Multi-angle evaluation of kinetic Monte-Carlo simulations as a tool to evaluate the distributed monomer composition in gradient copolymer synthesis

Variations of the comonomer structure and synthesis conditions allow a wide range of comonomer sequences for polymer chains, with copolymer precision control mechanisms (e.g. anionic polymerization, cationic ring opening polymerization (CROP) and reversible deactivation radical polymerization (RDRP)) aiming at well-defined structures, such as gradient, block, and block–gradient–block copolymers. A main challenge remains a generic quality tool for evaluation of a synthesized polymer at a given overall monomer conversion or reaction time, for which recent research has pointed out that matrix-based kinetic Monte Carlo (kMC) simulations are crucial as they provide information on monomer sequences of individual chains. Via post-processing of these individual chains, a structural deviation (SD) distribution can be derived, which represent the number fraction of chains with a given deviation versus an ideally composed chain of a selected compositional target. Historically the average structural deviation (〈SD〉) is the main input for such kMC-based quality control labeling. The present work showcases that a multiangle evaluation is much more recommended, including besides 〈SD〉 calculation, the additional calculation of the SD variance and skewness as well derived characteristics for the segment (SEG) distribution. It is shown that copolymers codefined by non-gradient compositional distributions such as alternating, random, block and homopolymeric chain can have very similar 〈SD〉 = 〈GD〉 (G for gradient) values but still be distinguished by examining the skewness of the GD peak and the SEG distributions. Copolymers with a distinct A/B to B/A transitions show (high) positive GD skewness (3,GD), while values near 0 or negative values indicate no dominant A/B to B/A transition characteristics as the case for alternating, random or homopolymeric copolymers. The average SEG values show the increasing trend: alternating, random, gradient, block, and homopolymer. It is first highlighted that only certain combinations of the kinetic parameters under CROP conditions in the absence of side reactions deliver a certain control over gradient copolymer structure. Due to side reactions the gradient quality significantly decreases, especially due to chain transfer to monomer. Moreover, for the more non-gradient structures also extra SD-based evaluations can be performed using cumulative probability distribution functions to define specific gradient/block proportions