J. Phys. Chem. B 2000, 104, 313-318
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Characterization of Porous Materials by Gas Adsorption: Do Different Molecular Probes Give Different Pore Structures? S. Scaife Department of Chemistry, UniVersity of Wales at Bangor, Bangor, Gywnedd, LL57 2DG, U.K.
P. Kluson and N. Quirke* Department of Chemistry, Imperial College, South Kensington, London, SW7 2AY, U.K. ReceiVed: August 30, 1999; In Final Form: October 26, 1999
Amorphous materials are typically characterized using nitrogen adsorption isotherms at 77 K to obtain pore size distributions. However, higher temperatures and different adsorbates could also be used. We have measured the adsorption isotherms of carbon dixoide, methane, nitrogen, and argon at room temperature and 77 K on the typical high surface area amorphous activated carbon AX21. We analyze these isotherms using density functional theory to obtain pore size distributions and explore whether they vary with the adsorbate used or with temperature. We find, for example, that the pore structures predicted for AX21 using nitrogen at 77 K and carbon dioxide at 293 K are quite different, with carbon dioxide showing a unimodal micropore peak at 10.3 Å not seen at 77 K by nitrogen or argon.
1. Introduction Gas adsorption is a standard tool for the characterization of porous materials.1 In particular, the nitrogen adsorption isotherm taken at 77 K for a given adsorbent is commonly used as input to methods for obtaining pore size distributions based on the solution of the integral
V(P) )
∫HH
max
f(H)ν(H,P) dH
(1)
min
where V(P) is the experimentally determined excess volume of nitrogen (at STP) per gram of material, f(H) is the required pore size distribution, and V(H,P) is the excess volume of nitrogen at pressure P in a pore of size H. The integral is over all pore sizes H. The adsorption integral, eq 1, is a Fredholm equation of the first kind. These present many difficulties; solutions may only be possible for certain “kernels” V(H,P) for certain functions f(H). There may, on the other hand, be an infinity of solutions, from which we must choose the physically reasonable one corresponding to our problem. The equation is ill conditioned in that small changes in the kernel or the function V(P) may cause large changes in f(H). Despite these theoretical difficulties, there are several procedures available which, for the materials of interest here, provide useful solutions: for example, the zero-order regularization methods2 or a straightforward best fit to V(P) by varying f(H).3,4 In order to employ such methods to solve eq 1, a model of the pore structure geometry is required. It is usual when treating carbons to assume that the microstructure can be approximated by a polydisperse assembly of infinite slit pores whose walls are formed by semiinfinite graphite slabs. Other geometries may be chosen for different materials. Given a fixed geometry, the “local” isotherms V(H,P) can be calculated and the integral solved for f(H). The conventional approach1 has been to obtain V(H,P) by employing macroscopic approximations such as the Kelvin * Corresponding author.
equation or semiempirical methods such as the Horvath and Kawazoe5 correlation. For materials containing a range of pores including subnanometer voids, such procedures can be very inaccurate. It was suggested by Seaton et al.3 in 1987 that molecular theory and simulation could provide accurate data for the isotherms of model pores provided reasonable assumptions were made concerning the interaction of gas molecules with graphitic surfaces. Subsequent work by a range of authors6-11 has shown that local isotherms obtained from density functional theory or molecular simulation provide a more complete description of adsorption in regular pores and as a result more reliable pore size distributions. In contrast to the polydisperse regular pore models, several authors have suggested the use of “virtual carbon” models which contain more of the local disorder likely to be present in real carbons. For example, MacElroy et al.12 used networks of randomly etched graphitic slit pores, Segarra and Glandt13 simulated collections of randomly oriented carbon crystallites (see also the random pore sequences of Biggs and Agarwal14), an approach extended by Gubbins and co-workers15 using reverse Monte Carlo to generate assemblies of idealized basal planes of graphite consistent with input carbon-carbon radial distribution functions. Such approaches, while likely to lead to a much improved understanding of adsorption on amorphous microporous materials, have the disadvantage of introducing many more variables to describe the microstructure. Because of its simplicity and undoubted success in practical applications, the slit pore model is likely to remain for some time yet the method of choice for the characterization of disordered carbons and the basis for linking properties such as fluid adsorption, separation, and transport to microstructure. In view of its continuing importance, we have undertaken a detailed study of the slit pore size distribution for a typical material, the activated carbon AX21, refining methods outlined in previous papers, and extending them to different gases (argon, methane, carbon dioxide) and to room temperature. We explore whether mi-
10.1021/jp9930752 CCC: $19.00 © 2000 American Chemical Society Published on Web 12/18/1999
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cropore characteristics determined within the slit pore model change with temperature or with the nature of the physical interactions between the adsorbing gas molecule and the micropore surface. We find significant differences between the microstructures determined at 77 K and room temperature, which we speculate, may be due to the blocking of the smallest pores by frozen nitrogen (or argon) at 77 K (see section 5). 2. Experimental Measurements In order to be sure of comparing isotherms for the same material (different samples of activated carbon with the same designation may vary considerably in their adsorption characteristics) we have performed a new set of measurements of gas adsorption (nitrogen, methane, argon and carbon dioxide) on a single sample of AX2116 and on graphitized carbon Vulcan.17 The adsorption equilibria of argon (77 K), nitrogen (77 K, 293.1 K), methane (293.1 K), and carbon dioxide (293.1 K) on graphitized carbon Vulcan and activated carbon (AX21) were measured. The gases were supplied as follows: argon, methane, and carbon dioxide as ultra-high-purity gas (99.99%) supplied by BDH Lab. Gas Services; nitrogen as high-purity gas (99.999%) supplied by Air Products; and helium (used for “dead space” calibration) as high-purity gas (99.9%) supplied by Air Products. The volumetric adsorption measurements were carried out in a static regime on standard Coulter commercial equipment, the Omnisorp 100. At 293.1 K the adsorption equilibrium of each gas was measured repeatedly under constant conditions (five to seven times) to evaluate the average adsorption isotherm and standard deviation of each point. Each sample was outgassed under high vacuum (10-5 Torr) before a measurement (523 K for 16 h (Vulcan), 573 K for 24 h (AX21)). The volume of gas adsorbed was determined as a function of the gas bulk pressure. At 293.1 K the low-pressure-high-temperature adsorption of gases was particularily sensitive to kinetic effects. To reduce them, 4-7 g of an adsorbent was used in each experiment and the default equilibration time was set to its lowest limit. When the change in gas pressure became negligible for nine consecutive data points recorded in a 10 s interval, the adsorption of gas was considered to be at equilibrium and the gas pressure changed to the next step. In this way, reproducible data were obtained. The adsorption dose value was typically 5-15 Torr. The dead space volume (volume of the sample holder) was measured by allowing helium to enter the glass holder with a sample under experimental conditions. After each set of runs the apparatus (pressure transducers) was recalibrated; the zeroing and spanning of the low 10 Torr, high 1000 Torr transducers were corrected if necessary. At 77 K except for the cryogenic bath and different equilibration conditions (20 data points in a 20 s interval) the experimental arrangement was identical to 293.1 K. 3. Methods The method used to obtain the pore size distribution comprises three stages: (a) determine a molecular model for the gas-pore wall interaction, (b) generate a database of local isotherms V(H,P) using density functional theory (DFT),6,8 and (c) invert the adsorption integral, eq 1. In what follows, we assume that the inner surface of a pore in AX21 adsorbs in the same way as the low surface area standard carbon Vulcan. Section 3.1 describes the formulation of a molecular model which reproduces the measured isotherms for gas adsorption on Vulcan when used in density functional theory (described in detail in refs 6 and 8). Section 3.2 contains
Figure 1. Fit to the low-pressure nitrogen adsorption on Vulcan at 77 K: (full line) experimental data (error bars represent the standard deviation of a series of experiments on the same sample); (filled circles) the best fit one-center Lennard-Jones model from DFT.
Figure 2. Fit to the low-pressure argon adsorption on Vulcan at 77 K: (full line) experimental data (error bars represent the standard deviation of a series of experiments on the same sample); (filled circles) the best fit one-center Lennard-Jones model from DFT.
TABLE 1: Lennard-Jones Parameters for the Fits to Nitrogen and Argon Adsorption on Vulcan at 77 K (Figures 1 and 2) gas
ff (K)
sf (K)
σff (nm)
σsf (nm)
N2 Ar
93.98 119.8
53.46 54.86
0.3572 0.341
0.3486 0.3405
comments on the local isotherm databases, and section 3.3 discusses the solution of eq 1. 3.1. Gas-Solid Interaction Model. The inner pore surface of a slit pore is assumed to interact with adsorbing gases in the same way as Vulcan. This assumption has the merit of including in the model of the gas-solid interactions some of the effects of surface roughness (Vulcan has a surface area of ∼70 m2/g compared to an apparent surface area of 3080 m2/g for AX21) likely to be present in the real material. The gas-solid interaction is taken to be a one-center Lennard-Jones/Steele 104-3 potential18 with parameters determined by fitting to our new experimental data for Vulcan. Gas-gas parameters were taken from the literature19 in the first instance and adjusted as necessary. Figures 1 and 2 compare measured and predicted adsorption isotherms for nitrogen and argon at 77 K obtained from a non local density functional theory known to be in good agreement with Gibbs ensemble simulation of adsorption in slit graphitic pores (a full description of the method and comparisons with molecular simulation are given in refs 7 and 8.) The best fit parameters are given in Table 1. In previous work we have shown that it is not possible to fit both low- and high-pressure nitrogen adsorption data on Vulcan using a one-center Lennard-Jones7 or a two-center LennardJones model20 combined with the Steele potential. A considerably improved fit can be obtained using a hybrid model20 but for our present purposes we employ the fit shown in Figures 1
Characterization of Porous Materials by Gas Adsorption
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Figure 5. Sample slit pore isotherms (reduced density) from the room temperature CO2 database: from top to bottom H ) 7, 8, 9, 10, 15, 20, and 31 Å. Figure 3. Fit to gas adsorption on Vulcan at 293 K: (full line) experimental data in the order from top to bottom, CO2, CH4, and N2 (error bars represent the standard deviation of a series of experiments on the same sample); (filled circles) best fit one-center Lennard-Jones model from DFT.
TABLE 2: Model Parameters at 293 K (Used in DFT with 5σ Cutoff and Standard Carbon Parameters σss (nm) ) 0.34, Ess (K) ) 28) ff (K)
sf (K)
σff (nm)
σsf (nm)
CO2 CH4 N2
165 148.1 105
67.97 64.4 54.47
0.391 0.381 0.3572
0.366 0.3605 0.3486
σ
gas
data (potential parameters listed in Table 1) display sharp phase transitions in the larger pores due to capillary condensation and in the smaller pores resulting from the simultaneous formation of monolayers (layering) on both pore surfaces, filling the pore.7 The room temperature CO2 database (to 1 bar, potential parameters listed in Table 2) displays simple pore filling with adsorption a linear function of pressure for all but the smallest pores. Clearly pore filling in the larger pores takes place at pressures higher than one bar. No sharp features are present in the isotherms at room temperature. This leads to much smoother fits of the experimental isotherms (compare Figures 8 and 10). 3.3. Inverting the Adsorption Integral. The final stage in deriving a pore size distribution from the measured adsorption isotherms is to invert the adsorption integral (eq 1). In this work we employ the procedure described in previous papers3,7 of assuming f(H) to be a sum of log-normal functions
f(H) )
Figure 4. Sample slit pore isotherms (reduced density) for nitrogen at 77 K. From left to right the pore widths are 9, 10, 15, 20, 30, and 31 Å; the weakest adsorption is for H ) 8 Å (bottom right).
and 2 up to 0.1 bar for nitrogen and 0.022 bar for argon where they are satisfactory. The layering seen in the DFT argon fit is to be expected on a smooth Steele model surface at low temperatures but is probably disrupted in the experimental isotherm by defects on the Vulcan surface. The adsorption isotherms of carbon dioxide, methane, and nitrogen at room temperature on Vulcan are shown in Figure 3. In order to obtain the best possible fit to the nitrogen data, the Lennard-Jones parameters have been changed slightly. An excellent fit is obtained for all three gases to 1 bar. The room temperature parameters are reported in Table 2. The use of effective spherical Lennard-Jones model potentials for anisotropic molecules with permanent charge distributions is an approximation which will be removed in later work.21 In all calculations the surface area of Vulcan has been fixed at 72.64 cm3/g, the BET surface area obtained from the experimental nitrogen isotherm at 77 K. 3.2. Local Isotherm Databases. Figures 4 and 5 show selected isotherms from the nitrogen database at 77 K and the CO2 database at room temperature, respectively. The nitrogen
∑i Ri/(γiH(2π)0.5) exp(-(ln H - βi)2/(2γi))
(2)
and varying the free parameters Rβγ until a satisfactory fit is achieved to the experimental isotherm. Various procedures were used to achieve a good fit, all leading to similar solutions. The data presented here were obtained using a Monte Carlo search procedure22 to minimize the root mean square deviation r between the predicted adsorption isotherm for a given set of parameters {Rβγ} and the experimental isotherm, typically in a minute or less on a 266 MHz processor laptop. Section 4 includes a comparison between the pore size distribution (PSD) resulting from a “free fit”, treating f(H) as a histogram23 in which the volume associated with each range ∆H is varied to minimize r and the PSD obtained from eq 2. 4. Results 4.1. Pore Size Distributions at 77 K. The adsorption isotherm for nitrogen on AX21 at 77 K is shown in Figure 6 together with the best fit for P < 0.1 bar. The pore size distributions resulting from fitting to the full and partial (
