Kinetic Equations and Mass Balances

To obtain the evolution of the concentration of functional groups and temperature, the constitutive equations for the reaction rates must be introduced into mass balances (in fact, balances of functional groups) and in a thermal energy balance. The form of these balances depends on the characteristics of the reactor in which the thermosetting polymerization is taking place (the reactor may be a DSC pan, a heated mold, a flow reactor, etc.). 

Let us assume a polymerization that may be described by the evolution of the concentration of three functional groups or active species y (i = 1—3). If the reaction takes place in an isothermal DSC pan (a batch reactor with uniform values of composition and temperature), the following mass balances may be stated  

instead of isothermal conditions, the cure is performed at a eonstant heating rate, the constitutive equations for the reaction kinetics are not altered, but a thermal energy balance must be included to describe the system. In this ease, this balance may be reduced to 

If the same polymerization is carried out in a heated mold, concentrations and temperature vary with both position and time. For a one-dimensional system (for example, when variations along the thickness are only relevant), mass and thermal energy balances are written as 

The system of Eqs (5.82)-(5.85), with the necessary initial and boundary conditions, may be numerically solved (Chapter 9). 

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