A Deterministic Model for Positional Gradients in Copolymers

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.