Introducing an algorithm to accurately determine copolymer block-length distributions

Copolymers are attractive for developing advanced materials with widespread applications such as medical devices, implants, or self-healing coatings for space stations and satellites. Their physical properties are tunable by controlling polymeric characteristics such as molecular weight and chemical composition. Another characteristic that has a significant influence on the material properties is the block-length distribution (BLD). Synthetic chemists can alter the BLD independently from molecular weight and chemical composition. However, analytically characterizing these BLDs, for copolymers composed out of multiple monomers, remains a huge challenge.

In this study, an algorithm was developed that enables the accurate determination of copolymer BLDs. Copolymers were computationally simulated and fragmented by either a repeated-sampling approach or an analytical solution to obtain unbiased ground-truth data to objectively evaluate such algorithms. The performance of the novel analytical solution, coupled with an optimization algorithm, was assessed under various conditions. We have demonstrated that a trust-region-reflective algorithm yields highly accurate BLDs when fragment data up to the tetramer level is available. Although the presence of noise in the input data led to some noise in the output, it did not notably impact the overall performance of the algorithm.

The proposed algorithm demonstrated significant improvements over existing algorithms for the determination of copolymer BLDs. Using accurately simulated copolymer fragment data, which can be obtained through chemical reactions or physical processes, such algorithms could objectively be evaluated on their performance for the first time. These observations indicate that the proposed algorithm holds great potential for application to experimental copolymer fragment data.