The kinetics of cure and network formation

Although the cure of an epoxy resin involves reaction between epoxy and hardener reactive groups, as discussed in chapter 2, the full characterization of the cure process involves many other factors. During cure, a liquid or fluid resin-hardener mixture is converted to a solid (chapter 1, section 1.1 and Figure 1.1). Critical features are gelation and the onset of vitrification. The latter effect occurs as the glass transition temperature, T g , approaches the cure temperature, T c . The determination and alternative definitions of T g will be considered later (section 3.2). However, it should be noted that the glass transition temperature is a function of the extent of reaction, X e , \({X_e} = \frac{{{E_o} - {E_{({t_c})}}}}{{{E_o}}}\) with E o and \({E_{({t_c})}}\) being the concentrations of epoxy groups present initially and at cure time te and has been used as a measure of the extent of reaction (Wisanrakkit and Gillham, 1990). When the difference between the cure temperature and the glass transition temperature becomes ‘small’, that is, ΔT = T c - T g (X e ) is small, curing reactions become diffusion controlled because molecular mobility is rapidly reduced as ΔT → 0. Cure may continue very slowly even when ΔT becomes negative. Then the glass transition temperature exceeds the cure temperature.

[1]  D. Soane,et al.  High-conversion diffusion-controlled copolymerization kinetics , 1988 .

[2]  D. Plazek,et al.  Epoxy resins (DGEBA): The curing and physical aging process , 1990 .

[3]  A. Schouten,et al.  GRAFTING KINETICS OF POLY(METHYL METHACRYLATE) ON MICROPARTICULATE SILICA , 1990 .

[4]  C. Boned,et al.  Application of the percolation model to gelation of an epoxy resin , 1990 .

[5]  V. B. Gupta,et al.  The effects of stoichiometry and structure on the dynamic torsional properties of a cured epoxy resin system , 1984 .

[6]  W. H. Carothers Polymers and polyfunctionality , 1936 .

[7]  S. Senturia,et al.  Monitoring the cure of a composite matrix resin with microdielectrometry , 1989 .

[8]  C. Macosko,et al.  A new derivation of average molecular weights of nonlinear polymers. , 1976, Macromolecules.

[9]  Henry Eyring,et al.  Basic chemical kinetics , 1980 .

[10]  B. Steinmann Investigations on the curing of epoxy resins with hexahydrophthalic anhydride , 1989 .

[11]  R. Larson Constitutive equations for polymer melts and solutions , 1988 .

[12]  Dietrich Stauffer,et al.  Gelation and critical phenomena , 1982 .

[13]  K. Dušek,et al.  Effect of diffusion control in the glass transition region on critical conversion at the gel point during curing of epoxy resins , 1978 .

[14]  Yoshio Waseda,et al.  The structure of non-crystalline materials , 1980 .

[15]  Roberto J. J. Williams,et al.  A kinetic scheme for an amine-epoxy reaction with simultaneous etherification , 1986 .

[16]  Jinhwan Kim,et al.  Cure kinetics of epoxy formulations of the type used in advanced composites , 1984 .

[17]  G. McKenna,et al.  Volume recovery in epoxy glasses subjected to torsional deformations: the question of rejuvenation , 1991 .

[18]  R. Young,et al.  The mechanical properties of epoxy resins , 1980 .

[19]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[20]  P. Flory Principles of polymer chemistry , 1953 .

[21]  R. Arridge,et al.  Linear viscoelastic properties of epoxy resin polymers in dilatation and shear in the glass transition region. 1. Time-temperature superposition of creep data , 1979 .

[22]  D. V. Krevelen,et al.  Properties of polymers, their estimation and correlation with chemical structure , 1972 .

[23]  C. Morris,et al.  Chromatography of Epoxy Resins , 1984 .

[24]  J. M. Parker,et al.  Viscosity models for fluorozirconate and fluoroaluminate glasses , 1989 .

[25]  L. C. Case Molecular distributions in polycondensations involving unlike reactants. I. Gelation , 1957 .

[26]  G. A. Pogany Gamma relaxation in epoxy resins and related polymers , 1970 .

[27]  H. Stutz,et al.  A generalized theory for the glass transition temperature of crosslinked and uncrosslinked polymers , 1990 .

[28]  James E. Martin,et al.  Time-cure superposition during crosslinking , 1990 .

[29]  Allan F. M. Barton,et al.  CRC Handbook of solubility parameters and other cohesion parameters , 1983 .

[30]  J. Galy,et al.  Effects of the structure of the aromatic curing agent on the cure kinetics of epoxy networks , 1989 .

[31]  R. B. Prime,et al.  CHAPTER 5 – Thermosets , 1981 .

[32]  D. J. Boyle,et al.  A model for the curing reaction of epoxy resins , 1989 .

[33]  E. Sacher,et al.  Kinetics of epoxy cure: (1) The system bisphenol-A diglycidyl ether/m-phenylene diamine , 1971 .

[34]  W. Bascom,et al.  Kinetics of epoxy resin polymerization using differential scanning calorimetry , 1977 .

[35]  Roberto J. J. Williams,et al.  Curing reaction of epoxy resins with diamines , 1984 .

[36]  Musa R. Kamal,et al.  Differential scanning calorimetry of epoxy cure: isothermal cure kinetics☆ , 1976 .

[37]  J. Koenig,et al.  Application of FT-IR and NMR to epoxy resins , 1986 .

[38]  Andre Lee,et al.  Effect of crosslink density on physical ageing of epoxy networks , 1988 .

[39]  K. Horie,et al.  Diffusion-Controlled Reactions in Polymer Systems , 1987 .

[40]  C. A. May,et al.  Epoxy Resins: Chemistry and Technology , 1973 .

[41]  J. H. Speake,et al.  Mechanical relaxation studies of the cure of epoxy resins: 1. Measurement of cure , 1972 .

[42]  R. E. Robertson,et al.  The Physics of Glassy Polymers , 1973 .

[43]  Joseph H. Flynn,et al.  General Treatment of the Thermogravimetry of Polymers. , 1966, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[44]  Graham Williams,et al.  Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function , 1970 .

[45]  J. Charlesworth An analysis of the substitution effects involved in diepoxide‐diamine copolymerization reactions , 1980 .

[46]  J. P. Bell Structure of a typical amine‐cured epoxy resin , 1970 .

[47]  R. P. Tiger,et al.  Reaction Kinetics in the Liquid Phase , 1976 .

[48]  L. Miller,et al.  Fracture toughness and mechanical behaviour of an epoxy resin , 1975 .

[49]  M. Gordon,et al.  The structure and properties of molecular trees and networks , 1975 .

[50]  John Ziman,et al.  Models of disorder , 1979 .

[51]  A. Malkin,et al.  Rheokinetics of curing , 1991 .

[52]  L. Drzal The interphase in epoxy composites , 1986 .

[53]  James E. Martin,et al.  Evolution of structure and viscoelasticity in an epoxy near the sol-gel-transition , 1990 .

[54]  M. Ashby,et al.  Modulus-maps for amorphous polymers , 1986 .

[55]  Xiaorong Wang,et al.  Tg-temperature property (TgTP) diagram for thermosetting systems : anomalous behaviour of physical properties of vs extent of cure , 1993 .

[56]  K. Dušek,et al.  Formation, structure, and elasticity of loosely crosslinked epoxy‐amine networks. II. Mechanical and optical properties , 1984 .

[57]  A. Kovacs La contraction isotherme du volume des polymères amorphes , 1958 .

[58]  J. K. Gillham,et al.  The glass transition temperature (Tg) as an index of chemical conversion for a high‐Tg amine/epoxy system: Chemical and diffusion‐controlled reaction kinetics , 1990 .

[59]  D. Harran,et al.  Rheological study of the isothermal reticulation of an epoxy resin , 1986 .

[60]  R. Fava,et al.  Differential scanning calorimetry of epoxy resins , 1968 .

[61]  B. Ellis,et al.  The glass transition temperatures of highly crosslinked networks: Cured epoxy resins , 1982 .

[62]  E. Rabinowitch,et al.  Collision, co-ordination, diffusion and reaction velocity in condensed systems , 1937 .

[63]  Arthur Victor Tobolsky Properties and Structure of Polymers. , 1960 .

[64]  George W. Scherer,et al.  Relaxation in Glass and Composites , 1986 .

[65]  John M. Barton,et al.  The application of differential scanning calorimetry (DSC) to the study of epoxy resin curing reactions , 1985 .

[66]  J. D. Campbell,et al.  The low-temperature macro deformation of an epoxide resin , 1974 .

[67]  D. Plazek,et al.  The physical properties of bisphenol-A-based epoxy resins during and after curing. II: Creep behavior above and below the glass transition temperature , 1989 .

[68]  A. Argon A theory for the low-temperature plastic deformation of glassy polymers , 1973 .

[69]  A. Bondi,et al.  Physical properties of molecular crystals liquids, and glasses , 1968 .

[70]  Roberto J. J. Williams,et al.  Statistical structural model for the build-up of epoxy-amine networks with simultaneous etherification , 1986 .

[71]  Guillet Polymer Photophysics and Photochemistry , 1985 .

[72]  Norman F. Sheppard,et al.  Dielectric Analysis of Thermoset Cure. , 1986 .

[73]  R. Larson Reptation Theories For Melts and Concentrated Solutions , 1988 .

[74]  J. K. Gillham,et al.  The glass transition temperature (tg) as a parameter for monitoring the cure of an amine/epoxy system at constant heating rates , 1990 .

[75]  S. A. Sojka,et al.  The curing of an epoxy resin as followed by carbon‐13 NMR spectroscopy , 1976 .

[76]  J. Williams,et al.  Stress analysis of polymers , 1973 .

[77]  Lawrence E. Nielsen,et al.  Cross-Linking–Effect on Physical Properties of Polymers , 1969 .

[78]  M. Keenan Autocatalytic cure kinetics from DSC measurements: Zero initial cure rate , 1987 .

[79]  S. Benson foundations of chemical kinetics , 1960 .

[80]  Christopher W. Macosko,et al.  Rheological changes during crosslinking , 1985 .

[81]  G. A. Pogany The β-relaxation in epoxy resins; the temperature and time-dependence of cure , 1969 .

[82]  J. P. Bell Mechanical properties of a glassy epoxide polymer: Effect of molecular weight between crosslinks , 1970 .

[83]  L. Sperling Introduction to physical polymer science , 1986 .

[84]  K. Dušek,et al.  Formation‐structure relationships in polymer networks , 1985 .

[85]  S. Senturia,et al.  Chemical interpretation of the relaxed permittivity during epoxy resin cure , 1986 .

[86]  H. S. Hsich Kinetic model of cure reaction and filler effect , 1982 .

[87]  J. Mijovic,et al.  A comparison of chemorheological models for thermoset cure , 1989 .

[88]  P. Gennes Scaling Concepts in Polymer Physics , 1979 .

[89]  Ralph G. Pearson,et al.  Kinetics and mechanism , 1961 .

[90]  J. Klaban,et al.  Reaction kinetics of aromatic diamines with epoxide compounds , 1975 .

[91]  John G. Williams The beta relaxation in epoxy resin‐based networks , 1979 .

[92]  A. North The collision theory of chemical reactions in liquids , 1964 .

[93]  J. K. Gillham,et al.  Time-temperature-transformation (TTT) cure diagram of thermosetting polymeric systems , 1986 .

[94]  David S. Soong,et al.  A computer model for the gel effect in free-radical polymerization , 1983 .

[95]  Andre Lee,et al.  Aging in glasses subjected to large stresses and deformations , 1991 .

[96]  R. F. Goddu,et al.  Determination of Terminal Epoxides by Near-Infrared Spectrophotometry , 1958 .

[97]  J. Verdu,et al.  Structure-properties relationships for densely cross-linked epoxide-amine systems based on epoxide or amine mixtures , 1989 .

[98]  Kazuyuki Horie,et al.  Calorimetric investigation of polymerization reactions. III. Curing reaction of epoxides with amines , 1970 .

[99]  Andre Lee,et al.  The physical ageing response of an epoxy glass subjected to large stresses , 1990 .

[100]  J. Seferis,et al.  Kinetic Viscoelasticity for the Dynamic Mechanical Properties of Polymeric Systems , 1989 .

[101]  H. Furukawa,et al.  Curing Mechanisms and Mechanical Properties of Cured Epoxy Resins , 1986 .

[102]  J. K. Gillham,et al.  Time–temperature–transformation (TTT) cure diagram: Modeling the cure behavior of thermosets , 1983 .

[103]  B. A. Rozenberg,et al.  Kinetics, thermodynamics and mechanism of reactions of epoxy oligomers with amines , 1986 .

[104]  I. T. Smith The mechanism of the crosslinking of epoxide resins by amines , 1961 .

[105]  D. Plazek,et al.  Volume-dependent rate processes in an epoxy resin , 1991 .

[106]  P. R. Pinnock,et al.  The mechanical properties of solid polymers , 1966 .

[107]  A. V. Khabenko,et al.  Isothermal transformation of dynamic DSC curves for thermosetting polymers in curing kinetics analysis , 1990 .

[108]  Fred W. Billmeyer,et al.  Textbook Of Polymer Science , 1971 .

[109]  R. E. Camargo,et al.  Bulk Polymerization Kinetics by the Adiabatic Reactor Method , 1983 .

[110]  Musa R. Kamal,et al.  Kinetics and thermal characterization of thermoset cure , 1973 .

[111]  D. Adolf,et al.  Viscoelasticity of near-critical gels. , 1988, Physical review letters.

[112]  Henry Lee,et al.  Handbook of Epoxy Resins , 1967 .

[113]  R. Hertzberg,et al.  Tensile, impact and fatigue behavior of an amine‐cured epoxy resin , 1978 .

[114]  R. Mccullough,et al.  A free‐volume‐based approach to modeling thermoset cure behavior , 1990 .

[115]  D. J. Montgomery,et al.  The physics of rubber elasticity , 1949 .

[116]  J. Gérard,et al.  Epoxy networks based on dicyandiamide: effect of the cure cycle on viscoelastic and mechanical properties , 1990 .

[117]  D. Plazek,et al.  The physical properties of bisphenol-A-based epoxy resins during and after curing† , 1986 .

[118]  Mitsukazu Ochi,et al.  Mechanical relaxation mechanism of epoxide resins cured with diamines , 1985 .

[119]  P. B. Bowden,et al.  The Yield Behaviour of Glassy Polymers , 1973 .

[120]  M. J. Richardson,et al.  Factors influencing the glass transition of DGEBA-anhydride epoxy resins , 1983 .