Successive Three-Point Method for Weibullian Chemical Degradation
Successive Three-Point Method for Weibullian Chemical Degradation
This Demonstration considers nonisothermal chemical degradation of a labile compound, in which the temperature can vary with time . Under isothermal conditions (), the degradation follows a Weibullian model: , where is the time-dependent concentration ratio, , is a temperature-dependent rate parameter, and is a dimensionless temperature-independent curvature index ("shape factor"). An exponential model for the temperature dependence of the rate parameter is used, a simpler substitute for the Arrhenius equation, , where is the rate parameter at a reference temperature and a constant in units of reciprocal temperature. The decay pattern for is then described by an ordinary differential equation whose three parameters, , and can be estimated from three successive experimentally determined concentration ratios. These are subsequently used to predict the concentration ratio at different times under the same and/or different temperature histories. The concept is demonstrated with simulated storage under three different fluctuating temperature regimes. The three model parameters are obtained by selecting a degradation curve generated with the model for the specified temperature history through the three selected concentration ratios, using the mean squared error (MSE) as a guide and for fine tuning.
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T(t)≠constant
T(t)=T
logC(t)=-b(T)
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0<C(t)≤1
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b(T)=exp(c(T-))
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T(t)≠constant
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T(t)