A Linearization Procedure for the Determination of the Radical Reactivity Ratios in Restricted Penultimate Copolymerization Systems

Abstract

A newly developed method for the determination of the radical reactivity ratios is presented. Two main equations are used and the parameters can be calculated from the ordinate and the slope of the linearization plots. Both equations yield identical values when applied to synthetic data which conforms to the ideal situation of no error in the input data. As experimental data are always subject to some kind of error, a sensitivity analysis was carried out which took into account a relatively pronounced error in the monomer reactivity ratios. It turned out that the new linearization method may even be indicative of the quality of the input data under favorable conditions.magnified image

A Linearization Procedure for Determining Radical Reactivity Ratios in Restricted Penultimate Copolymerization Systems, 2

“…Before this, however, we will give a short description of the restricted penultimate model and our linearization method as published recently. [8] Theoretical Background All rate constants that appear in the following discussion refer to propagation. Accordingly, the lowercase index 'p' commonly used to indicate propagation constants is omitted.…”

“…Only those quantities that depend on the absolute values of individual rate constants such as the rate of copolymerization or the apparent rate constant of propagation k p for a given comonomer composition [4,7,8] ( f 1 and f 2 denoting the mole fractions of monomers 1 and 2)…”

“…As y 1 , y 2 , z 1 , and z 2 are different versions of a common least squares problem that result from rearrangements only, methods z 1 and z 2 clearly fail in the case of r 1 ¼ 1/r 2 , in the same way as do y 1 and y 2 . [8] In Figure 1 the applicability of all four methods is demonstrated by use of synthetic data (r 1 ¼ 0.5, r 2 ¼ 0.5, k 111 ¼ 150 L Á mol À1 Á s À1 , k 222 ¼ 450 L Á mol À1 Á s À1 , s 1 ¼ 0.4, and s 2 ¼ 0.6). In Figure 1a the input data (k p vs. f 1 ) are shown.…”

“…For convenience and completeness Table 1 also includes the results already published for the much investigated system S-MMA given as an example in our former communication. [8] All copolymerizations carried out in the presence of acrylates have the common feature that k 222 is at least one order of magnitude larger than k 111 . In some cases k 222 was not measured but only estimated [20,23] (values written in parentheses) or calculated by published Arrhenius equations [21] (values written in italics).…”

“…This system with r 1 Á r 2 close to 1 appears to be a rare case where the method does not work as outlined in the preceding contribution. [8] j) p-Methoxystyrene-Methyl Methacrylate (MOS-MMA) [19] This system resembles the system S-MMA in many respects. The original data for s 1 are well reproduced by all the four linearization methods, the agreement being slightly less satisfactory for s 2 .…”