ARTICLE pubs.acs.org/JPCC
Physisorption and Chemisorption of Linear Alkenes in Zeolites: A Combined QM-Pot(MP2//B3LYP:GULP)Statistical Thermodynamics Study Cuong M. Nguyen, Bart A. De Moor, Marie-Franc-oise Reyniers,* and Guy B. Marin Laboratory for Chemical Technology, Ghent University, Krijgslaan 281 S5, B-9000 Gent, Belgium
bS Supporting Information ABSTRACT: Physisorption and chemisorption of C2C8 linear alkenes in HFAU, HBEA, HMOR, and HZSM-5 have been quantified up to 800 K by combining QM-Pot(MP2//B3LYP:GULP) with statistical thermodynamics calculations. The influence of the zeolite topology and the alkene CC double bond position on the alkene sorption thermodynamics is addressed on the basis of linear variations of sorption enthalpies and entropies as a function of the carbon number. The physisorption strength and entropy losses increase in the order HFAU < HBEA < HMOR < HZSM-5. Higher physisorption strength is computed for 2-alkenes (HMOR) and 2-, 3-, and 4-alkenes (HZSM-5) as compared with 1-alkenes. Protonation of physisorbed alkenes leads to significantly more stable alkoxides. In contrast to the physisorption, higher chemisorption strength does not lead to larger chemisorption entropy losses. Also, the intrinsic stability of the alkoxides, i.e., relative to gas phase H2 and graphite, only depends on the carbon number and not on the detailed alkoxide structure in HFAU, HBEA, and HMOR. In the narrower pores of HZSM-5, the 3- and 4-alkoxides are however more stable than the 2-alkoxides.
1. INTRODUCTION Zeolites are frequently used in the petrochemical industry as acid catalysts for hydrocarbon conversion processes such as fluid catalytic cracking, hydrocracking, alkylation of aromatics, and aromatics conversion.14 In many of these processes, alkenes are involved as reaction intermediates or are formed as products. In hydrocracking, heavy oil fractions are converted into more valuable lighter fractions, such as diesel and kerosene.5 The zeolites used for hydrocracking are bifunctional, containing metal sites for the dehydrogenation/hydrogenation function next to the acid sites. In this process, alkanes are dehydrogenated on metal sites to alkenes which then undergo further reaction on the acid sites of the zeolite.6,7 In catalytic cracking, heavy feeds including vacuum gas oils and residues are converted to lower molecular weight hydrocarbons, such as diesel, gasoline, and light olefins. In this process, CC bonds are broken at the acid sites of the zeolite catalysts. Whereas a wealth of experimental work on the adsorption thermodynamics of alkanes in various zeolites has been reported, this is not the case for alkenes. Due to their high reactivity even at relatively low temperatures, alkenes rapidly undergo isomerization, oligomerization, or other reactions, making it difficult to extract reproducible data from experiments. Therefore, theoretical simulations are indispensable for gaining insight into the adsorption of alkenes in zeolites. Physisorption of an alkene in acid zeolites is characterized by the formation of a π-complex, i.e., the interaction between the acid proton and the π-electrons of the CC double bond. Protonation of physisorbed alkenes leads to r 2011 American Chemical Society
the formation of alkoxides that are characterized by a CO alkoxy bond. Monte Carlo or molecular dynamics simulations have successfully been applied to explore the sorption of alkanes in zeolites, ranging from the calculation of sorption thermodynamics to the study of the diffusion of hydrocarbons and shape selectivity.815 These methods typically use force fields or interatomic potentials to describe intra- and intermolecular interactions. However, potentials for accurately describing specific interactions in the alkene sorption, such as the π-complex (physisorption) or CO alkoxy bond (chemisorption) formation, are not available. Therefore, quantum chemical and/or hybrid quantum mechanics/molecular mechanics (QM/MM) methods are especially interesting to study the sorption of alkenes in zeolites as these methods are fully capable of describing this type of interaction.1624 In this work, hybrid quantum mechanicsinteratomic potential function periodic calculations QM-Pot(MP2//B3LYP: GULP) developed by Sauer and co-workers25,26 have been performed to study physisorption and chemisorption of various linear alkenes, i.e., C2C8 1-alkenes, C4C8 2-alkenes, 3-hexene, 3-octene, and 4-octene, in HFAU,16 HBEA, HMOR, and HZSM-5. A small cluster that is treated at the quantum mechanical level for the proper description of bond breaking and Received: July 15, 2011 Revised: September 22, 2011 Published: September 29, 2011 23831
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bond formation is embedded in a zeolite unit cell described by a zeolite force field that has recently been extended with potentials describing carboncarbon, carbonhydrogen, and carbon oxygen bonds.17 For all structures, harmonic frequency calculations have been performed and statistical thermodynamics has been used to calculate physisorption/chemisorption enthalpies and entropies. The influences of the carbon number, the position of the CC double bond, and the zeolite topology on physisorption/ chemisorption enthalpy and entropy are investigated. A compensation effect between the physisorption enthalpy and entropy on the physisorption equilibrium coefficient at relevant industrial temperatures is highlighted. Thermodynamic data obtained in this work using the combined QM-Pot(MP2// B3LYP:GULP)statistical thermodynamics method can be used as input in microkinetic modeling of hydrocarbon conversion processes, e.g., hydrocracking or catalytic cracking in zeolites,27,28 where the sorption thermodynamics of alkenes in zeolites is not amenable to experimental measurements.
have been studied. Initial zeolite structures have been taken from the International Zeolite Association (IZA) Web site.29,30 All unit cells, i.e., HFAU (HAlSi95O192), HBEA (HAlSi63O128), HMOR (HAlSi95O192), and HZSM-5 (HAlSi95O192), have been optimized using a GULP constant pressure optimization applying the shell-model ion-pair potential zeolite force field.31 Detailed information on optimized unit cell parameters and proton affinities of all four zeolites was presented in an earlier work.32 2.2. QM-Pot(MP2//B3LYP:GULP) Method. Alkene sorption inside the zeolite pores has been optimized using the QM-Pot approach, using periodic boundary conditions and accounting for the entire zeolite structure. Calculations are performed with the QMPOT program,25 coupling TURBOMOLE33,34 for the QM calculations and GULP35,36 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.
2. METHODS
EQM-Pot ¼ EðSÞPot þ EðCÞQM EðCÞPot
2.1. Zeolite Models. Physisorption and chemisorption of
1-alkenes (C2C8), 2-alkenes (C4C8), 3-alkenes (C6, C8), and 4-octene in HFAU,16 HBEA, HMOR, and HZSM-5
ð1Þ
The physisorption/chemisorption energy is obtained by subtracting the QM-Pot electronic energies of the optimized gas phase sorptive and the zeolite from the electronic energy of the optimized physisorbed/chemisorbed species. QM-Pot QM-Pot ¼ EQM-Pot ΔEQM-Pot phys elec, physisorption Eelec, sorptiveðgÞ þ Eelec, zeolite
ð2Þ QM-Pot QM-Pot ΔEQM-Pot ¼ EQM-Pot chem elec, chemisorption Eelec, sorptiveðgÞ þ Eelec, zeolite
ð3Þ The protonation energy of an alkene is defined as the electronic energy difference between the chemisorbed σ-complex and the physisorbed π-complex, i.e., the reaction energy for the alkoxide formation from physisorbed alkenes. Figure 1. Definitions of the physisorption, chemisorption, and protonation energies of alkene in zeolite.
QM-Pot ¼ EQM-Pot ΔEQM-Pot prot elec, chemisorption Eelec, physisorption
ð4Þ
Table 1. Averaged Geometric Parameters (Distances in picometers and Angles in degrees) of the Linear Alkene Physisorption Complexes in HBEA, HMOR, and HZSM-5 HaCa
HaCb
CaCb
CbOb
HaOa
SiaOa
AlOa
SibOb
AlOb
SiaOaAl
SibObAl
97.8
170.8
189.4
161.4
172.9
135.4
135.4
1-alkenes 2-alkenes
225.9 238.5
230.4 220.6
134.0 134.3
353.8 345.2
99.9 100.0
170.5 170.6
188.7 188.8
162.3 162.8
173.0 173.1
133.0 132.5
135.9 136.2
3-alkenes
258.8
220.0
134.2
349.5
99.7
170.8
188.9
162.4
173.3
133.0
135.5
4-octene
260.9
232.2
134.3
337.2
99.4
170.8
189.1
160.9
173.1
132.0
136.5
97.6
170.6
190.7
160.7
171.6
129.5
140.5
1-alkenes
233.3
250.2
133.9
379.1
99.4
170.2
190.0
160.4
171.9
127.0
140.7
2-alkenes
218.6
212.6
134.3
345.0
100.2
169.8
189.3
160.5
172.4
128.1
141.4
3-alkenes
260.9
278.1
134.2
406.2
99.5
170.3
190.1
160.5
172.0
128.2
141.4
4-octene HZSM-5
357.3
386.3
133.8
523.4
97.8 97.6
170.6 171.8
190.8 190.3
160.7 161.8
171.6 172.2
128.6 134.1
140.0 146.5
1-alkenes
235.0
241.5
134.0
343.6
99.5
171.5
190.2
161.3
172.3
131.1
147.8
2-alkenes
248.8
233.7
134.2
356.3
99.5
171.4
190.3
161.3
172.4
130.9
148.8
3-alkenes
251.1
229.1
134.3
344.0
99.5
171.5
190.3
161.3
172.4
130.7
149.4
4-octene
254.4
234.5
134.2
353.4
99.3
171.5
190.2
161.3
172.3
131.1
146.4
HBEA
HMOR
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These definitions are illustrated in Figure 1. QM-Pot energies consist of a long-range (low level) MM contribution, ΔELR, and a high-level QM contribution, ΔE(C)QM (eqs 5 and 6). ΔEQM-Pot ¼ ΔELR þ ΔEðCÞQM
ð5Þ
ΔELR ¼ ΔEðSÞPot ΔEðCÞPot
ð6Þ
All optimizations of the physisorbed and chemisorbed species have been performed on a 4T cluster embedded in the zeolite unit cells of HBEA, HMOR, and HZSM-5. In HFAU, a 3T embedded cluster was used.16 Earlier work has shown that embedding of a T3 or T4 cluster is sufficient for the optimization of alkenezeolite systems.17 High level calculations on the embedded cluster are done at the B3LYP/ T(O)DZP level of theory.3740 Hydrogen link atoms lie on the broken OSi bond, and (Si)OH and (Al)OH termination distances are kept fixed at 96.66 and 96.28 pm, respectively.20 The remainder of the zeolite unit cell is modeled by interatomic potential functions, employing the DFTparametrized zeolite force field developed by Sierka and Sauer31 that has been extended with internal hydrocarbon and alkoxy bond and bond angle describing potentials.17 The van der Waals (vdW) interactions are described by LennardJones potentials acting between the zeolite Si, Al, and O atoms
Figure 2. Formation of (a) physisorption π-complex and (b) chemisorption σ-complex.
on one hand and the hydrocarbon C and H atoms on the other hand.41 After optimization, the resolution-of-the-identity (RI) approximation42 as implemented in the TURBOMOLE package has been used to obtain single point MP2 energies for the embedded 4T cluster employing Ahlrichs’s TZVP basis set.40 The level of theory for geometry optimization and energy calculation are denoted as QM-Pot(B3LYP:GULP) and QMPot(MP2//B3LYP:GULP), respectively. As pointed out recently for the physisorption of C2C8 nalkanes in HFAU, HBEA, HMOR, and HZSM-5,32 vdW stabilizing interactions are overestimated using the method described above and therefore single point corrections for all structures have been performed removing the Si/AlC/H Lennard-Jones contributions from the QM-Pot(MP2//B3LYP: GULP) energies and retaining only OC/H Lennard-Jones potentials. This was also suggested by Clark et al.43,44 For the further discussion in this work, only the corrected physisorption and chemisorption electronic (ΔEQM‑Pot,corr) energies obtained using eq 7 are presented. ΔEQM-Pot, corr
¼ ΔEQM-Pot þ ΔELR, vdw, corr ¼ ΔEQM-Pot þ ðΔELR, vdWðO C=HÞ ΔELR, vdWðSi=Al=O C=HÞ Þ
ð7Þ
where ΔELR,vdW(OC/H) and ΔELR,vdW(Si/Al/OC/H) present the vdW stabilization in the long-range MM contribution considering Lennard-Jones potentials between OC/H and Si/Al/OC/H atoms, respectively. More information on this correction can be found in the Supporting Information. Unless otherwise mentioned, the physisorption, chemisorption, and protonation energies reported in the paper are always corrected QM-Pot(MP2// B3LYP:GULP) energies and are denoted as ΔEphys, ΔEchem, and ΔEprot, respectively. 2.3. Statistical Thermodynamics. Frequency calculations have been performed for all physisorbed and chemisorbed structures. Statistical thermodynamics allows the calculation of enthalpies and entropies, and applying subtraction schemes similar to eqs 24 yields standard physisorption, chemisorption,
Figure 3. Linear alkene physisorption complexes in HBEA, HMOR, and HZSM-5. 23833
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Table 2. Total QM-Pot(MP2//B3LYP:GULP) Physisorption, Chemisorption, and Protonation Electronic Energies (kJ mol1) of the Linear Alkenes in HFAU, HBEA, HMOR and HZSM-5 HFAU π-complex f σ-complex
ΔEphys
ΔEchem
HBEA ΔEprot
ΔEphys
HMOR
ΔEchem
ΔEprot
ΔEphys
ΔEchem
HZSM-5 ΔEprot
ΔEphys
ΔEchem
ΔEprot
1-alkenes ethene f ethoxy
39
93
54
49
119
71
45
95
49
52
130
78
propene f 2-propoxy 1-butene f 2-butoxy
51 54
100 109
49 55
61 66
127 132
66 67
59 73
99 108
40 36
70 72
141 147
71 75
1-pentene f 2-pentoxy
60
116
56
70
140
70
76
120
44
84
156
71
1-hexene f 2-hexoxy
67
119
52
83
148
65
87
129
42
94
155
62
1-heptene f 2-heptoxy
71
126
55
84
155
71
88
139
51
98
158
60
1-octene f 2-octoxy
80
133
53
91
161
70
98
150
51
103
167
64
2-alkenes 2-butene f 2-butoxy
59
92
33
71
119
48
76
102
26
83
136
54
2-pentene f 3-pentoxy 2-hexene f 3-hexoxy
58 75
101 108
42 32
78 85
125 132
46 48
85 93
106 114
21 21
93 101
147 157
54 56
2-heptene f 3-heptoxy
76
111
35
82
140
58
102
123
20
110
167
57
2-octene f 3-octoxy
80
118
38
96
149
54
111
131
20
103
158
55
3/4-alkenes 3-hexene f 3-hexoxy
65
104
39
88
132
45
79
113
34
105
156
50
3-octene f 4-octoxy
77
114
37
89
145
56
85
133
38
118
175
58
4-octene f 4-octoxy
78
113
35
99
148
49
83
133
50
125
178
54
and protonation enthalpies and entropies at a pressure of 1 bar and a temperature of 298 K. The standard physisorption or chemisorption enthalpies consist of three contributions: the QM-Pot(MP2//B3LYP:GULP) energy, the zero-point vibrational energy (ZPVE), and the thermal contribution to the enthalpy, which is calculated from the total partition function and accounts for the influence of the temperature. For brevity, the standard physisorption and chemisorption enthalpies and entropies are shortly called physisorption and chemisorption enthalpies and entropies further on in the text and are denoted as ΔH0phys, ΔH0chem, ΔS0phys, and ΔS0chem. For loosely bonded physisorbed hydrocarbons, the mobile adsorbate method has been applied.16,45 This implies removing up to three frequencies corresponding to translational and/or rotational modes of the adsorbed hydrocarbon relative to the zeolite from the vibrational partition function and replacing them by a free translational or free rotational contribution (eq 8). More details on this method can be found elsewhere.16 qmobile
qvibr trans=rot ¼ immobile qnD qvibr nD
ð8Þ
Frequencies corresponding to translational or rotational modes are visualized, and if translation or rotation of the hydrocarbon in the zeolite occurs with no significant internal motions for the hydrocarbon and the zeolite, they are removed from the total partition function and replaced by free translational or rotational contributions according to eq 8. In the case of alkene physisorption in HBEA and HMOR, this results in two-dimensional free translation;with molecular surface areas of respectively 800 pm 800 pm and 200 pm 800 pm;and one-dimensional free rotation. In HZSM-5, no low frequencies corresponding to rotational modes could be identified and therefore only two-dimensional free translation with a molecular surface area of 200 pm 600 pm is considered.
Figure 4. Physisorption energies of 1-alkenes in HFAU, HBEA, HMOR, and HZSM-5 as a function of the carbon number illustrating the influence of the zeolite framework.
The values for the molecular surface area have been chosen accounting for the size of the pores and the adsorption site (e.g., channel and channel intersection). In the previous work,16 it has been shown that the sensitivity of the calculated physisorption entropies to the choice of the molecular surface area is rather limited. The influence of using the mobile adsorbate method on the physisorption enthalpies is small, while the physisorption entropies shift up by around 50 J mol1 K1 compared to the immobile adsorbate method;in which enthalpies and entropies are calculated purely based on the harmonic frequencies. For n-alkane physisorption in zeolites, excellent agreement between the combined QM-Pot(MP2//B3LYP:GULP)statistical thermodynamics approach and available experimental data is observed.16,32 The chemisorbed alkenes are characterized by the formation of a CO alkoxy bond and have no free rotational and free 23834
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translational degrees of freedom. Hence, thermodynamic quantities are calculated based on harmonic frequencies only. qimmobile ¼ qvibr immobile
ð9Þ
3. RESULTS AND DISCUSSION In this work, physisorption and chemisorption of C2C8 linear alkenes have been studied in HBEA, HMOR, and HZSM-5 zeolites. Sorption of the linear alkenes in HFAU has been discussed in an earlier work,16 but the results are Table 3. Parameters α and β, Describing the Linear Variation of the Physisorption Energy as a Function of Carbon Number, Standard Deviation (in Parentheses), Correlation Coefficient (R2), and Mean Absolute Deviation (MAD) α
β
R2
MAD
6.2((0.4)
30.3((2.7)
0.9339
2.3
6.8((0.6)
40.3((3.7)
0.8947
3.7
1-alkenes
8.3((0.8)
33.6((4.2)
0.9550
2.9
2-alkenesa
8.8((0.0)
40.8((0.3)
0.9999
0.1
8.2((0.0)
41.0((4.4)
0.9496
3.2
9.5((0.0)
45.4((4.9)
0.9684
2.0
HFAU 1/2/3/4-alkenes HBEA 1/2/3/4-alkenes HMOR
HZSM-5 1-alkenes 2/3/4-alkenesb a
Physisorption of 3-hexene, 3-octene, and 4-octene in HMOR is excluded from the fitting procedure. b Physisorption of 2-octene in HZSM-5 is excluded from the fitting procedure
included for comparison with the other zeolites. To evaluate the influence of the carbon number and the position of the double bond on the adsorption of the linear alkenes, linear relations describing the variation of adsorption energies (and by extension enthalpies) and entropies as a function of the carbon number (CN) have been fitted for the different types of linear alkenes. ΔEads ¼ αðCNÞ þ β
ð10Þ
ΔS0ads ¼ γðCNÞ þ δ
ð11Þ
where “ads” can be “phys” (physisorption) or “chem” (chemisorption). The parameters α and γ are mainly determined by the dispersive vdW interactions, while the parameters β and δ are mainly determined by local interactions with the acid site, e.g., the π-complex or the CO alkoxy bond formation. 3.1. Physisorption. 3.1.1. Geometry of Physisorption Complexes. Table 1 summarizes the most important geometric parameters of the physisorption complexes in HBEA, HMOR, and HZSM-5, averaged for the following groups: 1-alkenes, 2-alkenes, 3-alkenes, and 4-octene. Geometric parameters of all individual physisorbed alkenes in HBEA, HMOR, and HZSM-5 are listed in the Supporting Information (Tables S1S3). Figure 2 illustrates the notations used for the atoms, and Figure 3 shows some representative physisorbed alkenes inside the zeolite channels. Geometries of the physisorption complexes in HFAU are discussed elsewhere.16 Formation of the π-complex between the π-electrons of the CaCb double bond and the acid proton Ha results in insignificant changes in the structure of the linear alkenes and the geometry of
Figure 5. Physisorption energies of 1-, 2-, 3-, and 4-alkenes as a function of the carbon number in HFAU, HBEA, HMOR, and HZSM-5. Linear fits for different types of alkenes are indicated. Physisorption energies of 3- and 4-alkenes in HMOR and 2-octene in HZSM-5 are excluded from the fitting procedure. 23835
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Table 4. Physisorption, Chemisorption, and Protonation Entropies (J mol1 K1) at 300 K in HFAU, HBEA, HMOR, and HZSM-5 for the Linear Alkenes Obtained from the Combined QM-Pot(MP2//B3LYP:GULP)Statistical Thermodynamics Calculations physisorption π-complex
σ-complex
FAU
BEA
MOR
chemisorption ZSM-5
FAU
BEA
MOR
protonation ZSM-5
FAU
BEA
MOR
ZSM-5
1-alkenes ethene
ethoxy
86
90
98
106
165
158
162
165
79
68
64
59
propene
2-propoxy
96
98
103
117
187
173
181
189
91
75
78
72
1-butene
2-butoxy
96
104
112
131
198
183
185
191
102
79
73
60
1-pentene 1-hexene
2-pentoxy 2-hexoxy
107 107
103 116
110 121
130 143
206 208
177 188
181 200
202 213
99 101
74 72
71 79
72 70
1-heptene
2-heptoxy
109
119
127
151
215
197
210
230
106
78
83
79
1-octene
2-octoxy
115
118
129
150
221
207
216
229
106
89
87
79
2-alkenes 2-butene
2-butoxy
98
96
122
121
185
166
183
188
87
70
61
67
2-pentene
3-pentoxy
102
100
130
136
204
180
197
196
102
80
67
60
2-hexene
3-hexoxy
105
103
136
139
214
179
208
197
109
76
72
58
2-heptene 2-octene
3-heptoxy 3-octoxy
110 114
108 110
145 166
160 152
215 220
179 195
216 220
218 236
105 106
71 85
71 54
58 84
3/4-alkenes 3-hexene
3-hexoxy
104
105
109
145
205
179
205
216
101
74
96
71
3-octene
4-octoxy
110
112
104
171
215
188
219
220
105
76
115
49
4-octene
4-octoxy
114
115
110
149
211
178
213
211
97
63
103
62
the zeolites (see Table 1). More significant variations among the different zeolites and among the different types of linear alkenes are observed for the HaCa and HaCb distances and for the orientation of the linear alkenes in the zeolite pores. In HBEA, the HaCa distance increases from 226 to 261 pm in going from 1- to 4-alkenes, while the HaCb distance varies between 220 and 232 pm. Figure 3 shows that the HBEA pore system provides sufficient space to accommodate the alkyl chains of the linear octenes in the c direction without any steric constraint as the position of the CC double bond is shifted in the octene molecule. In HMOR, the shortest HaCa and HaCb distances of respectively 219 and 213 pm are observed for the 2-alkenes, while for the 1-alkenes slightly longer average distances of 233 and 250 pm are obtained. For 3- and 4-alkenes, much larger average HaCa and HaCb distances of 261357 and 278386 pm are observed. These differences in HaCa and HaCb distances relate to the differences in orientation of the linear alkenes in the zeolite pores, as shown in Figure 3. The 2-alkenes are physisorbed along the b direction with a methyl group pointing inside a side pocket of HMOR, as illustrated for 2-hexene and 2-octene physisorption in Figure 3. Since the acid proton is located at the crossing of the main channel and a side pocket, this arrangement enables the 2-alkenes to form tighter π-complexes. The 1-alkenes are however entirely located in the 12MR channel with the long alkyl chain oriented along the b direction for carbon numbers e6 (see 1-hexene in Figure 3) or along the c direction for carbon numbers g7 (see 1-octene in Figure 3). This orientation of the 1-alkenes leads to slightly longer HaCb distances. The 3- and 4-alkenes are oriented along the c direction, and the steric constraints imposed by the alkyl groups bonded to the CC double bond prevent a close approach of the double bond to the acid proton. Due to their different orientation, 3- and
Figure 6. Physisorption entropies of 1-alkenes in HFAU, HBEA, HMOR, and HZSM-5 as a function of the carbon number.
4-alkenes have been excluded from the parameter determination in eqs 10 and 11. In HZSM-5, the HaCa distance slightly increases from 235 to 254 pm in going from 1- to 4-alkenes while the HaCb distance varies between 242 and 229 pm. Figure 3 clearly shows different orientations for the various linear alkenes. The alkyl chain of the 1-alkenes is entirely physisorbed into the straight channel (b axis). In contrast, the shorter methyl, ethyl, or propyl chain of the 2-, 3-, and 4-alkenes tends to physisorb in the zigzag channel (a axis). Note that 2-octene deviates from this trend as it is entirely physisorbed in the straight channel. Therefore, 2-octene physisorption data have been excluded from the parameter determination in eqs 10 and 11. In the literature, HaCa and HaCb distances ranging from 214 to 236 pm have been reported for the linear alkenes physisorbed in HFAU and no influence of the position of the CC double bond 23836
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on the orientation of the linear alkenes in HFAU was observed.16 Also for other zeolites and applying other computational methods, Table 5. Parameters γ and δ, Describing the Linear Variation of the Physisorption Entropy as a Function of Carbon Number, Standard Deviation (in Parentheses), Correlation Coefficient (R2), and Mean Absolute Deviation (MAD) γ
δ
R2
MAD
1/2/3/4-alkenes HBEA
4.0((0.3)
81.5((2.0)
0.9160
1.6
1/2/3/4-alkenes
3.8((0.6)
84.5((2.6)
0.7473
3.5
1-alkenes
5.4((0.5)
87.3((2.7)
0.9569
1.8
2-alkenesa
10.3((1.5)
78.2((9.5)
0.9329
3.4
7.6((0.9)
94.5((4.7)
0.9355
3.5
10.4((1.8)
81.4((11.7)
0.8475
4.9
HFAU
HMOR
HZSM-5 1-alkenes 2/3/4-alkenesb
similar HaCa and HaCb distances from 194 to 280 pm were reported.1924 3.1.2. Physisorption Energy and Enthalpy. The physisorption energies of the linear alkenes are given in Table 2 for HFAU,16 HBEA, HMOR, and HZSM-5. The separate contributions to the total physisorption energies in HBEA, HMOR, and HZSM-5 are given in Tables S4S7 of the Supporting Information. Physisorbed alkenes are mainly stabilized by the formation of a π-complex and vdW interactions. The contribution of the latter to the total physisorption energy varies from 5070% for ethene to 7580% for octene in the various zeolites. As explained above, enthalpies consist of the electronic energy, the ZPVE, and the thermal contribution term. The contribution of latter two terms however is in all cases very small. In general, this contribution is less than 6 kJ mol1 in the temperature range 300800 K for all linear alkenes in all zeolites (Figure S1 in the Supporting Information). The physisorption enthalpies can thus be taken equal to the calculated physisorption electronic energies and can be considered independent of temperature in the range 300800 K. 0 ¼ ΔEphys ΔHphys
a
Physisorption of 3-hexene, 3-octene and 4-octene in HMOR is excluded from the fitting procedure. b Physisorption of 2-octene in HZSM-5 is excluded from the fitting procedure
ð12Þ
The same identity of physisorption enthalpy and energy was found for physisorption of alkenes in HFAU16 and
Figure 7. Physisorption entropies of 1-, 2-, 3-, and 4-alkenes as a function of the carbon number in HFAU, HBEA, HMOR, and HZSM-5. Linear fits for different types of alkenes are indicated. Physisorption entropies of 3- and 4-alkenes in HMOR and 2-octene in HZSM-5 are excluded from the fitting procedure. 23837
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Figure 8. Linear relation between the physisorption enthalpy and the physisorption entropy at 300 K of 1-alkenes (a) and the other alkenes (b) illustrating the compensation effect between both thermodynamic quantities. Physisorption of 3- and 4-alkenes in HMOR and of 2-octene in HZSM-5 is excluded from the linear fitting.
physisorption of n-alkanes in HFAU, HBEA, HMOR, and HZSM-5.32 Influence of the Zeolite Framework. Figure 4 shows the physisorption energies of the 1-alkenes as a function of the carbon number and indicates that the alkene physisorption strength increases in the order HFAU16 < HBEA < HMOR < HZSM-5. This order results from the increase in vdW stabilization with increasing zeolite framework density, i.e., with decreasing size of the zeolite pore (see ΔE(S)Pot,vdW, Tables S4S6 in the Supporting Information). Various authors reported analogous conclusions on the influence of the zeolite framework in the physisorption of n-alkanes, based on both experimental and computational studies.8,32,4651 Pantu et al. have studied alkene physisorption in HFAU and HMOR applying an ONIOM2 approach that accounts for the important vdW interactions.18 The reported physisorption energies for ethene, propene, and 1-butene amount to 38, 46, and 51 kJ mol1 in HFAU and to 42, 56, and 72 kJ mol1 in HMOR, in agreement with the QM-Pot(MP2//B3LYP: GULP) physisorption energies (see Table 2). Namuangruk et al. report ethene, 1-butene, and 2-butene physisorption energies in HZSM-5 of respectively 53, 96, and 75 kJ mol1 using ONIOM3.19 The reported physisorption energies of ethene and 2-butene are in agreement with the values obtained
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using QM-Pot(MP2//B3LYP:GULP), while the reported physisorption strength of 1-butene seems to be overestimated compared to the QM-Pot(MP2//B3LYP:GULP) value of 72 kJ mol1 (see Table 2). Influence of Carbon Number and Position of the CC Double Bond. To evaluate the influence of the CC double bond position on the physisorption, linear fits have been performed for the different types of linear alkenes and are given in Table S8 in the Supporting Information. Table 3 presents the retained parameter estimates describing the physisorption energy as a function of the carbon number for the various zeolites. Also, the parameters α and β, their standard deviations, the correlation coefficient (R2), and the mean absolute deviation (MAD) are included. For HFAU16 and HBEA, the location of the double bond has no significant influence on the physisorption energy and a single linear relation can thus be used for the physisorption of all considered linear alkenes (see Figure 5). This agrees with the similarity in geometric parameters for all linear alkenes, independent of the CC double bond position, as discussed above. The value of the parameter α amounts to 6.2 kJ mol1 in HFAU and to 6.8 kJ mol1 in HBEA, indicating that in HBEA the physisorption energy increases somewhat faster with increasing carbon number. The parameter β equals 30.3 kJ mol1 in HFAU and 40.3 kJ mol1 in HBEA, suggesting a stronger π-complex interaction in the latter zeolite. In HMOR and HZSM-5, on the other hand, the different orientation of the linear alkenes in the zeolite pores leads to a clear influence of the double bond position on the physisorption energy. In HMOR, the physisorption of the 2-alkenes is stronger than that of the 1-alkenes mainly owing to the tighter π-complex interaction of the former alkenes (see α and β, Table 3) in agreement with the observed HaCa and HaCb values. In HZSM-5, the stronger physisorption of the 2-, 3-, and 4-alkenes as compared to the 1-alkenes is attributed to both stronger vdW and π-complex interactions (see see α and β, Table 3). The more negative value of α computed for the 2-, 3-, and 4-alkenes results from the partial physisorption in the narrower zigzag channel (see section 3.1.1), resulting in a better vdW stabilization. This was also observed for n-alkane physisorption in HZSM-5.32 3.1.3. Physisorption Entropy. Physisorption entropy losses increase by up to only 4 J mol1 K1 with increasing temperature from 300 to 800 K. This small increase is practically independent of the carbon number and the zeolite framework (see Figure S2, Supporting Information). Therefore, physisorption entropies can be considered independent of temperature. Influence of the Zeolite Framework. Entropy losses upon physisorption of linear alkenes in HFAU,16 HBEA, HMOR, and HZSM-5 at 300 K are given in Table 4. Figure 6 shows the variation of the entropy loss with increasing carbon number for physisorption of the 1-alkenes and illustrates that entropy losses increase in the order HFAU < HBEA < HMOR < HZSM-5. Clearly, in narrower zeolite environments, physisorption of linear alkenes leads to higher entropy losses. This is in agreement with experimental studies reported in the literature for n-alkane physisorption in different zeolites.4649 Influence of Carbon Number and Position of the CC Double Bond. In all zeolites, entropy losses increase with increasing carbon number. In HFAU,16 HBEA, HMOR, and HZSM-5 the physisorption entropies vary from 86 to 115 J mol1 K1, from 90 to 119 J mol1 K1, from 98 to 166 J mol1 K1, and 23838
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Table 6. ln(Kphys) as a Function of Carbon Number at 300, 500, and 800 K for 1-Alkene Physisorption in HFAU, HBEA, HMOR, and HZSM-5 ln(Kphys) at 300 K a
FAU
BEA
MOR
6.3
10.5
8.4
8.3 10.3
12.7 15.0
11.1 13.8
ln(Kphys) at 500 K b
ZSM-5
a
ln(Kphys) at 800 K b
FAU
BEA
MOR
ZSM-5
FAU
9.8
0.5
1.9
0.3
0.6
4.4
12.2 14.5
0.5 1.5
3.0 4.2
1.7 3.0
1.7 2.7
3.9 3.5
MORa
ZSM-5b
3.0
4.2
4.6
2.4 1.9
3.6 3.0
4.3 3.9
BEA
1-alkenes ethene propene 1-butene 1-pentene
12.3
17.2
16.4
16.9
2.5
5.4
4.4
3.8
3.0
1.3
2.4
3.6
1-hexene
14.2
19.5
19.1
19.3
3.5
6.5
5.7
4.8
2.6
0.8
1.8
3.3 3.0
1-heptene
16.2
21.7
21.8
21.6
4.5
7.7
7.1
5.9
2.2
0.2
1.2
1-octene
18.2
24.0
24.5
24.0
5.5
8.9
8.4
6.9
1.7
0.4
0.6
2.7 2.3
2-alkenes 2-butene
10.3
15.0
16.1
18.6
1.5
4.2
3.9
5.3
3.5
1.9
2.9
2-pentene 2-hexene
12.3 14.2
17.2 19.5
18.4 20.7
21.2 23.8
2.5 3.5
5.4 6.5
4.8 5.7
6.3 7.3
3.0 2.6
1.3 0.8
2.9 2.8
2.1 1.9
2-heptene
16.2
21.7
23.0
26.3
4.5
7.7
6.6
8.4
2.2
0.2
2.7
1.7
2-octene
18.2
24.0
25.3
5.5
8.9
7.4
1.7
0.4
2.6
3/4-alkenes
a
3-hexene
14.2
19.5
23.8
3.5
6.5
7.3
2.6
0.8
1.9
3-octene
18.2
24.0
28.9
5.5
8.9
9.4
1.7
0.4
1.5
4-octene
18.2
24.0
28.9
5.5
8.9
9.4
1.7
0.4
1.5
3- and 4-Alkenes in HMOR are excluded. b 2-Octene in HZSM-5 is excluded
Figure 9. Linear alkene chemisorption complexes in HBEA, HMOR, and HZSM-5.
from 106 to 171 J mol1 K1 (see Table 4). All the ΔS0adsCN linear fits for the different types of linear alkenes are given in Table S9 in the Supporting Information. Table 5 summarizes the retained values of γ and δ, their standard deviation, R2, and the MAD for the
various zeolites. Figure 7 presents the calculated alkene physisorption entropies together with the linear fits from Table 5. In HFAU16 and HBEA, the position of the CC double bond has no or only a limited influence on the physisorption 23839
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Table 7. Geometric Parameters (Distances in picometers, Angles in degrees) of the Linear Alkene Chemisorption Complexes in HBEA, HMOR, and HZSM-5 Corresponding to Primary and Secondary Alkoxides CaCb
HaOa
ObCbCa
ObCbR3
ObCbR4
SiaOa
AlOa
SibOb
AlOb
SiaOaAl
SibObAl
170.8
189.4
161.4
172.9
135.4
135.4
ethene f ethoxya 1-alkenes f2-alkoxyb
150.8 151.3
151.7 156.6
250.6 241.8
111.3 107.9
104.2 110.2
105.2 101.8
160.8 160.6
172.7 173.1
170.8 171.2
190.8 192.3
136.6 137.2
128.0 124.2
2-alkenes f 3-alkoxyb
152.1
156.7
232.9
110.3
109.3
101.5
160.5
172.9
171.3
192.8
137.7
123.2
3-alkenes f 4-alkoxyb
152.5
156.8
232.3
111.2
109.4
101.5
160.4
173.0
171.4
193.2
137.7
122.4
4-octene f 4-octoxyb
152.3
157.0
230.1
111.1
109.2
101.4
160.4
172.9
171.4
193.2
137.6
122.4
170.6
190.7
160.7
171.6
129.5
140.5
ethene f ethoxya
150.9
152.5
254.2
111.8
103.2
104.6
160.7
173.2
170.2
189.2
130.8
128.8
1-alkenes f 2-alkoxyb
151.3
158.2
237.7
108.8
109.4
101.3
160.5
173.1
170.4
189.8
132.4
126.4
2-alkenes f 3-alkoxyb 3-alkenes f 4-alkoxyb
152.0 152.1
158.6 159.0
251.9 243.6
109.9 110.2
109.0 109.0
101.5 101.3
160.5 160.4
173.3 173.3
170.7 170.8
190.0 190.1
132.2 133.2
125.6 125.7
4-octene f 4-octoxyb
152.0
159.2
250.6
109.6
109.1
101.3
160.5
173.4
170.8
190.0
132.0
125.4
171.8
190.3
161.8
172.2
134.1
146.5
ethene f ethoxya
150.7
150.7
276.6
110.6
104.4
105.6
161.4
172.6
172.3
189.7
140.5
122.7
1-alkenes f 2-alkoxyb
151.2
156.2
257.5
108.4
108.6
102.5
161.1
172.6
172.5
190.9
142.5
119.8
2-alkenes f 3-alkoxyb,b
151.9
156.6
235.8
109.6
108.4
101.5
161.1
172.6
172.3
190.9
143.5
119.0
3-alkenes f 4-alkoxyb
151.9
156.6
235.2
108.9
108.6
101.3
161.5
172.9
172.6
191.0
141.3
120.1
4-octene f 4-octoxyb
152.2
156.1
236.7
110.0
108.4
101.3
161.0
172.6
172.3
190.7
143.9
119.4
HBEA
HMOR
HZSM-5
a
CbOb
Primary alkoxides. b Secondary alkoxides.
Figure 10. Chemisorption energies of 1-alkenes leading to 2-alkoxides in HFAU, HBEA, HMOR, and HZSM-5 as a function of the carbon number illustrating the influence of the zeolite framework.
entropy and a single ΔS0adsCN linear relation can be used for all the linear alkenes. In HMOR and HZSM-5 however, different parameters γ and δ are estimated for the 1-alkenes on one hand and 2(2/3/4)-alkenes on the other hand. In both zeolites, physisorption entropies are more negative for the latter alkenes. The higher entropy loss obviously results from the different orientation of the respective alkenes in the HMOR and HZSM-5 pores, as discussed in section 3.1.1. Comparison with the linear relations for the physisorption energies reveals that higher enthalpy strengths lead to higher entropy losses, as could be expected intuitively. Compensation Effect. With increasing carbon number, the physisorption entropy and the physisorption enthalpy have an inverse effect on the Gibbs free energy for physisorption. This well-known compensation effect has been observed experimentally as well as theoretically for the physisorption of alkanes in various zeolites.4648,5255 In this study, an analogous interplay
between enthalpy (ΔH0phys = ΔEphys) and entropy (ΔS0phys) is observed in all zeolites (Figure 8). For a given physisorption enthalpy, entropy losses in HFAU and HBEA are smaller than those in HMOR and HZSM-5. Moreover, in HZSM-5, the entropy loss for the 1-alkenes increases faster with increasing physisorption enthalpy as compared with the other zeolites. This indicates that the physisorption of 1-alkenes in the more confined pores of HZSM-5 is accompanied by an additional loss in configurational entropy of the physisorbed alkene molecule (see Figure 8a). 3.1.4. Physisorption Equilibrium Coefficient. Physisorption equilibrium coefficients, Kphys, are important thermodynamic quantities as they determine the amount of hydrocarbon physisorbed in the zeolite pores at a given partial pressure of the gas phase hydrocarbon. Physisorption equilibrium coefficients have been calculated for all the alkenes at 300, 500, and 800 K in HFAU, HBEA, HMOR, and HZSM-5 using eq 13: ! 0 ΔHphys TΔS0phys ð13Þ Kphys ¼ exp RT where physisorption enthalpies and entropies are calculated from the linear relations given in Tables 3 and 5, respectively. Values of ln(Kphys) for all the linear alkenes are listed in Table 6. In HFAU and HBEA, ln(Kphys) values are independent of the CC double bond position at all sampled temperatures. In HMOR and HZSM-5, an influence of the CC double bond position is however observed. In HZSM-5, for instance, physisorption of the 2-, 3-, and 4-alkenes is favored over the 1-alkenes at all temperatures. The influence of the zeolite framework and the carbon number on ln(Kphys) is also observed (Table 6). At 300 K, physisorption is significantly less favored in HFAU than in the other zeolites. At higher temperatures, the physisorption preference among the zeolites becomes less pronounced. Furthermore, Table 6 shows 23840
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that for a given type of alkenes ln(Kphys) increases with increasing carbon number in all zeolites and at all temperatures. This implies a higher concentration of longer alkenes in the zeolite pores. The preferential physisorption of longer alkenes however becomes less Table 8. Parameters α and β, Describing the Linear Variation of the Chemisorption Energy as a Function of Carbon Number, Standard Deviation (in Parentheses), Correlation Coefficient (R2), and Mean Absolute Deviation (MAD) α
β
R2
MAD
HFAU 1-alkenes
6.5((0.3)
81.2((1.4)
0.9924
1.0
2/3/4-alkenes
5.4((0.5)
72.2((3.6)
0.9419
1.7
7.0((0.1)
105.3((0.6)
0.9986
0.4
7.3((0.3)
89.0((2.0)
0.9895
0.9
HBEA 1-alkenes 2/3/4-alkenes HMOR 1-alkenes
9.5((0.4)
72.4((2.0)
0.9921
1.4
2/3/4-alkenes
8.1((0.5)
67.1((3.0)
0.9810
1.4
HZSM-5 1-alkenes [C2C8]
5.5((0.7)
123.1((3.7)
0.9215
2.5
1-alkenes [C2C5] 2/3/4-alkenesa
8.4((0.7) 10.1((0.3)
113.8((2.7) 96.3((2.0)
0.9851 0.9953
1.0 0.8
a Chemisorption of 2-octene in HZSM-5 is excluded from the fitting procedure.
pronounced with increasing temperature. The iso-equilibrium temperature (Tiso‑eq = α/γ), i.e., the temperature at which the physisorption equilibrium coefficients become independent of the carbon number, is computed in the range 8541553 K, above the industrial relevant range of 500800 K. 3.2. Chemisorption. The chemisorbed alkoxide is formed by protonation of the alkene and is characterized by a CO alkoxy bond. The protonation of 1-alkenes to 2-alkoxides, of 2-alkenes to 3-alkoxides, and of 3- and 4-alkenes to 4-alkoxides has been studied, as indicated in Figure 9, Table 2, and Table 7. 3.2.1. Geometry of Chemisorption Complexes. Figure 9 shows some representative chemisorption complexes in HBEA, HMOR, and HZSM-5. In the first two zeolites, no difference in the orientation of the chemisorption complexes among various linear alkenes is observed. For HZSM-5, the orientation of the alkyl chains in the chemisorption complexes of the 1-alkenes differs from those of the 2-, 3-, and 4-alkenes, similar to that of physisorbed complexes (see section 3.1.1). Also, the chemisorption of 2-octene to 3-octoxy in HZSM-5 has been excluded from the parameter estimation in eqs 10 and 11. Table 7 summarizes the most important distances and bond angles of chemisorption complexes averaged for different groups of alkenes/alkoxides for which two criteria are used: (i) the type of alkoxide formed, i.e., primary or secondary and (ii) the alkene type, i.e., 1-, 2-, 3-, or 4-alkene. Notations used in Table 7 are explained in Figure 2. Ethene is chemisorbed to the primary ethoxy, while the other alkenes are converted to the secondary alkoxides. Geometric parameters of all individual chemisorbed
Figure 11. Chemisorption energies of 1-, 2-, 3-, and 4-alkenes as a function of the carbon number in HFAU, HBEA, HMOR, and HZSM-5. Linear fits for different types of linear alkenes are indicated. Chemisorption energy of 2-octene in HZSM-5 is excluded from the fitting procedure. 23841
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Figure 12. Stability of chemisorption complexes (ΔEstab = ΔEchem + ΔH0f ) relative to the standard states of the elements [H2(gas) and C(graphite)].
complexes in HBEA, HMOR, and HZSM-5 are listed in Tables S10S12 in the Supporting Information. An obvious consequence of the protonation of an alkene is the change of the CaCb bond order from double to single, with typical bond lengths around 151152 pm and the formation of a CbOb alkoxide bond. Formation of the CbOb alkoxide bond results in an important shortening of both the SiaOa and AlOa bonds and an elongation of the AlOb and ObSib bonds compared to the unloaded zeolites. Observations are similar for HFAU,16 HBEA, HMOR, and HZSM-5. Other alkoxide-related geometric parameters ObCbCa, ObCbR3, and ObCbR4 hardly differ among the different alkoxides and among the different zeolites (Table 7). The CbOb bond length is independent of the zeolite framework and amounts to 151153 pm for the primary ethoxy and 156159 pm for the secondary alkoxides (Table 7). Similar observations for CbOb bond lengths of primary and secondary alkoxides in different zeolites have been reported by various authors employing different computational methods.16,20,22,24 A more important difference among the different zeolites is observed for the SiaOaAl and the SibObAl angle changes which can be taken as a measure of the flexibility of the zeolite framework upon alkoxide formation.20 The SiaOaAl bond angle slightly increases by 57° in HFAU,16 by 12° in HBEA, by 13° in HMOR, and by 69° in HZSM-5. A more pronounced change is noticed for the SibObAl bond angle as the Ob oxygen atom is directly involved in the alkoxide bond formation. The SibObAl bond angle sharpens significantly upon chemisorption by 710°, 712°, 1214°, and 2427° in HFAU,16 HBEA, HMOR, and HZSM-5, respectively. Comparing the SibObAl changes for the different zeolites
indicates that the deformation of the zeolite increases with decreasing pore dimensions. 3.2.2. Chemisorption Energy and Enthalpy. The chemisorption energies of all the linear alkenes are given in Table 2 for the HBEA, HMOR, and HZSM-5 zeolites. The separate contributions to the total chemisorption energies are given in Tables S13S15 in the Supporting Information. The correction term to compensate for the overestimation of the vdW contribution is given in Table S16 in the Supporting Information. Chemisorption complexes are mainly stabilized by the formation of the alkoxy bond, by electrostatic interactions, and by vdW interactions. The contribution of the latter to the total chemisorption energy varies from 2025% for ethene to 5060% for octene, which is less than for physisorption (see section 3.1.2). Influence of the Zeolite Framework. Figure 10 shows the chemisorption energies of the 1-alkenes as a function of the carbon number and indicates that the 1-alkene chemisorption strength increases in the order HFAU16 < HMOR < HBEA < HZSM-5. The stronger chemisorption in HZSM-5 can be attributed to (1) higher vdW stabilization in the narrower pores of HZSM-5 (see parameters α in Table 10) and (2) more favorable CO alkoxy bond formation (see parameters β in Table 10) due to the flexibility of the HZSM-5 framework as discussed above. Furthermore, this order is different from that for the 1-alkene physisorption strength where physisorption complexes in HMOR were found to be more stable than those in HBEA. Tables S13 and S14 in the Supporting Information show that, as expected from the framework density, the vdW stabilization (ΔELR,vdW) in HBEA is lower than in HMOR but that long-range electrostatic and/or repulsive interactions between the alkoxide and the zeolite framework, 23842
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The Journal of Physical Chemistry C i.e., ΔELR ΔELR,vdW, are much more in favor of alkene chemisorption in HBEA. Influence of Carbon Number and Position of the CC Double Bond. Table 2 shows that, in going from ethene to octenes, the alkene chemisorption energies vary from 93 to 133 kJ mol1, from 119 to 161 kJ mol1, from 95 to 150 kJ mol1, and from 130 to 178 kJ mol1 in HFAU,16 HBEA, HMOR, and HZSM-5, respectively. Figure 10 shows that the linear increase of the chemisorption energy with the carbon number for the 1-alkenes chemisorbed in the various zeolites is entirely due
Figure 13. Chemisorption entropies of 1-alkenes in HFAU, HBEA, HMOR, and HZSM-5 as a function of the carbon number illustrating the influence of the zeolite framework.
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to the higher vdW stabilization for the longer alkenes (see Tables S13S15 in the Supporting Information). Table 8 summarizes the estimated parameters α and β for the fitting of the chemisorption energy as a function of the carbon number, their standard deviations, R2, and the MAD. The ΔEchemCN linear fits for different zeolites are illustrated in Figure 11. Note that the parameter β relates to the energy change upon CO bond formation relative to the gas phase alkenes and includes contributions stemming from the strength of the alkoxy bond, steric repulsion, deformation of the zeolite, etc. Similar α values for 1-alkenes and 2-, 3-, and 4-alkenes are observed in HFAU (6.5 and 5.4 kJ mol1),16 HBEA (7.0 and 7.3 kJ mol1), and HMOR (9.5 and 8.1 kJ mol1). Also, the β values indicate a difference of around 516 kJ mol1 in chemisorption energies between 1-alkenes and 2-, 3-, and 4-alkenes for HFAU,16 HBEA, and HMOR. This can be explained by the difference in stability between the gas phase alkenes. Indeed, standard enthalpies of formation (ΔH0f ) of 1-alkenes differ by 11 kJ/mol from those of the 2-, 3-, and 4-alkenes according to the values reported in the NIST database or calculated using Benson’s additivity method.56,57 Therefore, it can be concluded that, in HFAU, HBEA, and HMOR, the stability of the secondary alkoxides (ΔEchem + ΔH0f ) (see Table S17 in the Supporting Information for ΔH0f ) relative to the standard states of the elements [H2(g) and C(graphite)] only depends on the carbon number and not on the detailed alkoxide structure (Figure 12).
Figure 14. Chemisorption entropies of 1-, 2-, 3-, and 4-alkenes as a function of the carbon number in HFAU, HBEA, HMOR, and HZSM-5. Linear fits for different types of alkenes are indicated. Chemisorption entropy of 2-octene in HZSM-5 is excluded from the fitting procedure. 23843
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Table 9. Parameters γ and δ, Describing the Linear Variation of the Chemisorption Entropy as a Function of Carbon Number, Standard Deviation (in Parentheses), Correlation Coefficient (R2), and Mean Absolute Deviation (MAD) γ
δ
R2
MAD
7.3((0.9)
162.7((5.5)
0.8021
5.0
Table 10. Simultaneous Fits of Physisorption and Chemisorption Energies versus Carbon Number, Standard Deviation (in Parentheses), Correlation Coefficient (R2), and Mean Absolute Deviation (MAD)a
HFAU 1/2/3/4-alkenes 1-alkenes
7.1((0.9)
148.0((4.9)
0.9161
3.6
2/3/4-alkenes
4.2((1.6)
153.4((10.8)
0.2576
4.5
8.7((0.7)
149.4((4.5)
0.9069
3.8
10.6((1.0)
149.8((5.7)
0.9507
3.8
7.0((2.2)
162.9((13.8)
0.5252
5.6
1-alkenes
β
σβ
R2
MAD
π 1/2/3/4-alkenes
6.1
0.3
30.4
1.7
0.9332
2.3
σ 1-alkenes
6.1
0.3
82.9
1.7
0.9886
1.1
σ 2/3/4-alkenes
6.1
0.3
67.8
2.0
0.9418
1.7
π 1/2/3/4-alkenes
6.9
0.3
39.3
2.1
0.8992
3.7
σ 1-alkenes σ 2/3/4-alkenes
6.9 6.9
0.3 0.3
105.8 91.5
2.0 2.4
0.9983 0.9852
0.4 1.0
HBEA
HMOR
2/3/4-alkenesa
σα
HFAU
HBEA
1/2/3/4-alkenes HZSM-5
α
HMOR
Chemisorption of 2-octene in HZSM-5 is excluded from the fitting procedure. a
In HZSM-5, the linear fit for the chemisorption energy considering the C2C8 1-alkenes yields an α of 5.5 kJ mol1, while from the higher vdW stabilization in HZSM-5, a more negative value of α is expected than for the other zeolites. The high level ΔE(C)MP2 contributions to the 1-alkene chemisorption energies (Table S15 in the Supporting Information) reveal that in the C6C8 2-alkoxides significant steric repulsion is present and refitting of eq 10 considering only the C2C5 1-alkenes yields an α value of 8.4 kJ mol1. Chemisorption of the 2-, 3-, and 4-alkenes leading to 3- and 4-alkoxides is characterized by a more negative α value of 10.1 kJ mol1 resulting from the higher vdW stabilization due to the partial chemisorption of the 2-, 3-, and 4-alkenes in the zigzag channel (see section 3.2.1). Due to this difference in vdW stabilization, the difference in β between the 2-alkoxides and the 3- and 4-alkoxides cannot be explained solely by the difference in gas phase stability between the various linear alkenes. In contrast to HFAU, HBEA, and HMOR, the intrinsic stability of the secondary alkoxides in HZSM-5 thus depends, next to the carbon number, on the detailed alkoxide structure (Figure 12). Chemisorption Enthalpies: Influence of Temperature. The contribution of the ZPVE and the thermal correction to the chemisorption enthalpy modestly increases from around 10 kJ mol1 at 300 K to 15 kJ mol1 for at 800 K, rather independent of the zeolite type and the carbon number (see Figure S3 in the Supporting Information). Neglecting this modest increase and assuming a constant correction for going from chemisorption electronic energies to chemisorption enthalpies, the following relation can be proposed. 0 ¼ ΔEchem þ 12 ΔHchem
ð14Þ
3.2.3. Chemisorption Entropy. In agreement with the physisorption entropies, the chemisorption entropies modestly increase by 68 J mol1 K1 with increasing temperature in the range 300800 K. This small increase is practically independent of the carbon number and the zeolite framework (see Figure S4 in the Supporting Information). In view of the rather small influence of temperature, chemisorption entropies could be considered independent of temperature. Influence of the Zeolite Framework. Entropy losses upon chemisorption of linear alkenes in HFAU,16 HBEA, HMOR,
π 1-alkenes
8.7
0.3
31.5
1.8
0.9569
3.2
π 2/3/4-alkenesb
8.7
0.3
41.0
2.1
0.9999
0.1
σ 1-alkenes
8.7
0.3
76.4
1.8
0.9823
1.9
σ 2/3/4-alkenes
8.7
0.3
62.7
2.1
0.9779
1.3
π 1-alkenes π 2/3/4-alkenesc
8.2 9.8
0.5 0.5
40.8 43.5
2.6 3.5
0.9501 0.9694
3.2 2.0
σ 1-alkenes [C2C5]d
8.2
0.5
114.6
2.2
0.9837
0.9
σ 2/3/4-alkenesc
9.8
0.5
98.2
3.5
0.9941
0.8
HZSM-5
The same value for α is assumed for physisorption and chemisorption. b 3-Hexene, 3-octene, and 4-octene physisorption in HMOR are excluded from the fitting procedure. c 2-Octene physisorption and chemisorption in HZSM-5 are excluded from the fitting procedure. d C6C8 1-alkene chemisorption in HZSM-5 is excluded from the fitting procedure. a
and HZSM-5 are given in Table 4. Figure 13 shows that chemisorption entropy losses increase in the order HBEA < HMOR < HFAU < HZSM-5; for the lower carbon numbers, entropy losses are even higher in HFAU than in HZSM-5. This order differs from the chemisorption strength order: HFAU < HMOR < HBEA < HZSM-5 (see section 3.2.2). Influence of Carbon Number and Position of the CC Double Bond. In all zeolites, entropy losses linearly increase with increasing carbon number and vary from 165 to 221 J mol1 K1, from 158 to 207 J mol1 K1, from 162 to 220 J mol1 K1, and from 165 to 236 J mol1 K1 in H FAU,16 HBEA, HMOR, and HZSM-5, respectively. This is illustrated by the ΔS0chemCN linear fits for all alkenes in Figures 13 and 14. Table 9 summarizes the estimated parameter values γ and δ describing the linear increase of the chemisorption entropy losses with the carbon number in HFAU,16 HBEA, HMOR, and HZSM-5, together with their standard deviation, R2, and the MAD. Figure 14 illustrates that a single linear ΔS0chemCN for both 1-alkenes and 2-, 3-, and 4-alkenes is found in HFAU16 and HMOR. However, separate fits for the 1-alkenes on one hand and for the 2-, 3-, and 4-alkenes on the other hand are obtained in HBEA and HZSM-5. In both zeolites, entropy losses upon chemisorption of the later alkenes are lower. Clearly, many other factors than the zeolite pore dimension may influence the values of the chemisorption entropies, e.g., the geometry of the chemisorption complex, the strength of the alkoxy bond, and the flexibility and deformation of the zeolite framework. Understanding the interplay among those factors is therefore not straightforward. 23844
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Figure 15. Physisorption and chemisorption energies of the linear alkenes together with the linear fits from Table 10 describing their variation as a function of the carbon number in HFAU, HBEA, HMOR, and HZSM-5, assuming the same influence of the carbon number. Resulting protonation energies are mentioned.
Comparison of the δ parameters (physisorption 82 to 95 J mol1 K1 vs chemisorption 148 to 163 J mol1 K1) indicates much higher entropy losses for the chemisorption complexes than for the physisorption complexes. This relates to the CO alkoxy bond formation and the immobile character of the alkoxides, in contrast to the physisorbed alkenes which are characterized by a significant mobility in the zeolite pores. 3.2.4. Protonation Energy, Enthalpy, and Entropy. The protonation energies of linear alkenes in the four zeolites is presented in Table 2. The linear relations for physisorption and chemisorption energies as a function of the carbon number were refitted assuming the same α value for physisorption and chemisorption. In HZSM-5 two α values are considered: one for the 1-alkene physisorption (C2C8) and chemisorption (C2C5, see section 3.2.2) and one for the 2-, 3-, and 4-alkene physisorption and chemisorption. Table 10 shows the resulting parameters, together with the standard deviations, correlation coefficient, and the mean absolute deviation. In view of the high values for R2 and the low values for the MAD and the standard deviations, the assumption of an equal value for α seems acceptable. Figure 15 illustrates the obtained linear fits and the resulting protonation energies. For all zeolites, the protonation energy of the 1-alkenes is more negative than that of 2-, 3-, and 4-alkenes. The difference in protonation energies between 1-alkenes and 2-, 3-, and 4-alkenes amounts to 1415 kJ mol1 in HFAU16 and HBEA and is mainly explained by the difference in stability of 11 kJ/mol between the gas phase 1-alkenes and the gas phase 2-, 3-, and 4-alkenes (see section 3.2.2). In HMOR and HZSM-5, the protonation energies however differ by 23 and 19 kJ mol1, respectively, and can be attributed not only to the
difference in gas phase stability but also to the different orientation of the physisorbed alkenes in the pores of HMOR and of both the physisorbed and chemisorbed alkenes in HZSM-5 as discussed above. Accounting for eqs 12 and 14, protonation enthalpies are easily calculated from the protonation energies. 0 ¼ ΔEprot þ 12 ΔHprot
ð15Þ
Protonation entropies of all alkenes in zeolites are presented in Table 4. For 1-alkenes in all zeolites, protonation entropy losses slightly increase with increasing carbon number. This is attributed to a higher increment of chemisorption entropy losses as compared with that of physisorption entropy losses (see Figure S5 in the Supporting Information). However, no systematic trend is observed for protonation entropy losses of the other alkenes (Table 4).
4. CONCLUSIONS This work clearly shows that the combined QM-Pot(MP2// B3LYP:GULP)statistical thermodynamics method is a very efficient tool for the simulation of alkene sorption in zeolites at industrially relevant temperatures. For both physisorption and chemisorption of C2C8 1-alkenes, C4C8 2-alkenes, 3-hexene, 3-octene, and 4-octene in HFAU, HBEA, HMOR, and HZSM-5, a unique relation between the energies and enthalpies is found, independent of the carbon number and zeolite type. Enthalpies and entropies are practically independent of temperature in the range 300800 K. The physisorption strength of the alkenes is governed by the formation of a π-complex and to a much greater extent by vdW 23845
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The Journal of Physical Chemistry C interactions. The latter factor increases with increasing alkene length and with decreasing zeolite pore dimension. In addition to vdW forces, the chemisorption strength of alkoxides depends on the strength of the covalent CO alkoxy bond and/or electrostatic interactions. Destabilizing steric repulsion between the alkoxide and the zeolite wall can, at least partly, be alleviated by the flexibility of the zeolite framework as noticed from the deformation of the zeolite upon chemisorptions. The CC double bond position affects not only the physisorption strength but also the physisorption entropies. Physisorption strength and entropy losses increase in the order HFAU < HBEA < HMOR < HZSM-5. The CC double bond position is only important in HMOR and HZSM-5. Higher physisorption enthalpies and entropies are obtained for 2-alkenes (HMOR) and 2-, 3-, and 4-alkenes (HZSM-5) as compared with 1-alkenes owing to the stronger π-complex/vdW interactions of the former alkenes. A compensation effect between the physisorption enthalpy and the physisorption entropy of alkenes on the physisorption equilibrium coefficient, Kphys, is calculated. Also, an additional configurational entropy loss is indicated for alkene physisorption in HZSM-5. In all zeolites, the physisorption preference of longer alkenes over the shorter ones becomes more delicate with increasing temperature. The influence of the zeolite framework on the chemisorption enthalpy and entropy is clearly demonstrated in the case of 1-alkenes. The 1-alkene chemisorption strength increases in the order HFAU < HMOR < HBEA < HZSM-5. It is apparent that more stable alkoxides are found in HBEA than in HMOR even though vdW stabilizing interactions are in favor of the latter zeolite. The entropy losses upon chemisorption of 1-alkenes increase in the order HBEA < HMOR < HFAU < HZSM-5, which is different from the order for the chemisorption enthalpies, indicating that stronger chemisorption not necessarily leads to a higher entropy loss. In HFAU, HBEA, and HMOR, the intrinsic stability of the alkoxides, i.e., relative to gas phase hydrogen and graphite, depends only on the carbon number. In HZSM-5, on the other hand, 3- and 4-alkoxides are found to be more stable than 2-alkoxides, due to the different orientation of the chemisorption complexes in the pore. Also in HBEA and HZSM-5, chemisorption entropy losses associated with the former alkoxides are lower. Protonation enthalpies depend only on the alkene CC double bond type and not on the carbon number. Differences in protonation enthalpies of 1-alkenes and 2-, 3-, and 4-alkenes in HFAU, HBEA, HMOR, and HZSM-5 (partly;for the last two zeolites) relate to the different stabilities of the corresponding gas phase alkenes. On the other hand, protonation entropy losses somewhat increase with increasing carbon number in the case of 1-alkenes. No systematic variation is however found for the other alkenes.
’ ASSOCIATED CONTENT
bS
Supporting Information. Geometric parameters for the physisorption and chemisorption of all linear alkenes considered in this work are given. Next to this, detailed information on their physisorption and chemisorption energies, including the corrections of the original QM-Pot(MP2//B3LYP:GULP) energies, the separate QM and MM contributions, etc., is mentioned. Also, the different linear fits for the different types of linear alkenes
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describing the variation of physisorption enthalpies and entropies as a function of the carbon number are listed. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel.: +32 (0)9 264 4516. Fax: +32 (0)9 264 4999. E-mail:
[email protected].
’ ACKNOWLEDGMENT This work is supported by the Long Term Structural Methusalem Funding by the Flemish Government;Grant BOF09/ 01M00409, the FWO (Fund for Scientific Research Flanders), the BELSPO (Belgian Federal Science Policy Office in the frame of IAP/6/27), and the European Commission (Network of Excellence IDECAT, NMP3-CT-2005-011730). ’ REFERENCES (1) Corma, A. Chem. Rev. 1995, 95, 559–614. (2) Degnan, T. F. Top. Catal. 2000, 13, 349–356. (3) Guisnet, M.; Gilson, J.-P. In Zeolites for Cleaner Technologies; Guisnet, M., Gilson, J.-P., Eds.; Imperial College Press: London, 2002; pp 127. (4) Jacobs, P. A.; Martens, J. A. In Introduction to Zeolite Science and Practice, 1st ed.; van Bekkum, H., Jacobs, P. A., Flanigen, E. M., Jansen, J. C., Eds.; Elsevier: Amsterdam, 1991; pp 445496. (5) Corma, A.; Martinez, A. In Zeolites and Ordered Mesoporous ejka, J., van Bekkum, H., Eds.; Materials: Progress and Prospects, 1st ed.; C Elsevier: Amsterdam, 2005; pp 337366. (6) Narasimhan, C. S. L.; Thybaut, J. W.; Marin, G. B.; Jacobs, P. A.; Martens, J. A.; Denayer, J. F.; Baron, G. V. J. Catal. 2003, 220, 399–413. (7) Thybaut, J. W.; Marin, G. B.; Baron, G. V.; Jacobs, P. A.; Martens, J. A. J. Catal. 2001, 202, 324–339. (8) Bates, S. P.; van Well, W. J. M.; van Santen, R. A.; Smit, B. J. Am. Chem. Soc. 1996, 118, 6753–6759. (9) Clark, L. A.; Ye, G. T.; Gupta, A.; Hall, L. L.; Snurr, R. Q. J. Chem. Phys. 1999, 111, 1209–1222. (10) Dubbeldam, D.; Calero, S.; Vlugt, T. J. H.; Krishna, R.; Maesen, T. L. M.; Smit, B. J. Phys. Chem. B 2004, 108, 12301–12313. (11) Fuchs, A. H.; Cheetham, A. K. J. Phys. Chem. B 2001, 105, 7375–7383. (12) Pascual, P.; Ungerer, P.; Tavitian, B.; Pernot, P.; Boutin, A. Phys. Chem. Chem. Phys. 2003, 5, 3684–7693. (13) Pascual, P.; Ungerer, P.; Tavitian, B.; Boutin, A. J. Phys. Chem. B 2004, 108, 393–398. (14) Jakobtorweihen, S.; Hansen, N.; Keil, F. J. Mol. Phys. 2005, 103, 471–489. (15) Smit, B.; Maesen, T. L. M. Chem. Rev. 2008, 108, 4125–4184. (16) De Moor, B. A.; Reyniers, M. F.; Marin, G. B. Phys. Chem. Chem. Phys. 2009, 11, 2939–2958. (17) De Moor, B. A.; Reyniers, M. F.; Sierka, M.; Sauer, J.; Marin, G. B. J. Phys. Chem. C 2008, 112, 11796–11812. (18) Pantu, P.; Boekfa, B.; Limtrakul, J. J. Mol. Catal. A: Chem. 2007, 277, 171–179. (19) Namuangruk, S.; Tantanak, D.; Limtrakul, J. J. Mol. Catal. A: Chem. 2006, 256, 113–121. (20) Boronat, M.; Viruela, P. M.; Corma, A. J. Am. Chem. Soc. 2004, 126, 3300–3309. (21) Namuangruk, S.; Pantu, P.; Limtrakul, J. J. Catal. 2004, 225, 523–530. (22) Rozanska, X.; van Santen, R. A.; Demuth, T.; Hutschka, F.; Hafner, J. J. Phys. Chem. B 2003, 107, 1309–1315. (23) Benco, L.; Hafner, J.; Hutschka, F.; Toulhoat, H. J. Phys. Chem. B 2003, 107, 9756–9762. 23846
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