A deterministic modelling approach is developed to predict the internal structure of gradient copolymer chains. A key innovation of the modelling approach is the introduction of a positional variable that gives direct access to quantitative gradient characteristics: the ensemble average composition and the gradient deviation. This positional variable is used to develop multi-dimensional population balance equations that can be solved numerically to calculate gradient quality measures. The methodology is illustrated using the gradient copolymerisation of ethylene and 1-octene via coordinative chain transfer mechanism, which is representative of a variety of polymerisation schemes for gradient copolymers. Simulation results are validated with those obtained by stochastic simulations which, until now, were the only means of predicting detailed gradient quality.
Kryven, I., Zhao, Y. R., McAuley, K. B., & Iedema, P. (2018). A deterministic model for positional gradients in copolymers. Chemical Engineering Science, 177, 491–500. https://doi.org/10.1016/j.ces.2017.12.017