A.Afaghi ;S.Asiaei ;M.Baniasadi
Mechanical engineering department;University of Tehran.
The three-dimensional continuum percolation problem of hard-core and soft-core (permeable) objects was an area of active research in the 1980s. Among the considered geometrical objects a very important category is the case of permeable sticks with the form of capped cylinders . Advancements in capabilities of theories and numerical studies has lead to recent developments of polymer reinforced nanocomposites which overcome the need for having certain combination of electrical and mechanical properties . While great strides have been made in exploiting the properties of carbon nanotubes (CNT) [5, 6] several publications document the progress made in fabrication and characterization of CNT nanocomposites [7-10]. In relation to percolation , it is diﬃcult to draw deﬁnite conclusions about electrical conductivity from these published studies because the reported levels of CNT loading required to achieve a percolation concentration (i.e. an appreciable increase in electrical conductivity) vary widely, ranging from less than 1 to over 10% . In general the main parameters affecting percolation are geometry (aspect ratio) and the state of orientation of sticks. However there are other production factors that will change expected percolation concentration such as "size distribution" .The laser counting carried out on the suspension of the particles reveals that the size distribution is asymmetrically extended on the side of the higher-than average values . This fact itself tends to reduce the threshold since it has been shown that with percolating objects having large aspect ratios, the critical concentration diminishes as the size distribution is widened [12 ,13]. On the effects of polydispersed particles, Charlaix, Guyon, Riviers  peciﬁcally
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