I don't know what you're after Fred (power from surface effects? All I can
do is confirm the e-field calculation, it's 0.5GV/m all right :) but the
quotes are interesting!
Michel
----- Original Message -----
From: "Frederick Sparber" <[EMAIL PROTECTED]>
To: <[email protected]>
Sent: Tuesday, May 16, 2006 1:58 PM
Subject: Re: Helmholtz Layer Metal-Water Interface, Joe Cell Etc
A 0.1 volt "Zeta Potential" across the 0.2 nanometer Metal-Water
interface is 500 million volts per meter.
http://en.wikipedia.org/wiki/Fowler-Nordheim_equation
" The Fowler-Nordheim equation in solid state physics relates current,
work and electric field strength to determine field emission. It has two
parts: an equation for field emitted current density, and the equation for
total current.
For the Fowler-Nordheim tunneling current density :
J = K1 × E2 × e-K2/E
"The point is that the current increases with the voltage squared
multiplied by an exponential increase with inverse voltage. While the
second factor, E2, obviously increases rapidly with voltage, the third
factor, the exponential, deserves another sentence"
Compare Fowler-Nordheim with the Richardson-Dushman Equation for
Thermionic Emission:
http://www.virginia.edu/ep/SurfaceScience/thermion.html
http://www.virginia.edu/ep/SurfaceScience/electron.html
"Jellium model. The charge of the ion cores is spread over the solid
(jellium) and the electrons then move in the potential produced by this
jellium. Density functional theory is used where the properties of the
electron "gas" depends only on the electron density. This is sometimes
refined by adding non-local corrections to the properties. We note that a
uniform electron gas is not a good approximation at the surface"
Surface dipole
"In the jellium model, the positive background terminates abruptly at the
surface (jellium edge). The electrons are allowed to readjust. The finite
wavelength of the electrons causes Friedel oscillations in the electron
density near the surface (this is analogous to what happens when one tries
to express a step function as a sum of sinusoidal functions up to a
maximum frequency). The sharpness of the jellium and the spread of the
electron density (which decays exponentially outside the solid) produces a
deficit of electrons just inside the jellium edge and an excess outside.
This produces a dipole layer. This dipole attracts electrons to the
surface and produces a step in the surface potential"
"The total potential seen by the electrons (inner potential) is the
electrostatic potential caused by the distribution of charge density
(Poisson equation), plus the exchange-correlation potential produced by
electron-electron correlations. The exchange-correlation potential
evolves into the image potential outside the solid. The electrostatic
potential includes the surface dipole whose value depends on the roughness
of the surface, both at the atomic scale and that produced by steps.
Thus, the work function, which is the inner potential minus the Fermi
energy, depends on the crystallographic orientation of the face of the
crystal. For instance, the work function of Cu (fcc) is 4.94 eV, 4.59 eV
and 4.48 eV for the (111), (100) and (110) surfaces, respectively. The
work function will be changed when permanent or induced dipoles are added
during adsorption of gases on the surface. These additional dipoles can
increase or decrease the work function."
