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The structure and rheological properties of multiwall carbon nanotube (MWNT)/polydimethylsiloxane (PDMS) composites under shear are investigated, as the molecular weight of PDMS, aspect ratio and concentration of MWNT are systematically varied. Negative normal stress differences (N) are observed at low shear rates for samples with low molecular weight (M_w) of PDMS (lower than the critical entanglement molecular weight (M_c)), whereas positive DN is found in samples with high molecular weight of PDMS (M_w > M_c). More interestingly, negative DN is also observed for some samples under confinement when the molecular weight of PDMS is higher than the critical value (M_w > M_c). Moreover, the aspect ratio and concentration of MWNT show negligible influence on the sign of N. Based on the results of optical-flow experiments, a phase diagram for the structures of samples under shear is obtained. It is concluded that the vorticity banding of MWNT aggregates results in the negative N under shear through relating the evolution of structure and the rheological properties of samples under shear.