Langmuir 1993,9, 2758-2760
2758
Applicability of the Dubinin-Radushkevich Equation to COa Adsorption on Activated Carbons F. Carrasco-Marin, M. V. L6pez-Ram6n, and C. Moreno-Castilla' Departamento de Qulmica Inorgirnica, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain Received March 19,1993. In Final Form: August 1 8 , 2 9 9 9
The Dubinin-Radushkevich equation (DR)is generally applied to the C02 adsorption data on activated carbons in order to find their micropore volume and also their apparent surface area. This equation is an adaptation of the more general Dubinin-Astakhov equation (DA) with n = 2. The value of n in the DA equation decreases with the percentage of burn-off of the activated carbon, and therefore, the DR equation can be appropriately applied to a few activated carbons with low to medium burn-off. For activated carbonswith medium to high burn-off,the applicationof the DR equation to the C02 adsorption isotherm leads to wrong conclusions. In these cases the experimental data are better fitted by the DA equation with a value of n lower than 2, which makes the apparent surface area obtained by the DA equation greater than that obtained by the DR equation and similar or higher to that obtained with N2 at 77 K by applying the BET equation. Introduction Physical adsorption of gases and vapors is a very useful technique for the characterization of porous solids such as activated carbons. Many molecules with different sizes and polarities can be used as adsorptives,and information about the surface area and pore texture of the solid can be obtained by applying the appropriate equation or method to the adsorption isotherms. The complementary use of N2 at 77 K and C02 at 273 or 298 K, applying the BET equation to the N2 isotherm and the Dubinin-Raduschkevich (DR) equation to the C02 one, has been recommended13 to characterize the carbonaceous materials, and at present, these methods are routinely used. When N2 adsorption at 77 K is compared with C02 adsorption at 273 or 298 K for a series of activated carbons obtained from the same raw material after carbonizing and activating it at a different level of burn-off (BO), one of three situations may occur.3 (i)The apparent surface area with N2, S N is ~ lower , than the apparent surface area with C02, Sco,. This is the case for carbonized materials and even for activated carbons with low BO. This occurs because the microporosity is very narrow or there are constrictions in the entry of the micropores so that there is restricted diffusion of N2 at 77 K. (ii) SN)is quite similar to Sco,. This is the case for activated carbons with low to medium BO, because the above constrictions are removed and the microporosity is equally accessible to both adsorptives. (iii) SN,> SCO,. This generally happens with activated carbons with medium to high BO, and this situation has been explained as due to a wider and very heterogeneous microporosity. Therefore, C02 at 273 K does not detect the same type of microporosity as N2 at 77 K when the micropore size distribution is wide. Thus, whereas Nz at 77 K may fill narrow and wider micropores, C02 at 273 or 298 K willfillthe narrow micropores because of the higher adsorption temperature and lower relative pressure range covered. ~~~
* To whom correspondence should be addrewed. Abstract published in Advance ACS Abstracts, October 1,1993. (1) Marsh, H.; Wynne-Jones, W. T. K. Carbon 1964,1, 269. (2) Mahajan, 0.P.; Walker, P. L., Jr. In Analytical Methods for Coal and Coal Products; Karr, C., Jr., Ed.; Academic Press: New York, 1978; Vol. 1, p 125. (3) Rodriguez-Reinoso,F.; L h - S o l a n o , A .In ChemistryandPhyeics of Carbon;Thrower,P. A., Ed.;Mane1Dekker, Inc.: New York, 1989; Vol. 21, p 1. Q
0743-7463193124O9-2758$Q4.O0/ 0
These explanations are generally accepted and used, in spite of the fact that the DR equation has a limitedvalidity when applied to the characterization of activated carb o n ~ .Since ~ ~ it is only applied to carbons with a homogeneous microporoaity, as is the case for some activated carbons with low to medium burn-off. For activated carbons with a nonhomogeneous microporous structure, Dubinin proposes1° three ways of describing the adsorption isotherms in terms of the theory of the volume f i i g of the micropores (TVFM). The first is based on the assumption of random formation of micropores of different dimensions and normal size distribution. The equation of adsorption obtained is known as the Dubinin-Stoeckli equation.lOJ1 The second way is the application of the two-term DR equation, which may be used only if the microporesare divided into two classes. Finally, the third way involves the use of the DubininAstakhov equation.1°-12 Therefore, some of the above three situations could be a result of the misapplicationof a determined equation or model to the experimental adsorption isotherms. The DR equation13J4reads
W = W,, ex~[-(A/j.3E~)~l (1) This equation (1) is a particular case of a more general expression proposed by Dubinin and A ~ t a k h o v known ~~J~ as the DA equation which reads W = W oexp[-(AIBEJI
(2)
It has been ~ h o w n ~that ' J ~eq~ 2~could be based on a theoretical model involving adsorption energies and their (4) Marsh, H.; Rand, B. J. Colloid Interface Sci. 1970,33, 101. (5) Freeman, E. M.; Siemieniewska, T.; Marsh, H.; Rand, B. Carbon 1970,8, 7. (6)Mahajan,0. P.; Moriehita, M.; Walker, P. L., Jr. Carbon 1970,8, 167. (7) Rand, B. J. Colloid Interface Sci. 1976,56, 337. (8) Huber, U.; Stoeckli,F.; Hourier, J. P. J. Colloid Interface Sci. 1978, 67, 196. (9) Finger, G.; Biilow, M. Carbon 1979,17, 87. (10) Dubinin, M. M. Carbon 1989,27,457. (11) Dubinin, M. M.; Stoeckli,H. F. J. ColloidInterface Sci., 1980,75, 34. (12) Dubinin, M. M.; Astakhov, V. A. Adv. Chem. Ser. 1970,102,69. (13) Dubinin, M. M.; Zaverina, E. D.; Raduahkevich, L. V. Zh. Fiz. Khim. 1947,21, 1351. (14) Dubinin, M. M. In Progress in Surface and Membrane Science; Cadenheed, D. A., Ed.;Academic Press: New York, 1975; Vol. 9, p 1. (15) Stoeckli, H. F. Carbon 1981,19,325. (16) Bansal, R. C.; Donnet, J. B.;Stoeckli, H. F. Active Carbon;Marcel Dekker, Inc.: New York, 1988.
0 1993 American Chemical Society
Langmuir, Vol. 9,No.11,1993 2769
Letters sample BO (%I
Table I. Characteristics of the Activated Carbons from AP and CP Series. SN,( m 2 d Sco,(DR) (mz.gl) Sco,(DA)(m2-g1) WO(cma.gl) VI(cm3.g1) VZ(cm3-g1) Eo(DA)(kJ.mol-l) ~~
AP-2.5 AP-5 Ap-10 CP-5 CP-10
16
490
30 48
633 828 905 1114
40 55
530 587 593 694 744
530 633 920 1081 1423
0.20 0.24 0.35 0.41 0.55
0.25 0.29 0.34 0.40 0.46
0.11 0.19 0.25 0.22 0.27
22.6 19.8 15.2 17.0 13.9
n ____
2.00 1.86 1.56 1.66 1.38
The COz adsorption isotherm was obtained at 273 K.
distribution. In this approach, n reflects the width of the energy distribution, which is related in a complicated way to pore-size distribution. Values of n between 1 and 4 are observed for most carbon adsorbents, with a value of n > 2 for molecular sieve carbons or carbon adsorbenta with very homogeneous and small micropores,9J8J9 whereas values of n < 2 have been found for strongly activated and heterogeneous carbons. Thus, Rand' has used the DA equation with noninteger values of n between 1 and 2 in the case of activated carbons with a broad micropore size distribution, and Dubinin and Stoeckli'l showedthat there is a linear relationship between the parameter n and the heterogeneityof the microporosity when n varies between 1 and 2. It is well known that an increase in the level of BO of an activated carbon makes the micropore size distribution broader, and in these samples the DR equation, i.e., the DA equation with n = 2,applied to the adsorption data could lead to wrong resultsP9J6 and therefore wrong conclusions. Thus, the objective of this paper is to ascertain the validity of the three situations stated above when comparing, for different series of activated carbons, the apparent surface area obtained with nitrogen from the BET method with the apparent surface area obtainedwith carbon dioxide from the DA equation with the value of n that better fits the experimental C02 adsorption data.
Experimental Section Four seriesof activated carbonswere used in the present work. The HA series was obtained from olive stones after carbonizing in N2 at 1273 K and activating in C02 at 1263 K for different periods of time as described elsewhere.20 The B series was prepared from a lignite coal char by activation in C02 at 1113 K as described elsewhere.21*22 The seriesAP and CP were prepared from a subbituminous coal char steam activated at 1113 K as described elsewhere.23 The AP series comes from the original subbituminous coal char and the CP series from the demineralized subbituminous coal char. All the activated carbons were characterized by N2 and CO2 adsorption at 77 and 273 or 298 K, respectively, mercury porosimetry, and He density. The equilibrium time taken to measure N2 and C02 adsorption*was1 h. This time was enough to attain the equilibriumin all cases. The BET equation was applied to the N2 adsorption isotherm in a PIP0 range between and 1.8 X 10-l; the straight lines obtained in the BET plot had a correlation coefficient better than 0.999. The DR and DA equations (17) Stoeckli, H. F. Carbon 1990,28,1. (18) Kraehenbuehl, F.; Stoeckli, H. F.; Addoun, A.; Ehrburger, P.; Donnet, J. B. Carbon 1986,24,483. (19) Dubinii, M. M.; Astakhov, V. A. Zzu. Akad. Nauk SSSR. Ser. Khim. 1971, I, 5. (20) Moreno-Castilla, C.; Carrasco-Marfn,F.; Rivera-Utrilla, J. Fuel 1990,69,354. (21) Rivera-UMla,J.; Utrera-Hidalgo,E.; Ferro-Garch,M. A.; MorenoCastilla, C. Carbon 1991,29,613. (22) Moreno-Castilla, C.; Carrasco-Marln, F.; Utrera-Hidalgo, E.; Rivera-Utrilla, J. Langmuir 1993,9, 1378. (23) Lbpez-Ram6n, M. V.; Moreno-Castilla, C.; Rivera-Utrilla, J.; Hidalgo-Alvarez, R. Carbon 1993,31, 815.
were applied to the C02 adsorption isotherm. The DA equation has three unknown parameters: WO,EOand n. In order to calculate them, it was therefore necessary to apply a computer program with an iterative method to the experimental results. The iterative method utilizes an approach based on minimizing the residual sum of squares. The initial values of W Oand EO were those obtained from the DR equation, and n was taken as 2 in order to start with the computer program. The fiial WO, EO,and n values were those that better fitted the DA equation to the experimental data points. In all cases the residual sum of squares was better than lo". Both DR and DA equationswere applied in the same range of relative pressures. Thus, the PIP0 range in the case of C02 adsorption at 273 K was between 2 X 10-4 and 2 X 10-2, and in the case of CO2 adsorption at 298 K it was between 1 X 10-4 and 1 X From the measurements of He density and mercury porosimetry up to 4000 kg/cm2,values of VIand V2 were obtained. VIis the volume of pores with diameter smaller than 3.6 nm, i.e., the micropore volume plus the volume of the lower limit of the mesopores (from 2 to 3.6 nm in diameter). V2 is the volume of pores with diameter greater than 3.6 nm. Since in microporous activated carbons the term surface area does not have much physical meaning, it is better to refer to pore However, despite its limitations in these cases,surface area data are widely used: and they are termed as apparent surface area, which means the area that would result if the amount of adsorptiverequired to fill the micropores were spread as a close-packed monolayer of molecules, as suggested by Barrer.2s Thus, in order to calculate the apparent surface areas of the samples, the cross sectional area for the N2 molecule was taken as 0.162 nm2, and for C02 at 273 or 298 K it was taken as 0.187 or 0.195 nm2, re~pectively.~The value of the affinity coefficient, 6,in eq 1 and 2 for C02 was taken as The CO2 liquid density at 273 and 298 K was taken as 1.03 and 0.97 g / ~ m ~respectively. ,"~~
Results and Discussion Some of the characteristics of the samples used in this work are summarized in Tables 1-111. In all series of activated carbons, the value of n of the DA equation decreases when the BO increases; this trend was found before, and it is well documented in the literature.7J6This variation has been related to an increase in the heterogeneity of the microporosity as the BO progresses. The variation of n with the BO seems to depend on the raw material and the method of preparation of the activated carbon, as shown in Figure 1. However, it can be said that for activated carbons with low to medium BO (APseries up to about 16% BO, BC series up to about 32% BO, and HA series up to about 17% BO) n 2 2.This is indicativethat the microporosityis rather homogeneous (24) Gregg,S. J.; Sing,K. 5.W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982. (25) Barrer, R. M. In Structure and Properties of P o r o u Materials; Everett, D. H., Stone, F. S., E&.; Butterworths: London, 1958. (26) Ismail, I. M. K. Carbon 1991,29, 119.
2760 Langmuir, Vol. 9, No. 11, 1993
Letters
Table 11. Characteristics of the Activated Carbons from BC Series. sample BO ( % ) SN,(m2-g1) Sco,(DR) (mz.gl) Sco,(DA) (m2.g1) W O(cm3.g9 VI (cm3-gl) V2 (cm3.g9 Eo(DA) (kJ-mol-l) BC-1 BC-7 BC-14 BC-18 BC-23 BC-32 a
1 7 14 18 23 32
210 310 432 533 540 700
408 478 527 660 674 736
368 422 475 527 681 711
0.14 0.16 0.18 0.20 0.26 0.27
0.15 0.17 0.18 0.21 0.27 0.32
0.05 0.05 0.06 0.07 0.05 0.08
n
27.7 27.6 26.5 24.5 22.7 21.8
2.32 2.30 2.32 2.21 1.98 1.91
The COz adsorption isotherm was obtained at 273 K.
Table 111. Characteristics of the Activated Carbons from HA Series. sample BO (% ! ) SN,(m2.g1) ScoADR) (mz-gl) ScdDA) (m2-g1) W0(cm3-g1) VI (cm3.g1) VZ(cmg-gl) Eo(DA) (kJ-mol-l) HA1 HA2 HA3 HA4 HA5
HA6
0 5 8 17 27 44
333 412 424 594 790 1171
671 709 717 821 886 930
580 751 764 834 1025 1419
0.22 0.29 0.30 0.32
0.28 0.30 0.30 0.35 0.40 0.50
0.40 0.55
0.15 0.15 0.20 0.27 0.29 0.40
n
22.8 22.0 21.9 21.4 20.5 17.6
2.22 1.93 1.91 1.88 1.84 1.64
The COz adsorption isotherm was obtained at 298 K.
1
-0.70
1.60
1.20
-I I
0
I
I
20
40
1
60
-2.20
I
0.00
I
4.00
I
I
8.00
12.00
I
16.00
4) Figure 1. Variation of n with the BO of the different series of activated carbons: ( 0 ) BC samples, (A)HA samples, (0) AP samples, (v)CP samples.
Figure 2. Application of DR and DA (with n = 1.38)equations to COz adsorption at 273 K on the CP-10sample.
within this range. The Scoz (DA) values are fairly close or similar to the Sco, (DR) and higher than or close to the SN,values, depending on whether or not there is restricted accessibility of N2 at 77 K to the microporosity of the sample, as stated before in points i and ii. The values of the micropore volume, W O(DA), in these cases, is close to or coincident with the pore volume VI,which might indicate that the DA equation applied to the C02 adsorption isotherm essentially gives the micropore volume of the samples. For activated carbons with medium to high BO, n < 2, Figure 2 shows, as an example, how the DR equation fits the CO2 adsorption data on sample CP10. The DR plot is curved over the whole range of log2(P/Po), which according to Marsh and Rand4 is a type B deviation, and therefore, the application of this equation is pressured e ~ e n d e n t .Figure ~ 2 also shows that the best equation that fits the experimental data over the whole range of relative pressures is the DA with a value of n equal to 1.38. In these cases Sco, (DA) is always higher than ScoZ(DR), and if the DR equation is applied to the C02 adsorption data on samples with medium to high BO, wrong conclusions are obtained. Thus, if s~~ and Scoz (DR) are comparedfor samples AP-5, AP-10,CP-5,CP-10,and HA6, one can argue that for these samples COz only fills the
ultramicropores whereas N2 fills the ultra- and supermicropores (the same as stated in point iii of the Introduction); i.e., N2 and CO2 do not detect the same type of microp~rosity,~ and therefore, S N>~Sco, (DR). However, if the DA equation is used with the appropriate n value that better fits the experimental adsorption data, one can find that Sco, (DA) is equal or higher than SN,,which demonstrates that C02 can fill the ultra- and supermicropores, and even in some samples with well-developed meso- and macroporosities, as in samples AP-10, CP-5, CP-10, and HA-6, the C02 is adsorbed on the external surface of the micropores as is evident when comparing their WOand VI and from their low EOvalues. In conclusion, these data clearly show that for activated carbons with medium to high BO the DR equation applied to the C02 adsorption isotherm leads to wrong conclusions because it is not the best equation that fits the experimental data because it is pressure-dependent. So, in these cases it is better to use the DA equation with the appropriate value of n applied to a large number of experimental adsorption data obtained over a wide range of relative pressures. Acknowledgment. We thank CECA (ProjectNo.7220EC/758) and CICYT (Project AMB92-1032) for financial support.
00
lOB'(Po/P)
