Abstract
In the present contribution, a procedure to estimate parameters using non-isothermal data was applied. The estimation procedure is based on the use of an energy balance in DSC furnace. The approach found all kinetic parameters of autocatalytic model (E 1, E 2, A 1, A 2, m, n) besides the ultimate reaction heat and their confidence regions by using deterministic and heuristic algorithms. The application of this approach to isothermal data was done in a previous work and similar results were obtained. The results show that the use of an energy balance is a good methodology to estimate cure kinetic parameters of non-isothermal experiments.
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Eberhart RC, Shi Y, Kennedy J. Swarm intelligence. 1st ed. San Francisco, CA: Morgan Kaufmann; 2001.
Wang CS, Kwag C. Cure kinetics of an epoxy-anhydride-imidazole resin system by isothermal DSC. Polym Polym Compos. 2006;14:445–54.
Sbirrazzuoli N, Girault Y, Elegant L. Simulations for evaluation of kinetic methods in differential scanning calorimetry. Part 3—peak maximum evolution methods and isoconversional methods. Thermochim Acta. 1997;293:25–37.
Kosar V, Gomzi Z. Cure modeling of polyester thermosets in the copper mold. Polym Plast Technol. 2004;43:1277–98.
Jubsilp C, Damrongsakkul S, Takeichi T, et al. Curing kinetics of arylamine-based polyfunctional benzoxazine resins by dynamic differential scanning calorimetry. Thermochim Acta. 2006;447:131–40.
Ramis X, Salla JM, Cadenato A, et al. Simulation of isothermal cure of a powder coating—non-isothermal DSC experiments. J Therm Anal Calorim. 2003;72:707–18.
Rosu D, Mititelu A, Cascaval CN. Cure kinetics of a liquid-crystalline epoxy resin studied by non-isothermal data. Polym Test. 2004;23:209–15.
Kissinger HE. Reaction kinetics in differential thermal analysis. Anal Chem. 1957;29:1702–6.
Borchardt HJ, Daniels F. The application of differential thermal analysis to the study of reaction kinetics. J Am Chem Soc. 1957;79:41–6.
Ozawa T. A new method of analyzing thermogravimetric data. Bull Chem Soc Jpn. 1965;38:1881–6.
He Y. DSC and DEA studies of underfill curing kinetics. Thermochim Acta. 2001;367:101–6.
Atarsia A, Boukhili R. Relationship between isothermal and dynamic cure of thermosets via the isoconversion representation. Polym Eng Sci. 2000;40:607–20.
Rosu D, Cascaval CN, Mustata F, et al. Cure kinetics of epoxy resins studied by non-isothermal DSC data. Thermochim Acta. 2002;383:119–27.
Alonso MV, Oliet A, Perez JM, et al. Determination of curing kinetic parameters of lignin-phenol-formaldehyde resol resins by several dynamic differential scanning calorimetry methods. Thermochim Acta. 2004;419:161–7.
Perez JM, Rodriguez F, Alonso MV, et al. Curing kinetics of lignin-novolac phenolic resins using non-isothermal methods. J Therm Anal Calorim. 2009;97:979–85.
Kumari K, Raina KK, Kundu PP. DSC studies on the curing kinetics of chitosan-alanine using glutaraldehyde as crosslinker. J Therm Anal Calorim. 2009;98:469–76.
Doca N, Vlase G, Vlase T, et al. TG, EGA and kinetic study by non-isothermal decomposition of a polyaniline with different dispersion degree. J Therm Anal Calorim. 2009;97:479–84.
Zvetkov ZL. Comparative DSC kinetics of the reaction of DGEBA with aromatic diamines. I. Non-isothermal kinetic study of the reaction of DGEBA with m-phenylene diamine. Polymer. 2001;42:6687–97.
Zvetkov ZL. Comparative DSC kinetics of the reaction of DGEBA with aromatic diamines. II. Isothermal kinetic study of the reaction of DGEBA with m-phenylene diamine. Polymer. 2002;43:1069–80.
Barral L, Cano J, Lopez J, et al. Blends of an epoxy/cycloaliphatic amine resin with poly(ether imide). Polymer. 2000;41:2657–66.
Lopez J, Lopez-Bueno I, Nogueira P, et al. Effect of poly(styrene-co-acrylonitrile) on the curing of an epoxy/amine resin. Polymer. 2001;42:1669–77.
Rosu D, Mustata F, Cascaval CN. Investigation of the curing reactions of some multifunctional epoxy resins using differential scanning calorimetry. Thermochim Acta. 2001;370:105–10.
Sbirrazzuoli N, Mititelu-Mija A, Vincent L, et al. Isoconversional kinetic analysis of stoichiometric and off-stoichiometric epoxy-amine cures. Thermochim Acta. 2006;447:167–77.
Pagano RL, Calado VMA, Tavares FW, et al. Cure kinetic parameter estimation of thermosetting resins with isothermal data by using particle swarm optimization. Eur Polym J. 2008;44:2678–86.
Kamal MR, Sourour S. Kinetics and thermal characterization of thermoset cure. Polym Eng Sci. 1973;13:59–64.
Schwaab M, Pinto JC. Optimum reference temperature for reparameterization of the Arrhenius equation. Part 1: problems involving one kinetic constant. Chem Eng Sci. 2007;62:2750–64.
Kennedy J, Eberhart RC. Particle swarm optimization. Proc IEEE Int Conf Neural Netw. 1995;4:1942–8.
Costa CC, Pagano RL, Calado VMA, et al. Viscoelastic response and cure kinetic of a bisphenol a-derived epoxy. J Polym Mater. 2007;24:20–36.
Brenan KE, Campbell SL, Petzold LR. Numerical solution of initial-value problems in differential-algebraic equations. 2nd ed. Philadelphia: SIAM; 1989.
Pinto JC, Lobao MW, Monteiro JL. Sequential experimental-design for parameter-estimation—analysis of relative deviations. Chem Eng Sci. 1991;46:3129–38.
Schwaab M, Biscaia EC, Monteiro JL, et al. Nonlinear parameter estimation through particle swarm optimization. Chem Eng Sci. 2008;63:1542–52.
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Authors would like to thank CAPES, CTPETRO/FINEP (# 0104081500), and CNPq for financial support.
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Pagano, R.L., Calado, V.M.A., Tavares, F.W. et al. Parameter estimation of kinetic cure using DSC non-isothermal data. J Therm Anal Calorim 103, 495–499 (2011). https://doi.org/10.1007/s10973-010-0984-5
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DOI: https://doi.org/10.1007/s10973-010-0984-5