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First Principle Study on the Adsorption of Hydrocarbon Chains Involved in Fischer-Tropsch Synthesis over Iron Carbides José Guillermo Rivera de la Cruz, Maarten K. Sabbe, and Marie-Françoise Reyniers J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05864 • Publication Date (Web): 13 Oct 2017 Downloaded from http://pubs.acs.org on October 13, 2017

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The Journal of Physical Chemistry

First Principle Study on the Adsorption of Hydrocarbon Chains Involved in Fischer-Tropsch Synthesis over Iron Carbides José G. Rivera de la Cruz, Maarten K. Sabbe,∗ and Marie-Françoise Reyniers Laboratory for Chemical Technology, Ghent University, Technologiepark 914, B-9052 Ghent, Belgium E-mail: [email protected] Phone: +32 (0)9 331 17 33

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Abstract

1

2

The adsorption of n-alkyls, 1-alkenes and n-alkanes has been studied on the χ-

3

Fe5 C2 (010), Fe7 C3 (001), θ-Fe3 C(001) and η-Fe2 C(011) surfaces which have been re-

4

ported as active phases for an Fe-based Fischer-Tropsch catalysts. Spin-polarized den-

5

sity functional theory calculations with the vdW-DF2 functional were performed. The

6

most stable adsorption configuration for n-alkyls is a bridge position for χ-Fe5 C2 (010),

7

Fe7 C3 (001) and θ-Fe3 C(001), whereas for η-Fe2 C(011) the most stable configuration is

8

on-top. The surfaces with the larger surface carbon content present a higher affinity for

9

the adsorption of n-alkyls. For adsorption of 1-alkenes the χ-Fe5 C2 (010) surface shows

10

the strongest adsorption, with a di-σ adsorption mode. For n-alkanes the strongest ph-

11

ysisorption was found for the smoothest surface, i.e., the θ-Fe3 C(001). The adsorption

12

energies are found to be independent of the length of the hydrocarbon chain from a

13

chain length of three carbon atoms for n-alkyl species, five carbon atoms for 1-alkenes

14

and four for n-alkanes.

15

Introduction

16

Fischer-Tropsch Synthesis (FTS) is a process to transform CO and H2 into a wide range of

17

products such as hydrocarbons and oxygenated compounds that can be used as high quality

18

fuels. Commonly, FTS uses syngas as feedstock, which is commonly generated from supplies

19

such as coal, natural gas, and biomass. As a result, FTS is increasing its relevance because

20

it can be an alternative for the depleting crude oil resources. 1,2

21

Several transition metals (Ru, Fe and Co) can be employed as catalysts for FTS, but

22

only Fe and Co are used industrially. Fe-based catalysts are widely available at a low price,

23

and they possess a high activity, a wide operating range and a high selectivity towards

24

alkenes. 1,3–10

25

Fe-based catalysts are mainly precipitated iron oxide phases, such as α-Fe2 O3 , γ-Fe2 O3 ,

26

FeOOH, Fe3 O4 and FeO. These phases are inactive for FTS until they are subjected to 2


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1

an activation process with syngas, in which the catalyst undergoes several transformations,

2

leading to metallic, oxide and carbide phases. 1,3,4,11–13

3

Experimental evidence from Transmission Electronic Microscopy (TEM), X-ray diffrac-

4

tion (XRD) and Mössbauer spectroscopy shows that iron carbides are the main active phases

5

in FTS. 5,9,12–18 Previous theoretical and experimental research has identified the phases χ-

6

Fe5 C2 , Fe7 C3 , θ-Fe3 C and η-Fe2 C under FTS conditions. 4,8,14,16,19–23 In addition to the carbide

7

phases, other phases such as α-Fe and Fe2 O3 can coexist. 1,5,13

8

Comprehension of the formation pathways of long-chain hydrocarbons on these surfaces

9

represents a deeper understanding for further optimization of FTS. However, such complex

10

systems with several coexisting phases are difficult to study in detail using analytical tech-

11

niques. Therefore, the use of theoretical studies opens up the possibility to describe the

12

properties of the iron carbides phases in detail, providing structures and energies for the

13

different species present on the catalytic surface. 24

14

Most of the theoretical research on iron carbides is focused on the adsorption and ac-

15

tivation of CO and H2 on the catalyst. 21,22,24–26 These studies have found several stable

16

adsorption sites depending on the studied surface. Regarding the activation of CO and H2

17

on iron carbides it has been reported that the most feasible route for CO activation is the

18

H-assisted dissociation, leading to different surface species such as HCO and Cx Hy , which

19

can be the building blocks for larger hydrocarbons in FTS. However, the actual identity of

20

the building blocks is still under debate, 8,19,27–30 whereas the surface hydrocarbons species

21

are properly identified yet little studied. 6,31,32 Therefore, because of the high complexity of

22

Fischer-Tropsch synthesis, typically several hypothesis are made to reduce the degree of com-

23

plexity. One of the mostly widely used approaches in the context of surface hydrocarbons is

24

to assume that only for small hydrocarbon chains the adsorption strength will depend on the

25

chain length and that it will become constant after a certain length. For instance, Lozano

26

et al. 10 assumes a chain length dependence only up to a carbon chain length of three, with

27

constant adsorption energies for larger adsorbed hydrocarbons. However, this hypothesis

3



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1

has not yet been validated until now.

2

In this work, detailed density functional theory (DFT) calculations were performed to

3

study the adsorption of long hydrocarbon chains on iron carbide surfaces, in order to better

4

understand the effect of composition and morphology of the different phases present under

5

FTS conditions on the adsorption behaviour.

6

Methods and models

7

Electronic structure calculations

8

In this study, periodic DFT calculations were performed using the Vienna ab initio simulation

9

package (VASP 5.3.3), 33–36 to obtain adsorption energies and adsorption geometries. Plane-

10

wave basis sets via the projector augmented wave method (PAW) 37,38 describe the wave

11

function close to the nuclei. The wave function is expanded in terms of plane-wave basis

12

sets with a cutoff of 400 eV. Exchange and correlation energies were calculated using the

13

vdW-DF2 functional of Langreth and Lundqvist et al. implemented in VASP by Klimes

14

et al. 39–42 This non-local functional also describes long-range interactions such as van der

15

Waals (vdW) interactions. To the best of our knowledge there is no literature comparing the

16

use of vdW-DF functionals for iron carbides. Also, no accurate experimental information is

17

available to use as a benchmark for the adsorption of hydrocarbons on these phases. In the

18

absence of such studies, we can in a first approximation assume that the results obtained for

19

the adsorption of hydrocarbons on Pt by Gautier et al. can be transferred to this work. 43

20

Gautier et al. have studied the impact of the inclusion of vdW functionals on the adsorption

21

strength of different hydrocarbons on Pt and compared the obtained results with available

22

experimental data. It was found that in the case of saturated hydrocarbons vdW functionals

23

are able to predict the low adsorption strength, present in physisorption, which is commonly

24

underestimated or not accounted for by PW91 and PBE functionals. 43,44 Moreover, in the

25

framework of FTS, previous studies indicate that the use of vdW-DF functionals provides 4


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an accurate description of CO adsorption on hcp-Co(0001). 45

2

To describe the partial occupancies close to the Fermi level, the first-order Methfessel-

3

Paxton method was applied with a smearing width of 0.01 eV. Brillouin-zone integration

4

for bulk calculations was done on a 5×5×5 Monkhorst-pack grid, 46 whereas for the (2×1)

5

and (2×2) slabs it was carried out on a 5×5×1 (k-point grids in the reciprocal space can

6

be found in Supporting information Figures S1-S4). The approximate k-point spacing in

7

reciprocal space amounts to at most 0.03 Å−1 for θ-Fe3 C(001), 0.02 Å−1 for Fe7 C3 (001) and

8

η-Fe2 C(011) and to 0.015 Å−1 for χ-Fe5 C2 (001)0.00 . Gas phase calculations were carried out

9

in a 20Å×20Å×20Å unit cell considering only the Γ point. Due to the magnetic properties

10

of the system, spin polarization was included. The electronic energy convergence was set

11

to 1 × 10−6 eV. For the geometry optimization Davidson and RMM-DIIS algorithms 47 were

12

used, until the maximum forces on the atoms were lower than 1.5 × 10−2 eV/Å. Slabs were

13

repeated in three directions to create a periodic surface model. A vacuum layer of 20 Å was

14

included in the perpendicular direction to the surface, coupled with an artificial dipole layer,

15

to avoid interactions between periodic images. 48 Only the atoms of the upper half of the slab

16

were allowed to relax, together with the adsorbed species; the lower half of the slab remained

17

fixed at its corresponding bulk position (the precise fixed atoms are indicated Figure S5 of

18

the Supporting information). In the absence of literature data about the stability of the

19

different surface planes of a given phase the electronic surface energy, Γ, was calculated,

20

defined as the energy required to create a surface from the bulk (Eq. (1)):

Γ=

Eslab − nbulk Ebulk 2·A

(1)

21

in which, Eslab is the electronic energy of the relaxed slab, Ebulk is the electronic energy of

22

the bulk unit cell, nbulk is the number of bulk unit cells required to construct the slab, and

23

A is the surface area of the slab unit cell, which is multiplied by two because slabs used in

24

the periodic calculations possess two surfaces. In this case only the upper half of the slab

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is relaxed, whereas for the lower half atoms are fixed at their corresponding bulk positions.

2

This does not result in surface energies that can be compared to experiments but provides

3

sufficient information for relative stabilities.

4

The adsorption energy (∆Eadsi ) of the different adsorbates is calculated as: (Eq. (2))

∆Eadsi = Ei+slab − Eslab + Eig

(2)

5

in which, Ei+slab , Eslab and Eig are the electronic energies of the slab-adsorbate system, the

6

bare slab and the species i in gas phase, respectively. To understand adsorption trends better,

7

the adsorption energy can be decomposed in two parts: the surface-adsorbate interaction

8

and the deformation energy (Eq. 3)

∆Eadsi =

Eint |{z}

interaction surface adsorbate

+ ∆Edefi + ∆Edefslab | {z }

(3)

deformation energy

9

Eint represents the interaction energy between the adsorbate and the surface. ∆Edefi is the

10

deformation energy of the molecule i, calculated as the difference in energy between the

11

isolated adsorbate in the distorted geometry and the adsorbate at its relaxed geometry (Eq

12

4). ∆Edefslab is the deformation energy of the surface defined as the difference in energy

13

between the slab in the distorted geometry of the slab-adsorbate system and the clean slab

14

(Eq 5):

∆Edefi = Edefi − Ei

(4)

∆Edefslab = Edefs − Eslab

(5)

15

In order to have a clear view of the electron redistribution induced by the bonding between

16

the adsorbed molecule and the surface, electron density difference plots were constructed

6


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based on the electron densities calculated by VASP:

∆ρ = ρi+slab − ρdefi − ρdefslab

(6)

2

where, ρi+slab is the electron density of the slab-adsorbate system, ρdefi is the electron density

3

of the adsorbate in the same (distorted) geometry but without the slab, and ρdefslab corre-

4

sponds to the electron density of the distorted geometry of the slab without the adsorbate.

5

Harmonic vibrational analysis for all final structures indicates that no imaginary fre-

6

quencies are present. Only for Fe7 C3 (001) and adsorbates with five carbon atoms or more

7

on θ-Fe3 C this could not be checked due to computational constraints.

8

Bulk structure

9

The selected iron carbide phases were χ-Fe5 C2 , Fe7 C3 , θ-Fe3 C and η-Fe2 C. For all phases,

10

XRD patterns match well experimental spectra (see Supporting Information Figures S6-S10).

11

For χ-Fe5 C2 , the selected initial bulk structure corresponds to a monoclinic structure

12

as reported by Retief et al. 49 After an optimization the final bulk resembles the pseudo-

13

monoclinic structure reported by du Plessis et al., 7 based on a comparison of calculated XRD

14

patterns (see Supporting Information Figures S6-S7). This slightly distorted monoclinic

15

structure, in which a different position of the C atoms causes the Fe atoms to be distorted

16

from their regular prismatic trigonal arrangement in the monoclinic structure, is the bulk

17

structure according to the latest experimental findings. 7 This failure of DFT methods to

18

predict the monoclinic χ-Fe5 C2 bulk structure has been previously addressed by de Smit et

19

al., 5 but in the light of the work of du Plessis et al. 7 the structure predicted by de Smit et

20

al. 5 was most likely the correct pseudo-monoclinic structure. The selected bulk unit cell of

21

χ-Fe5 C2 consist of 20 Fe atoms and 8 C atoms as illustrated in Figure 1a.

22

23

The Fe7 C3 phase is an orthorhombic structure with 28 Fe atoms and 12 C atoms per unit cell, see Figure 1b.

7



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1

Slab models

2

Low Miller index surfaces were considered in this study. The generated slabs are stoichio-

3

metric to their corresponding bulk. The slabs are symmetric with the top and bottom faces

4

equivalent. All the modelled surfaces were built from the previously optimized bulk struc-

5

tures and all the studied surfaces were constructed with a similar surface area (Figure 2)

6

ranging between 1 and 1.35 nm2 , within the limitations dictated by the bulk structure. In

7

this work, to describe the slabs, a layer of atoms is defined as the collection of atoms which

8

coordinates are within 100 pm, in direction perpendicular to the surface. Hence iron carbide

9

surfaces are modelled as intermixed layers of Fe and carbon atoms.

10

For the χ-Fe5 C2 the (010) surface is considered because Steynberg et al. 16 identified it as

11

stable in their DFT study of fourteen different low miller index surfaces, finding differences

12

in the surface energy between 0.1 till 0.8 J/m2 . Their main conclusion is however that

13

because a large number of χ-Fe5 C2 carbide surfaces share similar surface energies, there is no

14

most representative catalyst surface and several surfaces will coexist. For χ-Fe5 C2 (010) the

15

only two possible stoichiometric, symmetric slabs that can be built are the plane (010)0.00

16

and the plane (010)0.25 . In this case the plane 0.00 was selected because it offers larger

17

differences in surface structure compared with the other studied carbides (particularly the

18

θ-Fe3 C(001) surface). Steynberg et al. 16 reported the plane (010)0.25 as the most stable

19

surface termination, but the difference in surface energy between the plane 0.00 and 0.25 is

20

small with surface energies of 1.88 and 2.28 J/m2 , respectively. Hence, both surfaces can be

21

expected to coexist. 16 The (010)0.00 surface was modelled by a slab of 4 layers of Fe atoms

22

and 4 layers of C atoms, where the resulting top layer is not flat. The surface exposes 4 C

23

atoms and 20 Fe atoms per p(1×2) slab on its top layer, see Figure 2a.

24

Despite Fe7 C3 being reported as active phase for FTS, 1 there are no previous studies

25

that have determined the most predominant surface, and hence, the electronic surface energy

26

calculated in this work was used as the criterion to select a surface (Eq. 1). Among the

27

three different low miller index surfaces ((100), (010), (001)), the (001) has the lowest energy 9



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value with an electronic surface energy of 2.21 J/m2 , compared to 2.45 and 2.34 J/m2 for

2

(100) and (010), respectively. The unit cell for the surface (001) is composed by 4 layers of

3

C atoms and 7 layers of Fe and the surface exposes 28 Fe atoms and 4 C atoms per p(2×2)

4

slab. The resulting surface is not flat (Figure 2b).

5

Theoretical calculations have reported the θ-Fe3 C(001) surface as the most stable surface

6

among several low miller index surfaces. 20–22 It was modelled by a slab of 8 layers of Fe

7

atoms and 8 layers of C atoms and due to the position of the atoms in each layer, the

8

exposed surface is not flat. The surface exposes 4 C atoms and 24 Fe atoms per p(2×2) slab,

9

see Figure 2c.

10

η-Fe2 C(011) has been reported as the most stable surface under FTS, 4,23 but also here the

11

energy differences between the different planes are small. 23 The (011) surface was modelled

12

by a slab of 5 layers of Fe atoms and 2 layers of C atoms. Due to the position of atoms

13

in each layer the surface is not flat. The surface exposes 8 C atoms and 12 Fe atoms per

14

p(2×2) slab, see Figure 2d.

15

Previous studies have used small unit cells in their adsorption studies, for small molecules

16

(CHx , C2 H4 , CO, and H2 ). 1,19,24,25,28,29,31,54,55 However, in this work due to the larger size

17

of the adsorbates studied, the surface area of the unit cells should be sufficiently large to

18

calculate adsorption energies that only depend on the interactions between the adsorbate

19

and the surface. To set the minimum thickness required a convergence test for the adsorption

20

energy with respect to the slab thickness was carried out (Supporting information Table S2).

21

It was found that doubling the slab thickness for χ-Fe5 C2 (010)0.00 and η-Fe2 C(011) results

22

in methyl adsorptions energies at most 5 kJ/mol less negative than those found in the thin

23

slabs. For the thicker slabs of the Fe7 C3 (001) and θ-Fe3 C(001) surfaces, doubling the slab

24

was not possible due to computational constrains, but halving the slab thickness provides an

25

indication of the convergence with slab thickness. This indicates that the adsorption energies

26

are converged within 8 and 4 kJ/mol, respectively, meaning the results obtained on all slabs

27

can be considered reliable.

10


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1

To minimize the possible lateral interactions between adsorbates, several calculations

2

were performed for the adsorption of n-alkyl species on θ-Fe3 C(001) at different coverages.

3

The coverages were decreased keeping the stoichiometry of the unit cell constant, increasing

4

the supercell from p(1×1) to p(2×1) and p(2×2) (Supporting information Figures S11-

5

S13). Larger unit cells lead to lower coverage implying larger space between adsorbates on

6

the surface, which reduces the interaction between them. The p(2×2) supercell for the θ-

7

Fe3 C(001) surface was chosen to evaluate the effect of lateral interaction between successive

8

images but the resulting trends are expected to hold for the other phases as well because

9

of the large similarities between the different iron carbides. It was found that for a p(2×1)

10

supercell the adsorption energy is already converged within 2 kJ/mol with respect to the

11

p(2×2) supercell, even for the largest adsorbate susceptible to the most lateral interactions

12

(n-hexyl). Taking the p(2×2) supercell for the calculation of adsorption energies should

13

therefore be even more reliable to reduce any possible lateral interaction, compared to taking

14

the p(2×1) supercell. (Supporting information Figure S14-S16). As a result, the other unit

15

cells were built with similar area, within the limitations of their stoichiometry.

16

Results and discussion

17

The large number of different atoms present in the top layer of each surface leads to a large

18

amount of different possible positions on which a molecule can be adsorbed. Each atom in

19

the top layer represents a possible on-top site, the gap between each two atoms a bridge

20

position, and the space between n atoms an n-fold hollow site. For example, the surface

21

χ-Fe5 C2 (010) with fourteen different atoms at the surface leads to a number of 52 possible

22

configurations to evaluate (Supporting information Figures S17-S20).

23

In order to find the most stable configuration for the adsorption of n-alkyl, 1-alkene and

24

n-alkane species a screening was performed, for all the possible adsorption sites on each

25

surface. The screening was carried out using the following species per family: CH3 for n-

11




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1

coverages were 1.38×10−6 mol/m2 for χ-Fe5 C2 (010), 1.28×10−6 mol/m2 for Fe7 C3 (001),

2

1.23×10−6 mol/m2 for θ-Fe3 C(001), and 1.66×10−6 mol/m2 for η-Fe2 C(011). As stated

3

before, these coverages warrant sufficient space between neighbouring adsorbates from the

4

periodic model to guarantee no or almost no lateral interactions.

5

Adsorption of n-alkyls

6

n-alkyl species can adsorb in two distinct ways on the surface: horizontal or perpendicular to

7

the surface. To select the most stable adsorption geometry, the adsorption energy of C3 H7 on

8

χ-Fe5 C2 (010) was calculated with the molecule horizontal and perpendicular to the surface.

9

When the hydrocarbon chain is located horizontal to the surface the adsorption energy

10

amounts to -185 kJ/mol, while, for the hydrocarbon chain perpendicular to the surface,

11

the adsorption energy amounts to -206 kJ/mol. This difference in stability can partially be

12

explained based on the structure of the studied surfaces where the horizontal configurations

13

are only possible if the n-alkyl adopts a non-staggered conformation, in which the adsorbate

14

is destabilized due to the interactions in the hydrocarbon chain such as gauche interactions.

15

The configuration perpendicular to the surface allows to have a staggered hydrocarbon chain.

16

Moreover, it reduces the interaction between successive hydrocarbon chains in adjacent unit

17

cells particularly for larger chains. As a result, for the calculations of the adsorption energy,

18

the hydrocarbon chain was set in a staggered conformation perpendicular to the surface

19

(Figure 3).

20

For χ-Fe5 C2 (010), Fe7 C3 (001) and θ-Fe3 C(001) (Figures 3a, 3b and 3c), n-alkyl species

21

adsorb the strongest at bridge sites, located between two iron atoms. In the case of adsorption

22

on η-Fe2 C(011) the most stable adsorption site was on-top on a surface C atom (Figure 3d).

23

All configurations have similar structures with only small changes in the bond distance

24

between the adsorbed n-alkyl species and the iron atoms involved in the bonding to Fe1 and

25

Fe2 (Table 1).

26

For each surface the bond length between surface and adsorbate as well as the bond 13




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Table 1: Selected structural parameters of n-alkyl adsorbed species surface

species

χ-Fe5 C2 (010)

CH3 C2 H5 C3 H7 C4 H9 C5 H11 C6 H13 CH3 C2 H5 C3 H7 C4 H9 C5 H11 C6 H13 CH3 C2 H5 C3 H7 C4 H9 C5 H11 C6 H13

Fe7 C3 (001)

θ-Fe3 C(001)

η-Fe2 C(011)

CH3 C2 H5 C3 H7 C4 H9 C5 H11 C6 H13

dF e1 −C (pm) 209 209 209 209 209 209 219 221 220 220 220 220 214 213 213 213 213 213 dCs −C (pm) 153 153 152 153 153 153

dF e2 −C (pm) 230 232 232 231 231 231 221 223 223 223 223 223 244 244 244 244 244 244 dF e1 −C (pm) 204 205 204 204 204 204

∡F e1 CF e2 (◦ ) 71 70 70 70 70 71 82 80 81 81 81 81 68 67 67 67 67 67 ∡Cs CF e1 (◦ ) 58 58 58 58 58 58

1

previously been attributed to the presence of a larger interaction between the alkyl groups

2

and the surface than those between the H atoms of the CH3 and the surface. 56 In our opinion,

3

the discrepancy of CH3 is mainly due to the lower stability of the CH3 radical in the gas

4

phase compared to the C2 till C6 radicals, which are used as the gas phase reference for

5

the calculation of the adsorption energy. For instance, the difference in stability between

6

a CH3 and C2 H5 radical in gas phase amounts to 18.8 kJ/mol, 57 which is similar to the

7

difference between the calculated electronic adsorption energies of methyl and ethyl on all

8

surfaces except η-Fe2 C(011). Moreover, if dissociative adsorption energies would be shown,

15




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1

The obtained adsorption energies for C2 H5 adsorption on Fe7 C3 (-166 kJ/mol) and θ-

2

Fe3 C(001) (-174 kJ/mol), the Fe-richest surfaces, are similar to the value of -159 kJ/mol

3

experimentally determined for Fe(100) at 300 K. 58

4

Decomposition of the adsorption energy into the contribution of (i) actual chemical bond-

5

ing and (ii) deformation can provide a further insight into differences in bonding on the four

6

studied surfaces (Equations (3)-(5)). This calculation was limited to CH3 , C2 H5 and C3 H7

7

adsorption, assuming that the interaction energies for larger n-alkyl groups will have similar

8

trends. The obtained values are listed in Table 2. Table 2: Calculated interaction and deformation energies for CH3 , C2 H5 and C3 H7 adsorption on iron carbide surfaces, in which i refers to the corresponding adsorbed n-alkyl species surface

species

χ-Fe5 C2

CH3 C2 H5 C3 H7 CH3 C2 H5 C3 H7 CH3 C2 H5 C3 H7 CH3 C2 H5 C3 H7

Fe7 C3

θ-Fe3 C

η-Fe2 C

∆Edefi ∆Edefslab Eint ∆Eadsi (kJ/mol) (kJ/mol) (kJ/mol) (kJ/mol) 45 9 -270 -216 45 7 -252 -200 44 8 -256 -204 46 14 -246 -186 48 10 -224 -166 47 15 -234 -172 42 7 -238 -189 45 9 -228 -175 46 8 -234 -181 49 21 -271 -201 54 23 -278 -201 52 23 -279 -204

9

The calculated values show that the largest interaction energies still correspond to sur-

10

faces where the strongest adsorption energies were found, i.e. χ-Fe5 C2 (010) and η-Fe2 C(011).

11

Furthermore, the largest deformation energy for the molecule corresponds to the observed

12

deformation of the adsorbates on the surface (Supporting information Figures S21, S22 and

13

Tables S15-S18).

14

In order to visualize the redistribution of electrons upon adsorption, the difference in

15

electron density (∆ρ) was calculated for CH3 adsorption on the different surfaces, assuming

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

that a similar behaviour will exist for larger n-alkyl species. The results are presented in

2

Figure 5.

18


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

As shown by the magnitudes of the electron density difference, most of the electron

2

redistribution occurs in the bonding region between the CH3 group and the neighbouring

3

surface atoms. For the surfaces χ-Fe5 C2 (010), Fe7 C3 (001) and θ-Fe3 C(001) (Figures 5a, 5b

4

and 5c), the adsorbed molecule seems to be losing some electron density in order to create

5

two new bonds C-Fe1 and C-Fe2 . In the case of η-Fe2 C(011) the electron density lost by

6

the molecule seems to create only one bond with a carbon atom from the surface (C-Cs ).

7

Despite the C atom from the molecule and one of the irons from the surface being sufficiently

8

close for a bond to exist (204 pm), there is no charge redistribution between those two atoms

9

(Figure 5d), and therefore, adsorption on η-Fe2 C(011) can only be considered as a carbon

10

on-top position.

11

Adsorption of 1-alkenes

12

In the case of 1-alkenes two different adsorption modes, π and di-σ, are possible. A π-mode

13

was found to be most stable for the surface Fe7 C3 (001) and η-Fe2 C(011), whereas the di-

14

σ configuration is present on the surfaces χ-Fe5 C2 (010) and θ-Fe3 C(001). The calculated

15

adsorbed structures and their key bond parameters are given in Figure 6 and Tables 3 and

16

4, respectively.

17

In the π coordination mode (see Table 3) for the surfaces Fe7 C3 (001) and η-Fe2 C(011),

18

the first two carbon (C1 and C2 ) and hydrogen atoms from the adsorbed molecule are located

19

approximately in the same plane parallel to the surface, whereas the rest of the hydrocarbon

20

chain (in the case of larger chains) is perpendicular to the surface. In the case of C2 H4

21

adsorbed, the four H atoms have H-C-C angles of 121 ±1◦ , remaining as in the gas phase

22

molecule (121 ±1◦ ), while the internal angles H-C-H are 116±1◦ as compared to 120◦ in

23

the gas phase molecule (Supporting Information Figures S23 and S24). The C1 -C2 distance

24

is slightly elongated in comparison with the molecule in gas phase, increased from 133 pm

25

to 139 pm (Table 3), showing that the bond is weakened. The geometries of the obtained

26

modes agree with previously reported structures of C2 H4 adsorbed on θ-Fe3 C(100) in a π 20


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Page 22 of 40

Table 3: Selected structural parameters of 1-alkenes adsorbed species at the most stable site in a π adsorption geometry for the Fe7 C3 (001) and η-Fe2 C(011) surfaces

C2 H4 C3 H6 C4 H8 C5 H10 C6 H12 C7 H14

dF e−C1 (pm) 218 220 219 220 220 220

dF e−C2 (pm) 219 225 224 223 223 223

dC1 −C2 (pm) 140 139 139 139 139 139

C2 H4 C3 H6 C4 H8 C5 H10 C6 H12 C7 H14

219 225 218 218 218 219

218 225 224 224 223 222

139 139 139 139 139 139

surface

species

Fe7 C3 (001)

η-Fe2 C(011)

1

For the di-σ configuration (see Table 4) the first two carbon atoms of the 1-alkene species

2

are bonded to two different Fe atoms of the surface. This configuration was found for the

3

surfaces χ-Fe5 C2 (010) and θ-Fe3 C(001) (Figures 6a and 6c). The C1 -C2 bond lengths increase

4

from 133 pm to 144 pm and 145 pm, still smaller than the 154 pm of a single C-C atom bond

5

(Table 4) but showing stronger bond weakening than for the π configuration. Moreover, the

6

angles of the four H atoms H-C-C are between 116◦ and 119◦ , which shows a modification

7

of the sp2 nature of the carbon atoms present in the molecule in gas phase towards a partial

8

sp3 character. The internal angles H-C1 -H and H-C2 -H are 113◦ (Supporting information

9

Figures S25 and S26), this configuration is similar to previously reported structures of C2 H4

10

adsorbed on a different surface plane (θ-Fe3 C(100)) in a di-σ mode. 55

11

On θ-Fe3 C(001), ethene (C2 H4 ) adsorbs in a different mode than the larger hydrocarbons,

12

called µ-bridging mode. µ-bridging is defined as the combination between a π adsorption

13

mode and two symmetric di-σ modes, in line with the definition previously reported for this

14

type of configuration. 55 A µ-bridging absorbed ethene is essentially π-bond, but the C2 H4

15

tilts such that both carbon atoms can also form a bond with the neighbouring Fe atom, 22


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Page 24 of 40

Table 4: Selected structural parameters of 1-alkenes adsorbed species in a di-σ adsorption mode surface

species

χ-Fe5 C2 (010)

C2 H4 C3 H6 C4 H8 C5 H10 C6 H12 C7 H14

dF e1 −C1 (pm) 212 214 214 214 214 214

dF e1 −C2 (pm) 206 206 206 206 206 206

dF e2 −C1 (pm) 238 237 237 237 237 237

212 212 212 211 211 211

211 214 214 214 215 215

249 249 246 243 243 243 243

C2 H4 a C3 H6 C4 H8 C5 H10 C6 H12 C7 H14 a µ-bridging adsorption b dF e3 −C2

θ-Fe3 C(001)

b

dC1 −C2 (pm) 145 144 144 144 144 144 145 145 145 145 145 145

1

The adsorption energies of 1-alkene species decrease as the carbon chain increases, but

2

from a chain length of five on the adsorption energy remains almost constant with variations

3

of ±1 kJ/mol (Figure 8). Furthermore, the µ adsorption mode can be present on surfaces that

4

are smoother, where more interactions between the surface and the adsorbate are expected.

5

To provide more information about the differences in adsorption energy, deformation and

6

interaction energies were calculated for C2 H4 and C3 H6 (Table 5). Table 5: Calculated interaction and deformation energies for C2 H4 and C3 H6 adsorption on iron carbide surfaces,in which i refers to the corresponding adsorbed 1-alkene species surface

species

χ-Fe5 C2 (010)

C 2 H4 C 3 H6 C 2 H4 C 3 H6 C 2 H4 C 3 H6 C 2 H4 C 3 H6

Fe7 C3 (001) θ-Fe3 C(001) η-Fe2 C(011)

adsorption mode di-σ di-σ π π µ-bridge di-σ π π

∆Edefi (kJ/mol) 82 70 22 15 88 88 18 18

24

∆Edefslab (kJ/mol) 9 9 10 10 9 9 10 10


Eint (kJ/mol) -209 -202 -109 -112 -187 -191 -99 -106

∆Eadsi (kJ/mol) -118 -123 -77 -87 -90 -95 -72 -86

Page 25 of 40




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1

As shown in the electron density difference plot, the main redistribution of electron

2

density takes place in the bonding region between adsorbate and the surrounding atoms of

3

the surface. For the surfaces Fe7 C3 (001) and η-Fe2 C(011), on which 1-propene adsorbs in a π

4

adsorption mode (Figures 9b and 9d) the adsorbed molecule loses some electron density from

5

the region between the C1 and C2 in order to interact with a surface Fe atom. In the case

6

of the di-σ adsorption modes present in χ-Fe5 C2 (010) and θ-Fe3 C(001) there is an electron

7

density redistribution from the 1-propene molecule to the two iron atoms of the surface to

8

create new bonds (Figures 9a and 9c). In the case of the µ-bridging mode, present on the

9

C2 H4 adsorption on Fe3 C(001) surface, the electron density redistribution resembles the π

10

adsorption mode with a small redistribution of electron density from the two surface iron

11

atoms, which form the di-σ contribution (Supporting information Fig. S28).

12

Physisorption of n-alkane species

13

To study the physisorption of n-alkane species different assumptions were made in order to

14

overcome some technical difficulties. The main problem to study physisorbed molecules is

15

the lack of a strong interaction between surface and adsorbate, ergo, finding a solution that

16

fulfils the convergence criteria is difficult. On the other hand, the most stable way to adsorb

17

n-alkanes is parallel to the surface, however, this configuration leads to spatial limitation

18

problems, because the size of the surface unit cell is not sufficiently large to avoid the

19

interaction between neighbouring images of the periodic model, having a direct influence on

20

the adsorption energies. Therefore, these configurations were avoided. The results presented

21

in this work provide a qualitative insight about the adsorption trends of large n-alkanes.

22

For optimization, the n-alkanes are placed perpendicular to the iron carbide surfaces.

23

The final geometries obtained after relaxation remain perpendicular, with similar geometries

24

for the different studied slabs (Figure 10).

25

In Table 6 the reported distances between adsorbate and the surface are listed. The

26

reported values correspond to the distance between the first carbon atom of the hydrocarbon 27




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Table 6: Closest distance between n-alkanes physisorbed and the surface surface χ-Fe5 C2 (010)

Fe7 C3 (001)

θ-Fe3 C(001)

η-Fe2 C(011)

species CH4 C2 H6 C3 H8 C4 H10 C5 H12 C6 H14 CH4 C 2 H6 C 3 H8 C4 H10 C5 H12 C6 H14 CH4 C 2 H6 C 3 H8 C4 H10 C5 H12 C6 H14 CH4 C 2 H6 C 3 H8 C4 H10 C5 H12 C6 H14

d (pm) 351 352 352 351 351 351 388 385 385 360 360 363 342 330 320 320 317 317 369 369 353 353 353 350

1

The data in Table 6 show that for all the surfaces CH4 and C2 H6 are located slightly

2

further from the surface than larger hydrocarbon chains, which position for a chain length

3

> 3 remains almost constant on χ-Fe5 C2 (010), θ-Fe3 C(001) and η-Fe2 C(011). In the case

4

of the Fe7 C3 (001) surface, the changes in distance are more pronounced and the molecule is

5

located at a larger distance from the surface; this can be related to the lower smoothness of

6

the surface, leading to a higher number of adsorbate-surface interactions compared with the

7

other studied surfaces. Nonetheless, given the lack of an actual chemical bond between the

8

molecule and the neighbouring surface atoms, and the fact that mainly dispersive interactions

9

play a role in the physisorption of n-alkanes, it is difficult to establish a direct relation of

10

the effect of the surface on the physisorption strength. 29




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1

kJ/mol, calculated for η-Fe2 C(011) and θ-Fe3 C(001). 4

2

Conclusions

3

The adsorption of n-alkyls, 1-alkenes and n-alkanes was studied for different hydrocarbon

4

chain lengths using periodic DFT calculations. These species were adsorbed on four different

5

carbide phases considered active in FTS. The studies were carried out at low coverages.

6

For n-alkyl adsorption a bridge position between two iron atoms was found as the most

7

stable configuration for the χ-Fe5 C2 (010), Fe7 C3 (001) and θ-Fe3 C(001) surfaces, whereas, an

8

on-top position on a surface carbon atom was found as the most stable for η-Fe2 C(011). It

9

was found that the adsorption energy is correlated with the ratio of C/Fe atoms exposed in

10

the top layer of the iron carbide surface. As a result, surfaces with a larger carbon content

11

have a higher affinity for n-alkyl adsorption (χ-Fe5 C2 (010) and η-Fe2 C(011)).

12

The adsorption of 1-alkenes displays two different adsorption modes: π and di-σ. In

13

this case, adsorbed 1-alkenes in a di-σ mode are the most stable (χ-Fe5 C2 (010)0.00 and θ-

14

Fe3 C(001)).

15

n-alkane physisorption energies are similar for all the studied surfaces. Moreover it was

16

found that the morphology of the surface has an effect on the value of the physisorption en-

17

ergy, leading to the strongest physisorption energies on the smoothest surface (θ-Fe3 C(001)).

18

In all cases, it was found that adsorption energies do not depend on the length of the

19

hydrocarbon chain adsorbed after a particular chain length: three carbon members for n-

20

alkyl species, five for 1-alkenes and four for n-alkanes.

21

A commonly made hypothesis in Fischer-Tropsch microkinetic modelling is to assume

22

that adsorption energies are independent of chain length from a length of three carbons on.

23

This study confirms that the adsorption strength of hydrocarbon chains with more than 3

24

carbon atoms can indeed be considered to be independent of the hydrocarbon chain length

25

in good approximation when experimental or theoretical information is not available, but

31



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Page 32 of 40

1

that for alkenes a better threshold amounts to a carbon chain length of five.

2

Acknowledgement

3

This work is undertaken in the context of the project “FASTCARD, FAST Industrialisa-

4

tion by CAtalysts Research and Development”. FASTCARD is a Large Scale Collabora-

5

tive Project supported by the European Commission in the 7th Framework Programme

6

(GA no 604277). For further information about FASTCARD see: http://www.sintef.no/

7

fastcard, and by the “Long Term Structural Methusalem Funding by the Flemish Gov-

8

ernment.” The computational resources (Stevin Supercomputer Infrastructure) and services

9

used in this work were provided by the VSC (Flemish Supercomputer Center), funded by

10

Ghent University, FWO and the Flemish Government-department EWI.

11

Supporting Information Available

12

Irreducible k-point grids in reciprocal space, relaxed and constrained atoms, calculated and

13

experimental lattice vectors of the different studied phases, calculated and experimental

14

XRD paterns, details on the effect of slab thickness over the adsorption energies, details on

15

the effect of coverage over the adsorption energies, detailed description of all the available

16

adsorption sites for the different studied surfaces, the results of screening for the preferential

17

adsorption sites for the different adsorbates in the simulations for all the studied surfaces,

18

structural parameters of CH3 , and C2 H5 adsorbed, structures of C2 H4 adsorbed and the

19

electron density distribution of C2 H4 adsorbed.

20

The following files are available free of charge.

21

• Supportinginfo.pdf: Supporting information file

22

This material is available free of charge via the Internet at http://pubs.acs.org/.

32


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1


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