For polymer nanocomposites with two-dimensional filler materials, intercalation/exfoliation is required to maximize internal connectivity. Previous work has shown that clay exfoliation can be achieved through mild thermal annealing in the presence of a low-molecular-weight, hydroxyl-terminated "telechelic" polybutadiene (tPB) matrix. However, the specific role of the hydroxyl groups, their placement, and polymer mobility in the intercalation/exfoliation process still remains unclear. In this study, these matrix parameters were evaluated by replacing the tPB with randomly functionalized polybutadienes (rPBs) of increasing hydroxyl group densities. The rPB was synthesized by covalently grafting mercaptoethanol to the PB backbone, and its ability to exfoliate organically modified montmorillonite clay was evaluated. While some functional groups are required to exfoliate the clay, it was found that exfoliation proceeds successfully regardless of the number of hydroxyl groups or their location on the PB backbone. Instead, it was found that polymer mobility played a key role in the extent of exfoliation. As the grafting concentration was increased, the rPB molecular mobility decreased because of its higher glass transition temperature (T-g). A detailed analysis of their linear viscoelastic properties was able to decouple the two phenomena, change in mobility and effectiveness of polymer-clay interaction. Nanocomposites using highly grafted polymers showed a decrease in their connectivity because of reduced exfoliation of the clay. This was overcome by introducing a highly grafted and highly mobile rPB with a low T-g (low vinyl content), which successfully exfoliated the clay. The combined results suggest that intercalation can be achieved through favorable polymer-clay interactions, whereas exfoliation can proceed beyond intercalation only when there is enough polymer mobility.