The effect of the temperature on the electrical resistivity of polymer nanocomposites with carbon nanotube (CNT) and graphene nanoplatelets (GNP) fillers was investigated. A three-dimensional (3D) continuum Monte Carlo (MC) model was developed to first form percolation networks. A 3D resistor network was subsequently created to evaluate the nanocomposite electrical properties. The effect of temperature on the electrical resistivity of nanocomposites was thus investigated. Other aspects such as polymer tunneling and filler resistivities were considered as well. The presented comprehensive modeling approach is aimed at providing a better understanding of the electrical resistivity behavior of polymer nanocomposites in conjunction with experimental works.

References

References
1.
Neitzert
,
H. C.
,
Vertuccio
,
L.
, and
Sorrentino
,
A.
,
2011
, “
Epoxy/MWCNT Composite as Temperature Sensor and Electrical Heating Element
,”
IEEE Trans. Nanotechnol.
,
10
(
4
), pp.
688
693
.10.1109/TNANO.2010.2068307
2.
Heo
,
C.
, and
Chang
,
J. H.
,
2013
, “
Polyimide Nanocomposites Based on Functionalized Graphene Sheets: Morphologies, Thermal Properties, and Electrical and Thermal Conductivities
,”
Solid State Sci.
,
24
(Oct.), pp.
6
14
.10.1016/j.solidstatesciences.2013.06.012
3.
Kim
,
J. S.
,
Yun
,
J. H.
,
Kim
,
I.
, and
Shim
,
S. E.
,
2011
, “
Electrical Properties of Graphene/SBR Nanocomposite Prepared by Latex Heterocoagulation Process at Room Temperature
,”
J. Ind. Eng. Chem.
,
17
(
2
), pp.
325
330
.10.1016/j.jiec.2011.02.034
4.
Manivel
,
P.
,
Kanagaraj
,
S.
,
Balamurugan
,
A.
,
Ponpandian
,
N.
,
Mangalaraj
,
D.
, and
Viswanathan
,
C.
,
2014
, “
Rheological Behavior and Electrical Properties of Polypyrrole/Thermally Reduced Graphene Oxide Nanocomposite
,”
Colloids Surf. A
,
441
(Jan.), pp.
614
622
.10.1016/j.colsurfa.2013.10.031
5.
Patole
,
A. S.
,
Patole
,
S. P.
,
Kang
,
H.
,
Yoo
,
J. B.
,
Kim
,
T. H.
, and
Ahn
,
J. H.
,
2010
, “
A Facile Approach to the Fabrication of Graphene/Polystyrene Nanocomposite by In Situ Microemulsion Polymerization
,”
J. Colloid Interface Sci.
,
350
(
2
), pp.
530
537
.10.1016/j.jcis.2010.01.035
6.
Natsuki
,
T.
,
Endo
,
M.
, and
Takahashi
,
T.
,
2005
, “
Percolation Study of Orientated Short-Fiber Composites by a Continuum Model
,”
Physica A
,
352
(
2–4
), pp.
498
508
.10.1016/j.physa.2004.12.059
7.
Ma
,
H. M.
, and
Gao
,
X. L.
,
2008
, “
A Three-Dimensional Monte Carlo Model for Electrically Conductive Polymer Matrix Composites Filled With Curved Fibers
,”
Polymer
,
49
(
19
), pp.
4230
4238
.10.1016/j.polymer.2008.07.034
8.
Dalmas
,
F.
,
Dendievel
,
R.
,
Chazeau
,
L.
,
Cavaille
,
J. Y.
, and
Gauthier
,
C.
,
2006
, “
Carbon Nanotube-Filled Polymer of Electrical Conductivity in Composites. Numerical Simulation Three-Dimensional Entangled Fibrous Networks
,”
Acta Mater.
,
54
(
11
), pp.
2923
2931
.10.1016/j.actamat.2006.02.028
9.
Li
,
C.
,
Thostenson
,
E. T.
, and
Chou
,
T. W.
,
2008
, “
Effect of Nanotube Waviness on the Electrical Conductivity of Carbon Nanotube-Based Composites
,”
Compos. Sci. Technol.
,
68
(
6
), pp.
1445
1452
.10.1016/j.compscitech.2007.10.056
10.
Li
,
C. Y.
, and
Chou
,
T. W.
,
2007
, “
Continuum Percolation of Nanocomposites With Fillers of Arbitrary Shapes
,”
Appl. Phys. Lett.
,
90
, p.
174108
.10.1063/1.2732201
11.
Li
,
C. Y.
,
Thostenson
,
E. T.
, and
Chou
,
T. W.
,
2007
, “
Dominant Role of Tunneling Resistance in the Electrical Conductivity of Carbon Nanotube-Based Composites
,”
Appl. Phys. Lett.
,
91
, p.
223114
.10.1063/1.2819690
12.
Ounaies
,
Z.
,
Park
,
C.
,
Wise
,
K. E.
,
Siochi
,
E. J.
, and
Harrison
,
J. S.
,
2003
, “
Electrical Properties of Single Wall Carbon Nanotube Reinforced Polyimide Composites
,”
Compos. Sci. Technol.
,
63
(
11
), pp.
1637
1646
.10.1016/S0266-3538(03)00067-8
13.
Logakis
,
E.
,
Pandis
,
C.
,
Peoglos
,
V.
,
Pissis
,
P.
,
Pionteck
,
J.
,
Potschke
,
P.
,
Micusik
,
M.
, and
Omastova
,
M.
,
2009
, “
Electrical/Dielectric Properties and Conduction Mechanism in Melt Processed Polyamide/Multi-Walled Carbon Nanotubes Composites
,”
Polymer
,
50
(
21
), pp.
5103
5111
.10.1016/j.polymer.2009.08.038
14.
Bilotti
,
E.
,
Zhang
,
R.
,
Deng
,
H.
,
Baxendale
,
M.
, and
Peijs
,
T.
,
2010
, “
Fabrication and Property Prediction of Conductive and Strain Sensing TPU/CNT Nanocomposite Fibres
,”
J. Mater. Chem.
,
20
(
42
), pp.
9449
9455
.10.1039/c0jm01827a
15.
Bahrami
,
A.
,
Talib
,
Z. A.
,
Yunus
,
W. M. M.
,
Behzad
,
K.
,
Abdi
,
M. M.
, and
Din
,
F. U.
,
2012
, “
Low Temperature Hall Effect Investigation of Conducting Polymer-Carbon Nanotubes Composite Network
,”
Int. J. Mol. Sci.
,
13
(
11
), pp.
14917
14928
.10.3390/ijms131114917
16.
Karimov
,
K. S.
,
Abid
,
М.
,
Saleem
,
M.
,
Akhmedov
,
K. M.
,
Bashir
,
M. M.
,
Shafique
,
U.
, and
Ali
,
M. M.
,
2014
, “
Temperature Gradient Sensor Based on CNT Composite
,”
Physica B
,
446
(Aug.), pp.
39
42
.10.1016/j.physb.2014.04.018
17.
Yang
,
Z.
,
Cao
,
Z.
,
Sun
,
H.
, and
Li
,
Y.
,
2008
, “
Composite Films Based on Aligned Carbon Nanotube Arrays and a Poly (N‐Isopropyl Acrylamide) Hydrogel
,”
Adv. Mater.
,
20
(
11
), pp.
2201
2205
.10.1002/adma.200701964
18.
Sheng
,
P.
,
1980
, “
Fluctuation-Induced Tunneling Conduction in Disordered Materials
,”
Phys. Rev. B
,
21
(
6
), p.
2180
.10.1103/PhysRevB.21.2180
19.
Matzeu
,
G.
,
Pucci
,
A.
,
Savi
,
S.
,
Romanelli
,
M.
, and
Di Francesco
,
F.
,
2012
, “
A Temperature Sensor Based on a MWCNT/SEBS Nanocomposite
,”
Sens. Actuators A
,
178
(May), pp.
94
99
.10.1016/j.sna.2012.02.043
20.
Sibinski
,
M.
,
Jakubowska
,
M.
, and
Sloma
,
M.
,
2010
, “
Flexible Temperature Sensors on Fibers
,”
Sensors
,
10
(
9
), pp.
7934
7946
.10.3390/s100907934
21.
Hu
,
N.
,
Karube
,
Y.
,
Yan
,
C.
,
Masuda
,
Z.
, and
Fukunaga
,
H.
,
2008
, “
Tunneling Effect in a Polymer/Carbon Nanotube Nanocomposite Strain Sensor
,”
Acta Mater.
,
56
(
13
), pp.
2929
2936
.10.1016/j.actamat.2008.02.030
22.
Marsaglia
,
G.
,
1972
, “
Choosing a Point From the Surface of a Sphere
,”
Ann. Math. Stat.
,
43
(
2
), pp.
645
646
.10.1214/aoms/1177692644
23.
Matsumoto
,
M.
, and
Nishimura
,
T.
,
1998
, “
Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator
,”
ACM Trans. Model. Comput. Simul.
,
8
(
1
), pp.
3
30
.10.1145/272991.272995
24.
Yu
,
Y.
,
Song
,
G.
, and
Sun
,
L.
,
2010
, “
Determinant Role of Tunneling Resistance in Electrical Conductivity of Polymer Composites Reinforced by Well Dispersed Carbon Nanotubes
,”
J. Appl. Phys.
,
108
(
8
), p.
084319
.10.1063/1.3499628
25.
Oskouyi
,
A.
,
Sundararaj
,
U.
, and
Mertiny
,
P.
,
2014
, “
Tunneling Conductivity and Piezoresistivity of Composites Containing Randomly Dispersed Conductive Nano-Platelets
,”
Materials
,
7
(
4
), pp.
2501
2521
.10.3390/ma7042501
26.
Oskouyi
,
A. B.
, and
Mertiny
,
P.
,
2011
, “
Monte Carlo Model for the Study of Percolation Thresholds in Composites Filled With Circular Conductive Nano-Disks
,”
Procedia Eng.
,
10
, pp.
403
408
.10.1016/j.proeng.2011.04.068
27.
Simmons
,
J. G.
,
1963
, “
Generalized Formula for the Electric Tunnel Effect Between Similar Electrodes Separated by a Thin Insulating Film
,”
J. Appl. Phys.
,
34
(
6
), pp.
1793
1803
.10.1063/1.1702682
28.
Bao
,
W. S.
,
Meguid
,
S. A.
,
Zhu
,
Z. H.
, and
Weng
,
G. J.
,
2012
, “
Tunneling Resistance and Its Effect on the Electrical Conductivity of Carbon Nanotube Nanocomposites
,”
J. Appl. Phys.
,
111
(9), p.
093726
.10.1063/1.4716010
29.
Almohamad
,
H. A.
, and
Selim
,
S. Z.
,
2003
, “
An Algorithm for Computing the Distance Between Two Circular Disks
,”
Appl. Math. Model.
,
27
(
2
), pp.
115
124
.10.1016/S0307-904X(02)00080-X
30.
Simmons
,
J. G.
,
1964
, “
Generalized Thermal J-V Characteristic for the Electric Tunnel Effect
,”
J. Appl. Phys.
,
35
(
9
), pp.
2655
2658
.10.1063/1.1713820
31.
Chen
,
Y.
,
Wang
,
S.
,
Pan
,
F.
, and
Zhang
,
J.
,
2014
, “
A Numerical Study on Electrical Percolation of Polymer-Matrix Composites With Hybrid Fillers of Carbon Nanotubes and Carbon Black
,”
J. Nanomater.
,
2014
, p.
614797
.
32.
Ebbesen
,
T.
,
Lezec
,
H.
,
Hiura
,
H.
,
Bennett
,
J.
,
Ghaemi
,
H.
, and
Thio
,
T.
,
1996
, “
Electrical Conductivity of Individual Carbon Nanotubes
,”
Nature
,
382
(4 July), pp.
54
56
.10.1155/2014/614797
33.
D, S.,
1985
,
Introduction to Percolation Theory
,
Taylor & Francis
,
London
.
34.
Neitzert
,
H. C.
,
Sorrentino
,
A.
, and
Vertuccio
,
L.
,
2010
, “
Epoxy/MWCNT Composite Based Temperature Sensor With Linear Characteristics
,”
Sensors and Microsystems
,
P.
Malcovati
,
A.
Baschirotto
,
A.
d'Amico
, and
C.
Natale
, eds.,
Springer
,
The Netherlands
, pp.
241
245
.
35.
Shang
,
S. M.
,
Zeng
,
W.
, and
Tao
,
X. M.
,
2011
, “
High Stretchable MWNTs/Polyurethane Conductive Nanocomposites
,”
J. Mater. Chem.
,
21
(
20
), pp.
7274
7280
.10.1039/c1jm10255a
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