Aromatics/Aliphatics Separation by Adsorption: New Sorbents forSelective Aromatics Adsorption by π-Complexation

Akira Takahashi, Frances H. Yang, and Ralph T. Yang*

Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136

New sorbents for benzene/cyclohexane separation based on π-complexation were prepared bydispersion of transition metal salts on a high-surface-area substrate. PdCl2 or AgNO3 dispersedon SiO2 gel exhibited high equilibrium adsorption ratios of benzene over cyclohexane. PdCl2loading of 0.88 g/g of SiO2 showed the best benzene/cyclohexane ratio of 3.2. The heats ofadsorption of benzene on these sorbents were in the range 7-12 kcal/mol and followed the rankorder CuCl > PdCl2 > AgNO3 > AuCl3 > PtCl4, compared to 5-7 kcal/mol for cyclohexane.Molecular orbital calculations for the bonding of benzene and chlorides of these metals wereperformed at the Hartree-Fock (HF) and density functional theory (DFT) levels using effectivecore potentials. The theoretical bond energies were (in kcal/mol) 12.5 (CuCl), 10.8 (PdCl2), 8.6(AgCl), 6.5 (AuCl3), and 5.2 (PtCl4), in fair agreement with the experimental results. The M-Cinteractions followed classical π-complexation in most cases, and differences in the bonds withthese metal ions are explained by natural bond orbital results.

Introduction

Separations of aromatics/aliphatics are crucially im-portant in the chemical and petrochemical industries.They are also a most difficult class of separations.Simple fractional distillation is not useful because of theclose relative volatilities between aromatics and ali-phatics; for example, the boiling point of benzene is 80°C, while that of cyclohexane is 81 °C.

Aromatics/aliphatics separation is a key step in theproduction of the basic chemical feedstock, BTX (i.e.,benzene, toluene, and xylene), as well as in the produc-tion of fuels. Aromatics are premium blending stocksfor motor fuels, as the high-octane-number hydrocar-bons in the gasoline boiling range are primarily aro-matic hydrocarbons. In these processes, high-purityaromatics must be separated from the catalytic refor-mates containing 45-60% aromatics.1-4 In a typicalprocess, the reformate from the catalytic reactor (e.g.,“Platforming”) is sent to a reformate splitter column.The C7

- fractions from the overhead are sent to aseparation process to separate benzene or toluene fromaliphatics, while the C8

+ fractions from the bottom aresent for xylene recovery.

Aromatics/aliphatics separations are being accom-plished by solvent extraction. A number of solvents havebeen used.1,5-7 The first efficient method for recoveryof aromatics was the Udex process of Union Carbide (in1952) using a glycol-based solvent. Since then, severalother solvents, such as sulfolane and N-methyl pyrroli-done, have also been developed. These solvent extractionprocesses generally consist of three parts: extractor,extractive distillation column, and solvent strippercolumn. Although these separation processes are ef-ficient, they are highly energy intensive, and moreimportantly, the solvents are increasingly posing asenvironmental hazards. One of the most representativesolvents, sulfolane, is potentially hazardous and is nowregulated by the Federal Toxic Substances Control Act

of EPA, Section 8(a) (http://www.epa.com). It was re-cently reported that the groundwater in Brisbane,Australia, was contaminated by sulfolane from dumpingthat occurred over 20 years ago.8

Another possible separation technique is fractionaldistillation. As mentioned, it is difficult because of theclose relative volatilities. For benzene/cyclohexane, themixture has a minimum azeotrope at about 53%.Therefore, acetone is added as an entrainer, and acomplex hybrid system (distillation combined withextraction in this case) can be used for separation.9

Because of the importance of aromatics/aliphaticsseparation and the problems associated with solventextraction, possible alternatives have been studied.These include pervaporation,10 liquid membranes,11 andthe use of liquid inclusion complexes.12 Purification ofdilute aromatics from aliphatics (e.g., toluene and/orxylene in heptane) by temperature swing adsorption(TSA) was also studied in the liquid phase.13 Theadsorbents considered by Matz and Knaebel were silicagel, activated alumina, activated carbon, zeolite 13X,and polymeric adsorbent (XAD-7). They claimed thatsilica gel was the best sorbent because of its superiorthermal property.

Among the separation technologies, adsorption isplaying an increasingly important role.14 It is energy-efficient and does not produce wastes. However, itsutility depends entirely on the availability of selectivesorbents. The conventional sorbents and separationsusing these sorbents are restricted to van der Waals andelectrostatic interactions between the sorbent and sor-bate. Studies of new sorbents/separations using weakchemical bonds such as chemical complexation havebegun only recently in our laboratory. As suggested byKing,15 chemical complexation bonds are generallystronger than van der Waals interaction, yet weakenough to be reversible. Therefore, tremendous op-portunity exists for developing new sorbents by usingweak chemical bonds, including various forms of com-plexation bonds.

* Corresponding author. Telephone: (734)936-0771. Fax:(734)763-0459. E-mail: yang@umich.edu.

3856 Ind. Eng. Chem. Res. 2000, 39, 3856-3867

10.1021/ie000376l CCC: $19.00 © 2000 American Chemical SocietyPublished on Web 09/14/2000

π-complexation is a subclass of chemical complex-ation. It pertains to the main-group (or d-block) transi-tion metals, i.e., from Sc to Cu, Y to Ag, and La to Auin the periodic table.16 These metals or their ions canform the normal σ bond to carbon, and in addition, theunique characteristics of the d orbitals in these metalsor ions enable them to form bonds with unsaturatedhydrocarbons in a nonclassical manner. This type ofbonding is broadly referred to as π-complexation. Thisπ-complexation was seriously considered for olefin/paraffin separation and purification by employing liquidsolutions containing silver or cuprous ions.17-22 Theseinvolved gas-liquid operations. Although gas-solidoperation can be simpler as well as more efficient,particularly by pressure swing adsorption, the list ofattempts for developing solid π-complexation sorbent isa short one. CuCl, which is insoluble in water, has beenconsidered in the powder form for olefin/paraffinseparations.23-25 However, CuCl, in the solid particulateform, dose not have a high surface area for the desiredhigh olefin sorption capacity. Other attempts at devel-oping solid sorbents for π-complexation included silversalts supported on anion-exchange resins,26,27 Ag+-YZeolite, 28 and Cu-Y Zeolite.29 However, these were metwith limited success. The only commercially availablesorbent based on π-complexation is CuCl/γ-Al2O3 for COseparation.30-33 Selectivities for olefins of the knownsorbents are not high enough to be used for commercialPSA processes. Hence, their use would require ad-ditional, substantial operations.34

More recently, several new sorbents based on π-com-plexation were prepared for selective olefin adsorption.These include Ag+-exchanged resins and monolayerCuCl/γ-alumina,28,35 monolayer CuCl on pillared clays,36

and monolayer AgNO3/SiO2.37-39

No selective sorbents are known for aromatics/ali-phatics separations. Based on our understanding ofπ-complexation, it is certainly possible to develop suchsorbents based on π-complexation. In the benzenemolecule, the carbon atom is sp2 hybridized. Hence, eachcarbon has three sp2 orbitals and another pz orbital. Thesix pz orbitals in the benzene ring form the conjugativeπ bond. The pz orbitals also form the antibonding π*orbitals, which are not occupied. When benzene inter-acts with transition metals, the π orbitals of benzenecan overlap with the empty outer-shell s orbital of thetransition metal to form a σ bond. Moreover, it ispossible that the vacant antibonding π* orbital ofbenzene can overlap with the d orbitals in the transitionmetal, in a manner similar to the formation of theolefin-Cu+ bond.40 In this work, monolayer salts con-taining transition metals spread on high-surface-areasubstrates were prepared and studied as selectivesorbents for aromatics for use in aromatics/aliphaticsbulk separations.

Benzene and cyclohexane form an ideal pair of modelcompounds for developing selective sorbents for aromat-ics. These molecules have similar shapes, and asmentioned, the boiling point of benzene is 80 °C, whilethat of cyclohexane is 81 °C. The kinetic diameter ofbenzene, which is calculated from the minimum equi-librium cross-sectional diameter, is estimated to be 5.85Å, compared with 6.0 Å for cyclohexane.41 Therefore,benzene and cyclohexane were used in this work.

Experimental SectionSorbent Preparation. The sorbents in this work

were transition metal salts that were dispersed on high-

surface-area substrates. Based on the results of selectiveolefin sorbents for olefin/paraffin separations,28,35-39

Cu+, Ag+, Pt4+, and Pd2+ cations were the most promis-ing sorbents because of their strong interactions withthe olefin molecules. From the results of molecularorbital calculations, Cu+ cation would form strongerπ-complexation bonds than Ag+.40

PdCl2 (Strem Chemicals), CuCl2 (Aldrich), AgNO3(Strem Chemicals), PtCl4 (Strem Chemicals), and AuCl3(Strem Chemicals) were selected for transition metalsalts because of their solubilities to water. The high-surface-area substrates were SiO2 gel (8-20 mesh or100-200 mesh, Strem Chemicals), Al2O3 (PSD-350,ALCOA), and activated carbon (BPL 4 × 10, Calgon).

Dispersion of salts on the substrates was performedby the incipient wetness method, which is used in themanufacturing of supported catalysts, except for PdCl2/activated carbon. An aqueous solution of the desired saltwas first prepared. A volume of the solution equal tothe total pore volume of the substrate was brought intocontact with the substrate. After the substrate hadimbibed the solution containing the salt into its porestructure, the sample was heated at 100 °C to removethe solvent. This procedure was repeated several timesuntil the predetermined loading amount was achieved.39

As for the Cu+ sorbent, it was prepared by two steps:(1) impregnation of Cu2+ salt from solution on thesubstrates by incipient wetness and (2) reduction ofCu2+ to Cu+ by temperature-programmed reduction(TPR). This procedure was necessary because stable Cu+

salts were not water-soluble. The TPR conditions willbe explained shortly.

PdCl2/activated carbon was prepared by the impreg-nation method, as described by Tamon et al.42 Becauseactivated carbon has a low affinity for water, theincipient wetness method is not suitable in the aqueoussystem because of poor wetting. A predetermined amountof PdCl2 was magnetically stirred in 15 cm3 of 1 N HClaqueous solution at room temperature, and 4 g ofactivated carbon was added to the mixture. The carbonwas impregnated with the solution for 1 day. It waswashed by deionized water and was dried at 110 °C inair.

The adsorbents prepared and studied in this work aresummarized in Table 1. BET surface areas and porevolumes determined by N2 isotherms at 77 K are alsoprovided.

Adsorption Isotherms and Uptake Rates. Single-component isotherms for benzene and cyclohexane weremeasured using a standard gravimetric method. AShimadzu TGA-50 automatic recording microbalancewas used. Helium (Prepurified grade, Metro welding99.995%) was used as the carrier gas and was firstpassed through two consecutive gas-wash bottles thatcontained benzene (HPLC grade, Sigma-Aldrich, >99.9%)or cyclohexane (HPLC grade, Aldrich, >99.9%) in orderto obtain saturated benzene or cyclohexane vapor. Afterthe concentration was diluted to the desired value bybeing blended with additional helium (total flow vol-ume: 250 cm3/min), the mixture was directed into themicrobalance. Isosteric heats of adsorption were calcu-lated using the Clausius-Clapeyron equation, eq 1,from isotherms at different temperatures.

(d ln PdT ) )

qst

RT2(1)

Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3857

Adsorption isotherms of propylene (CP grade, Mathe-son minimum purity 99.0%) and propane (CP grade,Matheson minimum purity 99.0%) were measured volu-metrically using a Micromeritics ASAP 2010 system.Nitrogen isotherms at 77 K, also measured with theMicromeritics ASAP 2010, were used for BET surfacearea and pore volume determinations. BET surfaceareas were calculated from the isotherms at a relativepressure (P/Po) of 0.06-0.20. Pore volumes were calcu-lated at 0.95 P/Po. The overall diffusion time constantvalues, D/r2, were calculated from the uptake rates.43

In this work, the short time region (Mt/Mi < 0.3) wasused for the calculation of D/r2 by plotting Mt/Mi vs t1/2

based on following relation

Molecular Orbital Computational Details. Mo-lecular orbital (MO) studies on π-complexation bondingfor olefins and sorbent surfaces have been extensivelyinvestigated.40,44-45 In this work, similar MO studieswere extended to benzene and sorbent surfaces. TheGaussian 94 progam46 in the Cerius2 molecular model-ing software47 from Molecular Simulation, Inc., wasused for all calculations. MO calculations for benzeneand sorbent surfaces were performed at the Hartree-Fock (HF) and density functional theory (DFT) levelsusing effective core potentials (ECPs).48-50 The LanL2DZbasis set51 is a double-ú basis set containing ECPrepresentations of electrons near the nuclei for post-third-row atoms. The reliability of this basis set hasbeen confirmed by the accuracy of calculation resultsas compared with experimental data. Therefore, theLanL2DZ basis set was employed for both geometryoptimization and natural bond orbital (NBO) analysis.

Geometry Optimization and Energy of Adsorp-tion Calculations. The restricted Hartree-Fock (RHF)theory with the LanL2DZ level basis set was used todetermine the geometries and the bonding energies ofbenzene on AgCl and CuCl, as Ag+ and Cu+ have filledd orbitals with spin ) 1. However, the unrestrictedHartree-Fock (UHF) theory with the LanL2DZ levelbasis set was used to determine the geometries andbonding energies of benzene on PdCl2, AuCl3, and PtCl4,because Pd2+, Au3+, and Pt4+ have unfilled d orbitalswith spin > 1.

Two of the computational models used for the adsorp-tion systems are shown in Figures 17 and 18. Thesimplest models with only a single metal chloride

interacting with a benzene molecule were chosen forπ-complexation studies. The optimized structures werethen used for bond energy calculations according to thefollowing expression:

where Eadsorbate is the total energy of benzene; Eadsorbentis the total energy of the bare adsorbent, i.e., the metalchloride; and Eadsorbent-adsorbate is the total energy of theadsorbate/adsorbent system. A higher value of Eadscorresponds to a stronger adsorption.

Natural Bond Orbital (NBO) Analysis. The opti-mized structures were also used for NBO analysis atthe B3LYP/LanL2DZ level. The B3LYP52 approach isone of the most useful self-consistent hybrid (SCH)approaches,53 which is Beck’s three-parameter nonlocalexchange functional54 with nonlocal correlation func-tional of Lee, Yang, and Parr.55 The NBO analysisperforms population analysis that pertains to localizedwave-function properties. It gives a better descriptionof the electron distribution in compounds of high ioniccharacter, such as those containing metal atoms.56 It isknown to be sensitive for calculations of localized weakinteractions, such as charge transfer, hydrogen bonding,and weak chemisorption. Therefore, the NBO program57

was used for studying the electron density distributionof the adsorption system.

Results and Discussion

Temperature-Programmed Reduction of CuCl2/Al2O3. Because CuICl is not water soluble, CuI sorbentwas prepared by incipient wetness of CuIICl2 on Al2O3followed by temperature-programmed reduction (TPR)to convert Cu2+ to Cu+. To understand its reductionbehavior, CuCl2/Al2O3 was first heated in a flow of 5.3%H2 in He up to 700 °C at a heating rate of 10 °C/min.The TPR effluent from the bed of the sample wasanalyzed by a gas chromatograph (Shimadzu, GC-14A).The intensity measured by the thermal conductivitydetector (TCD) indicated H2 consumption. The result isshown in Figure 1a. During the heat treatment of CuCl2/Al2O3 (0.50 g/g) in H2, two distinct peaks, at 270 °C and410 °C, were detected. These two peaks correspondedto two reduction steps. The first peak at 270 °Cindicated the change from Cu2+ to Cu+, and the secondpeak indicated the change from Cu+ to Cu0. Thedifference in intensities of the two peaks was likelycaused by incomplete conversion of Cu+ to Cu0. Conse-quently, a long tail from 450 to 700 °C appeared. From

Table 1. Adsorbents Examined in This Work

salt substratesalt loading(g/g of SiO2) sample preparation

BET area(m2/g)

pore volume(cm3/g)

PdCl2 SiO2 (100-200 mesh) 0.045 incipient wetness 599 0.35PdCl2 SiO2 (100-200 mesh) 0.121 incipient wetness 485 0.28PdCl2 SiO2 (100-200 mesh) 0.305 incipient wetness 306 0.18PdCl2 SiO2 (100-200 mesh) 0.600 incipient wetness 341 0.20PdCl2 SiO2 (100-200 mesh) 0.880 incipient wetness 284 0.17AgNO3 SiO2 (8-20 mesh) 0.330 incipient wetness 298 0.18CuCl Al2O3 0.500 incipient wetness+TPR 214 0.28CuCl SiO2 (100-200 mesh) 0.500 incipient wetness + TPR 437 0.24PtCl4 SiO2 (100-200 mesh) 0.460 incipient wetness 271 0.14AuCl3 SiO2 (100-200 mesh) 1.000 incipient wetness 356 0.20PdCl2 activated carbon 0.305 Impregnation 673 0.39none SiO2 (100-200 mesh) 0 as-received 669 0.38none SiO2 (8-20 mesh) 0 as-received 650 0.40none Al2O3 0 as-received 340 0.57none activated carbon 0 as-received 891 0.52

Mt

Mi) 6

xπ(Dtr2 )1/2

(2)

Eads ) Eadsorbate + Eadsorbent - Eadsorbent-adsorbate (3)

3858 Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000

the result above, it was determined that 270 °C was theappropriate temperature for reduction to CuCl. Theintensity change of the TCD detector during the CuCl2/Al2O3 (0.50 g/g-SiO2) sorbent preparation is shown inFigure 1b. The intensity at 270 °C began to decreaseafter 70 min, indicating that most of the Cu2+ wasconverted to Cu+. Subsequently, CuCl2/Al2O3 sorbentswith different salt loadings were reduced at 270 °C for1 h in the presence of 5.3% H2.

Propane/Propylene Isotherms. Before isothermsfor benzene and cyclohexane were measured, isothermsfor propylene and propane were determined in order toconfirm the π-complexation capabilities of the sorbents.The optimum loading amounts of transition metal salts,at which propylene/propane adsorption ratios (at 1.0atm and 70 °C) reached maxima, were determinedexperimentally by changing the salt loadings. Theexperimental optimum loading amounts were found tobe almost the same as the theoretical monolayer loadingamounts, as shown in Table 2. XRD analysis by Padinrevealed that the diffraction peaks of AgNO3 disappearcompletely after incipient wetness dispersion on SiO2,indicating monolayer dispersion.58 Additional evidencefor monolayer dispersion was the absence of the adsorp-tion characteristics of alumina, indicating the lack ofany bare surface. Theoretical monolayer loading amountsfor these chlorides were calculated using the assumptionthat Cl- (radius: 0.181 nm) was dispersed on the

surface as a monolayer in a close-packing manner.59 Inthe case of PtCl4/SiO2, 0.83 g/g loading of PtCl4 showeda slightly higher adsorption ratio of propylene overpropane than 0.46 g/g loading. However, the BETsurface area was reduced to 137 m2/g with the higherloading. Therefore, PtCl4/SiO2 (0.46 g/g) was used forbenzene/cyclohexane adsorption.

The isotherms of propane and propylene on sorbentsat optimum loadings are shown in Figures 2-4, andthey are compared with those on bare SiO2 and Al2O3(Figure 5). Isotherms fit by eqs 4 and 5, which will bediscussed later, are also plotted in these figures as solidcurves. Here,a heterogeneity factor of 5 was used forpropylene isotherms except for that of AuCl3/SiO2. ForAuCl3/SiO2, s ) 3 was used for proper fitting.

Pure-component adsorption ratios of propylene overpropane at 70 °C by bare Al2O3 and SiO2 were near 1.5.In contrast, those by transition metal salts dispersedon SiO2 or Al2O3 were around 3-4 (except for CuCl/SiO2and AuCl3/SiO2), indicating π-complexation with theolefin. PdCl2/SiO2 (0.88 g/g) and PtCl4/SiO2(0.46 g/g)showed the highest ratios of 4.0 at 70 °C. However,CuCl/SiO2 (0.50 g/g) showed a poor ratio of 1.4.

Figure 1. Temperature-programmed reduction (TPR) of CuCl2supported on Al2O3 in H2 (5.3% H2 in He). The intensity showsH2 consumption. (a) H2 consumption at 10 °C/min. (b) H2 con-sumption during sample preparation for CuCl/SiO2.

Table 2. Calculated Monolayer Dispersion Amounts

salt substratemonolayer

loading (g/g)

PdCl2 SiO2 0.88PdCl2 activated carbon 1.16CuCl Al2O3 0.49CuCl SiO2 0.96PtCl4 SiO2 0.83AuCl3 SiO2 1.00

Figure 2. Pure-component equilibrium isotherms for propyleneand propane adsorption on PdCl2/SiO2 (0.88 g/g) and AgNO3/SiO2(0.33 g/g) at 70 °C. Symbols are experimental data, and lines areisotherms fit by eqs 4 and 5.

Figure 3. Pure-component equilibrium isotherms for propyleneand propane adsorption on CuCl/Al2O3 (0.50 g/g) at 70 °C andCuCl/SiO2 (0.50 g/g) at 25 °C. Symbols are experimental data, andlines are isotherms fit by eqs 4 and 5.

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Benzene/Cyclohexane Isotherms. Benzene andcyclohexane adsorption isotherms were measured forthe selected sorbents that showed π-complexation ca-pability for propylene. PdCl2 impregnated on activatedcarbon (0.305 g of PdCl2/g of SiO2) was also used forbenzene/cyclohexane adsorption measurements, as thissorbent exhibited excellent sorption capability to carbonmonoxide, also by π-complexation.42 Adsorption iso-therms are shown in Figures 6-11. Isotherms fit by eqs4 and 5, which will be discussed later, are also plottedin the figures. For comparison, the isotherms for ben-zene and cyclohexane on the bare substrates are shownin Figures 12-14.

PdCl2/SiO2 (0.88 g/g) showed the best benzene/cyclo-hexane adsorption ratios among the sorbents examined(Table 3). The pure component adsorption ratio, at 0.1atm pressure, was 3.2 at 120 °C and 2.9 at 100 °C.Benzene and cyclohexane isotherms were also measuredon this sorbent at 70 °C (results not shown here). Theamounts adsorbed were higher but the benzene/cyclo-hexane ratios were lower, being 1.5 at 0.1 atm. Thereason for the higher adsorption ratios at higher tem-peratures is related to nonselective pore filling by

benzene and cyclohexane. At low temperatures, porefilling of benzene and cyclohexane occurs readily evenin the larger pores. According to the Horvath-Kawazoetheory,60 the pore diameters for pore filling by benzeneand cyclohexane at 0.1 atm and 70 °C are 3.2 and 3.1nm, respectively. Those at 120 °C are 1.8 and 1.7 nm,respectively. These calculation results indicate that bothbenzene and cyclohexane are adsorbed in the pores ofthe sorbent at lower temperatures, leading to loweradsorption ratios. At higher temperatures, pore fillingdoes not occur, and benzene is selectively adsorbed byπ-complexation, leading to the higher adsorption ratios.The ratios of 2.9 and 3.2 are encouraging for separationby cyclic processes. Furthermore, isotherms in thispressure range were not steep, which is also desirablefor cyclic adsorption/desorption. The pure-componentratio on AgNO3/SiO2 (0.33 g/g) at 120 °C was also higherthan that on bare SiO2. However, the ratio of 2.0 forAgNO3/SiO2 (0.33 g/g) was not high enough for bulkseparation. PtCl4/SiO2 and CuCl/Al2O3 showed lowbenzene/cyclohexane adsorption ratios, although thesesorbents had excellent propylene/propane adsorptionratios. In conclusion, PdCl2/SiO2 and AgNO3/SiO2 showedenhanced adsorption ratios due to π-complexation with

Figure 4. Pure-component equilibrium isotherms for propyleneand propane adsorption on PtCl4/SiO2 (0.46 g/g) and AuCl3/SiO2(1.00 g/g) at 70 °C. Symbols are experimental data, and lines areisotherms fit by eqs 4 and 5.

Figure 5. Pure-component equilibrium isotherms for propyleneand propane adsorption on bare SiO2 and Al2O3 at 70 °C. Symbolsare experimental data, and lines are isotherms fit by eqs 4 and 5.

Figure 6. Pure-component equilibrium isotherms for benzene andcyclohexane adsorption on PdCl2/SiO2 (0.88 g/g) at 100 and 120°C.

Figure 7. Pure-component equilibrium isotherms for benzene andcyclohexane adsorption on CuCl/Al2O3 (0.50 g/g) at 100 and 120°C. Symbols are experimental data, and lines are isotherms fit byeqs 4 and 5.

3860 Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000

benzene, though PtCl4/SiO2 and CuCl/Al2O3 did notyield high ratios.

PdCl2/activated carbon showed adsorption behaviorthat was different from that of other sorbents. Cyclo-hexane adsorption amounts in the low-pressure rangebelow 0.03 atm were very small, hence leading to verylarge benzene/cyclohexane adsorption ratios in thispressure range, indicating π-complexation with benzeneby PdCl2. The high benzene/cyclohexane ratios areexcellent for purification purposes. The stepped iso-therm behavior was very similar to the adsorptionbehavior of bare activated carbon, although the adsorp-tion amounts for bare activated carbon were larger thanthose for PdCl2-impregnated carbon. This reduction wasapparently caused by the reduction of surface area byPdCl2 dispersion. In this experiment, the PdCl2 impreg-nation amount to activated carbon was 1/4 of a mono-layer (Table 2). Much larger loading might be necessaryto enhance the benzene/cyclohexane ratio in a higherpressure range.

The reversibility of the isotherms of benzene andcyclohexane on PdCl2/SiO2 (0.88 g/g) at 120 °C was alsomeasured (results not shown here). Both benzene and

cyclohexane isotherms were reversible between 0 and0.1 atm. PdCl2/SiO2 sorbents with different salt loadingsalso showed reversible isotherms.

The step-shaped isotherms of cyclohexane on acti-vated carbon and also on PdCl2/carbon merit an expla-nation. This behavior has also been observed for cyclo-hexane on Y zeolites (results not shown here). Thisbehavior is best explained with the Horvath-Kawazoetheory,60 which predicts the threshold relative pressureat which pores begin to fill, on the basis of the sorbate-surface interaction potential. Using a reasonable Len-nard-Jones potential for cyclohexane and carbon, thethreshold pressure of 0.02-0.03 atm (from the experi-mental data) corresponds to a pore size around 1 nm.This is a reasonable size for the pore constrictions inactivated carbon. This phenomenon did not occur forbenzene, because the interaction is much stronger withbenzene; hence, the threshold pressure is much lowerand is not seen in the isotherms as plotted.

Effects of PdCl2 Loading on Benzene/Cyclohex-ane Selectivity. To understand the effect of PdCl2loading on benzene/cyclohexane adsorption, the loading

Figure 8. Pure-component equilibrium isotherms for benzene andcyclohexane adsorption on AgNO3/SiO2 (0.33 g/g) at 100 and 120°C. Symbols are experimental data, and lines are isotherms fit byeqs 4 and 5.

Figure 9. Pure-component equilibrium isotherms for benzene andcyclohexane adsorption on PdCl2/activated carbon (0.305 g/g) at120 and 180 °C.

Figure 10. Pure-component equilibrium isotherms for benzeneand cyclohexane adsorption on PtCl4/SiO2 (0.46 g/g) at 85 and 100°C. Symbols are experimental data, and lines are isotherms fit byeqs 4 and 5.

Figure 11. Pure-component equilibrium isotherms for benzeneand cyclohexane adsorption on AuCl3/SiO2 (1.00 g/g) at 100 and120 °C. Symbols are experimental data, and lines are isothermsfit by eqs 4 and 5.

Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3861

amount of PdCl2 was varied from 0.045 g/g to 0.88 g/gSiO2. Adsorption isotherms for benzene and cyclohexaneare compared in Figure 15. It is seen that both benzeneand cyclohexane adsorption amounts were decreasedwith increasing PdCl2 loading because of decreasedsurface areas. However, the pure-component benzene/cyclohexane ratio continued to increase with PdCl2loading, which was clearly due to π-complexation ofbenzene with Pd2+.

The pure-component adsorbed amounts at 0.1 atmand the adsorption ratios are plotted in Figure 16. Theadsorption ratio reached to 3.2 at a PdCl2 loading of 0.88g/g-SiO2. This loading corresponded to the calculatedmonolayer value for PdCl2 on SiO2 (Table 2).

As mentioned, the amount adsorbed continued todecrease as the loading was increased. The surface areaalso decreased (Table 1). After normalization of theadsorbed amounts by surface area, the amount adsorbedof benzene was always higher (by 15-75%) than thaton bare SiO2 because of π-complexation. At a PdCl2loading of 0.305 g/g of SiO2 in particular, a 75% increasewas obtained. On the other hand, the cyclohexane

adsorption was decreased at loadings between 0.60 and0.88 g/g when the surface area remained unchanged.This decrease was caused by the lower affinity of PdCl2for cyclohexane because of the nonpolar nature of thismolecule.

For both benzene and cyclohexane, the maximumamount adsorbed per surface area reached a maximumat the loading of 0.33 g/g. Ideally, benzene adsorptionshould reach its maximum at the monolayer loading(0.88 g/g). This result was attributed to the poordispersion of PdCl2 on SiO2 at high loadings, i.e.,loadings > 0.33 g/g. The poor dispersion was also relatedto pore blockage at high loadings. Pore blockage wouldlimit diffusion of the benzene and cyclohexane moleculesinto the sorbent. N2, on the other hand, is a smallermolecule; hence, it was not limited in the measurementsof surface area.

Equilibrium Isotherm Model. The adsorption ofcyclohexane molecules includes physical adsorptiononly; thus, it can be modeled well by the Langmuirisotherm with two parameters shown in eq 4.

On the other hand, the adsorption of benzene moleculeson PdCl2/SiO2 and AgNO3/SiO2 includes both physicaladsorption and chemisorption by π-complexation. There-fore, a different model is required to account for chemi-sorption. The isotherm model developed by Yang andKikkinides28 to account for both interactions is shownin eq 5.

The first term accounts for physical adsorption, whilethe second term represents contributions from chemi-sorption. The second term also takes into account theenergetic heterogeneity of the surface ion sites availablefor complexation.

When a chemical bond is formed, the electron distri-bution in the molecular orbital is altered, resulting insubstantial weakening of the van der Waals forces. Thisweakening is considered to be mainly due to the reduced

Figure 12. Pure-component equilibrium isotherms for benzeneand cyclohexane adsorption on bare SiO2 at 100 and 120 °C.Symbols are experimental data, and lines are isotherms fit by eqs4 and 5.

Figure 13. Pure-component equilibrium isotherms for benzeneand cyclohexane adsorption on bare Al2O3 at 100 and 120 °C.Symbols are experimental data, and lines are isotherms fit by eqs4 and 5.

Figure 14. Pure-component equilibrium isotherms for benzeneand cyclohexane adsorption on activated carbon at 120 and 180°C.

q )qmpbpP1 + bpP

(4)

q )qmpbpP1 + bpP

+qmc

2sln( 1 + bcPes

1 + bcPe-s) (5)

3862 Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000

polarizability, as electrons are localized and/or trans-ferred because of chemisorption. For this reason, thefirst term in eq 5 represents the adsorption on a sitewithout π-complexation, whereas the second term arisesfrom that with π-complexation.

Although eq 5 contains five parameters, certainconstraints must be imposed on some of the parametersin order for them to have physical meaning. Forexample, empirical values for s are available from theliterature.61,62 The value for s generally falls within therange 0-12 and increases with the carbon number forhydrocarbons as adsorbates. For physical adsorption,the values of the Langmuir constant (bp) are ap-proximately equal for aromatics and aliphatics with thesame carbon number. Consequently, the b value fromthe cyclohexane isotherm is imposed as the upper boundfor benzene. Therefore, the cyclohexane isotherms werefirst used to obtain the two parameters in eq 4. Because

an excellent fit was obtained, an isotherm with hetero-geneity was not needed for cyclohexane. Subsequently,eq 5 was used to fit the data on π-complexation withimposed values or constraints on qmp, bp, and s, leavingonly two parameters, qmc and bc, as the true fittingparameters. The estimated parameters using eqs 4 and5 are shown in Table 4. The isotherms for PdCl2/SiO2(0.88 g/g) could not be fit by the Langmuir isotherm and,hence, could also not be fit by eqs 4 and 5.

The pure-component adsorption ratios at 1 atm wereestimated using the parameters in Table 4, as thecommercial PSA process is usually operated at 1 atmor higher pressure. The adsorption ratios at 1.0 atmwere 4.1 for PdCl2/SiO2 (0.305 g/g) and 3.3 for AgNO3/SiO2 (0.33 g/g) compared to 1.2 for SiO2 and 1.4 forAl2O3. Although the extrapolation to 1 atm using thedata at less than 0.1 atm might contain a certain degreeof error, these high ratios are encouraging for com-mercial applications. Experimental investigations ofpure and binary component adsorption up to 1 atm areplanned for future studies. Computer simulations ofPSA processes will also give considerable insight intothe applicability of these sorbents and the optimumoperating conditions.

Isosteric Heats of Adsorption. Isosteric heats ofadsorption for selected sorbents were calculated by theClausius-Clapeyron equation, eq 1, using the isothermsat different temperatures, and the results are shownin Table 5. Heats of adsorption for cyclohexane werenearly the same for all sorbents in this study, rangingfrom 4 to 8 kcal/mol. On the other hand, heats of

Table 3. Pure-Component Adsorption Ratios for Benzene/Cyclohexane and Propylene/Propane

equilibrium adsorption ratios ofbenzene and cyclohexane at 0.1 atm

equilibrium adsorption ratios ofpropylene and propane at 1.0 atm

salt substrate loading (g/g) 100 °C 120 °C 25 °C 70 °C

PdCl2 SiO2 (100-200 mesh) 0.880 2.9 3.2 1.9 4.1AgNO3 SiO2 (8-20 mesh) 0330 - 2.0 3.0 3.9CuCl Al2O3 0.500 1.3 1.3 2.3 3.4CuCl SiO2 (100-200 mesh) 0.500 - - 1.4 -PtCl4 SiO2 (100-200 mesh) 0.460 1.5 - 2.7 4.0AuCl3 SiO2 (100-200 mesh) 1.000 1.9 - 1.7 2.1PdCl2 activated carbon 0.305 1.1 1.1 - -none SiO2 (100-200 mesh) 0 1.4 1.6 1.4 1.6none Al2O3 0 1.5 1.5 1.3 1.6none activated carbon 0 1.1 1.1 - -

Figure 15. Dependence of adsorption at 120 °C on PdCl2 loadingon SiO2. Symbols are experimental data, and lines are isothermsfit by eqs 4 and 5, except for 0.880-g loading.

Figure 16. Effects of PdCl2 loading on adsorption ratio of benzeneover cyclohexane and adsorbed amounts at 120 °C.

Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3863

adsorption for benzene on sorbents with salts werehigher than those on bare substrates. The heats ofadsorption for the PdCl2, AgNO3, CuCl, and AuCl3sorbents were in the range of 9-12 kcal/mol. The valuefor the PtCl4 sorbent was slightly lower than those forthe other sorbents. The order of heats of benzeneadsorption were CuCl > PdCl2 > AgNO3 > AuCl3 >PtCl4. This trend was consistent with the theoreticalcalculation results, which will be discussed shortly.

Heats of adsorption for other π-complexation systemsare available in the literature. For π-complexation witholefins, the heats of adsorption are 11.5 kcal/mol forpropylene on AgNO3/SiO2,37 14.2 kcal/mol for propyleneon CuCl/Al2O3,28 11.7 kcal/mol for ethylene on CuCl/Al2O3,28 and 9.4 kcal/mol for ethylene on Ag+/Amberlyst35.35 The heats of adsorption of corresponding paraffinson the same sorbents are 3.4 kcal/mol for propane onAgNO3/SiO2,37 5.6 kcal/mol for propane on CuCl/Al2O3,28

5.3 kcal/mol for ethane on CuCl/Al2O3,28 and 4.6 kcal/mol for ethane on Ag+/Amberlyst 35.35 The latent heatsof condensation for benzene and cyclohexane are almostthe same (7.2-7.3 kcal/mol at 80 °C). The higher heatsof benzene adsorption by salt-dispersed sorbents werecaused by π-complexation. Furthermore, it should benoted that no substrate effect on the heat of adsorptionwas observed, as the heats of benzene adsorptionbetween PdCl2/SiO2 and PdCl2/activated carbon werethe same.

The calculation of heats of adsorption was conductedusing the data at small adsorption amounts, as shownin the Table 5. In these regions, the calculated heat ofadsorption is based solely on the interaction betweenadsorbate and adsorbent. Therefore, experimental heats

of adsorption showed good agreement with molecularorbital results, in which only adsorbate-adsorbentinteractions were taken into consideration. However,energetic heterogeneity largely influences the shape ofadsorption isotherms and the adsorption amounts at 0.1atm. CuCl/Al2O3 had the largest heterogeneity factoramong the sorbents investigated. One possible reasonfor the largest s value for CuCl/Al2O3 is the coexistenceof Cu+ and Cu2+. CuICl exhibits strong π-complexationcapability, whereas CuIICl does not. This might resultin the poor adsorption ratios at 0.1 atm, even thoughthe heat of adsorption of benzene on CuCl/Al2O3 washigh.

Diffusion Time Constants. Uptake rates for ben-zene and cyclohexane were measured for all sorbents.The uptake curves consisted of two portions: a fastuptake portion at 0-0.7 fractional uptake and a slowuptake (long-tail) portion at 0.7-1.0 fractional uptake.The long-tail portion was probably due to the crowdingeffects of adsorbate molecules inside the pores at thelarge fractional uptakes.

The diffusion time constants calculated from 0 to 0.3fractional uptake are shown in Table 6. The values forolefin/paraffin adsorption are taken from the literatureand also given in Table 6 for comparison. The diffusiontime constants of benzene and cyclohexane in thesesorbents were on the order of 10-4 s-1, which is an orderof magnitude lower than those of propylene and propanein AgNO3/SiO2.37 However, they were higher or at leastthe same as those of ethylene and ethane for Ag+ ion-exchanged resins.35 Because the diffusion time constantswere not different for benzene and cyclohexane, π-com-plexation of benzene did not influence the diffusionrates. The fairly fast uptake rates at low fractionalcoverages are favorable for cyclic adsorption processes.

Theoretical Adsorption Bond Energies and Mo-lecular Geometries. Adsorption bond energies andstructural geometries were calculated from molecularorbital theory. The energies of adsorption calculatedusing eq 3 along with the experimental data are shownin Table 7. The theoretical and experimental valuesfollow the same trend, i.e., Cu > Pd > Ag > Au > Pt.The optimized structural data are also summarized inTable 7. The optimized geometries of the benzene-CuCland benzene-PdCl2 complexes are shown in Figures 17and 18. The structure for benzene-CuCl has a C6vsymmetry; that for benzene-AuCl3, a C3v symmetry;and those for benzene-PdCl2 and benzene-PtCl4, a C2v

Table 4. Fitting Parameters for Isotherms (eqs 4 and 5) of Benzene and Cyclohexane

adsorbent adsorbatetemp(°C)

qmp(mmol/g)

bp(atm-1)

qmc(mmol/g)

bc(atm-1)

s(-)

PdCl2/SiO2 benzene 120 0.23 9.74 3.38 0.031 5.7(0.305 g/g) cyclohexane 120 0.23 20.49 - - -

CuCl/Al2O3 benzene 120 0.30 16.32 0.69 0.075 7.0(0.50 g/g) cyclohexane 120 0.30 35.38 - - -

AgNO3/SiO2 benzene 120 0.30 3.63 1.92 0.232 5.7(0.33 g/g) cyclohexane 120 0.30 29.78 - - -

AuCl3/SiO2 benzene 120 0.91 1.52 12.42 0.028 4.3(1.00 g/g) cyclohexane 120 0.91 2.87 - - -

SiO2 benzene 120 1.27 4.44 - - -cyclohexane 120 1.29 2.27 - - -

Al2O3 benzene 120 0.59 10.13 - - -cyclohexane 120 0.45 7.84 - - -

PtCl4/SiO2 benzene 100 0.45 1.50 3.20 0.066 5.6(0.46 g/g) cyclohexane 100 0.45 11.78 - - -

SiO2 benzene 100 1.31 6.61 - - -cyclohexane 100 1.30 3.99 - - -

Al2O3 benzene 100 0.79 10.60 - - -cyclohexane 100 0.84 5.09 - - -

Table 5. Isosteric Heats of Adsorptiona

adsorbent

benzeneheat of adsorption

(kcal/mol)

cyclohexaneheat of adsorption

(kcal/mol)

PdCl2/SiO2 (0.88 g/g) 9.3-10.9 (0.10-0.19) 4.9-7.0 (0.025-0.050)AgNO3/SiO2 (0.33 g/g) 9.2-10.1 (0.15-0.25) -CuCl/Al2O3 (0.50 g/g) 10.1-11.0 (0.10-0.15) 4.4-5.8 (0.10-0.20)PtCl4/SiO2 (0.46 g/g) 7.2-9.0 (0.15-0.25) -AuCl3/SiO2 (1.00 g/g) 8.8-10.1 (0.10-0.30) -PdCl2/activated

carbon (0.305 g/g)9.5-10.6 (0.20-0.95) 3.9-5.9 (0.60-0.88)

SiO2 6.3-6.4 (0.10-0.30) 5.4-6.4 (0.05-0.15)Al2O3 4.7-7.3 (0.10-0.30) 7.4-7.9 (0.15-0.20)activated carbon 4.1-6.8 (0.50-0.75) 6.5 (1.5)

a Values in parentheses indicate the adsorption amounts (mmol/g) for calculation.

3864 Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000

symmetry, with the metal atom approaching the πorbital of benzene along the midpoint of the benzenering. The flat benzene ring is on the xy plane, and themetal atom is on the z axis. Six equal-length metal-carbon bonds were formed between each metal chloride

and the six carbons of the benzene ring. A comparisonof the bond length of free benzene with those of benzenein the complexes shows that, upon adsorption, the C-Cbond length increases slightly. Also, a comparison of thebond length of free metal chlorides with those of thecorresponding metal chlorides in the complexes showsthat, upon adsorption, the M-Cl bond length alsoincreases, indicating that the C-C bonds and M-Clbonds are weakened upon adsorption. The amounts ofpositive charge on the metal chlorides are determinedin the NBO analysis and are given as follows: PdCl2,0.732; CuCl, 0.644; AgCl, 0.625; AuCl3, 0.576; and PtCl4,0.539. Metals with a more positive charge will be abetter electron acceptors for π-complexation with ben-zene; thus, the bond distance between M and C will beshorter. This trend is confirmed in Table 7, where theM-C distances follow the order: benzene-PdCl2 <benzene-CuCl < benzene-AgCl < benzene-AuCl3 <benzene-PtCl4.

Natural Bond Orbital (NBO) Results. The natureof the metal-benzene bond can be better understoodby analyzing the NBO results. The main feature of thebonding can be seen from the population changes in thevacant outer-shell s orbital of the metal and in the dorbitals of the metal upon adsorption.63 The slightstretching of the M-Cl bond is due to chemisorption ofbenzene onto the metal. This is a reversible process andwill not cause decomposition or reaction. The NBOanalysis, summarized in Table 8, is in general agree-ment with previously reported results of metal-olefincomplexation.40,44,45,64 In most cases, the M-C interac-tion is a dative bond, i.e., donation of electron chargesfrom the π orbital of benzene to the vacant s orbital ofthe metal and, simultaneously, back-donation of electroncharges from the d orbitals of metals to the π* orbitalof benzene. Table 8 shows that, upon adsorption, theelectron occupancy of the valence s orbitals of Cu, Ag,Au, and Pt increases; this is caused by σ donation. Pdappears to be an exceptional case, for which the electronoccupancy of the valence s orbital decreases uponadsorption. As for Ni,17 where the same phenomenonwas attributed to electron redistribution from 5s to 4dyz

Table 6. Diffusion Time Constants (D/r2) of Benzene and Cyclohexane

adsorbenttemp(°C)

benzene(s-1)

pressure change(atm)

cyclohexane(s-1)

pressure change(atm)

PdCl2/SiO2 (0.305 g/g) 120 4.2E-04 (0.021 f 0.039) 4.9E-04 (0.020 f 0.038)PdCl2/SiO2 (0.88 g/g) 100 1.2E-04 (0.020 f 0.037) 1.5E-04 (0.037 f 0.046)

120 6.0E-04 (0.021 f 0.039) 7.8E-04 (0.022 f 0.032)AgNO3/SiO2 (0.33 g/g) 120 1.3E-04 (0.020 f 0.037) 2.9E-04 (0.020 f 0.037)CuCl/Al2O3 (0.50 g/g) 120 7.1E-04 (0.022 f 0.041) 9.0E-04 (0.021 f 0.039)PtCl4/SiO2 (0.46 g/g) 100 8.2E-04 (0.023 f 0.042) 9.1E-04 (0.023 f 0.042)AuCl3/SiO2 (1.00 g/g) 100 3.6E-04 (0.024 f 0.043) 1.6E-03 (0.024 f 0.043)PdCl2/activated carbon (0.305 g/g) 120 2.6E-04 (0.021 f 0.031) 1.1E-04 (0.023 f 0.042)

180 6.9E-04 (0.022 f 0.032) 9.7E-04 (0.036 f 0.047)SiO2 (100-200 mesh) 100 5.7E-04 (0.019 f 0.027) 3.7E-04 (0.018 f 0.026)

120 2.8E-04 (0.025 f 0.036) 3.1E-04 (0.021 f 0.030)Al2O3 100 4.7E-04 (0.040 f 0.064) 7.4E-04 (0.040 f 0.064)

120 8.4E-04 (0.037 f 0.060) 9.4E-04 (0.039 f 0.061)activated carbon 120 5.7E-04 (0.021 f 0.039) 7.8E-04 (0.023 f 0.042)

180 7.1E-04 (0.022 f 0.040) 7.8E-04 (0.022 f 0.042)

temp (°C) propylene (s-1) pressure change (atm) propane (s-1) pressure change (atm)

AgNO3/SiO2 (0.33 g/g)37 25 2.3E-03 (0 f 0.1) 8.7E-03 (0 f 0.1)AgNO3/SiO2 (0.33 g/g)37 70 3.5E-03 (0 f 0.1) - -

temp (°C) ethylene (s-1) pressure change (atm) ethane (s-1) pressure change (atm)

Ag-Amberlyst 3535 25 1.0E-04 1.1E-04 -Ag-Amberlyst 3535 70 1.5E-04 1.4E-04 -

Table 7. Summary of Energies of Adsorption andGeometries for Benzene-MClx Systema

M r(C-C) r(M-C) r(M-Cl)b r(M-Cl)c ∆H exptl ∆H

Cu 1.401 2.835 2.226 2.210 12.5 10.1-11.0Pd 1.403 2.827 2.324 2.301 10.8 9.3-10.9Ag 1.400 3.219 2.451 2.440 8.6 9.2-10.1Au 1.399 3.342 2.593 2.578 6.5 8.8-10.1Pt 1.400 3.645 2.613 2.595 5.2 7.2-9.0benzene 1.396

a The bond lengths (r) are in angstroms and the energies (∆H)are in kcal/mol. b MCl in complex. c In free MClx.

Figure 17. Optimized structure for benzene-CuCl.

Figure 18. Optimized structure for benzene-PdCl2.

Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3865

because the energy level of 4dyz is closest to that of 5sin Pd, and upon adsorption, the electron occupancy of4dyz increases and that of 5s decreases by electronredistribution within the Pd atom. Table 8 also showsthat, upon adsorption, the total occupancy of the metals’3d, 4d, and 5d orbitals (i.e., outer-shell d orbitals of therespective metal atoms) all decrease because of back-donation of electrons from the metals to benzene. Itappears that, in the case of benzene, σ donation plays amore important role than π back-donation. Pd has theshortest M-C bond distance, which leads to moreoverlap of π* orbitals of benzene with the d orbitals ofthe metal; therefore, Pd has the highest d-π* back-donation; in contrast, Cu has the highest σ donation andthe highest heat of adsorption.

Acknowledgment

This work was supported by National Science Foun-dation under Grant CTS-9819008. We are grateful toNGK Insulators, Ltd., Nagoya, Japan, for financialsupport to A.T. during his study at the University ofMichigan. We also thank Dr. Joel Padin for preparingthe AgNO3/SiO2 and some of the PdCl2/SiO2 sorbents.

Notation

b ) Langmuir constantD ) Diffusion coefficientMt/Mi ) Fractional uptake at time tp ) Pressureqm ) Monolayer or saturated amount adsorbedqst ) Isosteric heat of adsorptionR ) Gas constantr ) Particle radiuss ) Heterogeneity parameterT ) Temperaturet ) Time

Subscripts

c ) Chemisorption or π-complexationp ) Physical adsorption

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MCl q1 q2 q1 + q2

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Received for review April 5, 2000Revised manuscript received July 18, 2000

Accepted July 20, 2000

IE000376L

Ind. Eng. Chem. Res., Vol. 39, No. 10, 2000 3867