Snapshot 1: isothermal degradation curve following first-order kinetics with no asymptotic residual

Snapshot 2: nonisothermal degradation curve initially following first-order kinetics and having an asymptotic residual (rising temperature)

Snapshot 3: nonisothermal degradation curve following first-order kinetics with no asymptotic residual (rising temperature)

Snapshot 4: nonisothermal degradation curve initially following first-order kinetics and having an asymptotic residual (falling temperature)

Snapshot 5: nonisothermal degradation curve following first-order kinetics with no asymptotic residual (falling temperature)

The isothermal chemical degradation of L-ascorbic acid (AA) has two major pathways. The first and faster is the "aerobic" mechanism where the AA is first oxidized to dehydroascorbic acid (DHAA), which subsequently decomposes. The second is the much slower "anaerobic" mechanism where the AA molecules themselves decompose. (Since the DHAA formed in the aerobic pathway has a vitamin activity, the decrease in the AA concentration is not synonymous with vitamin C loss. Nevertheless, it is more convenient to monitor only the diminishing concentration of AA and treat it as a marker.)

When the two mechanisms operate simultaneously, experimentally observed degradation curves, based on the diminishing AA concentration, frequently follow the model

where

is the time-dependent concentration ratio

,

is the asymptotic residual concentration ratio

, and

a temperature-dependent rate constant [1, 2]. Thus, where

, the decay follows the conventional first-order kinetics.

The temperature-dependence of

has been traditionally described by the Arrhenius equation [1, 2]. It has been shown that experimental

versus

data described by the Arrhenius equation can also be described by the much simpler exponential model

without sacrificing the fit [3–5]. In this model,

is the rate constant at an arbitrary reference temperature

* *, both

* and * are in °C, and

is a characteristic constant having units

. Incorporating

so defined into the isothermal degradation equation renders the general isothermal model

.

For a nonisothermal temperature history

, we assume that the AA's momentary decay rate is the isothermal rate at the momentary temperature

, at a time

that corresponds to its momentary concentration ratio

[4]. Implementing this assumption renders the general degradation model in the form of the numerical solution for

of the rate equation

where

. The boundary condition is

.

In this Demonstration, you can choose between simulating isothermal degradation patterns of AA at chosen constant temperatures and dynamic degradation patterns of AA at linearly rising and falling oscillating temperatures as examples. You can vary the AA's degradation kinetic parameters, namely,

,

,

* *and

. You can also vary the chosen constant temperature

or dynamic temperature profile parameters

, the initial temperature in °C (

), the slope of the temperature rise (

) or fall (

) in

units

, the temperature oscillation's amplitude in °C, and

, their frequency in units of

.

Notice that certain combinations of

,

, and

in the dynamic temperature profile equation will render the isothermal solution for the initial temperature

.

[1] M. C. Viera, A. A. Teixeira, and C. L. M. Silva, "Mathematical Modeling of the Thermal Degradation Kinetics of Vitamin C in Cupuaçu (

*Theobroma grandiflorum*) Nectar",

*Journal of Food Engineering*,

**43**(1), 2000 pp. 1–7.

doi:10.1016/S0260-8774(99)00121-1.

[2] L. Verbeyst, R. Bogaerts, I. Van der Plancken, M. Hendrickx, and A. Van Loey, "Modelling of Vitamin C Degradation during Thermal and High-Pressure Treatments of Red Fruit,"

*Food Bioprocess Technology*,

**6**(4), 2013 pp. 1015–1023.

doi:10.1007/s11947-012-0784-y.

[3] M. Peleg, M. D. Normand, and M. G. Corradini, "The Arrhenius Equation Revisited,"

*Critical Reviews in Foods Science and Nutrition*,

**52**(9), 2012 pp. 830–851.

doi:10.1080/10408398.2012.667460.

[4] M. Peleg, A. D. Kim, and M. D. Normand, "Predicting Anthocyanins' Isothermal and Non-isothermal Degradation with the Endpoints Method,"

*Food Chemistry*,

**187**, 2015 pp. 537–544.

doi:10.1016/j.foodchem.2015.04.091.

[5] M. Peleg, M. D. Normand, and T. R. Goulette, "Calculating the Degradation Kinetic Parameters of Thiamine by the Isothermal Version of the Endpoints Method,"

*Food Research International*,

**79**, 2016 pp. 73–80.

doi:10.1016/j.foodres.2015.12.001.