Comparison between multidentate and monodentate approach

Hi!
I am recently using Zacros for my work, and I want to describe the adsorption of a big molecule. The comparison between a multidentate and monodentate approach to describe it let me thinking which one is the most feasible.
In case 1, when I used 4 dentates (since the molecule occupies four sites), has led to an average of 1250 adsorbed molecules. 
In case 2, when I used 1 dentate (without considering lateral interactions), the average was decreased to ~700 adsorbed molecules.

All the remaining input is the same for both of them. They undergo physisorption (delta G ~ -0. 4eV).

What could be the reason for this difference ? And what should be the most feasible to be used ?

Thank you in advance.
 

Hello!

When studying adsorption/desorption equilibrium (or quasi-equilibrium) problems, one has to be careful about how KMC events are represented and detected. The numbers of adsorption or desorption events detected on the lattice (lattice processes) scale linearly with the lattice size, assuming constant coverage and invariant “adlayer structure”, but certain multiplication factors arise which can result in different equilibrium coverage.

Consider for example the non-dissociative adsorption of a species A on a square 10×10 lattice having 100 equivalent sites (single site type). We will assume no lateral interactions throughout this discussion. Starting with an empty lattice, there will be 100 elementary adsorption events that will be detected in the beginning of the simulation. If one starts with a fully covered lattice, there will be 100 desorption events detected in the simulation. If the kinetic constants for adsorption (kads) and desorption (kdes) are equal, this will give and equilibrium coverage of 0.5. In general, the coverage will be kads/(kads+kdes), assuming a large enough lattice (small fluctuations).

Let us compare this with the non-dissociative adsorption of a bidentate species B. Starting with an empty lattice, the number of adsorption events detected is now larger, because B adsorbs on pairs of sites and there are 200 unique site-pairs on the lattice. In case this “200” is unclear, each site in a square lattice has 4 neighbours, but to avoid double counting the unique pairs can be formed by taking the north and east neighbour of each site, i.e. two site-pairs for each site on the lattice. This factor of two is sometimes referred as a “geometric multiplicity” factor. In addition to that, there is a second multiplicity factor, which gives us the number of instances that the KMC algorithm detects the same event. For Zacros, we usually refer to this as the “graph multiplicity” factor, and because both sites must be empty for adsorption to take place, the graph pattern is symmetric, so the graph multiplicity for this event (adsorption of bidentate species) is 2. Now, let’s consider the corresponding desorption process of a bidentate species. Zacros distinguishes between dentate 1 and dentate 2 of the species, and therefore for the desorption, the graph multiplicity is 1. Moreover, the geometric multiplicity is also 1, because if a lattice site is occupied by a dentate, there is only one distinct desorption event that can occur: the event involving that site and the neighbouring site that is occupied by the other dentate of that same bidentate adsorbate. As a result, there is a “proliferation” of adsorption events but not of desorption events. Assuming no “packing efficiency” effects (which is certainly an approximation that becomes progressively better at low coverages), the equilibrium coverage will now be 4*kads/(4*kads+kdes) (caution: this is not fraction of covered sites; it is numbers of adsorbed molecules per site capped at half the number of sites).

Thus, at low enough coverages (where packing efficiency effects are negligible), the numbers of molecules at equilibrium will be:

Monodentate: kads/(kads+kdes)*Nsites
Bidentate: 4*kads/(4*kads+kdes)*Nsites

We therefore see that the higher multiplicities result in higher numbers of molecules for the bidentate, at low coverages. At the high coverage limit, the population sizes are reversed; the monodentate species reaches a population of Nsites, while for the bidentate the population can be up to Nsites/2.

Without having much information about your system, I would suspect that you are dealing with “geometric multiplicity” and “graph multiplicity” effects. Note that the geometric multiplicity effects are “real”, in the sense that they encode configurational entropy, but the graph multiplicity effects are essentially artifacts of the detection algorithm and can be corrected by dividing the rate constant of the event by the corresponding multiplicity factor. Things like the existence of multiple site types, or the precise configurations of multidentate species can complicate things further, e.g., does you quadri-dentate species bind in a 4 linearly-arranged sites, or in sites arranged in a square geometry (in which case the graph-multiplicities for adsorption will be different). In any case, you can easily find out exactly how many events Zacros detects by enabling the debug_report_processes keyword and inspecting the process_debug.txt output file. Caution: this file can be very large, so you should do this only for small runs (small lattices, small number of events). You can also consider seeding adsorbates on specific sites to check if Zacros detects the reaction patterns according to your expectations. Moreover, Zacros-post can help you visualise the lattice, seed the adsorbates on the sites you want, and inspect the adlayer configurations as the simulation progresses.