Sensitivity analysis of isothermal free radical induced grafting through application of the distribution - Numerical fractionation - Method of moments

Abstract

Free-radical induced grafting (FRIG) is an important synthesis route to produce graft copolymer (GC), which possesses unique macroscopic properties but complicated non-linear molecular structures. To describe the many distributed GC molecular structures (e.g. p backbones and q grafts; p, q ≥ 1), a cost-efficient deterministic solver, i.e. distribution-numerical fractionation-method of moments (D-NF-MoM) has been recently introduced. To demonstrate the increased kinetic information once distributed molecular data are available and to confirm the low cost (simulation on a time scale less than one minute), both conventional MoM and D-NF-MoM are applied for FRIG of styrene on polybutadiene. This is done under a broad range of reaction conditions, assuming that the reaction process is isothermal and pseudo-homogenous. The effect of initial initiator concentration, initial loading of polybutadiene to styrene (PB/St), and the reaction rate coefficients for grafting initiation on the PB backbone (kha), macropropagation (kmp), and chain transfer to the PB backbone (kfp) is explored interpreting average and distributed characteristics. The simulations show that higher initial initiator loadings, initial PB/St loadings, and values of the aforementioned rate coefficients lead to more grafts. Moreover, higher values of the rate coefficients lead to GC species with more PB backbones, which is consistent with the growth of the number of H structures, as evidenced by the bivariate distributed properties. Moreover, D-NF-MoM application illustrates that with more initial initiator and PB/St loading, shorter grafts are more easily formed. The current work thus improves deterministic solvers for complex synthesis routes and will likely facilitate the identification of optimal reaction conditions for targeted products.