- Email: [email protected]
Correlation between the bet parameters and the parameters that characterize the microporous structures of activated carbons
Materials Chemistry and Physics, 25 (1990)
287-296
287
CORRELATION BETWEEN THE BET PARAMETERS AND THE PARAMETERS THAT CHARACTERIZE THE MICROPOROUS STRUCTURES OF ACTIVATED CARBONS
M. JARONIEC* and R. MADEY Department of Physics, Kent State University, Kent, Ohio 44242 (U.S.A.) J. CHOMA Institute of Chemistry, WAT, 00908 Warsaw (Poland) P. BRAUER Department of Physical Chemistry, K.M. University, 7010 Leipzig (G.D.R.) Received October 25, 1989; accepted December 12, 1989
ABSTRACT The well-known BET isotherm equation is used to describe benzene adsorption on microporous activated carbons of different degrees of microporosity.
It is shown that the parameters of
this equation evaluated for benzene-activated carbon systems correlate with the micropore parameters that are obtained by means of the Jaroniec-Choma equation.
This correlation indicates
that the BET parameters provide also some information about the microporosity of the solid adsorbents. INTRODUCTION The Brunauer-Emmett-Teller
(BET) isotherm equation [l] is
used widely for describing multilayer adsorption of gases and vapors on both nonporous and porous solid adsorbents
[2,3], and
for evaluating the monolayer adsorption capacity, which is usually converted to the specific surface area [2,4,5].
There
exists a controversy in the adsorption literature on the applicability of the BET equation for describing adsorption of gases and vapors on microporous solids [6,8].
Some authors [6,7] indicated that the BET equation is not suitable for evaluating
Institute of Chemistry, M. Curie-Sklodowska *Permanent address: University, 20031, Lublin (Poland) 0254-0584/90/$3.50
OElsevier Sequoia/Printed in The Netherlands
288
the maximum adsorption capacity and the specific surface area of microporous solids such as activated carbons.
Experimental and
theoretical studies performed by Choma [8] showed that the BET equation provides reasonable values of the maximum adsorption capacity for many microporous activated carbons provided it is used in the proper region of relative pressures.
For nonporous
solids and solids with large pores, the BET adsorption capacity is evaluated usually in the region of relative pressures p/p, from 0.05 to 0.3 [2,4]; however, for adsorption isotherms on microporous solids, this region is shifted in the direction of low relative pressures where the BET plot shows a linear behavior. In this paper, we will show that the BET maximum adsorption capacity for many microporous activated carbons correlates with micropore adsorption capacity.
In addition, a correlation
between other BET parameters and the average micropore size indicates that the BET parameters provide also some information about the microporosity of activated carbons.
To demonstrate the
above mentioned correlation, the benzene adsorption.isotherms measured on microporous activated carbons of different degrees of structural heterogeneity were analyzed by means of the BET isotherm equation that describes n-layer adsorption [2] and also by means of the Jaroniec-Choma
(JC) equation [9].
The JC
equation is associated with the gamma micropore-size distribution, which is useful for characterizing the microporosity of activated carbons [lo].
EQUATIONS EMPMYED
FOR ANALYSIS OF BENZENE ADSORPTION ISOTHERMS
The parameters that characterize microporous structures of activated carbons may be evaluated from the amount ami adsorbed in the micropores.
The adsorbed amount ami may be extracted from
the adsorbed amount a measured experimentally, which is a simple sum of ami and the amount a, adsorbed on the mesopore surface
1111.
Because the adsorbed amount a, may be expressed as a
product of the specific mesopore surface area S, and the adsorption u expressed in moles of the adsorbate per unit surface area of the adsorbent [ll], the amount ami may be evaluated as follows: amf =
a-us,
(1)
The adsorption isotherm a,i(p),which represents the dependence of the amount amiadsorbed in the micropores on the equilibrium pressure p, may be described by the JC equation [9]:
where A =
RTln (PO/p)
(3)
Here aO,,,i denotes the maximum amount adsorbed in the micropores (the micropore adsorption capacity), A is the adsorption potential, i3is the similarity coefficient [12], q and m are parameters of the gamma micropore-size distribution, T is the absolute temperature, and R is the universal gas constant. The isotherm eqn. (Z), which was derived for a strongly heterogeneous micorporous solid, is associated [13] with the following gammatype micropore-size distribution function J(x): J(x)
=
2r((gjl;1x-+1
exp(-qcx2)
(4)
where the constant c equals 0.00694 (mol/kJ.nm)2for benzene as estimated by Dubinin [ll], and x denotes the half-width of the slit-like micropores. The distribution function J(x) characterizes structural heterogeneity of a microporous solid. In a previous paper [lo], we proposed the use of the average micropore size 2 and the dispersion u, for characterizing structural heterogeneities of micropores instead of the parameters q and m. In contrast to the parameters q and m, the quantities z and 6, provide direct information about microporosity; j?defines the average size of the micropores, whereas u, is associated with the width of the micropore-size distribution J(x). The relationships between the quantities z, 0, and the parameters q,m are given below: z = y r (In+11/qcl1’2
(5)
and a x = [ (l-y21
Cm+11
I (gc) 1”’
(61
290 where y = r(n?+3,‘2)
/ [ ~m+l)l’a~im+l)
1
(7)
The benzene adsorption isotherms on various activated carbons will be analyzed by means of eqn. (2) in order to evaluate the parameters q and m, which may be converted through eqns. (5) and (6) to the quantities ? and u,. The RET equation for n-layer adsorption will be used also for analyzing the benzene adsorption isotherms on microporous activated carbons: this equation may be written as follows [23: a&C(P/P&-(n+1)
(P/P,)* +R(P/P,)"+l] (8)
a= (l-P/P,)[1+ (C-1) (P/P,)
-Cb/P,)“‘1]
Here aosETdenotes the monolayer capacity (the BET adsorption capacity), C is the BET constant associated with the adsorption energy, and n is the number of the statistical adsorption layers. Because the BET equation is used widely for analyzing the adsorption isotherms of gases and vapors on various adsorbents, it would be interesting to know how the BET parameters depend on the adsorbent microporosity.
RESULTS AND DISCUSSION To demonstrate the correlation between the BET parameters and the micropore parameters, we analyzed the benzene adsorption isotherms measured on various microporous activated carbons at 293 R.
These experimental isotherms were discussed in previous
papers [9,14-181. Listed in Table I are the 14 activated carbons studied and references to the source papers that contain information about these activated carbons and the benzene adsorption isotherms.
This table contains also the BET
parameters aoBET,C, and n calculated according to eqn. (8). comparison of the values of the
parameters
C
A
and n for various
activated carbons shows that the number of adsorption layers n usually decreases with increasing values of the BET constant C. This observation will be explained later.
291
Table I.
The BET parameters for benzene adsorption isotherms on
various activated carbons at 293 K. Adsorbent No. Code
Reference to the Adsorption Isotherm
BET Capacity 0 a BET
BET Constant C
Number of Adsorption Layers, n
(mmol/q) ACT-K
14
2
BH
15
3
AC
9
4
HS-43
16
5
T
15
1
12.46
31
4.44
3.53
34
4.19
5.30
78
3.78
5.73
96
2.52
5.00
127
2.05
6
ACZ
14
5.76
132
2.78
7
A-2
15
3.44
349
2.41
8
AG-5
15
3.69
153
1.78
9 10
BPL
17
3.91
749
2.36
cwz-3
18
5.75
351
2.29
15
4.55
654
2.84
9
4.77
562
2.04
11
NSW
12
RKD-4
13
PA
17
2.81
1309
1.85
14
AGS
14
4.42
3309
1.46
In Table II, we present the specific mesopore surface area and the parameters that characterize the microporous structures for the 14 activated carbons studied.
The specific mesopore
surface area S, was evaluated by using the as-method [15]. Activated carbons listed in Table II show different values of S, (from 10 m2/g for ACS and PA carbons up to 380 m2/g for BH carbon): these values are generated by different quantities of mesopores that may possess also different sizes and shapes.
The
values of S, listed in Table II were utilized to extract, according to eqn. (l), the amount a,i adsorbed in the micropores from the total adsorbed amount a; this procedure is described elsewhere [15].
Next, the pressure-dependence
of the amount ami
adsorbed in the micropores was described by means of the JC eqn. (2). The evaluated parameters q and m were converted according to eqns. (5) and (6) to the average micropore size x and the dispersion u,.
Table II contains the parameters aoni,x, and u,
that characterize the microporosity of the activated carbons studied.
292
Table 11.
The specific surface area of mesopores and the
parameters that characterize the microporous structure of activated carbons studied.
These parameters were evaluated
according to JC eqn. (2) and eqns. (5) and (6). Adsorbent No. Code
Mesopore Area S,(m'/g)
1
ACT-X
160
Micropore Capacity a",i(mmol/g) 15.51
Average Micropore Size X(nm)
Dispersion a,(nm)
1.44
0.62
2
BH
380
2.67
1.21
0.57
3
AC
150
6.18
1.06
0.43
4
Is-43
30
6.85
0.94
0.46
5
T
40
5.75
0.85
0.33
6
ACZ
250
5.85
0.78
0.39
7
A-2
130
3.64
0.66
0.23
8
AG-5
80
3.63
0.64
0.21
80
4.42
0.63
0.20
10
cwz-3
170
6.06
0.61
0.16
11
NSW
140
4.93
0.57
0.21
12
RKD-4
140
4.92
0.57
0.13
13
PA
10
3.22
0.55
0.19
14
ACS
10
4.82
0.39
0.12
9
BPL
First, we compare the adsorption capacities obtained by means of the BET eqn. (8) and the JC eqn. (2).
Plotted in Fig. 1 is
the BET adsorption capacity aoSE,versus the micropore adsorption capacity aomi;according to Fig. 1, the BET adsorption capacity tends to increase when the micropore adsorption capacity increases.
The fact that the experimental points cluster around
a straight line indicates a correlation between aoEI and aoai. For the majority of activated carbons studied, the values of a",,,i are greater than the values of aogE,. It is worth noting here that the physical meaning of the micropore adsorption capacity a",!is clear because this quantity denotes the maximum adsorption in the micropores. To obtain the total maximum adsorption a', we must sum the values of aomiand a", [19], where a", denotes the monolayer capacity for the mesopore surface. Because the mesopore surface areas are large for some activated carbons, the mesopore monolayer capacity a", contributes significantly to the total adsorption capacity a'; consequently, the difference
293
2 Micropore
4
6
Capacity,
8
aomi (mmol/g)
Fig. 1. A comparison of the BET adsorption capacity aosETon the micropore adsorption capacity a",,,i for the 14 activated carbons listed in.Table I.
between a0 and aosETis frequently greater than that observed for a",,,i and aosET. The presence of various functional groups on the mesopore surface also may increase a',, and consequently, the total adsorption capacity a'.
The above discussion of Fig. 1
shows that the BET equation provides values of the maximum adsorption capacity for microporous activated carbons that usually are lower than those obtained on the basis of the theory of micropore filling.
A linear correlation between a",,,and aomi
indicates that a",,,may be used only as an approximate value to represent the adsorption capacity of microporous solids. An interesting comparison is presented in Fig. 2, which shows the correlation between the natural logarithm of the BET constant C and the inverse average micropore size (l/z).
The BET constant
C contains the exponential of the average adsorption potential [2] as a factor; consequently, the natural logarithm of the BET constant C is proportional to the average adsorption potential x. For microporous solids, Bubinin [11,14] showed that the characteristic adsorption energy, which is proportional to the
0
1
2
3
Inverse Micropore Size l/5(
l/nm)
Fig. 2. The natural logarithm of the BET constant C versus the inverse average micropore size (l/i?) for the 14 activated carbons listed in Table I.
average adsorption potential x, is inversely proportional to the average micropore size 2; that is, 1nC - l/X
(9)
Shown in Fig. 2 is the proportionality between enc and l/z for the microporous activated carbons listed in Table I.
The fact
that the experimental points cluster about a straight line shows that the BET constant C increases as the average micropore size St decreases.
For solids with very small slit-like micropores, the
adsorption forces from the opposite walls overlap; consequently the BET constant C is large because the adsorption potential may be up to twice that associated with one flat surface.
This
overlap effect can be seen from Fig. 2; for example,. the average micropore size Ti is smallest and the BET constant C is largest for the ACS activated carbon (no. 14).
295
0.0
0.5
Micropore
1.0
1.5
Size, X (nm)
3. The number of statistical adsorption layers n versus the average micropore size % for the 14 activated carbons listed in Table I.
For small micropores, the number of adsorption layers formed on the micropore walls is limited: moreover, this number should be significantly smaller than that observed for nonporous solids. The experimental evidence for this statement is provided in Fig. 3 which shows the dependence of the number of statistical adsorption layers predicted by the BET eqn. (8) on the average micropore size 2; accordingly, the number of adsorption layers increases as the average micropore size X increases.
For small
micropores, the BET equation predicts that the number of statistical adsorption layers is less than two (cf., Table I). CONCLUSIONS For many microporous activated carbons, the comparisons shown in Figs l-3 of the BET parameters with the micropore parameters indicate that the BET parameters change gradually with an increase in the microporosity of these carbons. For activated carbons that are characterized by a small value of the average micropore size, the number of adsorption layers is less than two, and the BET constant has a large value; as the average micropore
296
size z increases, the number of adsorption layers increases but This gradual change of the BET
the BET constant C decreases.
parameters with microporosity indicates that the parameters provide valuable information about the microporous structure of activated carbons. ACKNOWLEDGMENT This work was supported in part by the National Science Foundation under Grant No. CBT-8721495 and by the Polish Program We thank Mr. Lu for providing the
of Basic Research RP-I-08. figures. REFERENCES 1
S. Brunauer, P.H. Emmett and E. Tellner, J. Am. Chem. Sot., &Q (1938) 309.
2
ica 1 Adsorntion of Gases, D.M. Young and A.D. Crowell, P hv s'
3
M. Jaroniec and R. Madey, Phvsical
Butterworths, London, 1962. mSolids, 4
Elsevier, Amsterdam, 1988.
D. Dollimore, Surface Technol ., & (1976) 121.
5
J. Cortes, Advan.,
6
M.M. Dubinin, Carbon, 2;L (1983) 359.
22 (1985) 151.
7
D. Burevski, Croatica Chem. A&q,
a
(1987) 649.
8
J. Choma, Polish J. Chem., 61 (1989) 173.
9
M. Jaroniec and J. Choma, Mater. Chem. Phvs., u
10
(1986) 521.
M. Jaroniec, R. Madey, X. Lu and J. Choma, v,
4 (1988)
911. 11
M.M. Dubinin, Carbon, 22 (1985) 373.
12
M.M. Dubinin, 1,
13
M. Jaroniec and J. Choma, e,
14
M.M. Dubinin, Carbon, a
15
M.
9 (1975) 1. 22 (1989)
197. (1987) 593.
Jaroniec, R. Madey, J. Choma, B. McEnaney and T.J. Mays,
Carbon, 27 (1989) 77. 16
0. Kadlec, J. Choma, H. Jankowska and A. Swiatkowski, Collection
17
M.
0
n., u
(1984) 2721.
Jaroniec, R. Madey, X. Lu and J. Choma, Carbon, 22 (1989)
485. 18
H. Jankowska, A. Swiatkowski, J. Oscik and R. Kusak, Carbon, a
19
M.
(1983) 117. Jaroniec and R. Madey, J.,
a
(1989) 5225.
287-296
287
CORRELATION BETWEEN THE BET PARAMETERS AND THE PARAMETERS THAT CHARACTERIZE THE MICROPOROUS STRUCTURES OF ACTIVATED CARBONS
M. JARONIEC* and R. MADEY Department of Physics, Kent State University, Kent, Ohio 44242 (U.S.A.) J. CHOMA Institute of Chemistry, WAT, 00908 Warsaw (Poland) P. BRAUER Department of Physical Chemistry, K.M. University, 7010 Leipzig (G.D.R.) Received October 25, 1989; accepted December 12, 1989
ABSTRACT The well-known BET isotherm equation is used to describe benzene adsorption on microporous activated carbons of different degrees of microporosity.
It is shown that the parameters of
this equation evaluated for benzene-activated carbon systems correlate with the micropore parameters that are obtained by means of the Jaroniec-Choma equation.
This correlation indicates
that the BET parameters provide also some information about the microporosity of the solid adsorbents. INTRODUCTION The Brunauer-Emmett-Teller
(BET) isotherm equation [l] is
used widely for describing multilayer adsorption of gases and vapors on both nonporous and porous solid adsorbents
[2,3], and
for evaluating the monolayer adsorption capacity, which is usually converted to the specific surface area [2,4,5].
There
exists a controversy in the adsorption literature on the applicability of the BET equation for describing adsorption of gases and vapors on microporous solids [6,8].
Some authors [6,7] indicated that the BET equation is not suitable for evaluating
Institute of Chemistry, M. Curie-Sklodowska *Permanent address: University, 20031, Lublin (Poland) 0254-0584/90/$3.50
OElsevier Sequoia/Printed in The Netherlands
288
the maximum adsorption capacity and the specific surface area of microporous solids such as activated carbons.
Experimental and
theoretical studies performed by Choma [8] showed that the BET equation provides reasonable values of the maximum adsorption capacity for many microporous activated carbons provided it is used in the proper region of relative pressures.
For nonporous
solids and solids with large pores, the BET adsorption capacity is evaluated usually in the region of relative pressures p/p, from 0.05 to 0.3 [2,4]; however, for adsorption isotherms on microporous solids, this region is shifted in the direction of low relative pressures where the BET plot shows a linear behavior. In this paper, we will show that the BET maximum adsorption capacity for many microporous activated carbons correlates with micropore adsorption capacity.
In addition, a correlation
between other BET parameters and the average micropore size indicates that the BET parameters provide also some information about the microporosity of activated carbons.
To demonstrate the
above mentioned correlation, the benzene adsorption.isotherms measured on microporous activated carbons of different degrees of structural heterogeneity were analyzed by means of the BET isotherm equation that describes n-layer adsorption [2] and also by means of the Jaroniec-Choma
(JC) equation [9].
The JC
equation is associated with the gamma micropore-size distribution, which is useful for characterizing the microporosity of activated carbons [lo].
EQUATIONS EMPMYED
FOR ANALYSIS OF BENZENE ADSORPTION ISOTHERMS
The parameters that characterize microporous structures of activated carbons may be evaluated from the amount ami adsorbed in the micropores.
The adsorbed amount ami may be extracted from
the adsorbed amount a measured experimentally, which is a simple sum of ami and the amount a, adsorbed on the mesopore surface
1111.
Because the adsorbed amount a, may be expressed as a
product of the specific mesopore surface area S, and the adsorption u expressed in moles of the adsorbate per unit surface area of the adsorbent [ll], the amount ami may be evaluated as follows: amf =
a-us,
(1)
The adsorption isotherm a,i(p),which represents the dependence of the amount amiadsorbed in the micropores on the equilibrium pressure p, may be described by the JC equation [9]:
where A =
RTln (PO/p)
(3)
Here aO,,,i denotes the maximum amount adsorbed in the micropores (the micropore adsorption capacity), A is the adsorption potential, i3is the similarity coefficient [12], q and m are parameters of the gamma micropore-size distribution, T is the absolute temperature, and R is the universal gas constant. The isotherm eqn. (Z), which was derived for a strongly heterogeneous micorporous solid, is associated [13] with the following gammatype micropore-size distribution function J(x): J(x)
=
2r((gjl;1x-+1
exp(-qcx2)
(4)
where the constant c equals 0.00694 (mol/kJ.nm)2for benzene as estimated by Dubinin [ll], and x denotes the half-width of the slit-like micropores. The distribution function J(x) characterizes structural heterogeneity of a microporous solid. In a previous paper [lo], we proposed the use of the average micropore size 2 and the dispersion u, for characterizing structural heterogeneities of micropores instead of the parameters q and m. In contrast to the parameters q and m, the quantities z and 6, provide direct information about microporosity; j?defines the average size of the micropores, whereas u, is associated with the width of the micropore-size distribution J(x). The relationships between the quantities z, 0, and the parameters q,m are given below: z = y r (In+11/qcl1’2
(5)
and a x = [ (l-y21
Cm+11
I (gc) 1”’
(61
290 where y = r(n?+3,‘2)
/ [ ~m+l)l’a~im+l)
1
(7)
The benzene adsorption isotherms on various activated carbons will be analyzed by means of eqn. (2) in order to evaluate the parameters q and m, which may be converted through eqns. (5) and (6) to the quantities ? and u,. The RET equation for n-layer adsorption will be used also for analyzing the benzene adsorption isotherms on microporous activated carbons: this equation may be written as follows [23: a&C(P/P&-(n+1)
(P/P,)* +R(P/P,)"+l] (8)
a= (l-P/P,)[1+ (C-1) (P/P,)
-Cb/P,)“‘1]
Here aosETdenotes the monolayer capacity (the BET adsorption capacity), C is the BET constant associated with the adsorption energy, and n is the number of the statistical adsorption layers. Because the BET equation is used widely for analyzing the adsorption isotherms of gases and vapors on various adsorbents, it would be interesting to know how the BET parameters depend on the adsorbent microporosity.
RESULTS AND DISCUSSION To demonstrate the correlation between the BET parameters and the micropore parameters, we analyzed the benzene adsorption isotherms measured on various microporous activated carbons at 293 R.
These experimental isotherms were discussed in previous
papers [9,14-181. Listed in Table I are the 14 activated carbons studied and references to the source papers that contain information about these activated carbons and the benzene adsorption isotherms.
This table contains also the BET
parameters aoBET,C, and n calculated according to eqn. (8). comparison of the values of the
parameters
C
A
and n for various
activated carbons shows that the number of adsorption layers n usually decreases with increasing values of the BET constant C. This observation will be explained later.
291
Table I.
The BET parameters for benzene adsorption isotherms on
various activated carbons at 293 K. Adsorbent No. Code
Reference to the Adsorption Isotherm
BET Capacity 0 a BET
BET Constant C
Number of Adsorption Layers, n
(mmol/q) ACT-K
14
2
BH
15
3
AC
9
4
HS-43
16
5
T
15
1
12.46
31
4.44
3.53
34
4.19
5.30
78
3.78
5.73
96
2.52
5.00
127
2.05
6
ACZ
14
5.76
132
2.78
7
A-2
15
3.44
349
2.41
8
AG-5
15
3.69
153
1.78
9 10
BPL
17
3.91
749
2.36
cwz-3
18
5.75
351
2.29
15
4.55
654
2.84
9
4.77
562
2.04
11
NSW
12
RKD-4
13
PA
17
2.81
1309
1.85
14
AGS
14
4.42
3309
1.46
In Table II, we present the specific mesopore surface area and the parameters that characterize the microporous structures for the 14 activated carbons studied.
The specific mesopore
surface area S, was evaluated by using the as-method [15]. Activated carbons listed in Table II show different values of S, (from 10 m2/g for ACS and PA carbons up to 380 m2/g for BH carbon): these values are generated by different quantities of mesopores that may possess also different sizes and shapes.
The
values of S, listed in Table II were utilized to extract, according to eqn. (l), the amount a,i adsorbed in the micropores from the total adsorbed amount a; this procedure is described elsewhere [15].
Next, the pressure-dependence
of the amount ami
adsorbed in the micropores was described by means of the JC eqn. (2). The evaluated parameters q and m were converted according to eqns. (5) and (6) to the average micropore size x and the dispersion u,.
Table II contains the parameters aoni,x, and u,
that characterize the microporosity of the activated carbons studied.
292
Table 11.
The specific surface area of mesopores and the
parameters that characterize the microporous structure of activated carbons studied.
These parameters were evaluated
according to JC eqn. (2) and eqns. (5) and (6). Adsorbent No. Code
Mesopore Area S,(m'/g)
1
ACT-X
160
Micropore Capacity a",i(mmol/g) 15.51
Average Micropore Size X(nm)
Dispersion a,(nm)
1.44
0.62
2
BH
380
2.67
1.21
0.57
3
AC
150
6.18
1.06
0.43
4
Is-43
30
6.85
0.94
0.46
5
T
40
5.75
0.85
0.33
6
ACZ
250
5.85
0.78
0.39
7
A-2
130
3.64
0.66
0.23
8
AG-5
80
3.63
0.64
0.21
80
4.42
0.63
0.20
10
cwz-3
170
6.06
0.61
0.16
11
NSW
140
4.93
0.57
0.21
12
RKD-4
140
4.92
0.57
0.13
13
PA
10
3.22
0.55
0.19
14
ACS
10
4.82
0.39
0.12
9
BPL
First, we compare the adsorption capacities obtained by means of the BET eqn. (8) and the JC eqn. (2).
Plotted in Fig. 1 is
the BET adsorption capacity aoSE,versus the micropore adsorption capacity aomi;according to Fig. 1, the BET adsorption capacity tends to increase when the micropore adsorption capacity increases.
The fact that the experimental points cluster around
a straight line indicates a correlation between aoEI and aoai. For the majority of activated carbons studied, the values of a",,,i are greater than the values of aogE,. It is worth noting here that the physical meaning of the micropore adsorption capacity a",!is clear because this quantity denotes the maximum adsorption in the micropores. To obtain the total maximum adsorption a', we must sum the values of aomiand a", [19], where a", denotes the monolayer capacity for the mesopore surface. Because the mesopore surface areas are large for some activated carbons, the mesopore monolayer capacity a", contributes significantly to the total adsorption capacity a'; consequently, the difference
293
2 Micropore
4
6
Capacity,
8
aomi (mmol/g)
Fig. 1. A comparison of the BET adsorption capacity aosETon the micropore adsorption capacity a",,,i for the 14 activated carbons listed in.Table I.
between a0 and aosETis frequently greater than that observed for a",,,i and aosET. The presence of various functional groups on the mesopore surface also may increase a',, and consequently, the total adsorption capacity a'.
The above discussion of Fig. 1
shows that the BET equation provides values of the maximum adsorption capacity for microporous activated carbons that usually are lower than those obtained on the basis of the theory of micropore filling.
A linear correlation between a",,,and aomi
indicates that a",,,may be used only as an approximate value to represent the adsorption capacity of microporous solids. An interesting comparison is presented in Fig. 2, which shows the correlation between the natural logarithm of the BET constant C and the inverse average micropore size (l/z).
The BET constant
C contains the exponential of the average adsorption potential [2] as a factor; consequently, the natural logarithm of the BET constant C is proportional to the average adsorption potential x. For microporous solids, Bubinin [11,14] showed that the characteristic adsorption energy, which is proportional to the
0
1
2
3
Inverse Micropore Size l/5(
l/nm)
Fig. 2. The natural logarithm of the BET constant C versus the inverse average micropore size (l/i?) for the 14 activated carbons listed in Table I.
average adsorption potential x, is inversely proportional to the average micropore size 2; that is, 1nC - l/X
(9)
Shown in Fig. 2 is the proportionality between enc and l/z for the microporous activated carbons listed in Table I.
The fact
that the experimental points cluster about a straight line shows that the BET constant C increases as the average micropore size St decreases.
For solids with very small slit-like micropores, the
adsorption forces from the opposite walls overlap; consequently the BET constant C is large because the adsorption potential may be up to twice that associated with one flat surface.
This
overlap effect can be seen from Fig. 2; for example,. the average micropore size Ti is smallest and the BET constant C is largest for the ACS activated carbon (no. 14).
295
0.0
0.5
Micropore
1.0
1.5
Size, X (nm)
3. The number of statistical adsorption layers n versus the average micropore size % for the 14 activated carbons listed in Table I.
For small micropores, the number of adsorption layers formed on the micropore walls is limited: moreover, this number should be significantly smaller than that observed for nonporous solids. The experimental evidence for this statement is provided in Fig. 3 which shows the dependence of the number of statistical adsorption layers predicted by the BET eqn. (8) on the average micropore size 2; accordingly, the number of adsorption layers increases as the average micropore size X increases.
For small
micropores, the BET equation predicts that the number of statistical adsorption layers is less than two (cf., Table I). CONCLUSIONS For many microporous activated carbons, the comparisons shown in Figs l-3 of the BET parameters with the micropore parameters indicate that the BET parameters change gradually with an increase in the microporosity of these carbons. For activated carbons that are characterized by a small value of the average micropore size, the number of adsorption layers is less than two, and the BET constant has a large value; as the average micropore
296
size z increases, the number of adsorption layers increases but This gradual change of the BET
the BET constant C decreases.
parameters with microporosity indicates that the parameters provide valuable information about the microporous structure of activated carbons. ACKNOWLEDGMENT This work was supported in part by the National Science Foundation under Grant No. CBT-8721495 and by the Polish Program We thank Mr. Lu for providing the
of Basic Research RP-I-08. figures. REFERENCES 1
S. Brunauer, P.H. Emmett and E. Tellner, J. Am. Chem. Sot., &Q (1938) 309.
2
ica 1 Adsorntion of Gases, D.M. Young and A.D. Crowell, P hv s'
3
M. Jaroniec and R. Madey, Phvsical
Butterworths, London, 1962. mSolids, 4
Elsevier, Amsterdam, 1988.
D. Dollimore, Surface Technol ., & (1976) 121.
5
J. Cortes, Advan.,
6
M.M. Dubinin, Carbon, 2;L (1983) 359.
22 (1985) 151.
7
D. Burevski, Croatica Chem. A&q,
a
(1987) 649.
8
J. Choma, Polish J. Chem., 61 (1989) 173.
9
M. Jaroniec and J. Choma, Mater. Chem. Phvs., u
10
(1986) 521.
M. Jaroniec, R. Madey, X. Lu and J. Choma, v,
4 (1988)
911. 11
M.M. Dubinin, Carbon, 22 (1985) 373.
12
M.M. Dubinin, 1,
13
M. Jaroniec and J. Choma, e,
14
M.M. Dubinin, Carbon, a
15
M.
9 (1975) 1. 22 (1989)
197. (1987) 593.
Jaroniec, R. Madey, J. Choma, B. McEnaney and T.J. Mays,
Carbon, 27 (1989) 77. 16
0. Kadlec, J. Choma, H. Jankowska and A. Swiatkowski, Collection
17
M.
0
n., u
(1984) 2721.
Jaroniec, R. Madey, X. Lu and J. Choma, Carbon, 22 (1989)
485. 18
H. Jankowska, A. Swiatkowski, J. Oscik and R. Kusak, Carbon, a
19
M.
(1983) 117. Jaroniec and R. Madey, J.,
a
(1989) 5225.