A microcomputer program for estimation of copolymerization reactivity ratios

Dubé, Marc A.; Sanayei, R. Amin; Penlidis, Alexander; O’Driscoll, K. F.; Reilly, Park M.

doi:10.1002/pola.1991.080290512

Cited by 246 publications

(199 citation statements)

References 22 publications

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“…An option is to transpose the error in xi to an error in y ; by using the derivative of the function to x and apply the nonlinear least squares method5). The Error-in-Variables-Model", 12) is dealing with the errors in all variables in a correct way. This model forms the basis of an often used microcomputer program (RREVM) to calculate reactivity ratios12).…”

Section: Finding the Optimal Parameter Valuesmentioning

confidence: 99%

Nonlinear least squares fitting applied to copolymerization modeling

Herk

Dröge

1997

Macro Theory & Simulations

113

116

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SUMMARYThe choice of the statistical method to determine the reactivity ratios in copolymerization modeling is shown to be very important. Problems in literature, as well as possible pitfalls when using available statistical programs that are in itself correct are pointed out. These problems mainly involve (knowledge of) the error structure, as the error structure determines the weighting scheme of the data points in fitting procedures. A simple, robust, statistically correct non-linear least squares (NLLS) method is reintroduced which is based on the visualization of the sum of squares of residuals in the so-called sum of squares space (SSS). The advantages of this method include the fact that the method is easy to understand and can be implemented in simple computer programs, as well as the fact that the method allows important aspects of the error structure to be incorporated. Furthermore, in the SSS the joint confidence interval (JCI) with exact shape can be constructed. The exact shape of the JCI is not always ellipsoidal and following a normal distribution, depending on the linearity of the fitted equations. This can sometimes lead to wrong conclusions.

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Section: Finding the Optimal Parameter Valuesmentioning

confidence: 99%

Nonlinear least squares fitting applied to copolymerization modeling

Herk

Dröge

1997

Macro Theory & Simulations

113

116

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“…This initial estimate of reactivity ratios, along with the copolymer composition data, were used for the calculation of reactivity ratios by the nonlinear least-squares EVM 28 method using the RREVM computer program. 29 The errors in determining the monomer composition in the feed and copolymer were estimated to be 1 and 3%, respectively. The values of the reactivity ratios calculated from the KT and EVM methods were r V ϭ 0.09 Ϯ 0.03, r M ϭ 0.41 Ϯ 0.09 and r V ϭ 0.09, r M ϭ 0.44, respectively.…”

Section: Reactivity Ratio Determinationmentioning

confidence: 99%

“…In this article, we report the reactivity ratios of the comonomers using the Kelen-Tudos (KT) 27 and nonlinear least-squares error-in-variable model (EVM) methods 28 via the RREVM computer program. 29 The complete assignment of complex and overlapped 1 H and 13 C{ 1 H} NMR spectra of V/M copolymers in terms of compositional and configurational sequences was done with DEPT and 2D HSQC NMR experiments. The various proton-proton couplings were confirmed by the 2D TOCSY NMR spectrum.…”

Section: Introductionmentioning

confidence: 99%

One‐ and two‐dimensional NMR characterization of N‐vinyl‐2‐pyrrolidone/methyl acrylate copolymers

Brar

Kumar

2002

J. Polym. Sci. A Polym. Chem.

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N-vinyl-2-pyrrolidone/methyl acrylate (V/M) copolymers were prepared by free-radical bulk polymerization using benzoyl peroxide as an initiator. The copolymer composition of these copolymers was calculated from 1 H NMR spectra. The radical reactivity ratios for N-vinyl-2-pyrrolidone (V) and methyl acrylate (M) were r V ϭ 0.09, r M ϭ 0.44. These reactivity ratios for the copolymerization of V and M were determined using the Kelen-Tudos and nonlinear least-squares error-in-variable methods. The 13 C{ 1 H} and 1 H NMR spectra of these copolymers overlapped and were complex. The complete spectral assignment of the 13 C and 1 H NMR spectra were done with distortionless enhancement by polarization transfer and two dimensional 13 C-1 H heteronuclear single quantum correlation spectroscopic experiments. The two-dimensional 1 H-1 H homonuclear total correlation spectroscopic NMR spectrum showed the various bond interactions, thus inferring the possible structure of the copolymers.

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“…The determination of copolymer composition and reactivity ratios of the monomers is important in evaluating the specific application of the copolymer [6]. The monomer reactivity ratios determined by conventional linearization methods are not always accurate and several non-linear methods have been attempted to determine their value [7][8][9]. 1 H-NMR spectroscopic analysis has been established as a powerful tool for the estimation of copolymer composition [10,11].…”

Section: Introductionmentioning

confidence: 99%

Copolymers of N-cyclohexylacrylamide and n-butyl acrylate: synthesis, characterization, monomer reactivity ratios and mean sequence length

Pazhanisamy¹,

Reddy²

2007

Express Polym. Lett.

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Abstract. Copolymerization of N-cyclohexylacrylamide (NCHA) and n-butyl acrylate (BA) was carried out in dimethylformamide at 55±1°C using azobisisobutyronitrile as a free radical initiator. The copolymers were characterized by 1 H-NMR spectroscopy and the copolymer compositions were determined by 1 H-NMR analysis. The reactivity ratios of the monomers were determined by both linear and non-linear methods. The reactivity ratios of monomers determined using linear methods like Fineman-Ross (r1 = 0.37 and r2 = 1.77 ), Kelen-Tudos (r1 = 0.38 and r2 = 1.77), ext. Kelen-Tudos (r1 = 0.37 and r2 = 1.75) Yezrieler-Brokhina-Roskin (r1 = 0.37 and r2 = 1.77) and non-linear methods like Tidwell-Mortimer (r1 = 0.37 and r2 = 1.76), ProCop (r1 = 0.36 and r2 = 1.82). The Q and e values for NCHA are 0.67 and 0.68 respectively. Mean sequence lengths of copolymers are estimated from r1 and r2 values. It shows that the BA units increases in a linear fashion in the polymer chain as the concentration of BA increases in the monomer feed.

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A microcomputer program for estimation of copolymerization reactivity ratios

Cited by 246 publications

References 22 publications

Nonlinear least squares fitting applied to copolymerization modeling

Nonlinear least squares fitting applied to copolymerization modeling

One‐ and two‐dimensional NMR characterization of N‐vinyl‐2‐pyrrolidone/methyl acrylate copolymers

Copolymers of N-cyclohexylacrylamide and n-butyl acrylate: synthesis, characterization, monomer reactivity ratios and mean sequence length

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