ABSTRACT
When two different metallic materials come into contact, electrons in the metal having the higher Fermi level move into the other metal so as to equalize the Fermi levels of the two materials. Then the number of electrons in the material having a lower Fermi level increases, resulting in electrifi cation to negative charge. As a matter of course, the other material is electrifi ed to positive charge. Contact electrifi cation of semiconductive materials is explained in a similar way. The contact region acts as an electrical capacitor. The amount of charge stored in the capacitor can be obtained by solving Poisson’s equation. Electrifi cation of a nonconductive material is, however, more complicated. For metalinsulator contact, the charge density is estimated by the following equation 1 :
s
1 0 0eN N
ez +
(5.1)
where charge density (C/m 2 )
N s density of surface states (l/(m 2 eV))
N b density of traps of acceptor type (l/(m 3 eV))
e elementary charge (1.602 × 10 19 C) e dielectric constant of solid (F/m) e
0 dielectric constant of vacuum (8.85 × 10 12 F/m) z
A similar equation is derived for insulatorinsulator contact by assuming surface states for both materials. 2
The difference of work functions divided by elemental charge e is called the contact potential difference. If the surface states have negligible effects ( z
0 0, N s 0), Equation 5.1 is simplifi ed to
s
z Vc
(5.2a)
where V c is the contact potential difference and z is the effective Debye length ( / / ). N eb
If the density of traps is negligible ( N
s = 0
(5.2b)
When the contact bodies are separated, charges are partly neutralized or discharged through the surrounding medium. The process is called charge relaxation. 3
The maximum charge of a spherical particle is controlled by discharge from the surface of the particle. The breakdown condition in air is given by an electric fi eld strength of 3 MV/m for particles larger than 200 µm and a surface potential of 300 V for those less than 200 µm. 4
Charge transfer between impacted materials proceeds during the very short time of collision. Such a high-speed electrifi cation will be represented by 5 :
q CV tc 1 exp t
⎛ ⎝⎜
⎞ ⎠⎟
⎡ ⎣⎢
⎤ ⎦⎥
(5.3)
where C is the capacitance of the contact region, t the time constant for electrifi cation, and t the effective duration time of contact. The capacitance C is given by
C S z
C S z
= =
(5.4)
corresponding to Equation 5.2a or 5.2b, where S is the contact area. Equation 5.3 shows that metallic particles ( t << t ) may be highly electrifi ed by impact as long as the back discharge is negligible. 6 For nonconductive particles, the time constant t is given by
t r d
(5.5)
where r d is the specifi c resistance of the particle. The charge transferred is given by
q SV z
(5.6)
Equation 5.6 shows that the perfect insulator ( r d → ∞) does not acquire charge, which coincides
with the experimental results obtained by the use of solid rare gases. 7 The contact area S depends on the mode of impact. It is nearly proportional to impact velocity v
for inelastic collision and proportional to v 0.8 for elastic collision. In both cases it is proportional to the square of the particle size. 5
If particles collide with the wall several times, they are all electrifi ed and produce a strong electric fi eld. Also, the contact potential difference V
charge of the particle. The electrifi cation process, including the electric-fi eld effect and the imagecharge effect, is represented by the following equation 8,9 :
Δ ⎛ ⎝⎜
⎞ ⎠⎟
⎛ ⎝⎜
⎞ ⎠⎟
⎡ ⎣⎢
⎤ ⎦⎥∞
q q N N
q N N
1exp exp
(5.7)
where N is the number of collisions of a particle, N 0 the relaxation number of collisions for charge
transfer, q 0 the initial charge of a particle, and q the fi nal charge attainable in the process.
