Polímeros

 

A simple proposal for modeling isothermal cure kinetics

 

Una propuesta simple para modelar cinéticas de curado isotérmicas

 

O.F. Aguilar-Gutiérrez¹, R.O. Vargas², J.E. Puig³, E. Mendizábal⁴ and F. López-Serrano¹*

 

¹ Departamento de Ingeniería Química, Facultad de Química. Universidad Nacional Autónoma de México. Ciudad Universitaria, D. F. 04510. México. *Corresponding author. E-mail: lopezserrano@unam.mx

² ESIME Azcapotzalco. Instituto Politécnico Nacional, Avenida de las Granjas No. 682, Col. Santa Catarina, Del. Azcapotzalco, D.F. 02250. México.

³ Departamento de Ingeniería Química. CUCEI. Universidad de Guadalajara. Guadalajara, Jalisco 44430. México.

⁴ Departamento de Química. CUCEI. Universidad de Guadalajara. Guadalajara, Jalisco 44430. México.

 

Received 7 of June 2012
Accepted 15 of January 2013

 

Abstract

A simple model for cure kinetics, based on the Churchill-Usagi correlation, is presented here. This proposal, intended for engineering purposes, is capable of reducing computational time to facilitate, even with analytic solutions, the kinetics description, especially when more complex systems are being studied. In spite of the model's simplicity, fundamental kinetic parameters, including the reaction order and the rate constant, (composed of the Arrhenius constant and the activation energy) can be determined in the diffusion free zone. A four-parameter model accurately described the previously reported conversion evolution of a cyanate ester resin, from 140 to 190 ^oC, presented as a case example. For the limit conversion and the Churchill-Usagi exponent, a linear dependence with reaction temperature was obtained.

Keywords: cure kinetics, cyanate ester resin, industrial applications, modeling and simulation.

 

Resumen

Se presenta un enfoque sencillo, basado en la correlación de Churchill-Usagi, para describir cinéticas de curado. Esta propuesta, destinada a aplicaciones industriales es capaz de reducir el tiempo de cálculo para facilitar, aún con soluciones analíticas, la descripción de la cinética de airado de resinas, especialmente cuando se estudian sistemas complejos. A pesar de la simplicidad del modelo, los parámetros cinéticos fundamentales, incluyendo el orden y la constante de reacción (compuesta por el pre-factor de Arrhenius y la energía de activación) se pueden determinar en la zona libre de problemas difusivos. Un modelo de cuatro parámetros describe con exactitud la evolución de la conversión de una resina de éster de dicianato (reportada previamente) de 140 a 190 ^oC la cual se muestra para ejemplificar la propuesta. Tanto para la conversión límite como para el exponente Churchill-Usagi, se obtuvo una dependencia lineal con la temperatura de reacción.

Palabras clave: cinética de curado, resina de éster dicianato, aplicaciones industriales, modelado y simulación.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgments

The funds provided for this work, by UNAM (PAPIIT IN114212) and the exchange program between U de G and UNAM, are gratefully acknowledged.

 

References

Abbassi, A., Shahnazari, M.R. (2004). Numerical modeling of mold filling and curing in non-isothermal RTM process. Applied Thermal Engineering 24, 2453-2465.         [ Links ]

Achilias, D. S. (2007). A Review of modeling of diffusion controlled polymerization Reactions. Macromolecular Theory & Simulations 16, 319-347.         [ Links ]

Arrillaga, A., Zaldua A.M.; Atxurra R.M.; Farid A.S. (2007). Techniques used for determining cure kinetics of rubber compounds. European Polymer Journal 43, 4783-4799.         [ Links ]

Bahrami, M., Yovanovich, M. M., Culham, J. R., (2005). Pressure drop of fully-developed laminar flow in microchannels of arbitrary cross-section. ASME Conference Procedures 128, 1036-1044.         [ Links ]

Batch G. L., Macosko C. W. (1992). Kinetic model for crosslinking free radical polymerization including diffusion effects. Journal of Applied Polymer Science 44, 1711-1729.         [ Links ]

Carothers, W. (1936). Polymers and polyfunctionality. Transactions of the Faraday Society 32, 39-49.         [ Links ]

Chen, Y. T., Macosko, C. W. (1996). Kinetics and rheology characterization during curing of dicyanates. Journal of Applied Polymer Science 62, 567-576.         [ Links ]

Churchill, S. W., Usagi, R. (1972). A general expression for the correlation of rates of transfer and other phenomena. AIChE Journal 18, 1121-1128.         [ Links ]

Comyn, J., Day, J., Shaw, S. J. (1998). Kinetics of moisture cure of silicone sealants. Journal of Adhesion 66, 289-301.         [ Links ]

Corcione, M. (2005). Correlating equations for free convection heat transfer from horizontal isothermal cylinders set in a vertical array. International Journal of Heat & Mass Transfer 48, 3660-3673.         [ Links ]

Crooke, P. S., Peterson, J., Tanner, R.D. (1981). Relating the exponential parameter in the Churchill-Usagi correlation to underlying system parameters. Chemical Engineering Communications 9, 39-50.         [ Links ]

Dibenedetto A. T. (1987). Prediction of the glass transition temperature of polymers: a model based on the principle of corresponding states. Journal of Polymer Science 25, 1949-1969.         [ Links ]

Dusi M. R., Lee W. I., Ciriscoli P. R., Springer G. S. (1987). Cure kinetics and viscosity of fiberite 976 resin. Journal of Composite Materials 21, 243-261.         [ Links ]

Fourier, J. G., Du Plessis, J. P. (2002). Pressure drop modeling in cellular metallic foams. Chemical Engineering Science 57, 2781-2789.         [ Links ]

Galwey, A. K. (2004). Is the science of thermal analysis kinetics based on solid foundations. A literature appraisal. Thermochimica Acta 413, 139-183.         [ Links ]

González-Romero V. M., Casillas, N. (1989). Isothermal and temperature programmed kinetic studies of thermosets. Polymer Engineering Science. 29, 295-301.         [ Links ]

Halley, P J., Mackay, M. E. (1996). Chemorheology of thermosets: an overview. Polymer Engineering Science 3, 593-609.         [ Links ]

Harsch, M., Karger-Kocsisb, J., Holsta, M. (2007). Influence of fillers and additives on the cure kinetics of an epoxy/anhydride resin. European Polymer Journal 43, 1168-1178.         [ Links ]

Hayes, R. E., Mok P.K., Mmbaga J., Votsmeier M. (2007). A fast approximation method for computing effectiveness factors with non-linear kinetics. Chemical Engineering Science 62, 2209-2215.         [ Links ]

Henne M, C., Breyer, C., Niedermeier, M., Ermanni, P. (2004). New kinetic and viscosity model for liquid composite molding simulations in an industrial environment. Polymer Composites 25, 255-269.         [ Links ]

Ho, T. C. (1991). A simple expression for the collective behavior of a large number of reactions. Chemical Engineering Science 46, 281-289.         [ Links ]

Kamal, M. R. (1974). Thermoset characterization for moldability analysis. Polymer Engineering Science 14, 231-239.         [ Links ]

Kazakov, A., Wang, H., Frenklach, M. (1994). Parametrization of chemically-activated reactions involving isomerization. Journal of Physical Chemistry 98, 10598-10605.         [ Links ]

Kenny J.M. (1994). Composite structures, application of modeling to the control and optimization of composites processing. Composite Structures 27, 129-139.         [ Links ]

Kim, D. S., Macosko, C. W. (2000). Reaction injection molding process of glass fiber reinforced polyurethane composites. Polymer Engineering Science 40, 2205-2216.         [ Links ]

Lei Y., Wu, Q., Lian, K. (2006). Cure kinetics of aqueous phenol-formaldehyde resins used for oriented strandboard manufacturing: analytical technique. Journal of Applied Polymer Science 100, 1642-1650.         [ Links ]

Loo A. C., Tanner R. D., Crooke P. S. (1978). Simplifying enzyme and fermentation kinetic models. Journal of Chemical Engineering 16, 137-149.         [ Links ]

Membre, J. M., Thurette, J., Catteau, M. (1997). Modelling the growth, survival and death of listeria monocytogenes. Journal of Applied Microbiology 82, 345-350.         [ Links ]

Mitrovic, B. M., Le, P. M., Papavassiliou, D. V. (2004). On the Prandtl or Schmidt number dependence of the turbulent heat or mass transfer coefficient. Chemical Engineering Science 59, 543-555.         [ Links ]

Naffakh, M., Dumon, M., Gerard J. F. (2006). Modeling the chemorheological behavior of epoxy/liquid aromatic diamine for resin transfer molding applications. Journal of Applied Polymer Science 102, 4228-4237.         [ Links ]

Payne, J.B., Osborne J. A., Jenkins P. K. (2007). Modeling the growth and death kinetics of salmonella in poultry litter as a function of pH and water activity. Poultry Science 86, 191-201.         [ Links ]

Petre, C. F., Larachi, F., Iliuta, I., Grandjean, B.P.A. (2003). Pressure drop through structured packings: Breakdown into the contributing mechanisms by CFD modeling. Chemical Engineering Science 58, 163-177.         [ Links ]

Rabinowitch, E. (1937). Collision, coordination diffusion and reaction velocity in condensed systems. Transactions of the Faraday Society 33, 1225-1233.         [ Links ]

Romeo, E., Royo, C., Monzon, A. (2002). Improved explicit equations for estimation of the friction factor in rough and smooth pipes. Chemical Engineering Journal 86, 369-374.         [ Links ]

Sanitjai, S., Goldstein, R. J. (2004). Forced convection heat transfer from a circular cylinder in crossflow to air and liquids. International Journal of Heat & Mass Transfer 47, 4795-4805.         [ Links ]

Shojaei A., Abbasi F. (2006). Cure kinetics of a polymer-based composite friction material. Journal of Applied Polymer Science 100, 9-17.         [ Links ]

Vilas J. L., Laza, J. M.; Garay M. T.; Rodríguez, M.; León L. M. (2001). Unsaturated polyester resins cure: kinetic, rheologic, and mechanical-dynamical analysis. I. Cure kinetics by DSC and TSR. Journal of Applied Polymer Science 79, 447-457.         [ Links ]

Yousefi, A., Lafleur, P.G., Gauvin, R. (1997). Kinetic studies of thermoset cure reactions: a review. Polymer Composites 18, 157-168.         [ Links ]

Zhao, L., Hu, X. (2007). A variable reaction order model for prediction of curing kinetics of thermosetting polymers. Polymer 48, 6125-6133.         [ Links ]