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A Generalized Least Square Model for the Determination of Monomer Reactivity Ratios in Free Radical Copolymerization Systems
Author(s) -
Habibi Ali,
VasheghaniFarahani Ebrahim,
Semsarzadeh Mohamad A.,
Sadaghiani Kambiz
Publication year - 2003
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.200390014
Subject(s) - reactivity (psychology) , copolymer , mathematics , monomer , methacrylate , estimator , mean squared error , chemistry , statistics , polymer chemistry , organic chemistry , polymer , medicine , alternative medicine , pathology
Abstract The reliable estimation of monomer reactivity ratios is a key problem in the development of process models, and, thus, is an important issue in both process design and control. Copolymers of isobutyl methacrylate (i‐BMA), and lauryl methacrylate (LMA) were prepared by free radical bulk copolymerization at 70 °C using 2,2′–azobisisobutyronitrile (AIBN) as initiator. The monomer reactivity ratios as well as the 95% confidence intervals were calculated from Fineman‐Ross, Ezrielev‐Brokhina‐Roskin, Kelen & Tudos, extended Kelen & Tudos and a linear iterative method proposed by Mao and Huglin. The estimation process was performed by applying nonlinear techniques based on Marquardt optimization, “ordinary least square” (OLS) and “generalized least square” (GLS) approaches and the results were compared with each other. The novel GLS estimator program developed during this study was employed to ascertain the shape of the copolymer composition curve and good agreement between experimental and calculated copolymer composition was obtained. Also, both real and simulated data was presented, which show GLS method is a statistically valid technique for estimating reactivity ratios by accounting response error structure. This new estimation method handles regression models with error terms that are heteroskedastic or serially correlated, or both.95% joint confidence interval for reactivity ratios from “NLLS” analysis.