Low field and high field transport properties of carbon nanotubes/polymer composites are investigated for different tube fractions. Above the percolation threshold f_c=0.33%, transport is due to hopping of localized charge carriers with a localization length xi=10-30 nm. Coulomb interactions associated with a soft gap Delta_CG=2.5 meV are present at low temperature close to f_c. We argue that it originates from the Coulomb charging energy effect which is partly screened by adjacent bundles. The high field conductivity is described within an electrical heating scheme. All the results suggest that using composites close to the percolation threshold may be a way to access intrinsic properties of the nanotubes by experiments at a macroscopic scale.
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