= Spike equilibration
<Spike equilibration> is the process by which added <analyte> comes to share the chemical forms or physical environments relevant to recovery of the native <analyte>. Mixing a solution uniformly is not sufficient if native material is bound, trapped or otherwise inaccessible to the added material. The <spike-recovery estimate> is representative only to the extent that the two undergo comparable processing.
IUPAC's recovery guidance makes this equivalence a condition for using an added surrogate to correct native recovery. It notes that even an isotopically modified <analyte> can fail to equilibrate with native material bound to the <sample matrix>.<Harmonised guidelines for the use of recovery information in analytical measurement by Michael Thompson and others>[Eurachem-hosted text, §§3.2–3.2.2, equivalence, isotope dilution and spiking.]{ref}
An original two-environment model describes a fast-extractable fraction $a(t)$ approaching $a_{\rm eq}$:
$$
a(t)=a_{\rm eq}+[a(0)-a_{\rm eq}]e^{-t/\tau}.
$$
Let the fresh spike start entirely accessible, $a(0)=1$, while native material has accessible fraction $a_{\rm eq}=0.20$. With stipulated <spike equilibration time> $\tau=5\,\mathrm{min}$, a 15-minute wait leaves $a\approx0.240$, not 0.20. If extraction measures only the accessible material, correcting a native recovered amount 20 by the spike's apparent recovery 0.240 gives approximately 83.4, below the true 100 amount units. The mismatch persists despite a high initial spike recovery.
A useful test varies the waiting time before extraction while keeping preparation and added <analyte> amount fixed. Compare the behavior of the spike with independent native-material or <reference material> evidence where available. A stable time series supports constancy over that window, but cannot prove that an inaccessible native compartment has been sampled.
More vigorous processing may change chemical forms or destroy the <analyte>; longer waiting alone does not guarantee equivalence. State addition timing, equilibration conditions and the extraction stage to which the measured <extraction recovery> applies. These choices are part of the <measurement model>, rather than details that can be recovered from the final percentage alone.
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