With respect to electrical conductivity, a composite of a polymer with a conductive filler will show reasonable low resistance as soon as the percolation limit is reached; with CNTs of high aspect ratio, this can be the case at considerably smaller volume fraction than with other more spherical conductive fillers.
Typical percolation limits over all systems are >0.2 wt.%, with the exemption of some epoxy-based systems.
where [[sigma].sub.f] is the electrical conductivity of the filler, [phi] is the volume fraction of conductor, and [[phi].sub.c] is the critical volume fraction of conductor at the percolation limit. The resistivity of the composite continues to follow this power law until a percolation limit is reached.
There is a wide range of electrical conductivities for a given volume fraction of nano-strands, even at the percolation limit. Samples exhibit a critical percolation threshold between 1 and 5.5 volume percent, and a percolation limit generally at 10-20 vol%.
Values for the percolation threshold, limit, and electrical conductivities at the percolation limit are given in Table 2.
However, measured resistivities for the unfilled polymers reveal that the electrical resistivity of the polymer does not regularly correlate to either the percolation threshold or percolation limit for available data.