Abstract
The applicability of the William, Landel and Ferry (WLF) equation with a modification to take into account the effect of melt-dilution and an empirical log-logistic equation were evaluated to model the kinetics of diffusion-controlled reactions in frozen systems. Kinetic data for the alkaline phosphatase catalysed hydrolysis of disodium- p-nitrophenyl phosphate (DNPP) in four model systems with different glass transition temperatures at maximal freeze-concentration ( T g′) comprising sucrose ( T g′=−34.2 °C), maltodextrin ( T g′=−14.4 °C), carboxymethylcellulose (CMC), ( T g′=−12.6 °C) and CMC–lactose ( T g′=−23.1 °C) in a temperature range of −28 to 0 °C were used. The modified WLF equation was used with a concentration-dependent glass transition temperature ( T g) as well as T g′ as reference temperatures. For both cases, the equation described well the reaction kinetics in all the systems studied. The log-logistic equation also described the kinetics in all model systems except in the vicinity of the melting temperature of ice. The effect of melt-dilution on reactant concentration was found to be significant only in the dilute model systems near the melting temperature of ice.
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