One-dimensional statistical mechanics models with application to peapods

Quasi one-dimensional systems of molecules Of C-60 encapsulated in (10/10) nanotubes were studied by both lattice-gas and Takashi-Gursey configurational integral methods of statistical mechanics for both open and capped finite nanotubes as well as infinite nanotubes. From well-established potentials, the energy, heat capacity compressibility, equation of state and absorption isotherms were computed as a function of temperature and molecular density. The existing theories were extended to include the calculation of clustering, and the number of clusters as a function of size was computed for a variety of temperatures and densities. For both models, all molecules are frozen into a single cluster, and increasing the temperature results in a break-up into smaller clusters. The corresponding heat capacity has a broad maximum, which is lower for the T-G model than for the lattice-gas model. The equations of state have a similar form in both models and are identical at low temperatures. The absorption isotherms show that filling of the tubes can take place at all temperatures of practical interest. Peapods are nearly ideal realizations of one-dimensional systems whose thermodynamic and structural properties can be accurately obtained by statistical mechanics.