Re: dielectric constant

[John Denker <jsd@MONMOUTH.COM>]

At 10:02 PM 1/29/01 -0700, Larry Smith wrote:
> We are doing capacitors this week and a student asked how the dielectric
> constant, \kappa, is determined for different materials.  Is it just
> empirically determined by what factor the capacitance is increased when
> inserted in a parallel plate capacitor?

1) Certainly it _can_ be, and often is, measured.

But..... it would be going too far to say it is "just" determined that
way.  Other possibilities include:

2) For some substances, it is easy to calculate the dielectric
constant.  For starters, there is the classic model substance consisting of
small conducting spheres imbedded in an insulator;  see _The Feynman
Lectures on Physics_ volume II, figure 10-3.

3) If you measure the dielectric constant of a compressible substance at
one density, you can predict the dielectric constant at other
densities.  (ibid., chapter 11.)

4) For a gas of atoms or other nonpolar particles, you can model the atom
as a charged-mass-on-a-spring and calculate the dielectric constant.  This
requires experimental (or perhaps theoretical) values for the oscillator
size and frequency.  (ibid.)

5) For a gas of polar molecules, you can calculate the dielectric constant
using basic thermodynamics.  All you need is the dipole moment and the
temperature (and of course a few fundamental constants).  (ibid.)

6) The polarizability of, say, a helium atom can be calculated _ab initio_,
using nothing but fundamental constants.  Thence you can calculate the
dielectric constant of helium gas.  This requires techniques considerably
beyond high school level, but it is a standard exercise for physics and
physical-chemistry grad students.

7) Indeed an _ab initio_ calculation has apparently been done for liquid
water (which is incomparably messier than helium).  "Static Dielectric
constant of the polarizable NCC water model" by J.C. Soetens, C. Millot and
M.T.C. Martins Costa, Molecular Physics 94, 577 (1998).
  http://www.lsmc.u-bordeaux.fr/soetens/abstract.html