Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2016.
Supporting Information
for Adv. Funct. Mater., DOI: 10.1002/adfm.201600580
Multiscale Wrinkled Microstructures for Piezoresistive Fibers
Yong Wei, Song Chen, Xue Yuan, Pingping Wang, and Lan
Liu*
Supporting Information
Multiscale Wrinkled Microstructures for Piezoresistive Fibers
Yong Wei, Song Chen, Xue Yuan, Pingping Wang, and Lan Liu*
College of Materials Science and Engineering, Key Lab of Guangdong Province for High
Property and Functional Macromolecular Materials, South China University of Technology,
Guangzhou 510641, PR China.
E–mail: psliulan@scut.edu.cn
S1
Supplementary Text: Theoretical calculation of the sensitivity ( S ) of piezoresistive
materials
According to the conventional conductive theory,[1-3] the total resistance ( rtotal ) between
two random conductive fillers in composites can be expressed by:
rtotal  rbulk  rin
(1)
Where rbulk is bulk resistance and the rin is the interface resistance between two random
conductive fillers (0D, 1D and 2D). When external stimuli (Pressure (kPa), strain (%),
bending (º), twist (º), et al) applied on the piezoresistive materials, the change of resistance
(Δr) of the contact point can be estimated by:
r  rin  rin
(2)
Where r′in is the interface resistance between two random conductive fillers with external
stimuli applied to the piezoresistive materials, thus the change of resistance (ΔR) of the
piezoresistive materials can be expressed in the following form:
R  Rin  Rin
(3)
Where Rin is the interface resistance of piezoresistive materials and the R′in is the interface
resistance with external stimuli applied on the piezoresistive materials. The traditional
percolating theory reveals the interface resistance of composites is the summation of contact
resistances, which can be given by:
n
Rin  rin1  rin2    rinn   rini
(4)
i 1
n
Thus, R 
n
n
 rini   rini   rini  rini
i 1
i 1
n
(5)
i 1


n

Under such circumstance, if rini  rin i , R   rini  rini ; and if rini  rin i , R   rini  rini
i 1
S2
i 1

In either case, we can draw the conclusion that R  n . In other word, if the
piezoresistive materials own higher conductivity, more conductive fillers should be added to
constructing the conductive networks, thus n increases, which results in higher ΔR. That
means piezoresistive materials with higher conductivity will lead to higher ΔR, which can be
expressed as: SC  n , where S C is the conductivity of the piezoresistive materials. The
sensitivity ( S ) of piezoresistive materials is calculated by: S  R / R0 /  , take the
interface resistance into consideration, S can be calculated according to the following
formula:
n
R / Rtotal Rin  Rin / Rtotal 
S 

 i 1


rini  rini / Rtotal

(6)
Where  can be pressure (kPa), strain (%), bending (º), twist (º), et al. Therefore,
piezoresistive materials with higher conductivity and more contact points will demonstrate
higher sensitivity ( S ). Surely, if n→+∞, Rbulk<<Rin and Rtotal=Rin, in this case, S should be
calculated by:
S 
If rini  rin i , S 
Rin  Rin / Rin

1
R
1 Rin
(1  in ) ; if rini  rin i , S 
(
 1) .

Rin
 Rin
S3
(7)
Figure S1 SEM images of the AgNWs.
S4
Figure S2 Digital photograph of commercial PU fiber.
S5
Figure S3 Schematic illustration of the intermolecular hydrogen bonding between PVP on the
surface of AgNWs and amino groups on the WPU molecular chain.
S6
Figure S4 (a) Digital photograph of AgNWs ink (3 mg·mL-1 AgNWs/ethanol suspension +15
wt% WPU) and Chinese brush used in this research; (b) schematic illustration of the writing
process for fabrication of stretchable conductive fibers.
S7
Figure S5 (a) Relative mass change of the fiber as a function of writing cycles, where Δm is
the measured mass (m) minus the initial mass (m0) of the fiber; (b) resistivity of PU fiber as a
function of the number of writing cycles.
S8
Table S1 Information about 4 separate samples to calculate the resistivity.
Writing Sample
cycles
No.
1#
50
2#
Writing
3#
cycles
4#
1#
100
2#
Writing
3#
cycles
4#
Length
(cm)
5.08
5.1
4.68
5.2
5.06
4.82
4.92
5.08
Diameter
(μm)
108
112
106
106
102
104
102
101
Resistance Resistivity
(Ω)
(Ω·cm)
5.105
9.2×10-5
5.610
1.08×10-4
5.106
9.62×10-5
5.411
9.18×10-5
4.660
7.52×10-5
4.912
6.89×10-5
4.412
7.32×10-5
4.759
7.5×10-5
S9
Average
(Ω·cm)
(9.7±0.38)×10-5
(7.30±0.21)×10-5
Figure S6 SEM images of core-shell conductive fibers with different writing cycles,
demontrating the increase of wrinkled microstructures on core PU fiber with writing cycles
and the PU fibers are completely covered after 50 writing cycles.
S10
Figure S7 SEM images of core-shell conductive fibers with 100 writing cycles under different
tensile strain, showing the wrinkled microstructures became gradually flattened when tensile
strain lower than the prestrain.
S11
Figure S8 The LED still work and the brightness does not change even the conductive fiber is
stretched to 400 % (2 cm to 10 cm), visually showing the excellent stretchability of the coreshell conductive fiber.
S12
Figure S9 Schematic illustration of the resistance measurement.
S13
Figure S10 (a) Relative resistance change–pressure curve for piezoresistive fibers built by
single core-shell conductive fiber; (b) resistance change of piezoresistive fibers built by single
wrinkle microstructured conductive fiber to several loading/unloading cycles.
S14
Figure S11 Response and relaxation properties of the piezoresistive fibers built by single
wrinkled PU fiber.
S15
Table S2 The summary of conductivity and sensitivity for typical flexible piezoresistive
sensors reported in recent years.
Fabrication strategy
Elastomers with interlocked
microdome arrays
Flexible pressure sensors
consisting of PANI NFs and Aucoated PDMS micropillars
Sandwich structured
PDMS/AgNWs/PDMS composites
Graphene/rubber composites
Raphene coated human hairs
Graphene/PI nanocomposite foam
Bioinspired interlocked and
hierarchical ZnO NWs arrays
Graphene based pressure sensor
Mimosa inspired design of flexible
pressure sensors
Electronic skin with petal molded
microstructure
Flexible pressure sensors with
gaussian random distribution
contact surface
Pressure sensors with micropyramid array
Pressure sensor with double layer
graphene
Flexible pressure sensors
consisting of PPy film and Aucoated PDMS micropillars
Strain gauge sensors with
interlocking of nanofibres
Silk-molded flexible e-skin
PDMS/carbonized cotton fiber
composites
Wearable pressure sensor based on
conductive hydrogel spheres
Pressure sensor based on hollowsphere microstructure
PPy/AgNWs Aero Sponges
AuNWs coated on tissue paper
Au nanoribbon coated PU sponge
CNTs/Ag sponges
Graphene/PU sponge with
fractured microstructure
Graphene force sensor
Honeycomb like graphene film
AgNWs coated on cotton fabric
Graphene coated on PU sponge
with fractured microstructure
WPU/AgNWs/LDH composites
Graphene-based composite fiber
with “compression spring”
architecture (Fiber-based)
Core-shell intertwined composite
fibers (Fiber-based)
Piezoresistive fibers with
multiscale wrinkled
microstructure
Stretchability
Conductivity
Sensitivity
References
120 %
1.4×104-3.9×109 Ω
15.1 kPa-1
[2]
15 %
PANI film: 0.03 Ω/□
PDMS micropillars:
420±14 Ω/□
2.0 kPa-1
[3]
~100%
> 7.5 Ω
0.63 Rad-1
[4]
GF=35
GF=4.46
0.49% N−1
0.18 kPa-1
[5]
4
6
700 %
10 -10 Ω
~30 %
Not provided
<5%
~450 Ω·cm
6
-1
[6]
[7]
Not provided
~10 Ω
6.8 kPa
Not provided
74300 Ω
8.5 mV/Bar
GF: 1.6
[9]
Not provided
110±14Ω/□
50.17 kPa-1
[10]
Not provided
Not provided
1.35 kPa-1
[11]
Not provided
>450 Ω·cm
13.8 kPa-1
[12]
Not provided
> 2×10-2 Ω·cm
4.88 kPa-1
[13]
Not provided
17000 Ω
0.24 kPa-1
[14]
Not provided
PPy film: 1 Ω·cm
PDMS micropillars:
thickness is 100 nm but the
conductivity is not provided
1.8 kPa-1
[15]
Not provided
102 Ω/□
~0.01 kPa-1
[16]
Not provided
~3.5 × 104Ω/□
1.8 kPa-1
[17]
-1
[8]
Not provided
~270 Ω·cm
6.04 kPa
0
>25000 Ω/□
0.176 kPa-1
[19]
0
106-107 Ω
133.1 kPa-1
[20]
-1
[18]
0
0
0
0
>10000 Ω
91100±52000 kΩ/□
~420 Ω·cm
~625 Ω·cm
0.33 kPa
1.14 kPa-1
0.31 kPa-1
GF < 1.6
[21]
[22]
[23]
[24]
0
Not provided
0.26 kPa-1
[25]
-1
0
0
0
971.6 Ω/□
Not provided
10-5-10-4 Ω·cm
0.024 kPa
1.61 kPa-1
3.40 kPa-1
[26]
[27]
[28]
0
> 400 Ω
26 kPa-1
[29]
-4
-1
10 Ω·cm
0.012 S/m-0.136 S/m
(8.3 ×103Ω·cm-7.4×102
Ω·cm)
0.16 Rad
[30]
GF<35
[31]
300%
6.25×10-4 Ω·cm
4.29N-1
[32]
400%
(7.30±0.21)×10-5
0.12 kPa-1
0.012 Rad-1
This work
0
~200%
S16
Abbreviations and Notes: CNTs, carbon nanotubes; NWs: nanowires; ZnO, zinc oxide; PDMS,
polydimethylsiloxane;
CB,
carbon
black;
PUD,
polyurethane
dispersion;
PEDOT,
poly(3,4-
ethylenedioxythiophene); PSS, poly(styrenesulfonate); PANI, polyaniline; NFs, nanofibers; PPy,
polypyrrole; LDH, layered double hydroxide; PUA, ultraviolet-curable polyurethane acrylate; SWNTs,
Single-walled carbon nanotubes; PU, polyurethane; PI, polyimide; GF, gauge factor; the stretchability is
“not provided” means the piezoresistive material may be stretchable yet the stretchability is not
investigated or provided and the value of the stretchability is zero means the piezoresistive material is not
stretchable.
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