Functionality dependence of the distribution of cyclic species in network formation
Abstract
The functionality dependence of the ring-size distribution is examined for the branching process of the A–R–Bf– 1 model. It is shown that the equilibrium concentration of j-rings decreases as (∂[Rj]/∂f)k⩽ 0 with increasing functionality f, for a fixed total bond number k. This directly gives rise to another inequality related to the cluster number Ω: (∂Ω/∂f)k⩽ 0.