Monomer addition programs to generate constant gradient block copolymers

Equations are derived to calculate the monomer addition programs for semi-batch copolymerization reactions that allow to prepare gradient copolymers and block gradient copolymers containing arbitrary, pre-defined compositional gradients along the polymer chain. An analytical solution is given for the special case of ideal random copolymerizations, and numerical calculations are applied to discuss non-ideal situations. Three classes of addition programs are proposed and discussed with respect to time efficiency. Time-linear addition programs are shown to be insufficient to generate perfectly constant gradients over the whole compositional regions.