Theoretical and Modeling Aspects of Curing Reactions

  • Paulo Jorge Bártolo


This chapter presents an integrated thermal-kinetic model to study photo-initiated curing reactions and determine different aspects associated with these reactions, describing both the heat transfer phenomenon all along the reaction and the cure kinetics. This model is sensitive to the resin composition, temperature and light intensity, apart from describing the main events occurring during cure reactions. The kinetic model and the law of the conservation of energy are coupled, while the integrated model is numerically solved.


Unsaturated Polyester Fractional Conversion Unsaturated Polyester Resin Polymerization Shrinkage Resin Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    C.M. Cheah and J.Y.H. Fuh, Characteristics of photopolymeric material used in rapid prototypes Part I. Mechanical properties in the green state, Journal of Materials Processing Technology, 67, 41–45, 1997CrossRefGoogle Scholar
  2. 2.
    J.Y.H. Fuh, L. Lu, C.C. Tan, Z.X. Shen and S. Chew, Curing characteristics of acrylic photopolymer used in stereolithography process, Rapid Prototyping Journal, 5, 27–34, 1999CrossRefGoogle Scholar
  3. 3.
    P.C. Powell and A.J.I. Housz, Engineering with polymers, Stanley Thornes, Cheltenham, 1998Google Scholar
  4. 4.
    I.C. Choy and D.J. Plazek, The physical properties of bisphenol-A-based epoxy resins during and after curing, Journal of Polymer Science Part B: Polymer Physics, 24, 1303–1320, 1986CrossRefGoogle Scholar
  5. 5.
    S.L. Simon and J.K. Gillham, Reaction kinetics and TTT cure diagrams for off-stoichiometric ratios of a high-Tg epoxy/amine system, Journal of Applied Polymer Science, 46, 1245–1270, 1992CrossRefGoogle Scholar
  6. 6.
    T.G. Fox and P.J. Flory, Second‐order transition temperatures and related properties of polystyrene. I. Influence of molecular weight, Journal of Applied Physics, 21 (6), 581–591, 1950CrossRefGoogle Scholar
  7. 7.
    X. Ramis and J.M. Salla, Time-temperature transformation (TTT) cure diagram of an unsaturated polyester resin, Journal of Polymer Science Part B: Polymer Physics, 35, 371–388, 1997CrossRefGoogle Scholar
  8. 8.
    S. Lunak, J. Vladyka and K. Dušek, Effect of diffusion control in the glass transition region on critical conversion at the gel point during curing of epoxy resins, Polymer, 19, 931–933, 1978CrossRefGoogle Scholar
  9. 9.
    K.P. Pang and J.K. Gillham, Competition between cure and thermal degradation in a high Tg epoxy system: effect of time and temperature of isothermal cure on the glass transition temperature, Journal of Applied Polymer Science, 39, 909–933, 1990CrossRefGoogle Scholar
  10. 10.
    P.J. Bartolo, Optical approaches to macroscopic and microscopic engineering, PhD Thesis, University of Reading, UK, 2001Google Scholar
  11. 11.
    C.C. Riccardi, H.E. Adabbo and R.J.J. Williams, Curing reaction of epoxy resins with diamines, Journal of Applied Polymer Science, 29, 2481–2492, 1984CrossRefGoogle Scholar
  12. 12.
    H.E. Adabbo and R.J.J. Williams, The evolution of thermosetting polymers in a conversion-temperature phase diagram, Journal of Applied Polymer Science, 27, 1327–1334, 1982CrossRefGoogle Scholar
  13. 13.
    J.P. Pascault and R.J.J. Williams, Glass transition temperature versus conversion relationships for thermosetting polymers, Journal of Polymer Science Part B: Polymer Physics, 28, 85–95, 1990CrossRefGoogle Scholar
  14. 14.
    L.E. Nielsen, Crosslinking effect on physical properties of polymers, Journal of Macromolecular Science Reviews in Macromolecular Chemistry C3, 69–103, 1969Google Scholar
  15. 15.
    J.B. Enns and J.K. Gillham, Time-temperature-transformation (TTT) cure diagram: modelling the cure behaviour of thermosets, Journal of Applied Polymer Science, 28, 2567–2591, 1983CrossRefGoogle Scholar
  16. 16.
    S. Montserrat, Effect of crosslinking density on ΔCp(Tg) in an epoxy network, Polymer, 36, 435–436, 1996CrossRefGoogle Scholar
  17. 17.
    P.R. Couchman, Thermodynamics and the compositional variation of glass transition temperatures, Macromolecules, 20 (7), 1712–1717, 1987CrossRefGoogle Scholar
  18. 18.
    Y.G. Lin, H. Sautereau and J.P. Pascault, Epoxy network structure effect on physical aging behaviour, Journal of Applied Polymer Science, 32, 4595–4605, 1986CrossRefGoogle Scholar
  19. 19.
    R.A. Venditti and J.K. Gillham, A relationship between the glass transition temperature (Tg) and fractional conversion for thermosetting systems, Proceedings of the American Chemical Society, Division of Polymeric Materials: Science and Engineering, 69, 434–435, 1993Google Scholar
  20. 20.
    O. Georjon, J. Galy and J.P. Pascault, Isothermal curing of an uncatalyzed dicyanate ester monomer: kinetics and modelling, Journal of Applied Polymer Science, 49 (8), 1441–1452, 1993CrossRefGoogle Scholar
  21. 21.
    A. Hale, C.W. Macosko and H.E. Bair, Glass transition temperature as a function of conversion in thermosetting polymers, Macromolecules, 24 (9), 2610–2621, 1991CrossRefGoogle Scholar
  22. 22.
    E.A. DiMarzio, On the Second-order transition of a rubber, Journal of Research of the National Bureau of Standards. Section A Physics and Chemistry, 68A(6), 611–617, 1964Google Scholar
  23. 23.
    J.H. Gibbs and E.A. DiMarzio, Nature of the glass transition and the glassy state, Journal of Chemical Physics, 28 (3), 373–383, 1958CrossRefGoogle Scholar
  24. 24.
    D.R. Miller and C.W. Macosko, A new derivation of post gel properties of network polymers, Macromolecules, 9 (2), 206–211, 1976CrossRefGoogle Scholar
  25. 25.
    K. Dusek, in Development in polymerisation Vol. 3, Edited by R.N. Haward, Applied Science, London, 1982Google Scholar
  26. 26.
    M.A. Zumbrum, G.L. Wilkes and T.C. Ward, in Radiation curing in polymer science and technology, Vol. III: Polymerisation mechanisms, Edited by J.P. Fouassier and J.F. Rabek, Elsevier, London, 1993Google Scholar
  27. 27.
    Y.Y. Chiu and L.J. Lee, Microgel formation in the free radical crosslinking polymerization of ethylene glycol dimethacrylate (EGDMA). I. Experimental, Journal of Polymer Science Part A-1: Polymer Chemistry, 33 (2), 257–267, 1995CrossRefGoogle Scholar
  28. 28.
    A. Battisti, A.A. Skordos and I.K. Partridge, Percolation threshold of carbon nanotubes filled unsaturated polyesters, Composites Science and Technology, 70, 633–637, 2010CrossRefGoogle Scholar
  29. 29.
    M. Ghiass, A.D. Rey and B. Dabir, Microstructure evolution and simulation of copolymerization reaction using a percolation model, Polymer, 43, 989–995, 2002CrossRefGoogle Scholar
  30. 30.
    K. Dusek, in Polymer networks. Principles of their formation, structure and properties. Edited by R.F.T. Stepto, Blackie Academic & Professional, London, 1998Google Scholar
  31. 31.
    P.J. Flory, Molecular size distribution in three dimensional polymers. I. Gelation, Journal of American Chemical Society, 63 (11), 3083–3090, 1941CrossRefGoogle Scholar
  32. 32.
    P.J. Flory, Molecular size distribution in three dimensional polymers. II. Trifunctional branching units, Journal of American Chemical Society, 63 (11), 3091–3096, 1941CrossRefGoogle Scholar
  33. 33.
    P.J. Flory, Molecular size distribution in three dimensional polymers. III. Tetrafunctional branching units, Journal of American Chemical Society, 63 (11), 3096–3100, 1941CrossRefGoogle Scholar
  34. 34.
    W.H. Stockmayer, Theory of molecular size distribution and gel formation in branched‐chain polymers, Journal of Chemical Physics, 11 (2), 45–55, 1943CrossRefGoogle Scholar
  35. 35.
    W.H. Stockmayer, Theory of molecular size distribution and gel formation in branched polymers II. General cross linking, Journal of Chemical Physics, 12 (4), 125–131, 1944CrossRefGoogle Scholar
  36. 36.
    M. Gordon and G.N. Malcolm, Configurational statistics of copolymer systems, Proceedings of the Royal Society London A, 295 (1440), 29, 1966CrossRefGoogle Scholar
  37. 37.
    R.S. Whitney and W. Burchard, Molecular size and gel formation is branched poly(methyl methacrylate) copolymers, Makromolecular Chemistry, 181, 869, 1980CrossRefGoogle Scholar
  38. 38.
    K. Ito, Y. Murase and Y. Yamashita, Polymerization of diallyl phthalate and gelation of poly(diallyl phthalate) by copolymerization with styrene, Journal of Polymer Science: Polymer Chemistry Edition, 13 (1), 87–96, 1975CrossRefGoogle Scholar
  39. 39.
    B. Soper, R.N. Haward and E.F.T. White, Intramolecular cyclization of styrene-p-divinylbenzene copolymers, Journal of Polymer Science Part A-1: Polymer Chemistry, 10 (9), 2545–2564, 1972CrossRefGoogle Scholar
  40. 40.
    T. Holt and W. Simpson, Observations on intramolecular reaction in addition polymerization systems, Proceedings of the Royal Society London A, 238 (1213), 154–174, 1956CrossRefGoogle Scholar
  41. 41.
    C. Walling, Gel formation in addition polymerization, Journal of American Chemical Society, 67 (3), 441–447, 1945CrossRefGoogle Scholar
  42. 42.
    B.H. Zimm, F.P. Price and J.P. Bianchi, Dilute gelling systems. IV. Divinylbenzene–styrene copolymers, Journal of Physical Chemistry, 62 (8), 979, 1958CrossRefGoogle Scholar
  43. 43.
    J. Maunsky; J. Klaban and K. Duŝek, Vinyl-Divinyl Copolymerization: copolymerization and network formation from styrene and p- and m-Divinylbenzene, Journal of Macromolecular Science, Part A Pure and Applied Chemistry, 5 (6), 1071–1085, 1971CrossRefGoogle Scholar
  44. 44.
    D.R. Miller and C.W. Macosko, Substitution effects in property relations for stepwise polyfunctional polymerization, Macromolecules, 13 (5), 1063–1069, 1980CrossRefGoogle Scholar
  45. 45.
    G.R. Dobson and M. Gordon, Theory of branching processes and statistics of rubber elasticity, Journal of Chemical Physics, 43 (2), 705–713, 1965CrossRefGoogle Scholar
  46. 46.
    M. Gordon, Good’s theory of cascade processes applied to the statistics of polymer distributions, Proceedings of the Royal Society London A, 268 (1333), 240–256, 1962CrossRefGoogle Scholar
  47. 47.
    J. Bastide and L. Leibler, Large-scale heterogeneities in randomly cross-linked networks, Macromolecules, 21 (8), 2647–2649, 1988CrossRefGoogle Scholar
  48. 48.
    H. Boots and N. Dotson, The simulation of free-radical crosslinking polymerization: the effect of diffusion, Polymer Communication, 29, 346, 1988Google Scholar
  49. 49.
    H.M.J. Boots and R.B. Pandey, Qualitative percolation study of free-radical cross-linking polymerization, Polymer Bulletin, 11 (5), 415–420, 1984CrossRefGoogle Scholar
  50. 50.
    R. Bansil, H.J. Herrmann and D. Stauffer, Computer simulation of kinetics of gelation by addition polymerization in a solvent, Macromolecules, 17 (5), 998–1004, 1984CrossRefGoogle Scholar
  51. 51.
    J.M. Morancho, A. Cadenato, X. Ramis, X. Fernández-Francos and J.M. Salla, Thermal curing and photocuring of an epoxy resin modified with a hyperbranched polymer, Thermochimica Acta, 510, 1–8, 2010CrossRefGoogle Scholar
  52. 52.
    P. Cañamero-Martínez, M. Fernández-García and J.L. Fuente, Rheological cure characterization of a polyfunctional epoxy acrylic resin, Reactive and Functional Polymers 70, 761–766, 2010CrossRefGoogle Scholar
  53. 53.
    C.E. Corcione, A. Previderio and M. Frigione, Kinetics characterization of a novel photopolymerizable siloxane-modified acrylic resin, Thermochimica Acta, 509, 56–61, 2010CrossRefGoogle Scholar
  54. 54.
    B. Jankovíc, The kinetic analysis of isothermal curing reaction of an unsaturated polyester resin: estimation of the density distribution function of the apparent activation energy, Chemical Engineering Journal, 162, 331–340, 2010CrossRefGoogle Scholar
  55. 55.
    L. Zhao and X. Hu, Autocatalytic curing kinetics of thermosetting polymers: a new model based on temperature dependent reaction orders, Polymer, 51, 3814–3820, 2010CrossRefGoogle Scholar
  56. 56.
    P.J. Bartolo, Computer simulation of stereolithographic curing reactions: phenomenological versus mechanistic approaches, Annals of the CIRP, 55, 221–226, 2006CrossRefGoogle Scholar
  57. 57.
    P.J. Bártolo, Photo-curing modelling: direct irradiation, International Journal of Advanced Manufacturing Technologies, 32, 480–491, 2007CrossRefGoogle Scholar
  58. 58.
    J.M. Matias, P.J. Bártolo and A.V. Pontes, Modelling and simulation of photofabrication processes using unsaturated polyester resins, Journal of Applied Polymer Science, 114, 3673–3685, 2009CrossRefGoogle Scholar
  59. 59.
    C. Popescu and E. Segal, Critical considerations on the methods for evaluating kinetic parameters from nonisothermal experiments, International Journal of Chemical Kinetics, 30 (5), 313–327, 1998CrossRefGoogle Scholar
  60. 60.
    A. Yousefi, P.G. Lafleur and R. Gauvin, Kinetic studies of thermoset cure reactions: a review, Polymer Composites, 18 (2), 157–168, 1997CrossRefGoogle Scholar
  61. 61.
    M.R. Kamal and M.E. Ryan, in Fundamentals of computer modeling for polymer processing. Edited by C.L. Tucker, Hanser, Munich, 1989Google Scholar
  62. 62.
    G.L. Batch and C.W. Macosko, Kinetic model for crosslinking free radical polymerization including diffusion limitations, Journal of Applied Polymer Science, 44 (10), 1711–1729, 1992CrossRefGoogle Scholar
  63. 63.
    J.K. Stevenson, Free radical polymerization models for simulating reactive processing, Polymer Engineering and Science, 26 (11), 746–759, 1986CrossRefGoogle Scholar
  64. 64.
    C.D. Han and D.S. Lee, Analysis of the curing behavior of unsaturated polyester resins using the approach of free radical polymerization, Journal of Applied Polymer Science, 33 (8), 2859–2876, 1987CrossRefGoogle Scholar
  65. 65.
    Y.J. Huang, J.D. Fan and L.J. Lee, Casting of diffusion-controlled free radical polymerization-experimental and theoretical analysis, Journal of Applied Polymer Science, 33 (4), 1315–1341, 1987CrossRefGoogle Scholar
  66. 66.
    S. Swier and B.V. Mele, Mechanistic modelling of the reaction kinetics of phenyl glycidyl ether (PGE) + aniline using heat flow and heat capacity profiles from modulated temperature DSC, Thermochimica Acta, 411, 149–169, 2004CrossRefGoogle Scholar
  67. 67.
    C.W. Wise, W.D. Cook and A.A. Goodwin, Chemico-diffusion kinetics of model epoxy-amine resins, Polymer, 38, 3251–3261, 1997CrossRefGoogle Scholar
  68. 68.
    F.X. Perrin, T.M.H. Nguyen and J.L. Vernet, Chemico-diffusion kinetic and TTT cure diagrams of DGEBA-DGEBF/amine resins cured with phenol catalysts, Journal of European Polymer, 43, 5107–5120, 2007Google Scholar
  69. 69.
    L. Flach and R.P. Chartoff, A process model for nonisothermal photopolymerization with laser light source I: basic model development, Polymer Engineering Science, 35, 483–492, 1995CrossRefGoogle Scholar
  70. 70.
    Y. Tang, C. Henderson, J. Muzzi and D.W. Rosen, Stereolithography cure modelling and simulation, International Journal of Materials and Product Technology, 21, 255–272, 2004CrossRefGoogle Scholar
  71. 71.
    M. Abdalla, D. Dean, R. Robinson and E. Nyairo, Cure behavior of epoxy/MWCNT nanocomposites: the effect of nanotube surface modification, Polymer, 49, 3310–3317, 2008CrossRefGoogle Scholar
  72. 72.
    L. Zhao and X. Hu, A variable reaction order model for prediction of curing kinetics of thermosetting polymers, Polymer, 48, 6125–6161, 2007CrossRefGoogle Scholar
  73. 73.
    Y.T. Chen and C.W. Macosko, Kinetics and rheology characterization during curing of dicyanates, Journal of Applied Polymer Science, 62, 567–576, 1996CrossRefGoogle Scholar
  74. 74.
    R.W. Lewis, K. Morgan, H.R. Thomas and K.N. Seetharamu, The finite element method in heat transfer analysis, Wiley, Chichester, 1996MATHGoogle Scholar
  75. 75.
    J.N. Reddy and D.K. Gartling, The finite element method in heat transfer and fluid dynamics, CRC Press, Boca Raton, FL, 1996Google Scholar
  76. 76.
    G. Comini, S.D. Giudice and C. Nonino, Finite element analysis in heat transfer, Taylor and Francis, London, 1994Google Scholar
  77. 77.
    O.C. Zienkiewicz, The finite element method, McGraw-Hill, London, 1977MATHGoogle Scholar
  78. 78.
    J.N. Reddy, Introduction to the finite elements method, McGraw-Hill, New York, 1993Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Centre for Rapid and Sustainable ProductPolytechnic Institute of LeiriaLeiriaPortugal

Personalised recommendations