Microporous and Mesoporous Materials 65 (2003) 267–276 www.elsevier.com/locate/micromeso
Adsorption of light hydrocarbons on HMS type mesoporous silica B.L. Newalkar
a,1
, N.V. Choudary b,1, U.T. Turaga c,2, R.P. Vijayalakshmi b, P. Kumar b, S. Komarneni a,*, T.S.G. Bhat b,*
a
c
Materials Research Laboratory, Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USA b Research Centre, Indian Petrochemicals Corporation Limited, Vadodara 391346, India Fuel Science Program, Department of Energy and Geo-Environmental Engineering, The Pennsylvania State University, University Park, PA 16802, USA Received 3 June 2003; received in revised form 8 August 2003; accepted 15 August 2003
Abstract Equilibrium adsorption isotherms for light hydrocarbons namely, ethane, ethylene, acetylene, propane, and propylene have been measured on hexagonal mesoporous silica (HMS)-type mesoporous silica. The measured data are analyzed using Langmuir–Freundlich adsorption isotherm model. The adsorption capacity for C2 and C3 olefins are found to be higher than for corresponding alkanes. Further, uptake of acetylene is observed to be more comparable to ethylene. The isosteric heats of adsorption for ethylene are marginally higher than ethane but those observed for propylene are found to be significantly higher than for propane. The isosteric heats observed for propylene are found to be comparable with those reported for p-complexation based systems. Such a trend has in turn suggested a higher affinity of HMS framework for propylene over propane. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Mesoporous silica; HMS-framework; Light hydrocarbons; Adsorption
1. Introduction
* Corresponding authors. Tel.: +1-814-865-1542; fax: 1-814865-2326 (S. Komarneni), Tel.: +11-91-265-262011x3673; fax: +11-91-265-262098 (T.S.G. Bhat). E-mail addresses:
[email protected] (S. Komarneni),
[email protected] (T.S.G. Bhat). 1 Present address: Corporate R&D, Bharat Petroleum Corporation Limited, Plot 2A, Udyog Kendra, Greater Noida, India. 2 Present address: Conoco Phillips Company, 92-E, Bartlesville Technology Center, Bartlesville, OK 74004, USA.
The synthesis of the family of ordered mesoporous materials, M41S, in 1992 sparked worldwide interest in the field of synthesis, heterogeneous catalysis, and separation science [1]. This has also stimulated great interest in the development of supra-molecular templated approach for mesostructure formation which resulted in three general pathways namely electrostatic charge matching, neutral, and dative bond formation routes [2]. Among the three general pathways, neutral pathway involving pair formation of neutral amine or
1387-1811/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.micromeso.2003.08.008
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nonionic polyoxyethylene surfactants with neutral inorganic precursors has led to the successful formation of hexagonal mesoporous silica (HMS) through hydrogen bonding [3]. Silica framework obtained by the above method has been reported to have higher wall thickness than those formed by electrostatic assembly. As a result, considerable efforts have been made to investigate the synthesis aspects of HMS to tailor its textural and framework properties [4]. Successful attempts have also been reported for hetero element substitution such as Al, Ti, V, Cr, Mo, Mn in HMS framework for evaluating its catalytic potential [5]. In contrast to the extensive syntheses efforts described above, no attempt has been made, to the best of our knowledge, to understand and explore the adsorptive potential for HMS type of mesoporous framework pertaining to separation of hydrocarbons. Therefore, the main objective of the present study is to investigate the adsorption properties of HMS with a view to understand its usefulness as an adsorbent for commercially important light hydrocarbon separations, particularly C2 and C3 hydrocarbons. Therefore, equilibrium adsorption isotherms for ethane, ethylene, acetylene, propane, and propylene were measured using volumetric adsorption measurement technique at 303 and 323 K and the data were analyzed using various models. The isosteric heat of adsorption, adsorption capacity, and selectivities were estimated to learn about the usefulness of mesoporous material, HMS, as an adsorbent for the separation of hydrocarbons.
2. Experimental 2.1. Materials Mesoporous material, HMS was synthesized at ambient conditions by adopting the approach reported elsewhere [6] using dodecyl amine and tetraethylorthosilicate, TEOS, (Aldrich) as a neutral template and silica precursor, respectively. Thus obtained sample was filtered, washed with warm distilled water, dried at 383 K and finally calcined at 813 K in air for 6 h. The obtained sample was
characterized by means of X-ray diffraction and nitrogen adsorption/desorption measurements at 77 K. 2.2. Adsorption isotherms measurements Adsorption isotherms for methane, ethane, ethylene, acetylene, propane, and propylene were measured using volumetric adsorption measurement unit at 303 and 323 K. Typically, about 1 g of activated sample was loaded in a volumetric adsorption unit, which was fitted with two MKS absolute pressure transducers model 122AA (100 and 1000 mmHg range, 0.01 and 0.1 mmHg accuracy, respectively). The sample temperature was maintained to 0.01 K using JULABO F10 thermostatic circulating bath. All the adsorbates used in the present study were UHP grade (purity > 99.99%). At the end of the adsorption run, desorption experiment was performed to check the reversibility of the adsorption isotherm. All the measurements were performed in duplicate to ensure the quality as well as reproducibility of the data. The measured adsorption data were analyzed using Langmuir– Freundlich adsorption isotherm model.
3. Results and discussion 3.1. Adsorbent characterization X-ray pattern for calcined HMS sample displayed a sharp peak with a ÔdÕ spacing of about 3.2 nm which matched well with the reported pattern. Typical nitrogen adsorption/desorption isotherms for HMS sample measured at 77 K showed a typical type IV adsorption behavior. The measured BET surface area for HMS sample was about 980 m2 /g whereas the pore size distribution was found to be centered at about 2 nm. The obtained results confirmed the structural as well as the adsorption crystallinity of the adsorbent. 3.2. Adsorption isotherms of C2 and C3 hydrocarbons Fig. 1 depicts the adsorption isotherms for various adsorbates measured at 303 K. Similar
B.L. Newalkar et al. / Microporous and Mesoporous Materials 65 (2003) 267–276
Owing to a non-polar nature of the adsorbent surface, this may be ascribed to the higher quadrupole moment of olefin molecules over corresponding paraffins. The trend observed in adsorption capacities for various hydrocarbons are found to be comparable to those reported for silica gel, and SBA-15 type of material [8]. The pure-component adsorption ratios for propane over ethane at 303 K and 1 atm is observed to be 2.6 (Table 1). Furthermore, adsorption capacity ratios for propylene/propane and ethylene/ethane are found to be about 1.6. The pure component adsorption ratio for propylene over ethylene is about 2.7 at 303 K. On the other hand, adsorption of acetylene is favored over ethylene with a ratio of about 1.8.
2.50 Ethane Propane Acetylene
Ethylene Propylene
2.00
Amt. adsorbed, mmol/g
269
1.50
1.00
0.50
3.3. Evaluation of equilibrium isotherm model
0.00 0
200
400
600
800
1000
1200
p, mm Hg
Fig. 1. Equilibrium adsorption isotherms for various hydrocarbons on HMS at 303 K.
trend is also noticed at 323 K. The measured adsorption isotherms are observed to be non-rectangular in shape. The adsorption uptake is found to vary almost linearly with an increase in pressure for ethane, ethylene, and propane. However, the uptake of propylene is found to be linear only up to a loading of about 200 mmHg. Furthermore, adsorption isotherms are found to be reversible. Similar adsorption nature is also reported for C2 and C3 hydrocarbons over Silicalite–I and Na–Y framework [7]. The equilibrium adsorption capacities for various hydrocarbons at 1 atm are compiled in Table 1. The isotherms showed that the adsorption capacity for unsaturated hydrocarbons is substantially higher than the corresponding paraffin. For example, at 303 K and 1 atm, 1.74 mmol/g of propylene was adsorbed compared to 1.01 mmol/g of propane. The following trend in adsorption capacity was observed for various hydrocarbons: propylene > acetylene > propane > ethylene > ethane. Further, the rise in the adsorption capacity with pressure was higher for olefins compared to corresponding paraffins.
The adsorption data were analyzed using Langmuir and Langmuir–Freundlich models by non-linear regression approach. The experimental data was well represented by Langmuir–Freundlich adsorption isotherm model i.e. V ¼ Vm bpn = ð1 þ bpn Þ where V and Vm are the amount adsorbed at equilibrium pressure p in mmHg and monolayer adsorption capacity in mmol/g, b and n are Langmuir and Freundlich constants, respectively. The equilibrium adsorption parameters so obtained are also compiled in Table 1. It can be seen that the Langmuir–Freundlich constant, b, which is a measure of interaction between adsorbate and adsorbent, of unsaturated hydrocarbons are higher than those of saturated ones, thus suggesting a stronger interaction of the former with the adsorbent surface. 3.4. Isosteric heats of adsorption The isosteric heats of adsorption (DH ) for various adsorbates are estimated using the Clausius–Clapeyron equation (Table 1) and their dependence on adsorption coverage is shown in Fig. 2. The heats of adsorption for propylene, propane, ethylene, ethane, and acetylene were 13.3, 9.0, 8.4, 6.3, and 9.7 kcal/mol, respectively. The isosteric heats of adsorption are found to be higher for ethylene and propylene compared to
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Table 1 Isosteric heats (DH ) of adsorption at low coverage, equilibrium adsorption capacities, (Q), at 1 atm and fitted Langmuir–Freundlich constants (Vm , b, and n) for various hydrocarbons on HMS type mesoporous silica (panel A) and selectivity ratio (ratio of pure gas adsorption capacity) at 1 atm for various hydrocarbon gases on HMS type mesoporous silica (panel B) Adsorbate
DH, kcal/mol
Panel A Ethane (C2 H6 )
6.3
Ethylene (C2 H4 )
8.4
Acetylene (C2 H2 )
9.7
Propane (C3 H8 )
9.0
t/K
Q, mmol/g
Vm , mmol/g
b 103 , mmHg1
n
303 323 303 323 303 323 303 323 303 323
0.56 0.38 0.89 0.60 1.55 1.11 1.24 0.87 1.94 1.40
3.70 3.04 6.99 4.84 4.18 3.29 5.50 4.99 5.71 5.50
0.32 0.18 0.72 0.48 1.85 0.87 0.78 0.44 4.18 1.44
0.89 0.95 0.75 0.80 0.81 0.88 0.86 0.88 0.70 0.78
Propylene (C3 H6 )
13.3
System
Adsorption selectivity ratio at 1 atm
Panel B Ethylene/ethane Propylene/propane Acetylene/ethylene Propane/ethane Propylene/ethylene
303 K
323 K
1.6 1.6 1.8 2.2 2.2
1.6 1.6 1.9 2.3 2.3
14.00 Ethane Propane Acetylene
12.00
Ethylene Propylene
∆H, kca/mol
10.00
8.00
6.00
4.00
2.00
0.00 0.00
0.20
0.40
0.60
0.80
1.00
mmol/g Fig. 2. Dependence of isosteric heats of adsorption for C2 , and C3 hydrocarbons on HMS with coverage.
ethane and propane, respectively, over the entire adsorption coverage. The heats of adsorption of acetylene are higher than those obtained for ethylene. Furthermore, a sharp drop in the heats of adsorption is noticed for unsaturated hydrocarbons particularly for propylene with an increase in adsorption coverage. Heats of adsorption for ethylene and propylene on HMS are found to be higher than those reported for silica gel [8a] and MCM-41 [8c] type mesoporous silica (Table 2). Interestingly, the measured values are found to be in good agreement with those reported on SBA-15 type of mesoporous silica (Table 2) [8b]. Furthermore, the measured heat values are found to be similar with those reported for respective C2 and C3 hydrocarbons on three-dimensional silica frameworks like Silicalite–I [7]. Typically, dependence of heat of adsorption with coverage is usually observed to display three regions namely adsorbent–adsorbate interaction followed by adsorbate– adsorbate interaction and finally condensation. Among these interactions, adsorbent–adsorbate
B.L. Newalkar et al. / Microporous and Mesoporous Materials 65 (2003) 267–276 Table 2 Initial heats of adsorption for C2 , and C3 hydrocarbons on different types of mesoporous silica samples Adsorbent MCM-41a SBA-15a Silica gela HMSb a b
DH , kcal/mol Ethane
Ethylene
Propane
Propylene
4.2 5.9 – 6.3
5.0 8.4 – 8.4
–
– 14.8 8.6 13.3
9.2 7.6 9.0
Ref. [7]. Present work.
interaction takes place in the initial region wherein high heats of adsorption are noticed. On the other hand, adsorbate–adsorbate interaction occurs with an increase in coverage because of which an increase in heats of adsorption is noticed. With still further increase in coverage, the heats of adsorption show downward trend wherein heat values are observed to approach condensation value of respective adsorbate. In view of this, the observed high heats of adsorption noticed in the initial region for light hydrocarbons reflect adsorbent– adsorbate interaction and gradual drop with an increase in coverage indicates the presence of surface heterogeneity in the form of specific adsorption sites for these molecules in HMS framework. Such heterogeneity is found to be more pronounced for unsaturated alkenes over corresponding alkanes. The presence of specific adsorption sites is not fully understood at present and attempts are being made to investigate this aspect in detail. Unlike, Silicalite–I and Na–Y frameworks [7], no adsorbate–adsorbate interaction is noticed with an increase in coverage. This could be due to the semicrystalline nature of HMS framework. 3.5. Adsorption selectivity The higher adsorption capacity and heats of adsorption observed for unsaturated hydrocarbons compared to corresponding alkanes indicate a possibility of HMS as a medium for adsorptive separation of the hydrocarbon mixtures. In fact, over the last 50 years these separations have been accomplished through cryogenic processes (distillations), which are very energy-intensive due to close relative volatilities [9]. Therefore, many al-
271
ternatives are being investigated [10–18] world over to achieve this separation, among which adsorption based processes are emerging as prominent candidates. The key factor for the commercial viability of adsorption process is the availability of selective adsorbent. To explore the potential of HMS as an adsorbent we have estimated adsorption selectivity for binary mixtures of ethane/ethylene, and propane/ propylene, using the extended Langmuir–Freundlich model [19a] which is given by Vi ¼ ðVm Þi bi pini =ð1 þ b1 p1n1 þ b2 p2n2 Þ, where pi are partial pressure, bi are the Langmuir constants and ni are Freundlich constants for component i. Vi are the amounts adsorbed from the mixture, and ðVm Þi are the monolayer capacity for component i. Thus for a two component (1 and 2) system the amount adsorbed of each component can be expressed as V1 ¼ ðVm Þ1 b1 p1n1 =ð1 þ b1 p1n1 þ b2 p2n2 Þ and V2 ¼ ðVm Þ2 b2 p2n2 =ð1 þ b1 p1n1 þ b2 p2n2 Þ and the total volume adsorbed can be expressed by V ¼ V1 þ V2 ¼ fðVm Þ1 b1 p1n1 þ ðVm Þ2 b2 p2n2 g=ð1 þ b1 p1n1 þ b2 p2n2 Þ. The adsorbed phase composition with respect to component 1 ðX1a Þ can also be obtained from the ratio of amount adsorbed of component 1 to the total volume i.e. X1a ¼ V1 =V ¼ ðVm Þ1 b1 p1n1 = fðVm Þ1 b1 p1n1 þ ðVm Þ2 b2 p2n2 g ¼ 1=ð1 þ ððVm Þ2 b2 p2n2 = ðVm Þ1 b1 p1n1 Þ. Based on the above equation, for a given gas phase composition, X1a can be calculated from the values of L-F constants for the two pure gases. Adsorption selectivity ð/1=2 Þ in a binary mixture can also be calculated from adsorbed phase and gas phase compositions of the two gases using the relation, /1=2 ¼ X1a X2g =X1g X2a . Thus, the predicted adsorbed phase composition and adsorption selectivity for binary mixtures of ethane/ethylene, and, propane/propylene are shown in Figs. 3 and 4, respectively as a function of gas phase composition. The results show a high selectivity for propylene over propane and ethylene over ethane. Such a trend is anticipated as the stronger component is expected to dominate in mixture adsorption [19b]. High adsorption selectivity of olefin at low gas phase concentration decreases with increase in olefin concentration in gas phase. Such high selectivity for unsaturated hydrocarbons over corresponding alkanes at low gas phase concentration makes HMS an attractive
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1.0
0.8
X1a
0.6
0.4 C2H4/C2H6 C3H6/C3H8
0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.0
X1g Fig. 3. Adsorption isotherms for binary mixtures of C2 and C3 hydrocarbons on HMS predicted by Langmuir–Freudliech (LF) model at 303 K. (Suffix 1 is for ethylene (C2 H4 ), and propylene (C3 H6 ) in a binary mixture of ( ) C2 H4 /C2 H6 , and (r) C3 H6 /C3 H8 . X1g and X1a are gas and adsorbed phase compositions of ethylene/propylene).
adsorbent for olefin enrichment of lean hydrocarbon streams. Therefore, owing to the observed selectivity of about 4 for C3 olefin over corresponding alkane and non-rectangular nature of adsorption isotherm, HMS framework could be a potential candidate for designing separation processes based on pressure/vacuum swing adsorption principles [7,20]. Similar potential is also noticed for Silicalite–I and Na–Y framework for separation of light hydrocarbon.For this purpose, it is also essential to learn about the adsorption behavior for impurities present in the C3 enriched feedstock. Generally, methane, nitrogen, carbon dioxide, and carbon monoxide are commonly observed impurities in C3 stream. Therefore, adsorption behavior of HMS framework for these impurities was investigated by measuring the individual adsorption isotherm at 303 K. The measured adsorption data is represented in Fig. 5. The isotherms showed that the adsorption capacity at 1 atm for methane (0.098 mmol/g), carbon monoxide (0.05 mmol/g), and nitrogen (0.04 mmol/g) is
7.0 0.90
C2H4/C2H6
6.0
Carbon dioxide
C3H6/C3H8
Carbon monoxide
0.70
Methane Nitrogen
4.0
0.60 Amt. adsorbed, mmol/g
Selectivity (α)
5.0
0.80
3.0 2.0
0.50 0.40 0.30
1.0
0.20 0.0 0.0
0.2
0.4
0.6
0.8
1.0
0.10
X1g 0.00 Fig. 4. Variation of olefin selectivities (a) as a function of gas phase composition at 303 K. (Suffix 1 is for ethylene (C2 H4 ), and propylene (C3 H6 ) in a binary mixture of (r) C2 H4 /C2 H6 , ( ) C3 H6 /C3 H8 , and X1g is the gas phase composition of ethylene/propylene).
0
200
400
600 p, mmHg
800
1000
Fig. 5. Equilibrium adsorption isotherms for carbon dioxide, carbon monoxide, methane, and nitrogen on HMS at 303 K.
B.L. Newalkar et al. / Microporous and Mesoporous Materials 65 (2003) 267–276
insignificant over HMS surface as compared to hydrocarbon uptake. However, uptake for carbon dioxide at 1 atm (0.62 mmol/g) is found to be significant. Therefore, it is recommended to use C3 feed stream free of carbon dioxide to achieve better performance for HMS-based separation processes.
4. Conclusion Mesoporous material, HMS, shows a reversible uptake of light hydrocarbons and is selective for propylene. The high adsorption capacity and selectivity for propylene over propane shows the potential of HMS for tailoring a suitable adsorbent for C3 hydrocarbon separation.
273
Appendix B lists adsorption data for methane, nitrogen, carbon dioxide, and carbon monoxide at 303 K.
Acknowledgements Authors (BLN and SK) gratefully acknowledge the support of this work by the NSF MRSEC program under grant number, DMR-0213623. NVC, PK and TB are thankful to the management of Indian Petrochemicals Corporation Limited (IPCL), Vadodara, India, for supporting this work. The authors are also thankful to Mr. S.P. Patel, IPCL, India, for his assistance during adsorption measurements.
5. Supplementary information
Appendix A. Supplementary information
Appendix A lists adsorption isotherm data for various hydrocarbons on HMS at 303 and 323 K.
Adsorption of ethane and ethylene on HMS (experimental data)
Ethane
Ethylene
30 °C
50 °C
30 °C
50 °C
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
14.91 37.35 75.36 126.4 172.5 229.9 285 341.3 429.3 527.6 646 759.2 863.5 987.8 1008.9
0.012 0.0286 0.0597 0.0889 0.1167 0.1494 0.1792 0.2089 0.2528 0.2995 0.3534 0.4025 0.4462 0.4963 0.5055
18.97 42.35 68.17 100.3 151.4 246.5 334.5 446.5 547.7 653.3 759.4 887.2 1005.7
0.008 0.0179 0.0286 0.043 0.0622 0.0972 0.1282 0.1657 0.1986 0.232 0.2646 0.3024 0.3366
14.93 34.91 58.36 83.89 111.7 147.4 204.8 270.6 357.7 460.1 554.8 663.3 768.3 894.9 1006.3
0.0213 0.0474 0.0758 0.1017 0.1342 0.1697 0.2237 0.281 0.35 0.4246 0.4895 0.5583 0.622 0.6938 0.7531
18.72 39.55 69.07 109.5 145.4 176 229.3 327.9 452.2 566.4 676.1 778 897.9 1011.9
0.0142 0.0292 0.0497 0.0774 0.1002 0.1188 0.1501 0.2041 0.2674 0.3216 0.3715 0.4153 0.4637 0.5091
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Adsorption of propane and propylene on HMS (experimental data) Propane
Propylene
30 °C
50 °C
30 °C
50 °C
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
15.36 54.56 100.7 156.2 267.1 423.6 614.6 713.5 756.3 935.5 1004.2
0.0499 0.1487 0.2304 0.3276 0.494 0.6883 0.9175 1.0223 1.071 1.2463 1.316
15.00 37.27 60.14 85.71 114.7 156.2 218.3 290.3 382.5 491.9 581.3 675.7 771.8 885.4 1001
0.0228 0.0511 0.081 0.1075 0.1417 0.1843 0.2441 0.3093 0.388 0.4744 0.5409 0.6067 0.6708 0.7462 0.8214
6.06 21.2 46.8 90.06 175.8 295 463.7 620 732.5 761.6 935.3 997.7
0.0679 0.1884 0.3355 0.5202 0.7753 1.0554 1.3483 1.5673 1.7082 1.7417 1.9233 1.9819
15.46 36.11 78.11 116.8 166.7 212.5 284.2 363.5 459 560.9 670.1 778 895.6 1010.9
0.0625 0.1283 0.2291 0.3167 0.415 0.494 0.6085 0.7212 0.8418 0.9584 1.0713 1.1741 1.2787 1.3757
Adsorption of acetylene on HMS (experimental data) 30 °C
50 °C
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
13.47 40.67 79.06 149.4 239.9 364.1 487.8 600.9 743.3 935.6 1023.8
0.0536 0.1493 0.2598 0.4074 0.5733 0.7613 0.9181 1.048 1.1888 1.3548 1.4241
17.43 36.23 62.19 91.92 139.4 191.5 280.1 377.4 476.1 582.8 683.3 778.8 892.6 1011.1
0.033 0.0651 0.1072 0.1476 0.2131 0.2813 0.3768 0.4718 0.559 0.6467 0.7232 0.7917 0.8667 0.9429
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275
Appendix B. Supplementary information Adsorption of carbon dioxide, carbon monoxide, methane, and nitrogen on HMS at 30 °C (experimental data) Carbon dioxide
Carbon monoxide
Methane
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
p, mmHg
n, mmol/g
26.56 66.35 112.7 167 245.8 342.6 451.8 649.2 749.8 855.9 1001.7
0.0315 0.0813 0.1247 0.1777 0.2491 0.3298 0.4161 0.556 0.6234 0.691 0.78
42.81 102.7 145.4 193.3 292.8 386 483.9 583.9 677.8 776.3 888.1 1017.6
0.003 0.0055 0.0084 0.0118 0.0183 0.0244 0.031 0.0379 0.0438 0.0505 0.0578 0.0667
39.39 87.53 140.5 188.4 237.7 287.4 337.8 388 437.1 488.4 538 587.7 639.3 689.2 739.4 791.2 973.3 1017.5
0.0056 0.0175 0.0225 0.0287 0.035 0.0417 0.048 0.0544 0.0608 0.0666 0.0723 0.0779 0.084 0.0898 0.0955 0.1019 0.1216 0.1269
40.24 91 141.7 189.8 239.4 289 382.1 438.5 490.4 538.6 590.3 685.1 803 928.8 1028.5
0.0021 0.0096 0.0108 0.0133 0.0157 0.0182 0.0227 0.0253 0.0278 0.03 0.0327 0.0372 0.0425 0.0459 0.0484
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