Adsorption of C2− C8 n-Alkanes in Zeolites

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Adsorption of C2-C8 n-Alkanes in Zeolites† Bart A. De Moor,‡ Marie-Franc¸oise Reyniers,*,‡ Oliver C. Gobin,§ Johannes A. Lercher,§ and Guy B. Marin‡ Laboratory for Chemical Technology, Ghent UniVersity, Krijgslaan 281 S5, B-9000 Gent, Belgium, and Department of Chemistry, Technische UniVersita¨t Mu¨nchen, Lichtenbergstrasse 4, D-85747 Garching, Germany ReceiVed: July 14, 2010; ReVised Manuscript ReceiVed: September 24, 2010

Adsorption of n-alkanes has been studied in the industrially relevant zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5 combining QM-Pot(MP2//B3LYP) with statistical thermodynamics calculations and assuming a mobile adsorbate. In H-ZSM-5, adsorption at the intersection site with the hydrocarbon chain extending in the straight channel (SC+I) as well as in the zigzag channel (ZC+I) has been studied. In addition, differential heats of adsorption and adsorption isotherms at temperatures from 301 to 400 K of all C3-C6 n-alkane in H-ZSM-5 have been measured simultaneously via calorimetry and gravimetry. Calculated adsorption enthalpies are independent of temperature and are virtually identical to the adsorption energies. The adsorption strength increases in the order H-FAU < H-BEA < H-MOR < H-ZSM-5 (SC+I) < H-ZSM-5 (ZC+I) and varies linearly with the carbon number. As compared to experimental values, the calculated adsorption strength is overestimated by some 2 kJ mol-1/CH2 in FAU up to some 4 kJ mol-1/CH2 in H-ZSM-5 suggesting that the QM-Pot(MP2//B3LYP) calculations overestimate van der Waals stabilizing interactions and a correction term has been proposed. Adsorption entropy losses are independent of temperature and increase in the order H-FAU < H-BEA < H-MOR < H-ZSM-5 (SC+I) < H-ZSM-5 (ZC+I), according to the pore size of the zeolites. The calculated adsorption entropies agree nicely with available experimental results in all zeolites. QM-Pot(MP2//B3LYP) calculated adsorption equilibrium coefficients (using the corrected adsorption enthalpies) correspond relatively well to experimentally determined values. Comparison of relative turnover frequencies with relative adsorption equilibrium coefficients indicates that the variation of the equilibrium coefficient with the carbon number or with the zeolite can only partly explain the observed reactivity differences in monomolecular cracking of n-alkanes. In agreement with experimental observations, our results indicate that the difference in reactivity of the n-alkanes for monomolecular cracking in a given zeolite mainly originates from a difference in intrinsic monomolecular cracking rate coefficients. obtained from transition state theory and assuming equilibrium for adsorption.8,9,11,12

Introduction Owing to their specific micropore systems, consisting of channels, pores, and cages, zeolites are widely used in industry as catalysts to enhance hydrocarbon conversion reactions such as cracking, isomerization, alkylation, etc., and for the separation of various hydrocarbons such as n-alkanes and mono- or multibranched alkanes.1-4 In any of the possible zeolite applications, molecules need to diffuse to and adsorb at the acid sites inside the zeolite pores before any reaction can take place. Therefore, understanding the thermodynamics of hydrocarbon adsorption is crucial for a molecular level understanding of hydrocarbon conversion processes using zeolites as catalyst. In the monomolecular cracking of alkanes on acidic zeolites, both the adsorption enthalpy and the adsorption entropy are of importance for understanding cracking rates.5-13 This is illustrated by eq 1 that shows the relation between the cracking rate and adsorption and activation enthalpies and entropies, as

r

) kCads,alkane ) kKadspalkane

[

( )][ ( ) ( ( ) ( )]

0 0 -Eact ∆Sads -∆Hads exp exp RT R RT 0 kBT ∆Sact -Eact ) exp × e exp h RT RT 0 0 ∆Sads -∆Hads exp exp palkane R RT

) Aact exp

[ [ ( ) (

)]

)]

palkane

(1)

The Arrhenius pre-exponential factor Aact directly relates to the activation entropy ∆S0act, while the link between the Arrhenius activation energy Eact and the activation enthalpy ∆H0act is Eact ) ∆H0act + RT. The apparent activation energy and apparent pre-exponential factor can be expressed as

†

Part of the “Alfons Baiker Festschrift”. * Corresponding author. Tel: +32 (0)9 264 4516. Fax: +32 (0)9 264 4999. E-mail: [email protected]. ‡ Ghent University. § Technische Universita¨t Mu¨nchen.

( )

kapp ) Aapp exp

10.1021/jp106536m  2011 American Chemical Society Published on Web 10/20/2010

-Eapp ) kKads RT

(2-a)

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Eapp ) Eact + ∆H0ads ln(Aapp) ) ln(Aact) +

∆S0ads R

(2-b)

(2-c)

Experimental observations reported in the literature indicate an exponential increase of the cracking rate with increasing carbon number of the alkane.5,6,8 Many authors report that intrinsic activation energies, Eact, are independent of the carbon number and insensitive to the zeolite type due to the similarity in acid strengths between the industrially relevant zeolites, e.g., FAU, BEA, MOR, and ZSM-5.5-10,12 Therefore, Eact only plays a minor role in understanding variations of monomolecular cracking rates. In contrast, the apparent activation energy, Eapp, depends on the carbon number and differs from one zeolite to the other since alkane adsorption enthalpies obviously vary with the carbon number and the zeolite framework (eq 2-b). Furthermore, due to confinement effects,14 different cracking rates are observed in the various zeolites that have been subjected to experimental studies and a strong correlation with the pore size has been observed as cracking rates increase in the order H-Y < H-BEA < H-MOR < H-ZSM-5 < H-FER.7,8,10,12 Especially the observed increase of the cracking rate with the carbon number is subject of debate in literature. Most authors attribute this increase of the cracking rate to the increase in the adsorption equilibrium coefficient, Kads, for longer alkanes, i.e., to the prevalent concentration of the adsorbed alkanes within the zeolite channels, implying that the intrinsic kinetics for monomolecular cracking are independent of the alkane carbon number within a given zeolite.5,6,8 Bhan et al., on the other hand, came to different conclusions stating that, at temperatures relevant for monomolecular cracking, the observed differences in the thermodynamic adsorption coefficients, Kads in eq 1, cannot explain the observed variation of the cracking rates with the length of the hydrocarbon.11 Instead, the authors conclude that, since the intrinsic activation energy Eact is independent of the carbon number,5,6,8 the observed increase of the cracking rates with the carbon number originates from the higher activation entropies for monomolecular cracking of longer alkanes. A variation of the activation entropy with the carbon number implies a variation of the pre-exponential factor of the rate constant. The question thus remains whether the higher cracking rate for the longer alkanes results from the (adsorption) thermodynamics, from the intrinsic kinetics or from a combination of both. With regard to the observed difference in rate between different zeolites, the obvious difference in the adsorption thermodynamics in the various zeolites influences the cracking rates in the respective zeolites.7-10 However, Bhan et al. state that also the intrinsic rate constants differ from one zeolite to the other.11 Moreover, Gounder and Iglesia conclude that not only the zeolite type but also the location of the acid sites in the zeolite pores may influence the intrinsic rate constants; these authors especially emphasize the role of the activation entropy.12,13 Comparison of equilibrium adsorption coefficients, obtained from our calculations or taken from literature, for various n-alkanes in the zeolites of interest with reported cracking rates allows answering to what extent variations of the equilibrium adsorption coefficient can explain variations in experimentally observed cracking rates. Various experimental and molecular simulation studies available in literature deal with the adsorption of n-alkanes in different zeolites.15-40 Important quantities for describing ad-

sorption processes are the Henry coefficient, adsorption enthalpies, adsorption entropies, saturation concentrations, also called the maximum loading, of n-alkanes, adsorption isotherms, etc. At very low partial pressures of n-alkanes, Henry coefficients provide the link between the gas phase hydrocarbon pressure and the n-alkane loading in the zeolite. Denayer et al. have determined Henry coefficients for a broad range of n-alkanes in various industrially relevant zeolites using a gas chromatographic technique.16,17 Other authors derive the Henry coefficient from the adsorption isotherm assuming a particular adsorption isotherm model, e.g., the Langmuir isotherm18,19 or the Virial equation.20-24 Also (configuration bias) Monte Carlo (CBMC) techniques using a united atom or all atom force field has proven to be able to yield reliable Henry coefficients.25,27,30 Adsorption enthalpies can be determined experimentally, e.g., from (i) the temperature dependence of the Henry coefficients,16,17 (ii) calorimetry,18,19 or (iii) the Virial equation.20,21 In addition, a large number of different types of simulations allow the calculation of the adsorption enthalpy accounting for the particular zeolite structure, such as classical force fields,26 CBMC,27-30 (classical) molecular dynamics,31 periodic DFT(+D)33-36 and hybrid (QM: MM or QM:QM) methods.37-40 In order to obtain reliable results, a proper description of the important van der Waals stabilizing interactions is crucial. In contrast to adsorption enthalpies, adsorption entropies cannot be experimentally determined or measured in a direct way but have to be calculated indirectly from, e.g., the Henry coefficient16,17 or from the (Langmuir) equilibrium coefficient, which is obtained from a measured adsorption isotherm.18,19,24 Preliminary assumptions related to the adsorption model and standard states of gas phase n-alkane, unloaded zeolite and the adsorption complex have to be made. Especially for the latter there is little consensus in literature41 which complicates comparison of adsorption entropies reported by different authors since comparison is only possible if the same standard states are chosen. In this work we present, next to experimental results for C3-C6 n-alkane adsorption in H-ZSM-5, a theoretical study on the adsorption of linear alkanes in different zeolites, i.e., H-FAU, H-BEA, H-MOR, and H-ZSM-5. The combined QM-Pot(MP2// B3LYP)-statistical thermodynamics method assuming a mobile adsorbate has been applied and has shown to give good agreement with experimental results in earlier work.39,40 An extensive comparison with literature data is also presented. 2. Models and Methods 2.1. Zeolite Models. In all zeolites, i.e., H-FAU, H-BEA, H-MOR, and H-ZSM-5, one silicon atom has been replaced by an aluminum atom and an acid proton has been added to compensate for the negative charge. All unit cells have been optimized using a GULP constant pressure optimization applying the shell-model ion-pair potential zeolite force field.42 Initial zeolite structures have been taken from the International Zeolite Association (IZA) Web site.43 H-FAU is a large pore zeolite consisting of characteristic supercages with a diameter of 1300 pm, interconnected through 12-membered rings with dimensions of 740 pm × 740 pm.44 The noncubic unit cell is doubled in the a direction in order to ensure sufficient separation between the hydrocarbons in the neighboring unit cell images. The AlO1H is the most preferred acid site and is therefore chosen in this study, this results in a unit cell composition of HAlSi95O192 and Si/AlF ) 95. This location has also been proposed by Sauer and co-workers.42 The optimized unit cell parameters are a ) 3497.1 pm, b ) 1743.0 pm, c ) 1749.3 pm, R ) 59.995°, β ) 59.870°, and γ ) 59.898°.39,40

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H-BEA is a large pore zeolite with a three-dimensional network of 12-membered ring channels, of which two are straight in the a and b direction with pore dimensions of 660 pm × 670 pm and one is sinusoidal in the c direction with dimensions of 560 pm × 560 pm.44 The acid site chosen is Al6O61H, located at the intersection of the channels and easily accessible for n-alkanes. The resulting composition of the unit cell is HAlSi63O128 and the Si/AlF ratio is 63. The optimized unit cell parameters are a ) 1260.3 pm, b ) 1255.8 pm, c ) 2678.2 pm, R ) 90.029°, β ) 90.074°, and γ ) 90.284°. H-MOR is a large pore zeolite with a monodimensional pore system running parallel to the c axis and consisting of large 12-membered ring channels with dimensions 650 pm × 700 pm, which are interconnected along the b axis via 8-ring side pockets with dimensions 260 pm × 570 pm.44 The unit cell is doubled in the c direction to ensure sufficient separation between the periodic images of the hydrocarbon structure adsorbed in the zeolite. The acid site chosen is Al4O2H and the resulting unit cell thus has composition HAlSi95O192 and a Si/AlF ratio of 95. This acid site has also been proposed in literature.45 The optimized unit cell parameters are a ) 1830.8 pm, b ) 2019.5 pm, c ) 1500.3 pm, R ) 90.013°, β ) 89.825°, and γ ) 90.016°. H-ZSM-5 is a medium pore zeolite consisting of 10membered ring straight channels (530 pm × 560 pm) parallel with the b axis and sinusoidal channels (510 pm ×550) along the a axis.44 Al12024H, located at the intersection of the sinusoidal (or zigzag) and the straight channel, is chosen as acid site because of its accessibility for bulky reactants. This location for the acid site has also been proposed by Sauer and co-workers as channel intersection site.45 The optimized unit cell parameters are a ) 2035.8 pm, b ) 1985.9 pm, c ) 1352.1 pm, R ) 89.905°, β ) 89.808°, and γ ) 89.974°. All simulations have been performed and compared to literature data for the adsorption of the various n-alkanes assuming a negligible influence of the location and the number of the acid sites in acidic zeolites. The justification of this assumption is at least partly confirmed by the experimental results reported by Denayer et al. in their study on adsorption of n-alkanes in H-FAU zeolites with various Si/AlF ratios (H-Y, CBV720, and CBV760). These authors observed a very small dependence of the adsorption enthalpies and entropies on the Si/AlF ratios ranging from 2.7 to 30.16 2.2. Computational Methods. Hydrocarbon species inside the zeolite pores have been optimized using a combined quantum mechanics-interatomic potential functions approach (QM-Pot), using periodic boundary conditions and accounting for the entire zeolite structure. Calculations are performed with the QMPOT program,46 coupling TURBOMOLE47,48 for the QM calculations and GULP49,50 for the force field calculations. The QM-Pot energy of the periodic system S is obtained from the interatomic potential functions energy of the total system S, E(S)Pot, corrected by the difference between the QM energy and the interatomic potential energy of the cluster C, i.e., the active site and the hydrocarbon, E(C)QM - E(C)Pot. As such, the total QM-Pot energy consists of a QM contribution, E(C)QM, and a net force field contribution, E(S)Pot - E(C)Pot. The latter is also called the long-range contribution, ELR

EQM-Pot ) E(S)Pot + E(C)QM - E(C)Pot

(3)

Energies are calculated at the QM-Pot(MP2//B3LYP) level, correctly describing the important van der Waals stabilizing interactions in the whole system S. Optimizations and frequency

TABLE 1: Overview of the Number of Free Translational and Free Rotational Contributions Considered for the Statistical Thermodynamics Calculations of n-Alkane Adsorption in the Different Zeolites free translation

zeolite

framework density [T/nm3]

H-FAU H-BEA H-MOR H-ZSM-5

13.3 15.3 17.0 18.4

number

molecular surface area [pm × pm]

free rotation number

2 2 2 2

800 × 800 800 × 800 200 × 800 200 × 600

2 2 2 1

calculations have been performed at the QM-Pot(B3LYP) level; no scaling factor has been applied for the obtained harmonic frequencies. Statistical thermodynamics are applied to calculate enthalpies and entropies assuming a mobile adsorbate. The latter means that a number of frequencies, corresponding to a translation and rotation of the n-alkane in the zeolite, obtained from the harmonic oscillator approximation are removed from the vibrational partition function and are replaced by a free translational and/or rotational contribution. This approach has been shown to describe reliably physisorption and chemisorption of hydrocarbons in various zeolites.39,40 It has especially been shown in the case of H-FAU that this mobile adsorbate method leads to a much better agreement between simulation and experiment as compared to the immobile adsorbate method, in which enthalpies and entropies are calculated from harmonic frequencies only. The adsorption energy is obtained by subtracting the electronic energies of the optimized gas phase sorptive and the zeolite from the electronic energy of the optimized physisorbed species: QM-Pot QM-Pot QM-Pot ∆EQM-Pot ) Eelec,adsorbate - Eelec,sorptive(g) + Eelec,zeolite ads

(4) The adsorption enthalpy and the adsorption entropy are determined from a similar subtraction scheme. Table 1 summarizes the number of free translations and rotations of the n-alkane considered in each zeolite. This number is mainly based on visualization of the frequencies. In particular, low frequencies ( H-BEA > H-MOR > H-ZSM-5. This

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TABLE 2: Experimental Adsorption Enthalpies and Entropies of n-Alkanes in H-ZSM-5

propane n-butane n-pentane n-hexane

KLb,c [10-5 Pa-1]

∆Hadsa [kJ mol-1]

341 K

370 K

-41.0 -52.0 -62.5 -72.0

24 233 1604 49099

8 71 480 5822

Kads [-]

400 K

∆Sadsd [J mol-1 K-1]

373 K

773 K

1139 K

3 50 155 1238

-94 -104 -118 -121

6.9 68.2 397.3 5513.8

0.0073 0.0116 0.0118 0.0334

0.0014 0.0015 0.0010 0.0019

a ∆Hads is independent of temperature, because the heat signals from the calorimeter are similar at different temperatures. b Langmuir coefficient obtained from the experimentally measured adsorption isotherm. c The standard state for the gas phase hydrocarbon is taken as p0 ) 105 Pa. d ∆Sads is calculated from eq 6 and is practically independent of the temperature.

order is also confirmed by the zeolite framework density as mentioned in Table 1.44 H-FAU and H-BEA are large pore zeolites, and a molecular surface area of 800 pm × 800 pm is used, in view of the open structure of the former (supercages) and the acid site location at the intersection of three channels in case of the latter. In H-MOR, a molecular surface area of 200 pm × 800 pm is proposed, because of the unidimensional 12-membered ring channel system in H-MOR. In H-ZSM-5, a molecular surface area of 200 pm × 600 pm has been used, reflecting the smaller pore size as compared to the other zeolites. In previous work, it has been shown that the influence of the size of the molecular surface area chosen for the respective zeolites is rather limited indicating that the calculated adsorption entropies are accurate to within some (10 J mol-1 K-1.40 2.3. Experimental Methods. C3-C6 n-alkane adsorption experiments in H-ZSM-5 have been performed. Differential heats of adsorption and adsorption isotherms of all hydrocarbons are measured simultaneously via calorimetry and gravimetry, respectively, using a SETARAM TG-DSC 111 instrument. Sorption experiments have been carried out at temperatures from 301 to 400 K and the results are reported in Table 2. Further details about used materials (H-ZSM-5 with Si/AlF ) 35), the experimental setup and procedures can be found in the papers of Eder et al.18,19 The isotherms have been fitted to a (sum of) Langmuir type adsorption isotherm(s), allowing the estimation of the saturation concentration, qsat, and the Langmuir coefficient, KL (see eq 5)

q ) qsat

KLp 1 + KLp

(5)

The Langmuir coefficient KL relates to the thermodynamic equilibrium coefficient K via the standard state for the gas phase n-alkane, p0 (eq 6-a). Since the standard adsorption enthalpy is known from the calorimetric experiments, the standard adsorption entropy is easily calculated (eqs 6-b and 6-c).

Kads ) p0KL

Kads

(6-a)

(

0 ∆Hads - T∆S0ads ) exp RT

∆S0ads ) R ln Kads +

0 ∆Hads T

)

(6-b)

(6-c)

Further details on the Langmuir adsorption model and on the experimental method used for obtaining thermodynamic data can be found in the Supporting Information. For brevity, the standard adsorption enthalpy and the standard adsorption entropy are shortly called adsorption enthalpy and adsorption entropy further on in the text and are denoted as ∆Hads and ∆Sads. 3. Results and Discussion 3.1. Experimental Results. As explained in the previous section, adsorption enthalpies and Langmuir coefficients are directly obtained from calorimetry and the measured adsorption isotherms. Thermodynamic equilibrium coefficients for adsorption are calculated from the Langmuir coefficients and, using the measured adsorption enthalpies, the Gibbs free energies and adsorption entropies are calculated. Adsorption enthalpies are

Figure 1. (a) van’t Hoff plot showing the iso-equilibrium point for adsorption and (b) interdependency between adsorption enthalpies and entropies, as obtained from the experimentally determined adsorption enthalpies and entropies of C3-C6 n-alkanes in H-ZSM-5.

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found to be independent of the temperature, since heat signals from the calorimeter are similar at different temperatures and adsorption entropies only slightly depend on the temperature. Table 2 summarizes the adsorption enthalpy, the Langmuir coefficients (at 341, 370, and 400 K), the mean adsorption entropy, and the thermodynamic equilibrium coefficients at 373, 773, and 1139 K. The adsorption enthalpy and the adsorption entropy show the typical trend with the carbon number: with increasing length of the n-alkanes, the adsorption strength and the entropy loss increase; this is further discussed infra. The adsorption equilibrium coefficients determined at 341, 370, and 400 K clearly indicate that at lower temperatures, adsorption of the longer hydrocarbons is strongly favored due to the higher relative contribution of the adsorption enthalpy (compared to the entropy) to the Gibbs free energy of adsorption. However, with increasing temperature, the entropic contribution becomes more dominant and the differences in adsorption equilibrium coefficients level off. At 773 K, a temperature relevant for monomolecular cracking of n-alkanes, the n-hexane adsorption equilibrium coefficients is approximately 5 times larger than for propane, while at 373 K this factor amounts to around 800. At a temperature of 1139 K, a (quasi) iso-equilibrium is obtained: at this temperature, adsorption equilibrium coefficients of the C3-C6 n-alkanes have nearly the same value and, hence, an equal concentration of the n-alkanes in the zeolite pores, independent of the carbon number can be expected. This is nicely illustrated in Figure 1a, showing the van’t Hoff plot for all C3-C6 n-alkanes and the iso-equilibrium at 1139 K where all lines (approximately) cross at the same value of ln(Kads). As shown in Figure 1b, n-hexane slightly deviates from the expected interdependency between the adsorption enthalpy and entropy for the C3-C5 n-alkanes. This might indicate that, from n-hexane onward, ordering phenomena are beginning to play a role. A more in depth discussion about the role of adsorption in understanding the variation of the monomolecular cracking rate as function of the alkane carbon number and the zeolite type is presented in section 3.3. 3.2. Simulation Results. Adsorption of n-alkanes has been investigated in the zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5 using QM-Pot(MP2//B3LYP) calculations combined with statistical thermodynamics. Adsorption in H-FAU has been described in an earlier paper.39 However, some subtle issues related to the adsorption entropies as well as the comparison with the other studied zeolites are further discussed in this paper. In H-ZSM-5, adsorption at the intersection side with the hydrocarbon chain extending in the straight channel (SC+I) and in the zigzag channel (ZC+I) has been considered. Figure 2 shows views for n-octane adsorption in the various considered zeolites. In the following sections, the geometry of the adsorbed n-alkanes, the adsorption enthalpies and entropies, and the adsorption equilibrium coefficients are discussed. Next to this, an extensive comparison with available data, experimental and/ or molecular simulations, in literature is made. 3.2.1. Geometrical Parameters. Table 3 shows the averaged geometrical parameters for n-alkane adsorption in the various zeolites using the nomenclature explained in Figure 3: Oa is the acid oxygen bonded to the acid proton Ha, Ob the Lewis base oxygen closest to the n-alkane; Ca and Cb are the n-alkane carbon atoms closest to Ha of which Cb is the n-alkane carbon atom closest to Ob. Similarly, Sia and Sib are bonded to Oa and Ob respectively. Geometrical parameters for all individual n-alkanes in the various zeolites can be found in the Supporting Information.

Moor et al.

Figure 2. n-Octane adsorption in H-FAU, H-BEA, H-MOR, and H-ZSM-5. In H-ZSM-5, adsorption at the intersection site with the hydrocarbon chain extending in the straight channel (SC+I) and the zigzag channel (ZC+I) has been studied.

Only a very weak interaction between the zeolite acid proton and the alkane exists in most zeolites; this is illustrated by the HaCa and HaCb distances amounting to values between 297 and 515 pm. Since the n-alkane is loosely bonded to the zeolite, the variation of these distances for the various n-alkanes is

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TABLE 3: Geometrical Parameters of the Adsorbed Alkanes in H-FAU, H-BEA, H-MOR, and H-ZSM-5a H aCa zeolite n-alkanes 333.3 H-BEA zeolite n-alkanes 408.5 H-MOR zeolite n-alkanes 496.7 H-ZSM-5 zeolite n-alkanes (SC+I) 472.3 n-alkanes (ZC+I) 338.6 H-FAU

HaCb

CaCbc

C bO b

b

((55.8) 376.3 ((88.3) 153.1 499.4 ((67.0) ((30.5) 437.1 ((35.1) 152.9 503.1 ((45.6) ((38.9) 504.7 ((19.0) 152.9 504.8 ((52.1) ((17.9) 514.8 ((19.9) 152.9 465.1 ((26.9) ((19.8) 296.6 ((21.3) 152.8 418.4 ((29.2)

HaOa SiaOa

AlOa

SibOb

AlOb

97.5 97.6 97.8 97.8 97.6 97.6 97.6 97.7 97.9

190.2 190.0 189.4 189.8 190.7 190.6 190.3 189.9 190.5

160.8 160.8 161.4 161.5 160.7 160.6 161.8 162.0 161.6

171.5 171.6 172.9 173.3 171.6 171.6 172.2 172.3 172.3

172.4 172.5 170.8 171.2 170.6 170.7 171.8 172.0 171.7

SiaOaAl SibObAl 124.7 124.4 135.4 135.3 129.5 129.4 134.1 134.4 133.0

133.7 133.8 135.4 134.0 140.5 140.5 146.5 141.4 148.6

a Distances are reported in pm and angles in degrees. Standard deviations accounting for the differences observed for the various n-alkanes of the HaCa, HaCb,and CbOb distances are given in parentheses. b The geometrical parameters are taken from De Moor et al.40 c The average CaCb bond length for gas phase n-alkanes is 152.8 pm.

Figure 3. Schematic representation of the adsorption of n-alkanes at the acid site of the zeolite.

relatively large as illustrated by the standard deviations. No unambiguous trend of the HaCa and HaCb distances as function of the carbon number is observed in the various zeolites. A significant difference of the HaCa and HaCb distances is however observed for adsorption in SC+I (472-515 pm) and in ZC+I (297-339 pm) of H-ZSM-5 suggesting a weaker acid protonn-alkane interaction in the former case. In the optimized structure of the n-alkane/H-ZSM-5 (SC+I), the acid proton is pointing away from the n-alkane. Adsorption of n-alkanes induces practically no changes in the zeolite structure and in the n-alkane. For H-ZSM-5, however, remarkable differences are observed for the SibObAl bond angle. In case of adsorption at SC+I, this angle amounts to 141.4°, i.e., a decrease of 5° compared to the unloaded zeolite. In case of adsorption at ZC+I, on the other hand, the SibObAl angle equals 148.6°, i.e., an increase of 2° compared to the unloaded zeolite. The larger deviation of the SibObAl angle in SC+I than in ZC+I compared to the unloaded zeolite, indicates that adsorption of n-alkanes in SC+I leads to a larger distortion of the zeolite. Pantu et al.38 and Benco et al.34 also report that geometrical changes in the zeolite and the n-alkane upon adsorption are negligible. Pantu et al. report for both H-FAU and H-MOR HaCa and HbCb distances of the order 2.5-3.5 Å, which is slightly smaller than the values we report for those zeolites. As shortest distances, Benco et al. report values around 3.1 Å for the adsorption of n-alkanes in the large cavities of gmelinite, which are similar to the cages in H-FAU. 3.2.2. Adsorption Enthalpy. In the following sections, the influence of temperature, carbon number, and zeolite framework on the adsorption enthalpies are discussed. QM-Pot(MP2// B3LYP) results are compared with literature data. The value of the adsorption enthalpy for all n-alkanes in the different zeolites can be found in the Supporting Information.

Figure 4. ∆EZPVE + ∆E0fT correction term for the adsorption of n-alkanes in the zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5 (SC+I and ZC+I). The line connects the average values; the maximum positive and negative deviations from these values are indicated by the bars.

Influence of Temperature. Adsorption enthalpies consist of three contributions: (i) the electronic energy, (ii) the zero-point vibrational energy (ZPVE), and (iii) a temperature dependent correction term, which is calculated from the vibrational, translational, and rotational partition functions

∆Hads ) ∆EQM-Pot + ∆EZPVE + ∆E0fT ads

(7)

The electronic energy is obtained from the QM-Pot(MP2// B3LYP) calculation, whereas the two last terms in eq 7 are calculated from statistical thermodynamics and represent the temperature correction term. Figure 4 shows this temperature correction in the range 100-800 K. The line connects the average values of the different n-alkanes studied in the respective zeolites, while the minimum and maximum temperature corrections of an individual n-alkane are indicated by the bars (as deviation from the average value). For H-FAU, H-BEA, and H-MOR, temperature corrections practically coincide and are almost identical to 0 kJ mol-1. The temperature corrections for adsorption in SC+I and ZC+I in H-ZSM-5 are nearly the same but somewhat higher than the corrections in the other zeolites and modestly increase with increasing temperature. Temperature corrections remain however smaller than 4 kJ mol-1 at 800 K; this largely falls within the uncertainty on the energies that can be expected for the QM-Pot(MP2//B3LYP) method used. The different behavior of the temperature corrections in H-ZSM-5 as compared to the other zeolites relates to the different number

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Figure 5. n-Alkane adsorption enthalpies as function of the carbon number in the zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5 (SC+I and ZC+I); linear fits are indicated.

of free rotational contributions considered in the statistical thermodynamics calculations. In general, since the variation with temperature of the corrections is small and since the corrections are close to 0 kJ mol-1, we conclude that (i) adsorption enthalpies are practically independent of temperature and (ii) adsorption enthalpies are virtually identically to the adsorption electronic energies. This was also concluded for adsorption of alkanes and alkenes in H-FAU.40 The reported adsorption enthalpies infra are, for the above-mentioned reasons, taken as the adsorption electronic energies and can be considered to be independent of the temperature. Influence of Zeolite Framework. Figure 5 shows the calculated adsorption enthalpies as function of the carbon number in the various zeolites. The adsorption strength in the studied zeolites decreases in the order H-FAU < H-BEA < H-MOR < H-ZSM-5 (SC+I) < H-ZSM-5 (ZC+I); this order is inverse to the order of zeolites as function of increasing pore or cage size (see section 2.1, discussion of zeolite models) and is in accordance with the zeolite ordering as function of increasing framework density (see Table 1). Smaller pores lead to a tighter fit of n-alkanes in the various zeolites and as such lead to stronger adsorption, mainly due to higher contributions of the stabilizing van der Waals interactions between the n-alkane and the zeolite. This was also found experimentally by Eder et al. and Denayer et al.16-19 Also, van Genechten and Mortier pointed out that the polarizability of the zeolite lattice increases with increasing framework density (FWD),51 which consequently leads to stronger adsorption of n-alkanes. For the adsorption in the SC+I vs the ZC+I channel in H-ZSM-5, we observe from Figure 5 a stronger adsorption for the C2-C5 n-alkanes in ZC+I; from C6 onward, the adsorption strengths hardly differ. Influence of Carbon Number. Next to the values of the calculated adsorption enthalpies, Figure 5 also shows the linear fits for the various zeolites, given by

∆Hads ) RCN + β

(8)

The parameter R reflects the increase of the adsorption strength with increasing carbon number of the n-alkane, and the parameter β reflects a constant contribution to the adsorption enthalpy, independent of the carbon number. Based on infrared spectroscopic analysis of the changes in the O-H stretching frequency and n-alkane related frequencies, Eder et al. pointed

out that adsorption in acidic zeolites at low n-alkane partial pressures involves a local interaction between the acid proton and the n-alkane.18 This stabilizing interaction is expected to be independent of the carbon number and should therefore be reflected in the parameter β. The value of the H+-alkane interaction has been estimated through comparison between adsorption in acidic and all silica zeolites and amounts to -6 to -7 kJ mol-1 in H-FAU19,40 and -7 to -10 kJ mol-1 in H-ZSM-5.19,26 As the interaction manifests itself as hydrogen bonding in the IR spectra of adsorbed alkanes, it is related to the polarization induced in secondary and tertiary C-H bonds of the alkane and will hence subtly depend on the acid strength of the OH group, i.e., on the positive charge of its proton. Table 4 summarizes the obtained values for the parameters R and β, together with their standard deviation, the correlation coefficient (R2), the mean deviation (MD), and the mean absolute deviation (MAD). Note that all fits yield a correlation coefficient very close to 1, no systematic mean deviation from the calculated values, and a mean average deviation which is small. The values of the parameter R amount to -8.6, -10.8, -13.8, -16.5, and -14.0 kJ mol-1 for H-FAU, H-BEA, H-MOR, H-ZSM-5 (SC+I), and H-ZSM-5 (ZC+I), respectively. The parameter R is more negative in case of the denser frameworks (Table 1) and a linear relation, with a correlation coefficient R2 ) 0.98, between R and the framework density (FWD) exists.

R ) -1.56FWD + 12.47

(9)

The variation of the adsorption enthalpy with the carbon number (R) exclusively originates from dispersive forces (see also the Supporting Information), and as such, adding an extra -CH2- group to the n-alkane leads to a higher increase of the adsorption strength in those zeolites with smaller pores or channels. In H-ZSM-5, the adsorption enthalpy decreases faster in case of adsorption in SC+I (R ) -16.5 kJ mol-1) as compared to ZC+I (R ) -14.0 kJ mol-1), although intuitively, based on the channel dimensions, the opposite would be expected. The values for the parameter β amount to -8.7, -7.2, -8.7, -2.6, and -22.0 kJ mol-1 for H-FAU, H-BEA, H-MOR, H-ZSM-5 (SC+I), and H-ZSM-5 (ZC+I), respectively. In principle, one could expect that the absence of a local interaction between the n-alkane and a zeolite, would yield a β value of 0 kJ mol-1. Accounting for this and for the above-mentioned experimentally determined estimates for the contribution of the acid proton-n-alkane interaction to the adsorbate stability, the β values of H-FAU, H-BEA, and H-MOR appear to have the right order of magnitude. These β values are also in agreement with the range of values of -2 to -9 kJ mol-1 for adsorption of n-alkanes in various medium and large pore acidic zeolites reported by Denayer et al.16,17 Note that the β value for H-ZSM-5 (SC+I) is somewhat smaller, i.e., closer to zero, which seems to confirm the rather weak H+-alkane interaction if the n-alkane is adsorbed in SC+I of H-ZSM-5, as pointed out in section 3.2.1. For adsorption in H-ZSM-5 (ZC+I) on the other hand, even considering the present interaction with the acid proton (in view of the short HaCa and HaCb distances), the β value of -22.0 kJ mol-1 is more negative than expected. Comparison with Literature Data. In literature, many studies on n-alkane adsorption in H-FAU, H-BEA, H-MOR, and H-ZSM-5 are available.15-32,38,40 Table 5 summarizes the values for the parameters R and β reported in experimental studies and in molecular simulations for n-alkane adsorption in the different zeolites. In case only adsorption energies or enthalpies are

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TABLE 4: Parameters r and β, Describing the Linear Relation between the Adsorption Enthalpy and the Carbon Number, Their Standard Deviation (in Parentheses), the Correlation Coefficient (R2), the Mean Deviation (MD), and the Mean Absolute Deviation (MAD) for the Adsorption of n-Alkanes in H-FAU, H-BEA, H-MOR, H-ZSM-5 (SC+I), and H-ZSM-5 (ZC+I) R a

H-FAU H-BEA H-MOR H-ZSM-5 SC+I ZC+I a

R2

β

MD

MAD -5

-8.6 ((0.2) -10.8 ((0.4) -13.8 ((0.3)

-8.7 ((1.5) -7.2 ((2.2) -8.7 ((1.4)

0.9977 0.9930 0.9982

-2.4 × 10 -2.5 × 10-5 2.1 × 10-5

0.9 1.6 1.0

-16.5 ((0.3) -14.0 ((0.7)

-2.6 ((1.8) -22.0 ((4.0)

0.9978 0.9861

-1.9 × 10-5 6.2 × 10-6

1.1 2.7

Taken from De Moor et al.40

TABLE 5: Values for the Parameters r and β in the Zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5 as Obtained from the Linear Fit and as Found in Literaturea R

β

-8.6

-8.7

b 548-648 K

-10.8 -10.0

-7.2 -2.6

95 10 5 c c

b 323 K 548-648 K d b

-13.8 -9.3 -10.5 -10.1 -11.1

-8.7 -12.9 -3.5 -16.7 -11.8

95 95 35 35 137 95 c

b b 301-400 K 323 K 548-648 K d d

-16.5 -14.0 -10.4 -12.0 -11.0 -13.9 -10.1

-2.6 -22.0 -10.3 -10.0 -2.8 -16.9 -15.3

-6.9 -8.2 -10.3 -12.2 -10.3

-5.7 -5.3 -6.2 -2.8 -18.2

ref.

type

C range

Si/AlF

H-FAU QM-Pot(MP2//B3LYP)

40

sim

C4-C12

95

b

H-BEA QM-Pot(MP2//B3LYP) Denayer et al.

16

sim exp

C2-C8 C5-C9

63 12

H-MOR QM-Pot(MP2//B3LYP) Eder et al. Denayer et al. Dixit and Rao Pantu et al.

18 16 32 38

sim exp exp sim sim

C2-C8 C3-C6 C5-C9 C1-C8 C2-C4

18 17 26 32

sim sim exp exp exp sim sim

C2-C8 C2-C8 C3-C6 C3-C8 C5-C8 C1-C8 C1-C8

H-ZSM-5 QM-Pot(MP2//B3LYP) SC+I QM-Pot(MP2//B3LYP) ZC+I this work Eder et al. Denayer et al. Titiloye et al. Dixit and Rao H-FAU H-BEA H-MOR H-ZSM-5 (SC+I) H-ZSM-5 (ZC+I)

T

QM-Pot(MP2//B3LYP) Results Considering Only O-C/H Lennard-Jones Potentialse sim C4-C12 95 b sim C2-C8 63 b sim C2-C8 95 b sim C2-C8 95 b sim C2-C8 95 b

a In case the parameter values are not mentioned in the paper, the reported values were obtained from a linear fit based on the reported physisorption energies or enthalpies. b Parameter estimates are practically independent of the temperature. c Al atoms present in the framework, but Si/AlF not mentioned in the paper. d Temperature not mentioned in the paper. e Instead of Lennard-Jones potentials between Si/Al/O and C/ H atoms.

mentioned in the paper, a linear fit was performed. In Table 5, also the temperature, the Si/AlF ratio and the origin of the data (simulation or experiment) for each particular case are mentioned. Only adsorption data obtained on acidic zeolites are discussed here. An extensive comparison between the QM-Pot(MP2//B3LYP) results and literature data for adsorption of n-alkanes in H-FAU can be found elsewhere.40 For the parameter R, a good agreement with the experimentally reported value is observed for H-BEA. For H-MOR and H-ZSM-5 our estimated values, respectively -13.8 and -14.0 (ZC+I) to -16.5 (SC+I) kJ mol-1, are significantly more negative than the values obtained from experiment or molecular simulation: in H-MOR and H-ZSM-5 the reported values of R range from -9.3 to -11.1 kJ mol-1 and from -10.1 to -12.0 kJ mol-1. Since the adsorption studies on H-ZSM-5 zeolites mentioned in literature comprise in most cases experimental work or Monte Carlo type of simulations, the obtained linear relations do not correspond to adsorption at SC+I or ZC+I, but rather to an average of the different absorption modes. For H-BEA, the parameter β corresponds relatively well to the

experimentally obtained value reported by Denayer et al.; a difference of less than 5 kJ mol-1 is observed. For H-MOR, values of β reported in literature range from -3.5 to -16.7 kJ mol-1 while for H-ZSM-5 the reported values range from -2.8 to -16.9 kJ mol-1. Our value for β nicely falls within the literature range for H-MOR and H-ZSM-5 (SC+I), whereas the H-ZSM-5 (ZC+I) value falls outside the range. The scatter on the R and β parameters reported in literature is striking. Taking into account the temperature independence of the adsorption enthalpies (see supra), small variations for the values R and β would be expected for the various adsorption studies on the respective zeolites. Apparently, significantly different linear correlations between the adsorption enthalpy and the carbon number are obtained depending on the method used to obtain the adsorption enthalpies. This probably originates from the strong correlation between the parameters R and β; a small variation of R induces a much larger variation of β. Figure 6, panels a and b, shows the adsorption enthalpy range as obtained from the reported linear relations in literature (see Table 5) together with our simulation results in H-MOR and H-ZSM-5

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Figure 6. Adsorption enthalpy range as obtained from literature data (shaded part, see Table 5) vs QM-Pot(MP2//B3LYP) results in H-MOR and H-ZSM-5, respectively obtained (1) by applying Lennard-Jones (LJ) potentials between Si/Al/O and C/H ((a) H-MOR and (b) H-ZSM-5) and (2) by applying Lennard-Jones (LJ) potentials between O and C/H ((c) H-MOR and (d) H-ZSM-5).

zeolites. This shows on the one hand that the difference between minimum and maximum adsorption enthalpies from literature data can become quite large, up to 37 kJ mol-1 for n-octane adsorption in H-ZSM-5. In H-MOR, the observed scatter on the literature data is much smaller as the maximum difference amounts to 13 kJ mol-1 for n-octane adsorption. On the other hand, Figure 6 illustrates that, even accounting for the large scatter on the experimental and molecular simulation data reported in literature, the QM-Pot(MP2//B3LYP) method generally overestimates adsorption strengths in H-MOR and H-ZSM-5, or at least overestimates the slope describing the increase of the adsorption strength with increasing carbon number. Thus, the obtained values for R from QM-Pot(MP2// B3LYP) are more negative than most values reported in the literature (see Table 5), indicating that the calculated adsorption strength is overestimated by some 2 kJ mol-1/CH2 in FAU up to some 4 kJ mol-1/CH2 in H-ZSM-5. Since the increase of the adsorbate stability with increasing carbon number is entirely attributed to the stabilizing van der Waals interactions, this

seems to suggest that the Lennard-Jones potentials implemented in the force field overestimate the van der Waals stabilizing effect. This was also observed for n-alkane adsorption in H-FAU,40 although less pronounced compared to H-ZSM-5. In contrast however to H-MOR and H-ZSM-5, a much better agreement between simulation and experiment is observed for n-alkane adsorption in H-BEA (see Table 5). Also, a good agreement between the QM-Pot(MP2//B3LYP) and the MP2: PBE method had been observed for isobutene adsorption complexes in H-FER,40 the latter being an extremely high-level method.37,52 To evaluate the contribution of the van der Waals stabilization as obtained from the different Lennard-Jones potentials in the QM-Pot force field to the adsorbate stability, some additional calculations have been performed. In our calculations, interactions between Si/Al/O zeolite atoms on the one hand and C/H hydrocarbon atoms on the other hand have been considered.39 Clark et al. however considered Lennard-Jones potentials between the C/H hydrocarbon atoms and the zeolite O atoms

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Figure 7. Adsorption entropies at 300 K of the various n-alkanes as function of the carbon number in zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5 (SC+I and ZC+I) as obtained from the combined QM-Pot(MP2//B3LYP) statistical thermodynamics method.

only.53,54 Therefore, adsorption enthalpies have been calculated and linear relationships describing the adsorption enthalpy as a function of the carbon number in H-FAU, H-BEA, H-MOR, and H-ZSM-5 have been obtained from single-point force field calculations only considering Lennard-Jones potentials between the zeolite O atoms and the H/C hydrocarbon atoms. Further details can be found in the Supporting Information. Table 5 (bottom) shows the resulting values for the “corrected” parameters R and β describing the increase of the adsorption strength with increasing carbon number. It is noticed that, as expected, mainly the parameter R is influenced by removing the Si/ Al-C/H Lennard-Jones contributions from the adsorption enthalpy while the parameter β is much less influenced. Removing the Si/Al-C/H Lennard-Jones contributions clearly results in a much better agreement with the R values reported in literature for H-FAU,40 H-MOR, and H-ZSM-5 (SC+I and ZC+I). For H-BEA, on the other hand, the agreement with experiment becomes somewhat less good; the adsorption strength seems to be slightly underestimated. Figure 6, panels c and d, shows the adsorption enthalpy range from literature results (see Table 5) together with the simulation results in H-MOR and H-ZSM-5 zeolites obtained by removing the Si/ Al-C/H Lennard-Jones contributions. For both zeolites, simulation results now nicely fall within the range reported in literature. We conclude that, in general, a better agreement with literature data is obtained if Lennard-Jones potentials are only considered to act between the O zeolite atoms and the H/C hydrocarbon atoms. 3.2.3. Adsorption Entropy. In the next paragraphs, the QM-Pot(MP2//B3LYP) adsorption entropies for the adsorption of the various n-alkanes in the different zeolites are discussed. This comprises the discussion about the influence of the zeolite framework, the temperature and the carbon number, as well as

the comparison with the available data in the literature. The actual values of the adsorption entropies for all n-alkanes in the different zeolites can be found in the Supporting Information. Influence of Zeolite Framework. Figure 7 shows the adsorption entropies at 300 K as function of the carbon number in H-FAU, H-BEA, H-MOR, H-ZSM-5 (SC+I), and H-ZSM-5 (ZC+I). The loss of entropy increases in the order H-FAU < H-BEA < H-MOR < H-ZSM-5 (SC+I) < H-ZSM-5 (ZC+I). This corresponds to the ordering for the adsorption strength: stronger adsorption leads to a higher entropy loss. As mentioned earlier for the adsorption enthalpy, this order relates to the available space inside the zeolites pores or channels. Smaller pores obviously lead to more tightly bonded adsorption complexes and as such lead to higher entropy losses. This was also concluded by Denayer et al.16,17 Adsorption in H-ZSM-5 (ZC+I) leads to higher entropy losses compared to adsorption in H-ZSM-5 (SC+I) for n-alkanes from C4 onward, whereas ethane and n-propane adsorption entropies are similar in SC+I and ZC+I. Influence of Temperature. The adsorption entropies have been calculated for the temperature range 300-800 K. The variation of the adsorption entropy as a function of temperature is very small: in the industrially most relevant temperature range, 300-800 K, minimal variations of the adsorption entropy are observed as compared to the adsorption entropy obtained at 300 K, i.e., variations from -0.5 to +4.0 J mol-1 K-1. As such, it can be concluded that the adsorption entropy is virtually independent of the temperature, similar to the adsorption enthalpies. This is further discussed in the Supporting Information. Influence of Carbon Number. As for the adsorption enthalpies, parameters describing the linear relation between the adsorption entropy and the carbon number have been estimated for all zeolites

∆Sads ) γCN + δ

(10)

Table 6 shows the obtained values for the parameters γ and δ, together with their standard deviation, the correlation coefficient (R2), the mean deviation (MD), and the mean absolute deviation (MAD). Reasonable to good fits are obtained in all zeolites with a correlation coefficient higher than 0.9 in all zeolites. The largest mean absolute deviation is observed for H-ZSM-5 (ZC+I) with a value of 3.8 J mol-1 K-1, which is reasonable. The linear fits are also indicated in Figure 7, illustrating the increasing entropy loss with increasing carbon number. The corresponding increasing adsorption strength as discussed above, is known as a compensation effect since the adsorption enthalpy and the adsorption entropy have an opposite effect on the Gibbs free energy; this has been observed by many authors.16,18,19,55-58 Figure 8 shows this compensation relation

TABLE 6: Parameters γ and δ, Describing the Linear Relation between the Adsorption Entropy and the Carbon Number, Their Standard Deviation (in parentheses), the Correlation Coefficient (R2), the Mean Deviation (MD), and the Mean Absolute Deviation (MAD) for the Adsorption of n-Alkanes in H-FAU, H-BEA, H-MOR, H-ZSM-5 (SC+I), and H-ZSM-5 (ZC+I) γ a

H-FAU H-EA H-OR H-ZSM-5 SC+I ZC+I a

δ

R2

MD

MAD -6

-4.0 ((0.3) -5.9 ((0.5) -6.2 ((0.6)

-56.5 ((4.0) -53.6 ((2.8) -61.6 ((3.4)

0.9285 0.9601 0.9467

-3.3 × 10 7.1 × 10-7 1.4 × 10-6

2.4 2.1 2.5

-5.8 ((0.8) -8.7 ((1.0)

-78.8 ((4.2) -70.6 ((5.4)

0.9082 0.9340

-2.4 × 10-6 -2.9 × 10-6

3.0 3.8

Taken from De Moor et al.40

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Figure 8. Adsorption enthalpy as function of adsorption entropy showing the compensation effect between both thermodynamic quantities: (a) experimental results for H-FAU and H-MOR by Eder et al.18 and for H-ZSM-5 as presented in this work; (b) simulation results for H-FAU, H-BEA, H-MOR, and H-ZSM-5 SC+I and ZC+I as presented in this work. Trendlines for the large pore (full line) and the medium pore (dashed line) zeolites are shown.

for (a) the experimental results for n-alkane adsorption in H-FAU and H-MOR reported by Eder et al.18 and those in H-ZSM-5 presented in this work and (b) the QM-Pot(MP2// B3LYP) simulation results considering Lennard-Jones potentials between the C/H hydrocarbon atoms and the zeolite O atoms only. Figure 8, panels a and b, shows that the entropy loss is disproportionally stronger for the medium pore zeolite H-ZSM-5 compared to the large pore zeolites H-FAU, H-BEA and H-MOR. This higher entropy loss in H-ZSM-5 seems to indicate that adsorption of the n-alkanes in the more confined channels of H-ZSM-5 is accompanied by a loss in configurational entropy of the adsorbed molecule.18 In eq 10, γ reflects the change of the adsorption entropy when adding an additional -CH2- group and amounts to -4.0, -5.9, -6.2, -5.8, and -8.7 J mol-1 K-1 in H-FAU, H-BEA, H-MOR, H-ZSM-5 (SC+I), and H-ZSM-5 (ZC+I), respectively. In general, denser frameworks with smaller pore systems lead to a more pronounced increase of the entropy losses with increasing carbon number. Comparison with Literature Data. In the literature, few authors report experimentally determined adsorption entropies of linear alkanes in zeolites. Contrary to adsorption enthalpies, adsorption entropies cannot be directly measured; in stead, they are derived or calculated from other quantities such as the Langmuir coefficient or the Henry coefficient. This however requires choosing an adequate standard state for the gas phase hydrocarbon and the adsorption complex. Next to the fact that the choice of these standard states is not always unambiguously defined, caution is also required when comparing adsorption entropies since a different choice of standard states obviously leads to noncomparable adsorption entropies. Savary et al. pointed out the best, most logical, choice for the standard states when applying the Langmuir adsorption model.41 For the gas phase, the IUPAC recommendation is best followed, i.e., p0 ) 105 Pa; for the adsorption complex, no IUPAC recommended standard state value is available, but the authors concluded that for the Langmuir adsorption model half coverage (θ0 ) 0.5) is the best option because of the cancellation of the standard states for the adsorption complex and the unloaded zeolite in the Langmuir expressions. In order to be able to compare experimental results of Denayer et al.16,17 to other literature data, it was necessary to revise the calculation of the adsorption entropies from the Henry coefficients. This is discussed in more detail in the Supporting Information.

Figure 9 shows the variation of the calculated adsorption entropy as function of the n-alkane carbon number in H-FAU, H-BEA, H-MOR, and H-ZSM-5, together with the revised experimental data of Denayer et al.,16,17 the experimental data of Eder et al.18 and the experimental results in H-ZSM-5 presented in this work. For H-FAU, the simulated adsorption entropies fall within the range spanned by the revised results of Denayer et al. for various Y-zeolites.16,17 The values reported by Eder et al.18 appear to be some 10-15 J mol-1 K-1 more negative. The deviation seems to be related to a systematic shift in the reported enthalpy values stemming from differences in the calibration of the calorimeter. In H-BEA, our calculated adsorption entropies agree well with the experimental values of Denayer et al, although the variation with the carbon number seems to be somewhat less pronounced. For H-MOR, a very good agreement with the experimental values of Eder et al.18 and the revised values of Denayer et al.16,17 is observed. In H-ZSM-5, both the revised adsorption entropies of Denayer et al.16,17 and the experimentally obtained adsorption entropies presented in this work agree very well with the adsorption entropies obtained from the QM-Pot(MP2//B3LYP) calculations. Zhu et al.24 have studied the adsorption of light alkanes (up to C4) in silicalite. Distinguishing between two different adsorption sites, these authors report adsorption entropies of -79.5 to -87.8, -94.9 to -103, and -113 to -126 J mol-1 K-1 for respectively ethane, propane, and n-butane. These ranges practically coincide with the ranges spanned by our results for adsorption in SC+I and ZC+I. Table 7 shows the values γ and δ obtained from the QM-Pot(MP2//B3LYP) calculations, together with values reported by Denayer et al.,16,17 Eder et al.,18 and the experimentally obtained values reported in this work. A linear fit has been performed, in case only adsorption entropies are reported. The comparison for H-FAU is explicitly mentioned here since adsorption entropies of Denayer et al. have been revised as explained above, contrary to the comparison made in an earlier paper.40 In H-FAU and H-MOR, a reasonable to good agreement is obtained; in H-BEA on the other hand, γ and δ values significantly differ. In H-ZSM-5, there is a reasonable agreement between the ZC+I simulation results and the experimental results presented in this work. Adsorption in SC+I leads to a γ value which is apparently too small (5.8 J mol-1 K-1) compared to the experimentally reported values (-9.6 to -13.0 J mol-1 K-1). It is however important to consider that (i) adsorption

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Figure 9. Calculated adsorption entropies at 300 K of the various n-alkanes as function of the carbon number in zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5 (SC+I and ZC+I). The experimental adsorption entropies of Eder et al.,18 Denayer et al.16,17 (revised), and the experimental adsorption entropies presented in this work are shown.

TABLE 7: Values for the Parameters γ and δ in the Zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5 as Obtained from the Linear Fits and as Found in the Literaturea ref.

type

C-range

Si/AlF

H-FAU QM-Pot(MP2//B3LYP) Eder et al. Denayer et al.c Denayer et al.c Denayer et al.c

40 18 16 16 16

sim exp exp exp exp

C4-C12 C3-C6 C5-C9 C5-C9 C5-C9

95 10 2.7 13 30

H-BEA QM-Pot(MP2//B3LYP) Denayer et al.

16

sim exp

C2-C8 C5-C9

H-MOR QM-Pot(MP2//B3LYP) Eder et al. Denayer et al.c

18 16

sim exp exp

17

sim sim exp exp

H-ZSM-5 QM-Pot(MP2//B3LYP) SC+I QM-Pot(MP2//B3LYP) ZC+I this work Denayer et al.c

T

γ

δ

b 323 K 548-648 K 548-648 K 548-648 K

-4.0 -5.3 -3.8 -4.9 -5.9

-56.5 -60.3 -48.4 -43.0 -44.8

63 12

b 548-648 K

-5.9 -8.1

-53.6 -36.0

C2-C8 C3-C6 C5-C9

95 10 5

b 323 K 548-648 K

-6.2 -6.3 -7.5

-61.6 -64.9 -49.3

C2-C8 C2-C8 C3-C6 C5-C8

95 95 35 137

b b 301-400 K 548-648 K

-5.8 -8.7 -9.6 -13.0

-78.8 -70.6 -66.2 -43.9

a In case the parameter values are not mentioned in the paper, the reported values were obtained from a linear fit based on the reported physisorption entropies. b Parameter estimates are practically independent of the temperature. c Revised adsorption entropies have been used for obtaining parameters γ and δ (see text).

entropies are not directly experimentally measured and as such, uncertainties are larger than for e.g. adsorption enthalpies and (ii) there is a strong correlation between γ and δ (more negative γ leads to more positive δ and Vice Versa). The latter explains why even with considerably different values for γ, QM-Pot(MP2// B3LYP) simulation results are in nice agreement with experimentally determined adsorption entropies in the considered carbon number range, as shown in Figure 9.

3.3. Adsorption Equilibrium Coefficients. All QM-Pot(MP2//B3LYP) adsorption equilibrium coefficients, Kads, as reported in the next sections, are calculated from the linear relations for the “corrected” adsorption enthalpies as function of the carbon number (Table 5, bottom) and the adsorption entropies as function of the carbon number at 300 K (Table 6). Experimental adsorption equilibrium coefficients are calculated from the adsorption enthalpies and entropies

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TABLE 8: ln(Kads) Values at 773 K as Calculated from our QM-Pot Simulations and from Experimental Worka experimentb

simulation ln(Kads) (773 K)

H-FAU

H-BEA

H-MOR

H-ZSM-5 (SC+I)

H-ZSM-5 (ZC+I)

C3 n-C4 n-C5 n-C6 n-C7 n-C8

-3.6 -3.0 -2.4 -1.8 -1.2

-3.9 -3.3 -2.8 -2.2 -1.6 -1.1

-3.9 -3.0 -2.1 -1.3 -0.4 0.4

-5.4 -4.2 -3.0 -1.8 -0.6 0.6

-4.0 -3.5 -2.9 -2.3 -1.8 -1.2

H-Y

-2.6 -1.7 -1.2 -0.8

H-BEA

-1.0 -0.4 0.1 0.7

H-MOR

-1.8 -0.8 -0.4 0.3

experimentc H-ZSM-5

-4.1 -4.0 -3.8 -3.7

H-FAU

H-MOR

H-ZSM-5

-4.4 -3.7 -3.3 -2.8

-3.7 -3.0 -2.4 -1.7

-4.9 -4.5 -4.4 -3.4

a Linear relations for the “corrected” (see text and Table 5) adsorption enthalpies and entropies (see Table 6) as function of the carbon number have been used for the calculation of the QM-Pot(MP2//B3LYP) equilibrium coefficients. b Experimental data taken from Denayer et al.17 As explained in the text, adsorption entropies have been revisited. c Experimental data in H-FAU and H-MOR taken from Eder et al.18 H-ZMS-5 data are taken from this work.

reported in this work (Table 2), by Denayer et al.16,17 (revised) and by Eder et al.18,19 3.3.1. Comparison with Experiment. Table 8 shows the values for ln(Kads) at 773 K as obtained from our QM-Pot(MP2// B3LYP) simulations and from experimental data. A very good agreement between simulation and experiment is observed for adsorption in H-FAU and H-MOR. In H-BEA, ln(Kads), as calculated from our simulation results, seems to be slightly underestimated, i.e., it is too negative, compared to the results of Denayer et al.16 For example, for n-octane adsorption a difference of 1.8 is observed for ln(Kads) leading to a simulated Kads that is a factor 6 too small as compared to experiment. In the case of H-ZSM-5 on the other hand, a relatively good agreement between simulation and experiment is observed for propane and n-butane, while from n-pentane onward the ln(Kads) value is overestimated as compared to the experimental results. Obviously, discrepancies between simulation and experiment for the adsorption equilibrium coefficient are a result of differences between experimental and calculated adsorption enthalpies and adsorption entropies. E.g., a difference of 10 kJ mol-1 on the adsorption enthalpies leads to a difference of a factor of 5 for Kads at 773 K, whereas a difference of 10 J mol-1 K-1 on the adsorption entropy yields a difference of a factor of 3 for Kads. Table 8 also shows that both simulation and experiment indicate that, at a temperature of 773 K, adsorption of longer n-alkanes is favored in all of the zeolites, i.e., more negative values for ln(Kads) are found for shorter n-alkanes. Figure 10 shows the van t’Hoff plot for the adsorption of n-hexane in the zeolites H-FAU, H-BEA, H-MOR, and H-ZSM5. The QM-Pot(MP2//B3LYP) equilibrium coefficients Kads are indicated by the lines, whereas experimental results are shown by the empty symbols. First of all, the agreement between the different experimental results is striking; although obtained from different hydrocarbon ranges at different temperatures and using different methods, the available experimental data provide a coherent set of data. Also, the calculated equilibrium coefficients correspond rather well with the experimental data for all zeolites. The calculated adsorption equilibrium coefficients are slightly underestimated in H-BEA and slightly overestimated for H-ZSM-5, in agreement with the results reported in Table 8. For H-FAU and H-MOR, our simulation results practically coincide with the experimental data available in literature. 3.3.2. Influence of Carbon Number. In the introduction we have highlighted the influence of the carbon number on the monomolecular cracking rate of n-alkanes in H-ZSM-5. At a temperature relevant for this reaction, 773 K, higher cracking rates are observed for longer n-alkanes. The extent to which the adsorption equilibrium coefficient as well as the intrinsic rate constant contribute to the observed cracking rate is however

subject of debate (see eqs 1 and 2).5-13 Considering eq 1, it can be expected that, if the adsorption equilibrium would explain the observed differences in cracking rates, a 2-fold increase in the cracking rate would result from a doubling of the adsorption equilibrium coefficient. Therefore, Table 9 shows a comparison between relative turnover frequencies (TOF)6 and the relative adsorption equilibrium coefficients (Kads), both expressed relative to the value for n-propane. Equilibrium coefficients have been calculated from experimental data available in literature,17 from experimental data presented in this work and from our QM-Pot(MP2//B3LYP) results for adsorption in SC+I and ZC+I of H-ZSM-5. From Table 9 it can be seen that the TOF for monomolecular cracking exponentially increases with increasing carbon number: the TOF for n-hexane cracking is 46 times the TOF for cracking of propane. However, for the relative equilibrium coefficients for adsorption, a modest increase with increasing carbon number is observed from the experimental data presented in this paper, from the revised experimental results of Denayer et al.17 and from the QMPot(MP2//B3LYP) results for adsorption in ZC+I. The good agreement between the simulation results and the experimental results presented in this paper is striking. The simulated data for H-ZSM-5 (SC+I) indicate a somewhat faster increase of the relative equilibrium coefficient, in agreement with the data in Table 8 and as discussed in the previous section. Clearly, our simulation results indicate, that, in agreement with the experimental observations, the variation of the adsorption equilibrium coefficient, Kads, which determines the prevalent concentration of the adsorbed alkanes within the zeolite channels, only partly explains the observed increase of the monomolecular cracking rate and clearly indicates that the increase in cracking reactivity with carbon number mainly orginates from differences in the intrinsic kinetics as suggested by Bhan et al.11 Since Narbeshuber et al. have shown that intrinsic activation barriers are independent of the n-alkane carbon number,6 the variation of the intrinsic rate constant should relate to the preexponential factor and as such to a variation of the activation entropy with the carbon number.11 3.3.3. Influence of Zeolite Framework. In the introduction the influence of the zeolite framework on the monomolecular cracking of n-alkanes has been discussed. Various authors agree that the activation barriers for monomolecular cracking of n-alkanes are similar for different zeolite frameworks.7-10,12 The role of the pre-exponential factor, and as such of the activation entropy, however also plays an important role as pointed out by Gounder and Iglesia.12,13 To evaluate the contribution of the adsorption equilibrium coefficient to the n-alkane cracking reactivity in the four zeolites, relative TOF’s at 773 K for n-propane and n-hexane cracking

Adsorption of C2-C8 n-Alkanes

J. Phys. Chem. C, Vol. 115, No. 4, 2011 1217

Figure 10. van’t Hoff plot for the adsorption of n-hexane in the zeolites H-FAU, H-BEA, H-MOR, and H-ZSM-5. QM-Pot(MP2//B3LYP) simulated results are indicated by the lines. Experimental results are indicated by the empty symbols and are taken from Eder et al.,18 Denayer et al.16,17 (revised), or this work.

TABLE 9: Comparison of the Relative Turnover Frequencies (TOF) with the Relative Adsorption Equilibrium Coefficients at 773 K for C3-C6 n-Alkanes in H-ZSM-5a Kads(n-Ci)/Kads(C3)

C3 n-C4 n-C5 n-C6

TOF (n-Ci)/ TOF (C3)b

exp.c

exp.d

sim. (SC+I)

sim. (ZC+I)

1.0 4.4 17.0 45.8

1.0 1.6 1.6 4.6

1.0 1.2 1.3 1.5

1.0 3.4 11.2 37.7

1.0 1.7 3.0 5.3

a Both are expressed with regard to the TOF or adsorption equilibrium coefficient of propane. Linear relations for the “corrected” (see text and Table 5) adsorption enthalpies and entropies (see Table 6) as function of the carbon number have been used for the calculation of the QM-Pot(MP2//B3LYP) equilibrium coefficients. b Taken from Narbeshuber et al.,6 after correction for number of C-C bonds in each molecule. c Experimental data for adsorption of n-alkanes in H-ZSM-5 from this work. d Experimental data taken from Denayer et al.17 As explained in the text, adsorption entropies have been revisited.

in the four zeolites reported in literature7,10,12 are compared with relative equilibrium coefficients at 773 K from the literature16-18 and from this work, taking H-ZSM-5 as a reference. Also relative adsorption equilibrium coefficients for propane and n-hexane as obtained from our simulations are calculated. Both

adsorption in SC+I as ZC+I have been considered as reference. All data are summarized in Table 10. Clearly, higher monomolecular cracking rates are observed for zeolites with smaller pores; the highest rates are observed in H-ZSM-5, the lowest in H-FAU. In contrast, experimental adsorption studies suggest higher values for the equilibrium coefficients in H-FAU, H-BEA, and H-MOR compared to H-ZSM-5; this implies higher concentration of the n-alkanes inside the zeolite pores in the former zeolites compared to H-ZSM-5, which in its turn, should lead to higher cracking rates, if intrinsic kinetics would not be influenced by the zeolite framework topology. Also, the Kads(Hzeoi)/Kads(H-ZSM-5) values for propane and n-hexane as obtained from our simulations, indicate that variations in adsorption equilibrium coefficients cannot explain the observed variations in the experimentally determined cracking rates. This comparison shows that intrinsic kinetics do differ in the various zeolites: if activation barriers are similar in different zeolites, as independently concluded in many studies,7-10,12 it can be concluded that the activation entropy plays a significant role in understanding variations in monomolecular cracking rates as suggested by Gounder and Iglesia.12,13 4. Conclusions Adsorption of n-alkanes in H-FAU, H-BEA, H-MOR, and H-ZSM-5 has been studied using QM-Pot(MP2//B3LYP)

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Moor et al.

TABLE 10: Comparison of the Relative Turnover Frequencies (TOF) with the Relative Adsorption Equilibrium Coefficients at 773 K for C3 and C6 n-Alkanes in H-FAU, H-BEA, H-MOR, and H-ZSM-5a TOF(H-zeoi)/TOF(H-ZSM-5) C3 zeolite framework

exp.b

H-FAU H-BEA H-MOR H-ZSM-5

0.006 0.292 0.436 1

Kads(H-zeoi)/Kads(H-ZSM-5)

n-C6 exp.c

0.650 1

C3

n-C6

exp.d

exp.e

exp.f

sim.g

sim.h

exp.e

exp.f

sim.g

sim.h

0.135

1.752 3.289 1

3.496 4.479 4.695 1

0.941 1.156 2.903 1

1.743

0.475 1

2.673 8.736 3.399 1

9.590 34.542 24.295 1

0.536 0.658 1.653 1

0.858 1.099 1.152 1

5.733 1

a

both are expressed with regard to the TOF or adsorption equilibrium coefficient in H-ZSM-5. Linear relations for the “corrected” (see text and Table 5) adsorption enthalpies and entropies (see Table 6) as function of the carbon number have been used for the calculation of the QM-Pot(MP2//B3LYP) equilibrium coefficients. b Xu et al.:10 relative TOF obtained for monomolecular cracking of propane. Si/Al ratios of 2.6, 10.5, 16.7, and 39 for H-FAU, H-BEA, H-MOR, and H-ZSM-5. c Gounder and Iglesia:12 relative TOF obtained for monomolecular cracking of propane. Si/Al ratios of 10.1 and 19 for H-MOR and H-ZSM-5. d Babitz et al.:7 relative TOF obtained for monomolecular cracking of n-hexane. Si/Al ratios of 2.9, 17.5, and 25 for H-FAU, H-MOR, and H-ZSM-5. e Eder et al.18 (H-FAU and H-MOR) and this work (H-ZSM-5): Si/Al ratios of 2.7, 10, and 35 for H-FAU, H-MOR, and H-ZMS-5. f Denayer et al.:16,17 Si/Al ratios of 2.7, 12, 5, and 137 for H-FAU, H-BEA, H-MOR, and H-ZSM-5. g H-ZSM-5 (SC+I) taken as reference. h H-ZSM-5 (ZC+I) taken as reference.

calculations in combination with statistical thermodynamics and assuming a mobile adsorbate in the zeolite. Calculated adsorption enthalpies and entropies are compared with available experimental and molecular simulation data in literature. In addition, experimental data for the adsorption of n-alkanes in H-ZSM-5 are presented. Adsorption enthalpies are independent of the temperature and practically equal to the adsorption electronic energies. The QM-Pot(MP2//B3LYP) method describes the well-known change of the adsorption enthalpy as function of the carbon number, entirely resulting from van der Waals stabilizing interactions. The adsorption strength of the n-alkanes increases as follows for the various zeolites: H-FAU < H-BEA < H-MOR < H-ZSM-5 (SC+I) < H-ZSM-5 (ZC+I), according to the decreasing dimensions of the pores and channels of the respective zeolites. Linear fits describe the increase of the adsorption strength with the carbon number in the studied zeolites. The slope R is almost entirely determined by van der Waals interactions and is in general more negative for more confined zeolites. The intercept β reflects the strength of the polarization interaction between the acid proton and the n-alkane and generally amounts to a value between -2 and -10 kJ mol-1, in good agreement with literature. Subtle variations are can be attributed to differences in acid strength, which mainly depends on the zeolite Al content, rather than to differences in the zeolite framework. The overestimation of the adsorption enthalpy in most zeolites suggests that van der Waals stabilizing interactions are overestimated. Applying a Lennard-Jones potential in the force field calculation between O zeolite atoms and C/H hydrocarbon atoms, instead of between O/Si/Al zeolite atoms and C/H hydrocarbon atoms leads to a significantly better agreement with literature data. Adsorption entropies have been obtained in the industrially relevant temperature range 300-800 K. As the adsorption enthalpies, adsorption entropies are independent of the temperature, regarding the maximum deviations ranging from -0.5 to +4 J mol-1 K-1 (in the temperature range 300-800 K) with regard to the adsorption entropy at 300 K. The entropy losses upon adsorption of n-alkanes increases as follows for the various zeolites: H-FAU < H-BEA < H-MOR < H-ZSM-5 (SC+I) < H-ZSM-5 (ZC+I). This order is the same as for the adsorption strength: stronger adsorption leads to tighter bonded complexes and as such higher entropy losses. With decreasing pore diameter of the zeolite however, configurational entropy losses of the adsorbed molecule come into play. Within the various zeolites

the adsorption entropy linearly decreases with increasing n-alkane carbon number. The inverse effect of adsorption enthalpy and adsorption entropy on Gibbs free energies is known as a compensation effect. Adsorption entropies nicely correspond to available experimental data for all zeolites, when applying the Langmuir adsorption model for the calculation of adsorption entropies from experimentally determined Henry coefficients or adsorption isotherms. The QM-Pot(MP2//B3LYP) method predicts the adsorption equilibrium coefficients in de various zeolites reasonably well as shown in the van’t Hoff plots for adsorption of n-hexane. Comparison of relative turnover frequencies for monomolecular cracking of n-alkanes taken from literature with relative adsorption equilibrium coefficients calculated from experiment and simulation, indicates that changes of the monomolecular cracking rate with changing n-alkane carbon number and with changing zeolite topology cannot (only) be attributed to changes in the adsorption equilibrium coefficients. As a consequence we can conclude that intrinsic kinetics, and more specifically intrinsic pre-exponential factors which depend on the activation entropy, play an important role for understanding variations in observed monomolecular cracking rates. This work clearly shows that the QM-Pot(MP2//B3LYP) method is a very useful tool for the simulation of n-alkene adsorption in industrially applied zeolites. Contrary to n-alkanes, experimental data for n-alkene adsorption are much less available because of their high reactivity even at relatively low temperatures. Also, classical molecular simulations often lack a potential describing the nonbonding interaction between the alkene double bond and the acid proton, i.e., the π-complex interaction. As such, the QM-Pot(MP2//B3LYP) method offers a good compromise between computational cost and accuracy since the π-complex interaction is properly described at the ab initio level (MP2//B3LYP), while the long-range interactions are described via Lennard-Jones potentials in the force-field. Acknowledgment. This work is supported by the Long Term Structural Methusalem Funding by the Flemish Government Grant No. BOF09/01M00409, the FWO (Fund for Scientific Research Flanders), the BELSPO (Belgian Federal Science Policy Office), and by the E.C. (Network of Excellence IDECAT, NMP3-CT-2005-011730). Supporting Information Available: The Langmuir adsorption isotherm model, and the experimental determination of the

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