Lect 14 15 estatics

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```					A. D. D. 1/31/2013
Physics 850: Soft Condensed Matter Physics, Fall04
A.D. Dinsmore
Lecture 13 – Electrostatics in solution: Poisson-Boltzmann theory

MKS units
(m, kg, s,
C, V, etc)

Debye-Huckel is fairly
accurate even when es > kBT.

Phil Nelson’s view of electrostatic forces in solution:

Like-charged surfaces repel
Oppositely-charged surfaces attract because the
because the counter-ions must
counter-ions are not required in order to balance
remain in the gap to balance
charge. Neutral pairs can therefore depart into
charge. An entropic penalty
the bulk to decrease the local density and
arises (or, equivalently, there
is an osmotic pressure from the        pressure.
counter-ions)

Comment on the ideal-gas-like approach:
In class, there were several questions about the fact that we are using the ideal-gas
pressure law here to compute the pressure. It’s worth noting that we have already
assumed that the particles are point-objects that do not interact with one another. Recall
the first step of the derivation, when Boltzmann’s equation was invoked. We said n(r) ~
exp(-Ze(r)/kBT); this is only correct for point particles that interact with some external
potential , not directly with one another. The interactions among ions and counter-ions
are incorporated into Poisson’s equation, where n(r) determines the (r). In general, for
point particles the pressure on a surface is the kBT*density at the surface.

(see next page)

(see next page)

(with renormalized charge)