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Effect of Pore Blockage on Adsorption Isotherms and Dynamics: Anomalous Adsorption of Iodine on Activated Carbon S. K. Bhatia,*,† F. Liu,† and G. Arvind‡ Department of Chemical Engineering, The University of Queensland, Brisbane, Queensland 4072, Australia, and Department of Chemical Engineering, Indian Institute of Technology, Mumbai, Powai, Mumbai 400076, India Received October 27, 1999. In Final Form: December 21, 1999 Isotherm hysteresis and pore-blocking effects of trapped molecules on adsorption dynamics is studied here, using the iodine-carbon system in the 300-343 K temperature range. It is found that a portion of the iodine is strongly adsorbed, and does not desorb, even over very long time scales, while the remainder adsorbs reversibly as a homogeneous monolayer with a Langmuirian isotherm in mesopores. The strongly adsorbed iodine appears to adsorb in micropores and at the mesopore mouths, hindering uptake of the reversible iodine. The uptake data for the adsorption and desorption dynamics of the reversible part is found to be best explained by means of a pore mouth resistance control mechanism. It is concluded that the dynamics of the adsorption and desorption at the pore mouth is important at early stages of the process.
Introduction The understanding of both adsorption equilibrium and dynamics is crucial for the design and optimization of adsorption processes and has received much attention in the literature.1-4 Between these, adsorption equilibrium and the modeling of isotherms have received considerably greater attention than dynamics. Generally, investigations of the latter were devoted to hydrocarbon systems because of the related separation concerns and applications, and a number of transport models based on micropore and/or macropore diffusion were developed for such systems as well as for other related ones.5-10 In some works another mechanism, involving a pore mouth resistance and an evaporative barrier, was also proposed as being important in the dynamics.11,12 This prompted some workers13 to propose a modified transport model, utilizing an additional pore mouth incorporation step with Langmuirian kinetics. However, all such earlier studies were conducted in the presence of strong intraparticle gas-phase macropore concentration gradients, with multiparameter fits of the data. To unequivocally establish the importance of the pore mouth resistance, it is therefore necessary to operate in a regime not involving intraparticle and micropore * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: +61 7 3365 4199. Tel.: +61 7 3365 4263. † The University of Queensland. ‡ Indian Institute of Technology. (1) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. (2) Yang, R. T. Gas Separation by Adsorption Processes; Butterworth: Boston, 1987. (3) Karger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Microporous Solids; Wiley: New York, 1992. (4) Do, D. D. Adsorption Analysis: Equilibrium and Kinetics; Imperial College Press: London, 1998. (5) Bhatia, S. K. AIChE J. 1987, 33, 1707. (6) Gray, P. G.; Do, D. D. Gas Sep. Purif. 1990, 4, 149. (7) Bhatia, S. K.; Gray, P. G.; Do, D. D. Gas Sep. Purif. 1991, 5, 49. (8) Bhatia, S. K. Proc. R. Soc. London A 1994, 446, 15. (9) Hu, X. J.; Rao, G. N.; Do, D. D. AIChE J. 1993, 39, 249. (10) Bhatia, S. K. Chem. Eng. Sci. 1997, 52, 1377. (11) Barrer, R. M. Langmuir 1987, 3, 309. (12) Karger, J. Langmuir 1988, 4, 1289. (13) Do, D. D.; Wang, K. AIChE J. 1998, 44, 68.
diffusional resistances. To this end we have found that the iodine-carbon system provides a suitable means of investigating the pore mouth resistance, without complications of the above effects, because of its unusual characteristics as discussed below. Consequently, experiments have been conducted with this system to provide some insight into the pore mouth incorporation step, and they are reported as well as analyzed in detail here. Iodine is an important probe molecule used in structural and surface area analysis of carbons, but its adsorption has not been extensively investigated. Adsorption on activated carbon is also an important technique for trapping iodine from exhaust streams. In particular, radioactive gases released from nuclear reactors in the event of an accident are likely to contain large amounts of isotopic iodine, and adsorption on activated carbon is considered as one of the options for filtering these gases. Iodine-laden carbons have also been proposed for filtering odiferous gases. Studies of the adsorption equilibrium and dynamics of iodine on activated carbon are therefore of considerable interest. Despite its importance not much work has been reported on the iodine-activated carbon system. In early work Reyerson and Cameron14 reported that iodine adsorption was extremely slow and that a part of the adsorbed iodine remained in the charcoal, even after degassing for long periods of time. Subsequent studies by Kipling et al.15 and Kipling and Shooter16 confirmed these findings. The latter authors studied the adsorption on graphon and spheron 6 and found hysteresis to be present for the first adsorption-desorption cycle, after which both the isotherms coincided with the desorption isotherm. They ascribed the hysteresis or irreversibility of the first isotherm to strong lateral interactions among the iodine molecules, which they termed cooperative effects. Evidence of some chemisorption of the iodine over unsaturated surfaces was subsequently provided by Puri et al.17 Nevertheless, the hypothesis of physical adsorption with (14) Reyerson, L. H.; Cameron, A. E. J. Phys. Chem. 1936, 40, 233. (15) Kipling, J. J.; Sherwood, J. N.; Shooter, P. V. Trans. Faraday Soc. 1964, 60, 401. (16) Kipling, J. J.; Shooter, P. V. J. Colloid Interface Sci. 1966, 21, 238.
10.1021/la991418h CCC: $19.00 © 2000 American Chemical Society Published on Web 03/22/2000
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strong lateral interactions, proposed by Kipling and Shooter, is probably correct since they could extract much of the irreversibly adsorbed iodine by means of sodium thiosulfate. The presence of irreversibly adsorbed or trapped iodine suggests the possibility of pore-blocking effects which can alter the pore structure seen by molecules subsequently diffusing in the microstructure. This is supported by the results of Juhola18 who concluded that iodine was adsorbed predominantly in the micropores, and its relatively large size caused steric hindrance effects in these pores. The pore blocking by chemisorbed or irreversibly trapped molecules in the pore structure was also reported by Boehm et al.19 in studies of chlorine adsorption on carbon. They surmised that blockage of the pore mouths occurs, which significantly alters the pore width. In view of these interesting observations it was considered here that the pore blocking of activated carbon by iodine, and the effect on subsequent uptake dynamics of the reversibly adsorbed molecules, may help provide improved understanding of the pore mouth resistance. The use of pore-blocking agents such as nonane is important in the structural analysis of carbons,20 but little has been done on the effect of the pore blocking on the dynamics of adsorption. This article therefore attempts to provide some insight into this problem. Experimental Section To study the effect of pore blocking on adsorbate transport and dynamics, experiments were conducted with the adsorption of iodine on activated carbon. These experiments were conducted as part of an earlier study,21 but the results were not previously published. The experiments were conducted in both a static as well as in a dynamic flow apparatus, as discussed below. Sample Preparation. The activated carbon samples were obtained from Active Carbon India Ltd. (grade ACG-60). The samples were sieved and three narrowly sized cuts (7-10, 1014, and 16-22 mesh) were selected for use in the experiments. The samples were washed with absolute alcohol and then dried in an oven at a temperature of 470-500 K for a period of 24 h. They were then transferred to a desiccator and stored under helium. The activated carbon used had a micropore volume of 0.5 cm3/g, with a pore size distribution, obtained by CO2 adsorption at 194 K as discussed elsewhere.22 The iodine was resublimed iodine obtained from S.D. Fine Chemicals, Mumbai, and was used without further purification. Adsorption Data. Apparatus for Static Experiment. For the adsorption of iodine from a static vapor phase the following procedures were adopted. Exactly 25 mg of each of the three sample sizes was taken and placed in a Petri dish. This was then placed in a desiccator. A platinum boat with the iodine in the form of granules was placed in the center of the desiccator and the Petri dishes were kept at equal distances around the boat. The desiccator was then closed and evacuated to a pressure of around 3 Torr, after which the whole vessel was filled with helium. The samples were taken out and periodically weighed, and each time the evacuation and filling were done. When there was no change in the sample weight over a period of 24 h, it was assumed that saturation capacity had been reached. To keep the temperature constant, the desiccator was surrounded by a constanttemperature bath. In this way the equilibrium amount adsorbed (17) Puri, B. R.; Bhardwaj, S. S.; Sehgal, K. C. Indian J. Chem. 1971, 9, 574. (18) Juhola, A. J. Carbon 1975, 13, 437. (19) Boehm, H. P.; Treczki, B.; Schanz, K. In Adsorption at the GasSolid and Liquid-Solid Interface; Roquerol, J., Sing, K. S. W., Eds.; Elsevier Scientific: Amsterdam, 1982; p 395. (20) Martin-Martinez, J. M.; Torregrosa-Macia, R.; MittelmeijerHazeleger, M. C. Fuel 1995, 74, 111. (21) Arvind, G. Adsorption of Iodine on Activated Carbon, B. Tech. Thesis, Indian Institute of Technology, Mumbai, India, 1993. (22) Bhatia, S. K.; Shethna, H. K. Langmuir 1994, 10, 3230.
Bhatia et al. corresponding to saturation vapor pressure in the vapor phase was obtained. Apparatus for the Flow Experiment. In the flow experiments the iodine was carried over to activated carbon samples and then placed in the glass tube of a horizontal tube furnace, by means of a helium stream. The helium stream from the gas cylinder was first passed through a drier before being split into two parts. The first of these was saturated with iodine by passing it over a bed of I2 granules in a U-tube immersed in a controlledtemperature bath. This iodine-laden stream then mixed with the second helium stream, and the mixture flowed to the glass tube. The glass tube was placed at the center of a four-zone furnace having a tantalum heating element, and independent temperature control of each zone could be achieved using a PID controller. Baffles present at the entrance of the glass tube helped in mixing and reduced the time taken for steady state to be attained. The gas stream flowed continuously over the activated carbon samples that were periodically weighed to obtain the uptake data. When there was no weight change for a period of 24 h, it was assumed that steady-state conditions were obtained. The exit stream was stripped of iodine by passing it through a wash bottle containing a potassium iodide and sodium thiosulfate mixture. The flow rate was adjusted so that the iodine flow was always 4-5 times the adsorption rate, and the samples were not starved of iodine. Experiments were done at temperatures of 300, 323, and 343 K, to determine the first and second (after desorption) isotherms. The vapor pressure of iodine in the inlet stream could be varied by changing the ratio of the volumetric flow rates of the two helium streams as well as the temperature of the U-tube. The saturation of the stream exiting the U-tube was confirmed by collecting a sample in a gas bomb and determining the outlet iodine concentration by titration methods. Desorption data at each of the three temperatures was obtained by cutting off the stream flowing through the U-tube so that the mole fraction of iodine in the stream entering the glass tube was zero. Gravimetric measurements were made as mentioned above to determine the desorption dynamics.
Experimental Results and Discussion Adsorption-Desorption Isotherms. Figure 1 depicts the adsorption-desorption curves for the three temperatures, as obtained in the flow apparatus. Hysteresis is clearly evident at each of the three temperatures, with part of the iodine adsorbed in the first adsorption step being essentially irreversible. As seen from these figures, the amount of strongly retained or trapped iodine is less at higher temperatures. From the desorption curve at 300 K it is seen that the iodine capacity is 2.08 g/g of activated carbon, of which about 1.19 g/g of activated carbon is strongly adsorbed and is not removed upon desorption. Such apparent trapping of adsorbed molecules has been predicted by Seri-Levy and Avnir,23 and on the basis of their simulations, this trapping is attributable to surface and structural heterogenities. It was found here that this trapped iodine could be substantially extracted by sodium thiosulfate or desorbed by increasing the temperature. Upon re-adsorption following desorption it was found that the desorption isotherm was retraced, indicating that the desorbable iodine adsorbed reversibly. It was also found that this reversibly adsorbed iodine followed a modified Langmuirian isotherm
Ca(P*) ) Ct(P*) - C0 )
K*P*Cas [1 + (K* - 1)P*]
(1)
at all temperatures. Here, Ct(P*) is the total amount adsorbed at relative pressure P*, on the desorption or re-adsorption branch, Ca(P*) the amount of reversibly adsorbed iodine, and C0 the amount of trapped iodine [)Ct(0)]. Further, Cas is the amount of reversibly adsorbed (23) Seri-Levy, A.; Avnir, D. Langmuir 1993, 9, 3067.
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Figure 1. Adsorption isotherms obtained at (a) 300 K, (b) 323 K, and (c) 343 K. Table 1. Langmuirian Constants and Adsorption Parameters
Figure 2. Correlation of isotherms by the Langmuir model.
iodine at P* ) 1. Figure 2 depicts a plot of eq 1 on suitably transformed coordinates. The excellent linearity at all three temperatures indicates the adequacy of eq 1 for the reversibly adsorbed iodine. The success of eq 1 also implies that the sites on which the reversible iodine adsorbs are relatively homogeneous. This was also confirmed by using an energy distribution in conjunction with eq 1 in fitting the data, but the results indicated a highly peaked distribution, with all sites
temperature (K)
K*
300 323 343
29.97 90.09 125.68
Cas (g of I2/ g of activated carbon) Ps (Pa) K (Pa-1) 0.89 1.22 1.28
156.5 663.3 1913
0.1915 0.1358 0.0657
having a relatively uniform energy. Thus, the desorbable iodine is most likely adsorbing on mesopore surfaces, in which the dispersive forces are restricted to a narrow region near the pore walls, or on the surface of an apparently irreversibly adsorbed layer of iodine on micropore walls. Of these the former is also suggested by the results of Boehm et al.19 who observed that chemisorption of chlorine occurs predominantly on mesopore surfaces and micropore mouths, effectively blocking access to the micropores. Thus, the reversible iodine may be adsorbed over the chemisorbed layer. Table 1 lists the values of the various parameters, for eq 1 obtained from the slope and intercepts in Figure 2 at each temperature. The value of the equilibrium constant appears to increase by a significantly larger factor between 343 and 323 K, in comparison to that between 323 and 300 K. This result may signify a transition in state of the reversibly adsorbed iodine between 323 and 343 K, a feature supported by the dynamics studies discussed subsequently. In interpretation of the above results for the equilibrium constant, it may be noted that the heat of adsorption clearly
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varies with temperature. The low value of the adsorption energy, as obtained from the values of K in Table 1, in the range of about 3000-8000 cal/mol also confirms that the desorbable iodine is physically adsorbed rather than chemisorbed. Because this iodine is adsorbed on the mesopore surfaces as noted above, it is instructive to compare the above adsorption heats with the potential energy of an adsorbed iodine molecule on a carbon surface. To this end we use the well-known Steele potential:24
φ ) 2πFcClσCl∆
[(
) ( )
2 σCl 5 z
10
-
σCl z
4
-
(
σCl4
)]
3∆(0.61∆ + z)3 (2)
Here, Fc is the density of carbon sites and has the value 0.114 Å-3, while ∆ ()3.35 Å) is the interplanar distance of the graphitic sheets in carbon. σCI and CI represent the Lennard-Jones parameters for the I-C interaction and may be approximated in terms of the carbon-carbon and I-I parameters by
Cl ) xCCII σCl )
(
(3)
)
σCC + σII 2
(4)
For the carbon parameters we may use σCC ) 3.4 Å and CI/kB ) 28 K, while σII ) 5.16 Å and II/kB ) 474.2 K.25 With these constants eq 2 provides φIC ) -7356 cal/mol at z ) σCI. This may be slightly higher in magnitude at the location of the potential minimum. If instead it is assumed that the desorbable iodine is adsorbed on the surface of a strongly adsorbed monolayer, then it is necessary to consider the interaction with this layer as providing the primary contribution to the potential. This may be evaluated on the basis of the 10-4 potential
[ ( ) ( )]
2πIIσII2 2 σII φs ) a 5 z
10
σII z
4
(5)
Here, a represents the cross-sectional area of an adsorbed iodine molecule (22 Å2). Substitution of the parameter values given above, with z ) σII, provides φs ≈ -4300 cal/gmol. On the basis of eq 2 a further contribution of φIC ) -645 cal/mol may be estimated from the interaction with the underlying carbon yielding a total potential for the desorbable iodine of -4945 cal/gmol. These results would suggest that this desorbable iodine is adsorbed as a monolayer on a much more strongly adsorbed layer of the apparently irreversibly adsorbed iodine on the carbon surface at 300 and 323 K. At 343 K, however, the higher heat of adsorption indicates that the reversible iodine is predominantly on the mesopore carbon surface itself with little underlying iodine. At this temperature the trapped iodine is essentially restricted to the micropores where volume filling occurs. Indeed, the possibility of solid-like iodine multilayers at 300 K seems very likely in the mesopores. In support, it may be readily estimated that the potential energy of the desorbable iodine over a multilayer of solid iodine, obtained using the Steele24 9-3 potential, (24) Steele, W. A. Surf. Sci. 1973, 36, 317. (25) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987.
Figure 3. Uptake data for first adsorption at 300 K, for various particle sizes and closed as well as flow systems. (a) Closed system with P* ) 1 and flow system with P* ) 0.88. (b) Flow system with particle size 10-14 mesh and various pressures.
φ)
[ ( ) ( )]
2πn 3 2 σII σ IIIJ 3 15 z
9
-
σII z
3
(6)
has the value of -2750 cal/gmol. Here, n is the density of the multilayer, taken as that of solid iodine, and z has been chosen as σII. This value compares favorably in magnitude with the adsorption energy at 300 K. The total iodine capacity of 2.08 g/g at 300 K provides a volume of 0.42 cm3/g, based on an adsorbate density of 4.93 g/cm3. The latter corresponds to the bulk density of solid iodine which, as indicated by Juhola,18 may be higher than that of the adsorbate because of steric effects. This steric exclusion effect, related to the finite size of the iodine molecules, is therefore considered responsible for the slightly smaller micropore volume compared to the value of 0.5 cm3/g obtained from CO2 adsorption for this activated carbon.22 Adsorption-Desorption Dynamics. For the dynamics, initially, experiments were performed at 300 K using particles of three different sizes (7-10, 14-16, and 1622 mesh) in the static system with P* ) 1. Figure 3a depicts the first adsorption dynamics, indicating negligible effect of particle size. In this and all subsequent figures the uptake has been normalized by its maximum value as given by the isotherms in Figure 1. Also shown in the figure are the results from subsequent experiments with the flow apparatus, indicating consistency with the data from the static runs. In the flow experiments the value of P* used was 0.88; however, this difference is not of consequence as the adsorption is essentially complete, even at P* ) 0.88 as seen in Figure 1. The above independence of the adsorption dynamics to particle size clearly indicates that the transport resistance
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Figure 4. Temporal variation of uptake during desorption of iodine at 300 K. Symbols represent experimental data and solid lines the model calculations. (O) 7-10 mesh; (0) 10-14 mesh; (9) 16-22 mesh.
Figure 6. Temporal variation of uptake during desorption of iodine at 343 K. Symbols represent experimental data and solid lines the model calculations.
Figure 5. Temporal variation of uptake during desorption of iodine at 323 K. Symbols represent experimental data and solid lines the model calculations.
Figure 7. Temporal variation of uptake during re-adsorption of iodine at 300 K. Particle size: (O, b) 7-10 mesh; (2) 16-22 mesh. Symbols represent experimental data and solid lines the model calculations.
on the particle scale is negligible, and local microscale dynamics dominates. To test for the concentration dependence of the local microscale resistance, runs were conducted for the first adsorption dynamics in the flow apparatus with three different values of P*. Figure 3b shows the results of these runs, with values of P* ) 0.04, 0.22, and 0.88 for the three runs. The equilibrium amount adsorbed at these pressures follows that obtained from the first isotherm. It is clearly seen that the uptake is faster at higher P*, indicating that the local resistance decreases with concentration. The desorption experiments were carried out by taking a fully saturated sample (corresponding to P* ) 1) and passing a stream of pure helium over it continuously. Evidence that the particle size differences are not very significant in this case as well is clearly seen from Figure 4 which shows the desorption dynamics for the three different size particles at 300 K. The solid line in this figure and in Figures 5-7 discussed below represents model calculations to be subsequently discussed. Figures 5 and 6 depict the desorption results at 323 and 343 K respectively for 16-22-mesh particles. At these temperatures as well, independence from particle size may be expected, for gas-phase transport in macropores occurs at much faster time scales than those of the data. A distinctive feature of the above data is that the desorption occurs over considerably longer times than the
adsorption, indicating the asymmetry between them. This has in the past been considered to be due to an evaporative barrier11,12 between the adsorbate and bulk adsorptive, leading to a long tail in the desorption curve. An additional feature of interest is that at 343 K the desorption appears to be considerably faster (by over an order of magnitude) compared to that at 323 K, suggestive of a change of state of the desorbable iodine, possibly from a rigid solid-like layer to a more fluid liquid-like layer. The possibility that the adsorbed iodine is semisolid or liquid-like has already been suggested earlier.16 After the above desorption studies, re-adsorption studies were done at 300 K. As indicated the re-adsorption isotherm follows the desorption isotherm, and the desorbable iodine is reversibly adsorbed. Figure 7 shows the results for two different particle sizes, obtained in the static system with P* ) 1, again showing independence from this variable. The time scale of the adsorption of about 6 h is much smaller than that of desorption (≈250 h) shown in Figure 4, and about a third of the first adsorption shown in Figure 3. Figure 7 also depicts the results for P* ) 0.6 during the re-adsorption, obtained in the flow apparatus for 7-10 mesh particles. In this the re-adsorption time is about 22 h, and almost four times that for P* ) 1, again suggestive of strongly concentrationdependent transport coefficients.
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Interpretation of Uptake Dynamics. In interpreting the above results for the adsorption and desorption dynamics, it is important to note that the first adsorption isotherm, depicted in Figure 1, is a metastable one23 and does not represent the true adsorption equilibrium, in view of the fact that some of the iodine is apparently irreversibly adsorbed. Consequently, it was decided that only the uptake dynamics of the reversibly adsorbed iodine be analyzed in detail. In this case the isotherm, given by eq 1, is clearly an equilibrium one. A distinctive feature of the dynamics for the reversible iodine is that the desorption process at 300 K occurs about 30-40 times slower than the adsorption at P* ) 1 (cf. Figures 4 and 7). This is indicative of a kinetic resistance at the mesopore mouths,11 with desorption being impeded by the adsorption energy barrier. Such a resistance is also suggested by the observations of Boehm et al.19 of pore mouth blockage by the strongly or apparently irreversibly adsorbed material. Assuming the carbon to be comprised of microporous and mesoporous grains, a simple model based on a grain surface barrier as providing the controlling resistance, following Langmuirian kinetics, yields
dCa 3 ) [kaP*(Cs - Ca) - kdCa] dt rg
Figure 8. Plot of [-ln(1 - fa)] vs time for re-adsorption of reversible iodine at 300 K with P* ) 1. (b) 7-10 mesh; (2) 16-22 mesh.
(7)
which, when combined with eq 1, simplifies to
dC/a ) k′d[1 + (K* - 1)P*](1 - C/a) dt
(8)
for adsorption at bulk gas relative pressure P*. Here, rg is the grain radius while ka and kd are kinetic coefficients, kd′ ) kd/rg, and we have used the relations
ka ) K* - 1 kd Cs )
K*Cas (K* - 1)
(9)
Figure 9. Plot of [-ln(1 - fa)] vs time for re-adsorption of reversible iodine at 300 K with P* ) 0.6. Particle size: 7-10 mesh.
(10)
that arise when the steady state of eq 7 is compared with eq 1. Further,
fa ) C/a(t) )
Ca(t) K*P*Cas/[1 + (K* - 1)P*]
(11)
is the fractional uptake. For desorption from particles saturated at P* ) 1 eqs 1 and 7 yield
dC/a ) -k′ dC/a dt
(12)
with fa ) C/a ) Ca(t)/Cas, following eq 11. Equation 8 may be readily applied to the adsorption data by plotting [-ln(1 - fa)] versus time, while eq 12 suggests a plot of [-ln(fa)] versus time for desorption. Linearity of these plots is an indicator of the validity of the pore mouth resistance mechanism. Figures 8 and 9 depict the plots obtained for the data of Figure 7 for the re-adsorption at 300 K with P* ) 1 and P* ) 0.6, respectively, while Figure 10 depicts the plot for the desorption of the reversible iodine at 300 K (data of Figure 4). Excellent linearity over a wide uptake range is seen for each case, suggesting that the pore mouth resistance does indeed control the uptake dynamics. For the adsorp-
Figure 10. Plot of [-ln(fa)] vs time for desorption of reversible iodine at 300 K. (O) 7-10 mesh; (0) 10-14 mesh; (9) 16-22 mesh.
tion at P* ) 1 linearity occurs over the entire range of uptakes, while at P* ) 0.6 an initially higher uptake rate is seen, followed by a linear region with a subsequent rate increase at high uptake. This latter increased rate is also consistent with the initially higher rate during the desorption before the linear region (cf. Figure 10). A comparison of Figures 8 and 9 shows the initially higher
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Figure 11. Postulated mechanisms of iodine incorporation at the pore mouth. (a) Direct incorporation from macropore gas and (b) incorporation after adsorption at the pore mouth. SAI represents strongly adsorbed iodine at the pore mouth. Table 2. Incorporation Constants for Different Runs temperature (K)
path
k′d (h-1)
300
adsorption P* ) 1 adsorption P* ) 0.6 desorption desorption desorption
0.0264
300 300 323 343
0.0075
Figure 12. Plot of [-ln(fa)] vs time for desorption of reversible iodine at 323 K. Particle size: 16-22 mesh.
0.015 0.016 0.265
rate region observable for adsorption at P* ) 0.6 to be essentially absent at P* ) 1. The above results may be rationalized in terms of the processes at the mesopore mouths as follows. Initially, for the adsorption process the mesopore mouths are open for transfer of iodine into the pore body, as shown in Figure 11a and the uptake rate is rapid. However, adsorption of the iodine subsequently occurs at the pore mouth and, as depicted in Figure 11b, transfer into the mesopore occurs through this adsorbed layer. This slows down the process, and the linear region in Figures 8-10 therefore represents the transfer through the pore mouth adsorbate. At P* ) 1 the pore mouth adsorbate is formed very rapidly, with negligible adsorption into the pore during the initial period. At P* ) 0.6 the pore mouth adsorbate is at a lower chemical potential as compared to that at P* ) 1, and the value of k′d may consequently be expected to be lower. During desorption the pore mouth is initially full, but quickly reaches a reduced level of filling with a lower transfer rate, leading to a reduction in the slope after an initial period as depicted in Figure 10. Table 2 lists the values of k′d estimated for the different runs from the slopes of the linear regions in Figures 8-10, depicting results consistent with the above arguments. The values of k′d obtained reflect the pseudosteady chemical potential and density of the iodine established at the pore mouth during the adsorption or desorption process. Another feature supporting the above arguments is that the slope obtained between the last two points in Figure 9 is about 0.6 times that of the linear plot in Figure 8. This indicates essentially complete filling of the pore mouth during the last stage of the adsorption at P* ) 0.6, yielding the same rate as that at P* ) 1 for which the pore mouth is apparently completely filled as discussed above, based on eq 8. Figures 12 and 13 depict the plots corresponding to eq 12 for desorption at 323 and 343 K, respectively. As for 300 K a substantial linear region is noted, with an initial higher rate as the pore mouth is completely filled at the start of desorption. Table 2 lists the values of k′d obtained at these temperatures. Only a small increase in k′d is evident between 300 and 323 K, with a subsequent sharp increase at 343 K. This is consistent with our earlier proposal in this paper that the adsorbate at 343 K is much more fluid and liquid-like. The above results, while supporting the importance of the pore mouth resistance, also demonstrate that the
Figure 13. Plot of [-ln(fa)] vs time for desorption of reversible iodine at 343 K. Particle size: 16-22 mesh.
process is more complex than the simple first-order one represented in eqs 8 and 12. To model the incorporation more accurately, it is necessary to consider the adsorption at the pore mouth. This is however not possible without knowledge of the size of the pore mouth and its distribution. Consequently, a more detailed analysis of the incorporation has not been attempted in the present study. As an application of a new regularization technique for determining concentration-dependent diffusivities from transient uptake data, Arvind and Bhatia26 have previously analyzed the results for P* ) 0.6. However, when all the data are considered, it is evident that the current interpretation is more appropriate. To confirm this, we have also allowed for the possibility of a local adsorbate diffusional resistance at the microscale level. To this end we considered a model of diffusion in spherical grains.5
(
)
∂Ca 1 ∂ 2 ∂Ca ) 2 r De ∂t ∂r r ∂r
(13)
∂Ca ) 0 at r ) 0 ∂r
(14)
with the surface incorporation following the model in eqs 8, 11, and 12, that is, (26) Arvind, G.; Bhatia, S. K. Chem. Eng. Sci. 1995, 50, 1361.
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[
Bhatia et al.
]
∂Ca [1 + (K* - 1)P*] ) kdK*P*Cas 1 De Ca ∂r K*P*Cas at r ) rg (15) and the initial condition
Ca ) 0 at t ) 0, 0 e r e rg
(16)
for adsorption, while
Ca ) Cas at t ) 0, 0 e r e rg
(17)
for desorption. The transport coefficient De is considered concentration-dependent, following the well-known Darken equation that considers a chemical potential driving force; that is,
∂(ln P*) De ) De0 ∂ ln(Ca)
(18)
where De0 is an intrinsic mobility. For the isotherm in eq 1 this provides
De )
De0 [K* - (K* - 1)Ca/Cas]
(19)
Equations 13-17 and 19 may be readily solved numerically to obtain the temporal variation of the concentration profiles of the adsorbate, that is, Ca(t,r). Integration of these over the grain volume provides the fractional uptake, leading to
fa(t) )
3[1 + (K* - 1)P*] 3
rg K*P*Cas
∫0r r2Ca(t,r) dr g
(20)
for the adsorption at relative pressure P*, and
fa(t) )
∫0r r2Ca(t,r) dr
3 rg Cas 3
g
(21)
for desorption from a fully saturated adsorbent. When rendered dimensionless and applied to the current data, this model has the unknown parameters kd/rg and De0/rg2, with the other parameters Cas and K* obtained from the isotherm as listed in Table 1. In performing the fits at 300 K initially, it was sought to find suitable values of kd/rg and De0/rg2 that simultaneously matched the desorption data in Figure 4 and the re-adsorption data in Figure 7. Thus, the incorporation constant and the effective intrinsic mobility De0 were considered constant at a given temperature and independent of concentration. This approach was, however, unsuccessful and both adsorption and desorption data
could not be matched in this way. In particular, because of the large difference in adsorption and desorption times, a constant value of De0 was not possible unless it was large enough that the pore mouth resistance dominated. The latter is, of course, the limiting case already considered in eqs 7-12. In subsequent fits therefore only the value of kd/rg was kept constant at a given temperature while De0/rg2 was allowed to vary with P*. The solid lines in Figures 4 and 7 depict the results of the fits at 300 K, yielding kd/rg ) 0.097 h-1, with De0/rg2 ) 0.022 h-1 for desorption and 0.0897 h-1, with 0.41 h-1 for adsorption at P* ) 0.6 and P* ) 1, respectively. These values of De0/rg2 are clearly inconsistent with an unacceptably large variation. On the other hand, the variations in kd/rg ()k′d/3), assuming the pore mouth control limit, are much smaller (cf. Table 2). At 323 K the diffusion model yielded kd/rg ) 0.09 h-1 and De0/rg2 ) 0.1 h-1, while at 343 K these variables had values of 8.02 and 1.9 min-1 respectively, and the model fits are shown as the solid lines in Figures 5 and 6, respectively. In all of these cases the value of the ratio (kd/rg)/(De0/rg2) is of the order of unity or larger, lying in the region of mixed control. Nevertheless, despite the good agreement with data, seen in Figures 4-7, it is evident from the inconsistent values of the diffusivity at 300 K that the pore mouth resistance dominated, as discussed earlier. Conclusions The equilibrium and dynamics of iodine adsorption have been investigated here, with the view of studying the isotherm irreversibility and pore-blocking effects by the apparently “permanently adsorbed” iodine. The adsorbed iodine is found to comprise an “irreversibly” adsorbed part, and a reversibly adsorbed part with a Langmuirian isotherm. On the basis of the adsorption energies, the latter part is found to be adsorbed homogeneously in the mesopores, as a monolayer over a strongly adsorbed layer of iodine at 300 and 323 K, and as a monolayer over the carbon surface at 343 K. The strongly adsorbed layer is believed to adsorb in the micropores and mesopore mouths, thereby retarding the uptake of the reversibly adsorbed iodine. The uptake dynamics of the reversibly adsorbed iodine is seen to be largely controlled by the pore mouth resistance at temperatures between 300 and 343 K. However, the results suggest that between 323 and 343 K a transition in the state of the reversibly adsorbed iodine occurs, from a solid-like to a much more fluid or semisolid adsorbate phase. Acknowledgment. The experimental portion of this work was conducted while the first author was at the Indian Institute of Technology, Mumbai. The work has been subsequently continued at the University of Queensland, with funding from the Australian Research Council. LA991418H
