The chemistry of tyre materials is complex due the presence of several compounds, that are mixture of elastomers and other chemicals, such as curing agents, fillers etc… In more detail, the curing agent is one of the most important constituents, as it promotes the vulcanization process. This process is a chemical reaction in which cross-linking bonds are formed between the polymer chains of the elastomers. The final product properties are strictly dependent on the cross-linking density and, therefore, it is of crucial importance to determine this value. Up to date, one of the most common analytical methods to determine such parameter is the equilibrium-swelling method [1], which requires some days to be performed and a huge amount of solvents. The development of an analytical method fast and solvent-free can therefore be a huge advantage for the tyre industry. To the aim, Time-Domain Nuclear Magnetic Resonance (TD-NMR) spectroscopy is worthy of being studied, as its decay profile is highly correlated with the chain mobility in rubber-based materials. [2] In the present study, performed in collaboration with Pirelli Tyre S.p.A., TD-NMR decays (1H 18 MHz- obtained using the Carr-Purcell-Meiboom Gill (CPMG) sequence – developed in collaboration with Prof. Marco Geppi, University of Pisa) of 428 samples of compounds with a cross-linking density in the range 0.44-5.28 x 10-5 mol/g have been acquired. 285 of these samples, have been selected as training set (venetian-blind scheme) to build a regression model able to predict the cross-linking density value. The remaining 143 samples have been used to test the model. Partial Least Square (PLS) regression models changing the signal pre-treatments (Discrete Exponential Fitting (DEF) [3] or Inverse Laplace Transform (ILT) [3]) have been built and compared in cross-validation. Applying the PLS model built on raw data on the test set a value of Root Mean Square Error in Prediction (RMSEP) of 0.65 has been obtained. The results obtained on DEF- and ILT-pretreated data (RMSEPDEF = 0.63; RMSEPILT = 0.65) are comparable to the ones obtained with the raw data highlighting the robustness of the models. Finally, an in-depth physico-chemical interpretation of the results allows to understand how variance in cross-linking density is correlated to variance in raw signals and pre-treated profiles. References [1] B. A. Saville, A. A. Watson, Rubber Chemistry and Technology, 1967, 40(1), 100-148. [2] G. Eidmann, R. Savelsberg, P. Blümer, B. Blümich, Journal of Magnetic Resonance, 1996, 122(1), 104-109. [3] S. B. Engelsen, F. W. J. van den Berg, Modern Magnetic Resonance, 2018, 1669-1686.
Chemometrics for exploiting the information embodied in TD-NMR spectroscopic data: determination of cross-linking density in tyre compounds.
Voccio, Riccardo;Malegori, Cristina;Oliveri, Paolo;
2024-01-01
Abstract
The chemistry of tyre materials is complex due the presence of several compounds, that are mixture of elastomers and other chemicals, such as curing agents, fillers etc… In more detail, the curing agent is one of the most important constituents, as it promotes the vulcanization process. This process is a chemical reaction in which cross-linking bonds are formed between the polymer chains of the elastomers. The final product properties are strictly dependent on the cross-linking density and, therefore, it is of crucial importance to determine this value. Up to date, one of the most common analytical methods to determine such parameter is the equilibrium-swelling method [1], which requires some days to be performed and a huge amount of solvents. The development of an analytical method fast and solvent-free can therefore be a huge advantage for the tyre industry. To the aim, Time-Domain Nuclear Magnetic Resonance (TD-NMR) spectroscopy is worthy of being studied, as its decay profile is highly correlated with the chain mobility in rubber-based materials. [2] In the present study, performed in collaboration with Pirelli Tyre S.p.A., TD-NMR decays (1H 18 MHz- obtained using the Carr-Purcell-Meiboom Gill (CPMG) sequence – developed in collaboration with Prof. Marco Geppi, University of Pisa) of 428 samples of compounds with a cross-linking density in the range 0.44-5.28 x 10-5 mol/g have been acquired. 285 of these samples, have been selected as training set (venetian-blind scheme) to build a regression model able to predict the cross-linking density value. The remaining 143 samples have been used to test the model. Partial Least Square (PLS) regression models changing the signal pre-treatments (Discrete Exponential Fitting (DEF) [3] or Inverse Laplace Transform (ILT) [3]) have been built and compared in cross-validation. Applying the PLS model built on raw data on the test set a value of Root Mean Square Error in Prediction (RMSEP) of 0.65 has been obtained. The results obtained on DEF- and ILT-pretreated data (RMSEPDEF = 0.63; RMSEPILT = 0.65) are comparable to the ones obtained with the raw data highlighting the robustness of the models. Finally, an in-depth physico-chemical interpretation of the results allows to understand how variance in cross-linking density is correlated to variance in raw signals and pre-treated profiles. References [1] B. A. Saville, A. A. Watson, Rubber Chemistry and Technology, 1967, 40(1), 100-148. [2] G. Eidmann, R. Savelsberg, P. Blümer, B. Blümich, Journal of Magnetic Resonance, 1996, 122(1), 104-109. [3] S. B. Engelsen, F. W. J. van den Berg, Modern Magnetic Resonance, 2018, 1669-1686.
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