Nano Res.
Electronic Supplementary Material
High power triboelectric nanogenerator based on printed
circuit board (PCB) technology
Changbao Han1,§, Chi Zhang1,§, Wei Tang1, Xiaohui Li1, and Zhong Lin Wang1,2 ()
1
Beijing Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 100083, China
School of Material Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
§
These authors contributed equally to this work.
2
Supporting information to DOI 10.1007/s12274-014-0555-3
I. Derivation of the formulae (two methods)
Figure S1 Schematic showing the electricity generation process of TENG.
(I)
As shown in Fig. S1, when the disk rotates from one segment to the next segment, the total charge transfer
between the two electrodes for the whole device is Q1


Q1   r22  r12   0
where  0 is the triboelectric charge density on the surface of Kapton. At one rotation period (cycle) for the disk,
the total charge transfer is Q2


Q2  2 N  Q1  2 N    r22  r12   0
where N is the number of the gratings or the pairs of segments. In time t, the number of cycles of the disk rotation
is t/2. Here  is the rotation speed (rad/s) of the disk. So the amount of the charge Q flowing in time t is
Q  Q2 
t
2
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

 2 N    r22  r12   0 
t
2


 N   0  r22  r12  t
Nano Res.
The short-circuit (ISC) is
I SC
 
 
2
2
dQ d N  r2  r1  t


 N   0  r22  r12    2fN 0 r22  r12
dt
dt




where f is the rotational frequency of the disk. Therefore, the frequency f’ for the alternating electric field is
180 n
3n


 60 
f N f 
where n is the rotation speed (rpm) of the disk and  is the center angle (°) of a single electrode or metal grating
or segment.
(II)
When the top grating slides from one electrode to the next electrode (Figs. 1(a) to 1(c)) forming a sliding period,
the charge flow between the two segments is Q
Q 

 r22  r12
N
 
0
where  0 is the triboelectric charge density on the surface of Kapton and N is the number of the gratings or the
pairs of segments. In time t, the total number of sliding periods is t/. Here  is the angular speed (rad/s) of
the disk and  is the center angle (rad) of a single electrode or metal grating or segment. So the amount of the
charge transfer Q in t time is
Q  N  Q 
 N
 N

 r

t

 r22  r12
N
 r22  r12

N

 
 
0

 
0

t

t

 2
360
360
 t
2 
 N  t
0
 r22  r12   0 
2
2
 r12
where  is the center angle (°) of a single electrode or metal grating or segment and f is the rotational
frequency of the disk.
So the short-circuit (ISC) is
I SC



2
2
dQ d r2  r1   0  N  t


  0  N  r22  r12    2 fN 0 r22  r12
dt
dt




where f is the rotational frequency of the disk. So the frequency f  for the alternating electric field is
f N f 
180 n
3n


 60 
where n is the rotation speed (rpm) of the disk.
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Nano Res.
II. Schematic diagram of copper electrodes and gratings drawn by Protel99se
Figure S2 Schematic diagram of copper electrodes and gratings drawn by Protel99se: (a) Stator; (b) rotor.
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