Linear segmented polyurethanes. III. Mathematical model for a two-steps polymerization

Abstract

In the first article of this sequel (J. Appl. Polym. Sci., 2018, 135, 45747), an experimental and theoretical investigation was developed on the two-steps synthesis of linear segmented thermoplastic polyurethanes. The reactions were carried out at 60°C, with methylene diphenyl diisocyanate (MDI), two poly(tetramethylene oxide) macrodiols, and 1,4-butanediol (BD) as chain extender. In our second article (J. Appl. Polym. Sci., 2019, 136, 46946), a mathematical model for the prepolymerization was developed, that involved integrating a differential equation for each generated polymer species. The present article extends such model, and predicts the molecular structure along the finishing stage. In each stage, the new model first solves the molar balances at polymer topologies level (i.e.,: Disregarding the molar mass distribution [MMD] of the reacted macrodiol chains), and then calculates the MMD of the evolving polymer and its main subsets through an algebraic convolution procedure. The model reproduces the prepolymerization predictions of our previous article, but is three orders of magnitude faster. In the finishing stage, up to 156,000 polymer topologies and 4.53 × 108 polymer species were calculated; and the rate constant was readjusted to (k2 = 0.00129 L mol−1 s−1), in order to fit the measured MMDs.