6533b85bfe1ef96bd12bbd27

RESEARCH PRODUCT

Analytical representation of bimodality in bivariate distribution of chain length and chemical composition of copolymers

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Abstract Tuning the bimodality of microstructural features in polymers has provided novel properties and applications. A classic example is to overcome the trade-off between processability and mechanical properties in polyolefins. A recent example is to decrease the interfacial tension in blending incompatible polymers. Therefore, the development of a bimodality index (BI), especially for the chain length distribution (CLD) and the chemical composition distribution (CCD), is crucial for the quantitative design of materials. This study introduces quantitative expressions for the bimodality of univariate CLD on the linear scale, and CCD. Moreover, we develop a bimodality criterion for bivariate CLD–CCD while representing it graphically and analytically. As such, this analysis applies to linear polymers whose CLD–CCD is expressed by the Stockmayer bivariate distribution. Our results indicate that a specific chain length exists beyond which the CCD part of bivariate distribution becomes bimodal. Mathematical modelling of ethylene-propylene copolymerization in two loop reactors in series, operating at different conditions, was used to provide representative examples and to verify the suggested bimodality indices. We calculate the developed bimodality indices at representative operation conditions and compare them with the model bivariate distributions. The developed bimodality indices facilitate designing new products with bimodal microstructural features and are also beneficial for developing novel characterization techniques and providing a better understanding of the structure–property relationships in bimodal polymers.