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An Error in Variables Method for Determining the Implicit Penultimate Copolymerization Ratios by On‐Line Monitoring of Reactions
Author(s) -
Sünbül Didem,
Giz Ahmet T.
Publication year - 2006
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.200500083
Subject(s) - reactivity (psychology) , monomer , chemistry , copolymer , line (geometry) , kinetics , reaction rate constant , thermodynamics , analytical chemistry (journal) , polymer , mathematics , organic chemistry , physics , geometry , pathology , quantum mechanics , medicine , alternative medicine
Summary: In copolymerization systems with implicit penultimate effect, there are two radical reactivity ratios, s a and s b , which influence the reaction kinetics in addition to the monomer reactivity ratios, r a and r b , which govern the copolymer composition. Here, an error in variables method has been developed to determine s a and s b . 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 χ 2 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 ( r a r b ≅ 1) or if both reactivities are greater than one, only an average radical reactivity ratio, $\overline s$ , can be reliably determined.The 2 σ confidence contours for the 3 individual experiments. The reactivity ratios are r a = 0.5, r b = 0.2, s a = 0.3, s b = 0.4. For clarity the contours are plotted as functions of 1/ s a and 1/ s b .