Grafting Kinetics of End-Functional Polymers at Melt Interfaces

Expressions for the kinetics of grafting chains from a pure end-functional polymer melt to a reactive interface are derived under the assumption that the free energy of reaction is very large and negative. Two cases are considered: a case where the grafting is controlled by diffusion of free end-functional chains through the “brush” of previously grafted chains and a case where the grafting is controlled by the kinetics of the interface reaction itself. Both cases lead to the same form of the grafting kinetics, but with different characteristic times τ_D = R_ga/D, where R_g is radius of gyration, a is the statistical segment length, and D is the diffusion coefficient of the end-functional polymer; and τ_R = R_g/(ak_f[B]) where k_f is a forward rate constant and [B] is the concentration of groups at the interface that react with the end-function of the polymer chains. The grafting density Σ approaches a practical limit after long times for each value of the degree of polymerization N, and this limit decreases strongly with N. These predictions are compared with the results of recent experiments in which deuterated polystyrene chains with carboxylic acid end groups were grafted to either epoxy- or amine-rich cross-linked epoxy networks. The reaction-controlled grafting model fits the data best and permits us to extract forward rate constants of ˜0.18 kg s⁻¹ mol⁻¹ for the epoxy-rich networks and ˜5 × 10⁻³ kg s⁻¹ mol⁻¹ for the amine-rich ones.