An equation driven quality classification of (a)symmetric gradient, gradient-block, block-gradient-block and block copolymers

Abstract

The control of the A/B comonomer distribution over individual chains targeting block and/or gradient monomer distributions is essential to control the macroscopic properties of the resulting copolymers. Matrix-based kinetic Monte Carlo simulations allow to compare each chain of a representative copolymer sample with the desired (mathematical) composition, as defined by monomer inclusion probabilities (PA/B) taking the B-functionalization degree (B-Func) as maximally 50%. A so-called average deviation (SD∗ value) results per chain, with a close to 0 average (normalized) structural deviation 〈SD〉 corresponding to an almost perfect structure and a 〈SD〉 close to 1 representing the worst case scenario of a B-homopolymer. The previously assigned 〈SD〉 transitions from excellent to good and from good to poor are, however, somewhat arbitrary, e.g. for both symmetric gradient and block copolymers a threshold 〈SDGood/Poor〉 of 0.3 is currently utilized and only for specific asymmetric cases (30% B-Func block, block-gradient, and gradient) 〈SDExc/Good〉 and 〈SDGood/Poor〉 values have been reported. The present work puts forward an equation driven method to obtain 〈SD〉 threshold values, minimizing the arbitrary nature of the quality classification for a given copolymer type and more importantly aligning the quality assessment for any copolymer type containing block and/or gradient elements. Emphasis is on the complete SD distribution (instead of only its average) for (a)symmetric AB gradient, block A-gradient AB, block A-gradient AB-block B, and AB block copolymers by introducing the overall gradient and block fractions (fGr/Bl) as a novel parameter alongside the targeted degree of polymerization (target DP) and B-Func. Ideal theoretical structures with equal chain length and a perfect implementation of the desired PA/B profiles are dealt with, as they represent the best case an actual synthesis recipe could deliver in the limit. It is shown that the log-normal distribution can be reliably used to approximate the SD distribution, as coefficients of determination (R2) very close to one follow for (a)symmetric copolymers . It is further showcased that threshold values for gradient dominant structures must be higher than those for block-like structures and that well-defined symmetric structures are more difficult to achieve than asymmetric ones. It is also recommended to report 〈SD〉 together with its standard deviation σSD.