Multiresponse Kinetic Modeling of Heat-Induced Equilibrium of β‑Carotene cis–trans Isomerization in Medium-Chain Triglyceride Oil

The kinetics and mechanism of the stepwise cis–trans isomerization reactions of all-trans-β-carotene dissolved in MCT (medium-chain triglyceride) oil at temperatures in the range of 80–160 °C have been analyzed using multiresponse modeling. Quantitation of the cis-isomers was performed using HPLC-DAD and quantitation at the reaction isosbestic point at 421 nm. Multiresponse kinetic modeling using the Bayesian criterion was initially performed at 120 °C to determine the best model. Subsequently, the reparametrized Arrhenius equation was used to calculate the activation energies of all reactions. The equilibrium constants for the individual isomerization reactions were determined from the rate constants and the final product distributions. The enthalpies and entropies of the isomerization reactions were determined from the temperature dependence of the equilibrium constants. The 13-cis and 13,13′-di-cis isomers were found to be the fastest formed isomers followed by the 9-cis, 9,13-di-cis, and 13,15-di-cis isomers, where the latter was found to be formed from 13-cis and not the 15-cis isomer. The relative free energies of the β-carotene isomers were determined as all-trans < 13-cis < 9-cis < 13,13′-di-cis < 9,13-di-cis ≈ 15-cis < 13,15-di-cis. The entropic contribution of each reaction was found to play an important role in the ordering. It is concluded that the β-carotene system is quite labile at temperatures ranging from 80 to 160 °C and resulting in equilibrium distributions of the cis–trans isomers.