# How Kamal-Sourour parameters in Kinetics Neo correspond to original equation da/dt=(k1+k2*a^m)*(1-a)^n?

Kamal-Sourour model in the literature [1] is developed for curing of epoxy at isothermal conditions and therefore does not contain the temperature dependence for the rate constants:

In Kinetics Neo we use * extended*,

*version of equation, where the reaction rates have the*

**improved***:*

**Arrhenius dependence on temperature**If the pre-exponential factor A_{1} is placed outside of brackets, then the equation looks as following:

where *PreExp *= *A _{1}*,

*AutocatOrder*=

*A*

_{2}/A_{1}For reaction A→B the reactant A has concentration a (changes from 1 to 0 during reaction), and the product B has concentration b (changes from 0 to 1). Degree of conversion *alpha* corresponds to concentration *b of product B*, and *(1- alpha)* corresponds to concentration *a of reactant A*. After this replacement the kinetic equation is rewritten using concentrations (here is example for step A→B):

This equation is equal to equation in Kinetics Neo:

**d(a->b)/dt=PreExp*a^n* [Exp(-ActivationEnergy/(RT)) +AutocatOrder*(b^m)*Exp(-ActEnergy2/(RT))]**

where *ActivationEnergy *= *E _{1}*, and

*ActEnergy2*=

*E*.

_{2}For * isothermal *conditions this equation is

*:*

**equal to classical Kamal-Sourour equation****dα/dt=(k _{1}+k_{2}*α^{m})*(1-α)^{n } with k_{1}= PreExp* Exp(-ActivationEnergy/(RT)) and k_{2}= PreExp* AutocatOrder *Exp(-ActivationEnergy/(RT))**

## Simplified Kamal-Sourour models in Kinetics Neo:

**Cmn **is the simplified Kamal-Sourour reaction, where **E _{1}=E_{2}**

**Cn **is the simplified Kamal-Sourour reaction, where **E _{1}=E_{2}**and

**m=1**

**C1 **is the simplified Kamal-Sourour reaction, where **E _{1}=E_{2} m=1 **and

**n=1**

## Referencees

1. S.Sourour, M.R.Kamal Differential Scanning Calorimetry of Epoxy Cure: Isothermal Cure Kinetics, Thermochimica Acta, 14 (1976) 41-59.