= Autoxidation initiation-rate calibration
\b[Autoxidation initiation-rate calibration] estimates the effective rate at which radical chains enter the specified <inhibited autoxidation assay>. It connects a measured inhibition delay to chemical trapping capacity. Initiator concentration by itself is not necessarily this effective rate: decomposition, radical escape and reaction conditions can affect how many chains are actually initiated.
For a known reference <radical-trapping antioxidant> at concentration $C_s$ with trapping stoichiometry $n_s$, assume constant effective initiation rate $R_i$ and rapid, quantitative trapping until exhaustion. Capacity balance gives
$$
R_i\tau_s=n_sC_s,\qquad R_i=\frac{n_sC_s}{\tau_s}.
$$
This calibrates the initiation rate only to the extent that the reference stoichiometry and the inhibition-period interpretation are valid. A single unknown antioxidant cannot generally determine both its own trapping capacity and $R_i$.
<Autoxidation lag standard addition> can expose a background capacity. Under an additive-capacity model,
$$
\tau(C_s)=\tau_0+\frac{n_s}{R_i}C_s.
$$
An original series with added reference concentrations $0$, $5$ and $10\,\mathrm{\mu M}$ and measured periods $20$, $120$ and $220\,\mathrm s$ has slope $20\,\mathrm{s\,\mu M^{-1}}$. For $n_s=2$, this implies $R_i=0.10\,\mathrm{\mu M\,s^{-1}}$. The intercept represents an equivalent pre-existing trapping capacity $R_i\tau_0=2\,\mathrm{\mu M}$ under this model; it does not identify the background chemical species.
Using $n_sC_s/\tau$ without accounting for the intercept would give about $0.0833$ and $0.0909\,\mathrm{\mu M\,s^{-1}}$ at the two nonzero additions, instead of the common slope-based value. A concentration series therefore tests more than one isolated lag measurement. Curvature or changing slopes can indicate that addition changes the chemistry or that the initiation rate is not constant.
The signal still needs a reaction model. A primary visible-light method follows a <BODIPY>-based signal carrier co-autoxidizing with a hydrocarbon substrate, distinguishing radical-trapping kinetics from stoichiometry.<A Continuous Visible Light Spectrophotometric Approach To Accurately Determine the Reactivity of Radical-Trapping Antioxidants by Evan A. Haidasz and others>[Indexed abstract, signal-carrier method and kinetic/stoichiometric distinction]{ref} A fitted optical breakpoint is not automatically the instant of chemical exhaustion.
For time-dependent initiation, the balance becomes $\int_0^\tau R_i(t)\,\mathrm dt=n_sC_s$. Temperature, solvent, oxygen availability, reference identity and the observation procedure must therefore remain controlled or explicitly modeled. The calibration belongs to the assay conditions, rather than being an intrinsic constant transferable to every oxidation experiment.
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