Refined, bleached, and deodorized safflower, sesame and olive oils which did not contain any added synthetic antioxidants were supplied by the Narges and Golbarg-e-Baharan companies. The oils were stored at -18 °C. Curcumin (CAS No. 458-37-7) was purchased from Sigma-Aldrich (St. Louis, MO). All other chemicals were of analytical grade, and standard markers were supplied by Sigma-Aldrich (St. Louis, MO) and Merck (Darmstadt, Germany). The antioxidant capacity of curcumin was measured by the DPPH assay according to the method described by Sanchez et al., (1998). The amount of IC₅₀ for curcumin was 23.61 ± 3.45 µM.

Fatty acid composition was determined by gas-liquid chromatography (Hewlett-Packard, 5890, Palo Alto, CA) according to the AOCS official method Ce 2-66 (Firestone, 2009). For this purpose, oils (0.3 g in 7 mL n-hexane) were converted into their corresponding fatty acid methyl esters by mixing with a solution of methanolic potassium hydroxide (2 mL of 7 N) for 15 min at 65 °C. The gas chromatography device was equipped with a flame ionization detector and a CP-FIL 88 column (with 60 m length, 0.22 mm internal diameter, and 0.2 µm film thickness) (Supelco Inc., Bellefonte, PA). The injector, detector, and oven temperatures were set at 225, 265, and 195 °C, respectively. Nitrogen gas was applied as carrier gas at a flow rate of 1 mL·min^-1.

A Rancimat device (Methrom, model 743 Herisau, Switzerland) was used for determining the induction periods (IPs) of the oils under study. In brief, a batch of 3 ± 0.001 g per oil, containing 0.02, 0.06, or 0.1% (w/w) curcumin, 0.1% (w/w) tocopherol, or 0.02% (w/w) BHT was weighed in separate reaction vessels and placed into the heating channel of the Rancimat. The airflow rate was regulated on 20 L·h^-1, and the temperature inside the conductivity tube was constantly maintained at 25 °C. The oxidative stability of the oils was automatically determined at 373, 383, and 393 K by Apparatus software.

Temperature coefficient (T_C, 1/K) was calculated by the slope (parameter a) of the curve which fitted as follows:

where T is temperature (K), and IP₀ is IP at a reference temperature. The temperature acceleration factor was embodied in the Q ₁₀ number, showing the increase in reaction rate due to a 10 °C rise in temperature, as obtained from Eq. (2).

According to Eq. (3) (Arrhenius equation), the activation energy (E _a) and frequency factor (A) of the secondary oxidation products were calculated by plotting the natural logarithm of k (1/IP) vs the 1/RT.

where R and T represent the molar gas constant (8.3143 J/mol K) and temperature (K), respectively.

According to Eq. (4) and Eq. (5), the Arrhenius equation parameters were calculated using the obtained slope (a) and intercept (b) from Eq. (3).

Enthalpy (ΔH⁺⁺) and entropy (ΔS⁺⁺) of activation were determined by the Eyring equation (Eq. (6)) via drawing ln (k/T) against 1/RT.

where k _B and h are the Boltzmann constant (1.380658 × 10^-23 J K^-1) and Planck’s constant (6.6260755 × 10⁻³⁴ J s), respectively. The values for enthalpy and entropy were calculated using the slope and intercept related to the mentioned relationship, according to Eq. (7) and Eq. (8).

ΔH⁺⁺ and ΔS⁺⁺ were used to determine the Gibbs free energy equation according to Eq. (9).

The percentage of changes (C%) in the kinetic parameters, relevant to inhibited oxidation, were compared to non-inhibited and were calculated according to the following equation:

where X_i and X_c are kinetic parameters in the presence and absence of the antioxidant, respectively.

The percentage of changes in ΔG⁺⁺ due to temperature variations was determined using linear regression between the natural logarithm of changes (%) in ΔG⁺⁺ and temperature. A decrease in the effectiveness of antioxidants (Ef_d) due to an increase in temperature of 10 °C was measured by the slope (a) of said relationship according to Eq. (11).

All evaluations were carried out in triplicate, and the analysis of variance (ANOVA) of the results was performed by SPSS Software. Significant differences among means were compared by Duncan’s statistical test (P < 0.05).

The fatty acid composition of each oil showed a significant difference from other oils in terms of linoleic (C18:2), oleic (C18:1), and palmitic (C16:0) acids (Table 1). The highest amount of saturated fatty acids was found in olive oil, followed by sesame and safflower oils. The highest value for monounsaturated fatty acids, an important symbol of oxidative stability, was observed in olive oil; whereas no significant difference was observed between safflower and sesame oils in this respect. As expected, the highest and lowest polyunsaturation degrees (presented as the nutritional index of the oils) belonged to safflower and olive oils, respectively. Since the average relative rates of oxidation, pertaining to linolenic, linoleic, oleic, and stearic fatty acids were 2500, 1200, 100, and 1, respectively (Hsieh and Kinsella, 1989). The results provided information on the antioxidant activity of curcumin in the diverse lipid systems and in terms of degree of unsaturation.

The absolute values for the oxidation IPs are shown in Table 2. As predicted, the control samples exhibited different levels of oxidative stability. Even though the oxidative stabilities of the oils were not doubled compared to each other, this trend was somewhat maintained as temperatures rose from 373 to 393 K. The results showed that the addition of curcumin increased the oxidative stability of the oils. Despite the fact that increasing the concentration of curcumin improved the oxidative stability of the oils, the growth slope of the IP was unique for each oil (Figure 1a). Such contradictory behavior of curcumin can be attributed to the occurrence of complex chemical reactions. These reactions are most likely due to the residual radical of curcumin after releasing [H]⁺ and by the excitation of oxidation chain reactions, whereby lipid substrates are attacked (Fennema, 1996). Thus, the best and most economical concentration of curcumin was 0.02% in the bulk oils of this study. Also, the growth slope of IPs, due to increasing temperature eventuated in a significant decrease which appeared more noticeable in the sesame oil. By comparing the performance of the antioxidants in sesame oil, the presence of curcumin at a concentration of 0.02% could be seen as a competitive approach in comparison with the function of tocopherol and BHT. Nonetheless, the behavioral pattern of curcumin requires further discussion on specific measurements and detail in comparison with other antioxidants so as to elucidate the inhibitory mechanism of this valuable natural antioxidant.

It is clear that the rise in temperature is a critical parameter in consideration when monitoring the performance of antioxidants. The role of heat is important in two aspects. First, there are the potential effects on the mechanistic pathway of the oxidation process. It has been confirmed that the general trend of the oxidation process tends to change at temperatures higher than 60 °C (Zheng et al., 2020). Although the reaction rate also increases, the effect of the pathway change is much higher than the reaction rate (Keramat et al., 2021). Second, the effects of temperature on antioxidant molecules which can cause decomposition or evaporation. Meanwhile, heat can convert the antioxidants into per-oxidant compounds. The T_c and Q ₁₀ indices are considered very important tools for evaluating the performance of antioxidants against temperature rise. The percentage of changes in these parameters was lower in olive oil, with the highest amount of oleic acid, compared to the sesame and safflower oils (Table 2). The occurrence of such changes is likely related to the higher resistance of oleic acid at high temperatures.

In general, according to the data in Table 2, it was revealed that the shelf-life of oils in the presence of curcumin has no significant differences with the samples containing synthetic antioxidants. The observation of such effects reveals the favorable inhibitory power of curcumin.

Oxidation reactions of the unsaturated oils tend to occur under any circumstances, while heat accelerates the rate of these reactions like a catalyst. The parameters of the Arrhenius equation actually represent the relationship between temperature and the occurrence of chemical reactions. This relationship has been frequently used in predicting the behavior of reactants and in estimating how many reaction products can be produced (Golmakani et al., 2020a; Toorani and Golmakani, 2022; Zheng et al., 2020). Since the amount of secondary oxidation products was a criterion for estimating Arrhenius parameters such as E _a, the measured parameter was introduced as the “activation energy of curcumin”. In fact, the term refers to a rise in the required energy, created by curcumin or other antioxidants, for lipid oxidation to occur less easily. The results of E _a showed that curcumin desirably increased the oxidative resistance of all oils even at 393 K (Table 3). One of the concerns before starting the research was the thermal degradation of curcumin and the destruction of its inhibitory function at high temperatures due to the presence of many functional groups in the chemical structure of curcumin. However, the results showed that this antioxidant is highly capable of resisting 393 K. The highest value for E _a was observed in sesame oil when using 0.1% curcumin, which was higher than in samples with any other antioxidant.

Compared to the control samples, the percentage of increase in E _a by curcumin ultimately led to finding the optimal performance of this antioxidant in the lipid systems under study (Figure 1b). The highest amount of this parameter was found in sesame oil - in response to different concentrations of curcumin. It has been proven that this factor cannot be considered exclusively as an appropriate criterion for predicting the intensity of antioxidant activity (Toorani et al., 2021). It is clear that the function of an antioxidant is affected by both factors of the Arrhenius equation, namely E _a and A. The results of the A parameter (log A) showed that this factor increased significantly in the presence of curcumin. A powerful antioxidant is characterized by a high E _a and a low A value. Since the trend of changes in these two parameters was incremental, it became difficult to judge the optimal performance of curcumin. The percentage of increase in A showed a noticeable growth in all samples (Figure 1c). However, the lowest growth percent was observed in the safflower oil with a maximum amount of PUFA. It is clear that the variations in A values per antioxidant were proportional to the changes in E _a, so that a decrease in A significantly reduced the E _a value. The A value was mathematically defined as serving a reaction rate whereby all reactants have enough energy for a chemical reaction to occur ( i . e . E a = 0 ) or in a case where the temperature inclines to infinity ( T → ∞ ) (Toorani and Golmakani, 2022). In fact, A is a criterion of reaction rate, showing the reactivity of lipid systems against oxidation. Therefore, considering the two Arrhenius parameters together is the most reliable way to understand how fast a reaction proceeds.

According to the activation complex theory, the reactants should form an intermediate compound by interconnection and structural rearrangement to facilitate the production of the final product. As an activated complex, it has more energy than the reactants and the products, thereby defining the overall rate of chemical reactions. The stored energy (ΔH⁺⁺) in this structure is consumed, while changing the length and angles of reactant bonds, thereby causing structural integrity and molecular rearrangement (Atkins et al., 2014). ΔS⁺⁺ is a symbol of environmental disorder and indicates an associative mechanism in which the reactants create an intermediate complex (Espenson, 1995). Higher values for ΔS⁺⁺ show an increase in the possibility of creating activated complexes. In fact, the reaction is likely to occur by participating the fewer molecules of reactants. A lower ΔS⁺⁺ value (more negative) and higher ΔH⁺⁺ value are indicative of the high stability of lipid systems against temperature changes. According to Table 3, the highest and the lowest amount of ΔH⁺⁺ among lipid systems in the non-inhibited condition was observed in olive and safflower oils, (79.7 vs. 71.2 kJ mol^-1), respectively. In the presence of curcumin (0.1%), however, maximum ΔH⁺⁺ was observed in sesame oil (104.2 kJ mol^-1). The highest and lowest ΔH⁺⁺, considering all concentrations of curcumin, were observed in sesame and safflower oils, respectively. This can be attributed to a mismatch between the produced hydroperoxides and the function of inhibitory mechanisms of antioxidants (Toorani and Golmakani, 2021). As the precursor of oxidation products, the generated hydroperoxides in safflower oil were very unstable due to noticeable amounts of linoleic acid and the presence of allylic and bis-allylic carbons in its acyl chain. On the other hand, the presence of a methoxy group in the vicinity of the antioxidant agent (-OH), due to high electronegativity, decreased the rate of hydrogen release into the medium, thereby preventing quench free radicals (Barzegar, 2012). Thus, the tendency of curcumin to trap extremely active hydroperoxides is practically negligible.

The results indicated that adding curcumin to the oils increased ΔS⁺⁺ in all samples. The highest and lowest values for ΔS⁺⁺ were observed in sesame oil with 0.1% curcumin and in safflower oil with 0.02% curcumin, respectively. However, none of the parameters of the Eyring equation alone could predict the optimal performance of curcumin or any other antioxidant.

An analysis of the results showed that variations in the Eyring and the Arrhenius parameters were interdependent. Two appropriate linear models were obtained between the parameters of the Eyring and Arrhenius equations (Figure 2a and Figure 2b). These relationships were identical in the case of each oil with different unsaturation degrees. The obtained experimental models were quite similar to the equations reported by Farhoosh and Hoseini-yazdi (2014). Specifically, the slopes were identical, whereas the intercepts were slightly different. According to the transition state theory, the Eq.s (12) and (13) show the involved variables for converting the parameters of Eyring and Arrhenius models to each other.

It is proven that ΔG⁺⁺ is a suitable parameter for the purpose of comparing the oxidative stability of oils (Golmakani et al., 2020b; Veloso et al., 2020). Higher values for ΔG⁺⁺ indicate higher stability of the lipid systems against oxidation reactions. In olive and sesame oils, the ΔG⁺⁺ values showed that curcumin performance was better than tocopherol and BHT at 373 K (Table 3). However, higher temperatures slightly reduced the effectiveness of curcumin, since the ΔG⁺⁺ was more affected by ΔS⁺⁺ values than by ΔH⁺⁺. Accordingly, more negative ΔS⁺⁺ values further increased the ΔG⁺⁺, which means an increase in oxidative stability. In safflower oil, curcumin was less effective than tocopherol and BHT in enhancing oxidative stability at 373 K. Nonetheless, this trend changed at higher temperatures (383 and 393 K) and made curcumin show no significant difference in function compared to the other two antioxidants. While increasing the temperature enhances the effect of entropy coefficient in the equation of ΔG⁺⁺ (Eq. (9)), changes in this index are further revealed at higher temperatures. In safflower oil, ΔH⁺⁺ was much lower than in the other two oils, and the curcumin effect was more apparent in ΔS⁺⁺. It should be noted that the increase in ΔG⁺⁺, due to rising temperatures, arose from the endothermic nature of the active complex taking form during the oxidation reactions (Toorani and Golmakani, 2022).

The changes in ΔG ⁺⁺ at different temperatures indicated a lower dispersion of data pertaining to various lipid systems (Figure 2c). A lack of outlier data reflected the accuracy of the calculations and normality of the data. Also, the size of the box plots of the lipid systems was different, meaning that the growth coefficient in curcumin efficiency differed per oil when the curcumin concentration increased. Furthermore, the distribution of data indicated an increase in their dispersion, parallel to the increase in temperature. This can be attributed to a high degree of antioxidant susceptibility to heat, the decomposition caused thereof, and/or loss via volatilization, which is known as the carry-through property (Dugan and Kraybill, 1956).

Based on the percentage of increase in ΔG⁺⁺, the best performance of curcumin was observed in sesame oil, where its efficiency was higher than tocopherol but not significantly different from BHT (Figure 2d). Surprisingly, curcumin (0.02%) showed optimal performance, although the antioxidant activity of curcumin was less than that of the other two antioxidants in olive and safflower oils. The difference in the function of curcumin in various oils is likely due to a difference in the types of active radicals which were produced and of the hydroperoxides in these oils, which were not well adapted to the inhibitory mechanisms of this antioxidant. In all samples containing curcumin, the results showed that the percentage of growth in ΔG⁺⁺ decreased in a consistent manner when the temperature increased. Also, a similar trend was observed in the case of tocopherol, but the decline in growth was lower in the presence of BHT, possibly because of the high resistance of BHT to evaporation and thermal degradation. It is clear that an increase in temperature reduced the effectiveness of all antioxidants. The Ef_d of curcumin was 0.68 by an increase of 10 K (regardless of oil type and antioxidant concentration) (Figure 2e).

As can be seen in Figure 3, power equations with high correlations (R² > 0.99) can properly describe the relationship between the values for IP and ΔG⁺⁺. The obtained nonlinear relationships indicated that the inhibitory power of phenolic antioxidants did not increase linearly by an increase in their concentration. This approach did not change fundamentally by increasing the temperature. On the other hand, the obtained exponential equations enable predictions of ΔG⁺⁺ using simple data such as IP. It is clear that the estimation of ΔG⁺⁺ at various temperatures can enable suitable assessments of the efficiency of antioxidants.