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Calculation of tunneling distance in carbon nanotubes nanocomposites: effect of carbon nanotube properties, interphase and networks


In this paper, two developed models for electrical conductivity of polymer nanocomposites are linked to express an equation for tunneling distance between adjacent carbon nanotubes (CNT) by the effective properties of polymer matrix, CNT, interphase and networks. The tunneling distance is calculated for some samples at different CNT concentrations. In addition, the suggested equation is applied to justify the impacts of all parameters on the tunneling distance. The tunneling distance decreases as CNT concentration increases, but its variation reduces at high CNT loading. The suggested equation demonstrates that a thick interphase, thin and short CNT, high filler concentration, poor percolation threshold, low surface energy of polymer and high CNT surface energy produce a short tunneling distance.

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Figure 6


R :

CNT radius

l :

CNT length

t :

Interphase thickness

u :

Waviness parameter

σ f :

The nature conductivity of CNT

\( \phi_{\text{f}} \) :

Filler volume fraction

f :

The percentage of CNT founding the conductive networks

σ 0 :

Conductivity of polymer matrix

α :

Filler aspect ratio

cos (θ):

Wettability of nanoparticles by polymer matrix

γ p :

Surface energy of polymer

γ f :

Surface energy of filler

γ fp :

Surface energy of filler/polymer interface

θ :

Wetting angle

λ :

Tunneling distance

z :

Characteristic tunneling length


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Correspondence to Kyong Yop Rhee.

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Zare, Y., Rhee, K.Y. Calculation of tunneling distance in carbon nanotubes nanocomposites: effect of carbon nanotube properties, interphase and networks. J Mater Sci 55, 5471–5480 (2020).

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