A microkinetic model of the methanol oxidation over silver

Surface Science 544 (2003) 5–23 www.elsevier.com/locate/susc

A microkinetic model of the methanol oxidation over silver A. Andreasen 1, H. Lynggaard, C. Stegelmann, P. Stoltze

*

Department of Chemistry and Applied Engineering Science, Aalborg University, Niels Bohrs Vej 8, 6700 Esbjerg, Denmark Received 14 May 2003; accepted for publication 5 August 2003

Abstract A simple microkinetic model for the oxidation of methanol on silver based on surface science studies at UHV and low temperatures has been formulated. The reaction mechanism is a simple Langmuir–Hinshelwood mechanism, with one type of active oxygen and one route to formaldehyde and carbon dioxide, respectively. The model explains observed reaction orders, selectivity, apparent activation enthalpies and the choice of industrial reaction conditions. More interesting the model disproves the notion that the mechanism deduced from surface science in UHV cannot be responsible for formaldehyde synthesis at industrial steady-state conditions. The present work therefore seriously questions the prevailing models of formaldehyde synthesis in the literature. One of the reasons for this controversy is that many of the models in the literature are derived from transient experiments exhibiting dynamic effects that are not present at steady state under industrial conditions.
2003 Elsevier B.V. All rights reserved. Keywords: Computer simulations; Models of surface kinetics; Equilibrium thermodynamics and statistical mechanics; Oxidation; Catalysis; Silver; Alcohols; Oxygen

1. Introduction The partial oxidation of methanol to formaldehyde is an important industrial process due to the versatility of formaldehyde as an intermediate in chemical synthesis [1]. BASFÕs silver based process is carried out at
900 K and atmospheric pressure, the feed consist of a fuel-rich mixture of methanol and air. At typical reaction conditions the selectivity is approximately 90% and the conversion of oxygen approach 100%, and slightly

*

Corresponding author. Tel.: +45-79-12-76-63 (Office); fax: +45-75-45-36-43 (Department). E-mail address: [email protected] (P. Stoltze). 1 Present address: Department of Materials Research, Risoe National Laboratory, DK-4000 Roskilde, Denmark.

more water than hydrogen is produced [1,9]. Formaldehyde is only formed in the presence of oxygen [2]. Steam is added to increase selectivity and heat transport [1,3,4]. Traditionally the overall process is regarded as two parallel reactions: an oxidation (Eq. (1)) and a dehydrogenation (Eq. (2)) [3–5]. 1 CH3 OH þ O2 H2 CO þ H2 O 2

ð1Þ

CH3 OH H2 CO þ H2

ð2Þ

It has been proposed [1,3,4,6] that the selectivity towards formaldehyde is limited by the following reactions: 2CH3 OH þ 3O2 4H2 O þ 2CO2

0039-6028/$ - see front matter
2003 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2003.08.007

ð3Þ

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A. Andreasen et al. / Surface Science 544 (2003) 5–23

H2 CO þ O2 CO2 þ H2 O

ð4Þ

H2 CO CO þ H2

ð5Þ

The formation of carbon dioxide is favored by low temperatures [7–9]. The formation of carbon monoxide is favored by high temperatures (T > 900 K) [8], and is viewed as a pyrolytic gas phase reaction [4,6]. Despite the fact that the formaldehyde synthesis has existed for more than a century and a substantial research effort has been devoted to the reaction, the mechanism remains controversial. Based on UHV studies on Ag(1 1 0) at 200–300 K Wachs and Madix [10] proposed a simple mechanism for methanol oxidation with only one kind of active oxygen. According to this mechanism the oxidation of methanol to formaldehyde goes through a methoxy intermediate. The methoxy intermediate is formed by a reaction between methanol and atomic surface oxygen and decompose to formaldehyde and hydrogen. The formaldehyde may be oxidized to carbon dioxide through a formate intermediate i.e. a consecutive reaction path (Eq. (4)). Wachs and Madix results shows no indications of a direct reaction pathway from methanol to carbon dioxide i.e. a parallel reaction pathway (Eq. (3)) as proposed by some investigators [8,11]. The methoxy and formate intermediates have been identified and studied with in situ Raman, HREELS, XPS, UPS, and TPR on both single crystals and polycrystalline silver catalysts [10,12–17]. Surface science and density functional theory (DFT) calculations indicates that the mechanistic scheme of Wachs and Madix is general for the oxidation of alcohols on silver and other metal surfaces [12,18–20]. Bhattacharyya et al. [2] proposed a Mars–van Krevelen mechanism [21] from differential reactor data at 264–290 C. They observe positive reaction orders with respect to both methanol and oxygen and an inhibiting effect caused by water. Robb and Harriott [11] have performed kinetic investigations in a differential reactor at 420 C. The authors observe approximately zero order with respect to oxygen,
0.8 order with respect to methanol and decreasing selectivity with increasing conversion. On the basis of these experiments a modified

Langmuir–Hinshelwood kinetic expression based on adsorption on top of an oxide layer was proposed. The selectivity was explained by total oxidation of both methanol and formaldehyde. During the last decade Schl€ ogl and coworkers have studied the oxygen–silver system at high temperatures (500–1000 K) and atmospheric pressures in great detail (TPD, TPR, ISS, XPS, UPS, in situ-XRD, STM, SEM, RHEED, etc.) [22–27]. The authors have identified three different atomic oxygen species above room temperature, denoted Oa , Ob , and Oc which desorbs in UHV at 600, 600– 850, and
900 K, respectively. Oa (XPS (O 1s) ¼ 528.2 eV) is formed by dissociation of molecular oxygen and is the well known chemisorbed surface bound oxygen, also termed nucleophilic or ionic oxygen in the literature [28–31]. Oa is the active oxygen species in the mechanism proposed by Wachs and Madix [10]. Ob (XPS (O 1s) ¼ 530.3 eV) [26] is formed by dissolution of Oa in the bulk. This formation is activated and occurs via interstitial diffusion at a temperature above 450 K [23,27]. Oc (XPS (O 1s) ¼ 529.0 eV) is embedded in the uppermost layer of silver and is formed by the segregation of Ob from the bulk to the surface via interstitial diffusion above 580 K [23]. This formation only occurs in the terminating closed packed surface planes (Ag(1 1 1)) and leads to a pronounced reconstruction and morphological changes in silver catalysts [27]. Water induces morphological changes presumable by formation of subsurface OH by reaction with Oc [32–34]. Due to reaction-induced restructuring of silver catalysts and pronounced hysteresis Schl€ ogl et al. concluded that formaldehyde synthesis is extremely structuresensitive [8]. However steady-state kinetics has not been measured on different surface facets or particle sizes (1–5 nm), hence no conclusion on the structure sensitivity can be made according to the definition of structure sensitivity by Sajkowski and Boudard [35]. The conclusion of the measurements is a strong dependence on the preconditioning of the catalyst in transient experiments. This is consistent with the work of Wachs and coworkers [36] who showed that preoxidized silver surfaces initially results in more active catalysts, but after several hours the same steady-state is reached with or without the preoxidation. Schl€ ogl and coworkers

A. Andreasen et al. / Surface Science 544 (2003) 5–23

also claim that Oa due to its desorption at 600 K cannot be the dominant surface species involved in partial oxidation of methanol at
900 K [26]. Instead they suggest that Oc is active at industrial conditions. However this conjecture is only valid in UHV and Oa could easily be the active species at industrial conditions. Indeed it will be shown in this work that Oa is present at industrial conditions and most likely the active oxygen at all reaction conditions. This is in agreement with the work of Wachs and coworkers [36] who showed that only one type of atomic surface oxygen (TPD peak at
600 K) is active in the formaldehyde synthesis. In recent investigations Nagy et al. [8] and Nagy and Mestl [9] observe an increasing selectivity towards formaldehyde with increasing temperatures. At low temperatures the reaction is inactive; it ignites above 450 K. These observations are consistent with the investigations of Gavrilin and Popov [7], Leffert et al. [37], Qian et al. [38] and Obraztsov et al. [39]. With this in mind, Gavrilin and Popov [7] and Nagy et al. [8] suggest different kinetics at high and low temperatures. Nagy et al. also claim that different kinds of oxygen are required in order to explain their experiments [8]. At low temperatures Oa is active in oxi-dehydrogenation of methanol towards formaldehyde. However due to the strong nucleophility of Oa this reaction tends to go to complete oxidation products. At higher temperatures Oc is believed to catalyze the selective dehydrogenation of methanol to formaldehyde. Thus explaining increasing selectivity with temperature. However the experiments of Nagy et al. and Gavrilin and Popov was carried out with 100% oxygen consumption and kinetics can therefore not be deduced from these experiments yet alone reaction mechanisms. In our view the strongest evidence for the participation of Oc in formaldehyde synthesis was recently published by Muhler and coworkers [40]. By using a temporal-analysis-of-products approach (TAP) Muhler et al. showed that Oc does react with methanol to form formaldehyde with high selectivity. Oa also formed formaldehyde but with a lower selectivity. However the experiments with Oa was conducted at lower temperatures than the experiments with Oc and the lifetime of form-

7

aldehyde was significantly longer in these low temperature experiments. Assuming CO2 is formed by a consecutive reaction of formaldehyde a lower selectivity is expected due to the longer lifetime of formaldehyde. Decreasing the coverage of Oa led to a significant increase in selectivity which seems logical since more oxygen is needed to obtain total oxidation products. Furthermore Oa also seems to react more rapidly and more completely with methanol than Oc and besides that the experiments were transient and conducted without oxygen atmosphere. The experiments are therefore not conclusive. It is very likely that the formation of Oc is too slow to keep up with Oa at steady-state conditions. A slow formation rate of Oc (slow diffusion of Ob and Oc [27]) and hence a slow desorption rate due to microscopic reversibility seems to be the most reasonable explanation for the high thermal stability of Oc . Schl€ ogl and coworkers have shown that the amount of Oc decreased drastically in the presence of methanol even in oxygen rich mixtures [26]. It is evident that there is a conflict between the proposed mechanism deduced from UHV investigations and the mechanisms deduced from studies near industrial conditions. There can be two reasons for this discrepancy. Either the reactions proceeding at room temperature and UHV are different from the reactions at industrial conditions or the interpretation of the complex in situ experiments at industrial conditions is flawed. We believe the latter is the case because these experiments includes transient effects that are not present at industrial steady-state conditions. In this work we will show that it is indeed possible to interpret kinetic experiments performed at elevated pressures and temperatures with a simple microkinetic model consistent with the mechanism derived by Wachs and Madix [10] and various surface science experiments. Hence it is not necessary to invoke Oc in order to explain formaldehyde synthesis. This does not prove that Oc is not participating in the reaction, but the effect is probably insignificant in steady-state kinetics. The approach of microkinetic modeling has successfully been applied for a number of important industrial reactions [41–50], which proves a close connection between surface science and

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A. Andreasen et al. / Surface Science 544 (2003) 5–23

industrial catalysis. An important feature of a microkinetic model is that thermodynamic and kinetic parameters are physical meaningful and consistent with experiment and/or theoretical methods such as DFT and transition state theory (TST). From a microkinetic model it is possible to estimate surface coverages, reaction orders and activation enthalpy during reaction conditions. Hence the applicability of the model is not restricted to a particular set of conditions, but can be used under various conditions where simplified models e.g. Power-Law expressions may break down [44]. In short a microkinetic model should be able to bridge the pressure-, temperature-, structure-, and reactor gaps between experimental and theoretical surface science and industrial catalysis. To the best of our knowledge this is the first time microkinetic modeling has been applied to the partial oxidation of methanol to formaldehyde on silver catalysts.

2. Methods The starting point of a microkinetic model is a detailed reaction mechanism. The principle of microscopic reversibility is applied to each elementary step, and the kinetics is described by Arrhenius expressions. A statistical mechanical

description is used for all gas phase molecules and adsorbates, giving a correct description of the degrees of freedom for each species. Furthermore statistical thermodynamics ensures a correct description of the gas phase thermodynamics within the ideal gas approximation. The pivot in statistical mechanics is the partition function from which all thermodynamic information can be extracted e.g. the equilibrium constants for each step in the mechanism. Table 1 summarize the important formulas used in the thermodynamic modeling. 2.1. Reaction mechanism Our model is based on the Langmuir–Hinshelwood mechanism presented in Table 2. All the elementary steps in Table 2 have have been extracted from the UHV work of Wachs and Madix on Ag(1 1 0) [10]. It should be emphasized that O participating in the mechanism in Table 2 corresponds to the surface atomic oxygen denoted Oa by Schl€ ogl and coworkers. The reaction mechanism has been kept as simple as possible by ignoring known elementary reactions involving carbonate formation [51–53], OH formation [10], HCOOH formation [38] and oxidative decomposition of formate [54]. These elementary reactions has been ignored for several reasons. First of all the purpose of this work is not to develop a de-

Table 1 Statistical mechanical and thermodynamic functions applied in the microkinetic model Type Vibration

Translation Rotation (2D) Rotation (3D) Electronic Total

Partition function
 mj hc exp Q 2k T
B  zvib ¼ j mj hc 1  exp kB T
3 2pmkB T 2 kB T ztrans ¼ h2 p kB T rhcB
3 1 kB T 2  p 12 zrot ¼ r hc ABC
 Eg zelec ¼ exp kB T z ¼ zvib ztrans zrot zelec

zrot ¼

Enthalpy

Hvib


 1 mj hc C P B1 2k T
B C ¼ jB @2 hcmj þ mj hc A 1  exp kB T 0

exp

5 Htrans ¼ kB T 2 Hrot ¼ kB T 3 Hrot ¼ kB T 2 Helec ¼ Eg H ¼ Hvib þ Htrans þ Hrot þ Helec

Eg is the ground state energy, h is PlanckÕs constant, kB is BoltzmannÕs constant, m is the molecular mass, p is the reference pressure and c is the speed of light in vacuum. A, B and C are rotational constants, r is the symmetry number, mj are the vibrational frequencies.

A. Andreasen et al. / Surface Science 544 (2003) 5–23 Table 2 Reaction mechanism used for the microkinetic model CH3 OH(g) +  CH3 OH O2 (g) +  O2 O2 +  2O 2CH3 OH + O 2CH3 O + H2 O CH3 O +  H2 CO + H (slow) H2 CO H2 CO(g) +  2H H2 (g) + 2 H2 O H2 O(g) +  H2 CO + O H + HCOO HCOO +  H + CO2 (slow) CO2 CO2 (g) + 

(step (step (step (step (step (step (step (step (step (step (step

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

The  signifies a surface site and X  is an adsorbed specie.

tailed model in all respects but to demonstrate that the reaction mechanism established at UHV can explain kinetic experiments near industrial conditions. Secondly, the experimental knowledge of the ignored elementary reactions is too limited to extract reliable kinetic and thermodynamic parameters. Thirdly, by ignoring these elementary reactions the numerics of the model is greatly simplified and an analytical solution can be obtained. The consequences of excluding these elementary reactions will be discussed later in this section. But for now it should be stressed that including these elementary reactions will not change the results and conclusions of this work. The model would merely contain more parameters and maybe slightly different parameter values for those fitted to kinetic experiments. An important feature of the mechanism by Wachs and Madix is that the formaldehyde synthesis cannot be divided into a dehydrogenation and oxidation. Furthermore CO2 is only formed by the further oxidation of formaldehyde through a formate intermediate i.e. direct methanol combustion (Eq. (3)) is absent. Wachs and Madix observe simultaneous desorption of different products in TPR experiments when methanol is adsorbed on preoxidized Ag(1 1 0) [10] and this desorption occur at higher temperatures than the characteristic desorption spectra of these products [55–58]. This indicates that the products evolves from the same rate limiting step namely the decomposition of the methoxy intermediate (step 5). It has been shown that the decomposition of methoxy (step 5) is rate

9

limiting on copper [59]. Pepley et al. have proposed a kinetic model for methanol-steam reforming on copper and concluded that in order to explain kinetic data with their model the decomposition of methoxy must be rate limiting [60]. DFT calculations of methoxy decomposition on copper confirm a high activation barrier for this process. It is therefore reasonable to assume that methoxy decomposition is a slow process on silver. TPR studies of the decomposition of formic acid, formaldehyde, methanol and methyl formate have shown that CO2 and H2 desorbs simultaneously around 400 K [10,17,61,62]. The decompositions of all the above species are believed to go through the same formate intermediate [10,17]. This suggests that the further oxidation of formaldehyde to carbon dioxide is rate limited by the decomposition of formate (step 10). This conclusion is consistent with kinetic measurements of HCOOH decomposition on different crystal facets of silver [63–66]. Therefore its assumed in the following that the decomposition of methoxy and formate is rate limiting while all the other elementary reactions are equilibrated. This assumption will be justified later when the model successfully explain kinetic data. It might seem strange that the uptake of oxygen is not rate limiting as its dissociative sticking probability is very low (107 –105 ) [67,68]. However the kinetic data of Robb and Harriott [11] indicates a zero order reaction in oxygen, hence the uptake of oxygen cannot be rate limiting. This can be explained by the high oxygen pressure used in kinetic experiments which compensates for the low sticking. The following possible elementary reactions involving OH formation has been excluded from the model: O þ H OHþ

ð6Þ

2OH H2 O þ O

ð7Þ

OH þ H H2 Oþ

ð8Þ

Therefore the simplified model does not describe the selectivity towards water perfectly nor the existence of hydroxy species. At high selectivity toward formaldehyde the mechanism predicts the production of a 1:1 H2 :H2 O ratio. Including

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A. Andreasen et al. / Surface Science 544 (2003) 5–23

Eqs. (6)–(8) will increase the formation of water by decreasing the hydrogen production. Industrially only slightly more water than hydrogen is produced which justifies the neglection of these reactions at industrial conditions [1,3]. However at other reaction conditions especially transient kinetic experiments this approximation is poor as will become apparent in Section 3. Furthermore the formation of OH could serve as an oxygen scavenger. Since the stability of OH is low (desorbs at about room temperature) [57] and the oxygen uptake is assumed to be equilibrated this scavenger effect would be negligible for steadystate kinetics above room temperature. According to Wachs and Madix OH may react in a similar manner as O [10]. The production of HCOOH and HCOOCH3 observed at some experimental conditions has been ignored in the model [10,37,38]. These reactions seems to be unimportant in steady-state kinetics. However Qian et al. [38] found that the production of HCOOH increased to a significant level on an aged catalyst. The reason for this aging effect is not clear. In this paper there will be no attempts to model the decomposition of formaldehyde to carbonmonooxide (Eq. (5)) since this reaction is important only at very high temperatures [6,8, 37]. Furthermore it is believed to be a pyrolytic gas phase reaction [6] and should therefore not lead to site blockage of any kind on the catalyst. CO desorbs at low temperatures and reacts rapidly with Oa to form CO2 on silver hence CO should only be present in the absence of oxygen [51]. When adsorbed atomic oxygen and carbon dioxide interacts on a silver surface, carbonate is known to form [51–53]: CO2 þ O COþ 3

ð9Þ

This is considered to be a dead end in the mechanism and the most important effect is stabilization of carbon dioxide. The carbonate will compete with the other adsorbates in the consumption of active sites, but we consider this effect to be negligible at high temperatures, and the phenomena is not included in the further modeling.

Surface science experiments have indicated that the decomposition of formate could be promoted by oxygen [54]: HCOO þ O CO2 þ OH

ð10Þ

This formate decomposition pathway could be significant at low temperatures where a large coverage of O exists but will be of minor importance at industrial conditions. Applying the quasi-equilibrium approximation [69] to the Langmuir–Hinshelwood mechanism in Table 2 assuming steps 5 and 10 as rate limiting, the rate and equilibrium equations can be derived cf. Table 3. 2.2. Model catalyst When possible we have derived the model parameters from experiments on Ag(1 1 1) because it

Table 3 Rate and equilibrium equations for the kinetic model based on reaction steps 1–11 pCH3 OH hCH3 OH ¼ K1 h p pO2 hO2 ¼ K2  h p 1 hO ¼ ðK3 hO2 h Þ2  1 21 hCH3 O ¼ hCH3 OH K4 hO hH2 O k5 r5 ¼ k5 hCH3 O h  hH2 CO hH K5 1 pH2 CO hH2 CO ¼ h K6 p 1 1 pH 2 hH ¼ K7 2 2 h p 1 pH2 O  hH2 O ¼ h K8 p  hH CO hO hHCOO ¼ K9 2 hH k10  r10 ¼ k10 hHCOO h  hCO2 hH K10 1 pCO2 hCO2 ¼ h K11 p h ¼ 1  hCH3 OH  hO2  hO  hCH3 O hH2 CO  hH  hH2 O  hHCOO  hCO2 Ki are the equilibrium constants calculated from the molecular partition functions of the intermediates, ki are the rate constants assumed to be of the Arrhenius form, ri are the reaction rates of the rate limiting steps, hX  is the coverage of species X  , pi is the partial pressure and p is the thermodynamic reference pressure.

A. Andreasen et al. / Surface Science 544 (2003) 5–23

is the thermodynamically stable facet and therefore supposed to be the most abundant facet on the industrial catalyst. Nevertheless in some cases the Ag(1 1 0) surface has been used due to the absence of appropriate experiments on Ag(1 1 1). The density of sites (d) is estimated from oxygen chemisorption on Ag(1 1 1) [28] which results in a saturation coverage of approx. 0.5 ML oxygen atoms. This, combined with the fact that a Ag(1 1 1) facet has 1.38 · 1015 surface atoms per cm2 gives a site density of 6.9 · 1018 sites/m2 . In general, microkinetic modeling is not sensitive to the density or type of active sites as long as the experiments on the model catalyst used to derive the model parameters reflects what is happening on an industrial catalyst. This is due to an inverse proportionality between the site density and the prefactors of all the elementary reactions. The best way to establish if a model catalyst reflects an industrial catalyst is to compare steadystate kinetics of the two systems. Unfortunately such measurements has not been performed on Ag(1 1 1) for methanol oxidation. Furthermore the structure sensitivity of the reaction is unknown. Formate decomposition has been studied on different Ag facets showing a significant change in activation barrier with surface structure [63–66]. On the other hand the effect on activities was canceled by a large compensation effect. Silver reconstruct dramatically in the presence of oxygen and/or water during the formation of Oc and subsurface OH leading to faceting [27,32–34]. The reconstruction seems to be decreased in the presence of methanol. It is possible that a more accurate model could be produced by including a dependence of reaction conditions on the site density as in the case of methanol synthesis on copper [70,71]. However, as a first approximation we assume that the site density is constant. As it will be shown in Section 2.3 it has been necessary to fit some parameters to steady-state kinetics. These parameters may therefore not reflect the values on a particular facet but may be some kind of average value of all the facets/steps/defects present at industrial conditions. It should be emphasized that the purpose of this work is not to show which facet is the active one or that the reaction is structure insensitive but to demonstrate

11

that a simple mechanism deduced from surface science is able to explain experiments at industrial conditions. 2.3. Model parameters The equilibrium constants appearing in the microkinetic model can be calculated using statistical thermodynamics [72] from parameters for gas phase molecules and adsorbates. The central parameters are vibrational frequencies and ground state energies. All parameters for gas phase molecules can be extracted from the NIST database [73] or equivalent. For the adsorbates vibrational frequencies are determined from spectroscopic measurements e.g. EELS, IR, Raman. Ground state energies can be fitted from TPD experiments and measurements of sticking coefficients. The method used for parameter estimation will be explained below and the results are summarized in Tables 4– 6. For more details on the method we refer to other papers [74,75]. A first order desorption process in UHV for a generic gas phase molecule A is described by the following rate equation: dhA k ¼  hA  K dt

ð11Þ

where k is the rate constant of adsorption, K is the equilibrium constant and hA is the coverage of A. The equilibrium constant can be calculated from the partition function cf. Table 1: K¼

zA zA

ð12Þ

where zA is the partition function of the gas phase and zA is the partition function of the adsorbate. The equilibrium constants for adsorption and surface reactions can be calculated in a similar fashion. The rate constant k is found by equating the initial adsorption rate with the initial sticking rate: r0 p k ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d 2pmkB T

ð13Þ

where r0 is the initial sticking coefficient, p is the thermodynamic reference pressure, m is the mass

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A. Andreasen et al. / Surface Science 544 (2003) 5–23

Table 4 Model parameters for gas phase molecules to the statistical thermodynamical treatment Species

Parameters

H2

B ¼ 60:848 cm1 , r ¼ 2, m1 ¼ 4405:3 cm1 , H ¼ 0 @ T ¼ 298 K [75]

O2

B ¼ 1:45 cm1 , r ¼ 2, m1 ¼ 1580 cm1 , H ¼ 0 @ T ¼ 298 K [73]

H2 O

A ¼ 27:8847 cm1 , B ¼ 14:51181 cm1 , C ¼ 9:2806 cm1 , r ¼ 2, m1 ¼ 1594:7 cm1 , m2 ¼ 3651:1 cm1 , m3 ¼ 3755:9 cm1 , H ¼ 241:818 kJ/mol @ T ¼ 298 K [73].

CH3 OH

A ¼ 4:2554 cm1 , B ¼ 0:823 cm1 , C ¼ 0:7928 cm1 , r ¼ 1, m1 ¼ 270 cm1 , m2 ¼ 1033 cm1 , m3 ¼ 1060 cm1 , m4 ¼ 1165 cm1 , m5 ¼ 1345 cm1 , m6 ¼ 1477ð2Þ cm1 , m7 ¼ 1455 cm1 , m8 ¼ 2844 cm1 , m9 ¼ 2960 cm1 , m10 ¼ 3000 cm1 , m11 ¼ 3681 cm1 , H ¼ 201:2 kJ/mol @ T ¼ 298 K [45,73].

H2 CO

A ¼ 9:074 cm1 , B ¼ 1:2899 cm1 , C ¼ 1:129 cm1 , r ¼ 2, m1 ¼ 1163:5 cm1 , m2 ¼ 1247:4 cm1 , m3 ¼ 1500:6 cm1 , m4 ¼ 1746:07 cm1 , m5 ¼ 2766:4 cm1 , m6 ¼ 2843:4 cm1 , H ¼ 108:57 kJ/mol @ 298 K [73].

CO2

B ¼ 0:39038 cm1 , r ¼ 2, m1 ¼ 667:3ð2Þ cm1 , m2 ¼ 1384:26 cm1 , m3 ¼ 2349:49 cm1 , H ¼ 393:15 kJ/mol @ T ¼ 298 K [73].

A, B and C are the rotational constants, r is the symmetry number, mi are the vibrational frequencies and the degeneracy of a frequency is enclosed in parentheses. H is the enthalpy of formation.

Table 5 Model parameters for adsorbates to the statistical thermodynamical treatment Species

Parameters

H

m? ¼ 1121:0 cm1 , mk ¼ 927:5ð2Þ cm1 , H ¼ 25 kJ/mol [75].

O

m1 ¼ 350 cm1 , m2 ¼ 508ð2Þ cm1 , H ¼ 63 kJ/mol @ T ¼ 298 K [81].

O2

m1 ¼ 50ð2Þ cm1 , m2 ¼ 300ð2Þ cm1 , m3 ¼ 675 cm1 , m4 ¼ 220 cm1 , H ¼ 44:5 kJ/mol @ T ¼ 298 K [81].

CH3 OH

m? ¼ 29 cm1 , mk ¼ 35:51ð2Þ cm1 , mr ¼ 36:0ð3Þ cm1 , m1 ¼ 750 cm1 , m2 ¼ 820 cm1 , m3 ¼ 1030 cm1 , m4 ¼ 1150ð2Þ cm1 , m5 ¼ 1470ð3Þ cm1 , m6 ¼ 2860 cm1 , m7 ¼ 2970ð2Þ cm1 , m8 ¼ 3320 cm1 , H ¼ 241:6 kJ/mol @ T ¼ 298:15 K [12,45].

CH3 O

m? ¼ 330 cm1 , mk ¼ 36:49ð2Þ cm1 , mr ¼ 360ð3Þ cm1 , m1 ¼ 1040 cm1 , m2 ¼ 1150ð2Þ cm1 , m3 ¼ 1450ð3Þ cm1 , m4 ¼ 2840 cm1 , m5 ¼ 2940ð2Þ cm1 , H ¼ 104 kJ/mol @ T ¼ 298:15 K [12,45].

H2 CO

m? ¼ 400 cm1 , mk ¼ 37ð2Þ cm1 , mr ¼ 23ð3Þ cm1 , m1 ¼ 1476 cm1 , m2 ¼ 1694 cm1 , m3 ¼ 2839 cm1 , m4 ¼ 1218:15 cm1 , m5 ¼ 2839 cm1 , H ¼ 135 kJ/mol @ T ¼ 298:15 K [56,77].

H2 O

m? ¼ 27:9 cm1 , mk ¼ 27:9ð2Þ cm1 , mr ¼ 740ð3Þ cm1 , m1 ¼ 1660 cm1 , m2 ¼ 3410ð2Þ cm1 , H ¼ 293:2 kJ/mol @ T ¼ 298:15 K [57,75].

CO2

m? ¼ 410 cm1 , mk ¼ 30:6ð2Þ cm1 , mr ¼ 12:71ð3Þ cm1 , m1 ¼ 605 cm1 , m2 ¼ 1365 cm1 , m3 ¼ 2350 cm1 , H ¼ 414:607 kJ/mol @ T ¼ 298:15 K [77,90].

HCOO

m? ¼ 322 cm1 , mk ¼ 35:51ð2Þ cm1 , mr ¼ 400ð3Þ cm1 , m1 ¼ 770 cm1 , m2 ¼ 1340 cm1 , m3 ¼ 1640 cm1 , m4 ¼ 2900 cm1 , m5 ¼ 1050 cm1 , m6 ¼ 1377 cm1 , H ¼ 197 kJ/mol @ T ¼ 298:15 K [13,45,61].

mi are the vibrational frequencies and the degeneracy of a frequency is enclosed in parentheses. m? , mk and mr are the frustrated translational orthogonal frequency, the frustrated translational parallel frequency and the frustrated rotational frequency, respectively. H is the enthalpy of formation.

of A, kB is BoltzmannÕs constant and T is the temperature. Substituting this into Eq. (11) the following equation is obtained:

dhA r0 p ¼  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hA dt d 2pmkB T K

ð14Þ

A. Andreasen et al. / Surface Science 544 (2003) 5–23 Table 6 Arrhenius parameters for the two slow steps determined from optimization Reaction, i 5 10

Hiz

Ai 10

1

4.2 · 10 s 9.8 · 109 s1

60 kJ mol1 77 kJ mol1

A is the prefactor and H z is the activation enthalpy.

Experimental TPD spectra are simulated by integrating equation (14) using numerical techniques. The ground state energy comes into play through the equilibrium constant and is optimized until the experimental peak temperature is reproduced. It seems likely that the sticking coefficient of methanol, formaldehyde and water is near unity [56–58]. Assuming a sticking coefficient of unity, implies that the activation barrier for the sticking process is zero. These assumptions results in the parameters presented in Table 5 which results in TPD peaks at 167 K [58,76], 106 K [56], and 170 K [57] for methanol, formaldehyde and water, respectively which is consistent with experimental values. The exact stability of these species are not critical to the model, cf. Section 4. The stability of hydrogen is deduced from an experimental D2 desorption spectra by Wachs and Madix [10] and with vibrational parameters from Cu [77]. By assuming a desorption exponential of 1013 and an activation barrier of 55.6 kJ/mol the peak temperature of 228 K is reproduced by simulation. Assuming a non-activated sticking of hydrogen we come up with an H enthalpy of )27.8 kJ/mol. The sticking of hydrogen on silver is probably activated as for Cu [77], which results in a too high predicted value of the enthalpy of H. We have also neglected the isotope effect, which also leads to discrepancy between the stability of H and D. It turns out that the microkinetic model is rather insensitive to the choice of H parameters. All parameters for carbon dioxide are taken from Cu [77], because experiments on Ag are insufficient. Both for hydrogen and carbon dioxide the stabilities will be over predicted, but this is considered only to have minor importance due to the small coverage of these species cf. Fig. 7.

13

2.3.1. Adsorbed oxygen The stability of dissociative adsorbed oxygen on silver is controversial even though the oxygen/silver system has been studied extensively. On Ag(1 1 1) the value referenced to by most people is the one obtained by Campbell [67]. Campbell used the first order Redhead equation [78], a desorption preexponential of 1015 s1 and deduced a dissociative adsorption heat of 170.5 kJ/mol O2 from the TPD of dissociatively adsorbed oxygen. As stated by Campbell [67] the Redhead analysis is a simplification. The desorption is recombinative (second order) and an attractive interaction exists between dissociatively adsorbed oxygen. The attractive interaction is observed by island formation at low coverage below 490 K in UHV and by a very narrow TPD peak [30,31,67,68,79,80]. We have made a microkinetic model of oxygen chemisorption on Ag(1 1 1) that (within experimental uncertainties) describes molecular and dissociative sticking, and molecular and recombinative desorption [81]. The attractive interaction between dissociatively adsorbed oxygen has been modeled using the mean-field approximation. This model resulted in a heat of adsorption of 126 kJ/ mol O2 and the attraction was found to be 15 kJ/ mol O2 . In the following we will use the heat of adsorption in the limit of low coverage assuming that the attractive interactions should be ignored on polycrystalline or real silver catalysts due to the lack of long range order on such catalysts [82] and the presence of other adsorbates. 2.3.2. Methoxy and formate The methoxy and formate species are special in the sense that there are no corresponding gas phase molecules. The only information available for these adsorbates are vibrational frequencies and decomposition temperatures in TPR on Ag(1 1 0). From the TPR experiments it is only possible to establish the rate constants of methoxy and formate decomposition. The parameters that remains to be determined are ground state energies and the specific decomposition Arrhenius parameters of methoxy and formate. Fig. 1 shows the simulation of methoxy and formate decomposition for different Arrhenius parameters but identical

A. Andreasen et al. / Surface Science 544 (2003) 5–23 0.06 10

10 11 10 12 10 13 10

-1

Reaction rate [s ]

0.05 0.04 0.03 0.02 0.01 0 250

300

350

400

450

Temperature [K]

Fig. 1. Simulation of TPR experiments for methoxy (low temperature peak) and formate decomposition (high temperature peak) using different sets of Arrhenius parameters. b ¼ 15 K/s and initial methoxy and formate coverage is 10%.

rate constants at the peak temperatures. Its is clear from the figure that the specific Arrhenius parameters cannot be establish from such TPR experiments. The ground state energy of methoxy has been determined by ensuring that the models heat of reaction for decomposition of gas phase methanol into adsorbed methoxy and H is consistent with DFT calculations. The total energy calculation code DACAPO [83] is used for the DFT calculations. A four layer 2 · 2 slab representing Ag(1 1 1), periodically repeated in a super cell geometry with six equivalent layers of vacuum between successive slabs. The bottom layer is fixed while the other layers are allowed to relax. Ionic cores are described by ultra-soft pseudo-potentials [84], and the Kohn–Sham one-electron valence states are expanded in a basis of plane waves with a kinetic energy below 25 Ry. The surface Brillouin zone is sampled at 18 special k points. The exchangecorrelation energy and potential are described by the generalized gradient approximation (GGAPW91) [85–87]. Methoxy and H is placed in the fcc site found to be the best site for these species on copper [20]. It was not our intention to conduct a thorough DFT investigation of this reaction but merely to get an estimate of the methoxy stability on Ag(1 1 1). The remaining parameters are fitted to the kinetic measurements of Robb and Harriott [11],

Leffert et al. [37], Nagy et al. [8] and Nagy and Mestl [9] (see Figs. 2–5). The kinetic model is implemented in a plug-flow reactor model and kinetic experiments are simulated by integrating the design equations with an adaptive step size 4 order Runge–Kutta algorithm. The optimization occurs with a least-squares simulated annealing. The calculation ensures that the correct TPR decomposition temperatures of methoxy and formate are reproduced, cf. Fig. 1. These parameters are therefore not deduced explicitly from surface science but they reproduce all known surface science experiments and have physically realistic values according to DFT and TST. Other choices of parameters could give similar results. The prefactors of methoxy and formate decomposition is in the region 1010 s1 cf. Table 6. TST predicts a prefactor of about 1013 s1 for surface reactions varying few orders of magnitude dependent of the nature of the transition state (mobile/immobile) [41,82]. Experimentally preexponentials vary from 1010 –1016 s1 [82]. The values of the prefactors in the model seems low compared to TST, however within the range usually reported in the literature and hence physically realistic. Besides the mobility of the transition state the low preexponentials could be a result of overestimating 0.04

Methanol Conversion [mol]

14

0.9 % Methanol 1.8 % Methanol 2.8 % Methanol 5.5 % Methanol 8.8 % Methanol 19.1 % Methanol Simulations

0.03

0.02

0.01

0 0

0.05

0.1

0.15

Oxygen mole fraction Fig. 2. Simulation of the experiments by Robb and Harriott at 695 K and 1.12 atm. Points are experimental measurements from Ref. [11] and lines have been calculated with the microkinetic model. The figure shows the conversion of methanol as a function of the partial pressure of oxygen at different partial pressures of methanol.

A. Andreasen et al. / Surface Science 544 (2003) 5–23

15

1

Yield

0.4 0.3 0.2 0.1 0

0

0.2

0.4

0.6

0.8

Conversion of CH3OH

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Fig. 5. Simulation of 25 experiments by Leffert et al. [37] plotted on a predicted versus experimental plot.

values reported on Ag(1 1 1) facets (67 kJ/mol) and Ag(1 1 0) facets (127 kJ/mol) [63].

3. Results

1

Selectivety / Conversion

0.6

Measured yield

Fig. 3. Simulation of the experiments by Robb and Harriott at 695 K and 1.12 atm. Points are experimental measurements from Ref. [11] and lines have been calculated with the microkinetic model. The figure shows the yield of H2 CO and CO2 , respectively, as a function of the conversion of methanol. Set I is data obtained with an aged catalyst of silver particles of
on alumina (sintered). Set II is data obtained with about 120 A
on alumina. a fresh catalyst of silver particles of about 55 A

0.8 CH2O CO2 CH3OH CH2O (mes.) CO2 (mes.) CH3OH (mes.)

0.6

0.4

0.2

0 500

H2CO CO2

0.8

Predicted yield

0.5

Simulations CH2O Set I CO2 Set I CH2O Set II CO2 Set II

600

700

800

900

Temperature [K] Fig. 4. Simulation of the experiments by Nagy and Mestl. Points are experimental measurements from Ref. [9] and lines have been calculated with the microkinetic model. The figure shows the selectivity towards H2 CO and CO2 , respectively, and the conversion of methanol as a function of temperature.

the site density in the fitting process, inaccuracies of the estimated vibrational frequencies for methoxy and formate or perhaps a need for larger site ensembles for methoxy and formate decomposition. Interestingly the fitted activation barrier of formate decomposition (77 kJ/mol) is between the

In this section our simulations of the kinetic experiments of Robb and Harriott [11], Nagy et al. [8], Nagy and Mestl [9], and Leffert et al. [37] are presented using the parameters obtained in the previous section. Fig. 2 shows the simulation of the total rate of methanol oxidation as a function of oxygen and methanol pressures at 420 C as measured by Robb and Harriott. Robb and Harriott only reported a relative rate and analyzed their data according to the differential reactor approximation even though the conversion in some cases reached 30%. We have chosen to analyze their data according to the integral reactor approximation and converting the relative rates to absolute rates. This transformation was done by calibrating the relative rates to a reported standard measurement and approximating the density of sites from measurements of particle sizes. However it turns out that the trends deduced from the integral analysis is identical to those obtained in the differential reactor analysis by Robb and Harriott. Fig. 2 shows that our model correctly explains the reaction orders of oxygen and methanol.

A. Andreasen et al. / Surface Science 544 (2003) 5–23

Fig. 3 shows the simulation of Robb and HarriottÕs measurements of yield versus methanol conversion at 420 C. The simulation clearly captures the correct trends, i.e. the selectivity towards formaldehyde decreases with increasing conversions of methanol. However the experimental selectivity decreases much more rapidly with methanol conversion than predicted by the model. The reason for this discrepancy could be the use of alumina as a support in the experiments of Robb and Harriott. Experimental evidence shows that alumina decomposes formaldehyde [14]. This hypothesis has been confirmed by simulations including formaldehyde decomposition on alumina in the microkinetic model. Nagy et al. investigated the influence of temperature on selectivity by applying a low linear heating rate (1 K/min) on a steady-state flow reactor while running the reaction. The oxygen conversion was
100% at all conditions except at very low temperatures (
500 K) [8,9]. Fig. 4 shows the simulation of the experimental conversion of methanol and selectivity towards formaldehyde and CO2 , respectively. The model clearly captures the trend that formaldehyde selectivity increases with temperature and saturates at high temperature. The model also captures the trend that CO2 selectivity is high at low temperature but decrease with increasing temperature. In order to fit the experiment of Nagy et al. the inlet oxygen concentration was reduced with 15% otherwise total methanol consumption was achieved at high temperatures which is not observed experimentally. The reason for this problem is the exclusion of elementary reactions forming water from O and H through OH in the model. Therefore the oxygen consumption is too low for the model. Leffert et al. [37] investigated the effect of temperature on methanol oxidation in a similar fashion as Nagy et al. [8] and Nagy and Mestl [9]. Furthermore the authors investigated the effect of methanol and oxygen concentration on the yield towards formaldehyde and CO2 , respectively. Fig. 5 shows the predicted yield of formaldehyde and CO2 by the model versus experimental yields. As above it was necessary to reduce the inlet oxygen concentration by approx. 20% to explain the experiments.

4. Discussion In the previous section we have demonstrated that a microkinetic model based on a mechanism deduced from surface science is able to explain a broad range of kinetic experiments. Even more interesting some of these experiments has been used as proof in the literature for a mechanism different form the one observed in UHV. In this section we will proceed with a more detailed analysis in order to obtain a more thorough understanding of the model. 4.1. Coverages As mentioned in Section 1 Schl€ ogl and coworkers concluded that Oa cannot be active at industrial conditions of 900 K since it desorbs at 600 K in UHV. However in the previous section our microkinetic model explained experiments at high temperatures using parameters of O reproducing the experimental TPD peak temperature at 600 K in UHV. Fig. 6 shows the simulated coverage of O as a function of temperature for different oxygen pressures, which clearly indicates that O can be present at industrial conditions. At UHV the coverage of O approach zero at 600 K while a significant coverage is present at 900 K at oxygen pressures above 1 kPa. Interestingly, Scheffler and coworkers [88] found that surface

1 P = 0 Pa P = 1 Pa P = 10 Pa P = 100 Pa P = 1000 Pa P = 10000 Pa P = 100000 Pa

0.9 0.8 0.7 0.6

θO*

16

0.5 0.4 0.3 0.2 0.1 0 400

500

600

700

800

900

1000

1100

1200

Temperature [K]

Fig. 6. Simulated coverage of atomic oxygen on silver versus temperature at different oxygen pressures.

A. Andreasen et al. / Surface Science 544 (2003) 5–23

atomic oxygen is stable up to 830 K at atmospheric pressure by using the approach of atomistic ab initio (DFT) thermodynamics. Considering the systematic errors of DFT [88] the result of Scheffler and coworkers is very close to the result obtained in this paper by the microkinetic model. The conclusion of Schl€ ogl et al. that Oa should be absent at 600 K is therefore unfounded. Oa may be present at industrial conditions due to its thermal stability, however it could be absent for other reasons. For example, if a stable layer of Oc is formed, it could block the sites for Oa uptake. This might be the case in some of the transient experiments conducted by Schl€ ogl and coworkers. At steady-state industrial reaction conditions blocking of Oa uptake is unlikely for several reasons. First of all the formation of Oc is slow and activated and can never exceed the rate of Oa uptake since its formed from Oa . Secondly, the coverage of Oc decreases significantly in the presence of methanol and can therefore not block Oa uptake in a reactive atmosphere. From the above discussion it is clear that it is impossible to predict the presence of intermediates from TPD temperatures in UHV alone. Furthermore it is very important to note that an intermediate does not necessarily need a large coverage in order to be important. Fig. 7 shows the calculated coverages at different temperatures for the microkinetic model. The coverages of all intermediates has been calculated

* CH3OH* O2 * O* CH3O* H2O* H2CO* H* HCOO* CO2*

Coverage

0.01 0.001 0.0001

1e-06 500

600

700

800

4.2. Apparent activation enthalpies The apparent activation enthalpy Ez for steps 5 and 10 can be derived analytically from the definition [43]: E z ¼ kB T 2

d lnrþ dT

ð15Þ

where rþ is the forward reaction rate. This gives the results shown in Table 7 and it is observed that a simple relation between Ez and the coverage of surface species exist. Ez is a sum of the activation enthalpy for the rate limiting step and a weighted average of the desorption enthalpies for the intermediates. The sum of the activation enthalpy of the rate limiting step is the activation barrier of the elementary step itself plus the heat of formation/ adsorption of the reactants in the rate limiting step. The average desorption enthalpy is formed

E5z ¼ H5z þ H1 þ 1=2H4 þ 1=2H8 þ 1=4H2 þ 1=4H3 2H1 hCH3 OH  2H2 hO2  ðH2 þ H3 ÞhO ð2H1 þ H4 þ H8 þ 1=2H2 þ 1=2H3 ÞhCH3 O þ2H6 hH2 CO þ H7 hH þ 2H8 hH2 O þ 2H11 hCO2 ð2H9  2H6 þ H2 þ H3 þ H7 ÞhHCOO

1e-05

1e-07 400

at a gas composition of 32% CH3 OH, 4.5% O2 , 11.6% H2 CO, 1.3% CO2 , 7.4% H2 O and 6.5% H2 . This composition corresponds to an average gas composition between the inlet and outlet of an industrial reactor (without additional water in the feed) and we will refer to this as typical reaction conditions. The figure shows that O is the most dominating adsorbate. The number of free sites increases with the decrease of the coverage of O . The coverage of all intermediates are small except formate that becomes significant at low temperatures.

Table 7 Apparent activation enthalpies Eiz for the oxidation of methanol to formaldehyde (5) and further from formaldehyde to carbon dioxide (10)

1 0.1

17

900

Temperature [K]

Fig. 7. Initial coverages as a function of temperature at 1 atm, calculated at typical reaction conditions.

z z E10 ¼ H10 þ H9  H6 þ 1=2H2 þ 1=2H3 þ 1=2H7 2H1 hCH3 OH  2H2 hO2  ðH2 þ H3 ÞhO ð2H1 þ H4 þ H8 þ 1=2H2 þ 1=2H3 ÞhCH3 O þ2H6 hH2 CO þ H7 hH þ 2H8 hH2 O þ 2H11 hCO2 ð2H9  2H6 þ H2 þ H3 þ H7 ÞhHCOO

Hiz is the activation enthalpy for the two slow steps in the mechanism (5 and 10) and Hi is the reaction enthalpy for step i.

A. Andreasen et al. / Surface Science 544 (2003) 5–23

Apparent activation enthalpy [J/mol]

by multiplying the coverage of the intermediates by twice the enthalpy of desorption of the intermediates through equilibrium steps. The factor of two enters because the rate limiting step requires two free sites. Ez is thus the sum of the activation enthalpy of the rate limiting step plus the average cost of creating two free sites on the surface. In the literature most people seem to be aware of the fact that the apparent activation energy contain contributions from the activation barrier of rate limiting elementary step plus adsorption heats of the adsorbates participating in the forward rate limiting step. However the coverage dependent terms are usually ignored in the literature. This is a serious error in all systems that proceeds with a significant coverage of intermediates on the active sites. Coverage dependent terms are responsible for the variations in apparent activation energies with reaction conditions. The expressions in Table 7 have been used to calculate apparent activation enthalpies at typical reaction conditions as a function of temperature. Results of these calculations are shown in Fig. 8. Large variations in the activation enthalpies are observed, as a consequence of changes in coverages with temperature. This is an illustrative example of the difficulty in comparing activation enthalpies obtained at different reaction conditions. Both activation enthalpies decrease as a function of temperature, which is primarily due to the

200000 Methanol to formaldehyde Formaldehyde to carbondioxide

150000

200000 Bhattacharyya et al. Gavrillin et al. Obraztsov et al. Qian et al. Simulated (Differential) Simulated (Integral)

150000

100000

50000

0 400

100000

500

600

700

800

900

Temperature [K]

50000

0 400

increase in free sites cf. Fig. 7. Hence it is easy to create two free sites for the rate limiting steps at high temperatures. The activation enthalpy for the oxidation of methanol to formaldehyde is larger than the activation enthalpy for CO2 formation at all temperatures even though the activation barrier of step 5 is smaller than step 10 cf. Table 6. The difference in apparent activation enthalpy of steps 5 and 10 is almost constant in the entire temperature interval and correspond to the difference of the sum of the activation enthalpy of the rate limiting steps (steps 5 and 10) and the adsorption heats. In Fig. 9 calculated apparent activation enthalpies for the oxidation of methanol to formaldehyde are compared with experimentally observed values from the work of Obraztsov et al. [39], Gavrilin and Popov [7] and Bhattacharyya et al. [2]. The apparent activation enthalpies of Qian et al. [38] have been extracted from methanol conversions versus temperature. Calculated values are obtained from the differential reactor approximation according to Eq. (15) (solid line) and according to the integral reactor approach (dashed line) where rþ in Eq. (15) is substituted with the conversion of

Apparent activation enthalpy [J/mol]

18

500

600

700

800

900

Temperature [K]

Fig. 8. Apparent activation enthalpies for the oxidation of methanol to formaldehyde and further to carbon dioxide. Calculations has been performed at typical reaction conditions.

Fig. 9. Apparent activation enthalpy for the oxidation of methanol to formaldehyde calculated at differential and integral conditions and experimental observations from Refs. [2,7, 38,39]. Apparent activation enthalpies for differential conditions are calculated at typical reaction conditions. Apparent activation enthalpies for integral conditions are calculated from conversion of methanol in a plug reactor with a feed composition of 9.82% CH3 OH and 14.3% O2 . The amount of catalyst and flow rate is chosen to give nearly complete conversion of methanol at 900 K.

A. Andreasen et al. / Surface Science 544 (2003) 5–23

4.3. Reaction orders The reaction orders can be derived from the following definition [43]. ai ¼

d lnðrþ Þ   d ln ppi

ð16Þ

For the formation of formaldehyde the following reaction orders can be derived. aCH3 OH ¼ 1  2hCH3 OH  2hCH3 O

ð17Þ

aO2 ¼ 1=4  2hO2  hO  1=2hCH3 O  hH2 CO

1

Reaction order α i

methanol. As shown the differential model qualitatively explains the trend in experimental observations i.e. a decrease in activation enthalpy as a function of temperature. However the values seem to be over estimated. The discrepancy between calculated and measured values can be accounted for as deviations from differential conditions i.e. a substantial conversion in experimental observations. This is clearly shown by the activation enthalpies calculated for integral conditions giving a much better description of the experimental observations. In this context it is very important to mention, that none of the experimental activation enthalpies presented in Fig. 9 have been used in the optimization of parameters mentioned earlier.

19

0.5

CH3OH O2 H2CO CO2 O2

0

-0.5

400

500

600

700

800

900

Temperature [K]

Fig. 10. Calculated reaction orders for the oxidation of methanol to formaldehyde as a function of temperature at typical reaction conditions.

methanol. Experimentally an inhibiting effect from water [2] is observed. This observation is reproduced by the model, cf. Eq. (21). Calculated reaction orders cf. Eqs. (17)–(21) at typical reaction conditions are plotted in Fig. 10 as a function of temperature. The reaction order of methanol, formaldehyde, water and carbon dioxide are independent of temperature and denotes values of 1, 0, )0.5 and 0, respectively. The reaction order of oxygen varies between )0.75 at low temperatures (high coverage of O ) to 0.25 at high temperatures (low coverage of O ). Generally the quantitative values of the reaction orders presented in Fig. 10 reproduce the qualitative features discussed above.

ð18Þ 4.4. Selectivity and industrial conditions aH2 CO ¼ 2hH2 CO  2hHCOO

ð19Þ

aCO2 ¼ 2hCO2

ð20Þ

aH2 O ¼ 1=2 þ hCH3 O  2hH2 O

ð21Þ 

As the coverages of all intermediates except O are low according to Fig. 7, the model explains the positive reaction order with respect to methanol observed experimentally [2,11]. With respect to oxygen Eq. (18) shows, that oxygen will have a positive reaction order, if the coverage of oxygen, methoxy and methanol are moderate. It can be seen from Fig. 2 that the model captures the observed trends in reaction order at 695 K very well i.e. zero order in oxygen and nearly first order in

The observed selectivity versus conversion trend on Fig. 3 is due to the increasing amount of formaldehyde formed at higher conversions. Increasing the amount of formaldehyde leads to an increased combustion of formaldehyde. This is a classical effect of a consecutive reaction path. Robb and Harriott [11] postulated that two routes to CO2 formation was necessary to explain these data. However our model shows that one oxidation route for formaldehyde is enough to explain the experiment. The reason for the different conclusion reached by Robb and Harriott is that they used an aged catalyst for low conversion experiments and a fresh catalyst for high conversions.

20

A. Andreasen et al. / Surface Science 544 (2003) 5–23

They state in their paper that a fresh catalyst has a lower selectivity than an aged catalyst. This means that they amplified the effect of conversion on selectivity by using these different catalysts. The difference between fresh and aged catalysts may be explained by the use of alumina support. The most important selectivity trend observed experimentally and predicted by the model is an increased selectivity with temperature. This effect can be explained very simple by the microkinetic model. As demonstrated in Fig. 8 the apparent activation energy of formaldehyde synthesis is always larger than the apparent activation energy of formaldehyde combustion. Hence the rate of formaldehyde formation increases more rapidly than formaldehyde combustion at increasing temperature. In order to obtain a high selectivity the industrial process should be conducted at high temperatures. However the temperatures should not be high enough to promote the pyrolytic gas phase decomposition of formaldehyde. Furthermore a methanol rich feed should be used in the process to ensure high selectivity by achieving complete oxygen consumption. Otherwise the remaining oxygen would combust the formed formaldehyde. This is consistent with the work by Wachs and coworkers [36] who show that the selectivity towards formaldehyde decreases from 92.3% to 69.1% when CH3 OH/O2 molar ratio decreases from 3.08 to 0.95 in a fixed bed reactor. The rate of formaldehyde combustion does not decrease with temperature it just does not increase as rapidly as the rate for formaldehyde formation. Another way to increase selectivity would be to reduce the contact time in the reactor. However the rate of these reactions are so fast that total conversion is achieved very rapidly and this option is therefore not feasible. Hence the microkinetic model gives a very simple explanation for the choice of industrial conditions. Nagy and Mestl [9] observes that the reaction ignites at approx. 450 K with a partial pressure of methanol of 0.088 atm in the feed. Gavrilin and Popov [7] has shown that the reaction ignites at approx. 550 K with a partial pressure of methanol of 0.435 atm. From Fig. 8 it is clear that the apparent activation energy of both formaldehyde and CO2 formation becomes very high below

500 K due to the blockage of free sites by O . This site blockage therefore inhibits the reactions below 400–500 K dependent on the partial pressures of oxygen and methanol. It is informative to compare our modelÕs explanation of the experiment depicted in Fig. 4 and Nagy and MestlÕs own interpretation [8,9]. It should be noted that Nagy and MestlÕs interpretation was not supported by simulations. Our model explains the trends in Fig. 4 by a high production of CO2 at low temperatures due to a low apparent activation energy of CO2 formation leading to a low selectivity. Below 500 K the stability of O leads to site blockage and all methanol oxidation is inhibited as mentioned above. At high temperatures the selectivity increases due to a higher apparent activation barrier for formaldehyde formation compared to CO2 formation. However Nagy and Mestl explain the selectivity trends by the different temperature stability of various oxygen species (Oa and Oc ) formed, exhibiting different chemical reactivities. Oa participates in an oxi-dehydrogenation path which dominates at low temperatures and result in both formaldehyde and complete oxidation products. Oc participates in a direct dehydrogenation path at high temperatures which exclusively leads to formaldehyde. As evidence for this the authors claim that Oc is dominating at high temperatures and is able to react with methanol. However as mentioned earlier the uptake of Oc is probable too slow to keep up with the uptake of Oa . Furthermore the necessary reconstruction to form Oc could be absent in the presence of methanol rich mixtures [26]. Nagy and Mestl mention that the selectivity increases dramatically above Oa desorption temperature (580–620 K) indicating that Oc plays a significant role at high temperatures. This argument is questionable. First of all 620 K is the desorption temperature of Oa in UHV. Secondly, the selectivity increases more rapidly below the desorption temperature cf. Fig. 4. Nagy and Mestl also postulate that a reaction-in-series model in which formaldehyde is an intermediate product for CO2 formation cannot explain the observed increasing selectivity with temperature due to the higher thermodynamic stability of CO2 . The authors therefore conclude that the selectivity trends

A. Andreasen et al. / Surface Science 544 (2003) 5–23

is due to changing between two reaction paths i.e. oxi-dehydrogenation and direct dehydrogenation. However our simulations clearly demonstrate that a reaction-in-series model is able to explain this selectivity behavior (this conclusion is valid regardless if one accept our model or not). The solution to this apparent paradox is very simple: as for all other partial oxidation reactions the selectivity is determined by kinetics not thermodynamics. All the oxygen is simple consumed rapidly in the formation of formaldehyde leaving nothing to oxidize formaldehyde further. Furthermore if two very different reaction pathways operate at low and high temperatures, respectively one would intuitively expect some kind of evident bend in the data at a temperature corresponding to the change in mechanism. This is in contrast to the nice smooth data reported in Fig. 4. With regard to the above discussion we find our interpretation of Nagy and MestlÕs experiments much more consistent, simple and validated. It is well known that it is impossible to deduce reaction mechanisms explicitly from steady-state kinetics. It must be considered even more dangerous to deduce mechanisms from kinetic experiments with total conversion. The experiments of Nagy and Mestl led to 100% conversion of oxygen and can therefore not be used to deduce the intrinsic kinetics of methanol oxidation. It should be stressed that our model is not deduced from Nagy and Mestl experiments but their experiments are explained as a consequence of our model. It is well known that formaldehyde synthesis on silver can be poisoned with electronegative substances such as halides and sulphur, and considerable attention has been paid to their removal, particular from process air [4]. It has been established that electronegative substances such as chloride blocks the uptake of O and significantly lowers the rate of O chemisorption (Ref. [89] and references therein). This poisoning is consistent with our model because O is essential in our model to the production of formaldehyde. 4.5. Critical parameters The microkinetic model contains more than 100 parameters (see Tables 3–5). However it turns out

21

that only seven parameters are critical: the four Arrhenius parameters of steps 5 and 10 and the enthalpies of O , CH3 O and HCOO . It has not been possible to determine the Arrhenius parameters and the enthalpies of formate explicitly. In order to do so surface science experiments and/or DFT calculations are needed probing the stability of formate. In order to make a more complete model including Eqs. (6)–(10) more critical parameters will have to be determined. We believe that the experimental and theoretical knowledge of this reaction does not justify such a model at present. The present work has shown that the surface mechanism proposed by Wachs and Madix can explain industrial formaldehyde synthesis. However this does not explicitly prove that this is in fact the case. In order to validate the model or discard it high quality steady-state kinetics preferable close to industrial conditions are needed badly. Such kinetic experiments are lacking at present due to the difficulties in avoiding mass transfer limitation, non-isothermity, deactivation, and aging effects. Furthermore it would be very interesting to investigate formaldehyde synthesis on different single crystals especially Ag(1 1 1) to determine the structure sensitivity of the reaction.

5. Conclusion We have formulated a simple microkinetic model for the oxidation of methanol on silver based on surface science at UHV and low temperatures. The reaction mechanism used in the model is a simple Langmuir–Hinshelwood mechanism, with a statistical mechanical treatment of gases and intermediates, having one type of active oxygen and one route to formaldehyde and carbon dioxide, respectively. The mechanism contains two slow steps: methoxy decomposition to formaldehyde (step 5) and formate decomposition (step 10). All other steps are assumed to be equilibrated. Step 5 controls the rate of methanol oxidation to formaldehyde, whereas steps 10 controls the combustion of formaldehyde (selectivity). The model has been used to simulate different kinetic experiments and it explains observed reaction orders, selectivity, apparent activation enthalpies,

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A. Andreasen et al. / Surface Science 544 (2003) 5–23

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