Summary: A new error‐in‐variables method was developed to estimate the reactivity ratios in copolymerization systems. It brings the power of automatic, continuous, on‐line monitoring of polymerization (ACOMP) to copolymerization calculations. In ACOMP systems, monomer and polymer concentrations are measured by the monitoring of two independent properties of the system. The reactivity ratios are found by taking into account errors in the monomer concentrations determined from measurements and from calibration of the instruments. All the error sources are taken into account according to the error‐in‐variables method, and their effects are reflected in determining the confidence intervals of the reactivity ratios by the usual error propagation technique.
Summary: In copolymerization systems with implicit penultimate effect, there are two radical reactivity ratios, sa and sb, which influence the reaction kinetics in addition to the monomer reactivity ratios, ra and rb, which govern the copolymer composition. Here, an error in variables method has been developed to determine sa and sb. It is based on continuous on‐line monitoring of the polymerization process, where monomer and polymer concentrations are measured through the monitoring of two independent properties of the system. The ratios and the corresponding χ2 values were found by taking into account errors emanating from measurements and from calibration of the instruments. It is shown that the kinetic data allows both ratios to be found if both monomer reactivity ratios are less than one. If the system is near ideality (rarb ≅ 1) or if both reactivities are greater than one, only an average radical reactivity ratio, $\overline s$, can be reliably determined.
Reaction kinetics and composition of 4-vinylbenzenesulfonic acid sodium salt (VB)-acrylamide (Aam) copolymerization in 0.1M NaCl solution are investigated. Data obtained by the automatic continuous monitoring of copolymerization system, up to 80% conversion, are analyzed by an ''error-in-variables method'' developed for obtaining the reactivity ratios by on-line monitoring. Monomer reactivity ratios are found as r Aam ¼ 0.085 6 0.020, r VB ¼ 2.0 6 0.33. Although the terminal model describes the composition data well, it is seen to be inconsistent with the reaction rates. This discrepancy is attributed to implicit penultimate effects and using the recently developed calculation method, effective radical reactivity ratios are found as s VB ¼ 0.26 and s Aam ¼ 0.027, and both composition and rate data fit the implicit penultimate model extremely well. On-line monitored data showed that in the reactions where the VB was completely consumed, the subsequent Aam homopolymerization was very rapid; thus, the reaction showed definitely two rate regimes, before and after VB depletion. Acrylamide take up rate also showed these two rate regimes. We conclude that low conversion results can be misleading and reactions must be monitored up to a high conversion for a robust control of composition and reaction kinetics.
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