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

[Ulf Schiller]

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.

Best,
Ulf

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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