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Re: [ESPResSo-users] P3M epsilon

From: Stefan Kesselheim
Subject: Re: [ESPResSo-users] P3M epsilon
Date: Mon, 07 Nov 2011 09:45:39 +0100
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Dear Farnoosh,

On 11/07/2011 09:16 AM, Farnoosh Farahpoor wrote:
Dear Espresso developers

I have a question about P3M method. When we use the "inter" command with coulomb interaction we should set the Bjerrum length. This quantity contains all of the information about electrostatic strength in a medium with a specified temperature.
But there is another option in P3M method, "epsilon" (The dielectric constant of the surrounding medium). Why and when we should set this parameter? What does it mean that it "Defaults to metallic."?
When I am simulating a polyelectrolyte in water in the room temperature shall I set it to the reduced magnitude of permittivity of water?
This parameter is typical for coulomb interactions in 3D-periodic systems: When taking the limit of infinitely many replicas of the box in all directions the results of the sum depends on the boundary conditions "behind" the replicas. In other words: the limit of infinitely many replicas does not remove dependence on the dielectric permittivity outside of the considered system.

The dielectric properties outside of the system create a harmonic potential for the total dipole moment of the system proportional to 1/epsilon_{\infinity}. This means if epsilon_{\infinity}<\infinity the total dipole moment of the system will stay finite all the time and in thermal equilibrium be gaussian distributed, while it performs an unbounded random walk in case of metallic (infinity) boundary conditions.

We spend quite some time getting a good idea of what the physical meaning of this parameter is, but we did not find a very good interpretation. It is an artifact of the fact that all real systems are large, but finite, and infinite systems create mathematical difficulties with the 1/r coulomb potential. My personal opinion is that only metallic boundary conditions correspond to "proper" physics, because then the equations of motion don't  change when a particle is at the same folded position but in different replicas.

I know Kai Grass used metallic boundary conditions when simulating the electrophoretic mobility of a polyelectrolyte.

Maybe someone else has a better answer to that question...

Cheers and good luck,

Thank you in advance for your concern
With best regards

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