Kelen-Tudos equation

The composition of the copolymer was determined by either NMR analysis at 90 MHz according to the equations derived by Mochel (21) or by infrared. (22) The agreement of these methods was 2% when applied to copolymer taken to 100% conversion. The reactivity ratios were calculated according to the Mayo-Lewis Plot (13,15), the Fineman-Ross Method (14), or by the Kelen-Tudos equation.(16,17,18) The statistical variations recently noted by 0 Driscoll (23), were also considered. 

Even with the Kelen Tudos refinement there are statistical limitations inherent in the linearization method. The independent variable in any form of the linear equation is not really independent, while the dependent variable does not have a constant variance [O Driscoll and Reilly, 1987]. The most statistically sound method of analyzing composition data is the nonlinear method, which involves plotting the instantaneous copolymer composition versus comonomer feed composition for various feeds and then determining which theoretical plot best fits the data by trial-and-error selection of r and values. The pros and cons of the two methods have been discussed in detail, along with approaches for the best choice of feed compositions to maximize the accuracy of the r and r% values [Bataille and Bourassa, 1989 Habibi et al., 2003 Hautus et al., 1984 Kelen and Tudos, 1990 Leicht and Fuhrmann, 1983 Monett et al., 2002 Tudos and Kelen, 1981]. 

Even with the Kelen-Tudos refinement there are statistical limitations inherent in the linearization method. It has been shown [18] that the independent variable in any form of the linear equation is not really independent while the dependent variable does not have a constant variance. The most statistically sound method of analyzing the experimental composition data is the nonlinear method which involves direct curve fitting to the copolymer composition equation. 

Under the condition that the reaction capability is only affected by the nature of the last monomer unit of the growing polymer chain end (terminal model, Bernoulli statistics), the copolymerization equation can be transformed according to Kelen and Tudos ... 

Typically, the kinetics of ring-opening copolymerization is analyzed in terms of the four equations, set with all reactions being irreversible. The aim of a such an analysis is to determine the reactivity ratios ri = ku/ku and r2 = k22/k2i by means of the approaches elaborated by Mayo and Lewis or Finneman and Ross, or perhaps by Kelen and Tudos. Provided that the homopolymerization rate constants (fen and fe22> are known from the homopolymerization studies, under otherwise identical conditions-and assuming that the same values are valid in copolymerization (this is not necessarily tme for ionic or coordination ROP)-the crosspropagation rate constants (fen and fe2i) can eventually be determined. 

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