Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 51

combustion temperatures can be predicted from experimental kinetic measurements
conducted at significantly lower temperatures of thermal degradation.
Most commonly predicted parameter is the so-called lifetime. By its meaning, this
is the time beyond which the material loses its properties to such degree that it cannot
serve efficiently its intended purpose. For example, when exposed to heat, plastic
polymeric material may lose plasticizer together with it its plasticity. The methods of
thermal analysis such as TGA and DSC are among the most common experimental
techniques employed for estimating the lifetime of materials exposed to heat. As
long as decay in the property of interest can be linked to a change in the mass or heat,
the lifetime of a material can be estimated by the thermal analysis methods. TGA,
for instance, can be readily used to measure the kinetics of plasticizer loss while ex-
posing polymeric material to heating. Suppose that the critical decay of plasticity is
reached when the material has lost 20 wt. % of plasticizer. Then, in kinetic terms, the
initial state, when no plasticizer is lost, corresponds to the extent of conversion, ʱ = 0.
On continuous heating, the material would gradually lose 100 wt. % of plasticizer,
reaching the final state ( ʱ = 1). The critical state of the material would be reached at
ʱ = 0.2, i.e., at 20 wt.% loss of plasticizer. Then, the lifetime of the material can be
estimated as the time to reach ʱ = 0.2, i.e., t 0.2 . Let us consider several methods of
estimating (predicting) the time to reach a given extent of conversion, t ʱ .

2.3.2 Model Based Versus Model Free

For a single-step process taking place at constant temperature, T 0 , the time to reach
any given value of ʱ is readily determined by rearranging Eq. 2.3:

g () α

t = .

α

E
RT

− (2.39)

A exp

0

Equation 2.39 affords prediction of the lifetime of material exposed to isothermal
heating at the temperature T 0 . To employ this equation, one needs to evaluate the
whole kinetic triplet for the process responsible for the decay in the property of
interest. For example, in the aforementioned case of the polymeric material losing
its plasticity, this process is the mass loss of the plasticizer. The triplet can be evalu-
ated from isothermal as well as nonisothermal experiments. However, one should
be warned specifically against using single-heating-rate methods. These methods
produce notoriously unreliable kinetic triplets that give rise to meaningless kinetic
predictions [ 73 ].
Equation 2.39 provides a foundation for two American Society for Testing and
Materials (ASTM) methods developed for evaluating the thermal stability from
TGA (E1641 [ 74 ]) and DSC (E698 [ 75 ]) data. The predictive equation utilized by
E1641 is: