is "...the difference between the amount of component i actually present in the system, and that which would be present (in a reference system) if the bulk concentration in the adjoining phases were maintained up to a chosen geometrical dividing surface (Gibbs Dividing Surface)". The concept of the GDS is illustrated in Figure 3 , where ci is the concentration (density) of component i and z is the distance from the adsorbent surface. In particular, ciadsand cIgare the densities of component i in the adsorbed and bulk (gas or fluid) phases, respectively; z6 represent the location of the GDS and zg the point closest to the surface at which ci = cIg. The mathematical definition of the excess adsorbed" is
ny
A, ( JJ8(ci - ci4 dz +
Jod ci dz)
Where nia is the surface excess amount of i adsorbed. The 2854
Analytical Chemistry, Vol. 66, No. 18, September 15, 1994
C;&
C,g
I 0
Zb
Za
2
Distance Flgure 3. Illustration of the concept of the Gibbs divlding surface.
surface excess concentration, r i ,is given by the equation
ri = n y / A ,
(2)
The operational definition of ni" is (3)
Where n? is the total amount of component i in the system and Vis the volume of the bulk phase extendingout from the GDS. These equations are completely general; however, many authors additionally differentiate two subtypes of adsorption, viz., total and excess, distinguished by the physical interpretation of the void volume V. If the measured void volume extends out from the surface of the adsorbent and the GDS is located at the solid surface, the type of adsorption is designated as "excess", with the symbol YXs, and Vin eq 3 represents thegeometricor thermodynamic18 void volume of the column, Le., the void volume with nothing adsorbed. This is a fixed quantity which will be designated as V,. Otherwise, that is if the measured void volume extends out from the GDS which is located at the interfacial boundary of an adsorbed film, the adsorption data reflect the total quantity of component i in the adsorbed layer with the symbol rTotal and V is the geometric void volume minus the volume of the adsorbedfilm. This reduced or diminished void volume is a variable quantity which changes with the volume of material adsorbed. This volume has been referred to as the kinetic or dynamic void volume or dead volumeI8 and will be designated as V,. This parameter, V,, cannot be measured directly with either volumetric or gravimetric methods although it can be estimated if an accurate value of the molar volume or density of the adsorbed phase is available. Tracer Pulse Chromatography. Tracer pulse chromatography provides a direct method for the determination of the total amount of component i in the system, n?, for an adsorbable component of the mobile phase from the retention (18) Knox, J . H.; Kaliszan, R. J . Chromatogr. 1985, 349, 21 1-234
Table 2. Isotherm and Void Volume Data for Nltrogen on Silica Gel at 77 K Nz ressure total amt of N2 void vol (%om) adsorbed (mmol/g) (mL/g)
0 44 73 146 218 288 390 475 547 570
0 4.1 4.9 5.9 6.6 7.1 9.7 12.4 17.1 17.2
c
2.63 2.37 2.37 2.32 2.28 2.22 2.18 2.09 1.93 1.83
2
l0
15
Flgure 4. Summary of the void volume data at 77 K: (). carbon dioxide; (0)ethane; (X) propane.
nitrogen; (0)
Table 3. Isotherm and Vold Volume Data for Carbon Dloxlde on Slllca Gel at 195 and 77 K total amt of C o t void volume C02 pressure adsorbed (mmol/g) (mL/g) (Torr) 195 K 77 K 195K 71K
0 0 2.07 9.31 10.86 10.86 23.21 34.13 36.2
0 0 1.03 2.63 2.65 2.65 3.62 4.52 4.93
0 0 1.04 2.67 2.69 2.69 3.62 4.52 5.06
3.16 3.26 3.15 3.11 3.36 3.27 3.05
3.1 1 3.17 3.05 3.04 3.04 3.00 2.92 2.91 2.91
Table 4. Isotherm and Vold Volume Data for Ethane on Slllca Gel at 195 and 77 K total amt of C2Hs void volume CzHs pressure adsorbed (mmol/g) (mL/g) (Torr) 195 K 17 K 195K 77K
0 49.18 146.21 501.13 905.12 985.4
(4)
The excess concentration of i adsorbed can be determined from the relation
rixs = C; { v ~-,V~J ./ A ~
10
Amount of Adsorption (mmol/g)
volume of a distinguishable tracer. The retention volume of a tracer i*, VR$, is directly related to n? by the relation n? = V ~ p c p .This provides a basis for the chromatographic measurement of either the total concentration of i adsorbed riTotalorthe excess concentration of i adsorbed I')tS,depending upon the exact method for measuring the void volume, Le., whether VO or V, is used in place of V in eq 3. In a gas chromatographicsystem it is possible to distinguish the mobile and stationary phases even though the two phases may be chemically identical and differ only in density, if a truly unretained dead-time probe is available. Such a probe cannot penetrate the stationary phase and must be physically restricted to the volume of the bulk or gas phase up to the stationary-phase boundary. In this case, the boundary between the stationary and mobile phases explicitly marks the position of the Gibbs dividing surface, and the retention volume of the dead-time probe is a direct measure of the dynamic void volume V,. The total concentration of i adsorbed can be determined chromatographically from the relation
r F 1= C; { v ~ -, V~, ,J / A ,
5
(5)
where VOequals the retention volume of the dead-time probe with nothing adsorbed, i.e., I'iTotal = 0. Likewise I'iTotal can be calculated from I'Ps by the relation riTota* = I'Ps + cp (VO - V,)/A,, where the quantity VO- V, is equal to the volume, Pds, of i adsorbed or the volume of the stationary phase if the stationary phase consists only of adsorbed i. Equations 4 and 5 have been previously derived by Kobayashi13J4in a series of papers on tracer pulse chromatography based on radioactive tracers.
RESULTS AND DISCUSSION Equilibrium Systems. Equilibrium isotherms of nitrogen on silica gel at 77 K were measured using 15Nzas the tracer. Simultaneously, the void volume of the column was measured with 3He for each isotherm point. The results for nitrogen are given in Table 2 and Figure 4. For a given column, the geometric void volume of the column was fixed at a given temperature and VO= Vm + Pds. The volume adsorbed is related to the amount adsorbed by
0 0.55 1.16 2.94 8.61 10.34
0 0.57 1.22 3.14 8.94 10.89
2.95 3.29 2.88 2.74 2.61 3.87
3.08 3.09 2.99 2.87 2.52 2.42
the relation PdS = Dia*AJiTotal,where Diads is the molar volume of component i in the adsorbed film. Thus, V m = VO BiadsAsI'iTotal and a plot of V, vs AsI'iTotalwould be linear with a slope of -uiads. Linear regression of the data in Table 2 gave an intercept of 2.63 mL/g and a slope of -0.041 (f0.002) L/mol. The intercept is the void volume of the column with nothing adsorbed. This is the geometric void volume of the column or the thermodynamic void volume, using Knox's18 terminology. The slope gives a direct measure of the decrease in the mobile-phase volume, Le., the dynamic or kinetic18void volume, per mole of nitrogen adsorbed. Equilibrium isotherms of carbon dioxide, ethane, and propane were measured at 195 K with the column immersed in crushed dry ice. The higher temperature of 195 K was required for these solutes in order to achieve a measurable pressure of vapor in equilibrium with the adsorbed phase. The results for the adsorption and void volume measurements for these solutes are given in Tables 3-5. At 195 K, the CO2 system represented a gaseous COz-solid COZ equilibrium system. The experimental temperature of 195 K was higher than the boiling point of ethane (184 K) and only slightly below the boiling point of propane (231 K).
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Table 5. Isotherm and Void Volume Data for Propane on Slllca Gel at 105 and 77 K void volume total amt of C3Hg C3Hg pressure adsorbed (mmol/g) (mL/g) (Torr) 195 K 77 K 195K 77K
0 24.71 37.21 50.52 62.81 77.25
0 1.91 2.98 4.98 7.29 9.34
0 1.92 2.99 4.99 7.30 9.35
2.89 2.85 2.72 2.94 2.68 2.48
2.43 2.26 2.16 1.99 1.82 1.66 Figure 5. Volume-based isotherm of nitrogen on silica gel at 77 K. The line represents the calculated BET isotherm.
Table 6. Molar Volumes of the Adsorbates molar volumes (L/mol)
van der Waals b liquid at Tb solid
adsorbate
this work
nitrogen carbon dioxide methane ethane propane
0.041 (f0.002) 0.045 (f0.004) 0.042919 0.062 (fO.OO1) 0.083 (&0.001) 0.084419
0.0391 0.0427 0.0428 0.0638 0.0844
0.0347 0.028 0.0377 0.0550 0.0758
Contrary to the results observed for nitrogen at 77 K, the measured void volumes at 195 K did not systematically decrease with increasing amounts of C 0 2 adsorbed. That is, the adsorbed C02 did not exclude helium from the stationary phase. The same observation is true for the hydrocarbon adsorbates although some decrease in void volume was apparent with propane. The retention volume of the helium probe solute is proportional to the partition coefficient of helium in the adsorbed phase, KHe, according to the relation VR,He = V m + K H ~ and P ~VR,H~ ~ = VO { K H-~l)Pds. If K H =~ 0, then VR,H~= V,; if K H =~ 1, then V R , H=~VO;otherwise, there is no simple way to determine either V, or VO from VR,He. Nonequilibrium Systems. After each equilibrium adsorption experiment at 195 K, the column was isolated and cooled to 77 K, and the void volume was measured again with 3He as the dead-time probe. The results of these experiments are also given in Tables 3-5 and Figure 4. The amount adsorbed at 77 K was calculated from the total amount of solute in the mobile and stationary phases isolated in the column at 195 K. The void volumes measured at 77 K all showed a linear decrease in V, with increasing amount of material adsorbed, as shown in Figure 4. That is, the helium dead-time probe did not penetrate the adsorbed films of CO2, C2H6, or C3Hg at the temperature of liquid nitrogen. The results of linear regression of the V, = f ( r T o t a l ) data for four solutes are given in Table 6 . Even though the same column was used for every solute, the measured values of VOvaried among the data sets because differing lengths of the connecting tubing were immersed in the coolant bath for each experiment. Direct measurement of the density of an adsorbed phase by nonchromatographic methods is difficult, and many schemes have been proposed to estimate thedensity of adsorbed material. The three most commonly used estimators are the van der Waals 6 constant, the density of liquid adsorbate at the boiling point, and the density of solid adsorbate. Table 6 gives a summary of these estimators along with the measured molar volumes from this work. Tracer pulse data from Haydel
+
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Analytical Chemistry, Vol. 66, No. 18, September 15, 1994
and KobayashiI9 are also shown in Table 6 for comparison. The adsorbed-phase molar volumes measured in both this investigation and Kobayashi’s earlier workI9 agree well with the classical van der Waals b constant obtained from gasphase measurements. Both the boiling point and solid molar volumes significantly underestimate the experimental values. Kobayashi later remeasured the molar volume of adsorbed methane13,’4,20*21 and found that the molar volume changed with both surface coverage and temperature. The measured molar volumes increased with increasing temperaturez1 and decreased with increasing surface coverage. l 3 “Volumetric” Adsorption Isotherm of Nitrogen on Silica Gel at 77 K. If the molar volume of adsorbed species can be accurately assessed from the van der Waals b constant, then it should be possible to measure a classical adsorption isotherm simply by measuring the dynamic void volume as a function of the relative pressure of the adsorbate in the gas phase. Such an experiment was carried out for silica gel with a reported surface area of 675 m2/g. the volume-based isotherm is shown in Figure 5, where the left-hand Y-axis displays the volume of nitrogen adsorbed (mL/g). From this, volumetric data fit to the linear form of a modified BET equation involving the volume of N2 adsorbed rather than the amount adsorbed, a calculated monolayer volume of 282 bL/g was obtained. If the average film thickness of a monolayer of adsorbed nitrogen is known, the surface area of the adsorbent could be determined. The effective adsorption cross section of adsorbed nitrogen is 16.2 A2. If the molar volume of adsorbed nitrogen is assumed to equal the van der Waals b constant, which is 6.49 X pL/molecule of nitrogen, the average thickness of an adsorbed monolayer of nitrogen would be 0.40 nm. From the experimentally determined volume of a monolayer and an assumed average thickness, the calculated surface area for the adsorbent used in this investigation was 705 m2/g. This value is within 4-95 of the manufacturer’s value of 675 m2/g obtained from a classical BET measurement. With a known surface area, the volume of nitrogen adsorbed can be expressed in units of microliters per meter squared or nanometers. This scale is shown on the right-hand Y-axis in Figure 5. Displayed in this manner, the Y-axis represents the average thickness of the adsorbed film of nitrogen. Thus, the very simple and rapid method of measuring the void volume from the elution volume of helium-3 yields accurate isotherm ~
(19) Haydel, J J , Kobayashi, R Ind Eng Chem Fundam 1967, 6, 546-554 (20) Masukawa, S , Kobayashi, R J Gas Chromotogr 1968, 6 , 461-465 (21) Hori, Y , Kobayashi, R Bull Chem SOCJpn 1974, 7, 1838-1842
and surface area data for this fundamentally significant system.
CONCLUSIONS Tracer pulse chromatographic measurements can produce data for either total or excess adsorption, depending upon the exact void volume, Le., either Vm or VO,that is used in the calculation of r from eq 4 or 5. If a dead-time probe solute is used which has a partition coefficient of unity, chromatographic adsorption measurements will reflect the total amount of material adsorbed. Conversely, if the partition coefficient of the dead-time probe is zero, the total amount adsorbed will be produced from chromatographic measurements. Thus, accurate measurement of the dynamic void volume is critical for tracer pulse chromatographic methods, and the exact relationship between the void volume and the volume of the adsorbed phase must be accurately assessed before chromatographic data can be accurately determined. In the systems investigated herein, the density of the gas phase, cp, was very low, about 0.1-0.5 mol/L, whereas the density of the adsorbed phase was much higher in the range of 10-20 mol/L. Thus, YXs = rTota* even though VO > Vm and the clear distinction between the two types of adsorption is not critical. In studies involving supercritical fluids,14 however, the density of the gas or fluid phase can vary significantly and approach ciadsathigh pressures. In this case, total and excess adsorption can be significantly different and a clear distinction between the two types of data is critical. In at least one study of the tracer pulse investigation of the adsorption of supercritical carbon dioxide and mixtures of methanol and carbon dioxide,2 it was shown that the dynamic void volume, as measured with neon as the dead-time probe, decreased linearly with the amount of fluid adsorbed. The uncertainty of the data was high, so no accurate molar volume data could be obtained; however, the results indicate that the experimental data reflected the total amount adsorbed rather than the excess amount adsorbed. The maxima observed in the adsorption isotherms measured in the previous studies2 werecaused by multilayer adsorption of the supercritical fluids.
The novel technique of simultaneous pre- and postcolumn injection of a dead-time probe solute allows very accurate determination of the column void volume rather than the systemvoid volume (column plus extracolumn volume). This is especially valuable for thermodynamic measurements with GC/MS systems which may have multiple and variable flow paths between the end of the column and the detector. Another advantage of this method is that only relative rather than absolute time measurements are required for the evaluation of v,. The unique and very significant role of the void volume correction required for gas-solid adsorption isotherm measurements in static, volumetric, and dynamic chromatographic methods cannot be overemphasized. Precise measurement of the column void volume is necessary for any experimental or theoretical interpretation of adsorption or other thermodynamic measurements obtained by tracer pulse or other chromatographic techniques. In addition, the accurate measurement of the change in void volume with the gas-phase pressure or density provides a new method for the measurement of truly "volumetric" adsorption isotherms with very simple void volume measurements. Again, however, the exact role of the dead-time probe is critical for the accurate interpretation of the retention or elution volume of the dead-time probe.
ACKNOWLEDGMENT Acknowledgement is made to the National Science Foundation and to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. Scientific Parentage of the Author. J. F. Parcher, Ph.D. under P. Urone, Ph.D. under W. M. MacNevin, Ph.D. under I. M. Kolthoff. Received for review February 24, 1994. Accepted June 1, 1994.' e Abstract
published in Aduance ACS Abstracts, July 15, 1994.
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