Re: Coulomb-Energies and MMM2D

[Konrad Breitsprecher]

Hi Fabian,

I'm not sure about the energy calculation, the recent bug there shows that the energies are not well tested for the pot_diff 

feature. I took part in the development, so I'm sorry for that mistake. But I did compare density profiles of many ionic systems 

with MMM2D, ELC and also ICC* and got consistent results, so there's hope that the forces are correct. We also compared 

MMM2D energies of a thin metallic slit (which is pot_diff=0) against the analytical solution, which worked out well. 

(see eq. 3 in my paper, the comparison can be found in the supplemental). So I think it is really only the energy part of 

pot_diff ≠ 0 (hoping that the not equal sign survives).

About the pot_diff feature, you should be aware that this is not only another representation of fixed charges on the plates, but a 

method that adaptively changes the surface charge to obtain the target potential difference. This is done by balancing the global 

dipole moment of the free charges to get 0V between the system borders and then add the target potential difference (as a simple 

force in z-direction). This is different from using a linear external potential, which is just the force in z-direction.

Also note that due to this behavior, there might be metastable ion configurations that lead to the target potential difference, but 

give asymmetric density profiles. There was a debate if it is valid to model such systems with constant charges, see here for 

example. If that's the case for your system, try to increase the temperature, sample a bit more and review your profiles.

Regards,

Konrad

Fabian Glatzel <address@hidden> schrieb am Mo., 16. Dez. 2019, 13:40:

Dear espressomd developers,

because I haven't heard of you since I wrote to you three weeks ago, I wanted to ask if someone had a look at it already?

I should state that I get the same results using the new espresso version (4.1.2).

Best regards,

Fabian

On 11/26/19 3:32 PM, Fabian Glatzel wrote:

Dear espressomd developers,

I'm still heaving some issues with the Coulomb energy using ELC with the pot_diff parameter as well as using MMM2D with pot_diff.

The used system is a 2d plate capacitor (periodic boundary conditions along x&y) with charged hard spheres (Weeks-Chandler-Andersen) and with an external potential of 1V.

I simulated this system using three different setups:

1) ELC and the pot_diff argument

2) MMM2D and the pot_diff argument

3) ELC and a linear electric potential (corresponding to a constant surface charge density at the electrodes and hence neglecting the effect of image charges)

First, the density profile obtained with MMM2D shows some nonphysical behavior. For example, the density profile of the negative ions near the right electrode miss the typical rise that the positive ions near the left electrode show (see https://bwsyncandshare.kit.edu/dl/fiA9hy94kVktH579fNrU4z9F/density_profiles.png?inline ). Of course, the ions are identical up to their charge.

Concerning the Coulomb energy, I cannot make any sense from the numbers i get via MMM2D or ELC with pot_diff. However, they are more or less consistent with each other. From what I see I would guess that there is possibly a sign error. But maybe I should first explain where this impression comes from:

As stated above I also simulated the system using ELC without the pot_diff argument but using a linear electric potential instead. The density profiles obtained via this method fit the ones from ELC with ext_pot parameter quite good. However, the energy contributions using ELC and the linear electric potential are:

coulomb: ~ +10650

external_fields: ~ -23000

Using ELC with ext_pot i get:

coulomb: ~ +14400

I guess this explains part of my confusion. Further, if the change in the coulomb energy during charging is monitored another unexpected behavior can be seen using the pot_diff argument. A smaller Coulomb energy is obtained at pot_diff=0V than at pot_diff=1V. However, if the decrease in Coulomb energy due to the external charge (implicitly handled via pot_diff) was not bigger than the increase of the Coulomb energy  due to the ion-ion contributions in the system, the system should not change its density profile at all.

I wrote a little example script to show these effects. To keep it as simple as possible it contains some hard coded numbers etc... Via the index in line 8 the used method can be chosen (ELC, MMM2D or ELC + External Field). In line 10 it can be set if the density profile is written to a file. The other stuff should be self-explanatory.

The example script can be downloaded via:

https://bwsyncandshare.kit.edu/dl/fiSyz84gmxo2gwkN7KFTyNtP/coulomb_comparision.py

I look forward to hearing from you.

Also, let me thank you in advance since i know it can consume quite a bit of time...

Best wishes,

Fabian