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>3.3.co;2-h

Cited by 16 publications

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“…This prompted us to implement a less biased method, the "visualization of the sum of squared residuals space" (VSSRS), a nonlinear method 53,54 developed by Van den Brink et al This VSSRS method not only allows for an estimate of the reactivity ratios at high conversion, but also takes into account errors both on the monomer conversion and the co-monomer ratios, thus providing Page 12 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 unbiased estimates of the reactivity ratios as well as joint confidence regions. Data related to monomer conversion, copolymer composition (F) and co-monomer ratio (f) were fitted to the integrated form of the Mayo-Lewis copolymer composition equation, (1):…”

Section: Resultsmentioning

confidence: 99%

“…In particular, reactivity ratios of co-monomers have been determined, using both the Kelen-Tüdős linear method and a nonlinear method referred to as "the visualization of the sum of squared residuals space" (VSSRS). 53,54 The P(LA-stat-CL) statistical copolymers are characterized by combined analyses, including 1 H, 13 C and DOSY NMR, Page 4 of 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 DSC and SEC. The controlled character of this BA-OROcP process is further exploited to achieve PLA-b-P(LA-stat-CL)-b-PLA triblock copolymers, by sequential ROcP-mediated synthesis.…”

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confidence: 99%

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Bulk Organocatalytic Synthetic Access to Statistical Copolyesters from l-Lactide and ε-Caprolactone Using Benzoic Acid

et al. 2019

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The development of synthetic strategies to produce statistical copolymers based on L-lactide (L-LA) and ε-caprolactone (CL), denoted as P(LA-stat-CL), remains highly challenging in polymer chemistry. This is due to the differing reactivity of the two monomers during their ring-opening copolymerization (ROcP). Yet, P(LA-stat-CL) materials are highly sought-after as they combine the properties of both polylactide PLA and poly(ε-caprolactone) (PCL). Here, benzoic acid (BA), a naturally occurring, cheap, readily recyclable and thermally stable weak acid, is shown to trigger the organocatalyzed ring-opening copolymerization (OROcP) of L-LA and CL under solvent-free conditions at 155 °C, in presence of various alcohols as initiators, with good control over molar masses and dispersities (1.11 <Đ< 1.35) of the resulting copolyesters. Various compositions can be achieved, and the formation of statistical compounds is shown through characterization by 1 H, 13 C and DOSY-NMR spectroscopies and by DSC, as well as through the determination of reactivity ratios (r LA = 0.86, r CL = 0.86), using the visualization of the sum of squared residuals space method. Furthermore, this BA-OROcP process can be exploited to access metal-free PLAb-P(LA-stat-CL)-b-PLA triblock copolymers, using a diol as initiator. Finally, residual traces of BA remaining in P(LA-stat-CL) copolymers (< 0.125 mol%) do not show any cytotoxicity towards hepatocyte-like HepaRG cells, demonstrating the safety of this organic catalyst.As biodegradable, nontoxic and biocompatible polymers, polylactide (PLA) and poly(εcaprolactone) (PCL) can be attractive biosourced surrogates for petroleum-based polymers. 1-4 Both PLA and PCL have been intensively investigated in applications ranging from pharmaceutics to packaging and electronics. 4-7 Yet, both PLA and PCL show some limitations in these applications.For instance, PLA is brittle, exhibits a poor elasticity, 8 a low thermal stability and a modest permeability to drugs. PCL has higher thermal stability and elasticity than PLA, with a glass transition temperature (T g ) around -60 °C vs. 45 -65 °C for PLA, 9,3,10 but suffers from poor mechanical properties. PCL has also a higher permeability to drugs 11 and a half time in vivo of 1year, 12 vs. a few weeks for PLA. 13 As a result, statistical copolymers of lactide (LA) and caprolactone (CL), i.e. P(LA-stat-CL) aliphatic copolyesters, are highly sought-after materials as they combine the strengths and minimize the weaknesses of both homopolymers. P(LA-stat-CL)s have thus attracted a great deal of attention in the biomedical and pharmaceutical fields, 14-18 and as compatibilizers for PLA/PCL blends. 19 The precision synthesis of P(LA-stat-CL) copolymers is still particularly challenging whether organometallic 20 or organic 21-30 catalysts are used. This is due to the highly differing reactivity of the two monomers during ring-opening copolymerization (ROcP). LA is typically incorporated first, although CL gives faster rates than LA in homopolymerization reactions. [21][...

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Bulk Organocatalytic Synthetic Access to Statistical Copolyesters from l-Lactide and ε-Caprolactone Using Benzoic Acid

et al. 2019

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“…5) can be accounted for by the varying initiator concentrations. However, Figure 6 shows that the three copolymerizations are identical, because all GC data are well fitted,29 using only one pair of reactivity ratios (r Sty = 0.80 and r BA = 0.23). In other words, reactions C1–C3 are going through the same states in terms of composition, although the time at which a certain state is reached differs from reaction to reaction.…”

Section: Resultsmentioning

confidence: 96%

Measurement of partial conversions during the solution copolymerization of styrene and butyl acrylate using on-line raman spectroscopy

Van

Brink

Hansen

et al. 2000

J. Appl. Polym. Sci.

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The copolymerization of styrene and n‐butyl acrylate in dioxane was monitored by on‐line Raman spectroscopy. The calculation of the individual monomer concentrations on the basis of the individual vinyl peaks is not straightforward for this system, as these bands are overlapping in the Raman spectrum. To tackle this problem, univariate and multivariate approaches were followed to obtain monomer concentrations and the results were validated by reference gas chromatography data. In the univariate analysis, linear relations between various monomer peaks were used to calculate monomer concentrations from the Raman data. In principal component analysis, the main variation in the spectra could be ascribed to conversion of monomer. Furthermore, principal component analysis pointed out that the second‐largest effect in the spectra could be attributed to experiment‐to‐experiment variation, probably attributable to instrumental factors. In the multivariate partial least squares regression approach, single factor models were used to calculate monomer concentrations. Both the univariate and the partial least squares regression approaches proved successful in calculating the individual monomer concentrations, showing very good agreement with off‐line gas chromatography data. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 426–436, 2001

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“…Knowledge of the monomer reactivity ratios in a copolymerization represents a fundamental aspect for the synthesis of copolymers because these parameters provide valuable information related to the compositional drift at different stages of the reaction. Under the assumption that the terminal model describes the copolymerization kinetics, there are several methodologies to estimate the reactivity ratios, using the differential or integrated form of the copolymerization equation . The Tidwell–Mortimer (T–M) method is widely used due to its simplicity, but its validity is limited to low monomer conversion.…”

Section: Introductionmentioning

confidence: 99%

“…These latter methods, in many situations, may be regarded as inadequate from the statistical point of view because they are not able to provide reliable error estimates . On the other hand, as discussed by van Herk and co‐workers, the error in variables model (EVM) or the nonlinear least square (NLLS) method applied to the integrated form of the copolymerization equation provide both good estimates and appropriate confidence intervals without being limited to low monomer conversion. Furthermore, the NLLS method is preferred because of its rather simple implementation, where the integrated copolymerization equation is fitted to conversion, copolymer composition, and monomer fraction using a conventional spreadsheet in the Microsoft Excel Software .…”

Section: Introductionmentioning

confidence: 99%

Kinetic and Copolymer Composition Investigations of the Free Radical Copolymerization of 1‐Octene with Glycidyl Methacrylate

Rosales‐Guzmán

Pérez‐Camacho²,

Torres-Lubián³

et al. 2018

Macro Chemistry & Physics

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Kinetic and copolymer composition investigations of the free radical copolymerization of 1‐octene with glycidyl methacrylate are reported. The chemical structure of the obtained copolymers is elucidated by 1H, 13C, heteronuclear single quantum coherence nuclear magnetic resonance (NMR) and infrared spectroscopies. 1H NMR measurements indicate that a maximum statistical incorporation of 1‐octene in the copolymer chain of 32 mol% is obtained when 90 mol% of this comonomer is used in the initial monomer feed of the copolymerization reaction. Furthermore, the reactivity ratios of this comonomer system are estimated using the obtained experimental data, which are fitted to the integral form of the copolymerization equation utilizing a nonlinear least squares approach. To the best of knowledge, this is the first report on the reactivity ratios of this specific comonomer system. To evaluate the potential of the obtained materials as dispersants, the effect of the polymer concentration on the dispersion of copper nanopowders in organic solvents is studied for a copolymer with a 1‐octene composition of 25 mol%.

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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 16 publications

References 0 publications

Bulk Organocatalytic Synthetic Access to Statistical Copolyesters from l-Lactide and ε-Caprolactone Using Benzoic Acid

Bulk Organocatalytic Synthetic Access to Statistical Copolyesters from l-Lactide and ε-Caprolactone Using Benzoic Acid

Measurement of partial conversions during the solution copolymerization of styrene and butyl acrylate using on-line raman spectroscopy

Kinetic and Copolymer Composition Investigations of the Free Radical Copolymerization of 1‐Octene with Glycidyl Methacrylate

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