Electrical Percolation Model of Ternary Carbon Filler Mixture in Polymer Blends†

doi:10.7503/cjcu20150169

Abstract

Abstract:

A model was proposed for predicting the electrical percolation of ternary carbon filler mixture in polymer blends based on excluded volume theory. 2D and 3D models were used to describe the percolation model. Carbon black(CB), tangled carbon nanotubes(t-CNTs) and aligned carbon nanotubes(a-CNTs) were used as carbon-type conductive fillers. Taking polycarbonate(PC)/styrene-acrylonitrile(SAN)(70∶30, mass ratio) and PC/polyphenylene oxide(PPO)(70∶30, mass ratio) as the matrices, the equation developed from the percolation model is corrected by measuring the percolation thresholds of each carbon filler in polycarbo-nate and polymer blends. Predictions from the model match the conductivities well, proving the suitability and usefulness of the model. For those polymer blends with the same matrix polymer, the equation can be obtained by the ratio of the percolation threshold of one carbon filler in the polymer blend to that in the matrix polymer. The model can provide an important theoretical basis for structure designing and predicting the electrical properties of conductive polymer composites.

Key words: Electrical percolation model, Percolation threshold, Carbon black, Carbon nanotube, Polymer blend

CLC Number:

O631

TrendMD:

XIONG Zhuoyue, ZHANG Boyuan, WANG Weijia, GUO Zhaoxia, YU Jian. Electrical Percolation Model of Ternary Carbon Filler Mixture in Polymer Blends^†[J]. Chem. J. Chinese Universities, 2015, 36(8): 1641.

Figures/Tables 11

Fig.1 Schematic illustration of the percolation model for ternary carbon filler mix-filled PC/SAN(70∶30,

Fig.2 3D model of Eq.(2)

Fig.3 2D model of Eq.(2) for PC/SAN/a-CNTs/t-CNTs composites

Fig.4 SEM images of PC/SAN/CB/t-CNTs/a-CNTs(70∶30∶4∶2∶2)(A) and PC/PPO/CB/t-CNTs/a-CNTs(70∶30∶4∶2∶2)(B)

Fig.5 TEM images of PC/SAN/CB/t-CNTs/a-CNTs(70∶30∶5∶0.1∶0.3)(A) and PC/PPO/CB/t-CNTs/a-CNTs(70∶30∶3.33∶0.133∶0.3)(B)

Fig.6 Percolation curves of CB(A), t-CNTs(B) and a-CNTs(C) filled PC(a), PC/SAN(70∶30)(b) and PC/PPO(70∶30)(c)

Table 1 X values calculated from CB, t-CNTs, a-CNTs and their averages

System	m_CB(%)	m_t-CNTs(%)	m_a-CNTs(%)	Average(X)
PC/SAN(70∶30)	0.64	0.60	0.60	0.61
PC/PPO(70∶30)	0.77	0.77	0.83	0.79

Fig.7 2D figures of mCB=0(A), mCB=1%(B), mt-CNTs=0(C) and mt-CNTs=0.133%(D) in PC/SAN(70∶30)

Table 2 Composition, calculated value of Eq.(3), prediction of percolation and conductivity of each sample in PC/SAN

No.	m_a-CNTs(%)	m_t-CNTs(%)	m_CB(%)	Calculated value	Prediction	Conductivity(lgρ_v)
1	0.100	0.100	0	0.316	No	9.84
2	0.167	0.167	0	0.527	No	9.00
3	0.333	0.333	0	1.05	Yes	3.03
4	0.400	0.300	0	1.16	Yes	3.21
5	0.133	0.067	1.00	0.443	No	9.93
6	0.100	0.133	1.00	0.445	No	9.90
7	0.300	0.300	1.00	1.04	Yes	3.42
8	0.267	0.333	1.00	1.01	Yes	4.30
9	0.100	0	1.00	0.302	No	15.40
10	0.133	0	2.67	0.528	No	9.20
11	0.167	0	7.00	1.01	Yes	2.98
12	0.200	0	6.67	1.04	Yes	3.17
13	0.100	0.133	1.00	0.445	No	9.90
14	0.067	0.133	1.66	0.439	No	10.40
15	0.133	0.133	6.67	1.05	Yes	3.95
16	0.300	0.133	3.33	1.08	Yes	4.35

Fig.8 2D figures of mt-CNTs=0.1%(A) and mCB=2%(B) in PC/PPO(70∶30)

Table 3 Composition, calculated value of Eq.(4), prediction of percolation and conductivity of each sample in PC/PPO

No.	m_a-CNTs(%)	m_t-CNTs(%)	m_CB(%)	Calculated value	Prediction	Conductivity(lgρ_v)
1	0.067	0.100	1.67	0.404	No	16.3
2	0.133	0.100	1.00	0.479	No	10.3
3	0.300	0.100	5.00	1.20	Yes	6.39
4	0.267	0.100	6.00	1.23	Yes	5.88
5	0.067	0.133	2.00	0.471	No	16.2
6	0.100	0.100	2.00	0.504	No	16.4
7	0.267	0.333	2.00	1.10	Yes	5.90
8	0.300	0.300	2.00	1.14	Yes	5.69

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