But at 35C they are longer than eq 8 and 9 predict
moving at constant velocity, any electrical charge
picked by it has to relax, flowing over the distance Lt to
owing to the exponential dependencies of the charge
carrier concentrations on temperature. At 35C
the location of the opposite electrical charge behind the
slider. Then the resistance R in eq 3 is proportional to Lt
= τD . v and V is proportional to v2. (τD is the Debye
1
≅ 8 10 -8 m
(10)
κ1
relaxation time of the ice.) Measurements of τD re-
vealed that Lt ≈ 0.1 mm at 5C but Lt ≈ 1 cm at 35C.
Hence, at the high temperature the discharge takes place
1
≅ 1.6 10 -4 m.
(11)
locally under the slider since Lt is much less than the
κ2
slider dimensions (2.5 cm). In that case R does not de-
pend on v and V ∝ v. But when at the low temperatures,
Notice that both the liquid-like layer and the princi-
-
pal screening length κ1 1 are very small. That makes it
Lt becomes comparable with the slider dimensions, and
R ∝ Lt ∝ v and V ∝ v2.
likely that a slider, when rubbing ice, sweeps off the
surface charge together with the most of the screening
charge. That leaves just a small fraction of all λs on the
Effect of electrical fields on ice friction
ice surface (see Fig. 8). This may explain why the den-
Earlier (Petrenko 1994a), it was demonstrated that
sity of the surface charge taken away by the sliders (λ ≤
the application of an external dc bias to the ice/slider
105 C/m2) was much smaller than the theoretically
interface can double the force of dynamic and static
predicted λs ≈ 2 101 C/m2. Another factor decreas-
friction between ice and metals and between ice and di-
ing λ is that the real contact area is much smaller than
electrics. The experimental techniques, the ice samples
the slider surface, and hence the slider does not sweep
and experimental conditions used were similar to the
off the whole area of the interface as assumed in eq 2.
ones described in the previous section (see Fig. 1 and
The described mechanism of electrification by fric-
2). The measurements were performed at temperature
intervals from 5 to 30C, with sliding velocities from
tion, thus, though hypothetical, is based on firm and
clear deductions from the surface physics of ice and
0.5 to 8 m/s and the dc bias within the range from 3 to
can be tested experimentally in the future, since it im-
3 kV. All slider materials created a strong increase in
plies characteristic dependencies on temperature, slid-
ing velocity, thickness of the "erased" layer and dop-
was applied. Owing to the high dc impedance of pure
ing of ice.
ice, the electrical power consumed from the power sup-
ply was very small (about 103 W at 30C for metal
Other mechanisms that may in principle contribute
to the frictional electrification of ice are the motion of
sliders and even less for dielectric ones).
charged dislocations during the plastic deformation of
Figure 9 depicts the changes in polyethylene belt
tension T2 when a 3-kV bias was applied to the ice cyl-
ice subsurface regions (Takahashi 1969a, Petrenko and
Whitworth 1983), a charge separation by microcracks
inder and the foil electrode attached to the outer surface
in ice during cleavage of surface layers (Petrenko
100
1993a) and the Workman-Reynolds (1949, 1950) ef-
fect (charge separation during refreezing of ice). It is
unlikely that any of these phenomena is able to account
95
for the large magnitude of the potential difference, 1.6
kV, observed in our research. Under the most favorable
90
conditions, the first two mechanisms generated V val-
ues that are much less then 1 V and the Workman-Rey-
nolds effect generated about 100 V. Also, the Work-
85
off
man-Reynolds effect reaches a maximum in doped ice
on
on
samples while frictional electrification decreases with
off
80
doping. As discussed in the previous section, the ther-
moelectric effect can add only a negligible contribu-
75
tion.
40
50
0
10
20
30
The fact that at higher temperatures (5 to 10C)
Time (s)
the electrification is proportional to the sliding veloci-
Figure 9. Changes in tension of the polyethyl-
ty (V ∝ v) while at lower temperatures (≤ 25C) V is
ene belt (T2) when a 3-kV bias is switched on
proportional to v2 can be explained in terms of the
and off (after Petrenko 1994a). Temperature is
30C. Sliding velocity is 2 m/s. The friction co-
length of the electrically charged track on the ice sur-
efficient ≈0.3 at V = 0 and ≈0.5 at V = 3 kV.
face Lt that a slider leaves behind. When the slider is
7
Previous Page
