Sorry about sending the duplicate uncommented post! Just a sign of my
increasing senility.
On Aug 8, 2007, at 2:54 PM, Michel Jullian wrote:
----- Original Message -----
From: "Horace Heffner" <[EMAIL PROTECTED]>
Sent: Wednesday, August 08, 2007 10:18 PM
...
I certainly don't agree it is necessarily the field that counts in
Fig. 1 when it comes to electron fugacity. Referring to Fig. 1
again, if the "++" electrode is at +1,000,000 V and the "x"
electrode is at +980,000 V, the electron fugacity in the X electrode
will be reduced from what it would be if the "++" electrode were at
-1,000,000 V and the "x" electrode is at -1,020,00 V.
Not so, but at least our controversy is now clearly stated. If you
have two facing plates (= a capacitor) with a power supply
maintaining a 20kV difference of potential between them as is the
case in the two configurations you discuss, then whatever their
potential wrt ground,
It doesn't matter to what the voltage is relative. There are 4
potentials involved: +1,000,000 V +980,000 V, -1,000,000 V
-1,020,00 V. The surface electron fugacity is necessarily higher at
the most negative potential, -1,020,00 V. However, in earlier
discussions I think I defined the potentials I used as being with
respect to ground where ground was defined as a body having balanced
plus and minus charges. This is consistent with a fugacity of 0
being defined as being at a potential 0, at least with respect to the
above surfaces. I don't think there is a correlation of fugacity to
potential with regard to matter inside a conductor. This might all
be a fairly moot point inside a Faraday cage, from a practical point
of view.
Quote of
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On Jul 31, 2007, at 10:22 AM, Horace Heffner wrote:
On Jul 31, 2007, at 12:21 AM, Michel Jullian wrote:
A few comments on this:
1/ You mean extremely negatively charged I imagine, an extremely
negative electric potential being meaningless if you don't say
relative to what.
This is where the term "electron fugacity" instead of "potential"
has
usefulness. I mean relative to the potential of any material having
a neutral charge balance, one positive for every negative
charge. In
practical terms this means ground.
************* Note the above definition. *************
What do you mean? If you're saying that an object at ground
potential is necessarily neutral, or close to neutral, you
couldn't be more wrong.
I realize that ground (earth) potential varies a great deal, both
to the positive and to the negative, due to weather and solar wind
effects. This is why I said below that "ground electron fugacity
varies a great deal". This may in fact account for the "Salt Lake
City effect" and why CF cells that work at high altitude low storm
frequency places don't work for Scott Little in Texas. 8^)
However, I would expect that *typically*, setting the cathode
potential to -20 KeV or more would make for a high surface electron
fugacity.
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assuming that's what you mean by "at so many volts", the excess
charges at the facing surfaces will be _exactly_ the same.
But that is just it. I'm not talking about *relative* "excess
charges". I'm talking about electron fugacity, talking about the
importance of obtaining excess electrons over positive charges. I'm
talking about electron fugacity as defined by the energy cost to move
an electron from infinity (defined as infinitely far away from all
charge), or ground (as defined above), to the surface of interest
(also assuming no surfaces past through in between.) It's all about
an absolute number of excess electrons over positive charge.
In my article I footnote fugacity to:
http://www.mtaonline.net/~hheffner/DeflationFusion.pdf
which states:
"In statistical mechanics, the fugacity is one of the parameters that
define the grand canonical ensemble (a system that may exchange
particles with the environment). It represents the effort of adding
an additional particle to the system."
I guess I should spend more time in the article defining terms,
especially "electron fugacity". I thought it was very clear but on
reading I can see it is not actually well defined within the article
itself except maybe via footnote. Maybe I should even use a
different term to clear up any confusion, like "excess electron
density". (See below.)
In a capacitor, excess charge on each plate = capacitance times
voltage difference between the plates, q = C*Delta_V, as you know.
Can you see any dependence on absolute voltage in the formula?
No, and that is appropriate. The above formula is related only to
potential and not related to electron fugacity.
You see, potential is only defined by its derivative (or gradient),
the field, so as in any integral you can add any constant you
please to it it won't change a thing. Absolute value of potential
is totally meaningless, it doesn't have one in fact.
I think it does within my definition of fugacity because that
definition establishes the meaning of 0 potential for a conductor
surface.
Only differences of potential matter. Controversy solved?
Michel
Not yet! But thanks for trying. My concepts are certainly not clear
yet - even in my own head, which is usually a bit foggy anyway.
It is interesting that well inside a conductor without a current you
might think things should be neutral because it is a conductor.
There should be no "electron excess" or "electron deficit" because
the potential is everywhere the same. However, if a strong electric
field goes through that conductor then charges realign to neutralize
that field. If the conductor was neutral to begin with, i.e. had
exactly 0 "electron excess", then one part of the conductor will have
an electron excess, and one part will have an electron deficit.
Similar things happen in electrolytes in strong electrostatic
fields. This change in electron deficit value, what I was calling
electron fugacity, imposed throughout the Szpak electrodes and
electrolyte, I think had dramatic effects on the morphology of the
Szpak electrodes.
I think it may be useful to define the term rho_e to mean "excess
electron density" such that if a volume V of matter has N+ positive
charges and N- electrons then:
rho_e = q(N- - N+)/(V (N- + N+))
and the SI units for it would be Coul/m^3, but might seem more
meaningful in excess electron charge per cubic angstrom units. Note
rho_e can be positive or negative and there is no need to talk about
electron excess or electron deficit.
Of related interest is that in the case of a current through a CaO
barrier within a fully loaded PD matrix a rho_e gradient can develop
to either side of the barrier because fully loaded Pd is not really a
full fledged conductor, and because a field develops through the
barrier, and near the barrier, because the barrier tunnels nuclei and
electrons with differing probabilities.
Horace Heffner
http://www.mtaonline.net/~hheffner/
