The improvement in properties due to the incorporation of nanostructured materials, such as carbon nanotubes (CNTs), in polymers is most effective when they are uniformly dispersed with minimal agglomeration. Good dispersion results in large interfacial surface areas that facilitate strong interactions between the nanoadditive and polymer. When nanocomposite materials are subjected to thermal and mechanical stress, these interactions transfer the strain to the nanoadditives, which are typically stronger and more rigid than polymer chains, thereby reinforcing the host material. The dispersion of nanoadditives in polymers above a critical concentration is marked by a transition from liquid-like to solid-like flow behavior, due to the formation of a nanoparticle network. It is usually accompanied by significant enhancements in the properties of the host material. This is especially true with respect to flammability performance. Thus, it is known that the reduced heat release rates exhibited by many nanocomposite materials depends, in large part, on the ability of the nanoadditives to form a protective layer that insulates the unburnt polymer in the interior of the burning object from thermal energy incident on its surface. As the polymer (in a nanocomposite) decomposes in a fire, the network structure formed by the nanoadditives is left behind. Although it consists primarily of free volume, it must be sufficiently strong to withstand thermal motions that might otherwise break it apart. In poorly dispersed nanocomposites, the network structure has less free volume (because the nanoadditives are agglomerated) and the thermal protection of the unburnt polymer is correspondingly less effective. The extent to which it is possible to achieve and sustain good dispersion of the CNTs, especially at the high temperatures experienced during burning, depends on the nature of the interactions between the nanoadditives and polymer. The unique properties of polymer nanocomposites arise from interactions between nanoadditives and polymers that are limited to a range of about 10 nanometers. This is too small to be captured by continuum mechanics, but beyond the capabilities of conventional atom based molecular mechanics (MM) and dynamics. Problems that fall into this domain (commonly referred to as the mesoscale) can be handled by stochastic dynamics, such as dissipative particle dynamics (DPD), which require force fields that are resolved over length scales intermediate between atomic and continuum dimensions. In this talk, I will summarize progress made in the development of a stochastic dynamics model of the dispersion and agglomeration of CNTs in polymers.