Langmuir 1998, 14, 7271-7277
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Predictions of Adsorption Equilibria of Nonpolar Hydrocarbons onto Activated Carbon D. D. Do* and K. Wang Department of Chemical Engineering, University of Queensland, St. Lucia, Queensland 4072, Australia Received May 19, 1998. In Final Form: September 28, 1998 This paper presents a new approach to analyze the adsorption equilibria of nonpolar hydrocarbons onto activated carbon. The kinetic theory of gases and the 10-4-3 potential energy were employed to describe the adsorption process inside micropores. On the basis of this theory, a general isotherm model was proposed which possesses the potential capability of predicting the adsorption equilibria of an adsorbent by using the knowledge of its microporous structure and molecular properties of adsorbates. Experimental data of gases and vapors on Ajax activated carbon were employed to examine the model. Adsorption equilibria of binary mixtures were also investigated with the model, and it is shown that the model is capable of simulating the nonideal, or azeotropic, adsorption behaviors resulting from the structural heterogeneity of the adsorbent.
1. Introduction The physical adsorption process on microporous materials such as activated carbon (AC) is mostly controlled by the microporous structure of adsorbents. This is at least true for nonpolar adsorbates for which the adsorption is due to the dispersive forces between the adsorbate molecule and the surface atoms of the micropore. For polar adsorbates, the additional effect of electrostatic interactions between charges may also play an important role. However, for weakly polar adsorbates, the dispersive forces of the micropore still play a dominant role, and we will address the effect of micropore size distribution on the adsorption equilibria of nonpolar and weakly polar adsorbates in this paper. The pore structure of AC is usually characterized as that comprising of slit-shaped pores, and these pores are not straight as in graphite but rather twisted and interconnected. However, for the purpose of computation, we idealize the micropores as infinitely long slit pores with no imperfection within the slit as also assumed by many other workers in this area. Since this is the idealization of the “real” micropore, the micropore size distribution extracted from the fitting between the equilibrium data and the theory must be treated as our best approximation to the “intrinsic” micropore size distribution. It is practically impossible to account for all the fine details of the structure topology of AC. Nevertheless with this idealization we are able to compare in a qualitative sense the difference between AC in terms of the micropore size and its distribution and, thence, their performance in equilibria and kinetics. For nonpolar or weakly polar adsorbates the information of the micropore size distribution helps us to obtain the adsorption equilibria if the interaction between the adsorbate molecule and the surface atoms is assumed to be modeled by the LennardJones potential model. Thus, to obtain the adsorption equilibria, we need a model on the micropore structure and another model on the interaction between the adsorbate molecule and the micropore. If the micropore has a distribution, it is then regarded as the source of (1) Gusev, V. Y.; O’Brien J. A.. Langmuir 1997, 13, 2822. (2) De Boer, J. H. Dynamical Character of Adsorption; Oxford: London, 1968.
heterogeneity as pores of different size will exert different interaction energy with the adsorbate molecules. Furthermore the size of the adsorbate molecule also plays an important role because it will limit the range of pores for which they are accessible. In general, the smaller the micropore size, the stronger the interaction, but when the pore is smaller than a certain size, r*, the interaction is weaker due to the increasing importance of the repulsive force. For pores having openings smaller than the adsorbate molecular size, the adsorbate molecule will be excluded. All these factors will be taken into account in this paper to calculate the adsorption equilibria without using any fitting parameters. Research of this kind can be found in the literature, but it is limited to sophisticated approaches1 such as the statistical mechanics approach. In this study, we will employ the kinetic theory of gases in conjunction with the potential theory in a pore to derive the adsorption equilibria in that pore. If the micropore size distribution is known, the overall adsorption equilibria can be obtained by summing the contributions of all pores. 2. Theory The adsorption process is known to be a dynamics one with continuous adsorption into and evaporation (desorption) away from the surfaces or micropores. When the surface loading is very low, the rate of adsorption is the same as the rate of collision of adsorbate molecule onto the solid surface times a constant called the sticking coefficient R, which can be regarded as the fraction of molecules that when colliding with the rim of micropore opening will enter the pore. Thus if the molecular mass is m and the adsorbate pressure is P, the rate of adsorption is2
Ra )
RP
x2πmkT
(1)
Here k is the Boltzmann constant. The rate of desorption from a micropore is governed by the law of desorption
( )
Rd ) σmkd,∞ exp -
10.1021/la980592n CCC: $15.00 © 1998 American Chemical Society Published on Web 11/13/1998
Ed θ RT
(2)
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where σm is the monolayer coverage (molecules/cm2), kd,∞ the desorption rate constant at infinite temperature (or zero activation energy), Ed the desorption activation energy, and θ the fractional coverage. The rate constant for desorption at infinite temperature is related to the vertical vibration time of the adsorbate molecule as follows:
molecule-1 K-1), and the reference temperature, T0 ) 273 K, we calculate the first factor of eq 7 as follows:
kd,∞ ) 1/τd,∞
(6.2 × 10 )(1 × 10 )x2π(4.65 × 10-23)(1.38 × 10-16)273
(3)
For physical adsorption process, it has been shown by Kiselev and Poshkus that3
τd,∞ = 1 × 10-12 (s)
(4)
At equilibrium, the rate of adsorption is equal to the rate of desorption, resulting in the following expression for the fractional loading as a function of pressure under the conditions of very low loading (the Henry’s law region).
θ)
( )
Ed RP exp RT σmkd,∞x2πmkT
(5)
The preexponential coefficient in the above equation can be expressed in terms of a reference adsorbate and at a reference temperature. We take the reference adsorbate as nitrogen and the reference temperature of 273 K. Then the monolayer coverage of any adsorbate “k” is
σm,k ) σm,N2
( ) σN2
(6)
σk
D
σm,N2kd,∞x2πmN2kT0 14
) (1/4)
12
β ) 1.215 × 10-6 (kPa-1)
(8)
So the fractional loading of any species as a function of pressure (eq 7) will become
( )( ) ( ) ( )
θ)β
σ σN2
MN2
D
1/2
M
T0 T
mN2
1/2
mk
T0 T
1/2
exp
Ed RT
(7)
Now let us address the numerical values for some of the parameters in the above equation. If the collision mechanism of the adsorbate molecule at the pore rim is to follow the Knudsen mechanism, then the probability of molecule entry into the pore is:
The monolayer coverage for nitrogen and the desorption rate constant are obtained from the work of Hobson5 and Kiselev and Poshkus:3
σm,N2 ) 6.2 × 1014 (N2 molecules/cm2) kd,∞ ) 1 × 10
exp
Ed P RT
(9)
This is the general expression for the fractional loading versus the pressure. For example, with ethane as the adsorbate, its molecular diameter is 4.418 Å, and if the adsorption temperature is 303 K, we calculate
β
( )( ) ( ) σ σN2
D
MN2 M
1/2
T0 T
1/2
(1.215 × 10-6)
)
( )()( ) 4.418 3.681
28 30
2.5
1/2
273 303
1/2
)
where the molecular diameter of nitrogen has been taken as 3.681 Å.6 Thus the fractional loading of ethane at 303 K is
θ ) 1.75 × 10-6 exp
-1
(s )
( )(
)
Ed P RT 1 kPa
(10)
From the experimental data of ethane on Ajax AC,7 we obtain the following expression for the fractional loading:
θ ) 1.36 × 10-6 exp
( )(
)
Ed P RT 1 kPa
(11)
The calculated fractional loading is about 1.3 times larger than the experimental value, and this could be attributed to the lower probability of entry when ethane molecules hit the rim of the micropore. If this is so, then the probability of entry is 0.19 instead of 0.25 as suggested by the Knudsen theory. Thus beside a small numerical difference between the experimental value and the theoretical value, the fractional loading versus pressure for any species is given by eq 9 or
R ) 1/4
12
1/2
1.75 × 10-6 (kPa-1)
( )( ) ( ) ( )
σk σm,N2kd,∞x2πmN2kT0 σN2 RP
R
D
where D is the fractal dimension of the adsorbent.4 For a perfect flat surface the fractal dimension is 2, while for microporous solids the fractal dimension is between 2 and 3. In the absence of information on the fractal dimension, it can be taken as 2.5. On substitution of eq 6 into eq 5, we obtain the following expression for the fractional loading for any adsorbate written in terms of the reference adsorbate nitrogen and the reference temperature T0
θ)
β)
θ ) b∞ exp
( )
Ed P RT
(12)
where the preexponential coefficient is given by
b∞ ) β
( )( ) ( ) σ σN2
D
MN2 M
1/2
T0 T
1/2
(13)
Knowing the molecular mass of nitrogen, mN2 (g/molecule), the Boltzmann constant, k ) 1.38 × 10-16 (g cm2 s-2
Equation 12 is applicable for very low fractional loading on AC. For high loading, we assume that the Langmuir equation is applicable
(3) Kiselev, A. V.; Poshkus D. P. Trans. Faraday Soc. 1963, 59, 176. (4) Keller, J. U. Physica A 1990, 166, 180. (5) Hobson, J. P. J. Chem. Phys. 1965, 43, 1934.
(6) Bird, R.; Stewart, W.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 1960. (7) Do, D. D.; Do, H. D. Chem. Eng. Sci. 1997, 52, 297.
Adsorption of Nonpolar Hydrocarbons
Langmuir, Vol. 14, No. 25, 1998 7273
( ) ( )
Ed P RT θ) Ed 1 + b∞ exp P RT b∞ exp
(14)
〈θ〉 )
∫r
min
( ) ( )
Ed P RT f(r) dr Ed 1 + b∞ exp P RT b∞ exp
(15)
where rmin is the minimum pore half-width accessible to the adsorbate molecule and its value can be taken as 0.8885σsk for the 10-4 potential model.8 Knowing the overall fractional loading, the adsorption capacity can be calculated from the micropore volume W0 and the liquid molar volume of the adsorbate if the adsorbed phase inside the micropore is assumed to behave as liquid. So for species “k” adsorbing at a temperature “T”, the adsorption capacity is
Cµ,k )
W0
∫r
rmax
VM,k(T)
min
( ) ( )
Ek(r) P RT f(r) dr (16) Ek(r) 1 + b∞,k exp P RT b∞,k exp
where
b∞,k ) β with
( )( ) ( ) σk σN2
D
MN2 Mk
1/2
T0 T
{ [( ) ( ) ] [( ) ( ) ] [( )
2 σsk 5 * 3 sk 5 r + z σsk r-z
which under the limit of low pressures reduces to the linear equation as derived in eq 12. So far the adsorption equilibrium model is developed for a micropore of a given size. For solids such as AC, where we have a distribution of pore size, the overall adsorption equilibria can be obtained by summing the contributions of all pores. If we let the micropore size distribution as f(r) with f(r) dr being the fraction of volume of micropore having sizes ranging from r to r + dr, then the overall fractional loading is the average of the local fractional loading over the micropore size range
rmax
φ(r,z) )
1/2
β ) 1.215 × 10-6 kPa-1
and the interaction energy of adsorption is a function of micropore half width and other molecular properties as shown below
Ek(r) ) Ek(r;σk,sk*)
(17)
This interaction energy of adsorption is taken as the negative of the minimum adsorption potential energy inside the pore. For nonpolar and very weakly polar adsorbates, the potential energy of interaction is resulted from the dispersive forces between the adsorbate molecule and the surface atoms. Here we take the Lennard-Jones model of Steele, known as the 10-4-3 model, to describe the potential energy of interaction between a molecule and the micropore of slit shape, of which the wall is made of many parallel graphite lattice layers with a spacing between adjacent layers as ∆. The 10-4-3 model equation of Steele takes the following form (8) Wang, K.; Do, D. D. Langmuir 1997, 13, 6226.
4
-
10
+
σsk r-z
10
-
σsk4
3∆(0.61∆ + r + z)3 σsk4
σsk r+z
4
+
+
)]}
(
3∆(0.61∆ + r - z)3
(18)
where sk* ) (6/5)πFsskσsk2∆ is the minimum of the interaction energy between an adsorbate molecule and a single lattice layer and Fs is the number density of carbon molecule per unit volume. The values of ∆ and Fs are taken as 0.335 (nm) and 114 (nm-3), respectively.9 Equation 16 is the adsorption isotherm model for hydrocarbon molecules (in gas or vapor state) adsorbing onto AC. If the molecular properties of the adsorbate are known, we can compute for the interaction energy for each pore size by finding the minimum of eq 18, and if the micropore volume distribution is known, we can calculate the adsorption equilibrium by using eq 16 without using any fitting parameter. On the other hand, if the micropore volume distribution is not known, we can use eq 16 to fit the data to obtain the distribution. 3. Micropore Size Distribution from Isotherm Data To evaluate the potential of this theory, we apply the model eq 16 to the pure component adsorption equilibria of gases/vapors on the Ajax activated carbon,7 they are methane (5), ethane (3), propane (3), n-butane (4), benzene (4), and toluene (3). The number in parentheses next to the adsorbate is the number of isotherm curves available for that adsorbate. The applicability of the model is demonstrated in the following way. First, we use an optimization scheme to fit eq 16 to the experimental data of four species (methane, propane, butane, and benzene) simultaneously to obtain the structural parameters of the AC, namely, the micropore volume W0, the characteristic micropore half-width r0, and the degree of variance δ (eq 19a). Second, we use the obtained structural information to predict the experimental adsorption isotherm of ethane and toluene on the same adsorbent. The minimum interaction energies between an adsorbate molecule and a single lattice layer, sk*, are calculated from eq 18b using the molecular properties listed in Reid et al.10 and Breck.11 Since the accessibility of each species in microporous network of AC is dictated by its sizes and geometric configuration, the favorable geometry of each species is taken as its smallest configuration. The saturation liquid molar volume of each species at T ) 290 K are obtained from Perry’s handbook.12 These parameters are listed in Table 1 for all adsorbates studied in this paper. The micropore size distribution (MPSD) is represented by the following log-normal distribution function
f(r) )
{
}
[ln(r) - ln(r0)]2 1 exp 2δ2 rδx2π
(19a)
where r0 is the characteristic micropore half-width and δ is the degree of variance. This log-normal distribution is (9) Steele, W. A. The Interaction of Gases with Solid Surfaces; Pergamon: Oxford, 1974. (10) Reid, R. C.; Prausnitz, J. M.; Polling, B. E. The properties of gases and liquids; McGraw-Hill: New York, 1987.
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Table 1. The Molecular Properties of Hydrocarbon Adsorbates σk (Å) M (g/mol) sk* (kJ/mol) VM (cm3/mmol)
CH4
C2H6
C3H8
C4H10
C6H6
C7H8
CF4
3.81 16 9.885 0.130
3.9 30 12.40 0.0839
4.3 44 14.49 0.0877
4.3 58 16.61 0.1002
3.7 78 24.60 0.0885
3.81 92 26.10 0.1064
4.7 88 12.02 0.131
Figure 1. Adsorption isotherms of methane, propane, n-butane, and benzene on Ajax AC.
used to avoid the problem of negative domain encountered in the normal distribution. The log-normal distribution of eq 19a has the following mean and variance
rj ) r0 exp(δ2/2) and σ ) r0xexp(2δ2) - exp(δ2) (19b)
the temperature ranges between 30 and 200 °C. By optimally fitting the 16 isotherm curves, following structural parameters (PSD) of the adsorbent are derived:
W0 ) 0.47 cm3/g, r0 ) 0.4153 nm, δ ) 0.0920
3.1. Model Simulation. Using the values for the molecular parameters and liquid molar volume in Table 1 into eq 16, we compute the adsorption equilibria of the selected adsorbates for a given pore volume distribution of the Ajax AC. This is done for all temperatures of the adsorption isotherms. Once these equilibria have been computed, the calculated isotherms are compared with all the experimental data, and the optimization procedure is carried out to determine the pore volume distribution of the Ajax AC. In so doing, we obtain the good fit between the theory and all the experimental data (a total of 16 isotherm curves). The theoretical calculations (lines) and the experimental data (dots) are shown in Figure 1. The fit is regarded as good because several adsorbates and a wide range of temperatures are covered, e.g., for n-butane the temperature ranges from 10 to 150 °C, and for benzene
With these parameters, the mean pore half width and the variance of the adsorbent are calculated from eqs 19b as 0.417 and 0.0386 nm, respectively. These values are comparable to those obtained in the literature, and the micropore volume of 0.47 cm3/g is also comparable to most commercial AC. Carrying out the nitrogen adsorption onto this Ajax AC at liquid nitrogen temperature, a value of 0.44 cm3/g was obtained for the micropore volume.13 The lower value using nitrogen data at 77 K could be attributed to the extremely slow diffusion of nitrogen molecules in smaller micropores. Nevertheless the small difference between these two values could also be attributed to many other factors such as the difference in the intrinsic molecular properties, different experimental methods, the choice of the values for the molecular parameters, or the error in estimating the liquid molar volume. However, the important point of this work is
(11) Breck, D. W. Zeolite molecular sieves: structure, chemistry and use; John Wiley & Sons: New York, 1974. (12) Perry, R. H.; Green, H. Perry’s chemical engineer’s handbook; McGraw-Hill: Singapore, 1985.
(13) Do, D. D. Dynamics of Adsorption in Heterogeneous Solids. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces; Rudzinski et al., Eds.; Elsevier: Amsterdam, 1997; pp 777835.
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Langmuir, Vol. 14, No. 25, 1998 7275
Figure 2. Predicted adsorption isotherm of ethane and toluene on Ajax AC.
that equilibrium isotherm calculations can be made based on the knowledge of the micropore size distribution and the molecular properties of adsorbate. Thus if a carbon sample has a known micropore size distribution, the adsorption equilibrium isotherm can be calculated without a single fitting parameter. Our next step is to use the model equation and the derived structural parameters of the adsorbent to simulate the adsorption isotherm of ethane and toluene at various experimental conditions. The model prediction (lines) and the experimental data (symbols) are shown graphically in Figure 2. It can be seen that the model predictions are satisfactory, considering the simplicity of the theory and a range of the experimental conditions of ethane (283333 K) and toluene (303-363 K). It is also seen that the model predictions are much better for toluene than those for ethane. This can be explained as follows. Under the conditions used in the experiments, toluene is a subcritical fluid and its liquid molar volume has a physical meaning and is well tabulated. Ethane, on the other hand, is a supercritical fluid; hence we need to apply some empirical relations14 to estimate the effective “liquid molar volume”. This is the source of the uncertainty and hence could be the source for the discrepancy between the theory and the experimental data. Nevertheless, the agreement is very good as seen in Figure 2a, except over the high-pressure region. The micropore size distribution of Ajax AC is shown in Figure 3 (case 1), which is seen to be fairly symmetrical and around the mean value of 0.418 nm. The minimum pore half-width is 0.3 nm. This means that all the adsorbates studied for this AC can access all micropores. Also the maximum micropore of 1.2 nm is less than the upper limit for the micropore set by the IUPAC.15 This simple demonstration supports the theory presented in this paper, i.e., the adsorption process of gases/ vapors in microporous adsorbent like AC can be adequately described by the kinetics theory of gas and the adsorption potential energy in slit-shaped micropores. This finding also reinforces the theoretical basis of our previous study.8 More examples of the applicability of this model can also (14) Kapoor, A.; Yang, R. T. Gas Sep. Purif. 1989, 3, 187. (15) Sing, K. S. W.; Everett, D. H.; R. A. W. Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Reporting Physisorption Data for Gas/Solid Systems with Special Reference to the Determination of Surface Area and Porosity. Pure Appl. Chem. 1985, 57, 603.
Figure 3. Micropore size distributions of the three cases for the study of mean pore size effect.
be found in ref 8, in which the experimental data from the other group16 were used. 3.2. Effect of Mean Pore Half-Width and the Pore Variance. 3.2.1. Mean Pore Half-Width. We now apply the theory to study the effect of the mean pore halfwidth and the pore variance on the pure component as well as the multicomponent adsorption equilibria. The latter case will clearly show the significant influence of the micropore size distribution. We chose methane and carbon tetrafluoride (CF4, its molecular size is larger than methane) as the two model adsorbates and the PSD of Ajax AC obtained in section 3.1 as the reference (case 1). The effect of micropore half-width is studied by laterally shifting the distribution of Ajax AC such that in one case (case 2) the larger species CF4 is severely excluded while in the other case (case 3) almost all the micropores are accessible to both species. The variances of cases 2 and 3 are the same as the variance of the case 1 (Ajax). The distributions of all three cases are shown in Figure 3, where we also show the minimum accessible pore halfwidths for methane and CF4. Using the isotherm equation (16) the pure component equilibria of methane and CF4 at 273 K are simulated and (16) Valenzuela, D. P.; Myers A. L. Adsorption equilibrium data handbook; Prentice Hall: Englewood Cliffs, NJ, 1989.
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Figure 4. Pure component adsorption isotherm of CH4 and CF4 on ACs at 273 K.
Figure 5. Plot of adsorbed mole fraction of CH4 versus its gas-phase mole fraction for P ) 120 kPa.
Figure 6. Plot of adsorbed mole fraction of CH4 versus its gas-phase mole fraction, case 2 and P ) 5, 100, 500 kPa.
shown in Figure 4. We see that, in case 2 where CF4 is severely excluded, its adsorption isotherm is very sharp initially due to the strong affinity, but it has lower capacity due to the exclusion from entry into smaller micropores (Figure 4a). As a result, there is a crossover between the two isotherms at pressure of about 130 kPa. On the other hand, in case 1 where only a small fraction of the micropore is excluded toward the CF4, the saturation capacities of the two adsorbates are comparable (Figure 4b) and the crossover pressure occurs at a much higher pressure (6000 kPa compared to 130 kPa in case 2). Finally in case 3 where almost all micropores are accessible to both species, the adsorption isotherm of CF4 is very sharp initially and has a saturation capacity comparable to that of methane (Figure 5c). Next, we study the multicomponent equilibria of CH4/ CF4 on the above three ACs. The equation describing the adsorption equilibria of the component “k” in a mixture of NC adsorbates is given in the following equation:
Details of the features of the above equation can be found in our previous study.8 For cases 1 and 3 where the micropore volumes are accessible to methane and the majority of volumes are also available to carbon tetrafluoride, the binary system is favorable toward the stronger adsorbing species (CF4). The results are shown in Figure 5 as plots of the mole fraction of methane in the adsorbed phase versus the its mole fraction in the gas phase for a total pressure of 120 kPa and a temperature of 273 K. In case 2, where carbon tetrafluoride is excluded from entry to some of the micropores, the system is favored toward methane when its mole fraction is low and carbon tetrafluoride is favored when the mole fraction of methane in the gas phase is increased (see Figure 5). This is the case because when the mole fraction of methane is low (or the mole fraction of CF4 is high) the selectivity is favorable toward methane because most of the CF4 in the bulk phase is excluded. However, when the mole fraction of methane is increased, the selectivity is more favorable toward the stronger component, the CF4. Thus the azeotropic behavior is observed. It is important to point out here that the azeotropic behavior is observed only when the total pressure is greater than some threshold pressure. When the total pressure is less than this value, the system is more favorable toward the stronger component. We illustrate this in Figure 6 where we plot adsorbed mole fraction of methane versus
Cµ,k ) W0 VM,k(T)
∫r
b∞,k exp
rmax min(k)
NC
1+
( ) ( ) Ek(r) RT
b∞,j exp ∑ j)1
P(k)
Ej(r) RT
P(j)
f(r) dr (20)
Adsorption of Nonpolar Hydrocarbons
Figure 7. Pore size distributions of cases 1, 4, and 5.
its mole fraction in the gas phase for case 2, which has exhibited the azeotropic behavior when the total pressure is 120 kPa (Figure 5). Here three values of the total pressure, 5, 100, and 500 kPa, are used in the simulation. We see in Figure 6 that when the total pressure is 5 kPa, the system is always favorable toward carbon tetrafluoride at all compositions. On the other hand, when the total pressure is either 100 or 500 kPa, we observe azeotropic behavior and this is due to the exclusion of carbon tetrafluoride in some of the micropores, and in pores where only methane is accessible the total pressure is large enough for methane to have a strong competition with carbon tetrafluoride at some compositions, resulting in azeotropic behavior, and this azeotropic is stronger when the total pressure is increased, as expected. 3.2.2. Pore Variance. The effect of the variance of the micropore size distribution is also studied for binary adsorption equilibria. Figure 7 shows the other two distributions (case 4 and case 5) which have the same mean pore half width as the Ajax AC (case 1) but have different variances. Figure 8 shows the x-y diagram for the binary mixture of methane and CF4 at the temperature
Langmuir, Vol. 14, No. 25, 1998 7277
Figure 8. x-y diagram of cases 1, 4, and 5 with P ) 200 kPa.
of 273 K and the total pressure of 200 kPa. We note that the effect of variance is not as significant as the effect of mean pore half width as we have shown in the last section. 4. Conclusions Kinetics gas theory and adsorption potential energy in slit-shaped micropores are employed as the theoretical base to analyze the physical adsorption onto AC. The isotherm model gives two important results that are of both practical and theoretical significance. First it is able to predict the adsorption equilibria if the structural parameters of the adsorbent (by means of micropore size distribution) and the molecular properties of the adsorbate are known. Second it can explain the azeotropic behavior based on the micropore size distribution and the size difference between adsorbate molecules. The predictability of the model was verified with experimental data of various hydrocarbons on Ajax activated carbon. Acknowledgment. This project is supported by the Australia Research Council (ARC). LA980592N
