t

alkanes.hysisorp-modes ofhysisorp-s has beendorption

odes using

Journal of Catalysis 218 (2003) 135–147www.elsevier.com/locate/jca

Pore mouth physisorption of alkanes on ZSM-22: estimation ofphysisorption enthalpies and entropies by additivity method

C.S. Laxmi Narasimhan,a J.W. Thybaut,a G.B. Marin,a,∗ J.A. Martens,b J.F. Denayer,c

and G.V. Baronc

a Laboratorium voor Petrochemische Techniek, Universiteit Ghent, Krijgslaan 281, B-9000 Ghent, Belgiumb Centrum voor Oppervlaktechemie en Katalyse, Katholieke Universiteit Leuven, Kasteelpark Arenberg 23, B-3001 Heverlee, Belgium

c Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium

Received 31 October 2002; revised 14 February 2003; accepted 17 February 2003

Abstract

ZSM-22 (TON-type) zeolite has a pore size close to that of alkanes and exhibits pronounced molecular sieve effects withn-Alkanes physisorb through the pore mouths into the micropores while the iso-alkanes physisorb at the pore mouths only. Ption inside the micropores results in additional entropy and enthalpy loss compared to physisorption at the pore mouths. Multiplephysisorption exist at the pore mouths: each of the “straight ends” of the iso-alkane can protrude into the micropore. A two-step ption model distinguishing between physisorption at the pore mouths and subsequent transfer from pore mouths into the microporedeveloped. The standard physisorption enthalpy and entropy for each of the physisorption modes of iso-alkanes andn-alkanes are computefollowing an additivity principle. The Henry coefficient for each alkane is the sum of contributions calculated for the individual physismodes. The standard physisorption enthalpy and entropy for each alkane are calculated from the distribution of physisorption mideal mixing rules. 2003 Elsevier Inc. All rights reserved.

Keywords: Hydrocracking; Hydroisomerisation; ZSM-22 zeolite; Molecular sieve; Shape selectivity; Alkanes; Pore mouth catalysis; Physisorption

iny extoap-itstlls,ter-od-plainydrare

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1. Introduction

Molecular sieve-type zeolites are widely employedmany petroleum and petrochemical processes as thehibit shape selectivity. ZSM-22 (TON-type), belongingthe group of 10-membered ring zeolites, is commerciallyplied for skeletal isomerisation of alkanes [1,2]. Due tonarrow channel structure (0.44× 0.55 nm) [3] and resultanstrong overlapping force fields exerted by the zeolite waZSM-22 shows strong and peculiar physisorption characistics. Changes in physisorption behaviour of reaction pructs compared to feed molecules have been used to exshape-selective effects observed in processes such as hcracking and hydroisomerisation. Two different theoriesfound in the literature concerning this matter.

The first theory considers steric hindrance for physisotion of iso-alkanes inside the micropores due to their bu

* Corresponding author.E-mail address: guy.marin@rug.ac.be (G.B. Marin).

0021-9517/03/$ – see front matter 2003 Elsevier Inc. All rights reserved.doi:10.1016/S0021-9517(03)00069-1

-

o-

size [4–19]. Henry coefficients are high for normal alkanwhile for iso-alkanes the Henry coefficients are significanlower [4–6]. The saturation capacity forn-alkanes is 3 or-ders of magnitude higher than that for iso-alkanes. Fthe systematic observation of lower adsorption enthalpyentropy of iso-alkanes compared ton-alkanes, it was concluded that, under reaction conditions, iso-alkanes doaccess the micropores in contrast ton-alkanes [4–6].

Ocakoglu et al. [18] compared the physisorption prerties of iso-alkanes on ZSM-22 samples with open poand with blocked pores, respectively. They observed cparable standard physisorption enthalpies and entropieiso-alkanes on both forms, suggesting that iso-alkanenot penetrate and adsorb into “open” pores of ZSM-Significant differences between the physisorption propeof normal- and iso-alkanes were observed in open ZS22. Pronounced changes in physisorption properties fon-alkanes as compared to iso-alkanes were also founPieterse et al. [2] and lead to the conclusion that brancmolecules can physisorb at the pore mouths of ZSM-22 o

136 C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147

rönubsethanoliteole-ds”

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These authors also postulated the existence of strong Bsted acid sites at the pore mouth and the occurrence of squent acid-catalysed reactions at the pore mouth ratheron the external surface or inside the micropores of the zecrystallite. In the pore mouth mechanism, branched mcules physisorb in such a way that one of its “straight enprotrudes into the pore mouth. Straight ends of an alkanthe unbranched terminal ends of the main alkyl chain anthe alkyl substituents of the latter. The carbon atom on whthe straight end is attached is outside the pore. For lomolecules, which can span more than one pore mouth,lock configurations also exist, involving two or more pomouths [12,15,16].

The second theory proposed by Maesen et al. [20,21]Schenk et al. [22] favours product shape selectivity, baon differences in product diffusivities, along with transitistate shape selectivity. Branched molecules are assumenter the micropore, and due to differences in diffusiviamong the different product molecules, shape selectivitycurs. This theory was based on configurational bias MoCarlo (CBMC) calculations for estimating intermolecuinteractions and physisorption properties ofn-alkanes andiso-alkanes inside the micropores of ZSM-22. It follofrom the calculations that branched alkanes can entepores if properly oriented. The above theory seems toin contradiction with classical bifunctional mechanism [2which requires a very short time scale for diffusion ofactants from acid sites to metal sites, while inside ZSMmicropores large diffusion resistances exist due to a sinfile diffusion mechanism [24]. Also, there are significadeviations between calculated physisorption propertiesing the CBMC technique and experimentally measuredues [20].

In the pore mouth mechanism, different orientationsthe iso-alkane molecules can exist, depending uponstraight end that has entered the pore mouth cavity.to varying force fields inside and outside the pore mocavity, each of these orientations, termed as “modes,”hibits different physisorption properties. Each mode is cacterised by the carbon atoms inside and outside of themouth cavity. Chemisorption and subsequent acid-catalreactions occur at the pore mouth. As physisorptioncedes protonating chemisorption, each individual physistion mode determines the subsequent reactions and reaintermediates. To model the corresponding reaction kinethe distribution of physisorbed alkanes among their possphysisorption modes as well as the changes in physisorproperties during the course of reaction have to be accoufor quantitatively. A typical reaction mixture for hydrocabon conversion such as alkane hydroconversion is a mcomponent system involving alkanes and iso-alkanes inreaction mixture. The pure component physisorption perties and Langmuir isotherms are used to describe thesisorption of the multicomponent reaction mixture eitherclassical Langmuir-based approaches or through idealreal adsorption solution theories (IAST, RAST) [25–28].

--

-

o

n

-

The present paper aims at a model to describe the sicomponent physisorption phenomenon on ZSM-22 alwith a methodology to calculate physisorption propertiesn-alkanes and iso-alkanes for each of their individual pmouth physisorption modes. The methodology is analogto additivity methodologies for thermodynamic propertdetermination. Based on the estimates obtained for theditivity parameters, the physisorption properties are calated and compared with experimental data [4–6,18].physisorption properties and the model to describe the mple physisorption modes of pure components can be direused in any of the above-mentioned methods to descphysisorption of the multicomponent reaction mixture.

2. Procedures and data

2.1. Sorbent

Data obtained before on two types of ZSM-22, an “opand a “closed” form, have been used in the present wThe synthesis of the open form has been described in dby Ernst et al. [29], while the closed form was obtained wthe same procedure, however, without removal of thediaminohexane template from the micropores. The silicaluminum ratio of ZSM-22 is 30 and the crystals havneedle-like shape with a length varying from 1 to 2 µm. Tform of ZSM-22 synthesised following the normal recipi.e., with removal of the template and, hence, with free acsible pores, is referred to as open ZSM-22. The concetions of pore mouths and Brönsted acid sites for the sorare listed in Table 1. An as-synthesised ZSM-22 zeolite sple with the template left inside the micropores is referreas closed ZSM-22. Details about the latter can be founOcakoglu et al. [18].

2.2. Physisorption properties

The physisorption isotherm for alkane “i” based on Henry’s law is expressed as:

(2.1)Ci = Hipi,

where Ci is the physisorbed alkane concentration. THenry coefficientHi is obtained from the expression

(2.2)Hi =(

Ct,i

2p◦

)e�S◦

phys,i /Re−�H ◦phys,i /(RT )

,

Table 1Range of experimental conditions on ZSM-22 along with their critical cacteristics [4–6,18]

ZSM-22

Sorptive C5–C9 (normal, mono-, di- and tri-brancheTemperature (K) 473–623Ct,pm (10−3 molkg−1) 0.33Total Brönsted acid sites 0.54

(≈ Ct,mp) (molkg−1)

C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147 137

esovef theropyand

f’s

th-rop-penwasrredtionlaceen-[18]

hy-pa-omres.the

dardoef-rbeddards aes.

ionved

anes

d2;s

s oftropyenryopy,nry

2

beda-

orre-onendre-ob-

en-er-ork,r pa-sco-

.,theredreco-asiventhen

edres,res.

en-able

-neg-ob-een-om

byac-

whereCt,i is the total concentration of physisorption sitfor alkanei andp◦ is the standard state pressure. The abexpression is based on a standard state at which half oactive sites are occupied because of configurational entreasons [4–6,31]. The standard physisorption enthalpiesentropies are experimentally obtained from van’t Hofplots.

2.3. Physisorption data

Denayer et al. [4–6,19], using a chromatographic meod [30], have determined the low-coverage adsorption perties for normal and branched C5–C9 alkanes on oZSM-22. The fact that adsorption of the studied alkanescompletely reversible and that no secondary peaks occuduring the measurements indicated that only physisorpoccurred, and no chemical bounding or reaction took p[4,5,18]. Henry coefficients and standard physisorptionthalpies and entropies were reported. Ocakoglu et al.have confirmed the findings of Denayer et al. [4–6,19].

For n-alkanes, the strong increase of the standard psisorption enthalpy loss with carbon number is accomnied by a high loss of rotational and translational freedas the molecules are fully physisorbed inside the poFor iso-alkanes, the physisorption enthalpies vary withbranching position and degree of branching. The stanphysisorption enthalpy and entropy and, hence, Henry cficients depend on the number of carbon atoms physisoinside the pores. Fig. 1 shows the values for the stanphysisorption enthalpy on open and closed ZSM-22 afunction of carbon number for various classes of alkanA distinct linear relationship of the standard physisorptenthalpy and entropy with the carbon number is obser

Fig. 1. Experimental standard physisorption enthalpy of C5–C9 alkand iso-alkanes on open [4–6] and closed [18] ZSM-22: (F) n-alkanesin closed ZSM-22; (1) n-alkanes in open ZSM-22; (X) 2Me-branchealkanes in closed ZSM-22; (P) 2Me-branched alkanes in open ZSM-2(") 3Me-branched alkanes in closed ZSM-22; (!) 3Me-branched alkanein open ZSM-22.

Table 2Estimates with their 95% confidence intervals for the parameterEqs. (2.3) and (2.4) describing standard physisorption enthalpy and enfor n-alkanes on open ZSM-22 [4–6] obtained through regression of Hcoefficient relationship with standard physisorption enthalpy and entrviz. Eq. (2.2) along with Eqs. (2.3) and (2.4) with the experimental Hecoefficient on open ZSM-22

Parameter Open ZSM-2

α (kJmol−1) 12.84(±0.15)β (kJmol−1) −2.3 (±0.8)

γ (Jmol−1 K−1) 17.01(±0.29)δ (Jmol−1 K−1) 28.84(±0.19)

for each alkane class [4–6,19]

(2.3)−�H ◦phys,i = αCNi + β,

(2.4)−�S◦phys,i = γ CNi + δ,

where CNi represents the carbon number of the physisoralkane andα, β , γ , andδ are alkane class-dependent prameters. The carbon number dependence of the csponding Henry coefficients follows from the substitutiof Eqs. (2.3) and (2.4) into Eq. (2.2). Values for the opZSM-22 parametersα, β , γ , and δ have been estimateby Denayer et al. [4] and Ocakoglu et al. [18] throughgression of standard physisorption enthalpy and entropytained through van’t Hoff’s plots generated from experimtal determination of Henry coefficients at different tempatures for each alkane class [4–6,18]. In the present wHenry coefficients have been considered as responses forameter estimation. Consistent with this, the parameterα,β , γ , andδ have been re-estimated considering Henryefficients as responses. Estimation of parametersα, β , γ ,andδ corresponding to then-alkanes on open ZSM-22 vizTable 2, are obtained from regression with Eq. (2.2) togewith Eqs. (2.3) and (2.4) of the experimentally determinHenry coefficients of C5–C9n-alkanes over the temperaturange of 473–623 K [4–6,18] and extrapolated Henryefficients for 623–673 K using van’t Hoff’s relationshipresponses. The range of experimental conditions are gin Table 1. Ocakoglu et al. [18] have also determinedphysisorption properties forn-alkanes and iso-alkanes oclosed ZSM-22, viz., Fig. 1. Unlike open ZSM-22, closZSM-22, which has the template left inside the micropopresents effectively only pore mouths and no micropoFor iso-alkanes it has been observed that physisorptionthalpies and entropies on closed ZSM-22 are comparwithin 3–5 kJ mol−1 and 4–8 J mol−1 K−1, respectively, tothose obtained on open ZSM-22. Forn-alkanes, the physisorption enthalpies and entropies are significantly lessative [18]. The corresponding values are close to thosetained for iso-alkanes on closed ZSM-22 as can be sfrom Fig. 1. Physisorption ofn-alkanes inside the micropores on open ZSM-22 is thermodynamically different frphysisorption on closed ZSM-22, as it is accompaniedadditional loss of entropy and enthalpy [18], which are prtically carbon number-independent.

138 C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147

hednegantrem-e is

f a

hasAs-hibit

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icroniso-

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ths,De-

that,tionstomsthee foffi-

e 1,th-avethe

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bjec-lin-wtoneenr es-oft-rs ofsta-eanslcu-. Theba-

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The standard physisorption enthalpy of monobrancalkanes on open ZSM-22 was observed to become lesstive as the monobranching position moves toward the ceof the main alkyl chain of the alkane [5,18]. For exaple, standard physisorption enthalpy of 2-methylheptan−87.3 kJ mol−1 while that of 4-methylheptane is−77.4 kJmol−1. Moreover, the enthalpy loss upon physisorption obranched alkane for which the longest straight end hasi car-bon atoms is higher than that of ann-alkane withi carbonatoms upon physisorption at the pore mouth:

(2.5)−�H ◦phys(2MeC7) > −�H ◦

phys(nC6) > −�H ◦phys(nC5).

In its most stable physisorption mode, 2-methylheptanefive carbon atoms protruding inside the pore mouth.suming that carbon atoms outside the pore mouth exno enthalpy loss, a standard pore mouth physisorptionthalpy for 2-methylheptane close to the standard mipore physisorption enthalpy forn-pentane is expected. However, the standard pore mouth physisorption enthalpy2-methylheptane is more negative than the standard mpore physisorption enthalpy forn-pentane and even thafor n-hexane. Similar observations are made for otheralkanes.

The above observations indicate that standard physistion enthalpy loss for iso-alkanes at pore mouths existsonly for carbon atoms protruding inside the pore moubut also for the carbon atoms outside the pore mouth.nayer [6] and Martens et al. [9] have already postulatedin the case of branched alkanes, apart from the interacof carbon atoms inside the pore mouths, the carbon aoutside also interact to a relatively lower extent withexternal surface. Analogous observations can be madstandard entropy. The following trend of the Henry coecients results:

(2.6)H(2MeC7) > H(nC6) > H(nC5).

All the iso-alkane molecules in the database, viz. Tablexhibit only a pore mouth configuration except 2-meylheptane, 2-methyloctane, and 3-methyloctane, which hadditionally key-lock physisorption modes. These areonly molecules having a “straight end,” which is loenough to traverse the bridge between two neighboringmouths and enter the second pore mouth with the tail of tlong straight end while another, short straight end is infirst pore mouth. The requirement for the key-lock mecnism is that the length of the straight end has to be grethan the width of the bridge separating the pore mouths.bridge width corresponds to at least three methylene grof the straight end [12,15,16]. Because the descriptiopore mouth physisorption is the aim in the present paperalkanes exhibiting additional key-lock physisorption behiour are not considered in the regression.

-

-

-

r

2.4. Parameter estimation

Estimation of the parameters is performed by minimtion of the weighted sum of squares of the residuals betwthe experimental and calculated Henry coefficients.

(2.7)SSQ=nob∑j=1

wj

(Hj − H

expj

)2,

Hexpj is the experimental Henry coefficient corresponding

the j th observation, which pertains to an alkane at a giexperimental temperature. Extrapolation based on vHoff’s relation is carried out for obtainingH exp

j for temper-atures not covered by the experiments. As mentioned abalkanes having only a pore mouth configuration are conered for parameter estimation. The total number of obvations “nob” for parameter estimation for C5–C9 alkaamounts to 50 forn-alkanes, 70 for monobranched alkanand 60 for multibranched alkanes. The weighting factorwj

is expressed as follows:

(2.8)wj = (Hexpj )−1

∑nobj (H

expj )−1

.

Reparameterisation [32–34] has been performed. The otive function is minimised by applying the standard nonear least-square estimation technique, c.q., Gauss–Nealgorithm [35,36]. The parameter estimation has also bcarried out through a Bayesian technique for parametetimation [37] and leads to quasi-identical results. The sware package used for the purpose is Greg Pak solveAthena visual work bench [38]. During regression, thetistical significance of the regression is expressed by mof the F -test, comparing the sum of squares of the calated response values and the residual sum of squaresindividual significance of the parameters on the 95% probility level is tested using Studentst-value.

3. Langmuir description of physisorption of alkaneson ZSM-22

The Langmuir isotherm for physisorption of a pure coponenti is based on the following site balance

(3.1)Csati = Ce + Ci

and is expressed as

(3.2)Ci = KL,iCsati pi

1+ KL,ipi

,

whereCsati is the saturation concentration of componenti on

the sorbent. For low partial pressures of componenti, i.e.,KL,ipi 1, Eq. (3.2) is reduced to Eq. (2.1), valid in tHenry regime. Hence, the following relationship is obtain

(3.3)Hi = KL,iCsati .

C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147 139

anondply-no-n-

cura-

thekerpre-re-the

hy-tedtheher

e exthephyionthertialcannts

hanur-

thetheirmi-thsntlylpy

mhy-

gde-ths

her

e

outh

-

porens-n.esof

e aty-l to

eingcro-

ion,d as

,

The Langmuir physisorption equilibrium coefficient foralkane on a zeolite can be determined from the corresping Henry coefficient and saturation concentration by aping Eq. (3.3). A Langmuir isotherm corresponds to molayer formation. On ZSM-22, due to the molecular dimesions of micropores, multilayer formation does not ocinside the micropores. At the pore mouths multilayer formtion is theoretically possible. However, it is expected thatforces involved in the multilayer formation are much weathan the interactions of the sorbate with the pore mouth,venting multilayer formation also at the pore mouth. Thefore, a Langmuir expression can be applied to describephysisorption on ZSM-22 at low coverage [4–6] when psisorption is found to occur preferentially on the Brönsacid sites [6,18,39], which are at pore mouths and insidemicropores for ZSM-22. It has been observed that at higalkane partial pressures physisorption also occurs at thternal crystal surfaces [6,9,19]. Under such conditions,physisorption phenomenon can be described by a dualsisorption site model [6,9,19] with one type of physisorptsite corresponding to the pore and pore mouth and anocorresponding to the external surface. At lower alkane papressures, the effects of external surface physisorptionbe neglected, as the physisorption equilibrium coefficiefor micropores and pore mouths are significantly higher tthe physisorption equilibrium coefficient for the external sface [6,9,19].

On ZSM-22 a distinction has to be made betweenpore mouths and the micropores. Iso-alkanes, due tobulkiness, are sterically hindered to physisorb inside thecropores and, hence, physisorb only at the pore moun-Alkanes physisorb at the pore mouth and subsequecan enter the corresponding micropore. Additional enthaand entropy loss occurs whenn-alkanes are transferred fropore mouths to micropores. As a result, a two-step psisorption model is developed forn-alkanes physisorbininside the micropores, while a single-step physisorptionscribes the physisorption of iso-alkanes at the pore mouviz. Fig. 2.

3.1. n-Alkanes

n-Alkanes first physisorb at the pore mouths and furtenter the micropore:

Pj + Se,pm

Kj,pm

� Pj,pm,

Pi,pm + Se,mpl

Kpm−mp

� Pj,mp.

For a puren-alkane “j ” the equilibrium concentration at thpore mouth is given by

(3.4)Cj,pm = Kj,pmCe,pmpj .

A separate indexj is used because exclusivelyn-alkanesare considered, whereas the indexi in the previous sectioncovers both normal and iso-alkanes. From the pore m

-

-

-

r

.

,

Fig. 2. Schematic representation of physisorption ofn-alkanes and isoalkanes on open ZSM-22.

ann-alkane can enter the micropore connected to thatmouth. Due to the narrow micropore channels, the traport inside the micropore occurs via single-file diffusioIn single-file diffusion, the transfer into the micropore takplace via a series of activated site jumps [24]. The ratethis transfer is proportional to the concentration of alkanpore mouthCj,pm and the probability of finding an emptneighbouring micropore sitepe,mp while the rate of transfer from the micropore to the pore mouth is proportionathe alkane concentration in the micropores,Cj,mp, and theprobability of the pore mouth being emptype,pm. Consider-ing the transfer between pore mouth and micropore as bquasi-equilibrated, the alkane concentrations in the mipores can be expressed as follows:

Cj,mp = Kpm−mpCj,pmpe,mp

pe,pm

(3.5)= Kj,pmKpm−mppjCe,pmpe,mp

pe,pm.

Assuming uniform site strength, viz. unbiased physisorptprobabilities for finding the empty sites can be expresse

(3.6)pe,pm = Ce,pm

Ct,pm,

(3.7)pe,mp = Ce,mp

Ct,mp.

Substituting the above Eqs. (3.6) and (3.7) into Eq. (3.5)

(3.8)Cj,mp = Kj,pm

(Kpm−mp

Ct,pm

C

)pjCe,mp.

t,mp

140 C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147

s to

heofores-s

besi-

redpenon

hy-ns-uth

een

turen

--3), thetion

es:

poncal-orpSM-tionof

ion

th–

he

o-

be

or

nry.3).SM-pore

entviz.nd,

bon-nes,uleor-ored byrbon

odesular

A site balance for the micropore physisorption sites lead

(3.9)Ct,mp = Cj,mp + Ce,mp,

whereCt,mp is the total number of physisorption sites in tmicropores and corresponds toCsat

i because the numberpore mouths is negligibly small. After solving Eq. (3.9) fCe,mp and substituting in Eq. (3.8), the Langmuir exprsion for physisorption ofn-alkanej inside the microporeof ZSM-22 is written as

(3.10)Cj,mp = Kj,pmKapppm−mpC

satj pj

1+ Kj,pmKapppm−mppj

,

where

(3.11)Kapppm−mp = Kpm−mp

Ct,pm

Ct,mp.

Comparing the above expression with Eq. (3.2), it canseen that the Langmuir equilibrium coefficient for physorption ofn-alkanes can be expressed as

(3.12)KL,j = Kj,pmKapppm−mp.

KL,j can be obtained from the experimentally measuHenry coefficient and the saturation concentration on oZSM-22 using Eq. (3.3). Physisorption experimentsclosed ZSM-22 allows calculation of the pore mouth psisorption, coefficientKj,pm, because the subsequent trafer into the micropores after physisorption at the pore mois absent. The equilibrium coefficient for transfer betwthe pore mouth and the micropore,Kpm−mp, can then beobtained via Eqs. (3.11) and (3.12). From the temperadependence ofKL,j andKj,pm the standard physisorptioenthalpy and entropy on open ZSM-22,�H ◦

j,mp and�S◦j,mp

and on closed ZSM-22,�H ◦j,pm and�S◦

j,pm can be determined.�H ◦

j,mp and�S◦j,mp follow the carbon number de

pendency relationships forn-alkanes described by Eqs. (2.and (2.4), respectively. Based on Eqs. (3.11) and (3.12)following relationship between the standard physisorpenthalpies on open and closed ZSM-22 can be written

(3.13)�H ◦j,mp = �H ◦

j,pm + �H ◦pm−mp,

(3.14)�Happpm−mp = �H ◦

pm−mp.

A similar relationship holds for the physisorption entropi

(3.15)�S◦j,mp = �S◦

j,pm + �S◦pm−mp,

(3.16)�Sapppm−mp = �S◦

pm−mp + R ln

(Ct,pm

Ct,mp

).

As a result, the standard enthalpy and entropy loss utransfer from the pore mouth to the micropore can beculated from the difference between the standard physistion enthalpies and entropies on open and closed Z22 using Eqs. (3.13) to (3.16). The standard physisorpenthalpy�H ◦

pm−mp corresponds to the observed value

−19.6 kJ mol−1 [18]. The observed standard physisorptentropy�S

apppm−mp of −89.33 J mol−1 K−1 [18] is actually

-

not the true standard physisorption entropy for pore moumicropore transfer as it also contains the factorCt,pm/Ct,mp,viz. Eq. (3.16). Accounting for this factor, viz., Table 1, ttrue standard physisorption entropy�S◦

pm−mp is calculated

as−27.8 J mol−1 K−1.

3.2. Iso-alkanes

The physisorption of pure iso-alkane “k” on ZSM-22only occurs at the pore mouths:

Pk + Se,pm

Kk,pm

� Pk,pm.

This leads to the following Langmuir expression for isalkane physisorption at the pore mouth:

(3.17)Ck,pm = Kk,pmCt,pmpk

1+ Kk,pmpk

.

Comparing the above expression with Eq. (3.2), it canseen that the Langmuir coefficient for iso-alkanek, KL,k,corresponds toKk,pm while the saturation concentration fan iso-alkanek, Csat

k , corresponds toCt,pm. Kk,pm is ob-tained from the ratio of the experimentally measured Hecoefficient and the saturation concentration, viz. Eq. (3The above discussion holds for both open and closed Z22 because on both forms iso-alkanes physisorb at themouths only.

4. Modes of physisorption for alkanes on ZSM-22

An iso-alkane at the pore mouth can physisorb in differorientations, leading to multiple physisorption modes,Fig. 3. Inside the micropores strong force fields exist ahence, interactions with the crystal lattice occur for caratoms inside the micropore. Forn-alkanes, all of the carbon atoms are subject to such interactions. For iso-alkathese interactions are limited to the portion of the molecprotruding inside the pore mouth and are directly proptional to the number of carbon atoms protruding into the pmouth. However, apart from the interactions experiencecarbon atoms protruding inside the pore mouth, the ca

Fig. 3. Schematic representation of the three possible physisorption mof 4-methyloctane at a ZSM-22 pore mouth indicated by parallel rectangblocks.

C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147 141

ic int.um-Thes tothendstheiveetic

y-so-outanyout-nesosite

sin-idet

us-sidentsdes

t forree

,

n--ws:

n-ofhemo-for

ob-os-in-ntsen-ovected

is,

siteob-22.

peri-se-hing

tohy-

ffer-e.g.,

ysi--edoms

outhar-lhis

alpye

atoms outside the pore mouth also experience energetteractions with the crystal lattice, albeit to a lesser exten

Each physisorption mode is characterised by the nber of carbon atoms inside and outside the pore mouth.number of pore mouth physisorption modes correspondthe number of straight ends in the molecule. In each ofpore mouth physisorption modes one of the straight eof the molecule protrudes into the pore mouth, whileremaining portion of the molecule is outside. The relatdistribution of all existing modes depends on the energinteractions in these modes.

Fig. 3 is an illustration of the different pore mouth phsisorption modes for 4-methyloctane (4MeC8). This ialkane has three straight ends and, hence, in a pore mconfiguration there are three physisorption modes withone of the straight ends inside the micropore and othersside the micropore. The Henry coefficients for iso-alkadiscussed in the previous section correspond to a compvalue over all possible physisorption modes. Forn-alkanesthe observed physisorption behavior can be related to agle physisorption mode, i.e., with all carbon atoms insthe micropore. Hence, forn-alkanes the Henry coefficienis obtained by Eq. (2.2) along with Eqs. (2.3) and (2.4)ing the standard physisorption enthalpy and entropy inthe micropore. In the calculation of the Henry coefficiefor the iso-alkanes each of the possible physisorption mohas to be accounted for. The composite Henry coefficien4-methyloctane consists of the Henry coefficients of its thindividual physisorption modes, viz. Fig. 3:

Pk + Se,pm

Kkm,pm

� Pkm,pm

(for straight endm inside the pore mouth cavity).Considering the following site balance at pore mouths

(4.1)Ct,pm = Ce,pm +3∑

m=1

Ckm,pm

and

(4.2)Ckm,pm = Kkm,pmpkCe,pm,

where Ckm,pm is the concentration of the physisorptiomodem and Kkm,pm is the equilibrium constant for physisorption in modem. The Langmuir expression for individual physisorption mode (Eq. (2.2)) can be written as follo

(4.3)Ckm,pm = Kkm,pmCt,pmpk

1+ ∑3m=1 Kkm,pmpk

.

The total concentration of physisorbed alkanesk at poremouths is expressed as

Ck,pm =3∑

m=1

Ckm,pm =3∑

m=1

Kkm,pmCt,pmpk

1+ ∑3m=1 Kkm,pmpk

(4.4)=(∑3

m=1 Kkm,pm)Ct,pmpk

1+ (∑3K

)p

.

m=1 km,pm k

-

h

Extending Eqs. (4.1)–(4.4) to any alkane havingN poremouth physisorption modes leads to

(4.5)Kk,pm =N∑

m=1

Kkm,pm.

Multiplying both sides of Eq. (4.5) with the saturation cocentrationCsat

k , which corresponds to the concentrationpore mouthsCt,pm and using the relationship between tHenry coefficient and Langmuir physisorption equilibriucoefficient, viz. Eq. (3.3), the Henry coefficient for isalkane can be expressed in terms of “Henry coefficients”individual modes of physisorption at pore mouths as

(4.6)Hk,pm =N∑

m=1

Hkm,pm.

Hence, when multiple physisorption modes exist, theservable Henry coefficient for physisorption is a “compite,” which equals the sum of the Henry coefficients of thedividual physisorption modes. The latter Henry coefficiecan be calculated using correlations for physisorptionthalpy and entropy given in the next section. The abtreatment for pore mouth physisorption modes is expeto be extendable to key-lock physisorption modes, whichhowever, beyond the scope of the present paper.

For iso-alkanes, experimental values of the compoHenry coefficient for pore mouth physisorption can betained from classical physisorption experiments on ZSM-For n-alkanes the same can be obtained from such exments on closed ZSM-22. It will be evident from the subquent discussions that a major advantage of distinguisbetween different physisorption modes is the possibilitycome to a uniform set of parameters to describe the psisorption properties of all alkane classes, instead of dient parameter sets required now for each alkane class,2-methylalkanes, 3-methylalkanes, etc. [4–6,18].

4.1. Standard physisorption enthalpy

The standard physisorption enthalpy for a given phsorption mode of an iso-alkanek at a pore mouth of ZSM22,�H ◦

km,pm, consists of several contributions. As explainin Section 2.3, enthalpy losses occur via the carbon atinside and outside the pore mouth:

(4.7)�H ◦km,pm = �H ◦

CNPkm+ �H ◦

CNOkm.

The enthalpy loss of the carbon atoms inside the pore mcavity is calculated using Eq. (2.3) with the number of cbon atoms inside the pore mouth, CNPkm , instead of the totanumber of carbon atoms of the physisorbing iso-alkane. Tallows use of the values for the parametersα and β ob-tained from physisorption experiments onn-alkanes on openZSM-22 [4,6,18], viz. Table 2, to calculate�H ◦

CNPkmfor any

alkane at the pore mouths after accounting for the enthloss upon transfer ofn-alkanes from the pore mouth to th

142 C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147

l-lpy

bonnsis

n-side

ithunt-ed,ter-stalthe

omsdif-nes

pores tos inhedameedi-

ualariven-

ibu-de:

sedoms)

2if-orpl-bonrbed

side.car-tsidefor a

atom

en

ffi-ropyes.sitethermsndi-

dhecar-

atedn-ropyn byre-set,

andinedorp-om-

haslockC8.effi-een

, six

pa-ate

micropore,�H ◦pm−mp viz. Eq. (3.13). This leads to the fo

lowing expression for the iso-alkane physisorption enthain modem:

(4.8)−�H ◦CNPkm

= αCNPkm + β − �H ◦pm−mp.

The enthalpy loss corresponding to interactions of caratoms outside the pore mouth cavity is considered to coof two terms:

(4.9)−�H ◦CNOkm

= αoCNOkm + βo.

In the above equation,αo corresponds to the average ethalpy loss per carbon atom due to carbon atoms outNext to this linear contribution, the second termβo accountsfor structural differences in the alkyl chains interacting wthe external crystal surface and in particular allows accoing for the degree of branching of the alkyl chains. Indethese interactions vary with degree of branching. The inactions of monobranched alkanes with the external crylattice are stronger than multibranched alkanes. Also, incase of multibranched alkanes with tertiary carbon atdifferent tertiary carbon atoms are at the pore mouth inferent physisorption modes, while monobranched alkahave the same tertiary carbon atom interacting with themouth in all its physisorption modes. This also contributethe differences in energetic interactions. The differenceenergetic interactions of monobranched and multibrancalkanes are accounted for by considering separate parters:βo

mo, which accounts for interactions of monobranchalkanes, andβo

ml, which accounts for interactions of multbranched alkanes.

4.2. Standard physisorption entropy

The standard physisorption entropy for every individphysisorption mode,�S◦

km,pm, can be expressed in similterms as the standard physisorption enthalpy. For a gphysisorption mode of iso-alkanek at a pore mouth of ZSM22, �S◦

km,pm, consists of a contribution,�S◦CNPkm

, due tocarbon atoms inside the pore mouth cavity, and a contrtion, �S◦

CNOkm, due to interactions of carbon atoms outsi

(4.10)�S◦km,pm = �S◦

CNPkm+ �S◦

CNOkm.

Analogous to the loss in physisorption enthalpy discusabove, the loss in physisorption entropy due to carbon atinside the pore mouth,�S◦

CNPkmis calculated using Eq. (2.4

with the values for the parametersγ and δ obtained fromphysisorption experiments onn-alkanes on open ZSM-2[4,6,18], viz. Table 2, after accounting for the entropy dference between the pore mouth and micropore physistion, i.e.,�S◦

pm−mp, viz. Eq. (3.15). This leads to the folowing expression for the entropy loss due to the caratoms inside the pore mouth for the iso-alkane physisoin modem:

(4.11)−�S◦CNP = γ CNPkm + δ − �S◦

pm−mp.

km

t

.

-

-

The analogy further extends to the carbon atoms outA linear relationship between the entropy loss due to thebon atoms outside and the number of carbon atoms outhe pore mouth is proposed and is expressed as followsgiven physisorption modem:

(4.12)−�S◦CNOkm

= γ oCNOkm + δo.

γ o corresponds to the average entropy loss per carbondue to carbon atoms outside the pore mouth andδo accountsfor the differences in interactions with crystal lattice betwemono- and multibranched alkanes:δo

mo, for monobranchedalkanes, andδo

ml, for multibranched alkanes.

5. Parameter estimation

5.1. Model equations

Eq. (2.2) enables the calculation of the Henry coecients from the standard physisorption enthalpy and ent[4–6] and is applicable for individual physisorption modEq. (4.6) allows calculation of the observable compoHenry coefficient as the sum of the Henry coefficients ofindividual physisorption modes. This is expressed in teof standard physisorption enthalpies and entropies of ividual physisorption modes as follows,

(5.1)Hk,pm =(

Ct,pm

2p◦

)∑m

e�S◦

km,pm/R

e−�H ◦km,pm/(RT )

,

where�H ◦km,pm is obtained from Eqs. (4.7) to (4.9) an

�S◦km,pm from Eqs. (4.10) to (4.12). The contributions to t

standard physisorption enthalpy and entropy loss via thebon atoms protruding inside the pore mouth are calculusing theα, β , γ , andδ values reported in Table 2. The cotributions to the standard physisorption enthalpy and entloss via the carbon atoms outside the pore mouths giveEqs. (4.9) and (4.12), respectively, are determined viagression of experimental data. The experimental dataviz. Table 1, contains physisorption properties of normalbranched alkanes with 5–9 carbon numbers. As explain Section 2.3, alkanes having only pore mouth physistion modes have been considered for regression. A cposite Henry coefficient for pore mouth physisorptionalso been calculated for the iso-alkanes, exhibiting key-physisorption modes, i.e., 2MeC7, 2MeC8, and 3MeComparison of these values with the observed Henry cocients allows estimation of the relative importance betwpore mouth and key-lock physisorption modes.

5.2. Regression results

Based on the discussions in the preceding sectionsparameters are to be estimated:αo, βo

mo, βoml, γ o, δo

mo, andδo

ml from the regression of the experimental data. Therameter estimates along with their individual approxim

C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147 143

s ofd on2))

its)

ese

peruth,sstan

r for, i.e.e-edes.

Fororp-ore

d toasore

the

ocarthe

ntses-ow.ffi-.

entsal-to

arityreslcu-C8,thetesorb

nts

turingental

C

(4.9)

lock

dxperi-ltiplelcu--lockfrom

omsdic-ed

Table 3Estimates with their 95% confidence intervals for the parameterEqs. (4.9) and (4.12) obtained through regression of the model basemultiple physisorption modes (Eq. (5.1) along with Eqs. (4.7) to (4.1and experimental data sets for open ZSM-22 [4,5,18], viz. Table 1

Parameter Estimated value (95% confidence lim

αo (kJmol−1) 6.89(±1.44)γ o (Jmol−1 K−1) 8.97(±2.17)βo

mo (kJmol−1) 30.14(±2.34)δomo (Jmol−1 K−1) −2.60(±2.40)

βoml (kJmol−1) 9.02(±2.91)

δoml (Jmol−1 K−1) −27.80(±1.30)

Parameter values for Eqs. (4.8) and (4.11) from Table 2.

95% confidence intervals are reported in Table 3. Thconfidence intervals correspond tot values in the range101 to 102. As expected, the enthalpy and entropy losscarbon atom due to interactions outside the pore moαo and γ o, are lower than the enthalpy and entropy loper carbon atom inside the pore mouth. The constant sdard physisorption enthalpy and entropy loss are highemonobranched alkanes than for multibranched alkanesβo

mo > βoml andδo

mo > δoml, which is considered to be the r

sult from a more favourable interaction of monobranchalkanes with the zeolite lattice than multibranched alkanThe difference betweenβo

mo andβoml is 21.1 kJ mol−1 and

that betweenδomo and δo

ml is 25.2 J mol−1 K−1, which isclose to the typically observed experimental differences.example, 3-methylpentane in its most favourable physistion mode has two carbon atoms protruding inside the pmouth cavity. The enthalpy loss for this mode is observebe 61.7 kJ mol−1. For 2,2-dimethylbutane, which also hsame number of carbon atoms protruding inside the pmouth cavity in its most favourable physisorption mode,enthalpy loss is observed as 38.7 kJ mol−1. A differencein the interactions of 23 kJ mol−1 exists between these twmolecules, even though they have the same number ofbon atoms inside the pore mouth and outside. Similarly,difference in entropy loss is observed as 31 J mol−1 K−1.TheF value for the significance of the regression amouto 4500, indicating a high global significance of regrsion. Binary correlation between the estimates is very lThe highest absolute value of the binary correlation coecient was observed betweenβo

ml − δoml and amounts to 0.29

Table 4 shows a comparison of calculated Henry coefficiwith experimental data at 573 K. Henry coefficients cculated by CBMC [20] are also shown. They are foundunderpredict the experimental data. Fig. 4 shows the pdiagram of the Henry coefficients at various temperatufor all the normal and monobranched alkanes. The calated composite pore mouth Henry coefficients for 2Me3MeC8, and 2MeC7 are approximately 20% lower thanexperimentally obtained Henry coefficients. This indicathat about 20% of 2MeC8, 3MeC8, and 2MeC7 physisin a key-lock mode. For multibranched alkanes only, theF

value obtained during regression is 650. Henry coefficie

-

,

-

Table 4Henry coefficients(H) (molkg−1 Pa−1) for alkanes on open ZSM-22 a573 K: a comparison between estimates obtained from the model dregression using Eq. (5.1) along with Eqs. (4.7) to (4.12) and experimdata set of open ZSM-22 [4,5,18]), viz. Table 1

Alkanes Experimental Model based on Based on CBM[4,5] multiple physi- [20]

sorption modes

nC5 1.32 1.33 0.652MeC4 0.32 0.32 0.12nC6 2.59 2.54 1.432MeC5 0.54 0.52 0.233MeC5 0.44 0.50 0.1822DMC4 0.13 0.15 1.80× 10−9

23DMC4 0.23 0.14 7.42× 10−3

nC7 4.66 4.87 2.812MeC6 1.13 0.86 0.673MeC6 0.87 0.82 0.3423DMC5 0.42 0.21 0.0233DMC5 n.a.b 0.22 5.98× 10−10

nC8 8.82 9.33 n.a.b

2MeC7a 2.04 1.47 n.a.3MeC7 1.50 1.34 n.a.4MeC7 1.45 1.30 n.a.25DMC6 0.63 0.28 n.a.224TMC5 0.30 0.36 n.a.nC9 19.0 17.8 n.a.2MeC8a 3.80 2.50 n.a.3MeC8a 3.50 2.22 n.a.

Parameter values for Eqs. (4.8) and (4.11) from Table 2 and Eqs.and (4.12) from Table 3.

a Not included in parameter estimation as they also contain key-modes of physisorption.

b n.a.: not available.

Fig. 4. Henry coefficients(molkg−1 Pa−1) for normal and monobrancheC5–C9 alkanes at temperatures 473–673 K. A comparison between emental data on open ZSM-22 [4–6] and model regression based on muphysisorption modes using Eq. (5.1). Line, experimental; symbols, calated. The open symbols correspond to the molecules having also keyphysisorption modes. Parameter values for Eqs. (4.8) and (4.11) areTable 2 and for Eqs. (4.9) and (4.12) from Table 3.

for multibranched alkanes having quaternary carbon atare closely estimated with a systematic small overpretion within 5%. The Henry coefficients for multibranch

144 C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147

yl-(4.3)

(4.9)

d byter-

rnalary

en-pie

ng

lh-

inedn-.7)

n-10)ndtionsite

of-rp-pro-anebons anoncal-for

nedon-d thes-

s

[4–6]4.3),r in-

. Pa-(4.9)

] and7) tod for

orp-

areigh-ode

vity.hetheirtice

iso-sult,

Table 5Molar equilibrium fractions for the physisorption modes of 3-methheptane calculated from molar concentrations obtained using Eqs.and (4.4) along with Eqs. (4.7) to (4.12)

Physisorption CNPmk

xkm −�H ◦km,pm −�S◦

km,pmmodem (kJmol−1) (Jmol−1 K−1)

1 4 0.50 87.2 102.32 2 0.29 75.3 86.33 1 0.21 69.4 78.3

Parameter values for Eqs. (4.8) and (4.12) from Table 2 and Eqs.and (4.12) from Table 3.

alkanes with tertiary carbon atoms are underestimate30–40%. This indicates that multibranched alkanes withtiary carbon atoms interact more strongly with the extecrystal lattice than multibranched alkanes with quarterncarbon atoms.

The composite standard physisorption enthalpy andtropy have been calculated from the enthalpies and entrofor the individual physisorption modes using the followimixing rule:

(5.2)�H ◦k,pm =

N∑m=1

xkm�H ◦km,pm,

(5.3)�S◦k,pm =

N∑m=1

xkm�S◦km,pm − R

N∑m=1

xkm lnxkm,

where xkm is the equilibrium mole fraction of individuamode m within the mixture of possible pore mouth pysisorption modes for iso-alkanek. It is calculated fromthe molar concentration of each of these modes obtafrom Eq. (4.3).�H ◦

km,pm is the standard physisorption ethalpy for each individual mode calculated using Eqs. (4to (4.9) and�S◦

km,pm is the standard physisorption etropy for each individual mode calculated from Eqs. (4.to (4.12). The calculated molar equilibrium fractions athe enthalpy and entropy losses for the three physisorpmodes of 3-methylheptane, viz. Table 5, lead to a compostandard physisorption enthalpy of−80 kJ mol−1 and a com-posite standard physisorption entropy of−84 J mol−1 K−1,which is close to the experimentally observed values−84 kJ mol−1 and−84 J mol−1 K−1 [5,6,18]. From the molar distribution it is clear that the most favoured physisotion state is the one which has maximum carbon atomstruding inside the pore mouth cavity. For 3-methylheptit corresponds to the physisorption mode with four caratoms protruding inside the pore mouth cavity, which haequilibrium mole fraction of 0.5. This is the physisorptimode with the maximum enthalpy and entropy loss. Theculated composite pore mouth physisorption enthalpiesall alkanes correspond well with the experimentally obtaivalues [4–6,18], viz. Fig. 5. The same quality of correspdance has been observed between the calculated anexperimentally determined entropies. Fig. 6 shows thetimated physisorption enthalpy forn-octane and some of it

s

e

Fig. 5. Composite standard physisorption enthalpy(kJmol−1) of C5–C9alkanes. A comparison between experimental data on open ZSM-22values obtained using an ideal mixing rule (Eq. (5.2) along with Eqs. ((4.4), and (4.7) to (4.9)) considering standard physisorption enthalpy fodividual physisorption modes. Line, experimental; symbols, calculatedrameter values for Eqs. (4.8) and (4.11) are from Table 2 and for Eqs.and (4.12) from Table 3.

Fig. 6. Composite standard physisorption enthalpy(kJmol−1) of C8 alka-nes. A comparison between experimental data on open ZSM-22 [4–6calculated values using Eq. (5.2) along with Eqs. (4.3), (4.4), and (4.(4.9). Parameter values for Eqs. (4.8) and (4.11) are from Table 2 anEqs. (4.9) and (4.12) from Table 3.

isomers. The model describes the variations in physistion enthalpies of the normal and iso-alkanes.n-Octane hasthe highest enthalpy loss as all the eight carbon atomsinside the micropore. 2-Methylheptane has the next hest enthalpy loss as in its most favoured physisorption mfive carbon atoms are protruding into the pore mouth caThis is followed by 3-methyl- and 4-methylheptanes. Tmultibranched alkanes have the lowest enthalpy loss asinteractions with the poremouth and external crystal latare weaker.

6. Effect of physisorption on the kineticsof hydrocarbon conversion on ZSM-22

On wide pore zeolites such as USY, normal andalkanes can enter the micropores completely. As a re

C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147 145

and

SY.en-qui-

-acidnd,0].v-ionar-Yfol-

areer,ub-on

if-nceare

de-entodeoreoc-

aighHy-and

de)-keleeredon

orehichtion4-

heanend,rbe-re-

ns.

thed 4-es,

,

cid-thethe

uasi-ntsanork.larareing41].ong-ex-

on-ngesple,anethetionmberheycar-an

ption

M-eac-of

the

inof

tomside.

Fig. 7. Schematic representation of chemisorption of 4-ethylnon-4-ene4-ethylnon-3-ene on a ZSM-22 pore mouth.

there is only one physisorption mode for all alkanes on UFor a given carbon number, the standard physisorptionthalpies and entropies and, hence, the physisorption elibrium coefficients are comparable forn-alkanes and isoalkanes [4–6]. Subsequent alkene chemisorption on thesites inside the micropores occurs without restriction ahence, all reactions of the full reaction network occur [4As a result, the product distribution on USY is mainly goerned by the full reaction network kinetics and physisorpteffects are uniform for all molecules with the same cbon number. Forn-octane hydroconversion on Pt-H-US3-methylheptane is the most abundantly formed isomerlowed by 2-methylheptane and 4-methylheptane [40].

In contrast to USY, on ZSM-22, physisorption effectsnonuniform for molecules with the same carbon numbwhich significantly affects the acid-catalysed reactions ssequent to physisorption. The pore mouth physisorptionZSM-22 leads to different physisorption modes with a dferent standard physisorption enthalpy, entropy, and, heHenry coefficient. As a result, the physisorbed alkanesnot equally distributed over the different modes. Asscribed in Section 5.2, the distribution over the differphysisorption modes is such that the physisorption mwith the highest number of carbon atoms inside the pmouth occurs in abundance. For example, among thetane isomers the 2-methylheptane having the longest strend in one of its modes has the highest concentration.droconversion reactions of alkanes proceed via alkenecarbenium ion intermediates. (De)-hydrogenation and (protonation reactions in this case are fast compared to stal isomerisation and cracking and are generally considto be quasi-equilibrated [40]. In pore mouth catalysisZSM-22, a carbenium ion is always formed at the pmouth and, hence, the physisorption mode determines wcarbenium ion can be formed; e.g., different physisorpmodes are required for carbenium ion formation from

,

t

-

ethylnon-4-ene or from 4-ethylnon-3-ene, viz. Fig. 7. Tconcentration of a carbenium ion corresponding to an alkphysisorbed in a preferred mode will be relatively high ahence, the acid-catalysed reactions in which such a canium ion is consumed proceed at higher rates than theactions involving nonpreferentially formed carbenium ioThis is evident from the product distribution ofn-octanehydroconversion on ZSM-22 where 2-methylheptane ismost abundant product followed by 3-methylheptane anmethylheptanes [9]. Product distribution in the same line.g., 2-methylalkane> 3-methylalkane> 4-methylalkaneare observed for other alkanes [7,15].

The above discussion can be extended to other acatalysed reactions, e.g., catalytic cracking. Even if(de)-protonation reactions are not quasi-equilibrated,preceding physisorption step can be assumed to be qequilibrated. This leads to the distribution of the componeinvolved over the different physisorption modes which cbe calculated using the methodology developed in this wWithin the group of carbenium ions belonging to a particuphysisorption mode, the hydride shift reactions, whichmuch faster than alkyl shift, PCP branching, and crackreactions, are expected to lead to a quasi-equilibration [Hence, higher concentrations of the carbenium ions beling to the most favoured physisorption mode are stillpected under these conditions.

Apart from the steric effects on the carbenium ions ccentrations the reaction rates can also be affected by chain physisorption during the course of reactions. For examduring the PCP isomerisation from a normal to an iso-alkthe reacting carbenium ion slightly moves outward frompore mouth as shown in Scheme 1. These physisorpchanges are again characterised by changes in the nuof carbon atoms inside and outside the pore mouths. Tresult in changes in interactions between the reactingbenium ion and the zeolite lattice during the course ofelementary reaction and, hence, in changes in physisorenthalpy and entropy.

Compared to USY, the shape-selective effects on ZS22 affect the rates of the elementary acid-catalysed rtions and the resulting product distribution. The effectsphysisorption on the kinetics can be quantified usingmethodology discussed in the previous sections.

7. Conclusions

The physisorption of iso-alkanes on ZSM-22 resulttheir multiple pore mouth physisorption modes. Eachthese modes is characterised by the number of carbon aof the molecule inside the pore mouth cavity and outs

Scheme 1.

146 C.S. Laxmi Narasimhan et al. / Journal of Catalysis 218 (2003) 135–147

out-ionsno-orp-ore

o the

hy-ntsp-nrtiesachcid-dol-ona

runiov-stengen

nt

e

re

p-

pore

n,tice,

hem.

/

hem.

obs,

The enthalpy and entropy changes for carbon atomsside the pore mouth are due to their energetic interactwith the crystal surface. These interactions vary for mobranched and multibranched alkanes. A two-step physistion model distinguishing between physisorption at the pmouths and subsequent transfer from the pore mouth tmicropore describes the physisorption phenomenon.

The observable Henry coefficient for pore mouth psisorption of alkanes is the sum of the Henry coefficieof the individual physisorption modes. An additivity aproach using the properties ofn-alkane physisorption oZSM-22 adequately describes the physisorption propeof all given modes of iso- and normal alkanes. As ephysisorption mode plays a distinct role in subsequent acatalysed reactions on ZSM-22, the calculation methoogy of physisorption properties of individual physisorptimodes will allow the description of kinetics on ZSM-22 infundamental way.

Acknowledgments

This research has been done as a part of the Inteversitaire attractiepolen (IAP), funded by the Belgian gernment, Diensten van de Eerste Minister-Federale dienvoor wetenschappelijke, technishe en culturele aangeleheden.

Appendix A. Nomenclature

A.1. Roman symbols

CN Carbon numberCNP Carbon atoms inside the poreCNO Carbon atoms outside the poreCsat Saturation concentration(mol kg−1

cat)

Ci Concentration of physisorbed alkanei (mol kg−1cat)

Ct Total concentration of physisorption sites(mol kg−1

cat)

Ce Concentration of empty physisorption sites(mol kg−1

cat)

H Henry’s coefficient(mol kg−1cat Pa−1)

�H Enthalpy change(kJ mol−1)

KL Langmuir physisorption equilibrium coefficie(Pa−1)

Ki,pm Physisorption coefficient at pore mouth for alkani(Pa−1)

Kpm−mp Equilibrium coefficient for pore mouth–micropotransfer

P Alkane speciespi Partial pressure of alkanei (Pa)p◦ Standard state pressure (Pa)pe Probability of finding an empty site for physisor

tionr Rate of physisorption(mol s−1)

-

-

S Physisorption sites�S Entropy change(kJ mol−1 K−1)

T Temperature (K)w Weights for parameter estimation

A.2. Greek symbols

α Physisorption enthalpy loss per carbon atom(kJ mol−1)

β Constant physisorption enthalpy loss(kJ mol−1)

γ Physisorption entropy loss per carbon atom(J mol−1 K−1)

δ Constant physisorption entropy loss(J mol−1 K−1)

A.3. Superscript

app Apparantc Compositeexp Experimentalm Physisorption mode◦ Standard stateo Parameters for carbon atoms outside the microphys Physisorptionsat Saturation

A.4. Subscript

e Empty physisorption sitesi Index for alkanesiso Iso-alkanesj Index for experimental setj Index forn-alkanek Index for iso-alkaneL Composite Langmuir physisorption equilibriumm Index for physisorption modesml Multibranched alkanesmo Monobranched alkanesmp Microporenp n-Alkanesphys Physisorptionpm Pore mouthpm–mp Pore mouth–microporet Total physisorption sites

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