Kinetics is the study of the dependence of a chemical reaction on time and temperature. Kinetic reactions are often described using two equations. The first of these is known as the rate equation and describes the relationship between the rate of reaction, time and amount of material. For homogeneous decomposition or volatilization reactions, the reaction is almost universally found to follow the general rate equation which takes the form: ##EQU1## Where: .alpha.=reaction fraction
d.alpha./dt=rate of reaction PA1 k(T)=rate constant at a given temperature T PA1 T=absolute temperature PA1 f(.alpha.)=kinetic expression PA1 n=reaction order PA1 Z=the pre-exponential factor PA1 e=natural logarithm base PA1 E=activation energy PA1 R=gas constant PA1 d.alpha..sub.2 =rate of weight loss at temperature T.sub.2 PA1 f(.alpha..sub.1)=kinetic expression at the value of d.alpha..sub.1 PA1 f(.alpha..sub.2)=kinetic expression at the value of d.alpha..sub.2
The second equation describing kinetic reactions details the dependence of the rate constant on temperature and is known as the Arrhenius equation. EQU k(T)=Ze.sup.(-E/RT) (2)
Where:
The rate and Arrhenius equations may be combined into a single form: ##EQU2##
The parameters E, Z and n are called kinetic constants and may be used to model the dependence of a chemical reaction on time and temperature.
Thermogravimetry is used to obtain kinetic constants of decomposition or volatilization reactions using one of several common methods. One approach is known as the "factor jump" method where the temperature of the test specimen is "stepped" between two or more isothermally held temperatures in the weight loss region. The rate of weight loss (d.alpha./dt) at each of the isothermal regions may be substituted into equation (3), along with the respective isothermal temperature(T). Any two equations for adjacent steps may then be examined as their ratio and the resultant form may be solved for activation energy. ##EQU3## Where: d.alpha..sub.1 =rate of weight loss at temperature T.sub.1
Should the values for d.alpha..sub.1 and d.alpha..sub.2 be extrapolated to a common conversion level, then .alpha..sub.1 =.alpha..sub.2 and ln [f(.alpha..sub.1)/f(.alpha..sub.2)]=0, reducing equation (4) to a more easily evaluated form: ##EQU4##
USPTO Backgrounds
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