**3. Reaction mechanism**

Chemical mechanisms for the Fe(II) and oxygen reactions, Fe(II) and hydrogen peroxide reactions, and/or the oxidation of tartaric acid has been explored by several researchers [7, 8, 18–23]. However, these researchers have not had simultaneous measurements of iron, oxygen, and hydrogen peroxide, and the corresponding constraints that come with these time course measurements. These constraints specifically are: pH dependency on all autocatalytic phases, 1:1 molar oxygen consumption to Fe(III) formation during all autocatalytic phases, and 1:2 molar hydrogen peroxide consumption to Fe(III) consumption during termination. The three simultaneous curves and the constraints have led to the proposed comprehensive mechanism in **Figure 6**.

$$\begin{aligned} \text{Fe}^{\text{II}}(\text{RH}\_{2}) + \text{O}\_{2} &\xrightleftharpoons[\text{Fe}^{\text{III}}(\text{RH}\_{2})\text{-O}\_{2}^{\bullet}]^{2+} \\\\ \{\text{Fe}^{\text{III}}(\text{RH}\_{2})\text{-O}\_{2}^{\bullet}\}^{2+} + \text{Fe}^{\text{II}}(\text{RH}\_{2}) &\xrightarrow{k\_{z}} 2\text{Fe}^{\text{III}}(\text{RH}\_{2}) \text{ + H}\_{2}\text{O}\_{2} \end{aligned}$$

$$\mathrm{RH} \bullet + \mathrm{RH} \bullet \xrightarrow{k\_{\mathrm{II}}} \mathrm{RR}$$

#### **Figure 6.**

*Mechanism used for the modeling of the oxidation of tartaric acid (RH2).*

The chemical reactions associated with k1/k<sup>1</sup> and k2 describe the two-electron transfer to oxygen to produce hydrogen peroxide in the initiation phase of the overall tartaric oxidation reaction. These reactions consider the Fe(II) speciation and utilize Fe(II) tartrate as the oxygen activating species. As the pH increases the concentration of Fe(II) tartrate increases [12–14], thus leading to a shorter lag time during the initiation phase.

Reactions associated with k3/k3, k4, k5/k5, k6, k7, k8, k9, and k12 describe the propagation phase. This scheme describes two alternative propagation pathways; one that utilizes a ferryl (FeO2+) intermediate and another that utilizes a hydroxyl radical (•OH) intermediate. The ferryl intermediate provides an opportunity to explore pH and iron dependency in the propagation phase as it has pKa 4.7 [24]. This pKa allows for pH varying species concentration in the range of wine pH, whereas the hydroxyl radical will be pH independent. The kinetic modeling work described below will only use the ferryl pathway to fit the Fe(III), oxygen, and hydrogen peroxide simultaneous measurements; the pathway described by hydroxyl radical, k12, will not be explored here.

The oxidation of tartaric acid leads to the formation of dihydroxymaleic acid (R) [6, 11]. The reactions associated with k8 and k9 produce dihydroxymaleic acid while continuing to propagate the oxidation cycle by regenerating hydrogen peroxide or regenerating the tartaric radical respectively.

*The Kinetics of Autoxidation in Wine DOI: http://dx.doi.org/10.5772/intechopen.103828*

Finally, the reactions described by k10 and k11 describe termination. The reaction associated with k10 terminates the propagation cycle by producing dihydroxymaleic acid, while also regenerating Fe(II) in the process. On the other hand, k11 terminates the tartaric radical by allowing for a dimerization to occur (RR). This scheme attempts to provide a mechanism that describes the various constraints provided by the experimental measurements. However, it should be recognized that these reactions may not produce distinct isolatable species as proposed, but reactions may happen within an iron-ligand complex and/or multiple iron-ligand complexes.

#### **3.1 The chain reaction in fenton autoxidation**

The stoichiometry indicates that autocatalytic propagation reaction can be described as follows:

$$\text{Fe(II)} + \text{O}\_2 + \text{H}\_2\text{O}\_2 + 2(\text{RH}\_2) \to \text{Fe(III)} + \text{H}\_2\text{O}\_2 + 2\text{H}\_2\text{O} + \text{R} + \text{RH}\bullet \tag{1}$$

(proton needed on the right to balance the charge not shown)

In this reaction, H2O2 is regenerated, one electron is taken from Fe(II) and three remaining electrons for O2 reduction are taken from the substrate: two molecules RH2 are oxidized with the generation of dihydroxymaleic acid, R, and a tartaric radical, RH•. The generation of a radical will result in the formation of peroxy species RHOO• that would undergo the following oxidation,

$$\text{Fe(II)} + \text{RHO}\_2\text{:} \rightarrow \text{Fe(III)} + \text{H}\_2\text{O}\_2 + \text{R} \tag{2}$$

(again, a proton needed on the left to balance the charge)

which maintains the correct 1:1 oxidation stoichiometry and regenerates H2O2. The alternative process with correct stoichiometry is the dimerization of radicals in (Eq. 1) before peroxy radical formation. In addition, other processes such as catalytic reduction of Fe(III) in (Eq. 1) by oxidation of RH•, which would violate 1:1 Fe(II)/O2 stoichiometry, are possible; however, it appears such processes play only minor role at low pH, as experimental data indicate.

As written, in one cycle of the propagation reaction in (Eqs. 1) and (2), *two* H2O2 molecules are generated for each hydrogen peroxide entering the cycle. That means that in one cycle not only H2O2 is regenerated, but one *additional* molecule H2O2 is formed. This would result in the unlimited exponential growth of hydrogen peroxide in the system, unless some termination/dissipation processes stop the growth. Such processes are chain termination reactions, of which one is the radical dimerization reaction; another is oxidation of RH• by Fe(III) in (Eq. 1). The relative rates of chain multiplication and dissipation/termination define the condition of the exponential growth. The presence or absence of the propagation phase (or its limited form at high pH) observed in the autoxidation reaction can be related to the exponential growth condition in the kinetics using linear stability analysis.

In order to explore the condition of exponential growth we consider a simplified reduced description of the system, keeping track of only most important variables: hydrogen peroxide p1 (*h*), tartaric radicals p2 (*r*), oxygen p3 (*o*), and Fe(III), p4 (*f*). For hydrogen peroxide and tartaric radicals we have:

$$\begin{aligned} \dot{h} &= V\_0 - k\_{11}h + k\_{12}r\\ \dot{r} &= k\_{21}r - k\_{22}h - k\_{00}r^2 \end{aligned} \tag{3}$$

Here, V0 is the rate of hydrogen peroxide production by the initiation phase, in the reaction of oxygen and Fe(II); k11 is combined rate of conversion of hydrogen peroxide to hydroxyl radical and to ferryl complexes, and also decomposition of hydrogen peroxide by Fe(II); k12 is the rate of regeneration of hydrogen peroxide by the reaction of tartaric radicals with oxygen; k21 is the rate of generation of tartaric radicals (it may not be exactly same as k11, but close to it); k22 is the rate of tartaric radicals removal due to oxidation by Fe(III) (and generation of dihydroxymaleic acid), reaction that competes with oxidation and generation of hydrogen peroxide; and k00 is the rate of radical dimerization (these should not be confused with the actual rate constants, k11 and k12, in mechanism in the previous section).

As seen, we do not account for all intermediates involved, counting only the initial and final products, partially on the basis that those intermediates are formed on a very short time-scale, such as conversion of hydroxyl radical to tartaric radical, or formation of peroxy-radicals in the reaction of tartaric radicals with oxygen, compared to slow reaction of formation of hydrogen peroxide. The cumulative rates correspond to rate-limiting reactions; for example, formation of hydrogen peroxide from tartaric radical is defined by the proton-coupled electron transfer to peroxy-radical RHOO•. These rates themselves depend on the condition of the reaction, such as pH, and concentration of the substrates; some of them changing significantly in the reaction (oxygen, Fe(II)/Fe(III)), and some do not such as tartaric acid which is in excess. At any given condition, we can assume specific values of these reaction rates and ask what is the kinetics of the system?

The stability of the kinetic system is defined by the linearized equations. Given the current state of the hydrogen peroxide and radicals concentrations, one can ask how a small variation of these concentrations would change the state of the system in time. For small concentrations it is sufficient to consider only a linear part of the system, defined by the kinetic matrix Kij = k11, k12, k21, k22; (or with a modified coefficient k22, k22 + 2k00*r*, due to radical dimerization part). The kinetic solution is bi-exponential, the two rates are given by the eigenvalues of the kinetic matrix, and found from the following equation:

$$\begin{aligned} \det(\lambda - \hat{K}) &= \mathbf{0} \\ (\lambda - k\_{11})(\lambda - k\_{22}) - k\_{12}k\_{21} &= \mathbf{0} \end{aligned} \tag{4}$$

The populations are changing as combination of two exponentials:

$$p\_i(t) = c\_{i1}e^{-\lambda\_1 t} + c\_{i2}e^{-\lambda\_2 t} \tag{5}$$

where ci are some constants. When the product *k*12*k*<sup>21</sup> ¼ 0 the two eigenvalues are *λ*<sup>1</sup> ¼ *k*<sup>11</sup> and *λ*<sup>2</sup> ¼ *k*22. The two rates describe bi-exponential relaxation of hydrogen peroxide and tartaric radicals to their equilibrium values. However, when *k*12*k*<sup>21</sup> >0, one eigenvalue becomes larger (remaining positive), another becomes smaller and may become negative. In this case the negative eigenvalue gives rise to the exponential growth (and propagation phase of the reaction). The condition for a negative eigenvalue and exponential growth is

$$k\_{11}k\_{22} < k\_{12}k\_{21} \tag{6}$$

As we already mentioned, the rate k21 is essentially the same as k11, thus the condition is k21 > k22, that is the rate of generation of radicals is higher than their dissipation. As the determinant of a matrix is a product of its eigenvalues, det *<sup>K</sup>*^ <sup>¼</sup> *<sup>λ</sup>*1*λ*<sup>2</sup> and one eigenvalue is always positive, the condition of one negative eigenvalue is equivalent to:

$$\det \hat{K} < 0 \tag{7}$$

which is equivalent to condition found in (Eq. 6). The rate coefficients, kij of the kinetic matrix K, are themselves functions of the conditions of the reaction, which change with time, thus, the above condition may or may not be satisfied at a given every stage of the reaction.

When the exponential growth of hydrogen peroxide and tartaric radicals begins, the dissipation/termination processes get activated and stationary concentrations will be established, until oxygen and Fe(II) diminish. The stationary (maximum) values are found from (Eq. 3) at the stationary conditions \_ *h* ¼ 0, *r*\_ ¼ 0; assuming relatively small rate of initiation V0, the stationary (maximum) values of hydrogen peroxide and tartaric radicals are:

$$\begin{aligned} \mathbf{h}\_{\rm ss} &\simeq (\mathbf{k}\_{12}/\mathbf{k}\_{11})r\_{\rm ss} + V\_0/k\_{11} \\ r\_{\rm ss} &\simeq (\mathbf{k}\_{12} - \mathbf{k}\_{22})/\mathbf{k}\_{00} + V\_0/(\mathbf{k}\_{12} - \mathbf{k}\_{22}) \end{aligned} \tag{8}$$

here we assumed k21 to be about the same as k11, and thus in the exponential phase k12 > k22.

At low pH, the condition of exponential growth appears to be satisfied up to a very low concentration of oxygen; eventually, of course, it breaks down, as k12 – rate of regeneration of hydrogen, for which oxygen is needed, diminishes, and rate k22 – rate of removal of radicals, bypassing peroxidation, is increasing as Fe(III) increases. The initial lag before fully developed propagation stage is due to the absence of hydrogen peroxide initially, and the incubation period is simply an accumulation of hydrogen peroxide in the system; the exponential multiplication of the initially produced hydrogen peroxide results in the development of the chain reaction that is stabilized by various radical termination process. This fully developed and stabilized chain reaction is what forms the propagation stage of the reaction.

The transition to propagation stage therefore involves a competition between the chain multiplication of radicals and their dissipation. The negative eigenvalue in the kinetic coefficients is a signature of a condition when chain multiplication exceeds that of dissipation.
