Simplified Kinetic Model for NH3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NH}_3$$\end{document}-SCR Over Cu-CHA Based on First-Principles Calculations

Selective catalytic reduction with ammonia as reducing agent (NH3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NH}_3$$\end{document}-SCR) is an efficient technology to control NOx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NO}_\mathrm{x}$$\end{document} emission during oxygen excess. Catalysts based on Cu-chabazite (Cu-CHA) have shown good performance for NH3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NH}_3$$\end{document}-SCR with high activity and selectivity at low temperature and good hydrothermal stability. Here, we explore a first-principles based kinetic model to analyze in detail which reaction steps that control the selectivity for N2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {N}_2$$\end{document} and the light-off temperature. Moreover, a simplified kinetic model is developed by fitting lumped kinetic parameters to the full model. The simplified model describes the reaction with high accuracy using only five reaction steps. The present work provides insight into the governing reaction mechanism and stimulates design of knowledge-based Cu-CHA catalysts for NH3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NH}_3$$\end{document}-SCR.


Introduction
Copper-exchanged small-pore zeolites with chabazite structure (Cu-CHA), are state-of-the-art catalysts for ammonia assisted selective catalytic reduction ( NH 3 -SCR) in emission control of diesel exhaust [1]. Thanks to low-temperature activity, high selectivity for N 2 , and hydrothermal stability [2][3][4], Cu-CHA is a preferred catalyst for NH 3 -SCR and has matured to commercial application. NO is the main NO x component in diesel exhaust and selective reduction of NO to N 2 with NH 3 is known as the standard-SCR reaction: Each NO couples with one NH 3 and O 2 is needed to complete the stoichiometry.
Although high selectivity for N 2 has been achieved over Cu-CHA, a small amount of N 2 O is formed under NH 3 -SCR conditions [5,6]. N 2 O is an undesired by-product and has received wide attention due to its high greenhouse protential. An overall reaction where N 2 O is formed is: To further enhance the selectivity for N 2 over Cu-CHA, understanding of the reaction mechanism for N 2 O formation during NH 3 -SCR is desired. Advancing the atomic understanding of the reactions could in this respect guide the development of next generations of catalysts. For this purpose we have developed first-principles microkinetic models for low-temperature conditions [7] based on multisite reaction mechanisms [8].
The proposed reaction cycle for NH 3 -SCR is shown in Fig. 1. Under the reaction condition of standard NH 3 -SCR, Cu ions are at low temperatures solvated by NH 3 and mainly present as [Cu(NH 3 ) 2 ] + species [9][10][11]. O 2 adsorption is a key step in the reaction and a pair of [Cu(NH 3 ) 2 ] + complexes is needed for O 2 adsorption, forming a Cu-peroxo complex, [ Cu 2 (NH 3 ) 4 O 2 ] 2+ [9,12,13]. The oxidation state of Cu changes from +1 to +2 [14] during O 2 adsorption, which allows the adsorption of NO and NH 3 at relevant temperatures. Upon NO adsorption (reaction 2), NO reduction proceeds via formation of H 2 NNO and HONO intermediates. The intermediates is in this model assumed to diffuse from the Cu-sites to neighboring Brønsted acid sites where they decompose into N 2 and H 2 O by reactions with NH 3 [7,8]. Unwanted N 2 O formation (reaction 16) may occur via H 2 NNO decomposition over the Cu-sites [7,15]. The selectivity for N 2 depends on the competition between the diffusion of H 2 NNO from the [ Cu 2 (NH 3 ) 4 OOH] 2+ complex to the Brønsted acid sites (reaction 5) and the direct decomposition of H 2 NNO on the complex (reaction 16). If H 2 NNO desorbs from the Cu complex, the reaction will follow the outer cycle and give an overall reaction as R1. However, for the case that H 2 NNO decomposes over the Cu complex, the reaction will follow the dashed route which forms N 2 O as R2. NO conversion to either N 2 or N 2 O may be inhibited by NH 3 adsorption on the [ Cu 2 (NH 3 ) 4 O 2 ] 2+ complex (reaction 15). The NH 3 adsorption is in the reaction cycle yielding [ Cu 2 (NH 3 ) 5 O 2 ] 2+ , however, it may also lead to decomposition of the peroxo complex [7,13]. Note that NH 3 has four different roles in the catalytic cycle showed in 1. NH 3 is simultaneously i) a ligand that enable facile Cu-mobility, ii) a reactant, iii) adsorbed at the Brønsted acid site forming NH + 4 , which is the active site for H 2 NNO and HONO conversion, and iv) an inhibitor that prevents the adsorption of NO on the Cu-peroxo complex [7].
In this contribution, we further investigate factors that control the selectivity for N 2 and the NH 3 inhibition. For the selectivity for N 2 , the competition between reaction 5 and 1 3 16 is discussed in detail. It is revealed that a reduction of the H 2 NNO desorption energy on the Cu-peroxo enhances the selectivity for N 2 , which is one possibility to further improve the catalyst performance. The NH 3 inhibition is discussed in relation to the onset of the low-temperature activity and different mechanisms to exit the blocked state are presented. In addition to the mechanistic aspects, we show that the detailed microkinetic model with 18 steps can be replaced with a simplified model with only 5 steps, which accurately reproduce the results of the full model.

Density Functional Theory Calculations
Spin-polarized density functional theory (DFT) calculations are carried out with the Vienna Ab-initio Simulation Package (VASP) [16][17][18][19], using the gradient-corrected Perdew-Burke-Ernzerhof (PBE) functional [20] augmented with a Hubbard-U term of 6 eV for the Cu 3d states as proposed in previous studies [21,22]. To account for the van der Waals interactions of the molecules in the zeolites, Grimme-D3 corrections have been applied [23,24]. The valence electrons are described with a plane wave basis set with a cutoff energy of 480 eV, whereas the interaction between the valence and the cores are described using the projector augmented wave (PAW) method [25,26]. The k-point sampling is restricted to the gamma point. The Climbing Image Nudged Elastic Band (CI-NEB) method [27,28] is employed to calculate the reaction barriers and the transition states are confirmed by vibrational analyses. Ab initio molecular dynamics (AIMD) simulations are performed in the canonical (NVT) ensemble [29,30] at 300 K to probe the potential energy surface and low energy configurations are obtained by structural relaxation from the trajectories. The experimental lattice constants ( = = = 94.2 • , a = b = c = 9.42 Å) are used for the CHA unit cell.

Microkinetic Modeling
For the microkinetic modeling, MATLAB R2018b is used with the ode23s solver to numerically integrate the system of differential equations until steady-state is reached. The full model includes 16 reaction steps as shown in Fig. 1 and two steps over the Brønsted acid sites [7]. The kinetic parameters for the full model are published elsewhere [7].
Here, a simplified model with only five reaction steps is developed. The simplified model uses lumped reaction steps with kinetic parameters estimated by fitting to the detailed model. The simulannealbnd optimizer is applied to perform the non-linear regression. An objective function ( ) for the parameter estimation is chosen as the normalized difference between the results from the detailed model (denoted ref) and the simplified model (denoted sim): where the turnover frequency of NO and selectivity for N 2 are denoted TOF and S , respectively. A weighting factor (w = 10) is added to the part of the normalized difference in selectivity to enhance the importance of the selectivity.

Steps Controlling the Selectivity and Light-Off Temperature
Here we further investigate the steps that previously [7] were found to determine the selectivity for N 2 and the light-off temperature for NH 3 -SCR over Cu-CHA. The aim is to gain deeper insights into the mechanisms that control these steps and reveal how they influence the kinetic behavior.

Selectivity for N 2
In the kinetic model [7], the selectivity for N 2 depends on the ratio between reaction rate of reaction 5 and reaction 16.  [15], which makes it challenging to determine accurately the reaction barrier. Here we have considered the case where the spin state of the Cu-cations are preserved along the reaction path.
To investigate how the selectivity depends on the ratio between the barrier of reaction 5 and 16, we performed simulations where the ratio was changed, Fig. 2. In the simulations, the forward reaction barrier of Reaction 5 ( E 5f ) was fixed to 0.3 eV, whereas the forward reaction barrier of reaction 16 ( E 16f ) was changed from 0.3 to 0.42 eV.
The selectivity for N 2 depends strongly on the E 16f /E 5f ratio at low ratios. The selectivity at 373 K increase from 80% to 95% when the ratio increase from 1 to 1.2. The dependence is less pronounced at higher E 16f /E 5f ratios and the effect of increasing the ratio on the selectivity becomes small for cases when the ratio is larger than 1.3. E 16f is close to the calculated DFT barrier when the ratio is 1.3. The strong dependence of the selectivity on the E 16f /E 5f ratio shows that lowering the H 2 NNO desorption energy could lead to a higher selectivity for N 2 . The desorption energy could potentially be effected by the Al-distribution [31].

Site Blocking and Light-Off Temperature
complex blocks the site for the SCR-reaction [7]. The inhibiting effect of NH 3 is severe as the adsorption energy of NH 3 is higher than that of NO; -0.98 eV as compared to -0.70 eV. It was in Ref. [7] shown that the light-off temperature of the SCR reaction is determined by the NH 3 inhibition as the temperature should be high enough to facilitate NH 3 desorption. Adsorption of NH 3 on [ Cu 2 (NH 3 ) 4 (O 2 )] 2+ has also been observed experimentally using X-ray absorption spectroscopy (XAS) [13] where it was suggested that the [  Fig. 1). It could be noted that molecular crystals have been synthesized with the Cu 2 O 2 unit coordinated to six nitrogenbased ligands [32], which indicates that adsorption of additional NH 3  with an adsorption energy of -0.98 eV as shown in Fig. 3(B).
After forming structure B, an additional NH 3 can adsorb with an adsorption energy of -0.85 eV on the other Cu-cation forming [ Cu 2 (NH 3 ) 6 O 2 ] 2+ (structure C in Fig. 3). Without additional NH 3 , structure B could dissociate into structure E via the transition state D. The barrier for dissociation is calculated to be 0.33 eV. Configuration E is consistent with the experimental interpretation of the XAS spectra [13]. As the complex has dissociated, O 2 and NH 3 bonded with the Cu-cation may desorb sequentially with desorption energies of 0.60 eV and 0.49 eV, respectively. The Cu species return in this way to the [Cu(NH 3 ) 2 ] + state on which O 2 may adsorb forming structure A. The adsorption energy of O 2 is here calculated to be only 0.05 eV, which is lower than experiments and previous calculations [33]. The difference can be attributed to differences in the reference state of the initial state for the [Cu(NH 3 ) 2 ] + pairs as well as the poor description of molecular oxygen in the used exchange-correlation functional [34].
The potential energy landscape shows the possible ways of NH 3 hindering the SCR-reaction. The rate of NH 3 adsorption to C is at experimentally relevant conditions lower than the rate for dissociation of B to E, thus, the system will likely transform into E and eventually G. Kinetic analysis (not shown) reveals that this is indeed the case. 1 The kinetic analysis explains why structure C is not observed experimentally despite the strong NH 3 adsorption energy; B will dissociate before NH 3 adsorbs to form C. The system will at temperatures above 423 K mainly be in state G. The probability of being in state A, which is required for the NH 3 -SCR reaction has a maximum at about 473 K.   Fig. 1 The detailed reaction path for NH 3 inhibition shows that structure E is the dominating structure at low temperatures. For the SCR reaction to proceed, E should decompose allowing for regeneration of structure A. Effectively, however, the inhibition could in a kinetic model be accounted for by considering only structure B as the NH 3 poisoned state.

Reduced Kinetic Model
In our previous work, the reaction cycle in Fig. 1 was implemented in a kinetic model [7]. The model included 18 elementary steps and it is interesting to investigate whether it could be simplified by lumping reaction steps which do not control the reaction rate. We have shown [7] that the total rate is dominated by the adsorption steps, i.e. O 2 , NO and NH 3 adsorption onto a pair of [Cu(NH 3 ) 2 ] + complexes. Here we develop a model based on the three adsorption steps and lumped reactions for N 2 and N 2 O formation: The kinetic parameters for the elementary adsorption steps are taken from our previous study [7], whereas the parameters for the lumped reactions (R6 and R7) are determined by fitting to the detailed model. The initial values in the parameter estimation are given by the values corresponding to the highest energy barrier in the lumped reaction. The activation energies and entropy contributions from parameter estimation are listed in Table 1.
The TOF and selectivity from the simplified model is compared to the detailed model in Fig. 4. Both the TOF and selectivity for N 2 are in very good agreement. The onset of the reaction is at about 425 K and is associated with the desorption of NH 3 that blocks the Cu-site. The TOF approaches a maximum at about 525 K as the coverage of O 2 starts to decrease. Fig. 4 Simulated turnover frequency for NO conversion (a) and selectivity for N 2 (b) over Cu-CHA as a function of temperature. The simulations are performed with 600 ppm NH 3 , 500 ppm NO, 10% O 2 , and balance N 2 . The red dashed line in each figure is the results from the detailed model whereas the blue line is from the simplified model Table 1 Original and estimated parameters for the simplified kinetic model Energies are given in eV and entropies in J/mol ⋅ K . The pre-exponential factors ( A x ) are given in s −1 and evaluated at 473 K with 600 ppm NH 3 , 500 ppm NO, 10% O 2 , and balance N 2 Phenomenological models with lumped reaction steps have previously been developed from experimental data for NH 3 -SCR over Cu-CHA [35]. In Ref. [35], the pre-exponential factor for the NH 3 -SCR reaction was reported to be 4.83×10 8 s −1 and the corresponding activation energy to be 0.71 eV. Our model yields a comparable result for the prefactor, which is 9.3×10 8 s −1 for the lumped SCR-reaction (R6). However, our activation energy for R6 is 0.34 eV. The difference with respect to the phenomenological model is due to the fact that NH 3 -inhibition effectively was included in the SCR-reaction in Ref. [35], whereas it is treated explicitly in our model. In fact, the apparent activation energy of our simplified model is 0.76 eV, which is close to the value used in the phenomenological model. The comparison shows the advantage of a first-principles based model where the kinetic parameters can be associated with elementary reaction steps.

Conclusions
We have discussed a first-principles micro-kinetic model for low-temperature NH 3 -SCR over Cu-CHA. The selectivity for N 2 is found to be sensitive to the ratio between the barriers. The barrier for H 2 NNO diffusion originates mainly from the desorption from the [ Cu 2 (NH 3 ) 4 OOH] 2+ complex and one strategy to enhance the selectivity would be to reduce the desorption energy. The desorption energy could potentially be modified via the Al-distribution.
The micro-kinetic model shows that adsorption of extra The analysis of the detailed kinetic model allows for the formulation of a simplified model for NH 3 -SCR with N 2 O formation over Cu-CHA with only five reaction steps. The simplified model was constructed with the elementary reactions for adsorption and desorption of NH 3 , NO and O 2 together with lumped reactions for N 2 and N 2 O formation. The kinetic parameters for the lumped reactions were fitted via non-linear regression. The simplified model reproduces the results for the detailed model and provides a link to a previous kinetic model developed from experimental data.
Funding Open access funding provided by Chalmers University of Technology.
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