7/13/2007

Conductivity and electronic field

(1) Conductivity and Electronic field
An electrical current flows from an ion molecules in the air. There are 4 kinds of ions, large-positive, large-negative, small-positive and small-negative. Where the electric field strength is F, the total electrical current which flows from these 4 kinds of ions is it, and all ions have different mobility values (k/K/+/-) and ion counts (n/N/+/-).

[Mobility values]
k+: Positively charged small ion
k-: Negatively charged small ion
K+: Positively charged large ion
K-: Negatively charged large ion

[Ion counts]
n+: Positively charged small ion
n-: Negatively charged small ion
N+: Positively charged large ion
N-: Negatively charged large ion

Each current which flows from each ion:
[Current: Ion]
en+Fk+: small positive ion
en-Fk-: small negative ion
eN+FK+: large positive ion
eN-FK-: large negative ion

The total electrical current is the sum of each current and it is described by:

it = (en+Fk+) + (en-Fk-) + (eN+FK+) + (eN-FK-)

= F(en+k++en-k-+eN+K++eN-K-) ----- (A)
(e=4.77X1010C)

where

λ+ = (en+k++eN+K+) ----- (B)
λ- = (en-k-+eN-K-) ----- (C)
λ = λ+- ----- (D)

(A) can be descried by:

it = F(λ+-) = Fλ ----- (E)

Each term in λ+- is the ratio of the electronic field and the electrical current density, which shows the electrical conductivity.

λ+: Positive polar conductivity
λ-: Negative polar conductivity
λ: Whole conductivity

The SI unit of conductivity is: Sm-1

(2) Conductivity depending on environment
e.g. #1
where the air is well purified and n/N/k/K/+/- are:
n+ = 600
n- = 600
N+ = 2000
N- = 2000
k+ = 1.5(cm2/Vs)
k- = 1.5(cm2/Vs)
K+ = 0.0004(cm2/Vs)
K- = 0.0004(cm2/Vs)
ekn:eKN = 1125:1 (ref. to B/C)
This shows that the electronic conductivity in the purified air is largely determined by small ions.

e.g. #2 where the air is polluted and n/N/k/K/+/- are:
n+ = 100
n- = 100
N+ = 50000
N- = 50000
k+ = 1.5(cm2/Vs)
k- = 1.5(cm2/Vs)
K+ = 0.0004(cm2/Vs)
K- = 0.0004(cm2/Vs)
ekn:eKN = 7.5:1 (ref. to B/C)
This shows that large ions play a partial role to determine the electronic conductivity in the polluted air.

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