Energy & Fuels 2008, 22, 2641–2648
2641
Adsorption Equilibrium and Kinetics of Branched Octane Isomers on a Polyvinylidene Chloride-Based Carbon Molecular Sieve Georgina C. Laredo,*,† Edith Meneses,†,‡ Jesu´s Castillo,† Jesu´s O. Marroquin,† and Federico Jime´nez-Cruz† Programa de InVestigacio´n en Procesos y Reactores, Instituto Mexicano del Petro´leo, La´zaro Ca´rdenas 152, Me´xico 07730 D.F. MEXICO, and CICATA, Instituto Polite´cnico Nacional, Legaria 694, Me´xico 11500 D.F. MEXICO ReceiVed October 29, 2007. ReVised Manuscript ReceiVed March 13, 2008
Adsorption equilibrium and kinetics of four octane isomers: n-octane (nC8), 2-methylheptane (2MC7), 2,5dimethylhexane (25DMC6), and 2,2,4-trimethylpentane (224TMC4) were studied in a carbon molecular sieve obtained from the pyrolysis of a poly(vinylidene choride-co-vinyl chloride) (PVDC-PVC; Saran, Dow. Co) material. Adsorption capacities calculated at 325, 350, and 400 °C temperatures and partial pressures from 6.9 to 12.8 Pa (via the inverse gas chromatography method), were in the range of 0.5-3.0 g/100 gAds. All isotherms were of type I in Brunauer’s classification. Heats of adsorption (-∆H0) values were on the order of 76-77 kJ/mol for nC8, 2MC7, and 25DMC6 and 94 kJ/mol for 224TMC5 confirmed selectivity for separation of multibranched compounds with a gem-dimethyl group only. Adsorption kinetic studies at 175, 200, and 250 °C employing the zero length column chromatography (ZLC) technique presented a weak temperature dependence on desorption time (12.3, 10.3, 8.4, and 8.3 kJ/mol for nC8, 2MC7, 25DMC6, and 224TMC5, respectively). Additionally, as the degree of the hydrocarbon branching increases as well as critical size, the uptake was more rapid. Adsorption-desorption variations by temperature changes may be related to specific interactions of the C-H bonding in the hydrocarbon framework with the graphene structures in the carbon molecular sieve (CMS) material which are suggested to be dependent on loading levels and the pore size distribution in the carbonaceous material.
Introduction Continuing with the development of a new process to produce high octane gasoline from complex mixtures of light distillates, based in the separation of a C5-C8 linear and branched alkanes depending on their adsorption properties, chain length, and number of branches, the following experimentation was performed. As a rule, multibranched alkanes are related with high octane numbers.1,2 Isomerization process generates a mixture of isomers (linear alkanes, monobranched alkanes like methyland ethyl-alkanes, and multibranched alkanes) that usually require separation and recycle of the nonisomerized components.2,3 Therefore, to find materials with such adsorption capabilities to selectively separate highly branched alkanes from the gasoline mixture, with substantial regeneration and reutilization capacity is highly desirable. Molecular sieves have been of great industrial interest for many years due to their uniform pore structure and appropriate selective adsorptive properties.4 In this context, materials such as zeolites have the surface composition, area, and porosity suitable for shape selectivity in separations. Molecular sieve materials like zeolite 5A, ZSM-5, mordenite, H-Y, Na-Y, Na* Corresponding author. E-mail:
[email protected]. † Instituto Mexicano del Petro ´ leo. ‡ Instituto Polite ´ cnico Nacional. (1) Jime´nez-Cruz, F.; Laredo, G. C. Fuel 2004, 83, 2183–2188. (2) Gary, J. H.; Handwerk, G. E. Petroleum Refining: Technology and Economics; M. Dekker: New York, 1994. (3) Speight, J. G. Fuel Science and Technology Handbook; M. Dekker: New York, 1990. (4) Ruthven, D. M. Principles of adsorption and adsorption processes; Wiley Interscience: New York, 1984.
USY, ZSM-5, ZSM-22, beta, and silicalite-1 have been widely studied in selective adsorption of paraffins.5–25 The slit-shaped (5) Abdul-Rehman, H. B.; Hasanain, M. A.; Loughlin, K. F. Ind. Eng. Chem. Res. 1990, 29, 1525–1535. (6) Loughlin, K. F.; Hasanain, M. A.; Abdul-Rehman, H. B. Ind. Eng. Chem. Res. 1990, 29, 1535–1546. (7) Cavalcante, C. L., Jr.; Ruthven, D. M. Ind. Eng. Chem. Res. 1995, 34, 177–184. (8) Cavalcante, C. L.; Ruthven, D. M Ind. Eng. Chem. Res. 1995, 34, 185–191. (9) Miano, F. Colloids Surf., A 1996, 110, 95–104. (10) Silva, J. A. C.; Rodriguez, A. E. Ind. Eng. Chem. Res. 1997, 36, 493–500. (11) Denayer, J. F.; Baron, G. V.; Martens, J. A.; Jacobs, P. A. J. Phys. Chem. B 1998, 102, 3077–3081. (12) Denayer, J. F.; Souverijns, W.; Jacobs, P. A.; Martens, J. A.; Baron, G. V. J. Phys. Chem. B 1998, 102, 4588–4597. (13) Vlugt, T. J. H.; Zhu, W.; Kapteijn, F.; Moulijn, J. A.; Smit, B.; Krishna, R. J. Am. Chem. Soc. 1998, 120, 5599–5600. (14) Vlugt, T. J. H.; Krishna, R.; Smit, B. J. Phys. Chem. B 1999, 103, 1102–1118. (15) Webb, E. B., III.; Grest, G. S.; Mondello, M. J. Phys. Chem. B 1999, 103, 4949–4959. (16) Schuring, D.; Koriabkina, A. O.; de Jong, A. M.; Smit, B.; van Santen, R. A. J. Phys. Chem. B 2001, 150, 7690–7698. (17) Jolimaitre, E.; Tayakout-Fayolle, M.; Jallut, C.; Ragil, K. Ind. Eng. Chem. Res. 2001, 40, 914–926. (18) Krishna, R.; Calero, S.; Smit, B. Chem. Eng. J. 2002, 88, 81–94. (19) Koriabkina, A. O.; de Jong, A. M.; Schuring, D.; van Grondelle, J.; van Santen, R. A. J. Phys. Chem. B 2002, 106, 9559–9566. (20) Denayer, J. F.; Ocakoglu, R. A.; Huybrechts, W.; Martens, J. A.; Thybaut, J. W.; Marin, G. B.; Baron, G. V. Chem. Commun. 2003, 1880– 1881. (21) Ocakoglu, R. A.; Denayer, J. F.; Marin, G. B.; Martens, J. A.; Baron, G. V. J. Phys. Chem. B 2003, 107, 398–406. (22) Fox, J. P.; Rooy, V.; Bates, S. P. Microporous Mesoporous Mater. 2004, 69, 9–18.
10.1021/ef7006408 CCC: $40.75 2008 American Chemical Society Published on Web 05/22/2008
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pore sizes in carbon molecular sieves (about 2.9-10.0 Å in average) are comparable to the size and shape of small adsorbate molecules.26 Carbon molecular sieves (CMS) adsorption properties have been used in separation of nitrogen and oxygen by either pressure or temperature swing adsorption.4 An interesting source for preparing CMS are the polyvinylidene chloride (PVDC) copolymers, at suitable conditions of pyrolysis and/or activation.27–34 These PVDC-based CMS materials seem promising for octane boosting separation technologies because of their adsorptive and molecular sieve discrimination properties between linear and branched alkanes.28–34 Unfortunately, available information of this type of separation in CMS is scarce and incomplete, mainly due to the difficulty of achieving absolute reproducibility between different batches and the existence of a pore size distribution,4 which makes this material very difficult to study. Dacey and Thomas28 observed the possible separation between pentane and neopentane. Lamond et al.29 provided some adsorption capacities at equilibrium values for butane, isobutane and neopentane. Barton et al.30 presented some heat of immersion data at 27 °C for 3-methylpentane, 3-methylhexane, 2,3-dimethylbutane, 2,4dimethylpentane, 2,2,3-trimethylbutane, 2,2,4-trimethylpentane, and 2,2,5-trimethylhexane in the liquid phase. Ferna´ndezMorales et al.31 reported heat of adsorption data for four linear alkanes (n-butane to n-heptane). In the NL patent from Shell,33 the octane numbers obtained after processing different alkane mixtures (2-methylpentane, 2,3-dimethylbutane, 2,2-dimethylbutane, 2,4-dimethylhexane, 2,5-dimethylhexane, 2,3,4-trimethylpentane, and 2,2,4-trimethylpentane) were provided. Therefore, the main objective of this work was to obtain the thermodynamic and kinetic adsorption properties of a molecular sieve material produced from the pyrolysis of a vinylidene chloride-vinyl chloride copolymer (PVDC-PVC, Saran) employing n-octane (nC8), 2-methylheptane (2MC7), 2,5-dimethylhexane (25DMC6), and 2,2,4-trimethylpentane (224TMC5) as hydrocarbon probes. Thermodynamic data at 325, 350, and 400 °C temperatures and from 6.9 to 12.8 Pa partial pressures were obtained by means of an inverse gas chromatography (ICG) technique previously described elsewhere.34 In addition, kinetic properties of the same (23) Vinh-Thang, H.; Huang, Q.; Eic, M.; Trong-On, D.; Kaliaguine, S. Langmuir 2005, 21, 5094–5101. (24) Lu, L.; Wang, Q.; Liu, Y. J. Phys. Chem. B 2005, 109, 8845– 8851. (25) Ba´rcia, P. S.; Silva, J. A. C.; Rodrigues, A. E. Microporous Mesoporous Mater. 2005, 79, 145–163. (26) Suzuki, M. Adsorption Engineering; Elsevier: Amsterdam, 1990. (27) Pierce, C.; Wiley, J. W.; Smith, R. N. J. Phys. Chem. 1949, 53, 669–683. (28) Dacey, J. R.; Thomas, D. G. J. Chem. Soc., Faraday Trans. 1954, 50, 740–748. (29) Lamond, T. G.; Metcalfe, J. E.; Walker, P. L. Carbon 1965, 3, 59–63. (30) Barton, S. S.; Evans, M. J. B.; Harrison, B. H. J. Colloid Interface Sci. 1974, 49, 462–468. (31) Ferna´ndez-Morales, I.; Guerrero-Ruı´z, A.; Lo´pez-Garzo´n, F. J.; Rodrı´guez-Ramos, I.; Moreno-Castilla, C. Carbon 1984, 22, 301–304. (32) Kitagawa, H.; Yuki, N. Carbon 1981, 19, 470–472. (33) Kramer, J. K. Working method for separating mutually closely related aliphatic hydrocarbons with and without branched chains. NL Patent 7111508, 1971. (34) Jime´nez-Cruz, F.; Herna´ndez, J. A.; Laredo, G. C.; Mares-Gallardo, M. T.; Garcia-Gutierrez, J. L. Energy Fuels 2007, 21, 2929–2934. (35) Eic, M.; Ruthven, D. M. Zeolites 1988, 8, 40–45. (36) Grande, C. A.; Silva, V. M. T. M.; Gigola, C.; Rodriguez, A. E. Carbon 2003, 41, 2533–2545.
Laredo et al. Table 1. Physical Properties of CMS-IMP12 adsorbent properties calculated by the t-plot analysis343739
particle properties average size (m)
total area external average volumea (m3) (m2/g) area (m2/g)
1.59 × 10-4 2.10 × 10-12 a
Assuming a spherical
844
5.91
micropore volume (cc/g) 2t (nm) 0.3772
0.9148
shape.36
compounds on this material were attained by the zero length column chromatography (ZLC) technique25,35,36 at 175, 200, and 250 °C. Experimental Section Materials. n-Octane (nC8), 2-methylheptane (2MC7), 2,5dimethylhexane (25DMC6), and 2,2,4-trimethylpentane (224TMC5) of highest purity were purchased from Aldrich Co. CMS-IMP12 sample was prepared from pyrolysis of cylindrical shaped extrudates of poly(vinylidene chloride-co-vinyl chloride) (PVDC-PVC, Saran), according to the technique described in Jime´nez-Cruz et al.34 Particle size and volume assuming a spherical shape and surface properties calculated according to the t-plot analysis37–39 are shown in Table 1. Detailed description of chemical characterization is provided in the same paper.34 Inverse Gas Chromatography (IGC). IGC experiments were carried out in a Gow Mac 750P gas chromatograph (GC) equipped with a flame ionization detector. Detailed experimental conditions are listed in Table 2. A previously acetone washed and dried stainless steel tubing was packed with the CMS and coupled to the injection and detection systems. The flow rate of the carrier gas was set at 30 mL/min for a head column pressure of 2.11 × 105 Pa. Small amounts (1-10 µL) of pure hydrocarbons were injected separately with a 10 µL syringe into the GC and were eluted isothermally. Temperatures employed in this study and hydrocarbon partial pressures provided are given in Table 3. Prior to each experiment the column was activated for at least four hours at 500 °C under helium flow. The retention times were determined by means of a PC with the LABQUEST software as the integrator. Calculations were performed as described elsewhere.34 The net amount of moles of adsorbed hydrocarbon per gram of adsorbent (ns) was determined by40–42 ns )
[
( )]
Tcol nc 1 (t - t ) j w R m Tamb tR
(1)
w ) weight of the adsorbent (g); tR ) retention time of the injected hydrocarbon (min); tm ) retention time of a nonadsorbing marker (methane) (min); Tcol ) column temperature (K); Tamb ) ambient temperature (K); nc ) injected hydrocarbon (mol); j ) James-Martin factor correction of gas compressibility. The j factor was calculated according to
3 j) 2
[ ] ( ) ( ) Pin Pout Pin Pout
2
3
-1
(2)
-1
(37) Do, D. D. Adsorption Analysis: Equilibria and Kinetics; Imperial College Press: London, 1998. (38) Lippens, B. C.; de Boer, J. H. J. Catal. 1965, 4, 319–323. (39) Nakai, K.; Sonoda, J.; Kondo, S.; Abe, I. Pure Appl. Chem. 1993, 65, 2181–2187. (40) Conder, J. R.; Young, C. L. Physicochemical Measurement by Gas Chromatography; Wiley: New York, 1979. (41) Kiselev, A. V.; Yashin, Y. I. Gas-chromatographic determination of adsorption and specific surface for solids. In Gas Adsorption Chromatography; Plenum: New York, 1969; pp 104-145. (42) Montes-Moran, M.; Paredes, J. I.; Martı´nez-Alonso, A.; Tasco´n, J. M. D. J. Colloid Interface Sci. 2002, 247, 290–302.
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Energy & Fuels, Vol. 22, No. 4, 2008 2643
Table 2. IGC and ZLC Experimental Conditions IGC
ZLC
mass of adsorbent, kg column size, m column volume, m3 carrier gas flow rate, m3/s
3.7 × 10-4 2.0 × 10-3φ × 0.5 1.57 × 10-6 helium 5 × 10-7
head column pressure, Pa C8 concentrations, m3
1.72 × 104 1 × 10-9-1 × 10-8
5 × 10-5 3.2 × 10-3φ × 7.0 × 10-3 5.63 × 10-8 helium 5 × 10-7 2.33 × 10-6
mass of adsorbent, kg cell size, m cell volume, m3 carrier gas saturator flow rate, m3/s purge flow rate, m3/s
Table 3. Experimental Data for Breakthrough Curves of C8 Hydrocarbons run nC8
temperature, °C
hydrocarbon partial pressure (p) Pa (× 10)
amount adsorbed (q) g/100 gAds
0.79 1.81 3.57 6.06 9.96 1.28 3.69 7.17 11.87 17.98 4.35 11.86 22.96 37.31 52.92 0.69 1.64 3.17 5.46 8.47 1.32 3.78 7.33 10.80 15.74 4.05 11.02 20.47 34.06 48.92
0.53 1.05 1.58 2.10 2.63 0.55 1.10 1.65 2.20 2.75 0.59 1.18 1.77 2.36 2.94 0.53 1.06 1.59 2.13 2.66 0.54 1.07 1.61 2.14 2.68 0.60 1.19 1.79 2.38 2.98
325
350
400
2MC7
325
350
400
ncRT (tR - tm)Fc
( )
Fc ) jFm
Tcol Tamb
temperature, °C
25DMC6
325
hydrocarbon partial pressure (p) Pa (× 10)
amount adsorbed (q) g/100 gAds
0.76 2.20 4.30 6.93 11.05 1.88 5.21 10.09 16.35 22.34 4.89 12.95 24.92 38.91 59.37 1.35 3.49 6.68 11.41 17.11 3.13 8.09 15.59 26.02 38.96 12.30 28.51 49.66 87.48 128.05
0.53 1.06 1.59 2.12 2.65 0.55 1.10 1.64 2.19 2.74 0.59 1.18 1.77 2.36 2.94 0.52 1.04 1.57 2.09 2.61 0.54 1.07 1.61 2.15 2.68 0.57 1.15 1.72 2.28 2.85
350
400
224TMC5
325
350
400
where Pin and Pout are the inlet and outlet column pressure (Pa); the pressure at the outlet was measured in triplicate and resulted in a value of 1.72 × 104 Pa. Partial pressure (pHi, Pa) values were calculated by eq 3, in which R is the ideal gas constant (8.3145 × 106 cm3 Pa/mol K), T is the temperature of the column, and Fc is the corrected flow rate (eq 4) and Fm is the uncorrected flow rate (cm3/min): pHi )
run
(3) (4)
In general, the adsorption equilibrium isotherms experimental data were fitted to simple mathematic models with help of the software Matlab. The method of optimization used to fit the equilibrium constant was the Nelder-Mead Simplex Method of Optimization Toolbox.43 Zero Length Column Chromatography (ZLC). Kinetic studies were performed in an apparatus described by Eic and Ruthven.35 The central feature was a small amount of adsorbent (50 mg) placed between two sinter discs in a vertical portion of a stainless steel tube inside a gas chromatograph oven (Tremetrics 9001). Detailed experimental conditions are listed in Table 2. (43) Demuth, H.; Beale, M. Optimization Toolbox for Matlab-Users Guide, version 2.1.; The MathWorks Inc.: Natrick, MA, 2000.
The procedure implied to saturate the adsorbent with a diluted mixture of the adsorbate until equilibrium in the adsorbed phase was reached. Then, the inlet was switched to an inert stream to clean the adsorbent. The data obtained when the ZLC experiments performed at the same temperatures employed in the thermodynamic studies were not reliable due to the fast diffusion of the species studied (90%). Pure Component Adsorption Equilibrium. Table 3 shows the results of the adsorption equilibrium studies performed at 325, 350, and 400 °C. Figure 1 shows the data plotted. All isotherms are type I according to the Brunauer’s classification. At lowering temperature, increasing of the maximum amount adsorbed (q) was observed in the carbonaceous sample. Henry’s constants (H) which can give insight in the adsorption behavior were obtaining by extrapolation to zero coverage of the equilibrium data plotted in terms of virial plots, i.e. semilog plots of p/q versus q, where p is the partial pressure (Pa) and q is the amount adsorbed (g/100 gAds) (Figure 2, Table 4). According to this data, only 224TMC5 could be separated from nC8, 2MC7, and 25DMC6 on this material. The results mean that this carbon structure with pore ratio dispersion between (44) Horva´th, G.; Kawazoe, K. J. Chem. Eng. Jpn. 1983, 16, 470–475. (45) Characterization of Adsorbents for Sample Preparation Processes. SUPELCO, Sygma-Aldrich, T412026. EQG. (46) Kim, Y. J.; Horie, Y.; Ozaki, S.; Matuzusawa, Y.; Suezaki, H.; Kim, C.; Miyashita, N.; Endo, M. Carbon 2004, 42, 1491–1500.
Figure 1. Adsorption equilibrium isotherms of octane isomers on CMSIMP12 at different temperatures: (a) 325, (b) 350, and (c) 400 °C for nC8, 2MC7, 25DMC6, and 224TMC5. The continuous lines are the adsorption equilibrium Langmuir isotherms models fitted to experimental data.
0.5 and 1 nm was capable of a differentiation between multibranched alkanes with a gem-group like the 224TMC5 from multibranched alkanes without a gem-group like the 25DMC6. Heats of adsorption at zero coverage (-∆H0) obtained from the temperature dependence of Henry’s constants according to the Van’t Hoff equation (Figure 3) are given in Table 4. On
Branched Octane Isomers on a PVDC-Based CMS
Energy & Fuels, Vol. 22, No. 4, 2008 2645
Figure 2. Semilog plot of p/q versus q for analysis of the virial isotherm of (a) nC8, (b) 2MC7, (c) 25DMC6, and (d) 224TMC5 at 325, 350, and 400 °C. Table 4. Heats of Adsorption at Zero Coverage (∆H0) and Henry Constant (H) on CMS-IMP12 at 325, 350, and 400 °C for C8 Hydrocarbons compound critical molecular octane number
diameter17
T, °C 325 350 400 -∆H, kJ/mol b0, Pa correlation coefficient, R2
nC8
2MC7
25DMC6
224TMC5
0.45 -17
0.54 21.8
0.58 55.5
0.63 100
H, g/(gAds Pa) (× 10-3) 0.89 0.47 0.16
0.99 0.46 0.17
0.85 0.38 0.15
0.48 0.21 0.06
76.2
76.3
77.5
93.8
4.32 × 10-2 0.9999
4.19 × 10-2 0.9915
1.25 × 10-2 0.9955
3.4 × 10-4 0.9989
this material, adsorption enthalpies in the order of 76-77 kJ/ mol for nC8, 2MC7, and 25DMC6 and 94 kJ/mol for 224TMC5, confirmed selectivity for separation of compounds with a gemdimethyl group only. Some available heats of adsorption (-∆H) reported for nC8, 2MC7, 25DMC6, and 224TMC5 on other molecular sieves are shown in Table 5. It is very interesting to point out that while other materials showed a lower -∆H value for the multibranched alkane 224TMC5, in this CMS, the -∆H value for this compound was the highest. It seems that, although the 224TMC5 was the least adsorbed hydrocarbon under the experimental conditions studied, it thermodynamically presented
Figure 3. Arrhenius plot showing temperature dependence of equilibrium constants for nC8, 2MC7, 25DMC6, and 224TMC5 in the CMSIMP12.
the strongest interactions with the graphene subunits of the material.34 As it was already described by Jime´nez-Cruz et al.,34 the explanation may reside in CH-π interactions by either the methylene (C-H) or methyl (C-H) moieties from the hydrocarbon and π electrons in the carbon surface. The additive C-H interactions of the methyl moiety in a highly branched alkane can be accounted for the increase in the thermodynamic adsorption favoring the bulkier C8 alkane (224TMC5) over their isomers (Figure 4), although because of its size, its possibilities
2646 Energy & Fuels, Vol. 22, No. 4, 2008
Laredo et al.
Figure 4. Possible CH-π interactions between CH in n-octane and 2,2,4-trimethylpentane and π orbitals in the carbon walls. Table 5. Heat of Adsorption (-∆H) Reported in the Literature for n-Octane, 2-Methylheptane, 2,5-Dimethylhexane, and 2,2,4-Trimethylpentane on Different Materials -∆H, kJ/mol material
free pore diameter, nm
nC8
2MC7
25DMC6
224TMC5
ref
NaY Na-USY beta mordenite ZSM-5 ZSM-22 open ZSM-22 closed ZSM-22
supercage: 1.23 window: 0.73 supercage: 1.23 window: 0.73 0.57 × 0.75 0.56 × 0.61 0.70 × 0.65 0.26 × 0.57 0.54 × 0.56 0.51 × 0.55 0.45 × 0.55 0.45 × 0.55 0.45 × 0.55
57.5 60.1 82.9 87.3 90.7 100.5 100.6 81.7
57.2 59.0 81.2 85.1 88.6 84.6 87.3 81.0
57.1 57.6
56.8 57.5 73.4 76.8
12 12 12 12 12
60.2
48.2
of finding a pore wide enough for being adsorbed are lower. Higher thermodynamic adsorptions of methyl alkanes over linear ones on zeolites with pores size of 0.65-0.74 nm have already been observed by Santilli et al.47 They call this preference “inverse shape selectivity”, and it was explained by stabilizing interactions between the zeolite walls and the adsorbed methyl branched hydrocarbons. Differences between the behavior observed by Santilli et al.47 and this work may reside on the non uniform pore size distribution presented by the material. Values of affinity constants at zero loading (b0, Table 4) were from higher to lower: nC8 > 2MC7 > 25DMC6 > 224TMC5. The pre-exponential factor (b0) is related to the entropy of adsorption,48 and it can be controlled by the size of the alkane, the pore restrictions, and diffusion by loss of freedom degree. Thus, it is very interesting to point out that the difference in critical size between nC8 (0.45 nm) and 1,7 2MC7 (0.54 nm)1,7 did not seems to affect the affinity factor, while the size of the 25DMC6 (0.58 nm) and 224TMC4 (0.63 nm)1,7 affected b0 strongly. It is obvious that the sharp decrease in entropy for 25DMC6 and 224TMC5 may be explained in terms of additive CH-π interactions (Figure 4) and the restrictive pore size. The fit of the data by a nonlinear regression to the ideal Langmuir model q ) q0bp/(1 + bp) is shown in Figure 1. An excellent fit of the experimental data was attained (Table 6).49 Henry’s law constants were calculated by H ) q0b, where b and q0 were obtained from the Langmuir data. Equilibrium vapor pressure, at constant loading, should follow the Clausius-Clapeyron equation; therefore, a plot of log p (calculated by means of the fitted Langmuir isotherm) versus 1/T should yield a straight line with slope proportional to the heat of adsorption. Figure 5 shows the dependence of this isosteric heat of adsorption versus the coverage (q) for the four
20
Table 6. Parameters of Langmuir’s Isotherm Model for Adsorption of C8 Hydrocarbons on CMS-IMP12 and Correlation Coefficients (R2) between the Model and Experimental Data T, °C
parameter
nC8
2MC7 25DMC6 224TMC5
325 4.00 4.17 4.18 q0, g/100 gAds 18.78 19.98 15.16 b, Pa-1 (× 10-3) 2 R 0.9988 0.9979 0.9948 0.83 0.63 Ha, g/(gAds Pa) (× 10-3) 0.75
4.18 9.24 0.9995 0.37
q0, g/100 gAds b, Pa-1 (× 10-3) R2 Ha, g/(gAds Pa) (× 10-3)
4.95 5.21 0.9950 0.26
4.38 3.88 0.9960 0.17
q0, g/100 gAds 5.12 5.13 5.05 2.42 2.69 2.29 b, Pa-1 (× 10-3) R2 0.9926 0.9947 0.9961 0.14 0.12 Ha, g/(gAds Pa) (× 10-3) 0.12 b ∆H , kJ/mol 79.3 78.6 74.5
4.84 1.08 0.9978 0.05 88.4
350 4.88 6.98 0.9961 0.34
4.99 7.12 0.9938 0.36
400
a H ) b*q is the Henry’s constant. 0 constants.
b
Based in the calculated Henry
isomers for the Langmuir model described before. The results found are very alike for that described for Ba´rcia et al.25 for their study of C6 branched isomers on pellets of zeolite beta, where the isosteric heat of adsorption slightly decreases when the Langmuir isotherm is used. Kinetics of Adsorption. The kinetics of adsorption was measured by the ZLC technique.35 In order to obtain time constants of diffusion (τDif), data from the ZLC experiments were treated according the original model proposed by Eic and Ruthven35 and the method developed by Grande et al.36 when
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Energy & Fuels, Vol. 22, No. 4, 2008 2647
Figure 5. Dependence of isosteric heat of adsorption versus the coverage for nC8, 2MC7, 25DMC6, and 224TMC5. The representation shown in the figure is obtained from the fitted Langmuir isotherms as is shown in Figure 1. Table 7. Diffusional Time Constants and Activation Energies Obtained from ZLC Experimental Data and Correlation Coefficients (R2 and R2, Respectively) hydrocarbon nC8 Ea (kJ/mol) 0 (s-1) τDif R2 2MC7 Ea (kJ/mol) 0 (s-1) τDif R2 25DMC6 Ea (kJ/mol) 0 (s-1) τDif R2 224TMC5
temperature °C
L
τDifa (s-1)
R2
175 200 250
0.0803 0.0770 0.0823
0.9775 0.9704 0.9763
175 200 250
0.0775 0.1168 0.1247
175 200 250
0.1000 0.1208 0.1500
175 200 250
0.1348 0.1372 0.1870
0.249 0.300 0.401 12.33 6.85 0.9994 0.414 0.495 0.618 10.27 6.60 0.9922 0.540 0.588 0.743 8.43 5.13 0.9874 0.617 0.695 0.848 8.25 5.66 1.0
Ea (kJ/mol) 0 (s-1) τDif R2 a
0.9834 0.9965 0.9999
0.9947 0.9978 0.9999
0.9998 0.9993 0.9999
τDif ) Dc/rc2 or τDif ) Dp/Rp2(1 + K).
dealing with a CMS material. The ZLC technique has been successfully used by other authors.8,25,36 The data obtained when the ZLC experiments were performed at the same temperatures employed in the thermodynamic studies were not reliable due to the fast diffusion of the species studied (
