= Autoxidation lag standard addition
Autoxidation lag <standard addition> estimates an initiation rate or an equivalent background trapping capacity by adding known amounts of a reference <radical-trapping antioxidant> to a matched sample matrix. It uses a series of <autoxidation inhibition periods>, rather than treating one delay as a chemical concentration.
Under constant effective initiation rate $R_i$, fast quantitative trapping and unchanged reference stoichiometry $n_s$, let $K_b$ be the initial background capacity and $C_s$ the added reference concentration. Capacity balance gives
$$
R_i\tau=K_b+n_sC_s,\qquad
\tau=a+bC_s,\qquad R_i=\frac{n_s}{b},\qquad K_b=\frac{n_sa}{b}.
$$
Thus the <linear regression> intercept and slope have different roles. The concentration $a/b$ is an equivalent amount of the chosen reference; it does not identify the background <chemical species>.
For an original series, $C_s=0,4,8\,\mathrm{\mu M}$ gives delays $30,70,110\,\mathrm s$. Then $a=30\,\mathrm s$ and $b=10\,\mathrm{s\,\mu M^{-1}}$. With $n_s=2$, the model gives $R_i=0.20\,\mathrm{\mu M\,s^{-1}}$ and $K_b=6\,\mathrm{\mu M}$ of trapping capacity, equivalent to $3\,\mathrm{\mu M}$ of that reference. Using only the largest addition and dividing $n_sC_s$ by its full delay would give about $0.145\,\mathrm{\mu M\,s^{-1}}$, because it incorrectly includes the background delay in the reference-only balance.
At first order, if $n_s$ is known, $u(R_i)/R_i\approx u(b)/b$. Inference of $K_b=n_sa/b$ also involves the fitted intercept-slope <covariance>; treating fitted parameters as independent can misstate the <measurement uncertainty>. Replicates at several concentrations test linearity and estimate the delay variability.
The chemical observation must still be defined. A primary spectrophotometric method monitors a <BODIPY>-based signal carrier co-autoxidizing with a hydrocarbon and distinguishes 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>[Primary abstract, continuous visible-light method and kinetic/stoichiometric distinction]{ref} The regression above is a stated capacity model, not an assertion that this paper used this particular numerical series. Keep solvent addition, initiation, <temperature>, oxygen supply and breakpoint rule matched. Curvature can reveal altered chemistry, <oxygen-limited autoxidation> or time-varying initiation; it should not be hidden by forcing a straight line.
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