Seeking advices for modeling CO2RR to CO

[Nam Tran]

Hi Everyone,

I am trying to modeling the electrochemical reaction of CO2RR to CO as the product.

(*) + CO₂ + (H⁺ + e) <-> *COOH                  (1)

*COOH + (H⁺ + e) <-> *CO + H₂O                (2)

*CO <-> (*) + CO                                            (3)

I am planing to use the kinetic gas phase flux equation with a sticking coefficient of 1 for the desorption/adsorption of CO molecule (eq. 3). The equation of rate constant is taken from literature [1] and kmcos tutorial [2].

The desorption (forward reaction of eq.3) has a barrier energy (beta = 1/kbT)

p_CO*bar*A/sqrt(2*pi*umass*m_CO/beta)*exp(-beta*dG03*eV)               (5)

The adsorption (backward reaction of eq.3) is barrier less

p_CO*bar*A/sqrt(2*pi*umass*m_CO/beta)                                                              (6)

I have two questions regarding the methods

1). At low potential the reaction is slow and almost no CO is produced. As a result, there should be no available CO molecules for the adsorption (backward reaction of eq.3). However, if I use the eq.5 the surface will be fully covered by the adsorbed CO from the backward reaction because it consider there is a reservoir of CO with partial pressure. So I would like to know if there is any model/method to only tread the procuded CO molecules as a reservoir and use thems for the backward reaction? Possibly incoporate it into the partial pressure of CO.

2). I am a little bit confused why the parital pressure of CO (p_CO) appears in the equation of desorption, and the desorption rate is slower with smaller value of p_CO. If I have a surface that is fully covered by adsorbed CO and no gas CO molecules does it mean no desorption?

Any suggestion and recommendation for the problem is highly appreciated

Best regards

Nam

[1]. https://doi.org/10.1103/PhysRevB.73.045433

[2]. https://github.com/kmcos/kmcos/blob/master/examples/MyFirstDiffusion__build.py

[kmcos-users]

Unfortunately I have been sick for a few days and also have more things to finish this month than is possible to finish, so I will give a quick reply.

I also would like very much if we can have a simple toy example of electrochemistry like this, it was already on the longterm roadmap to have one.

Answer to Q1:

a)   "At low potential the reaction is slow and almost no CO is produced. As a result, there should be no available CO molecules for the adsorption (backward reaction of eq.3)."  <-- low CO is different from no  CO.

b)  "However, if I use the eq.5 the surface will be fully covered by the adsorbed CO from the backward reaction" <-- an infinitely extended surface will never be fully covered, but certainly a finite size surface can be covered completely.

    " because it consider there is a reservoir of CO with partial pressure. So I would like to know if there is any model/method to only tread the [produced] CO molecules as a reservoir and use thems for the backward reaction? Possibly incoporate it into the partial pressure of CO."

Ok, I think I understand the question now. In KMCOS, you can change various variables like P_CO, T, etc.  I suggest you start your runfile with CO pressure extremely low, like 1E-10 bar.  Then, by counting number of molecules of CO produced using the TOF, during the runfile you can update the pressure.  KMCOS does not model a reactor. So you'll need to make your own assumptions etc. of how quickly pressure will increase above surface as CO is produced, then update the variable.

Answer to Q2. The general case for an equilibrium is like this, where "std" means standard.

Eq. 1: K_std = k_f/k_r * (additional standard state terms)    <-- equilibrium

Eq. 2: DeltaG_std = -RTln(K_std)

Often, people will define **either** kf or kr explicitly, then the other via K_std.

For example, if somebody knows k_f, then can use  k_r = k_f/K_std

Then  use Eq. 1 and Eq. 2, and thus creates an equation for k_r based on DeltaG_std.

 I assume the person was using this approach.  mu_CO is related to DeltaG_CO, and may involve P_CO.  They defined k_f explicitly, then made k_r based on K_std, then used a version of DeltaG_std expression that depends on P_CO.  Maybe I am wrong, but this is my guess. Whether they did this carefully enough to do it correctly is beyond the scope of my answer.  My initial impression is that sounds like someone made a mistake. It sounds like someone used rate_forward/K_std when they should have used k_forward/K_std.

For second part of question 2, this statement does not make sense to me: "If I have a surface that is fully covered by adsorbed CO and no gas CO molecules does it mean no desorption?"  KMCOS does not track gas phase molecules unless you made some explicit cells above the surface somehow. However, if there is no gas phase CO, the definitely everything will desorb, eventually. If you mean you have a liquid above the surface, and CO in the liquid, but no gas CO above the liquid, then the CO could stay on the surface.  I think second part of question 2 was probably not important so I won't worry about my not understanding it. Also, maybe second part of Question 2 doesn't make sense because maybe somebody made an error in defining k_f, leading to strange question when you saw it.

[Nam Tran]

Hi,

Thank you for your response,

1). I think counting the number of CO molecule produced could be a really good idea. Perhaps, I could calculate the partial pressure suing the ideal gas law i.e., PV = nRT

2). I was used your Eq.1 and Eq.2 to get the rate constant. But I forgot the fact the dG03 could also involve P_CO due to the Gibb energy of CO gas phase, that may cancel the P_CO in the prefactor p_CO*bar*A/sqrt(2*pi*umass*m_CO/beta). A similar rate equation can be found in the kmcos tutorial (https://github.com/kmcos/intro2kmcos/blob/master/task_material/COoxRuO2__build.py), i.e., line #98.

For the second part of Q2, you are right, I was confused by the appreance of p_CO in prefactor without considering its contribution in the dG03. It give me wrong intutiation that low p_CO only leads to low desorption rate.

Best regards