The optimum experimental design for determining the kinetic parameters of the model resulting from the Weibull probability density junction was studied, by defining the sampling conditions that lead to a minimum confidence region of the estimates, for a number of observations equal to the number of parameters. It was found that for one single isothermal experiment the optimum sampling times corresponded always to fractional concentrations that are irrational numbers (approximately 0.70 and 0.19) whose product is exactly l/e'. The experimental determination of the equilibtium conversion (for growth kinetics) is vety important, but in some situations this is not possible, e.g. due to product degradation over the length of time required. Sampling times leading to a maximum precision were determined as a function of the maximum conversion (or yield) attainable. For studies of kinetic parameters over a range of temperatures, performed with a minimum of three isothermal experiments, it was proved that the optimum design consists of two experiments at one limit temperature with two sampling times (those corresponding to fractional concentrations of approximate[v 0.70 and 0.19) and another at the other limit temperature for a sampling time such that the fractional concentration is lie. Case studies are included for clarijication of the concepts and procedures.

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The thermal degradation of ascorbic acid (AA) in orange juice was analysed over in a 20–45 °C temperature range. Dehydroascorbic acid (DA), pH and browning were also monitored. Small amounts of AA degradation could be described by first order kinetics, but when only low amounts of AA were retained sigmoidal kinetics were clearly appropriate. The Weibull model was used to describe this pattern (R2adj > 0.995). The rate constant increased with temperature according to an Arrhenius‐type relationship. The activation energy was 38.6 kJ/mol and at the average temperature of the range tested, 32.5 °C, the rate constant was 64.4 × 10−3 h−1. The shape constant decreased linearly with temperature, from 2.17 to 1.13. Before the time when the maximum degradation rate occurred, pH, DA concentration and browning remained fairly constant, and then increased. It was found that this behaviour, as well as the dependence of the shape constant on temperature, might be explained by (i) the reconversion of DA into AA, following first order kinetics in relation to DA and second order kinetics in relation to AA, and by (ii) different sensitivities of the reaction rate constants to temperature. Browning was also well described by the Weibull model with a temperature independent shape constant.

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