Kinetic Parameters
The combinational kinetic model described by Farhoosh (2018) was used to determine the PV-based kinetic parameters. The kinetic curve of the accumulation of LOOH molecules was drawn by plotting PV changes over time (Fig. 2). IP (Eq. (4)) and CMC (Eq. (5)) of LOOH was calculated from the x- and y-coordinates of the intersection point of two straight lines fitted on the initiation and propagation stages of the kinetic curves, respectively. The second straight line precisely arose from the sigmoidal kinetic model (Eq. (6)) fitted on the whole range of PV changes over time.
\(\text{IP}=\frac{K_{1}\ \left(2-\ K_{1}C_{c}+lnK_{2}\right)-4\text{PV}_{0}K_{2}}{4K_{i}K_{2}-\ k_{1}^{2}}\)(4)
\(CMC=K_{i}\left(\text{IP}\right)+\ \text{PV}_{0}\) (5)
\(\text{PV}=\frac{K_{1}\ }{\text{exp\ }\left[K_{1}\left(C_{c}-t\right)\right]+K_{2}}\)(6)
where ki (meq kg−1h−1), k1 (h−1) and k2 (kg meq−1 h−1) are the parameters of the equations; Cc (kg meq−1) is an integration constant and PV0 (meq kg−1) is PV at t = 0.
Antioxidative activities of alkyl gallate and gallic acid in bulk oil peroxidation were examined by effectiveness factor (F ), oxidation rate ratio (ORR), antioxidant activity (A ), and mean rate of antiradical consumption (\(\overset{\overline{}}{W}\)AH).
Stabilization factor (F ) or antioxidant efficiency, which showing the potency of an antioxidant (AH) in delaying oxidation, was calculated by Eq. (7).
\(F=\frac{\text{\ \ \ \ }\text{IP}_{\text{AH}}}{\text{IP}_{0}}\) (7)
where IP0 and IPAH are the IP in the absence and presence of phenols, respectively.
The parameter ORR, which is inversely related to antioxidant power, was determined by Eq. (8).
\(\text{ORR}=\frac{\text{\ \ \ \ }K_{i}}{\text{\ \ \ \ \ \ }K_{i0}}\)(8)
where Ki and Ki0 are the pseudo-zero order rate constants in the presence and absence of phenolic antioxidants, respectively.
Antioxidant activity (A ) was obtained with Eq. (9).
\(A=\frac{F}{\text{ORR}}\) (9)
The parameter \(\overset{\overline{}}{W}\)AH, the average rate of AH consumption, was calculated by Eq. (10) (Marinova and Yanishlieva, 2003).
\({\overset{\overline{}}{W}}_{\text{AH}}=\frac{\text{\ \ }\left[\text{AH}\right]_{0}\text{\ \ }}{\text{IP}_{\text{AH}}}\)(10)