On Feb 24, 2010, at 9:45 AM, Michel Jullian wrote:
Hi Horace,
Another typo: Frick instead of Fick.
That's a funny one! Must have been a Freudian slip. 8^)
All these macroscopic phenomena you discuss regarding the motion of
ions in an electrolyte boil down, at the atomic scale, to the electric
force, don't you agree?
Of course I don't agree. Neither does Bockris. Did you check the
reference?
You are *assuming* that only a force affects random walk. The
gradient induced flow is not due to an actual force, even though it
acts just like a separate force on each species. If you draw a plane
perpendicularly through a concentration gradient, one side has a
higher concentration than the other. Random crossings therefore
occur more often going from the strong to the weak side of the
gradient. This results in a net flow that reduces the gradient.
In any case, in a dense conductor, whether liquid or solid or even a
dense gas such as atmospheric air, if you have a _steady_ current of
charged particles, then there exists a net DC electric field provoking
it, and in the absence of a magnetic field each charged particle does
a random walk whose average is the electric field line.
Things don't work this way in an electrolyte, especially if you have
a long inter-plate distance and a long equilibrium time.
Proof: the
average velocity (drift velocity) of each charged particle is equal to
its mobility times the local electric field, see e.g.
http://en.wikipedia.org/wiki/Electron_mobility for the case of
electrons, or look up "drift velocity" in the Feynman Lectures on
Physics. The electric field between the anode and cathode interfaces
of an electrolytic cell may be very small (it's indeed immensely
larger in the interface regions), but it explains entirely the steady
cell current.
Michel
I am already familiar with these concepts. These are *not* complete
electrochemistry concepts. The proof is invalid because the
conditions differ.
Michel, an electrolyte is *not* like a conductor, for the reasons I
already described. I repeat, The electrostatic gradients measured in
the center of very large cells do not come close to accounting for
the species flows required to support the steady state current that
develops.
I think there are some experiments you can do to demonstrate the
effect of diffusion gradients. One is to send a short pulse between
planar electrodes chosen such that the anode is partially dissolved
(with Faradaic efficiency of about 1) into the solution by the
pulse. This creates a planar concentration gradient near the anode
and results in a delayed current trace.
I would do some homework for you and type up some quotes from
Bockris, and draw some pictures, but I'm short on time right now.
Again I say, Bockris' Modern Electrochemistry, p. 288 ff is a good
place to start. It suffices to say ion concentration gradients in an
electrolyte produce ion flows, even bi-directional opposed ion flows,
even *without* the presence of an electrostatic field.
Diffusion based ion flow is not a trivial concept or second order
concept. It is an important concept for things like flow battery
design and modeling the mechanics of inter-interface currents.
2010/2/24 Horace Heffner <hheff...@mtaonline.net>:
On Feb 23, 2010, at 4:24 PM, Horace Heffner wrote:
Consider Frick's first law of steady state diffusion, which
states the
flow vector J_i for species i is proportional to the
concentration vector (d
c_i)/( d x) in typical cell conditions, i.e., one dimensionally
speaking:
J_i = - D (d c_i)/( d x)
where D is called the diffusion coefficient.
I accidentally left out a word above: "concentration vector"
above should
say "concentration gradient vector".
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
