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Langmuir 1997, 13, 539-544
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Adsorbent Helium Density Measurement and Its Effect on Adsorption Isotherms at High Pressure P. Malbrunot,* D. Vidal, and J. Vermesse Laboratoire d’Inge´ nierie des Mate´ riaux et des Hautes Pressions, CNRS, Universite´ Paris-Nord, Avenue Jean Baptiste Cle´ ment, 93430 Villetaneuse, France
R. Chahine and T. K. Bose Institut de Recherche sur l’Hydroge` ne, Universite´ du Que´ bec a` Trois-Rivie` res, CP 500, Trois-Rivie` res, Que´ bec, Canada G9A 5H7 Received July 5, 1995. In Final Form: October 28, 1996X On the basis of an experimental study in a large temperature range, it is shown that “helium densities” of adsorbents measured at room temperature could be erroneous due to a non-negligible effect of helium adsorption. It is proposed that the density obtained with helium at high temperature, for instance, at the regeneration temperature of the adsorbent, be considered as the adsorbent density. Using the corrected densities of 3A, 4A, 5A, and 13X zeolites and of activated and graphitized carbons and of silica gel, we experimentally determined the adsorption of helium on the above mentioned adsorbents at room temperature and in a large pressure range up to 500 MPa. The shape of the adsorption isotherm reveals no saturation at high pressure. These experimental data are in agreement with Monte Carlo simulations of adsorption of a Lennard-Jones gas by a rigid plane as well as by a microporous rigid solid interface. We also examined implications of the new helium density of activated carbon for our previous measurements of adsorption at high pressure. The result is the disappearance of the inexplicable negative part of the isotherms and even a renewed increase in the curves at high pressure. Moreover, a comparison with Monte Carlo simulations of argon adsorption on microporous graphite is in good agreement with the shape of the adsorption curve at high pressure. Finally, the role of the microporous structure of adsorbents and of the gas-adsorbent interaction in adsorption at high pressure is discussed.
I. Introduction Knowledge of the densities of porous materialssusually powderssis essential for the study of their structure and adsorbent properties. McBain1 used the term “true density” and, in a more descriptive word, Coolidge2 used “skeleton density” for the density of compact solid matter of which the adsorbent is composed. Among techniques for obtaining this density, that based on displacement of an equivalent helium volume has long been considered the most relevant. Suggested in 1922 by Washburn and Buntung,3 the method has been exhaustively studied4-7 and the term “helium density” is currently used in place of the term “true density”. Concerning the adsorption phenomenon, the calculation of the amount of gas adsorbed on a solid surface requires the definition of the gas-solid separationsthe Gibbs dividing surfaceswhich delimits the volume accessible to the gas. Helium density measurements is, in fact, an experimental means to determine the position of this surface which encloses the volume of space from which the solid excludes helium gas. The two basic reasons for the choice of helium as a volumetric fluid are (i) its inert small atom diameter, which should enable it to penetrate into very fine pores, and (ii) its low adsorption at room temperature, which is normally * To whom all correspondence should be addressed. X Abstract published in Advance ACS Abstracts, January 1, 1997. (1) McBain, J. W. The sorption of gases and vapours by solids; George Routledge & Sons: London, 1932; p 79. (2) Coolidge, A. S. J. Am. Chem. Soc. 1934, 56, 554. (3) Washburn, E. W.; Buntung, E. N. J. Am. Ceram. Soc. 1922, 5, 112. (4) Howard, H. C.; Hulett, G. A. J. Phys. Chem. 1924, 28, 1082. (5) Franklin, R. E. Trans. Faraday Soc. 1949, 45, 274. (6) De Boer, J. H.; Steggerda, J. J. K. Ned. Akad. Wetenschap. Proc. 1958, B61, 317. (7) Maggs, F. A. P.; Schwabe, P. H.; Williams, J. H. Nature 1960, 186, 956.
assumed to be negligible. However, the latter hypothesis is a doubtful assumption as has already been pointed out by Maggs7 and Sing.8 Density values thus obtained may be erroneous and can lead to important modifications in adsorption isotherms. The aim of the present work was to deal with this subject and to develop an understanding of porous adsorbent density. As a first step, we experimentally determined the temperature conditions for which helium is not adsorbed; we therefore measured the corresponding “helium density” of the adsorbent. Using these densities, we then measured the adsorption isotherms of helium at high pressure and at room temperature. We next compared experimental results with Monte Carlo simulations carried out by Vermesse and Levesque,9,10 and our conclusions are important statements concerning the role of micropores and gas-solid interactions in the phenomenon of adsorption of gases at high pressure. We also show that our earlier experimental results on excess adsorption on activated carbon as a function of density, for gases such as Ar, Ne, Kr, N2, and CH4,11 could be corrected for negative adsorption at high densities by taking into account the new helium density of the adsorbent. II. Helium Density Measurements Measurements of density of adsorbents were carried out at atmospheric pressure and at temperatures up to 400 °C in the volumetric expansion apparatus shown in Figure 1. It mainly consists of a temperature variable adsorption cell of calibrated volume Vt connected to a fixed (8) Sing, K. S. W. Fondamentals of adsorptionsProceedings of the Engineering Foundation Conference; Mears, A., Belfort, G., Eds.; Engineering Conference: New York, 1983; p 573. (9) Vermesse, J.; Levesque, D. Mol. Phys. 1992, 77, 837. (10) Vermesse, J.; Levesque, D. J. Chem. Phys. 1994, 101, 9063. (11) Malbrunot, P.; Vidal, D.; Vermesse, J.; Chahine, R.; Bose, T. K. Langmuir 1992, 8, 577.
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Figure 2. Temperature variation of helium densities of carbons and zeolites: O, activated carbon; ], graphitized carbon black; b, zeolite 13X; *, zeolite 3 A; [, zeolite 4 A; +, zeolite 5 A. Figure 1. Schematic diagram of the measuring device for the determination of helium density at high temperature: Vt, measurement capsule; R0, large port valve; R1, R2, operating valves; PRT, platinum resistance thermometer; F, furnace; Vr, reservoir capsule; DM, quartz digital manometer (Paroscintific 710); TCB, temperature-controlled bath.
temperature expansion cell of calibrated volume Vr. The adsorption cell enclosed in furnace F was a 316L stainless steel cylinder equipped with axial housing for a standard platinum resistance thermometer (PRT), an expansion valve R1 for helium inlet from the expansion cell, and a large diameter valve R0 allowing for adsorbent filling and regeneration (heating under vacuum). A high precision quartz digital manometer DM (Paroscientific 710, scale 0-100 PSIA) with an accuracy of 10-4 full scale was used for pressure measurements. The expansion cell, the manometer probe, and most of the expansion line including valve R2 were confined in a temperature-controlled bath maintained at constant temperature T0. The accuracy of temperature measurements in both cells was (0.01 K, the precision necessary for the present volumetric determination based on the PVT relationship of helium at high temperature given by the helium IUPAC Thermodynamic Tables.12 Volumes of adsorption cell, Vt, and of the expansion cell, Vr, included between valves R1 and R2 were previously determined by weighing with an accuracy better than 0.1% using xenon as the standard gas.13 They were 37.8 and 11.6 cm3, respectively. The volume of tubing submitted to the temperature gradient between valve R1 and the adsorption cell was sufficiently small (about 12 mm3) so as to be negligible with respect to the volume of the cell (about 38 cm3). Initially, the adsorption cell was completely filled with a weighed amount, m, of the regenerated adsorbent of interest and maintained under high vacuum at the measurement temperature Tm. The previous regeneration of the adsorbent was carried out at a temperature of 400 °C under a vacuum of 10-3 Pa for 12 h. Next, the expansion cell was filled with the helium gas and maintained at T0 under equilibrium at an initial pressure P1 and an initial density F1(T0,P1). Then, the expansion valve R1 was opened, allowing helium expansion into the dead space of the adsorption cell, and the pressure fell to a value P2, which was measured once the new equilibrium state, F2(T0,P2) in Vr and F(Tm,P2) in Vt, was reached and maintained without drift for 1 h. This waiting period was judged necessary to ensure that slow diffusion was not occurring during the measurement. To determine the initial and final equilibrium densities at their respective measured conditions of pressure and (12) IUPAC Helium, International Tables of Fluid State-4; Angus, S., de Reuck, K. M., Eds.; Pergamon Press: London, 1977. (13) Michels, A.; Wassenaar, T.; Louwerse, P. Physica 1954, XX, 99.
temperature, we used IUPAC’s tables for helium, which have a reported accuracy of 0.05%. By using a mass balance equation for the helium gas before and after expansion, and assuming zero adsorption, we calculated the density of the adsorbent via the relation
mF FHe )
FVt - Vr(F1 - F2)
where m is the mass of the adsorbent. Corrections were also made for thermal expansion of the adsorption cell and for the adsorbent. The volumetric thermal coefficients of that used in our experiments varied from 1.8 × 10-6 K-1 for silica gel to 2.7 × 10-5 K-1 for zeolites (given by the suppliers). The expression of the error analysis of the measured helium density contains a term depending on the two pressures P1 and P2 of the form
(P1 + P2)/(P1 - P2) Such a term is minimized for the ratio P2/P1 ) 21/2 - 1, a value obtained when the volume ratio Vt/Vr of the two cells is equal to 3.25. Thus, the total relative precision on FHe is 0.5%, in good agreement with the mean reproducibility of several independent measurement runs carried out on a same adsorbent sample. For measurement of densities at high temperature, the diffusion of helium atoms into the structure of the solid may be considered a possibility. However, two essential observations prove that no diffusion effect occurred. Firstly, the equilibrium pressure did not decrease slowly and continuously, as is normally observed when a diffusion effect takes place. Secondly, a diffusion phenomenon would lead to an increase in helium density with temperature. However, we observed the contrary in the latter case. Moreover, a Monte Carlo diffusion simulation performed under the same physical conditions showed that no gaseous molecules penetrate into the crystal lattice structure of the solid.14 We measured helium densities as a function of temperature up to 400 °C on activated carbon (GAC 250, CECA-ELF-ATOCHEM, France), graphitized carbon (E 1145, Le Carbone-Lorraine, France), zeolites type A and 13X (Siliporite, CECA-ELF-ATOCHEM, France), and silica gel (Kieselgel 60, MERK, Germany). Curves shown in Figure 2 represent the measured temperature variations. Obviously, the main effect of temperature is to decrease adsorbent densities, since it decreases helium adsorption. The exception of graphitized carbon is easily explainable by the fact that it is a nonporous carbon having (14) Levesque, D. Private communication, 1993.
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Langmuir, Vol. 13, No. 3, 1997 541
Table 1. High-Temperature Helium Densities of Carbon, Silica Gel, and Zeolites and Helium Adsorption at Room Temperature and Atmospheric Pressurea
activated carbon graphitized carbon black silica gel 3A zeolite 4A zeolite 5A zeolite 13X zeolite
As specific area (m2 g-1)
FsHe (400 °C) (g cm-3)
∆FsHe (%)
ma (mmol g-1)
ma (cm3 STP g-1)
1030 6 500
2.00 2.12 1.71 2.32 2.31 2.47 2.41
14.5 0.0 36.0 3.9 3.4 8.5 11.2
2.38 × 10-3 0.0 6.35 × 10-3 5.75 × 10-3 5.75 × 10-3 1.17 × 10-3 1.31 × 10-3
5.33 × 10-2 0.0 0.14 0.13 0.13 2.63 × 10-2 2.93 × 10-2
400 400 600
a A , specific area (BET); F s sHe (400 °C), helium densities measured at 400 °C; ∆FsHe, relative deviation defined as ∆FsHe ) (FsHe (400 °C) - FsHe (25 °C))/FsHe (400 °C); ma, amount of gas adsorbed.
a specific surface area of only 6 m2 g-1; thus, it has such weak adsorption that this is entirely negligible even at room temperature. We thus chose it as a nonporous, poorly adsorbing reference substance, and as such it cannot be considered a typical adsorbent. Apparently, for the other adsorbents, no adsorption effect occurs above 250-300 °C, as observed by Maggs et al.,7 for several different types of coals. Finally, taking into account that these adsorbents are regenerated at 400 °C, a temperature at which the all chemical species are desorbed, it is reasonable to consider helium densities obtained at this temperature as reliable densities of these porous materials (Table 1, column 2). This, in fact, follows from Sing’s recommendation.8,15 Deviations between these new density values and those obtained at room temperature were calculated (Table 1 column 3). In most cases, the differences are noticeable and lead to very significant modifications in adsorption isotherms, especially in the high-pressure range. This will be discussed in section IV. III. Helium Adsorption at Room Temperature and Atmospheric Pressure With the present apparatus, it is possible to determine helium adsorption at room temperature (25 °C) and atmospheric pressure. The furnace temperature is kept at 25 °C, and the helium density has the value determined at high temperature. Results are reported in Table 1, columns 4 and 5. It should be noted that because of the high value of the helium specific volume in standard conditions, the amount of adsorbed helium expressed in terms of mass units (column 4) appears to be negligible even though this is not the case when it is expressed in volume units (column 5), since adsorbent specific volumes are on the order of 0.4-0.5 cm3 g-1. This is the main reason why the volume measurement of a porous substance made with helium at room temperature was notably erroneous. A comparison is possible with the results of Maggs et al. for carbons7 and with Suzuki et al. for zeolite X, zeolite NaA, and activated carbon.16 Magg’s values of adsorption, between 3 × 10-2 and 5.5 × 10-2 cm3 STP g-1, are in a reasonably good agreement with our own value of 3.33 × 10-2 cm3 STP g-1 if the difference between our respective carbons is taken into account. On the other hand, adsorption values of Suzuki et al. are systematically higher than those obtained by us by a factor of 10. A comparative analysis of our respective measurements and adsorption procedures did not reveal a possible origin for such important discrepancies. As concerns Henry’s law upon which Suzuki et al. based the presentation of their results, it is well-known that it is particularly reliable at high (15) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603. (16) Suzuki, I.; Kakimoto, K.; Oki, S. Rev. Sci. Instrum. 1987, 58, 1226.
Figure 3. High-pressure adsorption isotherm of helium on activated carbon: +, helium density FsHe ) 2.29 g cm-3; b, FsHe ) 2.00 g cm-3; s, MC simulation curve with BET specific area of 1 030 m2 g-1. Table 2. High-Pressure Adsorption Isotherm of Helium on Activated Carbon at 25 °Ca
a
P (MPa)
1/vm (mol cm-3)
ma (mmol g-1)
19.0 56.5 81.0 109.1 202.6 314.1 401.1 494.5
0.006 948 0.018 213 0.024 146 0.029 953 0.044 743 0.057 346 0.066 057 0.071 980
0.33 0.684 1.01 1.432 2.00 2.70 3.31 3.965
P, pressure/; 1/vm, bulk density; ma, amount of gas adsorbed.
temperature, as shown by Hellemans et al.,17 who experimentally validated Henry’s law for helium above 21 K. IV. High-Pressure Helium Adsorption Isotherms Using the high pressure apparatus previously described,18 we measured helium adsorption up to 500 MPa on the adsorbents mentioned above. The absolute error in our method is on the order of 0.5 mg g-1, corresponding to 0.125 mmol g-1 (since adsorption is a quantity of excess, the relative error is not significant as it depends on the adsorption value itself). Tables 2 and 3 report the results obtained with adsorbent densities measured at high temperature (Table 1 column 2), i.e., with the values we consider as the most reliable. Figure 3 represents, in the case of activated carbon, the isotherms of adsorption (17) Hellemans, R.; Van Itterbeek, A.; Van Deal, W. Physica 1967, 34, 429. (18) Vidal, D.; Malbrunot, P.; Guengant, L.; Vermesse, J.; Bose, T. K.; Chahine, R. Rev. Sci. Instrum. 1990, 61, 1314.
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Table 3. High-Pressure Adsorption Isotherm of Helium on Zeolites at 25 °Ca P (MPa)
a
1/vm (mol cm-3)
ma (mmol g-1)
19.4 59.2 83.0 109.6 204.1 315.3 399.4 482.6
(a) Zeolite 3A 0.007271 0.01900 0.024653 0.030179 0.045009 0.057523 0.064973 0.071241
0.01 0.14 0.446 0.583 1.031 1.873 3.128 3.592
19.4 57.3 80.4 109.1 184.4 306.7 401.1 499.7
(b) Zeolite 4A 0.007084 0.018350 0.023989 0.029960 0.042218 0.056609 0.065045 0.072313
0.01 0.027 0.152 0.42 1.115 1.534 1.993 2.516
19.2 57.9 81.4 108.4 189.3 306.3 397.2 479.2
(c) Zeolite 5A 0.007174 0.018651 0.024334 0.029915 0.043011 0.056640 0.064797 0.070987
0.052 0.20 0.395 0.64 1.054 1.543 1.918 2.129
19.3 59.7 84.6 111.8 212.6 319.7 402.0 490.8
(d) Zeolite 13X 0.007099 0.019024 0.024939 0.030529 0.046098 0.057947 0.065178 0.071778
0.102 0.305 0.52 0.783 1.235 1.927 2.50 3.00
messe and Levesque attempted simulation of adsorption on a microporous rigid interface9 and afterward10 on a graphite crystal having micropores (in fact, missing atoms in the crystal). Their approach is the most well adapted to a comparison with present results, since it is close to the experimental reality, especially for adsorption at high pressure. The system of Vermesse and Levesque is a parallelipipedic cavity containing N gas molecules. Two opposite faces are the planes or the microporous adsorbing surfaces, while the others are submitted to the usual periodic boundary conditions. The interaction between gas molecules is represented by the Lennard-Jones 6-12 potential. As concerns the solid-gas interaction, the potential considered was a hard sphere potential when the adsorbing surfaces were rigid planes or planes comprising a lattice of cylindrical pores. Adsorption obtained with the Monte Carlo simulation is exactly the surface excess adsorption Γ* defined by
Γ* )
N - F*V 2S
F* is the gas bulk density and V the volume accessible to this gas, i.e., the volume in which average gas density is different from zero (considering that the distance between the two opposite adsorbing faces is the distance between the centers of two gas molecules, each one in contact with one of these opposite faces). 2S is the area of adsorbing surfaces and the asterisk signifies reduced quantities with respect to molecular quantities: Avogadro’s number, N; molecular mass, M; Lennard-Jones parameters and σ. The density, F*, is then related to the molar density 1/vm by
1/vm ) F*/Nσ3
P, pressure; 1/vm, bulk density; ma, amount of gas adsorbed.
obtained with the two possible values of helium density (measured at 25 °C and at high temperature). An immediate conclusion is that of the disappearance of the physically unexplainable negative part of the adsorption isotherms. For activated carbon (Table 2 and Figure 3), the slight hump of the isotherm at moderate pressures could be attributed to gradual filling of the microporous structure, the effect of which is to enhance adsorption. At high pressure, as micropores are filled, this contribution to adsorption vanishes and the corresponding curve increases monotonically. As concerns adsorption on zeolites (Table 3), results are very similar. The fact that helium is adsorbed somewhat more on zeolite 13X is probably due to a different cation arrangement and a greater accessibility of this type of zeolite. For zeolites A at low and moderate densities, isotherms are arranged in ascending order with respect to the order of the attractive force effect of their cation, i.e., sodium (4A), potassium (3A), and calcium (5A). At higher densities, for which repulsives forces predominate, adsorption increases, as in the case of activated carbon. V. Comparison with Numerical Calculation Above the critical temperature, a number of Monte Carlo simulations have been carried out to study adsorption of gases on rigid wall interfaces19,20 or inside the microporous structure, including slits21-24 and zeolite cages.25,26 Ver(19) Van Megen, W.; Snook, I. K. Mol. Phys. 1982, 45, 629. (20) Snook, I. K.; Van Megen, W. Mol. Phys. 1982, 47, 1417. (21) Van Megen, W.; Snook, I. K. Mol. Phys. 1985, 54, 741.
The experimental excess adsorption per unit mass of adsorbent, ma, of the preceding section is related to this adsorption Γ* by the equation
ma )
Γ*MAs Nσ2
As is the specific area of the adsorbent determined by the well-known BET method from the measured adsorption isotherm of vapor of nitrogen at 77 K. In fact, it is an essential quantity for comparing adsorptions obtained by experimentation and by simulation. The main result of these Monte Carlo simulations is a monotonic increase with density of adsorption isotherms irrespective of the porous character of the solid-gas interface. Figure 3 reports such an isotherm from simulation of adsorption on rigid nonporous and porous interfaces of a Lennard-Jones gas representing helium at room temperature (σ ) 0.2556 nm and /κ ) 10.22 K, with a reduced temperature T* ) kT/ equal to 29.17, corresponding to T ) 25 °C). This result is parametrized with the BET specific area value of GAC 250 activated carbon of 1 030 m2 g-1 (given by the supplier). Comparison with the experiment leads to the following conclusions: (a) the (22) Tan, Z.; Gubbins, K. E. J. Phys. Chem. 1990, 94, 6061. (23) Van Slooten, R.; Bojan, M. J.; Steele, W. A. Langmuir 1994, 10, 542. (24) Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir 1994, 10, 4606. (25) Razmus, D. M.; Hall, C. K. AIChE J. 1991, 37, 769. (26) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. J. Chem. Phys. 1993, 98, 8919.
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Langmuir, Vol. 13, No. 3, 1997 543 Table 4. Depth, E, of the Lennard-Jones Potential Well for Different Gases and Corresponding Reduced Temperatures, T*
/k T
Figure 4. Recalculated isotherms of adsorption on activated carbon: 0, helium; b, neon; O, argon; 9, krypton; +, nitrogen; 4, methane; e >
