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Re: [ESPResSo-users] Bjerrum Length for Explicit Solvent

From: Ulf Schiller
Subject: Re: [ESPResSo-users] Bjerrum Length for Explicit Solvent
Date: Sun, 6 Oct 2013 12:42:13 +0200
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Physics on a Sunday morning :-)

Hello everyone,

On 10/06/2013 08:48 AM, Stefan Kesselheim wrote:
> You say, that the Bjerrum length is the distance where the potential of mean force of two ions in water equals k_B T. > But this would mean, that the Bjerrum length ion (pair) specific. Would that be exactly what we want?

On 10/06/2013 11:43 AM, Stefan Kesselheim wrote:
To make it clear:
In my opinion the Bjerrum length can not be measured, and is not a physical 
quantity. It is a theoretical concept that is used to combine measurements of 
the bulk (!) dielectric permittivity and the temperature of a medium into a 
single quantity that is helpful to keep formulas brief.

Markus' opinion is that the Bjerrum length can be measured: You use to charged 
particles of known charge, hold them in appropriate tweezers (that can be 
tricky though) measure the force as a function of distance, integrate that 
force and where this integrated curve cuts the $k_B T$ line you read of the 
Bjerrum length.

Both definitions are possible, but not compatible. The first is a (bulk) 
material property at a particular temperature, the second is a property of ion 
pairs in a particular medium at a particular temperature.

Again, the Bjerrum length is defined as the distance at which the *electrostatic part* of the interaction energy between two *unit charges* equals the thermal energy. Note that this definition does not mention a dielectric constant. That only comes in when one assumes that the electrostatic energy can be written in a certain form. The definition of the Bjerrum length is independent of medium and ions. And thus it is very physical.

In practice, of course, it may be convenient to use the Bjerrum length to recast Poisson's equation in a certain form. At this point, it becomes more complicated and additional assumptions are needed. But the definition of a physical quantity should not require too many assumptions, and should not depend on how one uses it. Therefore, I prefer to stick to the generally accepted definition.


P.S.: Fun fact: spell checker suggests to replace Bjerrum by Cerebrum.

Dr. Ulf D. Schiller                        Building 04.16, Room 3006
Institute of Complex Systems (ICS-2)       Phone:   +49 2461 61-6144
Forschungszentrum Jülich, Germany          Fax:     +49 2461 61-3180

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