Dependence of computed copolymer reactivity ratios on the calculation method. II. Effects of experimental design and error structure

Abstract

Two calculation methods for estimating reactivity ratios, one method based on the differential Alfrey‐Mayo equation and one based on the integrated form of this model, are compared with respect to precision and bias. Both methods are characterized by the use of information about the monomer feed composition only and are assumed to be valid up to high conversion. As only monomer feed composition has to be analyzed, several sampling designs are feasible. Two extreme designs can be distinguished. One consists of repetitive sampling of the initial and final monomer feed mixture, whereas the other consists of sequential sampling during the course of the reaction. The influence of both designs of the calculated r‐values is investigated by means of simulation. In the present paper the second calculation method, based on the integrated form, is solved by a nonlinear least squares method considering errors in both variables. This method required additional information about the errorstructure of the data. As this information is mostly of approximate nature, the influence of misspecification of this error structure on the calculated r‐values is also examined.

Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression

“…It is well known that any experimental measurement contains errors, and for this reason a number of authors [17][18][19][20][21][22][23][24][25][26] have used the principle of minimizing these errors to obtain the true value of composition of the feed and the copolymer, and finally to obtain the best values of reactivity ratios.…”

“…This concept, called error in variable method (EVM), was originally developed by German [17] considering the error in only one variable. Later van der Meer et al [18] extended the concept to analysis the errors in both variables, after which various approaches appeared in the calculation methodology [19][20][21][22][23][24][25][26]. For the comparative analysis of the methods for calculating the reactivity ratios, the EVM variant proposed by Chee and Ng [26] was chosen, because it uses the integral equation proposed by Mayo and Lewis (12) and does not require to know the experimental error.…”

Using the Stochastic Gradient Descent Optimization Algorithm on Estimating of Reactivity Ratios

“…The Error in Variable Method (EVM) is a concept for calculating reactivity ratios rather than a method itself because there are many variants of it [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. When this concept was first used to determine the reactivity ratios, it was admitted that the measurement errors are only in one of the variables [ 11 ]; later, the concept used the analysis of errors in both variables [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ].…”

“…The Error in Variable Method (EVM) is a concept for calculating reactivity ratios rather than a method itself because there are many variants of it [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. When this concept was first used to determine the reactivity ratios, it was admitted that the measurement errors are only in one of the variables [ 11 ]; later, the concept used the analysis of errors in both variables [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. The EVM variant proposed by van der Meer et al [ 12 ], Patino-Leal et al [ 13 ], and Hautus et al [ 14 ] uses the mathematical model given by Equation (3); Yamada et al [ 10 ] use Equation 5 as a mathematical model and Kazemi [ 17 ] use the Meyer–Lowry model (Equation (6)).…”

Modern aspects of quantitative theory of free-radical copolymerization

“…Numerous reports are available [19,[229][230][231][232][233][234][235][236][237][238][239][240][241][242][243][244][245][246][247][248] on the development and analysis of the different procedures of estimating the reactivity ratio from the experimental data obtained over a wide range of conversions. These procedures employ different modifications of the integrated form of the copolymerization equation.…”