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Non‐uniqueness in determination of terminal and penultimate model reactivity ratios in the styrene‐methyl methacrylate free‐radical copolymerization system
Author(s) -
Kaim Andrzej,
Oracz Paweł
Publication year - 1997
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.1997.040060216
Subject(s) - reactivity (psychology) , copolymer , styrene , methyl methacrylate , simplex , uniqueness , chemistry , polymer chemistry , covariance , methacrylate , analytical chemistry (journal) , mathematics , combinatorics , mathematical analysis , statistics , chromatography , organic chemistry , polymer , medicine , alternative medicine , pathology
The terminal and penultimate model reactivity ratios in the free‐radical copolymerization of styrene and methyl methacrylate in bulk at 40°C were calculated by means of the simplex and scanning methods. Calculations showed that for the terminal model r 1 and r 2 vary in comparatively narrow ranges of 0.548–0.552 and 0.480–0.483, respectively. For the penultimate model, the most accurate reactivity ratios calculated by the simplex method, which were r 11 = 0.727, r 22 = 0.490, r 21 = 2.890, r 12 = 4.583, are surrounded with sets of reactivity ratio values of equal accuracy. The ranges of variation were found to be 0.711–0.746, 0.487–0.492, 2.810–2.970 and 4.213–5.049, respectively. Numerical values of the penultimate r ‐parameters calculated with the simplex method depend, due to the structure of the multidimensional space ( r 11 , r 22 , r 21 , r 12 , σ), on the initial guess for the r ‐parameters. Use of the covariance matrix for the estimation of the indetermination ranges is discussed.