polymers Article Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression Iosif Sorin Fazakas-Anca 1 , Arina Modrea 2, * and Sorin Vlase 3,4, *   Citation: Fazakas-Anca, I.S.; Modrea, A.; Vlase, S. Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression. Polymers 2021, 13, 3811. https://doi.org/10.3390/ polym13213811 Academic Editor: Nicolas Sbirrazzuoli Received: 14 October 2021 Accepted: 2 November 2021 Published: 4 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 AGIMED Sovata, 545500 Sovata, Romania; d-mec@unitbv.ro 2 Pharmacy, Science and Technology George Emil Palade Targu Mures, University of Medicine, 300134 Targu Mures, Romania 3 Department of Mechanical Engineering, Transilvania University of Brasov, B-dul Eroilor 20, 500036 Brasov, Romania 4 Romanian Academy of Technical Sciences, B-dul Dacia 26, 030167 Bucharest, Romania * Correspondence: arina.modrea@umfst.ro (A.M.); svlase@unitbv.ro (S.V.); Tel.: +40-722-643020 (S.V.) Abstract: This paper proposes a new method for calculating the monomer reactivity ratios for binary copolymerization based on the terminal model. The original optimization method involves a numerical integration algorithm and an optimization algorithm based on k-nearest neighbour non-parametric regression. The calculation method has been tested on simulated and experimental data sets, at low (<10%), medium (10–35%) and high conversions (>40%), yielding reactivity ratios in a good agreement with the usual methods such as intersection, Fineman–Ross, reverse Fineman–Ross, Kelen–Tüdös, extended Kelen–Tüdös and the error in variable method. The experimental data sets used in this comparative analysis are copolymerization of 2-(N-phthalimido) ethyl acrylate with 1-vinyl-2-pyrolidone for low conversion, copolymerization of isoprene with glycidyl methacrylate for medium conversion and copolymerization of N-isopropylacrylamide with N,N-dimethylacrylamide for high conversion. Also, the possibility to estimate experimental errors from a single experimental data set formed by n experimental data is shown. Keywords: k-NN regression; reactivity ratios; optimization; copolymerization; error estimation; propagation rate; monomers 1. Introduction Technological development brings with it the need to create new polymers with predefined physico-chemical properties. It is well known that the physico-chemical proper- ties of polymers are given by their microstructure, and the microstructure is determined by the reaction kinetics. By the nature of the monomers used in the copolymerization reaction and by a controlled kinetics, specific microstructures can be obtained such as: polymers with amorphous or crystalline areas, polymers with large molecular masses, branching polymers, crosslinked polymers or more other microstructure types. All these microstructure types have great influence on the mechanical and chemical behavior of the resulting polymers. The possibilities to obtain any kind of mechanical or chemical properties of copolymers are practically unlimited, but there exists only one limitation to our imagination. The mechanism of binary copolymerization in which it is considered that only the last structural unit attached to the polymer chain influences the growth mode of the polymer is described by the following kinetic relations [1]: P n − M ∗ 1 + M 1 k 11 → P n+1 − M ∗ 1 P n − M ∗ 1 + M 2 k 12 → P n+1 − M ∗ 2 Polymers 2021, 13, 3811. https://doi.org/10.3390/polym13213811 https://www.mdpi.com/journal/polymers