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Micropore Size Distributions of Activated Carbons S. Blacher,*,† B. Sahouli,† B. Heinrichs,† P. Lodewyckx,‡ R. Pirard,† and J.-P. Pirard† Laboratoire de Ge´ nie Chimique, University of Lie` ge, Sart-Tilman B6a, B-4000 Lie` ge, Belgium, and NBC Division, Belgian Army Service of Technological Applications, Martelarenstraat 181, B-1800 Vilvoorde (Peutie), Belgium Received July 26, 1999. In Final Form: May 11, 2000
Introduction Many applications of activated carbons require a good knowledge of microporosity. The relevant parameters which characterize a microporous system are the specific surface area of micropore walls, the total micropore volume, and the micropore size distribution (MPSD). In the last 10 years, various models have been developed to determine the MPSD. Those models are based on different geometric and physical assumptions. As was pointed out by Jaroniec et al.,1 “there is no universal method for this kind of characterization”. In fundamental research or in industrial applications the criterion used for choosing between the various models is sometimes not dictated by the underlying model assumptions but by calculation facilities or by the software included in the adsorption-desorption measurement device. The four most popular methods to derive the MPSD function are the following (we will only enumerate them briefly since they are extensively described in the literature). MP Method.2 This method is an extension of de Boer’s method for micropore analysis. It uses the t-plot to construct the PSD function. Its main disadvantage lies in the fact that the adsorption process on which it is based, the BET mechanism, is not relevant for microporous materials. It is generally applied assuming slit shape pores. TVFM Methods. These methods are based on the theory of micropore volume filling introduced and developed by Dubinin.3 In this context, we mention the models of Dubinin-Radushkevich4 (DR), Dubinin-Radushkevich-Astakhov (DA),5 Dubinin-Radushkevich-Stoeckli (DRS),6 Stoeckli (S),7 and Jaroniec-Choma (JC).8 In these models, the dependence of the characteristic adsorption energy on pore size is used to determine the micropore width (w) (DR, DA) and the MPSD (DRS, S, JC). Horvath-Kawazoe (HK) Method.9 An analytical equation for the average potential in a micropore of a † ‡
University of Lie`ge. Belgian Army Service of Technological Applications.
(1) Jaroniec, M.; Madey, R.; Choma, J.; McEnaney, B.; Mays, T. J. Carbon 1989, 27, 77. (2) Mikhail, R. S.; Brunauer, S.; Bodor, E. E. J. Colloid Interface Sci. 1968, 26, 45. (3) Dubinin, M. M. In Progress in Surface and Membrane Science; Cadenhead, D. A., Ed.; Academic Press: New York, 1975; Vol. 9, pp 1-70. (4) Dubinin, M. M.; Zaverina, E. D.; Radushkevich, L. V. Zh. Fiz. Khim. 1947, 21, 1351. (5) Dubinin, M. M.; Astakhov, V. A. Adv. Chem. Ser. 1971, 102, 69. (6) Dubinin, M. M.; Stoeckli, H. F. J. Colloid Interface Sci. 1980, 75, 34. (7) Stoeckli, F. Carbon 1989, 27, 962. (8) Jaroniec, M.; Choma, J. Carbon 1988, 26, 747. (9) Horvath, G.; Kawazoe, J. J. Chem. Eng. Jpn. 1983, 16, 470.
given geometry is derived. This equation relates the adsorption potential with the micropore size and allows each amount adsorbed at a relative pressure to be expressed in terms of the width of a slit shape pore. Saito et al.10 extended this model to cylindrical pore shapes. Simulation Methods Based on Statistical Mechanics. These methods are based on the solution of the generalized adsorption isotherm (GAI). In this equation the measured adsorption isotherm V(p) at pressure p and the unknown MPSD, f(w), are related by the expression
V(p) )
∫LL
F(p,w) f(w) dw
max
min
where F(p,w) is the model isotherm kernel and Lmin and Lmax are the widths of the smallest and largest pores in which adsorption takes place. To calculate the individual (or local) isotherm F(p,w,), two approaches have been used: grand canonical Monte Carlo (GCMC) molecular simulation of the pore adsorption12 and the density functional theory (DFT). A local mean field DFT was first used by Seaton et al.13 (SWQ), and later, Latoskie et al.14 and Olivier et al.15 improved this method using a nonlocal mean field DFT. These methods are considered as the more quantitatively accurate approach to determine the MPSD and small mesopore structures. However, when the GAI equation is solved, well-known mathematical difficulties arise because, as an ill-posed problem, it has no unique solution. Comparisons between MPSDs of activated carbons obtained by the various methods from N2 adsorptiondesorption measurements have been performed previously. Russel et al.16 compared MPSDs of BPL activated carbon by the MP, JC, HK, and SWQ models. They found that MP and HK MPSDs agree with a maximum at 0.8 or 0.9 nm, JC is broader with a maximum at 0.6 nm, and SWQ, which is highly asymmetric, has a sharp peak centered at 12 Å. Carrot et al.17 determined the MPSD of a series of active carbons with various burnoffs by the S, DRS, HK, and GCMC models. They discarded the MP model as they consider it to be incorrect. They found that HK gives unrealistically low values, that S and GCMC yield similar MPSDs, and that the DRS model yields a smaller estimate of pore sizes. The objective of this note is to show new comparisons of the MPSDs obtained using different models to discuss the relevancy of the use of this representation to characterize microporosity. 2. Experimental Section Three different types of commercially activated carbons have been investigated: BPL-HA (Chemviron Carbon, BPL), SCII (Chemviron Carbon), and R1 Extra (Norit, R1E). N2 adsorption (10) Saito, A.; Foley, H. C. AIChE J. 1991, 37, 429. (11) Jaroniec, M; Patrykiejew, A.; Borowko, M. In Progress in Membrane and Surface Science; Cadenhead, D. A., Danielli, J. F., Eds.; Academic Press: New York, 1981; Vol. 14, pp 1-68. (12) Mays, T. J. In Fundamental of adsorption; Le Van, M. D., Ed.; Kluwer: Dordrecht, The Netherlands, 1996; pp 603-608. (13) Seaton, N. A.; Walton, J. P. R. B.; Quirke, N. Carbon 1989, 27, 853. (14) Lastoskie, C.; Gubbins, K. E.; Quirke, N. J. Phys. Chem. 1993, 97, 4786. (15) Olivier, J. P. J. Porous Mater. 1995, 2, 9. (16) Russel, B.; Le Van, D. Carbon 1994, 32 (5), 845. (17) Carrott, P. J. M.; Ribeiro Carrott, M. M. L.; Mays T. J. In Fundamentals of Adsorption Conference FOA6; Meunier, F., Ed.; Elsevier: New York, 1998; p 677.
10.1021/la990997n CCC: $19.00 © 2000 American Chemical Society Published on Web 07/13/2000
Notes
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Figure 1. Adsorption isotherms of BPL, R1E, and SCII activated carbons. isotherms were measured at 77 K on a Micrometrics ASAP 2010M. MP, HK, and DA methods have been implemented in our laboratory using Matlab software. The MPSD from the DFT model was given by the software supplied with the Micrometrics ASAP 2010M device.
Results and Discussion The adsorption isotherms for the three activated carbons are shown in Figure 1. They are nearly of type I. Figure 2 shows the MPSDs of the three activated carbons determined by the MP, HK, and DFT methods. In the three cases, MP distributions look like normal distributions; i.e., they are nearly symmetrical and narrow. HK distributions correspond well with the MP distribution for the three samples. For the SCII sample a maximum arises at the very lower limit of the MPSD curve. DFT distributions often present noisy fluctuations that can mix with the real distribution and prevent determination of a mean pore width. To describe detailed features of the pore structure, Jagiello et al.19 applied a regularization procedure to smooth MPSD curves. In our case, the sharp minima observed at about 0.6 and 1 nm are clearly artifacts. These features, which have been reported and discussed by Olivier18 and recently observed by Jagiello et al.,19 are attributed to a pore model used in DFT calculations that is inadequate to represent activated carbons. Despite these limitations and for the sake of completeness, an average width has been calculated considering arbitrarily the range 0.3 nm < w < 2.5 nm. Table 1 presents the correspondent average width and the standard deviation for each carbon. It can be seen that the discrepancy between the various average widths given by the four models is less than 10%. Taking into account the distinct assumptions on which the used models are based, this result is quite surprising. After comparing MPSDs of BPL carbon obtained with five independent methods, Russel et al.16 conclude that “each model embodies a degree of uncertainty, and it is difficult to discern which is the most accurate”. We thought that the real dilemma is not the accuracy of the models but why a set of models based on so different assumptions gives so similar results. (18) Olivier, J. P. Paper presented at the 1997 AIChE Annual Meeting, Los Angeles. (19) Jagiello, J.; Tolles, D. In Fundamentals of Adsorption Conference FOA6; Meunier, F., Ed.; Elsevier: New York, 1998; p 629.
Figure 2. Micropore size distributions of (a) BPL, (b) R1E, and (c) SCII activated carbons.
We do not have the answer, but in our opinion this behavior could be the result of the extremely complex
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Notes
Table 1. Average Width and Standard Deviation of Activated Carbons method
BPL w (nm)
RIE w (nm)
SCII w (nm)
MP DA HK DFT
0.87 ( 0.14 0.84 ( 0.25 0.95 ( 0.09 1.01 ( 0.21
0.87 ( 0.13 0.83 ( 0.25 0.96 ( 0.13 0.84 ( 0.22
0.89 ( 0.11 0.78 ( 0.16 0.82 ( 0.08 0.84 ( 0.24
micropore structure of activated carbons. In fact, models attempt to describe the textural structure of a microporous material from adsorption measurements in which the dimensions of the pore space are commensurate with the dimensions of the adsorbate molecules. In this region, that is, the crossover between molecular scale and material texture, microporosity could be interpreted as a phase transition in which fluctuations are so important that model assumptions are irrelevant. This would mean that in the micropore range the pore distribution exhibits some kind of universality. A fundamental question remains open, how to choose a model to have an indication of surface heterogeneity. Common sense advises us to carefully examine adsorption isotherms before using sophisticated models. Indeed, in most cases, type I isotherms yield similar MPSDs. This behavior is patently shown in the study performed by Carrot et al.17 on various burnoff activated carbons. For low burnoff samples, isotherms of adsorption are similar to type I isotherms, and in this case MPSDs for the S and GCMC models agree very well. In the case of higher burnoff samples, the adsorption isotherm displays, after the initial rise, a more rounded knee than in the other cases. This signifies that pore sizes extend in the region of small mesopores,17 and in this case the agreement between the two considered models is no longer maintained.
The same kind of behavior has also been noticed in the evaluation of the microporosity of activated carbon. Wood20 demonstrated that, for most microporous activated carbons, the adsorbed volume in a monolayer (VM) calculated by the BET model and the micropore volume (VDR) calculated by the DR model, both determined from N2 isotherms, are related by the simple expression VDR ) 1.1VM. The author gives a maximal error on VDR of approximately 15%. Conclusions The four most popular methods developed in the last 10 years have been used to determine the MPSDs of four different types of commercially activated carbons. These methods differ in geometric and physical assumptions, and some of them require a very sophisticated numerical treatment and time-consuming calculations. Nevertheless, the average micropore size does not seem to depend on the model used. This behavior could signify that the pore distribution of activated carbon exhibits some kind of universality. Acknowledgment. S.B. is very much indebted to the Conseil de la Recherche, ULG, Belgium, for financial support. B.H. is grateful to the FRIA, Belgium, for a Ph.D. grant. We warmly thank the unknown “reviewer 3” for his constructive and interesting comments, and also for his good sense. LA990997N (20) Wood, G. O. The European Carbon Conference “Carbon 96”, Newcastle, U.K., 1996; p 606.
