Determination of reactivity ratios for acrylic acid and its dimer from classical parameter estimation and Bayesian approach

Abstract

The reactivity ratios of acrylic acid (AA, M1) and its dimer β‐acroyloxypropionic acid (diAA, M2) are determined from cumulative copolymerization data by two different methods: classical parameter estimation (PE) by minimizing the objective function and a Bayesian analysis. Classical PE gives r1=0.74 and r2=1.23 at the minimum of the residual. From the Bayesian analysis, the probability distribution of the parameter sets is obtained, revealing the existence of parameter sets with rather the same probability. The influence of the number of data and the size of the measurement error are discussed.

Probability Evaluation of the ternary polymerization and reactivity ratio of bio-based PA5T/56

“…analyzed the free base binary copolymerization reaction in 1944 and deduced the copolymer composition from the four chain growth reactions, a variety of methods for the determination of the monomer racemization rate have been derived [5][6] , and the estimation of the racemization rate of copolymerized monomers by Monte Carlo probability statistics is the most widely used and effective method of determination at present [7] .…”

Issue Highlights

“…While the classical PE gives optimal parameters at the minimum of the residual, from the Bayesian analysis we derive the probability distribution across the parameter set, revealing the existence of parameter sets with almost indistinguishable probability. Moreover, the influence of the number of data points and the size of the measurement error is investigated [4] …”

Preface to the special section in memory of Professor Kenneth F. O'Driscoll

“…This special section features 12 invited papers from researchers around the world, reflecting the extent and depth of Ken's scientific legacy in polymer science and engineering. [1][2][3][4][5][6][7][8][9][10][11][12] Ken was born 22 July 1931 in Staten Island, New York City. He attended the prestigious Regis High School in Manhattan and then the Pratt Institute for his BChE (1952).…”

“…This special section features 12 invited papers from researchers around the world, reflecting the extent and depth of Ken's scientific legacy in polymer science and engineering. [ 1–12 ]…”