Langmuir 1991, 7, 2719-2722
2719
Evaluation of Energetic Heterogeneity and Microporosity of Activated Carbon Fibers on the Basis of Gas Adsorption Isotherms M. Jaroniec. and R. K. Gilpin Department of Chemistry, Kent State University, Kent, Ohio 44242
K. Kaneko Department of Chemistry, Chiba University, Chiba-City, 260 Japan
J. Choma Institute of Chemistry, WAT 00908,Warsaw, Poland Received June 19,1991. In Final Form: August 1, 1991 Measurements of low-temperature nitrogen adsorption isotherms are used to study the energetic heterogeneity and microporosity of cellulose- and poly(acrylonitri1e)-basedactivated carbon fibers. The energeticheterogeneities of these materials are characterized by adsorptionpotential distribution functions which are the compositeof two overlappingpeaks that arise from the adsorbents biporous microstructures. A two-term Dubinin-Radushkevich equation is used to model the micropore-filling mechanism in the materials.
Introduction The activation of carbon fibers substantially changes their physicochemical properties, especially their surface and structural heterogeneities. During this process microporous structures are created in the materials. Simultaneously, new surface groups are formed and the population of the existing primary functional groups is altered. Consequently, activated carbon fibers (ACF) are highly porous materials with small mesopore surface areas1I2and internal structures which consist of slitlike micropores that are separated by thin graphite walls.3 Adsorption on ACF is a complex phenomenon. Since their structuresare not rigid, they can be perturbed during the adsorption process, resulting in shrinkage of the intergraphitic spacing and swelling of the micropores.4J Although micropore filling is the dominate adsorption mechanism on activated carbon fibers because of their high porosity,1121e the presence of graphite-like microcrystallites in these materials also seems to contribute additional adsorption features characteristic of those found on graphitized surfaces.' Extensive characterization studies of granulated activated carbons have shown that microporosity contributes substantially to their total energetic heterogeneity (see works 8 and 9 and references therein). Similarly, since the external surface areas of ACF are very small,lI2their microporosity is expected to be the primary source of energetic heterogeneity. Even for solids with uniform micropores which are similar in shape and size, one can (1) Kaneko, K.; Suzuki, S.; Kakei, K. Tam0 1989, 140,288. (2) Kakei, K.; Ozeki, S.; Suzuki, T.; Kaneko, K . J. Chem. SOC.,Faraday Trans. 1990,86,371. (3) Kakei,K.; Oaeki, S.; Suzuki,T.; Kaneko,K. The IUPAC Conference on Characterization of Poroua Solide, Alicaute, Spain, 1990. (4) Sumki, T.; Kaneko, K. Carbon 1988,26,743. (5) Suzuki, T.;Kaneko, K . J. Colloid Interface Sci. 1990, 138, 590. (6) Kaneko, K.; Sato, N.; Suzuki, T.; Fujiwara, Y.;Nishikawa, K.; Jaroniec, M. J. Chem. SOC.,Faraday Trans. 1991,87,179. (7) Kaneko, K.; Suzuki, S.; Kakei, K. Langmuir 1989,5, 879. (8) Jaroniec, M.; Msdey, R. Physical ALorptron on Heterogeneowr Solids, Elsevier: Amsterdam, 1988. (9) Jaroniec, M.; Choma, J. Chem. Phys. Carbon 1989,22, 197.
distinguish the micropore volume elements of different energetic properties.lO Such materials are energetically heterogeneous with a wide range of adsorption potentials that are up to twice as large as those for equivalent nonporous solids. This extended range of heterogeneity results from an overlap of adsorption forces generated by the opposite walls of the micropores.11J2 In many cases the adsorption potential distributions for granulated activated carbons are asymmetrical single peaks broadened in the direction of higher value^;^*^ however, dual-peak distributions can be obtained for microporous activated carbons that contain two distinctly different sizes of micropores.13 The problem of energetic heterogeneity of activated carbon fibers has not been discussed yet in adsorption literature. In the current work, the adsorption potential distributions of activated carbon fibers have been evaluated from measurements of their nitrogen adsorption isotherms. The resulting distributions differ significantly from those obtained for granulated activated carbons and provide quantitative information about the energetic heterogeneities of ACF due to microporosity.
Experimental Section Adsorption Isotherms. The low-temperature (77K)nitrogen adsorption isotherms for two commercial samples of ACF were measured at the Adsorption Laboratory of Chiba University by a computer-controlled gravimetric method.* The materials studied were prepared via carbonizationand activation of either cellulose (CEL)or poly(acrylonitri1e)(PAN) and were from Toyobo and Toho Rayon. The isotherms, analogous to those discussed in the previous paper? were found to be of type I according to BET classification,which is characteristic of highly microporous solids.l* The low-pressure parta of these isotherms are shown in Figure 1. (10) Jaroniec, M.; Piotrowska, J. Monatsh. Chem. 1986, 117, 7. (11) Everett, D. M.; Powl, J. C. J. Chem. Soc., Faraday Tram. 1 1976, 72, 619. (12) Dubinin, M. M.Carbon 1987,25,593. (13) Jaroniec, M.; Choma, J. Mater. Chem. Phys. 1988, 19, 267. (14) Gregg,S.J.; Sing,K. W.W.Adsorption,SurfaceAreaandPorosity; Academic Press: London, 1982.
0743-7463/91/2407-2719$02.50/0 0 1991 American Chemical Society
Jaroniec et al.
2720 Langmuir, Vol. 7, No. 11, 1991 20
1
0-0
Table I. Values of &, n,and Standard Deviation Associated with Equation 2 for Nitrogen Adsorption Isotherms on ACF at 77 K n SD, mmol/g ACF code 00,
CEL
CEL PAN
17.3 10.3
the exponential in eq
0.00
0.05
0.10
0.15
P/P, Figure 1. Nitrogen adsorption isotherms on the CEL and PAN samples of ACF. Results a n d Discussion Adsorption Potential Distributions. The evaluation of adsorption potential distributions from gas adsorption isotherms is discussed extensively in the literature (see monographs 8 and 15 and references therein) and it is commonly used as a quantitative measurement of the energetic heterogeneity of a solid. One of the simplest methods for calculating this distribution was proposed by Jaroniec,16who approximated the adsorption isotherm of a gas or vapor on a microporous solid by the following exponential polynomial:17 n
a = e~p[-xB*~(A/@)']
(1)
is0
4 5
0.05 0.08
1.16
a, E exp(-B*,) (6) It has been shown elsewhere8J7JQthat eq 1,which is a thermodynamically based expression,le is a good mathematical model for the adsorption of gases by microporous carbonaceousmaterials. Further, under special conditions, it is reducible to the Freundlich- and Dubinin-Radushkevich-type equations that are based on the Polanyi potential theory of adsorption20 and are the most popular mathematical models for adsorption on microporous solids.8J8V2l For gas adsorption on microporous carbonaceous solids the expression 1 - 6(A), which represents the integral adsorption potential distribution functionX*(A),is temperature-independent and denotes the fractional unoccupied micropore volume associated with adsorption potentials smaller than A.22 The first derivative of this distribution with respect to A is the differential distribution function X(A), i.e. X(A) = dX*(A)/dA = -dB(A)/dA (7) An expression for calculating the distribution function X(A) associated with the exponential eq 1 can be obtained by combining eqs 5 and 7. The resulting expression is
or n
ln a =
-CC,A' i=O
where
A = RT In ( p o / p )
(3)
and (4) Ci = B*J@ for i = 0, 1 , 2 , ...,n In the above expressions, a is the amount adsorbed at the equilibrium pressure p and the absolute temperature T, po is the saturation vapor pressure, R is the universal gas constant, /3 is the affinity coefficient that characterizes the similarity of the adsorbate to a reference adsorbate,18 andB*i (fori = 0,1,2, ...,n ) are temperature-independent coefficients associated with the successive derivatives of the logarithm of the average number of molecules in the adsorbed surface phase.16 The coefficient B*o is related to the adsorption capacity a0 (see eq 6 ) and the coefficients ofB*i (fori = 1,2,...,n ) characterize structural and surface heterogeneities of a solid.* Equation 3 defines the adsorption potential, which is equal to the change in the Gibbs free energy taken with the minus sign. The relative adsorption 6 associated with eq 1 is given by . )
6 = a / a o= e ~ p [ - z B * ~ ( A / @ ) ' ] i=l
where eq 6 defines the adsorption capacity associated with (15) Jaroniec, M.; Brauer, P. Surf. Sci. Rep. 1986, 6, 65. (16) Jaroniec, M. Surf. Sci. 1975,50, 553. (17) Jaroniec, M.; Jaroniec, J. A. Carbon 1977, 15, 107. (18) Dubinin, M. M. Chem. Phys. Carbon 1966, 2, 55; Prog. Surf. Membr. Sci. 1975, 9, 1.
Although evaluation of X(A) by means of eq 8 is relatively simple, the procedure gives results equivalent to those obtained by other numerical m e h ~ d s . ~ J ~ * ~ ~ In the current work, eq 8 was used to calculate the adsorption potential distributions X(A)for the CEL-ACF and PAN-ACF samples. In doing this the nitrogen adsorption isotherms shown in Figure 1 first were approximated by eq 2 by using /3 = 0.33.18 Summarized in Table I are the values of the micropore capacity, QO, calculated according to eq 6, the degree n of the best-fit polynomial, and the standard deviation (SD).Since the values of SD are less than 1%of the smallest measured values of the amount adsorbed, a , eq 2 was found to be an excellent description of the nitrogen adsorption isotherms measured on the CEL-ACF and PAN-ACF samples. The adsorption potential distributions X(A) shown in Figure 2 were calculated according to eq 8. For both of the ACF samples, the X(A) curves defined in the region of A from zero up to -9 kJ/mole are double-peak distributions with maxima a t similar values of A. The first maximum is at A = -1.75 kJ/mol and the second a t A = -6 kJ/mol. However, the X(A) curves for the CELACF and PAN-ACF samples differ in the heights of the maxima. In both cases the second peak is higher than the first peak, but the overall heights for PAN-ACF is greater than that for CEL-ACF (cf. Figure 2). The physical interpretation of the adsorption potential distributions for microporous carbonaceous solids is often (19) Ozawa, S.; Kusumi, S.; Ogino, Y.J. Colloid Interface Sci. 1976, 56, 83. (20) Polanyi, M. 2.Elektrochem. 1920,26,371; 1929,35,431. (21) Cerofolini, G. F. Colloid Sci. 1982,4, 59. (22) Jaroniec, M.; Madey, R. J. Phys. Chem. 1989,93,5225. (23) Hose, W. A. J. Chem. SOC.,Faraday Trans. I 1978, 74,1045.
Heterogeneity and Microporosity of Actiuated Carbon Fibers
Langmuir, Vol. 7, No.11, 1991 2721 Table 11. Parameters of the Model Adsorption Isotherms from Figure 3 Calculated According Equation 9 parameter model structure a model structure b 5.0 1.74 0.42 5.0 4.44 0.67 3.07
0.0
0
2
4
6
8
1
0
A (kJ/mole)
Figure 2. Adsorption potential distributions calculated according to eq 8 for the CEL and PAN samples of ACF.
difficult because energetic heterogeneity can be due to both their nonuniform microporous structure (structural heterogeneity) and their surface heterogeneity generated by various functional groups formed during the activation process.8 However, in the case of the currently studied ACF samples their external surface areas are relatively small (- 20 m2/g or less) compared to their internal surface areas (often 1000m2/g).2 Thus, it is reasonable to assume that the slitlike micropores formed between graphite layers are the main source of the energetic heterogeneity. This assumption is supported by the observation that the X(A) distributions for the two different ACF samples, which were prepared from different starting materials, are similar and this type of behavior is expected only when the surface heterogeneity is negligible compared to the total energetic heterogeneity. As noted in the Introduction, for a highly microporous solid a double-peak distribution of X(A) indicates the presence of a bimicroporous structure consisting of two groups of pores of considerably different sizes.13 Such distributions of X(A) are characteristic of many types of ACF and differ substantially from single-peakdistributions typical of those observed for granulated microporous activated carbons.9 The adsorption potential distribution functions X(A) for the CEL-ACF and PAN-ACF materials suggest that they are bimicroporous structures. A more detailed characterization of their microporosity is considered below using an isotherm equation that takes into account the existence of two groups of fine pores with different sizes. Modeling of Adsorption on Bimicroporous Solids. Although extensive studies of adsorption on microporous activated ~ a r b ~ n have ~ ~ demonstrated ~ ~ J ~ * that ~ *the~Du~ binin-Radushkevich (DR) equation is a good mathematical approximation of vapor adsorption in uniform (homogeneous) micropores, Izotova and D ~ b i n i have n ~ ~proposed a modification of this equation (i.e., a multi-DR equation) in order to describe adsorption on microporous solids with multiporous structures. Similarly, S t ~ e c k l also i ~ ~ has suggested an integral equation with a DR subintegral function to represent vapor adsorption on strongly heterogeneous microporous solids. Both of these latter approaches have initiated ~orkgJ0*22J’8-~~ on gas and vapor (24)Izotova, T.I.; Dubinin, M. M. Zh.Fiz. Khim. 1965,39,2796. (25)Stoeckli, H.F. J. Colloid Interface Sci. 1988,59,l&p. (26)Dubinin, M. M.; Stoeckli, H. F. J. Colloid Interface Sci. 1980,75, 34. (27)Dubinin, M. M. Carbon 1985,23,373;1989,27,457. (28)Stoeckli, H.F. Carbon 1990,28,1;1989,27,962. (29)Wojsz,R.; Rozwadowski, M. Carbon 1984,22,437; 1986,24,225. (30)Jaroniec, M. Langmuir 1987,3,795. (31)Jaroniec, M.; Madey, R. J. Phys. Chem. 1988,92,3986; J. Chem. SOC., Faraday Trans. 1 1988,84,1139.
=L 0.0 0
200
400
600
(A/p)2 (kJ/rnole)2 Figure 3. Plots In a vs ( A / @ ) of 2 the model adsorption isotherms calculated according to eq 9 for the parameters given in Table 11. The plots a and b refer to the biporous structures in Table 11.
adsorption on heterogeneous activated carbons to evaluate their validity. In addition to these extended DR equations, a y-type micropore-size distribution has been suggested as an alternate mathematical description for the structural heterogeneity of granulated activated carbons and it has been used successfully to model gas and vapor adsorption data obtained for strongly heterogeneous microporous s o l i d s ? * 2 2 ~ 2 8 However, ~~~32~~ in the current work, the y-type relationship was found to be an unsatisfactory model of the nitrogen adsorption isotherms on the CEL-ACF and PAN-ACF samples. This result further indicates that microporous structures of the materials currently studied differ significantly from those observed in granulated activated carbons and is consistent with the idea that they possess bimicroporous structures as discussed above. Further, the results from the current work are consistent with similar experimental findings for oxidized graphitized rayon fabrics, which recently were reported by I ~ m a i l . ~ ~ Gas or vapor adsorption on bimicroporous ACF can be described by the two-term DR equation:24 a = a, exp[-B1(A/kO21 + a2 e x ~ [ - B ~ ( A / 8 ) ~ 1(9)
where ai and Bi characterize the ith type of micropore: ai is the micropore capacity and Bi is the structural parameter. The other symbols in eq 9 are the same as those in eq 1. Model adsorption isotherms were calculated according to eq 9 for the parameters listed in Table I1 and are illustrated in Figure 3 as plots of In a vs coordinates. Such coordinates are frequently used to represent gas or vapor adsorption data on microporous carbonaceousadsorbents. For nearly uniform microporous carbons, the In a vs (A/B)2 is linear, as predicted by the simple DR equation. However, as can be seen in Figure 3, for a bimicroporous structure, this dependence deviates (32)Jaroniec, M.; Choma, J. Mater. Chem. Phys. 1986,15,521;1987,
18, 109; Carbon 1988,26,747;Colloids Surf. 1989,37,183.
(33)Jaron/ec, M.;Lu, X.; Madey, R. Chem. Scr. 1988,28, 369. (34)Jaroniec, M., Madey, R.; Lu, X.; Choma, J. Langmuir 1988,4,911. (35)Ismail, I. M. K. Carbon 1990,28,401;1991,29, 119.
Jaroniec et al.
2722 Langmuir, Vol. 7, No. 11,1991 3.01
I
Table 111. Parameters of Equation 9 for the Nitrogen Adsorption on the ACF Samples Studied parameter CEL PAN al, mmol/g 10% (mol/kJ)Z aa, " o h 103Bz,(mol/kJ)2
5 1-.
0
50
100
150
200
250
( A / P ) 2 (kJ/mole) 2
Figure 4. Plots In a vs (A/o)2 of the nitrogen adsorption isotherms for the CEL and PAN samples of ACF.
from linearity a t low values of A. The coefficients a1 and B1, which characterize the small micropores that are filled at low equilibrium pressures, may be evaluated from the linear part of the curves (Le., at higher values of A). The relationship between the structural parameter B and the half-width x of the slitlike micropores is complex, and different empirical treatments have been suggested.261-l A comparison of these treatments was reviewed previously.42 In order to estimate the micropore sizes for the carbon fibers studied, we used the most popular and simplest relationship between B and x, which was established experimentally by D ~ b i n i n : ~ ~
B = cx2 (10) where c = 0.01 (kJ.nm/mol)-z is an empirical parameter.43 Table I1 summarizes the values of x associated with the B values used to calculate the adsorption data in Figure 3. Comparison of the In a vs (A//3Pplots presented in Figure 3 shows that the linear part of the curves for the bimicroporous structure with micropores of considerably different sizes (plot a) is extended over a longer range than that of the bimicroporous structure (plot b) (see Table 11). Microporous Structures of ACF. The two-term DR eq 9 was used to describe the nitrogen adsorption isotherms (Figure 1) measured on the CEL-ACF and PAN-ACF samples. The resulting data are shown in Figure 4 as plots of In a vs and are analogous in shape to the model plot (Le., curve a) appearing in Figure 3. This behavior further suggests that the bimicroporous structures of the samples are made up of two groups of small pores with considerably different sizes. Summarized in Table I11 are the parameters of eq 9 calculated by fitting the nitrogen adsorption isotherms presented in Figure 1to this expression. These parameters provide an approximate estimation (by means of eq 10) of the micropore sizes. Table IV summarizes the values of x1 and x2 for the CEL-ACF and PAN-ACF samples. For both samples the half-widths of small slitlike pores are estimated to be -0.5 nm, whereas the larger pores are (36)Stoeckli, H. F.; Kraehenbuehl, F.; Ballerini, L.; DeBernardini, S. Carbon 1989,27, 125. (37)Stoeckli, H.F.;Ballerini, L.; DeBernardini, S . Carbon 1989,27,
---.
M1
(38)McEnaney, B. Carbon 1987,25,69. (39)Stoeckli, H.F.;Ftebstein, P.; Ballerini, L. Carbon 1990,28,907. (40)McEnaney, B. Carbon 1988,26, 267. (41)Dubinin, M. M. Carbon 1988,26,97. (42)Jaroniec, M.; Lu, X.;Madey, R.; Choma, J. Mater. Chem. Phys. 1990,26,87. (43)Dubinin, M. M.; Polyakov, N. S.; Kataeva, L. I. Carbon 1991,29,
481.
15.6 3.27 3.1 57.8
9.2 2.41 1.3 53.0
Table IV. Parameters of Microporous Structures of the ACF Samples micropores fine mesopores ACF code f 1 = al/ao X I nm , fa = az/ao X Z , nma CEL 0.83 0.57 0.17 2.40 PAN 0.88 0.49 0.13 2.30 a The values of xz are given for orientation purpose only; note that they were estimated by eq 10,which was established for the micropore region.
-2.3 nm. According to the IUPAC classification,44micropores are defined as those with half-widths below l nm, mesopores as those with half-widths from 1to 25 nm, and macropores as those with half-widths which exceed 25 nm. In the light of this classification, the currently studied ACF samples possess both micropores and small mesopores. Estimation of the mesopore sizes is very crude because the empirical relationship given by eq 10assumes the presence of only micropores. The micropore sizes given in Table IV are in a good agreement with values reported previously.'J For both types of ACF, the micropore fraction f1 is -0.85; this value is defined as the ratio of al to the total micropore capacity ao = a1 + 02. It follows from Table IV that the value of f1 for the PAN-ACF sample is greater than that for CEL-ACF, which explains why the second peak on the X ( A ) distribution for PAN-ACF is higher than that for CEL (cf, Figure 2).
Conclusion Analysis of the nitrogen adsorption data on the celluloseand poly(acrylonitri1e)-basedactivated carbon fibers suggests that these materials are bimicroporous with -85% of their volume made up of uniform micropores and 15% of fine mesopores (cf. Table IV). The dual-peak adsorption potential distributions (cf. Figure 3) reflect this biporous nature of activated carbon fibers, which makes them significantly different from the majority of granulated activated carbons. This last group of carbons possess heterogeneous microporous structures, which are usually represented by one-peak distribution functions. It has been shown that two-term DR eq 9 is suitable for modeling the micropore-filling mechanism for ACF samples; the first term of this equation describes the volume filling of the micropores, whereas the second term represents the volume filling of the fine mesopores. The micropore filling has a multistage character;1-2adsorption occurs on the walls of slitlike micropores and fine mesopores followed by filling of the interior volumes of these pores. Further theoretical and experimental studies are needed in order to obtain a better quantitative description of the microporosity in ACF. Questions concerning the uniformity of the micropores and the types of surface groups present remain. Additional studies are in progress in order address these questions. Registry No. Nz, 7727-37-9;cellulose, 9004-34-6;poly(acrylonitrile), 25014-41-9.
-
(44)Sing, K. W.W.; et al. Pure Appl. Chem. 1985,57,603.
