Fundamenrals of Adsorption Proc. IVth Inr. Conf, on Fundamentals of Adsorption, Kyoto, May 1722, 1992 Copyright 0 1993 International Adsorption Society
Heterogeneous Micropore Structure and Vapor Adsorption on Activated Carbons
Zili Xie , Cunqiao Yuan, Lan Ma, and Kunmin Guo Research Institute of Chemical Defence, West Building, P. 0. Box 925, Beijing, 100083, P. R. CHINA
ABSTRACT A new form of the JC equation, which is based on the DR equation but expresses the vapor adsorption on activated carbons with heterogeneous micropore structure, is presented in this paper by introducing the concept of characteristic adsorption energy. The parameters involved represent the characteristics of both the heterogeneous micropore structure and the vapor adsorption on activated carbons.
INTRODUCTION
The more and more practical applications of activated carbons as adsorbents are due to their welldeveloped micropore structure. At present these microporous solids are generally characterized by adsorption methods for there are few physical ones by which much information about the fine and complicated micropores can be given. Among them the QS method[ 1,2], which has been recommended by the International Union of Pure and Applied Chemistry (IUPAC) [31, is one of the most popular. By it the maximum amount adsorbed on micropores, which is equivalent to the total micropore volume, can be determined. Besides the total micropore volume, other information such as the micropore dimensions and distribution is also important, although the related adsorption theory is still in developing. For vapor adsorption occuring on microporous odsorbents, the theory of volume filling of microp ores (TVFM) [4,5] has been generally accepted. DR equation is successful in expressing vapor adsorption on activated carbons with homogeneous micropores [683, as has been verified by a great number of researches in the past few decades. Considering that most activated carbons in practical use have heterogeneous micropores on which the vapor adsorption behavior deviates more or less from the DR equation, Stoeckli assumed that the micropores take a form of the normal distribution and derived an adsorption isotherm equation (DRS equation) on the basis of DR equation by integration [S, 61. This idea is significant, but the micropore distributionnormal distribution is considered unrealistic [9] and the resulted adsorption equation DRS equation is too complicated. So Jaroniec and Choma developed the idea by proposing a gamma type distribution and obtained a simple adsorption equation JC equation [ l o , 111.
0 Note : This project was supported by the National Natural Science Fundation of China. 743
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In this paper, we will present some valuable ideas.
THEORETICAL Adsorption Equation The micropore distribution of activated carbons is assumed as follows :
where x is the slit halfwidth in the slitllike micropore model [5]; W, is the volume of microp ores whose halfwidths are less than x;
wo is the total volume of micropores;
qk and N are parame
ters and greater than zero; r(N) is the gamma function. The distribution function G ( x ) given by Eqn (1) is defined on the domain [O ,). It is noticed that the distribution function G ( x ) given by Eqn (1) is a little different from that proposed by Jaroniec and Choma [ l o , 113. This change will give a little more convenient results. The differential adsorbate amount dW adsorbed on every micropore element dw, in which the micropore sizes are from x to x+dx can & expressed by:
where 0 is the degree of micropore filling given by the DR equation [5]
:
In Eqn (3) , A is the adsorption potential 8 B is the similarity coefficient reflecting the nature of adsorbates which equals unity for benzene; k is the proportionality factor and equals 1 2 . 0 kJ * nm/ mol. The adsorption potential is defined by :
where P is the vapor pressure at adsorption equilibria, Ps is the saturation vapor pressure. T is the absolute temperature and R is the universal gas constant. Integrating Eqn (2) gives:
that is
Eqn (6) can be compared with the JC equation Ell, 1 2 ) :
Heterogeneous Micropore Structure in Activated Carbons 745 n+l
(7)
Both the meaning of parameters q and n in JC equation and how they influence the degree of micropore filling (W/Wo) are hard to find, so we introduce:
and the following adsorption equation is resulted from Eqn (6)
:
where
EO may be defined as the characteristic adsorption energy of benzene on activated carbons with heterogeneous micropore structure. The adsorption equation ( l o ) seems to be a little more complicated than the JC's one, but the parameters N and EO in it will give valuable information about both the heterogenous micropore structure and the vapor adsorption on activated carbons. Parameter N
According to the micropore distribution function G (x) given by Eqn (1 ) , the average value the dispersion a. and the most possible value x, can be found.
where
x,
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Z. Xie, C. Yuan,L. M a and K. Guo
y z = r ( ~ + m / ~ .~J( N i ;) I Combining Eqn (12) with (13) gives:
Eqn (1 6) shows that ax/
is the function of parameter N only and decreases with the increase of

N. Conversely, the parameter N is also the function of ux/ x only and increases with the decrease of u../ that is, the parameter N represents how homogeneous the micropore structure is. The more homogeneous the micropore structure is, the greater values the parameter N takes. Especially
x,
when ux+O,
N + m , and the adsorption equation (10) tends to DR equation :
(17)
On the other hand, Eqn (10) can be rewritten as, 1
Plotting 8 versus A/pEo at various values of N , we can find how the parameter N , which reflects the homogeneity degree of the heterogeneous micropore structure, influences 8cropore fillingat various values of A/BEo, as shown in Figl. I .o B
L
s =0 . 2
01 0 L.
S
5r


0.6
s 1 . 0
OD
6
s 2.J s 1 0 0
1 .o Reduccd rdsqrption potcritirl
2.0 A
FiR.1, Clieraakriatic Reduccd Adsorpliori C u r v e s AccorditiB L O Eqri (10) or (18)
the degree of mi
Heterogeneous Micropore Structure in Activated Carbons
747
Parameter EQ According to Eqns ( 1 2 ) , (13) and ( 1 4 ) , it is found that (19) OT
(20)
Eqn (11) combined with Eqn (19) or (20) gives
if
N>1/2

Eqns (21) to (24) show that EOis corresponding to a characteristic micropore size fa,x or f,x, in which fa, or f, is the function of the parameter N. On the other hard, Eqn (18) and Fig 1 indicate that, in spite of the parameter N , that is, however the micropore structure is, the degree of micropore filling reaches to l / e as long as the adsorp tion potential A reaches to the characteristic adsorption energy BEo. The higher the characteristic adsorption energy is, the lower the relative vapor pressure (P/Ps) is needed in order that the degree of micropore filling reaches to l/e or 0.368. In addition, Eqn ( 1 8) also gives
This means that, if two kinds of activated carbons have different values of the characteristic adsorption energy  one has a greater EOthan the other (but N is the same)  the degree of micropore filling on the former will be greater than that on the later at every relative vapor pressures (for a given adsorbate and temperature).
EXPERIMENTAL RESULTS AND DISCUSSION Three kinds of commercial activated carbons were selected as representative examples. Some information about them is contained in Table 1.
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Z. Xie, C. Yuan,L. Ma and K. Guo
Table 1. Information about Activated Carbons Code of Activated Carbon J1 GH 28 ZZ 07
Note: @ W, Stands for the Total Pore Volume (Including Mesopores and Macropores). It is Cor,S Stands for the Specific Surface Area of responding to the Adsorption Capacity at P=Ps. @ , Mesopores. It Was Evaluated According to Ref. [5]. The adsorption isotherms of benzene on the activated carbons were reliably determined at 25. 0% by the help of a gravimetric improved apparatus 112,131. These experimental isotherms ( in the relative pressure range from 0.907X l o v 5 to 0. 175 ) can be expressed by Eqn (10) with a good agreement, as shown in Fig 2. After evaluating the parameters N and EOin the adsorption equation (1 0) according to the experimental data (corrected [5]), we can calculate the parameters contained in Table 2 with Eqns (9), (12) to (16), and (21) to (24). The micropore distributions illustrated in Fig 3 were calculated with Eqn (1).
0.06
0.02
0.04
0.0
8’E: log
+
2
a
1 &,+
(e
I/!#
 2
.53
1)
A
Eaperimentrl, GH28
9 . .^ 4
a

I
Heterogeneous Micropore Structure in Activated Carbons Table 2. Parameters Characterizing Activated Carbons
J1
GH28 ZZ07
41.9 19.2 5.18
17.4 16.0 14.5
0.690 0.688 0.053 0.077 1.00 0.754 0.749 0.086 0.114 0.99 0.847 0.825 0.188 0.222 0.98
1.00 0.688 1.00 0.749 1 . 0 0 0.826
0.688 0.749 0.826
Table 2 and Fig 3 show that, carbon J 1 has the max N , min ux and the sharpest micropore distribution, whereas the activated carbon ZZ 07 has the min N , max ux and the widest micropore distribution. This means that J 1 has the most homogeneous micropore structure but ZZ  07 has the most heterogeneous micropore structure. In addition, it is also noticed that J 1 has the max Eo, min f,x, and the smallest micropores in general. Conversly ZZ  07 has the min EO, max f,x, x,
and the largest micropores in general. The characteristic micropore sizes are between
x and
but closer to x.,
On the other hand, Fig 1 indicates that, the characteristic reduced adsorption curve changes its form as the parameter N changes. It deviates more and more notable from that of DR equation (which is corresponding to infinite N or homogeneous micropore structure) with the decrease of N. The characteristic curves of the benzene on the three activated carbons are shown in Fig 4. It is apparent that, a t the same adsorption potential or relative vapor pressure, the degrecs of micropore filling of benzene on the activated carbons having higher EOare greater. To reach to the same degree of micropore filling, the lower relative vapor pressures are needed for benzene on the acdvated carbons having higher characteristic adsorption energy.
0
1.0

Calculated with Eqn. (10) JI Experimentul, CH28 Experimental, ZZ07
3 Erperimental, A
2 a
.i?
0.5
6
L
0
" U
i (*
a'
I
0
10 Adsorption potential
20
A [kI/ mol;
Fig.4. Characteristic Adsorption Curves of Benzene on Activated Carbons.
30
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Z. Xie, C. Yuan,L. Ma and K. Guo
CONCLUSIONS The adsorption equation (1 0) expresses the experimental data with a good agreement. The parameters N and EO involved in it represent the characteristics of both the heterogeneous micropore structure and the vapor adsorption on activated carbons. N reflects the micropore heterogeneity of activated carbons. It decreases as the micropore structure becomes more heterogeneous. the deviation of vapor adsorption from DR equation becomes more notable with the decrease of N. The parameter EOdenotes the characteristic adsorption energy and is corresponding to the adsorption potential at which the degree of benzene filling of micropores reaches to 0. 368. It increases as the micropores become smaller. The higher the characteristic adsorption energy is, the greater the degree of micropore filling becomes at a given adsorption potential, that is, easier vapor adsorption occurs on the activated carbons having higher Eo.
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