Kinetics Models
Curing is a process of forming the crosslinks that join polymer chains together. The term curing refers to the crosslinking of thermosetting resins, for example an unsaturated polyester and epoxy resin.
The evolution of the degree of cure or conversion cr is described by the convection equation with a source term:
where is the reaction rate.
One of the simplest models is the nth-order reaction
where nr is the polynomial order and kr is a temperature-dependent reaction rate constant that follows an Arrhenius equation
where Q is the activation energy and k0 is the frequency factor.
The Sestak–Berggren autocatalytic model describes a reaction that is slow initially, increases in rate as the reaction proceeds, before slowing down again as the reactants are depleted
where mr is the polynomial order.
Kamal–Sourour is a combination of the nth order and Sestak–Berggren models
where k1 and k2 are temperature-dependent reaction rate constants
where Q1,2 are the activation energies and the frequency factors.
The curing reaction stops before the complete conversion is achieve. The diffusion factor is introduced in curing model to take into account the drastic decrease of the rate of crosslinking due to vitrification. The reaction rate is limited by multiplying by the diffusion factor
or by the modified diffusion factor
where , , Cf, and Cd are the model parameters.