Visualization of Bivariate Sequence Length–Chain Length Distribution in Free Radical Copolymerization

Abstract

Copolymer properties and processability depend on copolymer microstructure, i.e., copolymer composition and monomer unit arrangements along the copolymer chains. To predict the ultimate properties of copolymers, one needs complete information on the length and position of sequences of each monomer type in every chain. A versatile kinetic Monte Carlo code is developed and applied for the simulation of typical free radical copolymerizations. The code allows explicit monitoring of every growing chain during the course and at the end of polymerization, can account for comonomer systems of any arbitrary reactivity ratios (r1 and r2) over the full range of monomer composition. Meanwhile, it eliminates the need for solving arrays of differential equations arising from deterministic modeling approaches. Since the code virtually synthesizes billions of copolymer molecules and keeps in storage information on each and every copolymer chain in the system, it allows for detailed statistical analysis. The simulator visualizes the bivariate sequence length–chain length distribution for typical copolymerization systems and examples with: r1 < 1 and r2 < 1; r1 > 1 and r2 < 1; (r1 × r2) = 1; and r1 = r2 = 1, and is also applied successfully to an experimental scenario described in the literature.

Modeling of Scattering Cross Section for Mineral Aerosol with a Gaussian Beam

“…In order to investigate the general average scattering cross sections of nonspherical mineral particles, three aerosols, that is, the feldspar, quartz, and red clay, are studied, and the spheroid model is used to represent the real nonspherical mineral particle. Since the scattering prosperities of particles within the Gaussian beam are related with the position information, the Monte Carlo statistical estimate method is used to determine the distributed positions of these random nonspherical particles [19,20]. After making the average of the position information, we can obtain the general location for the random particles, and then the average scattering cross section of particles is also calculated with the GLMT framework.…”

Intelligent Monte Carlo: A New Paradigm for Inverse Polymerization Engineering

“…We previously developed a KMC methodology for simulating copolymerization kinetics and microstructure of the virtually synthesized macromolecules within a relatively large simulation volume . In this work, complex OBCs produced by chain shuttling coordination copolymerization reactions have been selected to demonstrate the capabilities of the enhanced IMC approach.…”

Heuristic Search Strategy for Transforming Microstructural Patterns to Optimal Copolymerization Recipes

“…Manipulation and fine‐tuning of copolymer properties has so far been realized mostly through detailed mathematical modeling for the simultaneous regulation of microstructural features of copolymer chains (monomer sequences/arrangements and chain length); see, for instance, refs. . Understanding the microstructure–property relationships in copolymerization is a rather cumbersome activity, and this arises mainly due to the complexity of the macromolecular reactions.…”

“…DOI: 10.1002/mats.201700088 copolymer chains (monomer sequences/ arrangements and chain length); see, for instance, refs. [1][2][3][4][5]. Understanding the microstructure-property relationships in copolymerization is a rather cumbersome activity, and this arises mainly due to the complexity of the macromolecular reactions.…”