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A flexible technique to fingerprint and evaluate the oxidative behaviour of lipids past their oxidative stability

The becoming equation

To suit the experimental information of an oxygen uptake curve, a operate was chosen which is a mix of a sigmoidal operate (left(frac{1}{1+{e}^{-{lambda }_{0}left(t-{t}_{0}proper)}}proper)) and an exponential or bi-exponential (left(A{e}^{-{lambda }_{1}t}proper.) or (left.Aleft[q{e}^{-{lambda }_{1}t}+left(1-qright){e}^{-{lambda }_{2}t}right]proper)) decay operate. The bi-exponential operate was used each time the becoming of the mass loss area carried out with a single exponential will not be sufficiently correct. The time period t0 within the sigmoidal operate, accounts for the delay noticed within the mass enhance and, subsequently, correlates with the induction time within the peroxide formation course of. The worth of the time fixed ({lambda }_{0}) is correlated with the speed of the oxygen uptake. The time fixed ({lambda }_{1}), and when used ({lambda }_{2}), are correlated with the speed of all phenomena resulting in mass loss, (q) and ((1-q)) being the relative weight of the 2 exponentials, when each current. The selection of utilizing exponential capabilities to explain each the oxygen uptake step and the lack of mass implicitly implies that the underlying kinetic processes are assumed to be of the primary order or the pseudo first order with respect to the substrate focus. This assumption is in accordance with what’s reported within the literature for these experiments when carried out underneath non-limiting oxygen situations53,54.

An evaluation of experimental curves proven in earlier works31,32 means that it ought to at all times be ({lambda }_{0}gg {lambda }_{1},{lambda }_{2}), for the reason that spinoff (left(frac{dmass%}{dt}proper)), evaluated on the two inflection factors, is at all times considerably higher, in absolute worth, throughout mass acquire versus mass loss. In these works31,32 we proposed the usage of becoming capabilities of the sort:

$$masspercentleft(tright)=frac{A{e}^{-{lambda }_{1}t}}{1+{e}^{-{lambda }_{0}left(t-{t}_{0}proper)}}+B$$



$$masspercentleft(tright)=frac{Aleft[q{e}^{-{lambda }_{1}t}+left(1-qright){e}^{{-lambda }_{2}t}right]}{1+{e}^{-{lambda }_{0}left(t-{t}_{0}proper)}}+B$$


Since all exponentials cancel out when t approaches infinity, B represents the worth of the operate on the plateau. When t tends to zero, the operate tends to (left(frac{A}{1+{e}^{{lambda }_{0}{t}_{0}}}+Shiny)), subsequently the mass% at time zero needs to be between (frac{A}{2}+B)(when ({lambda }_{0}{t}_{0}) tends to zero) and B (when ({lambda }_{0}{t}_{0}) is giant). Due to this fact, the 2 beforehand proposed capabilities can describe precisely oxygen uptake curves when the induction occasions are comparatively quick, with a small inaccuracy solely within the preliminary half, simply disguised by the experimental error. In circumstances the place ({t}_{0}) (and consequently ({lambda }_{0}{t}_{0})) is giant, the capabilities 1a and 1b have a tendency as an alternative to the fixed worth B each on the restrict for (tto infty) and for (tto 0), which makes the becoming clearly unacceptable in all these circumstances by which the experimental development exhibits a step between the preliminary plateau and the asymptotic worth for (tto infty).

We subsequently right here suggest the brand new following capabilities:

$$masspercentleft(tright)=frac{A{e}^{-{lambda }_{1}t}-B}{1+{e}^{-{lambda }_{0}left(t-{t}_{0}proper)}}+100$$



$$masspercentleft(tright)=frac{Aleft[q{e}^{-{lambda }_{1}t}+left(1-qright){e}^{{-lambda }_{2}t}right]-B}{1+{e}^{-{lambda }_{0}left(t-{t}_{0}proper)}}+100$$


to precisely interpolate oxygen uptake curves independently from the worth of t0. The capabilities (2a) and (2b) have a tendency asymptotically to the worth (100-B) when (tto infty), whereas for (tto 0) they purchase values in between (frac{A-B}{2}+100) and (100). From the viewpoint of the interpretation of the becoming kinetic parameters, i.e. the time ({t}_{0}) and the time constants ({lambda }_{0}), ({lambda }_{1}) and ({lambda }_{2}), nothing modifications with respect to the becoming Eqs. (1a) and (1b). The identical will be stated in regards to the which means of the parameter q, which quantifies the relative weight of the 2 reducing exponentials, when each are current. The which means of A and B in Eqs. (2a) and (2b), nevertheless, is completely different. To summarize, the which means of every parameter of the brand new equations, Eqs. (2a) and (2b), is as follows:

  • A: amplitude issue of the exponential operate (or of the exponential capabilities) related to the lack of mass.

  • B: deviation of the curve from 100% as t tends to infinity.

  • λ0: obvious price fixed associated to the mass enhance.

  • λ1 and λ2: obvious price constants related to the mass loss.

  • q and (1 − q) (0 ≤ q ≤ 1): relative weights of the 2 related processes liable for the mass loss.

  • t0: is the abscissa of the inflection level of the sigmoidal operate, associated to the induction time of the oxygen uptake.

To estimate the quantity of mass of oxygen added, and the overall mass loss attributable to oxidative degradation, we right here introduce two extra parameters, ({A}_{corr}=A{e}^{-{lambda }_{1}t}) (or ({A}_{corr}=Aleft[q{e}^{-{lambda }_{1}t}+left(1-qright){e}^{-{lambda }_{2}t}right])) calculated on the tonset and ({varvec{C}}={A}_{corr}-B). tonset is the abscissa of the intersection level between the baseline and the tangent to the curve on the first inflection level. The which means of parameters B and C and Acorr is exemplified in Fig. 1.

Oxygen uptake profiles and information becoming

An oxygen uptake profile was recorded for every pattern by isothermal thermogravimetric evaluation underneath air stream. The form of the curve has been confirmed to be affected not solely by the oil composition, but additionally by exterior parameters, together with the temperature of research18,19,23,24. A number of efforts have been devoted within the literature to search out the working temperature that enables to hold out the isothermal experiments in a comparatively quick time, with out considerably affecting the response pathways with respect to these occurring at ambient temperature18,19,23,24. A variety of temperatures, from 80 to 150 °C, has been investigated. Within the evaluation of vegetable oils, 80–90 °C are thought of the very best compromise between a sooner oil oxidation price and a dependable oxygen uptake curve20,22,31. In our work, thermogravimetric curves of plant oils and triacylglycerols had been recorded at 80 °C. Throughout preliminary experiments on methyl linoleate, step one of mass enhance was not seen at 80 °C and solely a pointy lower of mass was noticed. Because of this, methyl linoleate and methyl linolenate had been analysed at 60, 55, 50 and 40 °C. Methyl oleate was analysed solely at 40 °C since already underneath this comparatively low temperature solely a sluggish mass lower was noticed inside 8000 min of research (Fig. 3b).

Oils, triglycerides, and methyl esters

Determine 2a exhibits the experimental thermogravimetric curves and the becoming curves calculated by Eq. (2a) for plant oils (linseed oil, Lo, sunflower oil, So, and olive oil, Oo). Desk 1 shows the curve-fitting parameters and their normal error, together with the relative χ2 and R2 coefficients, which point out the standard of the fittings.

χ2 and R2 values for each linseed oil and sunflower oil are excellent, however not pretty much as good for olive oil; for the latter the becoming equation is intrinsically unable to explain the experimental development within the quick interval between the tip of mass enhance and the start of mass loss, though it nonetheless completely describes the mass enhance and the mass loss areas, and all of the kinetics parameters present very small normal errors. Since in Oo the mass loss is delayed respect to the mass uptake, on this explicit case, the parameter C (efficient whole oxygen taken by the pattern) is the worth of the utmost of the curve, whereas the overall mass lack of the pattern is the distinction between the utmost and the tip of the curve (Acorr calculated at tendset that’s the abscissa of the intersection level between the baseline earlier than the mass uptake and the tangent on the inflection level of the mass decay).

Determine 2
figure 2

Thermogravimetric curves representing oxygen uptake profiles of (a) plant oils and (b) triacylglycerols obtained at 80 °C. Experimental (colored stable line), and theoretical (black sprint dot line) curves as obtained by Eqs. (2a) and (2b).

Desk 1 Values of parameters, χ2 and R2 coefficients obtained by becoming the experimental oxygen uptakes with Eqs. (2a) and (2b) for linseed oil (Lo), sunflower oil (So) and olive oil (Oo) and glyceryl trioleate (OOO) and with Eqs. (2a) and (2b) for glyceryl trilinolenate (LnLnLn) and glyceryl trilinoleate (LLL) at completely different temperatures.

Determine 2b exhibits the experimental thermogravimetric curves and the becoming curves calculated based on Eq. (2b) for triacylglycerols, whereas Desk 1 shows the curve-fitting parameters and their normal error, in brackets, together with the χ2 and R2 coefficients obtained. The similarity between the oxygen uptake curves of plant oils and people obtained for pure triacylglycerols, is fairly evident. OOO exhibits the identical quick delay between the mass enhance and the mass loss as Oo and the becoming equation describes nicely the mass enhance and the mass loss areas however is insufficient to suit the small interval in between. C and Acorr for OOO are thus calculated as for Oo. Acorr and C parameter of the triacylglycerols are calculated in the identical manner as described above for the oils Desk 1.

Determine 3 exhibits the experimental and calculated curves for methyl linolenate and methyl linoleate, whereas the becoming parameters obtained at completely different temperatures are reported in Desk 2. Though the final form of the curves displays fairly nicely that of the corresponding triglycerides, it needs to be famous that the oxygen uptakes had been measured at temperatures completely different than these of oils and acyl glycerides and subsequently the becoming parameters have to be in contrast with warning.

Determine 3
figure 3

Thermogravimetric curves representing oxygen uptake profiles of (a) methyl linoleate (Ln) and methyl linoleate (L) at 60 °C, (b) methyl oleate (O) at 40 °C. Experimental (colored stable line) and calculated (black sprint dot line) curves as obtained by Eq. (2a).

Desk 2 Values of parameters and their normal error in brackets, χ2 and R2 coefficients obtained by becoming the experimental oxygen uptakes with Eq. (2a) for methyl linoleate and methyl linolenate at 40, 50, 55 and 60 °C.

By evaluating the becoming parameters of the investigated techniques with completely different PUFA content material we are able to simply evaluate their oxidative behaviour as mentioned intimately within the following paragraphs.

Induction time

t0 values mirror the development of the oxidative stability of the lipid, and it has an inverse dependence on the variety of unsaturations41. Nevertheless, in plant oils, antioxidants play a serious position in inhibiting or retarding the autoxidation course of55. It’s thus not easy to differentiate, within the oils, the contribution, or the extent of the impact of the antioxidants and the oxidative stability of the constituting glycerides. The oxidative stability due to the quantity and sort of unsaturations is clearly seen after we evaluate the t0 values of acylglycerols which don’t include antioxidant.

Mass uptake

Evaluating the becoming parameters C and λ0 associated to the mass uptake, the noticed development is that linseed oil/glyceryl trilinolenate/methyl linolenate take extra oxygen than sunflower oil/glyceryl trilinoleate/methyl linoleate which, in flip, take extra oxygen than olive oil/trioleine (see Tables 1 and a pair of). The speed of autoxidation varies in the identical order apart from triglycerides for which λ0 is barely increased for glyceryl trilinoleate than glyceryl trilinolenate, though λ0 of glyceryl trioleate continues to be the bottom. The traits of the parameter C is completely according to the variety of double bonds current within the completely different supplies, because the focus of the first oxidation merchandise (hydroperoxides) in addition to the utmost autoxidation price enhance with the focus of unsaturations56,57. It additionally relates with the MBI index, that’s the variety of bis-allylic positions, as these are extra inclined to oxidation with respect to the allylic positions37,41,58. Linolenic, linoleic, and oleic acids current, respectively, two bis-allylic positions at C-11 and C-14, one bis-allylic place at C-11, and none. After we think about the numerical values, small variations are noticed between the oils and the corresponding acylglycerols, which will be simply defined by contemplating the variations of their chemical composition, supporting the robustness of the becoming mannequin. However, methyl esters are a lot sooner to react and take up extra oxygen. This completely different behaviour will be ascribed to the completely different mobility of the unsaturated tails within the two techniques and to the upper viscosity of triglycerides in comparison with that of methyl esters which decelerate the oxygen diffusion. These elements can each have an effect on pace and pathways of reactions.

Mass loss

Oils with the best PUFA content material produce the bottom quantities of secondary oxidation merchandise, which comprise unstable species59. This isn’t solely associated to the variety of unsaturations typically, however, once more, to the variety of bis-allylic positions obtainable upon oxidation. Peroxyl radicals can summary hydrogens solely in bis-allylic positions, whereas alkoxyl radical may additionally summary hydrogens in allylic positions60. Consequently, the focus of bis-allylic positions impacts the response pathways: a excessive focus of bis-allylic hydrogens favour propagation by way of radical abstraction, whereas addition of peroxides to double bonds is favoured in lipids with few bis-allylic hydrogens obtainable60. The ultimate result’s {that a} excessive variety of bis-allylic place favours cross-linking, whereas lipids with a low or null content material of bis-allylic positions are extra susceptible to oxidative degradation6. The becoming parameter A (amplitude of the reducing exponential) is consistent with this remark, displaying that linseed oil/glyceryl trilinolenate/methyl linolenate is much less susceptible to oxidative degradation with respect sunflower oil/glyceryl trilinoleate/methyl linoleate and olive oil/triolein, and that lipids based mostly on oleic acid present the best oxidative degradation.

As in polyunsaturated techniques, in monounsaturated ones, peroxides and different oxidation intermediates are fashioned and so they break all the way down to a variety of secondary oxidation merchandise which embody volatiles compounds61. In another way from oleic acid based mostly oils and triglycerides, the experimental mass change of methyl oleate exhibits solely a sluggish mass loss (Fig. 3b). Since this compound will not be topic to crosslinking to a big extent, it’s doable to invest that the evolution of unstable compounds happens on the identical timescale of the first oxidation giving rise to a globally reducing development of the mass p.c.

Methyl linoleate and methyl linolenate at completely different temperatures

The form of oxygen uptake curves doesn’t solely and unilaterally relate to the composition of the fatty acid substrates but additionally to response situations and particularly to the temperature of research, which essentially influences the response pathways18,19,23,24. As methyl esters are extra reactive than triglycerides9, they had been chosen to research the impact of temperature on the oxidative behaviour of polyunsaturated lipids, by finishing up isothermal thermogravimetry at completely different temperatures (40, 50, 55 and 60 °C).

Determine 4 exhibits the experimental and becoming curves [obtained from the fitting Eq. (2a)] for methyl linoleate and methyl linolenate at 40, 50, 55 °C together with these at 60 °C, already mentioned, for comparability. The becoming parameters are displayed in Desk 2.

Determine 4
figure 4

Thermogravimetric curves representing oxygen uptake profiles of (a) methyl linolenate and (b) methyl linoleate at 40, 50, 55 and 60 °C. Experimental curves are colored stable line; theoretical curves obtained by Eq. (2a) are represented by black dash-dot strains.

The upper the temperature of research, the decrease the utmost reached by the mass %. This may be associated to the speed of decomposition of hydroperoxides. Richaud et al.28 carried out a research on the oxidation of methyl esters of oleic, linoleic, and linolenic acids based mostly on chemiluminescence depth information over time. The authors noticed that the utmost of the curves of chemiluminescence depth will increase with temperature. The chemiluminescence sign is especially associated to the speed of hydroperoxides bimolecular decomposition: the upper the temperature, the upper the decomposition price. The rise of hydroperoxides decomposition noticed at increased temperatures promotes oxidative degradation, leading to a decrease mass % on the most of the curves.

Curves obtained on the completely different temperatures (40, 50, 55, and 60 °C) will be fitted with Eq. (2a).

The becoming of experimental information at 40 °C is kind of unsatisfactory, although. It is because the experimental measurement was stopped when the descent had not but assumed a reducing exponential development. Because of this parameters A, B and C aren’t reported in Desk 2. Nonetheless, concerns on the mass enhance among the many 4 temperatures (40, 50, 55 and 60 °C) are nonetheless doable. The upper the temperature of research, the smaller are the values of t0 and tonset and the upper are the values of the speed fixed λ0. That is in settlement with earlier work that confirmed that, when rising the temperature of research, the induction time turns into smaller25, whereas the speed of hydroperoxides formation will increase29. When the temperature rises (see parameters obtained at 50, 55 and 60 °C—Desk 2), the parameters that estimate the overall lack of mass and the quantity of oxygen taken up, i.e. Acorr and C, differ little. Certainly, a slight enhance of the efficient loss (Acorr) is noticed, whereas the quantity of oxygen taken up (C) drops down.

An Arrhenius plot will be constructed utilizing the values of λ0 at completely different temperatures, to estimate the obvious activation vitality of the oxygen uptake course of. The logarithm of λ0 decreases linearly with the reciprocal of temperature for each methyl esters (R2 = 0.9197 and 0.9759 for methyl linoleate and methyl linolenate, respectively). The activation vitality (Ea = – slopeR) of the uptake of oxygen was evaluated: Eact (methyl linoleate) = 55.6 ± 11.6 and Eact (methyl linolenate) = 44.2 ± 4.9 kJ mol−1. Methyl linolenate has an activation vitality for the uptake of oxygen decrease than methyl linoleate. The values are according to literature information obtained by chemiluminescence depth information28 and gas-chromatography62 and information from non-isothermal DSC curves for ethyl linolenate and ethyl linoleate37,63.

Evaluating the A, Acorr and C parameters obtained at 50, 55 and 60 °C, it’s fairly clear that the upper the temperature of research, the decrease the quantity of mass enhance due to oxygen addition, and the upper the mass loss. The upper mass loss noticed at increased temperatures may have a number of doable explanations. At increased evaluation temperatures the speed of evaporation of the compounds produced by oxidation will probably be higher. Furthermore, at increased temperatures, one can anticipate a better mobility of molecules within the pattern, which may have an effect on response pathways. Lastly rising temperatures of research would possibly overcome activation boundaries that are in place at low temperature.

Glyceryl trilinoleate and glyceryl trilinolenate at 25 °C

Primarily based on the experiments carried out at completely different temperatures on methyl esters (paragraph 3.4), it’s anticipated that kinetic parameters, and extent and price of response with oxygen are completely different upon pure fairly than accelerated evaluation situations. To visualise the extent of this distinction, the experimental oxygen uptake profiles of glyceryl trilinoleate and glyceryl trilinolenate at 25 °C had been recorded by weighing the identical pattern with a microbalance over a interval of two months. The curves are proven in Fig. 5. The noticed traits are qualitatively similar to these recorded at 80 °C by TG. The experimental information obtained at 25 °C in pure ageing situations had been fitted with Eq. (2a) though on this case, given the small variety of experimental factors (about 10 factors for every system), the statistical significance of the becoming parameters is much less good than these obtained with the TG experiments. The curve-fitting parameters obtained are reported in Desk 3. Probably the most evident distinction, clearly excluding the completely different time scale, is that, at room temperature, the mass enhance % is increased than that at increased temperature, as already noticed for methyl esters and reported in literatures for plant oils23. One other distinction issues the obvious price constants associated to the mass enhance (λ0). At 80 °C λ0 values are very related for each triacylglycerols (2.5 × 10–2 and a pair of.8 × 10–2 for glyceryl trilinolenate and glyceryl trilinoleate, respectively), whereas at 25 °C, λ0 of glyceryl trilinolenate is twice than that of glyceryl trilinoleate (10–3 in opposition to 5 × 10–4).

Determine 5
figure 5

Oxygen uptake profiles of glyceryl trilinoleate (LLL) and glyceryl trilinolenate (LnLnLn) obtained at 25 °C. Experimental (colored dot), and theoretical (black sprint line) curves as obtained by Eq. (2a).

Desk 3 Values of parameters and their normal error in brackets, χ2 and R2 coefficients obtained by becoming the experimental oxygen uptakes with Eq. (2a) for glyceryl trilinolenate (LnLnLn) and glyceryl trilinoleate (LLL) obtained at 25 °C.

Comparability of the 2 mannequin equations

As an additional check, the brand new mannequin equations had been examined on polyunsaturated oils (linseed and safflower oil) already studied in our earlier work31. TG curves of linseed and safflower oil, recorded underneath isothermal situations at 80 °C had been fitted based on the outdated Eq. (1b) and the brand new Eq. (2b). Desk 4 studies the outcomes of each becoming procedures. The numerical values obtained are typically completely according to one another, highlighting the identical traits, thus resulting in the identical conclusions.

Desk 4 Values of parameters and their normal error in brackets, Χ2 and R2 coefficients obtained by becoming the oxygen uptake profiles with Eqs. (1b) and (2b) for linseed oil (Lo), and safflower oil (So).


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