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Dual Langmuir Kinetic Model for Adsorption in Carbon Molecular Sieve Materials C. Nguyen and D. D. Do* Department of Chemical Engineering, University of Queensland, St Lucia, Qld 4072, Australia Received May 13, 1999. In Final Form: October 22, 1999 A model of adsorption in carbon molecular sieve materials (CMS) is presented in this paper. Adsorption kinetics is modeled as a series of two consecutive processes: nonselective adsorption of molecules in mesosupermicropores followed by the movement of such adsorbed molecules into small micropores through the pore mouth barriers. The rate of nonselective adsorption is found to be of the same magnitude for different probe molecules, and it is the second process that renders CMS the kinetic separation abilities. The model describes the experimental data very well, and the activation energy of the second step is analyzed with the aid of the molecular potential calculation to derive the effective width of the micropore mouth.
I. Adsorption in CMS Separation based on the difference in adsorption kinetics has been used in a number of gas treatment processes, such as air separation, etc. Its utilization can be found more often than before due to, on one hand, a better design and control of the sieving materials’ synthesis and, on the other, a better understanding of the processes undergoing in the kinetics separation. The theory to explain the exclusion mechanism is the most important aspect of the kinetic separation investigation. A large number studies have been carried out and reported in the literature. Broadly, they can be divided into three groups: (i) diffusion model;1-6 (ii) shell model;7-12 (iii) computer molecular simulation.13-17 In the first group, the separation ability is believed to arise from the difference in the diffusivities of molecules. This theory works well in zeolitic molecular sieves, where a regular pore network is present with quite uniform micropores on a relative scale. It does not, however, enjoy that success in carbon molecular sieves (CMS). This is mainly due to the irregularities in the pore system, which is an inherent characteristic of carbonaceous materials. The second approach is introduced largely due to the frequent failure of the first model in * Corresponding author. (1) Chihara, K.; Suzuki, M.; Kawazoe, K. J. Colloid Interface Sci. 1978, 64, 548. (2) Ruthven, D. M.; Raghavan, N. S.; Hassan, M. M. Chem. Eng. Sci. 1986, 41, 1325. (3) Chen, Y. D.; Yang, R. T.; Uawithya, P. AIChE J. 1994, 40, 577. (4) Trifonov, Y. Y.; Golden, T. C. J. Porous Mater. 1996, 3, 5. (5) Singh, A.; Koros, W. J. Ind. Eng. Chem. Res. 1996, 35, 1231. (6) Hu, Z.; Vansant, E. Carbon 1995, 33, 561. (7) Koresh, J.; Sofer, A. J. Chem. Soc., Faraday Trans. 1981, 77, 3005. (8) LaCava, A. I.; Koss, V. A.; Wickens, D. Gas Sep. Purif. 1989, 3, 180. (9) Dominguez, J. A.; Psaras, D.; LaCava, A. I. AIChE J. Symp. Ser. 1988, 84, 73. (10) Sykes, M. H.; Chagger, H.; Thomas, K. Carbon 1993, 31, 827. (11) Srinivasan, R.; Auvil, S. R.; Schork, J. Chem. Eng. J. 1995, 57, 137. (12) Reid, C. R.; O’Koye, I. P.; Thomas, K. M. Langmuir 1998, 14, 2415. (13) Suh, S. H.; MacElroy, J. M. D. Mol. Phys. 1986, 58, 445. (14) Rao, M. B.; Jenkins, R. G.; Steel, W. A. Langmuir 1985, 1, 137. (15) Schoen, M.; Cushman, J. H.; Diestler, D. H. J.; Rhykerd, C. L. J. Chem. Phys. 1988, 88, 1394. (16) Segarra, E. I.; Glandt, E. Chem. Eng. Sci. 1994, 49, 2953. (17) MacElroy, J. M. D.; Seaton, N. A.; Friedman, S. P. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces; Rudzinski, W.; Steele, W. A., Zgrablich, G., Eds.; Elsevier Science: New York, 1997.
describing the kinetics of CMS.8 It is based on the fact that CMS preparation involves a cracking process, which results in the narrowing of micropore openings. These constrictions allow smaller molecules to pass through quickly while they restrict the entry of larger molecules. Studies in the third group aimed at simulating the movement of probe molecules in the pore system with some assumed pore structure configuration. They can provide a good picture of kinetics if the pore configuration is well characterized to allow for the application of e.g. the Lennard-Jones potential equation. On the basis of observation gained during our work on CMS preparation, we believe that micropores of CMS are ink bottle shaped with the pore opening very comparable to the molecular size.18 This is to say that there are some advantages for CMS adsorption dynamic to be described by a shell model rather than by a diffusion model. In the literature, the shell model is often expressed by a Langmuir type mass action equation, in which only two phases, bulk gas and micropore adsorbed phases, are involved. An underlying assumption in this approach is that there is no or negligible adsorption in the region just outside the micropores. In other words, only transport pores and a uniform micropore system are present in CMS. In this paper, we argue that such an assumption is open for further improvement and that adsorption in CMS should be divided into selective and nonselective adsorption. Selective adsorption is adsorption in micropores, which imposes some exclusion effect against some adsorbates. On the other hand, nonselective adsorption comprises adsorption at all other sites, such as macromesopore walls, super-micropores, etc., that is, adsorption occurring before the entry of molecules into sieving micropores. The inclusion of the nonselective adsorption models adsorption in CMS as a process of mass transfer involving three phases, bulk gas P, nonselective adsorption S (hereafter also referred to as surface adsorption), and selective micropore adsorption M. A schematic diagram of the process is shown in Figure 1. The reason for including the third intermediate phase, the nonselective adsorption S, in the model is 3-folds: (i) Contribution of adsorption in mesopores of carbonaceous porous materials is small but not negligible. Furthermore, super-micropores, which are like mesopores do not exhibit selective adsorption properties. (ii) Due to a slow dynamic diffusion through (18) Nguyen, C.; Do, D. D. Carbon 1995, 33, 1717.
10.1021/la990584m CCC: $19.00 © 2000 American Chemical Society Published on Web 01/19/2000
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Figure 1. Schematic diagram of the two-step adsorption process in CMS and the potential energy diagram of adsorption in ink bottle pores.
micropore openings, contribution of adsorption in mesopores and super-micropores is significant in the early stage of adsorption. (iii) As an intermediate phase between P and M, surface adsorption may be an important factor in adsorption dynamics. A model allowing for the existence of all three phases is developed in this paper and tested against the experimental data for oxygen and nitrogen adsorption on Takeda CMS. II. Adsorption Model Very often in the literature, a Langmuir type rate equation is used for the shell model. This is because isotherms for CMS are by and large found to be of type I, which leads to the use of a Langmuir type kinetic. The classical Langmuir rate model assumes that the adsorption process has a zero activation energy and the desorption process has an activation energy equal to the heat of adsorption.8 When applied to adsorption in ink bottle shaped pores, however, the adsorption step exhibits a nonzero activation energy, which represents the energy that a molecule has to overcome to enter the pore opening. In this paper, we adopt a common potential energy diagram of the adsorbate molecules at different stages of adsorption shown in Figure 1. In the diagram, the potential energy of a molecule approaching the pore mouth decreases with distance to a minimum, after which it starts to increase rapidly due to the repulsive force of carbon atoms. To move further into the pore interior, the molecule must pass through the constriction at the pore mouth, that is,
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only when its potential is higher than the energy barrier exerted by the solid atoms. Once inside, the molecule moves along the pore axis by an activated surface diffusion process. In difference from others, we argue that the distance at which the potential energy is minimum in the diagram represents the location of the nonselective adsorbed molecules (phase S). Mass transfer between P and S includes a process of diffusion through the transport pore network and the surface adsorption, the latter of which controls the overall P-S mass transfer. This surface adsorption rate is assumed to be governed by Langmuir type kinetics. Similarly, the rate of mass transfer between S and M, which includes the penetration through the pore mouth constriction and the diffusion along the micropore axis, is determined by the slower pore penetration step. This process can be described by a Langmuir or a unimolecular reaction with activation energies of Eam and Edm. The definitions of these activation energies are shown in Figure 1. This model of adsorption will be referred to hereafter as the PSM model. 1. Rate Equations for Adsorption onto the Surface. We write the rate equations for the two adsorption steps: adsorption from the gas phase on the surface, kas(Ss S)P; desorption from the surface to the gas phase, kdsS; adsorption into micropores, kam(Ms - M)S; desorption from micropores, kdm(Ss - S)M. Here P is the pressure and M and Ms and S and Ss are the concentration and the maximum capacity of micropore and surface adsorption, respectively. The units of M and S are moles per unit mass of CMS. The rate coefficients are indexed as shown in Figure 1. 2. Adsorption Isotherms. Let us denote S* and M* the equilibrium concentrations of nonselective and selective adsorption, respectively. At equilibrium, rates of mass transfer in two directions are equal, leading to
kas(Ss - S*)P ) kdsS* kam(Ms - M*)S* ) kdm(Ss - S*)M* (1) from which we can derive the following isotherm equations for two adsorption sites:
S* ) Ss
bsP* bmS* M* ) Ms (2) 1 + bsP* Ss - S* + bmS*
Here bs ) kas/kda and bm ) kam/kdm are the affinity coefficients for surface and micropore adsorption, respectively. Substitution of eq 1 into eq 2 yields the equilibrium concentration of the micropore in terms of the bulk pressure:
M* ) Ms
bsbmP* 1 + bsbmP*
(3)
The overall adsorption isotherm is simply the sum of amounts adsorbed at two locations:
bsbmP* bsP* + Ss (4) C* ) M* + S* ) Ms 1 + bsbmP* 1 + bsP* At very low pressures (bsbmP*, bsP* , 1), eq 4 is reduced to C* ) (Msbsbm + Ssbs)P*, which is the Henry law with a Henry constant K ) (Msbsbm + Ssbs). The maximum capacity of CMS is (which is only achieved at sufficiently long time)
C s ) S s + Ms
(5)
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3. Rate Equations. Having defined equilibrium relations for CMS, we can now write the following Langmuir type kinetic equations for the three phases as follows. Gas phase:
V dP )[k (S - S)P - kdsS] dt mRT as s
(6)
Nonselective:
V dP dM dS )dt mRT dt dt
(7)
dM ) kam (Ms - M)S - kdm(Ss - S)M dt
(8)
Selective:
Here V is the gas-phase volume, m the sample mass, R the universal gas constant, and T the experimental temperature. Here we have assumed ideal gas behavior. 4. Model Parameters. The above equations are three differential equations describing the mass transfer between the three phases in CMS adsorption. The parameters of this model are Ss, Ms, kas, kds, kam, and kdm. They are not independent but rather related to each other according to some relations. For example kas and kds are related by the affinity of the surface phase (see eq 2), and so are kam and kdm. Furthermore the saturation capacities of the two phases are related to the overall observed saturation capacity (Cs ) Ss + Ms). Since the model will be used to describe kinetics data measured at different temperatures, the dependence of its kinetics parameters on temperature needs to be addressed. First we assume that the adsorption maximum capacity does not change significantly with T; that is, Ss and Ms are temperature independent. This is reasonable because the heat expansion coefficient for Cµs is small19,20 and the temperature variation is not that big. On the other hand, the dependence of the kinetic parameters kds and kam on temperature is described by an Arrhenius type equation; i.e., kds ) kds0 exp(-Eds/RT) and kam kam0 exp(-Eam/RT), respectively. Here Eds is the activation energy for a molecule to return to gas phase from the external surface to the micropore (which will be assumed to be equal to the minimum of the potential field between adsorbate molecule and the external surface). The parameter Eam is the activation energy for the external adsorbed molecule to penetrate the pore mouth. This activation energy is a function of the pore mouth diameter, as we would expect the smaller the pore mouth the higher is the activation energy Eam. Finally, the parameter kam is assumed to be proportional to the rate of molecules striking the surface, that is, from the kinetic theory of gases kam ) R/T1/2, where R is a proportionality coefficient. III. Experimental Section In this work, we used two CMS samples supplied from the Takeda Co. in Japan, Takeda-5A and 3A. Prior to the experiment, the samples were cleaned overnight in an oven at 130 °C to be rid of bulk water. The samples were then weighed and cleaned under high vacuum at 160 °C for at least 16 h. A volumetric batch adsorber, which is a common design for adsorption measurement,21 was set up with multiple MKS transducers (type 690) capable of measuring pressures over a wide range (1-20 000 Torr) and was used to measure the adsorption equilibrium and (19) Wang, K.; Do, D. D. Langmuir 1997, 13, 6226. (20) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by Powder and Porous Solids; Academic Press: London, 1999. (21) Nguyen, C.; Do, D. D. Langmuir 1999, 15, 3608.
Figure 2. Graphite stacking and pore wall configuration. the kinetic uptake curves at different temperatures. In the uptake experiments, the initial pressure was chosen close to 6.5 atm, which falls within the working pressure range of commercial air separation processes. The probe molecules used in this work are oxygen, nitrogen, and argon, which are supplied as high-purity gases by BOC (Australia).
IV. Results and Discussion 1. Calculation of the Potential Energy. Carbon Pore Wall Configuration. The potential energy of a molecule is a function of its position, and can be calculated theoretically as a sum of the interaction energy between the molecule and each carbon atom of the pore wall. In this work, we need to calculate the potential of a molecule along the adsorption path. Thus, a configuration for the pore wall structure is to be adopted such that, on one hand, it is capable of estimating the repulsive force exerted by the pore mouth atoms and, on the other hand, it is simple enough for the calculation. Various structureless pore wall configurations are usually assumed to derive compact integral potential energy equations such as the 10-4, 10-4-3, or 9-3 models. These models are not suitable for our purpose. This is because, due to the proximity of the adsorbate molecule to the pore wall, any assumption of homogeneous distribution of mass centers over the graphite plane or in the space of the graphite domain will lead to the underestimation of the effect of the repulsive forces exerted by individual carbon atoms nearest to the adsorbate molecule. This is the case of adsorption in CMS as we know that the molecules have to squeeze between carbon atoms at the pore aperture to get into the micropores. A more realistic model of the pore wall structure has been used in our previous work of equilibrium isotherm calculation. Here the micropore is visualized as the gap between the graphite sheets, which are stacked on top of each other with an interlayer spacing of 0.3354 nm. The stacking of the graphite layers is in a hexagonal arrangement, which is the most common form of stacking in graphite structure.22 The number of graphite layers of each pore wall is limited to 3 or 4, corresponding to a pore wall thickness of about 1.1-1.5 nm. This configuration of micropores is presented schematically in Figure 2. The mesopore wall is formed at the edges of the graphite sheets. Thus, mesopore adsorption is regarded as adsorption on the side surface of the stacking, while micropore adsorption occurs in the space between the graphite sheets. (22) Introduction to Carbon Science; Marsh, H., Ed.; Butterworths: Cornwall, U.K., 1989.
Adsorption in Carbon Molecular Sieve Materials
Figure 3. Potential field of nitrogen inside a micropore of halfwidth of 0.4 nm. Each minimum corresponds to the center of a benzene ring.
Figure 4. Activation energy as a function of the pore halfwidth (circle, oxygen; diamond, argon; triangle, nitrogen).
Potential Energy Field. This model structure of the pore wall makes possible the use of the Lennard-Jones pair potential energy between individual carbon atoms and the adsorbate molecule. We can calculate the potential energy field of a molecule attracted to the side of a graphite stacking, i.e., in mesopores. The minimum of this potential field is taken as the estimate for the activation energy Eds. Its value is approximately 8 kJ/mol for oxygen and 7 kJ/mol for nitrogen, which is quite close to the heat of adsorption on a graphite surface. Similarly, we can calculate the potential field distribution for an adsorbate molecule placed between the graphite layers, i.e., inside a micropore. Figure 3 shows the potential field of a nitrogen molecule in a micropore of half-width of 0.4 nm. The activation energy for the movement of the molecule within a micropore is the difference between the minimum and the energy at the saddle point of the potential field. For example, the activation energy for nitrogen diffusion in pores of half-width of 0.4 nm is less than 100 J/mol (cf. Figure 4). This activation energy for diffusion within a micropore is found not to be a strong function of pore width. Energy Barrier and the Activation Energy at the Pore Mouth. If we assign a structure for the deposited carbon at the pore mouth, we can calculate the potential of molecules passing the pore constriction. In this paper, we assume a simple structure for the deposited carbon such that its atoms are aligned with the carbon atoms of the pore wall. We also assume that the deposition creates a row of hexagonal carbon rings along both sides of the pore mouth and these rows of hexagonal rings are offset relative to the rings of the pore wall graphite sheet. The pictorial description of this structure is in Figure 2. In contrast to the case of a structureless pore wall config-
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uration, where the pore width is the same across the pore mouth, the pore wall configuration adopted here allows for the variation of the free clearance along the pore mouth. That is, the 3D arrangement of carbon atoms at the pore mouths creates a chain of apertures of different sizes, which impose different barrier energies for the adsorbate molecules. In this work, we take the activation energy Eam as the difference between the lowest energy barrier and the minimum of the potential field outside the pore mouth Eds. Results of the calculations are shown in Figure 4 for oxygen, nitrogen, and argon. We note that the activation energy increases rapidly with a decrease in pore size as we would expect. The order of the increasing in the activation energy is nitrogen > argon > oxygen. Using the same principles, we can calculate the activation energy Edm as a function of the pore width. Results of the calculation show that the activation energy at the pore entrance is always higher than the activation energy for surface diffusion inside the micropores. This supports the assumption that the movement through the pore mouth is the limiting process for adsorption in micropores. 2. Adsorption Equilibrium of Gases. Adsorption of oxygen and nitrogen is a frequent subject for CMS in the literature due to the importance of air separation by kinetics mechanism. This mechanism is known to be the only process for separation of nitrogen from oxygen as their equilibrium properties on carbon are very similar, making the separation based on affinity impossible.23 Knowing that nitrogen molecules have a size slightly greater than that of oxygen, the separation by kinetic mechanism has been shown in the literature as a nice means to take oxygen out of air by exposing it to CMS at relative high pressures. Of course this is possible only with materials having the pore mouth size such that nitrogen is partially or totally excluded from entry into the micropore interior. The equilibrium experiments showed that isotherms of nitrogen and argon are very close and quite similar to that of oxygen. At low pressures, they are almost identical. A Langmuir isotherm equation was used to fit the equilibrium data at all temperatures simultaneously to calculate the maximum capacity as well as the affinity as a function of temperature. The affinity coefficients calculated for nitrogen, oxygen, and argon are of the same order, but the maximum capacity of oxygen (∼4.5 mmol/ g) is higher than that of the others (3.4 mmol/g). A similar trend has been found in the work of O’koye et al.24 3. Dynamics of CMS Adsorption. Dynamic parameters are calculated by fitting the model to the dynamics data using a nonlinear optimization procedure. The optimization is carried out for all temperatures simultaneously on a Matlab platform. Examples of oxygen, argon, and nitrogen adsorption fittings are shown in Figure 5. As seen, the fitting for sample Takeda 3A is quite good for all gases and all temperatures. Results of the optimization process are shown in Table 1 and are discussed further below. Sieving versus Nonsieving Materials. For an ideal separation of nitrogen from oxygen, one would prefer to have a CMS that does not adsorb nitrogen at all. It is not possible, however, to achieve this due to the surface adsorption of nitrogen on regions of mesopores and supermicropores. The aim is then to minimize the extent of nonselective adsorption. Table 1 shows that the maximum surface capacities of all gases are of the same order, despite (23) Ruthven, D. M. Chem. Eng. Sci. 1992, 47, 4305. (24) O’Koye, I. P.; Benham, M.; Thomas, K. M. Langmuir 1997, 13, 4054.
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Figure 5. Fitting of uptake curves of oxygen (a), argon (b), nitrogen and (c) onto Takeda 3A at different temperatures (293 K, triangle; 303 K, circle; 313 K, diamond; 333 K, star). Table 1. Results of Molecular Calculation (Eds), Equilibrium Data Fitting (Cs), and Dynamic Data Fitting of Different Gases Takeda 3A param
oxygen
argon
nitrogen
Eds (kJ) Cs (mmol/g) Ss (mmol/g) Eam (kJ) kasa (1/(s/Pa)) kdsa (1/s) kama (g/(s/mol)) no. of curvesb
8 4.5 0.16 8.9 8.77 × 10-5 3.46 × 10-1 433 4
7.5 3.4 0.248 8.5 5.4835 × 10-5 4.27 × 10-1 3.14 3
7 3.4 0.328 24.4 3.97 × 10-5 6.12 × 10-1 3.22 3
a
At 303 K. b Used in optimization.
the fact that the oxygen total capacity is significantly higher than that of the others (4.5 compared to 3.4 mmol/ g). A possible explanation is that besides the difference in molecule packing density, nitrogen and argon may be excluded from some pores, which are accessible only to oxygen molecules. The maximum nonselective capacity of Takeda 3A represents only a small fraction (less that 10%) of the total capacity, which means that, for this commercial air separation adsorbent, more than 90% of the pore capacity is oxygen-nitrogen separation effective. When we apply the model to fit the experimental data of Takeda 5A, we observe that the time frame to reach equilibrium in dynamic measurement is similar for all three gases. This means that the movement of all three gases through the pore mouth is not restricted, and this sample shows no sieving effect against them. The assumption of a limiting pore mouth penetration step is no longer justified. The result is a much less satisfactory fitting than for the case of Takeda 3A. Another reason to show that the sieving effect is not applicable for the Takeda 5A sample is when the model is applied to the kinetic data of Takeda 5A, sometimes we obtain a negative activation energy Eam (though its magnitude is small). Thus the sieving mechanism is not applicable for Takeda 5A, but rather a diffusion model is more suitable for this adsorbent. Selective versus Nonselective Adsorption. As discussed above, the model simulates the uptake curve as a sum of selective adsorption in micropores and nonselective adsorption in mesopore. Results of the model simulation of adsorption onto Takeda 3A at 303 K are shown in Figure 6. We observe that surface adsorption is very fast and it is practically completed in very short time (of the order of a few seconds). This is true for all three gases. The time scale for the penetration into the micropore is much longer,
which is of the order of 1000 s for nitrogen and argon. During this time the driving force for mass transfer into the micropore is the difference between the equilibrium adsorbed concentration on the outer surface and the concentration inside the micropore. Since the concentration inside the micropore is low during the course of adsorption (except near the end), this driving force is nearly constant, giving rise to a linear uptake into the micropore as seen in Figure 6. Due to the differences in rate and saturation capacities of selective and nonselective adsorption, the relative contribution of these two sites varies with time as shown in Figure 7. The contribution of nonselective adsorption dominates in the early stage while the selective adsorption dominates the rest of the course of adsorption. The switching over between nonselective and selective adsorption is different for different adsorbates. This switch is much sooner for oxygen than for nitrogen, indicating the better penetration into the micropores by oxygen than by nitrogen. Another point that is also worthwhile to note is the adsorption of oxygen and other gases at different sites. Besides the difference in the time scale to reach equilibrium (cf. Figures 5 and 6), we observe that under given conditions, surface adsorption of nitrogen contributes up to 25% of the total adsorption, about two times higher than that of oxygen. It is worthwhile to note that, as discussed earlier, at saturation the contribution of surface adsorption is less than 10%, which implies that the relative contribution of the surface adsorption decreases with increasing pressure. Further, results of the fitting also show that the relative contribution of nonselective adsorption increases with temperature, meaning kinetic separation at raised temperatures is not favorable. In Table 1, we can see that the nonselective rate coefficients kas and kds of Takeda 3A are comparable for oxygen and nitrogen. On the other hand, the selective rate coefficients kam and kdm for oxygen and 2 orders of magnitude higher than those for nitrogen. This means that theoretically if there were no nonselective adsorption, the separation factor would have been of the order of 100. However, due to the effects of nonselective adsorption in pores larger than micropores, this factor is smaller. Activation Energy and Pore Mouth Width. As seen in Table 1, the pore entry activation energy Eam of oxygen is about the same as its activation energy Eds. This difference in slightly higher in the case of argon, while for nitrogen Eam is about three time higher than Eds; that is,
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Figure 6. Experimental (symbol) and model calculation (solid line, total adsorption; dotted, nonselective; dashed, selective) of adsorption dynamic of oxygen (a), argon (b), nitrogen (c) at 303 K onto Takeda 3A.
potential calculations, which means we can estimate the pore mouth width once the activation energy Eam is obtained from experiments. The so estimated pore mouth half-widths of Takeda 3A using different gases fall in the range from 0.3 to 0.31 nm. Considering the various errors associated with experimental measurements and assumption regarding the configuration of the pore mouth, such a close result for different probe gases at least points to the correct mechanism of sieving and the mathematical model proposed in this paper. It is important to note that the half-width reported here is the surface to surface distance between the two opposite graphite layers and that the dimension of the free clearance is larger due to the offset shifting of carbon rings and the 3D arrangement of individual carbon atoms. Figure 7. Contribution of nonselective (dotted line) and selective adsorption (solid line) of oxygen (left) and nitrogen (right) onto Takeda 3A at 303 K.
the probability of nitrogen and argon going back into the bulk gas is greater than that of entering the micropores. The following question then arises: why is the exclusion effective for argon while its activation energy is not much higher than that of oxygen? Here we put forward the explanation that it is the difference in the preexponential factor, which gives oxygen much faster kinetics compared with argon as the kinetic separation can be achieved for gases having different activation energies and/or preexponential factors (Eam and kam0, respectively). The differences in the preexponential factor were also mentioned in work of Chagger.25 As discussed before, Eam and Edm are a function of the pore mouth width as obtained from the theoretical (25) Chagger, H. K.; Ndaji, F. E.; Sykes, M. L.; Thomas, K. M. Carbon 1995, 33, 1411.
V. Conclusions The proposed model of two consecutive processes, nonselective followed by selective adsorption, is capable of describing the dynamic of adsorption in CMS supplied by Takeda. This means that the kinetic separation is possible even in the case where the nonselective adsorption is present and that a uniform pore size distribution is not a prerequisite for kinetic separation. Parameters extracted from the analysis of experimental data for nitrogen, oxygen, and argon are consistent with each other. In particular the activation energy for the process of penetration through the pore mouth can be used to provide information about the size of the pore mouth via the aid of the theoretical potential calculation. Acknowledgment. Support from the Australian Research Council (ARC) is gratefully acknowledged. LA990584M
