Dynamic rheological properties of multi-walled carbon nanotubes (MWCNTs) filled polystyrene (PS) melt were investigated in relation to a two phase model proposed by authors.The linear viscoelastic behavior of the composites is related to the strain amplification effect of the bulky polymer phase far away from the filler inclusions and the relaxation of the filler phase.Dependence of strain amplification factor (Af) on MWCNTs volume fraction (φ) at different temperatures accords with the diffusion-controlled cluster-cluster aggregation (CCA) model.At φ < 0.020

MWCNTs are rather homogeneously dispersed in the matrix

and no remarkable change appears in the relation between Af and φ with increasing temperature.Af decreases obviously with increasing temperature at higher φ where MWCNTs form cluster aggregates.Characteristic dynamic moduli (G′f1 and G″f0) of the filler phase as a function of temperature follow Arrhenius law with the corresponding activation energies (E′a and E″a) varying discontinuously at φ = 0.025

suggesting that the temperature dependence of viscoelasticity of the homogeneously dispersed MWCNTs at φ < 0.020 is considerably different from that of the MWCNTs percolation network at φ > 0.025.The viscoelastic percolation is closely related to the conduction percolation

and the discontinuous variations of activation energies in  range from 0.020 to 0.025 appear in the vicinity of the upper limit of the conduction percolation threshold.The dispersion of MWCNTs in the matrix has been verified in transmission electron microscope (TEM) observation.