Initiator-limited antioxidant exhaustion

Initiator-limited antioxidant exhaustion describes whether a finite radical source can consume all the trapping capacity in an inhibited autoxidation assay. A missing end to an autoxidation inhibition period can result from too little integrated initiation, rather than an unlimited amount of radical-trapping antioxidant.

Let $K_0=n{C}_{A0}$ be the initial radical-trapping capacity, measured in concentration of trapped chain carriers. Assume quantitative trapping, no regeneration or competing loss, and an initiation flux $R_i(t)=R_0{e}^{-kt}$ with $R_0,k>0$. Before exhaustion the remaining capacity isThe source can deliver only $Q_{\infty }=R_0/k$. Consequently, $K_0<Q_{\infty }$ gives finite exhaustion timeIf $K_0=Q_{\infty }$, capacity approaches zero only as $t\to \infty$. If $K_0>Q_{\infty }$, a positive capacity $K_0-Q_{\infty }$ remains even at infinite time. These are different outcomes despite both lacking a finite exhaustion breakpoint.

For an original example, $R_0=0.20\mu \mathrm{M}{\mathrm{s}}^{-1}$ and $k=0.010{\mathrm{s}}^{-1}$ give total supply $20\mu \mathrm{M}$. Initial capacities $10$, $20$ and $25\mu \mathrm{M}$ respectively give exhaustion at $69.3\mathrm{s}$, asymptotic exhaustion, and a residual $5\mu \mathrm{M}$. The initial-rate estimate $K_0/R_0$ would wrongly predict a finite $100\mathrm{s}$ exhaustion time in the middle case.

The logarithm explains a sensitive regime. For $\alpha =K_0/Q_{\infty }\ll 1$,but $t_{\ast }$ diverges as $\alpha \to 1^{-}$. Small capacity or initiation-calibration changes near that threshold can cause large lag changes.

A primary visible-light autoxidation method distinguishes trapping kinetics from stoichiometry through a coupled oxidation readout.^[ref] In the model here, a controlled second initiator addition can test whether capacity remains after the first source declines. A matched blank and independent autoxidation initiation-rate calibration are essential: extra initiation can change the optical reaction, and a persistent background source would eventually exhaust even capacity above $Q_{\infty }$. An absent breakpoint alone does not distinguish these mechanisms.