= SEC molar mass calibration
{c}
<SEC molar mass calibration> measures standards under the same column, <solvent>, and <temperature> conditions as the unknown. Over a suitable fractionation interval, a common empirical approximation is
$$
\log_{10}\!\left(\frac{M_{\rm app}}{M_{\rm ref}}\right)=a-bV_e,\qquad b>0,
$$
where $M_{\rm ref}$ specifies the <molar mass> unit and $b$ has inverse-<volume (thermodynamics)> units. Interpolation is conditional on the standards' size–<molar mass> relationship. <SEC> measures access associated with <hydrodynamic size>, so a branched <polymer>, an extended chain, and a compact <protein> need not share that relationship.
\Image[/size-exclusion-chromatography-theoretical-calibration.png]
{title=Theoretical <SEC chromatogram> peaks and a stipulated size-to-<molar mass> calibration}
{id=image-size-exclusion-chromatography-theoretical-calibration}
{description=Original model, not measured data: $V_0=5\,\mathrm{mL}$, $V_t=13\,\mathrm{mL}$, $K_d=\operatorname{clip}(1-\log_4(R_h/\mathrm{nm}),0,1)$, and standard-family $M=10^4(R_h/\mathrm{nm})^2\,\mathrm{g\,mol^{-1}}$. Equal-area <Gaussian distribution> peaks have a chosen width $0.28\,\mathrm{mL}$ and equal detector response factors. The lower curve includes model exclusion and full-access plateaus; its secondary mass scale applies only to the stipulated standards.}
In this model the $80{,}000$, $40{,}000$, and $20{,}000\,\mathrm{g\,mol^{-1}}$ standards have <hydrodynamic radii> $2\sqrt2$, $2$, and $\sqrt2\,\mathrm{nm}$ and elute at $7$, $9$, and $11\,\mathrm{mL}$. An unknown at $8\,\mathrm{mL}$ would be assigned $M_{\rm app}=40{,}000\sqrt2\,\mathrm{g\,mol^{-1}}$ by this calibration. But a $40{,}000\,\mathrm{g\,mol^{-1}}$ species that expands from $2$ to $2\sqrt2\,\mathrm{nm}$ elutes at $7\,\mathrm{mL}$ and is assigned $80{,}000\,\mathrm{g\,mol^{-1}}$ without gaining any <mass>. The numbers demonstrate ambiguity, rather than predict a real unfolding transition.
Changes in <conformational isomerism>, <protein folding>, <protein denaturation>, and <protein aggregation> can therefore shift peaks. Association usually increases size; compaction can reduce size at unchanged <molar mass>. <Adsorption> creates a different ambiguity: delayed elution need not indicate a smaller species. A different <solvent> can change both <polymer> coil dimensions and interactions with the packing. The <SEC protein conformation experiment> tests these alternatives with additional detectors.
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