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polymers
Article
Influence of Silicone Rubber Coating on the Characteristics of
Surface Streamer Discharge
Xiaobo Meng 1, Liming Wang 2,* , Hongwei Mei 2, * and Chuyan Zhang 3
Citation: Meng, X.; Wang, L.; Mei,
H.; Zhang, C. Influence of Silicone
Rubber Coating on the Characteristics
of Surface Streamer Discharge.
Polymers 2021,13, 3784.
https://doi.org/10.3390/
polym13213784
Academic Editor: Shaojian He
Received: 16 October 2021
Accepted: 28 October 2021
Published: 31 October 2021
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4.0/).
1School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China;
mengxb@gzhu.edu.cn
2Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
3School of Information Engineering, China University of Geosciences (Beijing), Beijing 100083, China;
zcy@cugb.edu.cn
*Correspondence: wanglm@sz.tsinghua.edu.cn (L.W.); mei.hongwei@sz.tsinghua.edu.cn (H.M.);
Tel.: +86-0755-26036695 (L.W.)
Abstract:
A pollution flashover along an insulation surface—a catastrophic accident in electrical
power system—threatens the safe and reliable operation of a power grid. Silicone rubber coatings
are applied to the surfaces of other insulation materials in order to improve the pollution flashover
voltage of the insulation structure. It is generally believed that the hydrophobicity of the silicone
rubber coating is key to blocking the physical process of pollution flashover, which prevents the
formation of continuously wet pollution areas. However, it is unclear whether silicone rubber coating
can suppress the generation of pre-discharges such as corona discharge and streamer discharge.
In this research, the influence of silicone rubber coating on the characteristics of surface streamer
discharge was researched in-depth. The streamer ‘stability’ propagation fields of the polymer
are lower than that of the polymer with silicone rubber coating. The velocities of the streamer
propagation along the polymer are higher than those along the polymer with silicone rubber coating.
This indicates that the surface properties of the polymer with the silicone rubber coating are less
favorable for streamer propagation than those of the polymer.
Keywords:
surface streamer discharge; silicone rubber coating; three-electrode arrangement; ther-
mally stimulated current method; surface properties
1. Introduction
Pollution flashover along the insulation surface occurs widely in electrical power
systems, which threatens the safe and reliable operation of the power grid. The hydropho-
bicity of silicone rubber coating can prevent the formation of continuously wet pollution
areas, and thus it can block the physical process of pollution flashover along the insulation
surface. Therefore, silicone rubber coatings have typically been applied to the surfaces
of other insulation materials in order to increase the pollution flashover voltage of the
insulation structure.
In the long-term operation of an electrical power system, a partial pre-discharge
may occur on the surface of the silicone rubber coating and cause it to gradually lose
hydrophobicity. At the same time, a partial arc can also develop more easily due to the
existence of a partial discharge, and then the pollution flashover voltage will decrease [
1
].
However, it is unclear whether the silicone rubber coating suppresses or promotes the
generation of pre-discharges such as corona discharges and streamer discharges. Therefore,
the influence of silicone rubber coating on the characteristics of partial pre-discharges needs
to be researched in depth. It is necessary to find ways to suppress the partial pre-discharge
on the surface of silicone rubber coating.
There have been many studies on the engineering applications of silicone rubber
coating in electrical power systems, which have provided many theoretical bases for
Polymers 2021,13, 3784. https://doi.org/10.3390/polym13213784 https://www.mdpi.com/journal/polymers
Polymers 2021,13, 3784 2 of 13
the engineering applications of silicone rubber coatings [
2
–
10
]. However, research on
the characteristics of the partial discharge on the surfaces of silicone rubber coatings
is rare. Streamer discharge is the most complex physical process in partial discharge,
which develops into leader discharge and surface flashover within high-enough electric
fields
[11–18]
. The streamer ‘stability’ propagation fields in air were lower than those on
the insulation surface [
13
]. When there was streamer propagation along the insulation
surface, there were ‘surface’ and ‘air’ components of the streamer discharge [
14
–
16
]. We
have previously obtained photographs of the streamer discharge, observing the ‘surface’
component of the streamer propagated along the insulation surface having a higher velocity,
and the ‘air’ component of streamer propagated in the air having a lower velocity [
17
].
In [
17
], the influence of the dielectric materials on the characteristics of the streamer
discharge was also researched; the conclusion was that both the permittivity and the
surface properties of dielectric materials affected the streamer discharge, which affected
the subsequent flashover processes. Therefore, research on the characteristics of streamer
propagation along the surface of the silicone rubber coating is conducive to a deeper
understanding of the mechanism of partial discharge. If the partial arc discharge can be
suppressed during the streamer propagation stage, the external insulation performances of
silicone rubber coating will be greatly improved.
The paper [
18
] designed an experiment to describe the quantitative influence of
permittivity and surface properties on the characteristics of streamer propagation along
insulation surfaces. In this paper, a test of the characteristics of the streamer propagation
along the polymer and the polymer with a silicone rubber coating was designed, which
measured them using three photomultipliers and an ultraviolet camera. Because the
silicone rubber coating was very thin, the overall permittivity of the polymer with the
silicone rubber coating hardly changed. The differences between the streamer propagation
along the polymer and the polymer with the silicone rubber coating were determined by
comparing the characteristics of the surface streamer discharge from those materials. Not
only could the test results be used as a verification of the previous test results in [
18
], but
also the influence of a silicone rubber coating on the surface streamer propagation process
was analyzed. In addition, the characteristics of the streamer propagation along the silicone
rubber coatings produced by different manufacturers were compared, which provided a
feasible method for evaluating the insulation performances of silicone rubber coatings.
2. Experiment Arrangement and Measurement System
Figure 1is a schematic diagram of the test equipment and measurement system
used. Two flat electrodes and one needle electrode formed a three-electrode structure.
The diameter of the parallel plates was 250 mm, and the distance between the upper and
lower plates was 100 mm. The needle electrode was located at the circular hole (10 mm in
diameter) in the center of the lower plates. The needle electrode was 2–3 mm above the
plane of the lower plate, and was insulated from the lower plate. A negative DC voltage
was applied to the upper plate, which was divided by a resistor divider, and then connected
to a voltage measuring instrument via a coaxial cable. The lower plate was grounded. A
square pulse voltage with adjustable amplitude and pulse width (1~6 kV, 100~250 ns) was
applied to the needle electrode to trigger the positive polarity discharge. The square pulse
voltage was divided by a high-voltage probe (Tektronix P6015A) that served as the trigger
signal of a 4-channel 2 GHz oscilloscope (Agilent DSO7104A).
Three photomultipliers, each with a narrow slit (1 mm wide), were respectively
directed at grazing incidence to the needle electrode, the middle position of the parallel
plates, and the upper plate. The photomultiplier could monitor the development process
of the streamer, because the head of the streamer would radiate photons into the space.
The ‘DayCor@Superb’ UV imaging detector made by Ofil Corporation was used to take
the photographs of the streamer discharge.
Polymers 2021,13, 3784 3 of 13
Polymers 2021, 13, 3784 3 of 13
Figure 1. Schematic of the experiment arrangement and measurement equipment.
The polymer sheet used in the test was made of polyamide, and was placed vertically
between two parallel plates. The polymer sheet was a square plate with a length of 100
mm, a width of 100 mm, and a thickness of 5 mm. The first polymer sheet was clean and
had no silicone rubber coating, namely it was a polymer sheet. The second polymer sheet
was coated with the first silicone rubber coating, namely Coating A. The last polymer
sheet was coated with the second silicone rubber coating made by another manufacturer,
namely Coating B. The permittivity of the polymer was 5, the permittivity of the first sili-
cone rubber coating was 3.6, and the permittivity of the second silicone rubber coating
was 3.8. The dielectric strength of Coating A was 22.2~22.8 kV/mm, and the dielectric
strength of Coating B was 22.5~23.2 kV/mm. Their volume resistivity was 1.6 × 1014~1.8 ×
1014 Ω m. For this study, the silicone rubber coatings were sprayed onto the surface of the
polymer sheets, their thickness was 0.5 mm, and their surface drying time was 18–25 min.
During the test, the indoor temperature was stable at about 25 °C, the relative humidity
was maintained at about 65%, and the air pressure was the standard atmospheric pressure.
3. Experimental Results
3.1. Streamer Propagation Fields
Allen defined the applied electric field with a probability of 97.5% of the streamer
propagating to the cathode plate as the streamer ‘stability’ propagation electric field Est
[13]. This definition was adopted in this study. The measurement method of the streamer
stable propagation electric field was briefly as follows. The pulse voltage amplitude on
the needle electrode was kept at a certain value Upulse, and the DC voltage Uapp applied
between the plates was increased gradually. The DC voltage between the two parallel
plates gradually increased from 450 kV/m to 750 kV/m. At each DC voltage value Uapp,
voltage pulses were applied to the needle electrode 20 times with a pulse interval of 20 s.
That setting of the pulse interval was to ensure that the remaining ions from the previous
streamer discharge were fully diffused. As the voltage between the two parallel plates
gradually increased, the propagation probability of the streamer gradually increased from
0% to 100%. The streamer propagation probability and the applied electric field satisfied
the Gaussian distribution function as shown in Figure 2. The Gaussian distribution func-
tion (1) was used to fit the statistical distribution curve of the streamer propagation prob-
ability with the electric field.
2
2
()
2
0e
/2
c
EE
w
A
yy w
−
−
=+
π
(1)
In Formula (1), E is the electric field, Ec is the mean value of the electric field; w is the
variance; y is the streamer propagation probability; A and y0 are undetermined coefficients.
Figure 1. Schematic of the experiment arrangement and measurement equipment.
The polymer sheet used in the test was made of polyamide, and was placed vertically
between two parallel plates. The polymer sheet was a square plate with a length of 100 mm,
a width of 100 mm, and a thickness of 5 mm. The first polymer sheet was clean and had
no silicone rubber coating, namely it was a polymer sheet. The second polymer sheet was
coated with the first silicone rubber coating, namely Coating A. The last polymer sheet
was coated with the second silicone rubber coating made by another manufacturer, namely
Coating B. The permittivity of the polymer was 5, the permittivity of the first silicone
rubber coating was 3.6, and the permittivity of the second silicone rubber coating was 3.8.
The dielectric strength of Coating A was 22.2~22.8 kV/mm, and the dielectric strength of
Coating B was 22.5~23.2 kV/mm. Their volume resistivity was 1.6
×
10
14
~
1.8 ×1014 Ωm
.
For this study, the silicone rubber coatings were sprayed onto the surface of the polymer
sheets, their thickness was 0.5 mm, and their surface drying time was 18–25 min. During
the test, the indoor temperature was stable at about 25
◦
C, the relative humidity was
maintained at about 65%, and the air pressure was the standard atmospheric pressure.
3. Experimental Results
3.1. Streamer Propagation Fields
Allen defined the applied electric field with a probability of 97.5% of the streamer
propagating to the cathode plate as the streamer ‘stability’ propagation electric field E
st
[
13
].
This definition was adopted in this study. The measurement method of the streamer stable
propagation electric field was briefly as follows. The pulse voltage amplitude on the needle
electrode was kept at a certain value U
pulse
, and the DC voltage U
app
applied between the
plates was increased gradually. The DC voltage between the two parallel plates gradually
increased from 450 kV/m to 750 kV/m. At each DC voltage value U
app
, voltage pulses
were applied to the needle electrode 20 times with a pulse interval of 20 s. That setting
of the pulse interval was to ensure that the remaining ions from the previous streamer
discharge were fully diffused. As the voltage between the two parallel plates gradually
increased, the propagation probability of the streamer gradually increased from 0% to
100%. The streamer propagation probability and the applied electric field satisfied the
Gaussian distribution function as shown in Figure 2. The Gaussian distribution function
(1) was used to fit the statistical distribution curve of the streamer propagation probability
with the electric field.
y=y0+A
w√π/2 e−2(E−Ec)2
w2(1)
Polymers 2021,13, 3784 4 of 13
Polymers 2021, 13, 3784 4 of 14
In Formula (1), E is the electric field, Ec is the mean value of the electric field; w is the
variance; y is the streamer propagation probability; A and y0 are undetermined
coefficients.
Then, the streamer ‘stability’ propagation fields Est (streamer propagation probability
of 97.5%) were obtained as shown in Figure 3. It was found that the streamer ‘stability’
propagation fields decreased linearly with the increase in the applied pulse amplitude.
The reason is that the energy initially obtained by the streamer from the applied pulse
increases with its amplitude, and the subsequent streamer propagation becomes easier. In
addition, it can be seen that the streamer ‘stability’ propagation fields with the polymer
with the silicone rubber coating are stronger than those with the polymer. Furthermore,
the electric fields for the streamer stable propagation along the surface of the different
silicone rubber coatings are quite different.
The fitting Formula (2) was used in Figure 3 to fit the curve. Est is the streamer
‘stability’ propagation field, E0 is the streamer stable propagation electric field when the
pulse amplitude is 0 kV, u is the pulse amplitude, and α is an undetermined coefficient.
st 0
EE u
α
=− (kV/m) (2)
400 440 480 520 560 600
0
10
20
30
40
50
60
70
80
90
100
Air
Polymer
Coating A
Coating B
Streamer propagation probability %
Electric field kV/m
Figure 2. Relationship between the probability of streamer propagation and the guiding electric field.
456
400
440
480
520
560 Air Est=510-13.5u
Polymer Est=621.3-23u
Coating A Est=635.8-24.5u
Coating B Est=631.7-22u
Streamer 'stability' propagation fields kV/m
Pulse amplitude kV
Figure 3. Relationship between the streamer ‘stability’ propagation fields and the pulse amplitude.
Figure 2.
Relationship between the probability of streamer propagation and the guiding electric field.
In Formula (1), Eis the electric field, E
c
is the mean value of the electric field; wis the
variance; yis the streamer propagation probability; Aand y
0
are undetermined coefficients.
Then, the streamer ‘stability’ propagation fields E
st
(streamer propagation probability
of 97.5%) were obtained as shown in Figure 3. It was found that the streamer ‘stability’
propagation fields decreased linearly with the increase in the applied pulse amplitude. The
reason is that the energy initially obtained by the streamer from the applied pulse increases
with its amplitude, and the subsequent streamer propagation becomes easier. In addition,
it can be seen that the streamer ‘stability’ propagation fields with the polymer with the
silicone rubber coating are stronger than those with the polymer. Furthermore, the electric
fields for the streamer stable propagation along the surface of the different silicone rubber
coatings are quite different.
Polymers 2021, 13, 3784 4 of 14
In Formula (1), E is the electric field, Ec is the mean value of the electric field; w is the
variance; y is the streamer propagation probability; A and y0 are undetermined
coefficients.
Then, the streamer ‘stability’ propagation fields Est (streamer propagation probability
of 97.5%) were obtained as shown in Figure 3. It was found that the streamer ‘stability’
propagation fields decreased linearly with the increase in the applied pulse amplitude.
The reason is that the energy initially obtained by the streamer from the applied pulse
increases with its amplitude, and the subsequent streamer propagation becomes easier. In
addition, it can be seen that the streamer ‘stability’ propagation fields with the polymer
with the silicone rubber coating are stronger than those with the polymer. Furthermore,
the electric fields for the streamer stable propagation along the surface of the different
silicone rubber coatings are quite different.
The fitting Formula (2) was used in Figure 3 to fit the curve. Est is the streamer
‘stability’ propagation field, E0 is the streamer stable propagation electric field when the
pulse amplitude is 0 kV, u is the pulse amplitude, and α is an undetermined coefficient.
st 0
EE u
α
=− (kV/m) (2)
400 440 480 520 560 600
0
10
20
30
40
50
60
70
80
90
100
Air
Polymer
Coating A
Coating B
Streamer propagation probability %
Electric field kV/m
Figure 2. Relationship between the probability of streamer propagation and the guiding electric field.
456
400
440
480
520
560 Air Est=510-13.5u
Polymer Est=621.3-23u
Coating A Est=635.8-24.5u
Coating B Est=631.7-22u
Streamer 'stability' propagation fields kV/m
Pulse amplitude kV
Figure 3. Relationship between the streamer ‘stability’ propagation fields and the pulse amplitude.
Figure 3. Relationship between the streamer ‘stability’ propagation fields and the pulse amplitude.
The fitting Formula (2) was used in Figure 3to fit the curve. E
st
is the streamer
‘stability’ propagation field, E
0
is the streamer stable propagation electric field when the
pulse amplitude is 0 kV, u is the pulse amplitude, and αis an undetermined coefficient.
Est =E0−αu(kV/m)(2)
Polymers 2021,13, 3784 5 of 13
3.2. Light Emission
A large number of photons are generated during the process of streamer discharge.
Some of them participate in the photoionization in the discharge area, while others escape
to the outside. The photoionization plays a vital role in the generation and development of
streamers. The secondary electron avalanches generated by the photoionization in front of
the streamer head supply the streamer discharge with positive and negative charges, and
then the streamer channel moves forward.
Based on the physical phenomenon of photons being emitted outward during the
streamer discharge, the photomultipliers and UV imaging detector were used to observe
the process of the streamer discharge. In our previous articles [
17
,
18
], we found that there
were ‘surface’ and ‘air’ components of the streamer discharge when streamer propaga-
tion occurred along the insulation surface. The ‘surface’ components of the streamers
propagated along the insulation surfaces at a higher velocity, and the ‘air ’ components
of the streamers propagated in the air at a lower velocity. However, there were only ‘air’
components of the streamer discharges when the streamers propagated in air alone. The
same conclusion was reached in this article. The photomultiplier detected two peaks of
light at the cathode plate when the streamers propagated along either the polymer or the
polymer with the silicone rubber coating as shown in Figure 4. Therefore, the ‘surface’ and
‘air’ components of the streamer discharges also occurred along both the polymer and the
polymer with the silicone rubber coating. The ‘surface’ components of the streamers had
higher velocities and their propagation paths lay along the insulation surfaces. The ‘air ’
components of the streamers had lower velocities and their propagation paths were in
the air.
Polymers 2021, 13, 3784 5 of 13
3.2. Light Emission
A large number of photons are generated during the process of streamer discharge.
Some of them participate in the photoionization in the discharge area, while others escape
to the outside. The photoionization plays a vital role in the generation and development
of streamers. The secondary electron avalanches generated by the photoionization in front
of the streamer head supply the streamer discharge with positive and negative charges,
and then the streamer channel moves forward.
Based on the physical phenomenon of photons being emitted outward during the
streamer discharge, the photomultipliers and UV imaging detector were used to observe
the process of the streamer discharge. In our previous articles [17,18], we found that there
were ‘surface’ and ‘air’ components of the streamer discharge when streamer propagation
occurred along the insulation surface. The ‘surface’ components of the streamers propa-
gated along the insulation surfaces at a higher velocity, and the ‘air’ components of the
streamers propagated in the air at a lower velocity. However, there were only ‘air’ compo-
nents of the streamer discharges when the streamers propagated in air alone. The same con-
clusion was reached in this article. The photomultiplier detected two peaks of light at the
cathode plate when the streamers propagated along either the polymer or the polymer with
the silicone rubber coating as shown in Figure 4. Therefore, the ‘surface’ and ‘air’ compo-
nents of the streamer discharges also occurred along both the polymer and the polymer
with the silicone rubber coating. The ‘surface’ components of the streamers had higher
velocities and their propagation paths lay along the insulation surfaces. The ‘air’ compo-
nents of the streamers had lower velocities and their propagation paths were in the air.
Positive pulse
Photomultiplier 1
l
t(200ns/div)
U1 U2
(5V/div) (2V/div)
U1
U2
Photomultiplier 2
l
Photomultiplier 3
l
Figure 4. Typical signals from the photomultiplier monitoring the streamer propagation along the
surface of the polymer.
The UV imaging detector was used to take the photographs of the streamer dis-
charges. The light emitted from a single propagation process of a streamer was able to be
recorded in a clear image. The white spots on each image are the signal displayed by the
light emitted from a streamer discharge. Figures 5 and 6 show the streamer propagation
photographs for the polymer and the polymer with the silicone rubber coating.
It can be observed that the ‘surface’ component of a streamer propagates along the
insulation surface, while the ‘air’ component of a streamer propagated in the air and was
away from the insulation surface. Within the same electric field, the luminous intensity of
the streamer propagation along the polymer was greater than that along the polymer with
the silicone rubber coating. Furthermore, the luminous intensity of the streamer propaga-
tion along the polymer with the different silicone rubber coatings was also different. It
was determined that the luminous intensity of a streamer was closely related to the sub-
sequent photoionization. The stronger the luminous intensity of a streamer was, the more
intense the subsequent photoionization would be, and it would promote the development
of the subsequent streamer. This also explains that the electric fields required for the
streamer stable propagation along the polymer with the silicone rubber coating were
greater than that along the polymer.
Figure 4.
Typical signals from the photomultiplier monitoring the streamer propagation along the
surface of the polymer.
The UV imaging detector was used to take the photographs of the streamer discharges.
The light emitted from a single propagation process of a streamer was able to be recorded in
a clear image. The white spots on each image are the signal displayed by the light emitted
from a streamer discharge. Figures 5and 6show the streamer propagation photographs
for the polymer and the polymer with the silicone rubber coating.
It can be observed that the ‘surface’ component of a streamer propagates along the
insulation surface, while the ‘air’ component of a streamer propagated in the air and was
away from the insulation surface. Within the same electric field, the luminous intensity of
the streamer propagation along the polymer was greater than that along the polymer with
the silicone rubber coating. Furthermore, the luminous intensity of the streamer propaga-
tion along the polymer with the different silicone rubber coatings was also different. It was
determined that the luminous intensity of a streamer was closely related to the subsequent
photoionization. The stronger the luminous intensity of a streamer was, the more intense
the subsequent photoionization would be, and it would promote the development of the
subsequent streamer. This also explains that the electric fields required for the streamer
stable propagation along the polymer with the silicone rubber coating were greater than
that along the polymer.
Polymers 2021,13, 3784 6 of 13
Polymers 2021, 13, 3784 6 of 13
(a) (b) (c)
(d) (e) (f)
Figure 5. Streamer propagation photographs for the polymer. (a) 500 kV/m, (b) 530 kV/m, (c) 550
kV/m (d) 590 kV/m, (e) 620 kV/m, (f) 660 kV/m.
(a) (b) (c)
(d) (e) (f)
Figure 6. Streamer propagation photographs for the polymer with the silicone rubber coating. (a)
510 kV/m, (b) 540 kV/m, (c) 560 kV/m, (d) 590 kV/m, (e) 630 kV/m, (f) 660 kV/m.
3.3. Streamer Propagation Velocity
The propagation velocity of the streamers was calculated by the ratio of the vertical
distance between the three photomultipliers and the time difference ΔT between the starting
points of the rising edge of the light signals from the three photomultipliers (Figure 4). The
streamer ‘stability’ propagation velocity Vst was defined as the streamer propagation veloc-
ity within the ‘stability’ electric field. Figure 7 shows the relationship between the
streamer ‘stability’ propagation velocities and the pulse amplitude. The ‘stability’ veloci-
ties of the streamer propagation along the surface of the polymer with a coating were
linearly related to the pulse amplitude. For Figure 7, Equation (3), which relates the
streamer ‘stability’ propagation velocities to the pulse amplitude, was used to fit the
curves. u is the pulse amplitude, kV; V0 is the streamer stable propagation velocity when
the pulse amplitude is 0 kV, 105 m/s; β is the undetermined coefficient.
𝑉
=𝑉
+𝛽𝑢 (3)
Figure 5.
Streamer propagation photographs for the polymer. (
a
) 500 kV/m, (
b
) 530 kV/m, (
c
)
550 kV/m (d) 590 kV/m, (e) 620 kV/m, (f) 660 kV/m.
Polymers 2021, 13, 3784 6 of 13
(a) (b) (c)
(d) (e) (f)
Figure 5. Streamer propagation photographs for the polymer. (a) 500 kV/m, (b) 530 kV/m, (c) 550
kV/m (d) 590 kV/m, (e) 620 kV/m, (f) 660 kV/m.
(a) (b) (c)
(d) (e) (f)
Figure 6. Streamer propagation photographs for the polymer with the silicone rubber coating. (a)
510 kV/m, (b) 540 kV/m, (c) 560 kV/m, (d) 590 kV/m, (e) 630 kV/m, (f) 660 kV/m.
3.3. Streamer Propagation Velocity
The propagation velocity of the streamers was calculated by the ratio of the vertical
distance between the three photomultipliers and the time difference ΔT between the starting
points of the rising edge of the light signals from the three photomultipliers (Figure 4). The
streamer ‘stability’ propagation velocity Vst was defined as the streamer propagation veloc-
ity within the ‘stability’ electric field. Figure 7 shows the relationship between the
streamer ‘stability’ propagation velocities and the pulse amplitude. The ‘stability’ veloci-
ties of the streamer propagation along the surface of the polymer with a coating were
linearly related to the pulse amplitude. For Figure 7, Equation (3), which relates the
streamer ‘stability’ propagation velocities to the pulse amplitude, was used to fit the
curves. u is the pulse amplitude, kV; V0 is the streamer stable propagation velocity when
the pulse amplitude is 0 kV, 105 m/s; β is the undetermined coefficient.
𝑉
=𝑉
+𝛽𝑢 (3)
Figure 6.
Streamer propagation photographs for the polymer with the silicone rubber coating. (
a
)
510 kV/m, (b) 540 kV/m, (c) 560 kV/m, (d) 590 kV/m, (e) 630 kV/m, (f) 660 kV/m.
3.3. Streamer Propagation Velocity
The propagation velocity of the streamers was calculated by the ratio of the vertical
distance between the three photomultipliers and the time difference
∆
T between the starting
points of the rising edge of the light signals from the three photomultipliers (Figure 4).
The streamer ‘stability’ propagation velocity V
st
was defined as the streamer propagation
velocity within the ‘stability’ electric field. Figure 7shows the relationship between the
streamer ‘stability’ propagation velocities and the pulse amplitude. The ‘stability’ velocities
of the streamer propagation along the surface of the polymer with a coating were linearly
related to the pulse amplitude. For Figure 7, Equation (3), which relates the streamer
‘stability’ propagation velocities to the pulse amplitude, was used to fit the curves. uis
the pulse amplitude, kV; V
0
is the streamer stable propagation velocity when the pulse
amplitude is 0 kV, 105m/s; βis the undetermined coefficient.
Vst =V0+βu(3)
Polymers 2021,13, 3784 7 of 13
Polymers 2021, 13, 3784 7 of 13
The ‘surface’ and ‘air’ components of the streamers occurred when the applied elec-
tric fields were larger than the streamer ‘stability’ propagation fields. The velocities of the
‘surface’ and ‘slow’ components under the varied electric fields are displayed in Figures
8 and 9, respectively. Equation (4) was used to draw the fitting curves in Figures 8 and 9.
Est and Vst come from Equations (2) and (3), and n and γ are the undetermined coefficients
listed in Table 1.
𝑉
=𝑉
(
(1 + 𝛾)) (4)
456
1.0
1.5
2.0
2.5
3.0
3.5
Air Vst=1.27+0.07u
Polymer Vst=1.91+0.12u
Coating A Vst=2.10+0.10u
Coating B Vst=2.25+0.08u
Streamer 'stability' propagation velocities x 105m/s
Pulse amplitude kV
Figure 7. Relationship between the streamer ‘stability’ propagation velocities and the pulse ampli-
tudes.
450 500 550 600 650 700 750
2
4
6
8
10 'Surface' component
Air
Polymer
Coating A
Coating B
Streamer propagation velocities x 105m/s
Electric field kV/m
Figure 8. Velocities of the ‘surface’ components under the varied electric fields.
Figure 7.
Relationship between the streamer ‘stability’ propagation velocities and the pulse amplitudes.
The ‘surface’ and ‘air’ components of the streamers occurred when the applied elec-
tric fields were larger than the streamer ‘stability’ propagation fields. The velocities
of the ‘surface’ and ‘slow’ components under the varied electric fields are displayed
in
Figures 8and 9
, respectively. Equation (4) was used to draw the fitting curves in
Figures 8and 9
.E
st
and V
st
come from Equations (2) and (3), and nand
γ
are the un-
determined coefficients listed in Table 1.
Vs=Vst(E
Est
(1+γ))
n
(4)
Polymers 2021, 13, 3784 7 of 13
The ‘surface’ and ‘air’ components of the streamers occurred when the applied elec-
tric fields were larger than the streamer ‘stability’ propagation fields. The velocities of the
‘surface’ and ‘slow’ components under the varied electric fields are displayed in Figures
8 and 9, respectively. Equation (4) was used to draw the fitting curves in Figures 8 and 9.
Est and Vst come from Equations (2) and (3), and n and γ are the undetermined coefficients
listed in Table 1.
𝑉
=𝑉
(
(1 + 𝛾)) (4)
456
1.0
1.5
2.0
2.5
3.0
3.5
Air Vst=1.27+0.07u
Polymer Vst=1.91+0.12u
Coating A Vst=2.10+0.10u
Coating B Vst=2.25+0.08u
Streamer 'stability' propagation velocities x 105m/s
Pulse amplitude kV
Figure 7. Relationship between the streamer ‘stability’ propagation velocities and the pulse ampli-
tudes.
450 500 550 600 650 700 750
2
4
6
8
10 'Surface' component
Air
Polymer
Coating A
Coating B
Streamer propagation velocities x 105m/s
Electric field kV/m
Figure 8. Velocities of the ‘surface’ components under the varied electric fields.
Figure 8. Velocities of the ‘surface’ components under the varied electric fields.
Polymers 2021,13, 3784 8 of 13
Polymers 2021, 13, 3784 9 of 14
450 500 550 600 650 700 750
1
2
3
4
5
6
7
'Air' component
Air
Polymer
Coating A
Coating B
Streamer propagation velocities x 105m/s
Electric field kV/m
Figure 9. Velocities of the ‘air’ components under the varied electric fields.
Table 1. Corresponding parameters in Equation (3).
Material Est ‘Surface’ Component ‘Air’ Component
Vst γ × 100 n Vst γ × 100 n
Air 456 1.56 0.22 3 1.56 0.23 3
Polymer sheet 528 2.37 0.15 4.3 1.23 3.24 2.2
Coating A 537 2.50 1.69 4.1 1.34 0.75 2.1
Coating B 544 2.58 1.16 4.1 1.3 2.48 2.2
Est and Vst in Equation (4) were replaced by Equations (2) and (3) to become Equation
(5). It describes the streamer propagation velocities under any pulse amplitude and
applied electric field.
𝑉
=(𝑉
+𝛽𝑢)(
()
) (5)
In Figures 8 and 9, it can be seen that the velocities of the ‘surface’ components of the
streamers were higher than those in the air alone, and they increased with the applied
electric field significantly. In contrast, the velocities of the ‘air’ components of the
streamers were lower than those in the air alone, and they increased with the applied
electric field slowly. It can be explained that the electric field in the head of the ‘air’
component of a streamer is suppressed by the charge in the head of the ‘surface’
component. Furthermore, it can be seen that the velocities of the ‘surface’ components of
the streamer decreased after the silicone rubber coating was applied to the polymer. In
addition, the velocities of the ‘surface’ components of the streamers propagating along the
different silicone rubber coatings were also different. However, the differences between
the velocities of the ‘air’ components of the streamers propagating along the different
insulation surfaces were relatively small.
4. Discussion
4.1. Permittivity
The main factors that affected the characteristics of the streamer propagation along
the insulation surfaces were the permittivity and surface properties (the attachment of the
charge to the surface, photoemission of secondary electrons from the surface, etc.) [18].
First, the influence of the silicone rubber coating on the permittivity of the polymer sheet
was analyzed. Figure 10 shows the variation of the electric field from the needle electrode
Figure 9. Velocities of the ‘air’ components under the varied electric fields.
Table 1. Corresponding parameters in Equation (3).
Material Est ‘Surface’ Component ‘Air’ Component
Vst γ×100 n Vst γ×100 n
Air 456 1.56 0.22 3 1.56 0.23 3
Polymer sheet 528 2.37 0.15 4.3 1.23 3.24 2.2
Coating A 537 2.50 1.69 4.1 1.34 0.75 2.1
Coating B 544 2.58 1.16 4.1 1.3 2.48 2.2
E
st
and V
st
in Equation (4) were replaced by Equations (2) and (3) to become
Equation (5)
.
It describes the streamer propagation velocities under any pulse amplitude and applied
electric field.
Vs=(V0+βu)(E(1+γ)
E0−αu)
n
(5)
In Figures 8and 9, it can be seen that the velocities of the ‘surface’ components of
the streamers were higher than those in the air alone, and they increased with the applied
electric field significantly. In contrast, the velocities of the ‘air’ components of the streamers
were lower than those in the air alone, and they increased with the applied electric field
slowly. It can be explained that the electric field in the head of the ‘air’ component of a
streamer is suppressed by the charge in the head of the ‘surface’ component. Furthermore,
it can be seen that the velocities of the ‘surface’ components of the streamer decreased
after the silicone rubber coating was applied to the polymer. In addition, the velocities of
the ‘surface’ components of the streamers propagating along the different silicone rubber
coatings were also different. However, the differences between the velocities of the ‘air’
components of the streamers propagating along the different insulation surfaces were
relatively small.
4. Discussion
4.1. Permittivity
The main factors that affected the characteristics of the streamer propagation along
the insulation surfaces were the permittivity and surface properties (the attachment of the
charge to the surface, photoemission of secondary electrons from the surface, etc.) [
18
].
First, the influence of the silicone rubber coating on the permittivity of the polymer sheet
was analyzed. Figure 10 shows the variation of the electric field from the needle electrode
Polymers 2021,13, 3784 9 of 13
up to 1 mm along the insulation surface. The thickness of the silicone rubber coating was
considered to be 0.5 mm. It can be seen that the electric fields from the needle electrode
up to 1 mm along both the polymer and the polymer with the silicone rubber coating
were basically the same, but the electric field along the polymer with the silicone rubber
coating was slightly strengthened. The permittivity of the silicone rubber coating was
smaller than that of the polymer. After the silicone rubber coating was applied to the
polymer, the volume of the polymer sheet with the silicone rubber coating became larger
than that of the polymer sheet. The overall capacitance (permittivity) increased, so the
electric field along the polymer sheet with the silicone rubber coating increased. However,
the silicone rubber coating only had a small increase in the electric field at the tip of the
needle electrode, which indicates that the silicone rubber coating produced a small change
in the overall permittivity (capacitance) of the polymer sheet. Therefore, the change in the
overall permittivity caused by the silicone rubber coating had a tiny impact on the electric
field distribution in the gap.
Polymers 2021, 13, 3784 9 of 13
up to 1 mm along the insulation surface. The thickness of the silicone rubber coating was
considered to be 0.5 mm. It can be seen that the electric fields from the needle electrode
up to 1 mm along both the polymer and the polymer with the silicone rubber coating were
basically the same, but the electric field along the polymer with the silicone rubber coating
was slightly strengthened. The permittivity of the silicone rubber coating was smaller than
that of the polymer. After the silicone rubber coating was applied to the polymer, the vol-
ume of the polymer sheet with the silicone rubber coating became larger than that of the
polymer sheet. The overall capacitance (permittivity) increased, so the electric field along
the polymer sheet with the silicone rubber coating increased. However, the silicone rubber
coating only had a small increase in the electric field at the tip of the needle electrode,
which indicates that the silicone rubber coating produced a small change in the overall
permittivity (capacitance) of the polymer sheet. Therefore, the change in the overall per-
mittivity caused by the silicone rubber coating had a tiny impact on the electric field dis-
tribution in the gap.
0.0 0.2 0.4 0.6 0.8 1.0
0
40
80
120
160
200
Polymer
Coating A
Coating B
Electric field kV/cm
Axial distances from the needle electrode mm
Figure 10. Variation of the electric field from the needle electrode up to 1 mm at axial distances.
With the increase in the permittivity, the charge (ions or electrons) accumulated on
the insulation surface increased [19–21]. On the one hand, there were many negative
charges accumulated on the insulation surface with the negative direct voltage applied to
the cathode plane [22–24]. Those would have reduced the electric fields in the latter half
of the sheet as shown in Figure 11. The negative charges on the surface weakened the
electric fields in the latter half of the sheet. Hence, the streamer propagation along the
sheet with the larger permittivity required higher electric fields [17]. On the other hand,
the sheet with the larger permittivity would have attached more positive charges in the
streamer. The ionization efficiency at the head of the streamer would have weakened,
which made the streamer propagation difficult and required high electric fields. Because
the silicone rubber coating made the overall permittivity (capacitance) of the polymer
sheet slightly increase, the silicone rubber coating caused a slight increase in the positive
charge in the streamers attached to the surface, which would have suppressed the devel-
opment of those streamers to a certain extent. However, the stable streamer propagation
fields of the polymer sheet and the polymer sheet with the silicone rubber coating dis-
played a large difference. The change in the overall permittivity caused by the silicone
rubber coating should not have caused such a large difference. It must have been caused
by the change in the surface properties of the polymer sheet after spraying the silicone
rubber coating.
Figure 10. Variation of the electric field from the needle electrode up to 1 mm at axial distances.
With the increase in the permittivity, the charge (ions or electrons) accumulated on the
insulation surface increased [
19
–
21
]. On the one hand, there were many negative charges
accumulated on the insulation surface with the negative direct voltage applied to the
cathode plane [
22
–
24
]. Those would have reduced the electric fields in the latter half of the
sheet as shown in Figure 11. The negative charges on the surface weakened the electric
fields in the latter half of the sheet. Hence, the streamer propagation along the sheet with
the larger permittivity required higher electric fields [
17
]. On the other hand, the sheet with
the larger permittivity would have attached more positive charges in the streamer. The
ionization efficiency at the head of the streamer would have weakened, which made the
streamer propagation difficult and required high electric fields. Because the silicone rubber
coating made the overall permittivity (capacitance) of the polymer sheet slightly increase,
the silicone rubber coating caused a slight increase in the positive charge in the streamers
attached to the surface, which would have suppressed the development of those streamers
to a certain extent. However, the stable streamer propagation fields of the polymer sheet
and the polymer sheet with the silicone rubber coating displayed a large difference. The
change in the overall permittivity caused by the silicone rubber coating should not have
caused such a large difference. It must have been caused by the change in the surface
properties of the polymer sheet after spraying the silicone rubber coating.
Polymers 2021,13, 3784 10 of 13
Polymers 2021, 13, 3784 10 of 13
0 20406080100
0
40
80
120
Polymer with negative charge 4e-6C/m2
Coating A with negative charge 8e-6C/m2
Coating B with negative charge10e-6C/m2
Electric field kV/cm
Axial distances from the needle electrode mm
Figure 11. Variation of the electric field in the gap at axial distances.
4.2. Surface Properties
When the silicone rubber coating was applied to the polymer sheet, the surface con-
dition changed greatly. The roughness of the materials was measured using the roughness
gauge. The roughness of the three materials was as follows: Coating B was the largest (Ra
of 0.93 μm), Coating A was second (Ra of 0.76 μm), and the polymer was the smallest (Ra
of 0.65 μm). The larger the surface roughness of the material was, the more serious the
accumulation of the surface charge was [21]. Therefore, the negative charges accumulated
on the surface increased with the increases in the surface roughness, which had two influ-
ences on the streamer discharges. One is that the electric fields in the latter half of the sheet
weakened due to the negative surface charges; the other is that the ionization efficiency at
the head of the streamers weakened due to the attachment of the positive charges in the
streamer to the surface. It was more difficult for the streamers to propagate along the sheet
with the higher surface roughness. That is the reason why the streamer ‘stability’ propa-
gation fields for the polymer with the silicone rubber coatings were larger than those for
the polymer. In addition, the electric fields for the streamer stable propagations along
Coating B were larger than those along Coating A at the different surface roughness levels.
Figure 12 shows the surface conditions of the three insulation materials measured by
the scanning electron microscope. It can be seen that the surface of the polymer had more
microporous defects than the polymer with the silicone rubber coatings. The trap charges
(nC) and trap levels (eV) of the three insulation materials were tested using the method of
the thermally stimulated current (TSC). The trap charges on the polymer surface were
greater than those on the silicone rubber coatings. The microporous defects on the insula-
tion surfaces could reflect the surface trap distributions [21]. The trap charges on the in-
sulation surface decreased with the decreases in the microporous defects. Hence, the re-
sults of the SEM figures and the TSC test corroborate each other.
The traps that had low trap levels are named “shallow traps”. In Table 2, the shallow
traps on the polymer surface were greater than those on the silicone rubber coatings. The
photoemission of secondary electrons from the surfaces can be described as follows: the
collisions of the high-energy photons detach the trap charges from the insulation surface
and produce many high-energy secondary electrons, which then promote the develop-
ment of the streamers [13,14]. Under the collision by the high-energy photons, a shallow
trap emits high-energy secondary electrons more easily. The reason why the streamer
propagation along the silicone rubber coating is more difficult than that along the polymer
is that the photoemission of secondary electrons from the silicone rubber coating is
Figure 11. Variation of the electric field in the gap at axial distances.
4.2. Surface Properties
When the silicone rubber coating was applied to the polymer sheet, the surface condi-
tion changed greatly. The roughness of the materials was measured using the roughness
gauge. The roughness of the three materials was as follows: Coating B was the largest (Ra
of 0.93
µ
m), Coating A was second (Ra of 0.76
µ
m), and the polymer was the smallest (Ra
of 0.65
µ
m). The larger the surface roughness of the material was, the more serious the
accumulation of the surface charge was [
21
]. Therefore, the negative charges accumulated
on the surface increased with the increases in the surface roughness, which had two influ-
ences on the streamer discharges. One is that the electric fields in the latter half of the sheet
weakened due to the negative surface charges; the other is that the ionization efficiency
at the head of the streamers weakened due to the attachment of the positive charges in
the streamer to the surface. It was more difficult for the streamers to propagate along the
sheet with the higher surface roughness. That is the reason why the streamer ‘stability’
propagation fields for the polymer with the silicone rubber coatings were larger than those
for the polymer. In addition, the electric fields for the streamer stable propagations along
Coating B were larger than those along Coating A at the different surface roughness levels.
Figure 12 shows the surface conditions of the three insulation materials measured
by the scanning electron microscope. It can be seen that the surface of the polymer had
more microporous defects than the polymer with the silicone rubber coatings. The trap
charges (nC) and trap levels (eV) of the three insulation materials were tested using the
method of the thermally stimulated current (TSC). The trap charges on the polymer surface
were greater than those on the silicone rubber coatings. The microporous defects on the
insulation surfaces could reflect the surface trap distributions [
21
]. The trap charges on the
insulation surface decreased with the decreases in the microporous defects. Hence, the
results of the SEM figures and the TSC test corroborate each other.
The traps that had low trap levels are named “shallow traps”. In Table 2, the shallow
traps on the polymer surface were greater than those on the silicone rubber coatings.
The photoemission of secondary electrons from the surfaces can be described as follows:
the collisions of the high-energy photons detach the trap charges from the insulation
surface and produce many high-energy secondary electrons, which then promote the
development of the streamers [
13
,
14
]. Under the collision by the high-energy photons,
a shallow trap emits high-energy secondary electrons more easily. The reason why the
streamer propagation along the silicone rubber coating is more difficult than that along
the polymer is that the photoemission of secondary electrons from the silicone rubber
coating is weaker. The shallow traps on the Coating A were greater than those on Coating
Polymers 2021,13, 3784 11 of 13
B. Therefore, the stronger photoemission of secondary electrons from Coating A led to the
streamer propagation more easily, which is consistent with the test results.
Polymers 2021, 13, 3784 11 of 13
weaker. The shallow traps on the Coating A were greater than those on Coating B. There-
fore, the stronger photoemission of secondary electrons from Coating A led to the
streamer propagation more easily, which is consistent with the test results.
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 12. SEM figures of the insulation surfaces. (a–c) Polymer. (d–f) Coating A. (g–i) Coating B.
Table 2. Trap parameters of the dielectric materials measured by TSC test.
Parameter Polymer Coating A Coating B
Current peak (PA) 1050 165 138
Trap charge (nC) 1879 246 225
Trap level (eV) 0.38 0.45 0.49
In a word, the polymer surface was more favorable for the streamer propagation than
the silicone rubber coating surface from the perspectives of both the surface roughness
and surface trap. The electric fields required for the streamer stable propagation along the
silicone rubber coating were larger than that required for the streamer stable propagation
along the polymer surface. The velocities of the streamer propagation along the silicone
rubber coating were lower than that along the polymer surface under the same electric
fields. From the perspective of surface properties, it was also a good explanation of the
differences between the streamer stable propagation fields and velocities along the differ-
ent silicone rubber coatings produced by the different manufacturers. There were differ-
ences in the characteristics of the streamer propagation along the different silicone rubber
Figure 12. SEM figures of the insulation surfaces. (a–c) Polymer. (d–f) Coating A. (g–i) Coating B.
Table 2. Trap parameters of the dielectric materials measured by TSC test.
Parameter Polymer Coating A Coating B
Current peak (PA) 1050 165 138
Trap charge (nC) 1879 246 225
Trap level (eV) 0.38 0.45 0.49
In a word, the polymer surface was more favorable for the streamer propagation than
the silicone rubber coating surface from the perspectives of both the surface roughness
and surface trap. The electric fields required for the streamer stable propagation along the
silicone rubber coating were larger than that required for the streamer stable propagation
along the polymer surface. The velocities of the streamer propagation along the silicone
rubber coating were lower than that along the polymer surface under the same electric
fields. From the perspective of surface properties, it was also a good explanation of the
differences between the streamer stable propagation fields and velocities along the different
silicone rubber coatings produced by the different manufacturers. There were differences in
the characteristics of the streamer propagation along the different silicone rubber coatings,
Polymers 2021,13, 3784 12 of 13
which indicates there are large differences in the insulation properties of the silicone
rubber coatings belonging to different manufacturers. These differences can be found by
measuring the characteristics of the streamer discharge. Therefore, tests of the streamer
discharge can be used to evaluate the insulation properties of silicone rubber coatings.
The test results of the characteristics of streamer propagation along the different
material surfaces have also taught us many things. Higher permittivity in a material is
unfavorable for streamer propagation along it. Hence, materials with higher permittivity
can be chosen to suppress the pre-discharge in some conditions of electrical power systems.
It is difficult for streamer propagation to occur along materials with higher macroscopic
surface roughness, so insulation surfaces can be made rougher to reduce pre-discharge in
electrical power systems. The microporous defects on the insulation surface can affect the
streamer propagation to a great extent. In the factory, more nanomaterials can be applied
to insulation materials to fill the microporous defects on the insulation surface, thereby the
pre-discharge will be prevented by the technology of reducing microporous defects. These
results provide a theoretical basis for promoting the application of the nanomaterials.
5. Conclusions
The streamer ‘stability’ propagation fields for the polymer, Coating A and Coating
B were 528 kV/m, 537 kV/m and 544 kV/m, respectively. The velocities of the ‘surface’
components of the streamer stable propagation along the polymer, Coating A and Coating
B were 2.37
×
10
5
m/s, 2.50
×
10
5
m/s and 2.58
×
10
5
m/s, respectively. The velocities
of the ‘air’ component of the streamer stable propagation along the polymer, Coating
A and Coating B are 1.23
×
10
5
m/s, 1.34
×
10
5
m/s and 1.30
×
10
5
m/s, respectively.
The streamer ‘stability’ propagation fields for the polymer were lower than those for the
polymer with the silicone rubber coatings. Within the same electric fields, the velocities of
streamer propagation along the polymer were higher than those along the polymer with
the silicone rubber coatings.
Higher permittivity in a material was unfavorable for streamer propagation along it.
The effects of permittivity on electric field distortion in front of needle tip, the effects of the
surface charge accumulation before the development of a streamer on the distortion of the
electric field in the gap and the effects of the charge attachment to the surface during the
development of streamer were analyzed to determine the reason.
It is difficult for streamer propagation to occur along materials with higher macro-
scopic surface roughness. The effects of the surface charge accumulations before the
development of streamers on the distortions of the electric field in the gap and the effects
of the charge attachment to the surface during the development of streamers were also
analyzed to determine the reason.
The streamer propagation along materials with more microporous defects on the insu-
lation surface was easier. The reason is that the photoemission of secondary electrons from
the surface increased with increased microporous defects, which would have promoted the
development of the streamer.
There are large differences in the characteristics of surface streamers along the different
silicone rubber coatings. Testing the streamer discharge can be used to evaluate the insula-
tion properties of the silicone rubber coatings produced by the different manufacturers.
Author Contributions:
Conceptualization, L.W.; methodology, L.W.; software, C.Z.; data curation,
X.M.; writing—original draft preparation, X.M.; writing—review and editing, C.Z.; project adminis-
tration, H.M.; funding acquisition, L.W. All authors have read and agreed to the published version of
the manuscript.
Funding:
This research was partially funded by the National Natural Science Foundation of China,
grant number 51907178.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Polymers 2021,13, 3784 13 of 13
Data Availability Statement: Not applicable.
Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the
design of the study; in the collection, analyses, or interpretation of the data; in the writing of the
manuscript; nor in the decision to publish the results.
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