Chain conformations dictate many of the important physical properties of polymers including their dynamics. Using small angle neutron scattering, we probed chain conformations, specifically the radius of gyration (R-g), in both SWCNT/polystyrene (r(SWCNT)/R-g similar to 0.4) and MWCNT/polystyrene (r(MWCNT)/R-g similar to 1) nanocomposites. We fit the scattering data using a model that includes an ideal Gaussian chain to describe the polymer conformation and a rod network to describe the carbon nanotube (CNT) network. The scattering contribution from the rod network increases with the CNT concentration in both SWCNT and MWCNT nanocomposites, and the contribution is higher for SWCNT nanocomposites due to the smaller Mesh size and higher mesh density. When the SWCNT and MWCNT concentrations are below 2 wt %, there is no significant change in R-g. Above 2 wt %, R-g in the MWCNT nanocomposites decreases slightly, while R-g in the SWCNT nanocomposites increases monotonically as a function of CNT concentration, showing a similar to 30% increase at 10 wt %. SWCNT loading. Although we previously found a minimum in the tracer diffusion coefficient near the critical nanotube concentration this trend is absent in the concentration-dependent' polymer conformation.