Modeling ring/chain equilibrium in nanoconfined sulfur.

The effect of nanoconfinement on the thermodynamics of free radical polymerization of sulfur is examined. We extend Tobolsky and Eisenberg's model of bulk sulfur polymerization to nanopores accounting for the confinement entropy of the chains and ring using scaling reported in literature. The model quantitatively captures literature data from Yannopoulos and co-workers for the extent of polymerization versus temperature for bulk sulfur polymerization and for polymerization in 20, 7.5, and 2.5 nm diameter Gelsil nanopores, assuming that the change of entropy of nanoconfined chains scales with molecular size to the second power and with nanopore diameter to either the -3.0 or -3.8 power, the former of which fits slightly better. The scaling, which is valid for strong confinement in spherical pores, predicts that the propagation equilibrium constant will depend on both nanopore size and chain length, such that the average chain length decreases significantly upon confinement.