Predictive CO and H2 Chemisorption by a Statistical Cuboctahedron

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Platinum Supported Catalysts: Predictive CO and H Chemisorption by a Statistic Cuboctahedron Clusters Model Anthony Le Valant, Clement Comminges, Fabien Can, Karine Thomas, Marwan C Houalla, and Florence Epron J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09241 • Publication Date (Web): 07 Nov 2016 Downloaded from http://pubs.acs.org on November 10, 2016

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The Journal of Physical Chemistry

Platinum Supported Catalysts: Predictive CO and H2 Chemisorption by a Statistic Cuboctahedron Clusters Model Anthony Le Valanta,*, Clément Commingesa, Fabien Cana, Karine Thomasb, Marwan Houallab and Florence Eprona. a: Université de Poitiers, UFR SFA, IC2MP, UMR-CNRS 7285, Bât B27, 4 rue Michel Brunet, TSA 51106, 86073 Poitiers cedex 9, France b: Laboratoire Catalyse et Spectrochimie, ENSICAEN – Université de Caen – CNRS, 6 Boulevard Maréchal Juin, 14050 Caen, France *: corresponding author: [email protected]

1 ACS Paragon Plus Environment


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Abstract Chemisorption of probe molecules such as hydrogen and carbon monoxide on the surface of Pt particles is the most common chemical technique used to estimate the crucial parameters of metal catalysts, namely the dispersion (D), the particle size (d) and the metallic specific surface area (SPt). However, it remains a controversy concerning the stoichiometry of adsorbate per surface metal atom, leading to an inaccurate estimation of D, d and SPt. A model describing the statistics of the surface atoms and sites on perfect cubooctahedron clusters was developed to assess values of D, d and SPt, assuming the most favourable adsorption sites based on DFT calculation of the literature. This model successfully predicted the experimental values of D, d and SPt determined from H or CO chemisorption data, and it allowed providing a set of simple equations for the accurate determination of these parameters from chemisorption experiments on Pt. Keywords: Platinum, H2, CO, adsorption sites, dispersion, particle size, metallic specific surface area, stoichiometric factors.


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1. Introduction Pt-based heterogeneous catalysts are well known to be very active for various catalytic reactions. They have been extensively investigated since several decades for chemical manufacturing, energy applications or environmental technologies1-4. Reactions at metallic surface of heterogeneous catalysts require to precisely know both the dispersion and the average metal particles size since the overall efficiency of metal catalysts is commonly determined using the turn over frequency

1

(TOF), reflecting the reaction rate per surface

atom. In addition, the particle size is used when geometric and electronic effects on activity and selectivity are examined 5. The determination of dispersion, particle size and metallic surface area is usually performed using physical and chemical methods 6.The main physical techniques for determining the dispersion and particle size are related to the use of scattering and absorption techniques or based on the direct observation of the particles by transmission electron microscopy (TEM) or X-ray diffraction (XRD) analysis. Chemisorption of probe molecules, such as hydrogen and carbon monoxide, on the surface of metal particles is the most common chemical techniques used to estimate the dispersion (D (%)), the particle size (d) and the metallic specific surface area (SPt) of Pt catalysts. This experimental method presents the great advantage not to require any expensive equipment. The principle of this technique is to quantify the amount of probe molecule (H2 or CO) adsorbed on the Pt surface (PtS) according to the following reactions: + →

(1)

+ →

(2)

where, 2α and β represent the chemisorption stoichiometric factors of H and CO over the surface of the metal, respectively, which are defined by Eq.1 and Eq.2:

2 =

=

Eq.1 Eq.2 3 ACS Paragon Plus Environment


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If the chemisorption stoichiometric factors 2α and β are known, the dispersion from H2 and CO chemisorption measurements (denoted DH and DCO, respectively) may be estimated, using the following equations (Eqs. 3 and 4): % =

×

×

% =

× 100 =

× 100

Eq.3

× 100 =

× 100

Eq.4

where, H/Pt and CO/Pt represent the number of chemisorbed molecules (H or CO) per total metal atoms.

Despite great deal of effort to understand the mechanisms of H2 or CO chemisorption, it remains a mismatch in the literature in terms of A/PtS (where A = H or CO) stoichiometric factor (α, β) for a given adsorbate molecule-metal system even if it remains a predominant extent in the evaluation of materials performance. For instance, the common assumption is that the values of CO/PtS

7-10

and of H/PtS

7, 9-11

supported on various materials is ~ 1.

However, some data also report H/PtS stoichiometry factor exceeding unity. For instance, Kip et al

12

performed careful characterization of supported platinum catalysts by hydrogen

chemisorption and EXAFS analysis and reported H/Pt 1.14. Several explanations have been advanced for H/M and/or CO/M ratios values higher than unity, such as the spillover of hydrogen to the support

13

or a localized increase of the adsorption stoichiometry of probe

molecules to the corners and edges of the small metal particles 12, 14.

Once the amount of metal atoms at the surface is determined by chemisorption of probe molecule, the metal particle size is generally simply calculated, directly from the dispersion value, assuming a particle shape similar to a sphere or a cube and an equal amount of low index planes (111), (110) and (100) 6, 15. However, this oversimplification can be a source of mistake since it is known that the amount of each type of plane depends also on the equilibrium shape. In the case of cubooctahedron for example, the most common shape 4 ACS Paragon Plus Environment

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admitted for noble-metals clusters, (110) planes are not present at the surface and the amount of (111) and (100) planes depends on metal particle size, and adequate mathematical models are strongly needed to link together the particle size, the dispersion and the chemisorption value 5.

Consequently, the key-points for an accurate determination of metal dispersion and the related metal particle size from H2 and CO chemisorption experiments are the exact knowledge of the chemisorption stoichiometry 16, which needs the development of a reliable and user-friendly mathematical model to calculate these parameters. Obviously, there is a real expectation to establish a molecular-level understanding for describing the interplay between adatoms and the metal surface. The aim of this study is to describe the hydrogen and carbon monoxide chemisorption properties on platinum and determine the stoichiometric ratios H/PtS and CO/PtS using a simple methodology based on the identification of the most favourable adsorption sites from Density Functional Theory (DFT) results of the literature .A statistical model, taking into account the particle shape, and then the H and CO chemisorptions on fcc metal clusters, will be developed to quantify the adsorption sites and estimate the dispersion, metal particle size and the metallic surface area from the H/Pt and CO/Pt ratios. The proposed statistical model will be confronted with the H/Pt and CO/Pt ratios and particle size values obtained from literature data.

2. Model calculation 2.1. Pt particle shape The equilibrium shape of the Pt particle depends on its size

17

. Fig. 1 shows the five main

shapes a Pt particle can adopt, namely, the icosahedron (Fig. 1a), the Marks decahedron (Fig.1b), the perfect truncated decahedron (Fig.1c), the cuboctahedron (Fig.1d) and the truncated octahedron (Fig.1e, also named Wulf polyhedron). Many molecular dynamics



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calculations for metal particles 18 show that for very small sized Pt clusters (< 100 atoms) the non-crystalline icosahedron structure (Fig.1a) is the most stable shape. Then, beyond a certain cluster size (> 100 atoms), the equilibrium shape changes from an icosahedron to a noncrystalline truncated decahedron structure (Fig.1b and c for Marks decahedron and perfect truncated decahedron, respectively) and finally, for a large size (> 6500 atoms), the equilibrium shape changes from a non-crystalline truncated decahedron structure to a fcccrystalline truncated octahedron structure (Fig.1e). The cuboctahedron (Fig.1d) is systematically less stable than the truncated octahedron for fcc-crystalline Pt structure. For describing the chemisorption properties on a given metal, it becomes necessary to precisely quantify the proportion of surface atoms for a given cluster size and shape. This can be achieved by using the methodology of Van Hardeveld and Hartog 19 consisting in a systematic way of atom (surface and total) numbering by using mathematical series. However, the phase transitions at NT = 100 and 6500 atoms induce an additional complexity when a global model for quantifying the number of surface atoms is needed. It turns out that the choice of the shape is detrimental since the surface statistics depends directly on the latter. There is a need of using a shape that can unify the evolution of surface atoms as a function of the cluster size, from nanometer to a massive size. Among all the shapes discussed above (Fig. 1), it appears that the cuboctaedron shape can perfectly mimic the evolution of surface atoms as a function of the cluster size, as shown in Fig. 2. In this figure, one can see that the surface ratio (denoted NS/NT) is well modeled in the full range of sizes when using the cubooctahedron single shape. Its surface ratio is identical to the most stable clusters in the 3 stability domains ( NT < 100 ; 100 < NT < 6500 and NT > 6500), providing a convenient way for describing all cluster sizes while keeping the surface ratio rigorously identical to the most stable shapes.


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(a)

(b)

(c)

(d)

(e)

Fig.1: Morphology of Pt particles. (a) Icosahedron with 147 atoms (m=2); (b) Marks decahedron with 75 atoms (m = n = r =2, see Baletto et al. 18 for more details); (c) perfect truncated decahedron with 147 atoms (m=2); (d) cuboctahedron with 147 atoms (m=2) and (e) truncated octahedron with 201 atoms (m=3). (m is the number of atoms lying on an equivalent edge, corner atoms included, of the chosen particle).

NS/NT

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


1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1

10

100

1000

10000 100000

NT Fig.2: Proportion of surface atoms for an icosahedron (cross), perfect truncated decahedron (square), cuboctahedron (circle) and truncated octahedron (triangle) particles comprising NT atoms with NS at the surface (with NT and NS determined according to the methodology of Van Hardeveld and Hartog 19, see section 2.2 for more details). The verticals lines represent the crossover among structural modifications in transition between icosahedron and perfect truncated decahedron (blue) and between perfect truncated decahedron and truncated octahedron (red) for Pt clusters, see Baletto et al.

18

for more details). (For interpretation of the references to

color in this figure caption, the reader is referred to the web version of this article).

In the present work, the shape of metal crystallite (or particle) is assumed to be a fcc cubooctahedron for the above mentioned reasons, with six square and eight triangular faces



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(see Fig.3). In addition, DFT calculations for energetic profiles for hydrogen adsorption sites have been described for cubooctahedron Pt clusters of various sizes 20-21. It also completes one missing shape to the library data base of Van Hardeveld and Hartog model

19

(see section

2.2).

2.2. Relationship between the surface atoms, dispersion, size and metallic specific surface area of the cuboctahedron crystallite In 1969, Van Hardeveld and Hartog developed a simple model (denoted VH model) to describe the surface structure (corners, edges and faces) for unsupported perfect fcc crystallites (tetrahedron, cube, octahedron, rhombic dodecahedron and Wulf cuboctahedron) 19

. These authors described that the total number of atoms (denoted NT) constituting a

crystallite is made up of a number of bulk atoms (denoted NB) and a number of surface atoms (denoted NS). Testing a series of geometrically similar crystallites of different value of m parameter (m is the number of atoms lying on an equivalent edge, corner atoms included, of the chosen crystallite), they proposed that the NT and NB are given by a 3rd order polynomial in m, whereas NS is given by 2nd order polynomial in m. In addition, the number of atoms with i coordination number (denoted NCi and corresponding to the atoms constituting the corners, edges and faces) is given by a 0th, 1th or 2nd order polynomial in m.


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Fig.3: Idealized representation of the fcc perfect cuboctahedron metal cluster. The numbers 5 (grey), 7 (red), 8 (blue) and 9 (green) represent the coordination number of the atoms located in the corners, edges, faces (100) and faces (111), respectively. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article).

Using the VH model methodology

19

, the NT, NB and NS numbers for a fcc perfect

cuboctahedron are determined from the following equations (Eqs. 5-7): =

!

× #" $ 5 × # +

& =

!

× #" $ 15 × # +

"

"

"

×#$1

' "

× # $ 13

= 10 × # $ 20 × # + 12

Eq.5 Eq.6 Eq.7

Using these data, it is possible to obtain directly the dispersion (denoted D (%)) and the particle size (d), with the following equations (Eqs. 8 and 9): % =

)

)*

× 100

Eq.8 .

+ ,# = 1.105 × / × +

Eq.9

where, 1.105 is an average constant for fcc lattice type and dPt is the metallic diameter (dPt = 0.279 nm). More details about Eq.9 are reported in the Van Hardeveld and Hartog work 19.



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The NCi numbers (denoted NC5, NC7, NC8 and NC9) for a fcc perfect cuboctahedron corresponding to the atoms located in the corners, edges, (100) and (111) faces, respectively (see Fig.1), are obtained from the following equations (Eqs. 10-13): 0 = 12

Eq.10

' = 24 × # $ 2

Eq.11

2 = 6 × # $ 2

Eq.12

4 = 4 × # $ 2 × # $ 3

Eq.13

For each cuboctahedron cluster size, it is possible to determine the fraction of surface atoms of type NCi (expressed in fraction of sphere) using the following equations (Eqs. 14-17): 50 = 1 $

678

Eq.14

5' = 1 $

;67
0 and >' represent the solid angle subtended at atoms of type NC5 (corner) and the dihedral angle corresponding to the intersection between two faces (square and triangle) on a given edge, respectively. The solid angle (expressed in steradian) and the dihedral angle (expressed in radian) are obtained from the following equations (Eqs. 18 and 19):

=>0 = 4 sinB C E

Eq.18

>' = F $ tanB I√2J

Eq.19

√"

Knowing the NCi numbers and the fraction of surface atoms of type NCi, it is possible to calculate the surface area of surface atom of type NCi exposed (denoted SCi) with the following equations (Eqs. 20-23): =0 ,# = 4F × C

KLM

E × 0 × 50

Eq.20


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KLM

Eq.21

KLM

Eq.22

KLM

Eq.23

=' ,# = 4F × C =2 ,# = 4F × C =4 ,# = 4F × C

E × ' × 5' E × 2 × 52

E × 4 × 54

Using these data, it is possible to obtain the metallic specific surface area (SPt) of the cuboctahedron particle for a given m (number of atoms lying on equivalent edge, corners atoms included, of the chosen crystallite), with the following equation (Eq.24): B

= # N =

78 O7< O7PO7Q ×!R.P / T S :×C LM ×!RV E ×)*×WLM / U

Eq.24

where X is the density of Pt. For each value of m, it is possible to determine the total and the surface atoms fraction (denoted NCi/NT and NCi/NS, respectively) using the values obtained for NT, NS and NCi. The evolution of the NCi/NT and NCi/NS fraction versus the dispersion, the metallic specific surface area and the particle size are represented in Fig.2a and b, Fig.2c and d and Fig.2e and f, respectively.



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Fig.4: Statistics of atoms (a) and surface atoms (b) versus the metal dispersion. Statistics of atoms (c) and surface atoms (d) versus the metallic specific surface area. Statistics of atoms (e) and surface atoms (f) versus the particle size. Population fraction of atoms are represented for bulk (circle, black), corners (square, grey), edges (triangle, red), (100) faces (lozenge, blue) and (111) faces (cross mark, green). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article).

As the metal dispersion (or metallic specific surface area) increases, there is an obvious decrease of the number of bulk atoms in the favor of surface atoms (Fig. 4a and c). Among these surface atoms, one can see that edges, (100) and (111) faces reaches a maximum value, whereas the number of corners monotonously increases. As can be intuitively expected, the NCi/Ns surface ratio of these atoms as a function of dispersion or metallic specific surface area (Fig. 4b and d) clearly highlights that atoms of low coordination number are favored at high 12 ACS Paragon Plus Environment

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dispersion and metallic specific surface area. When NCi/NT and NCi/NS are plotted against the particle size (Figs. 4e and f, respectively), it can be seen that the surface distribution of the different atoms becomes quite stable for particle size above ca. 6 nm, and atoms of low coordination number are favoured at low particle size. In terms of metal catalytic activity for a given reaction, it is expected that atoms with low coordination number are the most prone to chemisorb substrates since these atoms tend to complete their coordination to 12. In this sense, the surface statistics presented in Fig.4 can be seen as a picture of a metallic catalyst activity per gram of metal by using the total atom fraction (NCi/NT) or TOF by using the surface atom fraction (NCi/Ns).

2.3. Statistics of adsorption surface sites The surface of a cuboctahedron cluster has different populations of adsorption sites, which evolve with the increase of the particle size (or with the m value). One can classify these different adsorption sites into three kinds: top, bridge and hollow sites, respectively. Fig. 5 shows the different top, bridge and hollow (3-fold fcc or hcp and 4-fold) adsorption sites for different values of m over the square and the triangle faces. All these adsorption sites were characterised by the geometry (1, 2, 3 and 4, for top, bridge, hollow 3-fold hcp or fcc and hollow 4-fold sites, respectively) and the coordination number of the atoms constituting the 0,'

site. For example, the

site corresponds to a bridge site between NC5 corner and NC7

edge atoms.



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Fig.5: Representation of the adsorption sites considered in the present work over triangular and square faces of a cuboctahedral shape with different m value. Top sites: white circle with a T; bridge sites: yellow circle with a B and hollow sites: purple circle with a H. The numbers 5 (grey), 7 (red), 8 (blue) and 9 (green) represent the coordination number of the atoms located in the corners, edges, faces (100) and faces (111), respectively.(For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article).

Across the range of particle sizes studied (nanometric to bulk size), there are 24 kinds of possible adsorption sites (4, 8 and 12 kinds for top, bridge and hollow sites, respectively). Table 1 summarizes the enumeration and the equations giving the number of each adsorption site for a given m. Once knowing the complete surface statistics of the possible adsorption sites, it is necessary to determine the most favorable sites from an energetical point of view, so as to predict the hydrogen adsorption properties of any cluster size.


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Table. 1: Statistics of adsorption sites numbering for cuboctahedron cluster. Sites

Location 0

Top

'

2

4

Bridge

Hollow

0,0

0,'

','

[K\[ ','

]^_[ ',2

2,2

',4

4,4

0,0,0

"a_b 0,','

"a_b ',','

"a_b ',',4

"]__ ',',4

a_b ',4,4

"]__ 4,4,4

"]__ 4,4,4

"a_b 0,0,0,0

9 0,',',2

9 ',',2,2

9 2,2,2,2

9

m ≥5 12 24 × # $ 2

6 × # $ 2

2 12 0 0

3 12 24 6

4 12 48 24

0

0

8

4 × # $ 2 × # $ 3

24 0

0 48

0 48

0 48

0

0

24

24 × # $ 3

0

24

24

24

0 0 0 0

24 0 0 0

48 24 48 0

24 × # $ 2

12 × # $ 2 × # $ 3

48 × # $ 3

12 × # $ 3 × # $ 4

8

0

0

0

0

24

24

24

0

8

0

0

0

0

24

24 24 × # $ 3

0

0

24

0

0

0

0

0

0

24 × # $ 4

4 × # $ 4 × # $ 5

0

0

0

4 × # $ 3 × # $ 4

6 0 0 0

0 24 0 0

0 24 24 6

0 24 24 × # $ 3

6 × # $ 3

2.4 Surface hydrogen adsorption sites on Pt cuboctahedron crystallite (H/Pt) and H chemisorption stoichiometric factors (H/PtS) To obtain an estimate of the number of hydrogen atoms that can be placed around such a cuboctahedron crystallite (denoted NH for a given m), it is essential to know the most favorable adsorption sites of hydrogen atom for a given size. These parameters can be known by conducting systematic DFT calculations of hydrogen adsorption energy on cuboctahedral Pt clusters with different sizes. Okamoto

20

performed such calculations to clarify the

differences and similarities of hydrogen atom adsorption on fcc Pt cuboctahedron clusters (with m = 2, 3 and 4, denoted P13, Pt55 and Pt147, respectively) and on corresponding Pt flat surfaces (Pt(100) and Pt(111)). These calculations show that hydrogen atom adsorption 15 ACS Paragon Plus Environment


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energy on the clusters gradually decreases with increasing Pt cluster size. The adsorption on the faces of Pt147 cluster is similar to that on the corresponding Pt surfaces (Pt(100) and Pt(111)). Pt13 and Pt55 cuboctahedron clusters show quite different hydrogen adsorption behavior. The hydrogen atom adsorption energy calculated versus the nature of the adsorption site (with the nomenclature used in this work) is reported in Fig.6. For the flat surfaces, the most favorable sites for hydrogen adsorption (see horizontal lines in Figs. 6a-c) are the bridge sites and the hollow fcc sites (3-fold) for the Pt(100) and Pt(111), respectively. However, for small sized clusters (m < 4), bridge sites are the most favorable.

Fig.6: Hydrogen atom adsorption energy on cuboctahedron Pt13 (a), Pt55(b) and Pt147(c) clusters (based on the results of Okamoto 20). Top sites: white bar; bridge sites: yellow bar and hollow sites: purple bar. The black and the red dotted lines represent the hydrogen atom adsorption energies of the bridge sites on flat Pt(100) and the hollow fcc sites on flat Pt(111), respectively.(For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article).

An hydrogen adsorption repetitive sequence from m = 2 to m = ∞ can be elaborated by building a linear combination of adsorption sites determined from the DFT calculations shown in Fig. 6 adapted from ref.

20

. Once an adsorption site is selected for a given cluster

size on the basis of H adsorption energy, it will be kept for the full range of sizes. For the 16 ACS Paragon Plus Environment

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0,0

smallest Pt13 cluster (m = 2), it is obvious that bridge (

) adsorption site is the most

favoured. For the next Pt55 cluster (m= 3), two adsorption sites are energetically close to each ',2

other, the most favourable one being the bridge

0,'

followed by the bridge

. As the

latter site originates from the creation of an edge when m increases, this new adsorption site is 0,0

resulting from the original

observed for the smallest Pt13 cluster. The last Pt147 cluster ','

2,2

displays many new adsorption sites. Among them, [K\[ and

(corresponding to a Pt

(100) face) are the most favourable adsorption sites. In a more general view, bridge sites are the most favoured for small sized clusters. Then, from m = 5 (D = 52.4 %, SPt = 315 m² gPt-1, d= 2.08 nm), the amount of atoms located on faces (48 %) becomes to be similar and then higher than the amount of atoms located on corners and edges (52 %) (Fig. 4b, d and f). This indicates that for m > 5, adsorption sites on faces (100) and (111) have to be taken into 2,2

account. For the Pt(100) face, this site corresponds to the

already selected. Concerning 4,4,4

the Pt(111) face, this corresponds to an additional adsorption site "]__

(corresponding to

hollow fcc Pt(111), Fig.6 red dotted line). When a cluster tends to m = ∞, one can consider that atoms of coordination numbers 8 (face (100)) and 9 (face (111)) are constituting the majority of surface atoms. It is well known that for large Pt clusters the hydrogen coverage is equal to one monolayer (1 ML). When all the 4,4,4

possible "]__ (faces (111)) are occupied, a coverage of 1 ML is attained. However, if all the ',2

bridge sites over (100) faces are occupied (

2,2

and

), a coverage of 2 ML will be

reached (Fig. 7a), which has no sense. Consequently, it becomes necessary to eliminate half of these adsorption sites in a way to reach a pattern corresponding to 1 ML (Fig. 7b). ',2

For this reason, both bridge sites (

2,2

and

) are selected as adsorption sites.



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Fig.7: Representation of bridge H adsorption sites on (100) faces for different H coverages: 2 ML (a) and 1ML (b). Colors and symbols have the same significance as in Fig. 5 (for interpretation of the references to color in this figure caption, the reader is referred to the web version of this article).

Following this hypothesis, the number of H atoms adsorbed on the cuboctahedron surface (for a given m) can be calculated using the following equation (Eq.25): 0,0

=

0,'

+

','

',2

+ [K\[ + 0.5 ×

2,2

+ 0.5 ×

4,4,4

+ "]__

Eq.25

As the number of adsorbed hydrogen as well as the total number of Pt atoms are known, it is possible to calculate the theoretical H/Pt ratio with Eq.26.

=

)d

Eq.26

)*

The values of this statistical model have subsequently been confronted to numerous literature data

14, 22-25

, reported in Table 2. Results depicted in Fig. 8a show that the model predicts

accurately the literature values of H/Pt. In addition, the model predicts H/Pt values in the range 0-1.85. The latter result clearly indicates that a single stoichiometry for platinum cannot be used.


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Knowing the NH value as well as the NS number for each m value, it is possible to calculate the theoretical chemisorption stoichiometric factors with the following equation (Eq. 27):

=

)d

Eq.27

)

Table. 2: Literature results of probe molecule (H2 and CO) chemisorption measurements and average particle sizes (determined by TEM) for Pt catalysts. Catalyst Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/Al2O3 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/SiO2 Pt/Al2O3 Pt/Al2O3 Pt/Al2O3 Pt/Al2O3 Pt/Al2O3 Pt/Al2O3 Pt/Al2O3 Pt/Al2O3

H/Pt 0.62 0.33 0.49 0.59 0.58 0.58 0.81 0.28 0.52 0.28 0.98 0.36 0.89 0.24 0.19 0.53 0.49 0.36 0.29 1.15 1.35 0.98 0.75 0.53 1.11 0.29 0.2 0.37 0.21 0.19 0.89 0.76 0.67 0.53 0.70 0.88 0.62 0.38

CO/Pt 0.56 0.28 0.47 0.53 0.51 0.48 0.95 0.90 0.49 0.11 0.14 0.53 0.39 0.56 0.79 0.57 0.36

d (nm) 1.4 1.6 2.1 2.6 1.4 3.2 1.2 4 8.5 3.1 1.3 1.5 9.1 9.2 1.2 -

Ref 22

14

23

24

25

In order to have a representative view of the surface adsorption properties over Pt, the H/PtS theoretical chemisorption stoichiometric factors versus the theoretical H/Pt ratio are depicted in Fig. 8b. The adsorption of one hydrogen atom per surface Pt atom (PtS) is reasonably constant for H/Pt < 0.44, which corresponds to the large particle size domain (low dispersion). 19 ACS Paragon Plus Environment


However, when H/Pt ≥ 0.44 (small particle size domain and high dispersion), the H/PtS ratio increases with the H/Pt ratio to reach a maximum value of 2.00. This particular behaviour directly originates from the 6 different sites considered for hydrogen adsorption (Eq. 25) as

H/Pt

well as their relative proportion (Table 1). 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

(a)

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

d (nm) 2.4

(b)

2.0 1.6

H/PtS

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

Page 20 of 31

1.2 0.8 0.4 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

H/Pt Fig.8: Evolution of the H/Pt ratio versus the particle size (a). Evolution of the H/PtS ratio versus the H/Pt ratio (b). Full circle: literature data for Pt (see Table.2); and open circle: result of the statistic model calculation of this work.

2.5 Surface CO adsorption sites on Pt cuboctahedron crystallite (CO/Pt) and CO chemisorption stoichiometric factors (CO/PtS) Contrarily to hydrogen adsorption, the case of CO adsorption on Pt raises the additional difficulty to precisely establish in a theoretical way the location of the adsorption sites. It was experimentally demonstrated that CO adsorbs mainly on top sites with a minority of bridge sites for Pt(111) 26-27, whereas DFT prediction fails at describing this preference by favouring hollow (fcc 3-fold) adsorption sites

28

. This discrepancy between theoretical calculation and

experimental evidences is known as the CO/Pt(111) puzzle. A great deal of efforts was made 20 ACS Paragon Plus Environment

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to account for this mismatch and some advanced calculation methods could predict the top site as the most favourable one

29-31

. Concerning the Pt(100) face, it is experimentally

observed that both top and bridge sites coexist 32 as confirmed by DFT calculations 33. On step edges, a similar coexistence of top and bridge sites are observed experimentally

34

whereas

DFT predictions highlight a preference for bridge over top sites 35. This tends to predict that on corners as well as on step edges bridge sites are favored, which leads to the selection of 0,0

0,'

,

','

and [K\[ sites.

In the case of Pt(111) and Pt(100) faces, the ratio between adsorbed CO on top and bridge sites is depends greatly on the surface coverage as well as on the temperature 27. In the case of chemisorption experiments, a high CO coverage (> 0.5 ML) is generally observed. In this situation, an adequate model for compressed CO adlayers on Pt(111) faces based on I√19 × √19Jf23.4° hexagonal Moiré structure

36

corresponding to coverages above 0.5 predicts well

the coexistence of top and bridge sites as well as the adsorption of 13 CO atoms over 19 Pt atoms of coordination 9 (NC9). This coverage on the Pt(111) face corresponds to a value of 5 =

" 4

≈ 0.68. In a similar way, the CO adsorption on Pt(100) face (atoms NC8) is finely

described by the i 6 × 2 structure

37

which corresponds to a value of 5!! =

!

≈ 0.83.

Ultimately, the CO adsorption on Pt cuboctaedron clusters for any m value will be described according to Eq. 28 below: 0,0

=

0,'

+

','

+ [K\[ + 5!! × 2 + 5 × 4

Eq. 28

Using the NCO value for a given m, it is possible to obtain the theoretical CO/M and chemisorption stoichiometric factor CO/PtS ratio using the following equations (Eqs. 29 and 30):

=

)7j )*

Eq.29



=

CO/Pt

)7j

Eq.30

)

2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

(a)

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

d (nm)

2.4

(b)

2.0 1.6

CO/PtS

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

Page 22 of 31

1.2 0.8 0.4 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

CO/Pt

Fig.9: Evolution of the CO/Pt ratio versus the particle size (a). Evolution of the CO/PtS ratio versus the CO/Pt ratio (b). Full circle: literature data for Pt (see Table.2); and open circle: result of the statistic model calculation of this work.

In the same manner as shown for H/Pt (Fig. 8a), it is possible to plot the CO/Pt ratio as a function of the metal particle size. Fig. 9a demonstrates that the model calculations predict well the literature data and that CO/Pt ranges between 0 and 1.85. This clearly indicates that a single stoichiometry for platinum cannot be used. The surface adsorption properties are highlighted in Fig. 9b, where theoretical stoichiometric factor CO/PtS is plotted as a function of the theoretical CO/Pt ratio for Pt. The same general trends are observed when comparing the hydrogen with CO chemisorption properties for Pt. The adsorption of CO on Pts is monotonously increasing with the CO/Pt ratio. This increase is at first moderate with a low slope for low CO/Pt values (m > 5, large particle size domain) where the number of atoms located on faces are predominant, and


Page 23 of 31

secondly with a higher slope (m < 5, small particle size domain) where corner and edge atoms are more numerous. Globally, the values of CO/Pts vary between 0.77 and 2.00.

2.6 Model validity and relationship between H/Pt and CO/Pt. By comparing the adsorption of H2 and CO on highly dispersed Pt/SiO2 catalysts, Dorling et al

22

observed that the H/CO ratio is approximately constant with a mean value of 1.13 (or

CO/H = 0.88), showing a constant proportionality between both adsorbates. In another study, Freel made a comparison for H2 and CO chemisorption on supported Pt between his work and the literature data

14, 22, 38

24

and observed that all data points lies within the range 0.83 ≤

CO/H ≤ 0.96. He concluded that the results followed the empirical relationship established by Dorling et al. 22. As the values of H/Pt (see section 2.4) as well as CO/Pt (see section 2.5) can be predicted by the statistic cuboctahedron clusters model, a theoretical plot of CO/Pt as a function of H/Pt can be drawn and compared to the literature data

22, 24-25

for Pt (see Table 2). It is observed

that the theoretical calculated values matches the experimental observations (Fig. 10), giving rise to the predictive character of the statistic cuboctahedron clusters model.

CO/Pt

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


2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

H/Pt

Fig.10: Evolution of the CO/Pt ratio versus the H/Pt ratio. Full circle: literature data for Pt (see Table.2) and open circle: result of the statistic model calculation of this work.

To conclude, the use of the same stoichiometry for hydrogen and CO chemisorption would give quite incorrect results. It is therefore unacceptable to use the H/Pt and CO/Pt ratios as a 23 ACS Paragon Plus Environment


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

Page 24 of 31

measure of dispersion or particle size, without the knowledge of the chemisorption stoichiometric factors (H/PtS or/and CO/PtS).

2.7 Determination of the dispersion, particle size and metallic specific surface area from H/Pt and CO/Pt chemisorption ratios Knowing how to determine the statistic parameters (NT, NS, NH, NCO, D (%), d(nm) and B

= # N ) for a given m value obtained by the present model calculations, it is possible to

establish the relationship between dispersion, particle size, metallic specific surface area and A/Pt ratio (Figs. 11a-f), with A corresponding to the adsorbate (H or CO). With the aim of providing a ready-to-use relationship for the determination of these crucial parameters in catalysis, a general polynomial equation relevant for all cases was established. The best fits (with the R-squared value equal to one) were obtained with a 5th order polynomial trend line.


(a) D (%)

100 90 80 70 60 50 40 30 20 10 0

100 90 80 70 60 50 40 30 20 10 0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

CO/Pt

1.6

(c)

1.4

1.4

1.2

1.2

1/d (nm-1)

1/d (nm-1)

1.6

1.0 0.8 0.6 0.4

0.8 0.6 0.4 0.2

0.0

0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

H/Pt 700

(d)

1.0

0.2

800

(b)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

H/Pt

CO/Pt

800

(e)

(f)

700 600

SPt (m2 gPt-1)

600

SPt (m2 gPt-1)

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


D (%)

Page 25 of 31

500

500

400

400

300

300

200

200 100

100

0

0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

H/Pt

CO/Pt

Fig. 11: Evolution of the theoretical dispersion versus A/Pt theoretical ratio (A = H or CO) (a) and (b). Evolution of the theoretical reciprocal particle size versus A/Pt theoretical ratio (c) and (d). Evolution of the theoretical metallic specific surface area versus A/Pt theoretical ratio (e) and (f). Open circle: results of the statistic model calculation of this work. The black curves are the fitting result (R2=1.000) with a 5th order polynomial trend line (see Eqs.31, 32 and 33).

The expression of dispersion (Eq. 31), reciprocal particle size (Eq. 32) and metallic specific surface area (Eq. 33) are given below: 6 0

6 9

6 "

6

6

% = k;l × C E + m;l × C E + i;l × C E + +;l × C E + n;l × C E

Eq.31



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

K

6 0

6 9

Page 26 of 31

6 "

6

6

,#B = k/Kl × C E + m/Kl × C E + i/Kl × C E + +/Kl × C E + n/Kl × C E

Eq.32 6 0

6 9

6 "

6

B

= # N = kLMl × C E + mLMl × C E + iLMl × C E + +LMl × C E + nLMl ×

6

C E

Eq.33

Equations 31-33 can be generalized by the following single equation (Eq.34): 6 0

6 9

6 "

6

6

p6 = kq × C E + mq × C E + iq × C E + +q × C E + nq × C E

Eq.34

where kq , mq , iq , +q k,+ nq are constants depending on the nature of the couple adsorbate A (A = H or CO) / Pt considered. The values of these constants for Eq.34 are listed in the table 3. Finally, the application of the model through the equation 34, along with the corresponding constants provided in table 3, to the literature data of A/Pt as the sole input (table 2) gives access to: i) the Pt dispersion (Fig. 12a), ii) to the Pt particle size (Fig. 12b), and iii) to the Pt metallic surface area (Fig. 12c). Firstly these figures ultimately validate the model since the predicted values of dispersion, particle size and metallic surface area made on the basis of chemisorption experiments are in agreement with independent experimental determinations. Secondly, the predicted values obtained independently with either hydrogen or CO chemisorption are in total agreement.


Page 27 of 31

Table 3: Values of the constants kq , mq , iq , +q k,+ nq for the equation 34. (A: adsorbate; range of validity of the equation 34: 0-1.85 for H/Pt and CO/Pt).

p6 = kq × r

Equation

p6

>

6 %

100 90 80 70 60 50 40 30 20 10 0

kq

H CO H CO H CO

1 ,#B

+6 B = # N

> 0 > 9 > " > > s + mq × r s + iq × r s + +q × r s + nq × r s mq

-29.230 -8.022 -0.138 0.000 -169.517 -13.691

134.647 34.587 0.794 0.066 788.76 99.332

iq

-201.198 -37.990 -1.469 -0.239 -1237.546 -213.811

+q

70.105 -46.169 0.903 0.118 617.783 7.723

nq

98.611 129.198 0.703 0.935 493.468 658.448

DCO (%)

(a)

0

10 20 30 40 50 60 70 80 90 100

(b)

dCO (nm)

dCO (nm)

DH (%) 20 18 16 14 12 10 8 6 4 2 0

4 2 0 0

0

2

4

6

8

2

dH (nm)

4

10 12 14 16 18 20

dH (nm)

800

(c)

700 600

SPtCO (m2 gPt-1)

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


500 400 300 200 100 0 0

100 200 300 400 500 600 700 800 SPtH (m2 gPt-1)

Fig. 12: Evolution of the dispersion (a), the particle size (b) and the metallic specific surface area (c) determined by CO/Pt versus the dispersion, the particle size and the metallic specific surface area determined by H/Pt with Eq. 34. Open circle: results of the statistic model calculation of this work with the literature data (see Table.2); dotted line: DH = DCO, dH = dCO and SPtH = SPtCO



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

Page 28 of 31

3. Conclusion In this study, it was shown that values of H/PtS and CO/PtS, deduced from the chemisorption technique, higher than unity (over-stoichiometry) frequently observed on small sized Pt clusters can be physically described by the evolution of surface sites with the particle size. The statistics of the surface atoms and surface sites was determined by using a model for quantifying the speciation of each surface atom in a perfect cuboctahedron cluster. This model completes one missing shape in the library of Van Hardeveld and Hartog. Assuming different adsorption sites (bridge and hollow (3-fold fcc) sites) based on the literature DFT data for hydrogen on Pt, it was possible to predict precisely the H/Pts stoichiometry, which ranges from 1 to 2 for the smallest cluster. This model was also applied to CO chemisorption. As the adsorption sites for CO on Pt are not necessarily well defined, a combination between DFT calculations (bridge sites on corners and edges) as well as CO adsorption structure motive for adlayer over atoms of NC8 and NC9 (representing atoms forming faces (100) and (111), respectively) was used. The model explains the CO/Pts stoichiometry ranging from 0.77 to 2.00. It was validated by confronting the predictions of H/Pt and CO/Pt and the literature experimental data. This leads to the precise prediction of the metal dispersion, particle size as well as metallic specific surface area from H/Pt as well as CO/Pt. Finally, a set of “ready to use” equations was provided for the determination of dispersion, particle size and metallic specific surface area, which can be employed either for CO or H chemisorption experiments. The model was validated as these parameters, independently obtained from CO or H chemisorption experiments, are equal. This approach based on the combination between identification and quantification of adsorption sites for a given cluster shape is likely to be valid for other fcc metals (Ir, Rh, Pd...). We are currently investigating this assumption in our laboratory.


Page 29 of 31

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Acknowledgments A. Le Valant thanks S. Thomas (ICPEES Strasbourg, France), M. Rivallan (IFP Energies nouvelles Rueil-Malmaison, France). R. Moraes and M. Daturi (LCS Caen, France) for scientific discussions.

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Predictive CO and H2 Chemisorption by a Statistical Cuboctahedron

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