= SEC partition coefficient
{c}
{title2=$K_d=(V_e-V_0)/(V_t-V_0)$}
For ideal <SEC>, define the <SEC partition coefficient> by
$$
K_d=\frac{\overline c_{\rm pore}}{c_{\rm interparticle}},\qquad
V_e=V_0+K_dV_i,\qquad
K_d=\frac{V_e-V_0}{V_t-V_0}.
$$
Here $\overline c_{\rm pore}$ averages <solute> <concentration> over all pore liquid, including inaccessible regions. $V_e$ is column elution <volume (thermodynamics)>. Pure steric exclusion gives $0\le K_d\le1$; the endpoints mean exclusion and full access.<Size Exclusion Chromatography: Principles and Methods by GE Healthcare>[GE Healthcare, Size Exclusion Chromatography: Principles and Methods, printed pp. 15–16: concentration-ratio definition and Kd limits]{ref}
A storage argument explains the relation. Assume a dilute stable <solute>, unchanged packing and <solvent>, constant <volumetric flow rate> $Q$, rapid local <chemical equilibrium> between pore liquid and interparticle liquid, negligible binding, and negligible transport through the pores by bulk flow. At interparticle <concentration> $c$, the column holds an <amount of substance> $n=cV_0+K_dcV_i$. Its exit transports $Qc$ per unit time. The ratio $n/(Qc)$ is the mean residence time in this equilibrium transport model; multiplying by $Q$ gives $V_e=V_0+K_dV_i$. For a narrow symmetric <SEC chromatogram> peak, the peak maximum approximates that mean; a strongly asymmetric peak needs an explicitly stated location convention.
The handbook also uses an operational normalization
$$
K_{av}=\frac{V_e-V_0}{V_c-V_0}
=K_d\frac{V_i}{V_i+V_{\rm matrix}}.
$$
This denominator includes solid matrix, so full access gives $K_{av}<1$ when $V_{\rm matrix}>0$. It differs from the pore-liquid <SEC partition coefficient>. Read each source's volume convention before comparing coefficients.<Size Exclusion Chromatography: Principles and Methods by GE Healthcare>[GE Healthcare, Size Exclusion Chromatography: Principles and Methods, printed p. 16, Figure 1.8: Kav uses Vc, not Vt]{ref}
For an original numerical example, take $V_0=5\,\mathrm{mL}$, $V_i=8\,\mathrm{mL}$, and $V_{\rm matrix}=3\,\mathrm{mL}$. Then $V_t=13\,\mathrm{mL}$ and $V_c=16\,\mathrm{mL}$. Elution at $9\,\mathrm{mL}$ gives $K_d=1/2$ but $K_{av}=4/11$. Even a fully included tracer gives $K_{av}=8/11$, not $1$. These are stipulated volumes, not experimental measurements.
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