Nonlinear regression by visualization of the sum of residual space applied to the integrated copolymerization equation with errors in all variables. I. Introduction of the model, simulations and design of experiments

Brink, M.; Herk, Alex M. van; German, Anton L.

doi:10.1002/(sici)1099-0518(19991015)37:20<3793::aid-pola8>3.0.co;2-q

Cited by 38 publications

(25 citation statements)

References 31 publications

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“…The utilized experimental technique allowed reliable and comprehensive kinetic data ( i.e. , evolution in time of the conversion of the monomers, and molar mass and dispersity of the formed polymers) to be collected in a short period of time; this kinetic information was used to estimate the reactivity ratios of the co‐monomer system using a computer program1 based on the visualization of the sum of residual space method developed by van Herk and co‐workers 21. The obtained reactivity ratios of the system are in good agreement with literature values 22.…”

Section: Introductionsupporting

confidence: 67%

“…The kinetic information obtained from the high‐throughput experiment was used to determine the reactivity ratios of the monomers in the copolymerization system. Point estimates and joint confidence intervals for the reactivity ratios were determined using the visualization of the sum of squares method developed by van Herk and co‐workers 21. The integrated copolymerization equation was fitted to conversion, monomer fraction and copolymer composition data, assuming non‐negligible errors in all variables.…”

Section: Resultsmentioning

confidence: 99%

“…The integrated copolymerization equation was fitted to conversion, monomer fraction and copolymer composition data, assuming non‐negligible errors in all variables. As noted before,1, 21 this method is computationally inefficient but simple to implement in the conventional Microsoft Excel 2003 software 1. The instantaneous copolymer composition at various conversions was determined from the individual monomer to polymer conversions estimated by 1 H‐NMR, which, in general, showed that MA was consumed much more rapidly than VAc.…”

Section: Resultsmentioning

confidence: 99%

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High‐Throughput Method for RAFT Kinetic Investigations and Estimation of Reactivity Ratios in Copolymerization Systems

Guerrero‐Sánchez¹,

Harrisson²,

Keddie³

2013

Macromolecular Symposia

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A new high‐throughput experimental technique, namely automated parallel freeze‐evacuate‐thaw degassing method, is applied for the facile, rapid and reliable determination of reactivity ratios in copolymerization systems. The approach allowed carrying out a detailed kinetic investigation of the reversible addition‐fragmentation chain transfer (RAFT) copolymerization of methyl acrylate (MA) with vinyl acetate (VAc) monomers in 2‐methyl‐2‐butanol at 60 °C. Thereafter, the reactivity ratios of this copolymerization system were estimated utilizing the obtained kinetic data and a computer program based on the visualization of the sum of residual space method. The obtained reactivity ratios of the system (rMA = 8.2 and rVAc = 0.17) are comparable to values previously reported in the literature, which demonstrates the utility of this approach.

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Section: Introductionsupporting

confidence: 67%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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High‐Throughput Method for RAFT Kinetic Investigations and Estimation of Reactivity Ratios in Copolymerization Systems

Guerrero‐Sánchez¹,

Harrisson²,

Keddie³

2013

Macromolecular Symposia

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“…The usefulness of this method was confirmed previously. 18,25 The appropriate calculations were performed with help of computer program COPOINT, which was written specifically for this type of calculation. 26 For applied numerical integration technique calculations, the least-squares model was used.…”

Section: Calculation Of Reactivity Ratiosmentioning

confidence: 99%

Obtaining aliphatic branched polycarbonates via simple copolymerization of trimethylene carbonate with cyclic carbonate containing pendant ester groups

Pastusiak

Jaworska

Kawalec

et al. 2016

J. Polym. Sci. Part A: Polym. Chem.

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Different possibilities for obtaining branched, functional carbonate copolymers are presented in this study. Copolymers were synthesized according to the ring‐opening polymerization (ROP) of the cyclic carbonate monomers, containing pendant ester groups. As an example, we chose copolymerization of ethyl 5‐methyl‐2‐oxo‐1,3‐dioxane‐5‐carboxylate (MTC‐Et) with trimethylene carbonate (TMC), using zinc (II) and lanthanum (III) acetylacetonates as ROP initiators. The transesterification processes of ester groups in pendant, short chains, appearing during conducted copolymerization, led to the establishment of two different fractions: first‐branched and high molecular weight fraction and second‐linear and low molecular weight. The content of this high‐molecular‐weight fraction increased with both: the amount of MTC‐Et in started reaction mixture and the time of conducted copolymerization. Reactivity constants in studied reaction were determined. It was possible to obtain the copolymer fraction (ca. 30%) with molecular weight of up to a million g/mol, with a highly branched chain microstructure using lanthanum (III) acetylacetonate as initiator. Conclusions were based on detailed NMR analysis, determining microstructure of the copolymer chains and additionally on GPC and DSC measurement. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017, 55, 808–819

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“…The conversion of the two monomers versus time for the two comonomer feeds is represented in Figures S8 and S9 in SI. Then the reactivity ratios were determined by fitting the integrated form of the copolymer composition equation to the monomer feed composition versus conversion data using the visualization of the sum of squares method developed by van den Brink et al, 23 assuming non-negligible errors in both variables. This procedure gave a point estimate of 1.34 for r VTFBu and 1.16 for r VAc , with a 95% joint confidence region spanning the range of 1.21−1.48 for r VTFBu and 1.08−1.26 for r VAc (see Figure S10).…”

mentioning

confidence: 99%

Enhanced Solubility of Polyvinyl Esters in scCO₂by Means of Vinyl Trifluorobutyrate Monomer

Coutelier

Harrisson

et al. 2014

ACS Macro Lett.

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The novel monomer, vinyl trifluorobutyrate (VTFBu), when polymerized in a controlled fashion by RAFT/MADIX polymerization with a xanthate transfer agent, yields poly(vinyl ester)s with improved solubility in supercritical carbon dioxide. The thermodynamic parameters controlling the solubility of VTFBu/vinyl acetate statistical copolymers are discussed based on ab initio calculations, glass transition temperatures of the copolymers, and surface tension measurements. The enhanced solubility of this new class of CO 2 -philic polymer combined with its good chemical stability render it attractive for the preparation of next-generation macromolecular surfactants for the formation of water−scCO 2 emulsions. T he replacement of conventional organic solvents has been identified as a key step in reducing the environmental cost of chemical synthesis, processing, and separations. 1 Supercritical carbon dioxide (scCO 2 ) is a promising environmentally benign solvent that provides low flammability, toxicity, cost, reactivity at an accessible critical temperature, and pressure (31.1°C, 73 bar). For most compounds, however, scCO 2 is a poor solvent because of its very low dielectric constant and polarizability: only relatively nonpolar low molecular weight compounds and a few fluorinated or silicone polymers show significant solubility. This drawback can be overcome by the use of water-in-scCO 2 or scCO 2 -in-water emulsions or microemulsions, which allow high concentrations of polar, ionic, and nonpolar molecules to be solubilized within the dispersed and continuous phases. Surfactants are necessary to stabilize these emulsions. For this application, amphiphilic block copolymers are of interest as they offer better anchoring and steric stabilization at interfaces than low molar mass surfactants.While fluorinated polyacrylates, perfluoroalkylethers and polysiloxanes are the current CO 2 -philic materials of choice, 2 poly(vinyl ester)s combine moderate CO 2 -philicity with favorable price and toxicity. Low molecular weight (M n = 2060 g/mol) poly(vinyl acetate) (PVAc) is soluble at 5 wt % in CO 2 at 374 bar and 25°C. The cloud point pressure and solubility are strongly dependent on the chain length, however, which limits the usefulness of higher molecular-weight PVAc. 3,4 Different strategies have been used to enhance poly(vinyl ester) solubility, such as modification of the chain end with a CO 2 -philic fluorinated segment 4 or copolymerization of vinyl acetate (VAc) with a comonomer. In the latter strategy, incorporation of repulsive or bulky pendant groups increases CO 2 solubility by enhancing entropic contributions and decreasing polymer− polymer interactions. A large palette of comonomers are available by varying the vinyl ester group, allowing the incorporation of linear aliphatic or branched structures 5−7 and fluorinated moieties. 8−10 Thus, the cloud point pressure (P c ) of a 0.2 wt % solution of PVAc (M n = 4000 g/mol; P c = 280 bar at 40°C) falls dramatically to 222 or 177 bar for statistical copolymers containing 1...

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Nonlinear regression by visualization of the sum of residual space applied to the integrated copolymerization equation with errors in all variables. I. Introduction of the model, simulations and design of experiments

Cited by 38 publications

References 31 publications

High‐Throughput Method for RAFT Kinetic Investigations and Estimation of Reactivity Ratios in Copolymerization Systems

High‐Throughput Method for RAFT Kinetic Investigations and Estimation of Reactivity Ratios in Copolymerization Systems

Obtaining aliphatic branched polycarbonates via simple copolymerization of trimethylene carbonate with cyclic carbonate containing pendant ester groups

Enhanced Solubility of Polyvinyl Esters in scCO₂by Means of Vinyl Trifluorobutyrate Monomer

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Nonlinear regression by visualization of the sum of residual space applied to the integrated copolymerization equation with errors in all variables. I. Introduction of the model, simulations and design of experiments

Cited by 38 publications

References 31 publications

High‐Throughput Method for RAFT Kinetic Investigations and Estimation of Reactivity Ratios in Copolymerization Systems

High‐Throughput Method for RAFT Kinetic Investigations and Estimation of Reactivity Ratios in Copolymerization Systems

Obtaining aliphatic branched polycarbonates via simple copolymerization of trimethylene carbonate with cyclic carbonate containing pendant ester groups

Enhanced Solubility of Polyvinyl Esters in scCO2by Means of Vinyl Trifluorobutyrate Monomer

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Enhanced Solubility of Polyvinyl Esters in scCO₂by Means of Vinyl Trifluorobutyrate Monomer