Abstract
The error-in-variables-model (EVM) is the most statistically correct non-linear parameter estimation technique for reactivity ratio estimation. However, many polymer researchers are unaware of the advantages of EVM and therefore still choose to use rather erroneous or approximate methods. The procedure is straightforward but it is often avoided because it is seen as mathematically and computationally intensive. Therefore, the goal of this work is to make EVM more accessible to all researchers through a series of focused case studies. All analyses employ a MATLAB-based computational package for copolymerization reactivity ratio estimation. The basis of the package is previous work in our group over many years. This version is an improvement, as it ensures wider compatibility and enhanced flexibility with respect to copolymerization parameter estimation scenarios that can be considered.
Highlights
In copolymerization kinetics, reactivity ratios are important parameters
Do reactivity ratio estimates specify the degree of incorporation of each comonomer into the copolymer but they provide information about other copolymer microstructural indicators
Other common sources of error in parameter estimation include poorly designed experiments—too few data points, chosen at random—inherent experimental difficulties and inappropriate kinetic models. This has created a wide variety of reactivity ratios in the literature, even for similar copolymer systems
Summary
Do reactivity ratio estimates specify the degree of incorporation of each comonomer into the copolymer (i.e., average copolymer composition) but they provide information about other copolymer microstructural indicators (namely azeotropic point, sequence length distribution, triad fractions and so on) This knowledge of kinetics and microstructure can be useful in synthesizing copolymers with specific desirable properties for specific applications. Other common sources of error in parameter estimation include poorly designed experiments—too few (usually unreplicated) data points, chosen at random—inherent experimental difficulties (especially at low conversion levels) and inappropriate kinetic models. This has created a wide variety of reactivity ratios in the literature, even for similar copolymer systems (see, for example, reactivity ratios associated with the copolymer of 2-acrylamido-2-methylpropane sulfonic acid and acrylamide, as summarized by Scott et al [4])
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