Techniques for the Analysis of Crosslinked Polymers

Harrison, Daniel J. P.; Yates, W. Ross; Johnson, Julian F.

doi:10.1080/07366578508081963

Cited by 52 publications

(6 citation statements)

References 137 publications

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“…There is experimental evidence of polysulfidic structures obtained with costly IR, UV, ESR and Raman characterizations [8,9] or with chemical methods [10], as well as solid state 13 C nuclear magnetic resonances (NMRs) [11][12][13]. It has been shown that for EPDM, the polysulfidic structures are consistent with predictions based on model compounds and the presence of three different allylic positions in the repeating unit of NR [11].…”

Section: Introductionmentioning

confidence: 82%

Iterative robust numerical procedure for the determination of kinetic constants in Han’s model for NR cured with sulphur

Milani¹

2015

J Math Chem

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A closed form procedure to determine kinetic constants for NR vulcanized with sulphur is presented. The kinetic scheme originally proposed by Han et al. (Polymer (Korea) 22:223–230, 1998) and further modified by Milani et al. (Polym Test 32:1052–1063, 2013) is adopted as starting point to deduce a closed form expression for rubber curing degree. Rheometer experimental data collected at different temperatures are used to tune model parameters. After the normalization of the rheometer curves and the exclusion of induction period from calculations, the model requires the estimation of three kinetic constants, two of them describing incipient curing and stable crosslinks formations, the last reproducing reversion phenomenon. Whilst such constants are almost always determined by least-squares best fitting, here a numerical iterative procedure—much more stable and efficient from a computational standpoint—is proposed. The approach requires as input parameters only the degree of vulcanization at infinite (i.e. at the end of vulcanization), the instant where the maximum torque is reached and initial rate of vulcanization. The condition that the numerical curve reaches a maximum at a given time translates mathematically into a non-linear equation in two of the kinetic constants, which are determined iteratively in the paper. The numerical initial vulcanization rate is tuned in such a way to globally minimize the absolute error between numerical and experimental curves. The main capability of the procedure proposed stands in the very straightforward determination of reaction kinetic constants, avoiding demanding least-squares fittings on rheometer experimental data. A set of experimental data available, relying into rheometer curves of the same rubber blend conducted at five different temperatures are used to estimate the fitting capabilities of the mathematical model proposed. Very good agreement with experimental data is observed

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Section: Introductionmentioning

confidence: 82%

Iterative robust numerical procedure for the determination of kinetic constants in Han’s model for NR cured with sulphur

Milani¹

2015

J Math Chem

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“…This means that, irrespective of the dis tribution ratio in both phases, most of the AIBN in the usually applied concen tration range (about 1-6 g/1) is dissolved in the non-aqueous phase. Conse- 1 10 100…”

Section: Viscositymentioning

confidence: 99%

“…For a long time, insolubility was the major obstacle for characterization of crosslinked polymers because it excluded analytical methods applicable to lin ear and branched macromolecules. In particular, the most important structural characteristic of crosslinked polymers, the crosslink density, could mostly be determined by indirect methods only [ 1 ], or was expressed relatively by the frac tion of crosslinking monomers used in the synthesis. For a crosslinking polyreaction the functionality of the monomers is the basic parameter.…”

Section: Historymentioning

confidence: 99%

Microgels-Intramolecularly Crossünked Macromolecules with a Globular Structure

Funke

Okay

Joos-Müller³

Advances in Polymer Science

252

223

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“…This precursor can then react either with another rubber chain, resulting in a crosslink, or with the same rubber chain, by a backbiting reaction resulting in a cyclic structure. In this latter case, the polysulfidic structure does not contribute to the increase of the crosslink density.The evidence for these polysulfidic structures (both crosslinking and cyclic ones) is provided by an important physical chemistry literature, obtained by IR, UV, ESR and Raman characterizations [4,5] or with chemical methods [6], or by means of solid…”

mentioning

confidence: 99%

A closed form solution for the vulcanization prediction of NR cured with sulphur and different accelerators

Hanel

Donetti

Milani³

2014

J Math Chem

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The paper presents a novel efficient closed form approach to determine the degree of vulcanization of natural rubber (NR) vulcanized with sulphur in presence of different accelerators. The general reaction scheme proposed by Han and co-workers for vulcanized sulphur NR is re-adapted and suitably modified taking into account the single contributions of the different accelerators, focusing in particular on some experimental data, where NR was vulcanized at different temperatures (from 150 to (Formula presented. )) and concentrations of sulphur, using TBBS and DPG in the mixture as co-agents at variable concentrations. In the model, chain reactions initiated by the formation of macro-compounds responsible for the formation of the unmatured crosslinked polymer are accounted for. It is assumed that such reactions depend on the reciprocal concentrations of all components and their chemical nature. In presence of two accelerators, reactions are assumed to proceed in parallel, making the assumption that there is no interaction between the two accelerators. Despite there is experimental evidence that a weak process by which each accelerator affects the other, the reaction chemistry is still not well understood and therefore its effect cannot be translated into any mathematical model. In any case, even disregarding such interaction, good approximations of the rheometer curves are obtained. From the simplified kinetic scheme adopted, a closed form solution is found for the crosslink density, with the only limitation that the induction period is excluded from computations. The main capability of the model stands however in the closed form determination of kinetic constants representing the velocities of single reactions in the kinetic scheme adopted, which allows avoiding a numerically demanding least-squares best fitting on rheometer experimental data. Two series of experiments available, relying into rheometer curves at different temperatures and different concentrations of sulphur and accelerators, are utilized to evaluate the fitting capabilities of the mathematical model. Very good agreement between numerical output and experimental data is experienced in all cases analyzed

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Techniques for the Analysis of Crosslinked Polymers

Cited by 52 publications

References 137 publications

Iterative robust numerical procedure for the determination of kinetic constants in Han’s model for NR cured with sulphur

Iterative robust numerical procedure for the determination of kinetic constants in Han’s model for NR cured with sulphur

Microgels-Intramolecularly Crossünked Macromolecules with a Globular Structure

A closed form solution for the vulcanization prediction of NR cured with sulphur and different accelerators

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