Table 2.

Models and equations used to fit frontal analysis and zonal elution data

Method & Model [Reference]	Equationa
Frontal analysis:
One-site model [1]	$\frac{1}{m_{\mathit{Lapp}}}=\frac{1}{(K_a{m}_L[A])}+\frac{1}{m_L}$	(1)
Two-site model [37]	$\frac{1}{m_{\mathit{Lapp}}}=\frac{1+K_{a1}[A]+{\beta }_2{K}_{a1}[A]+{\beta }_2{K_{a1}}^2{[A]}^2}{m_L\{({\alpha }_1+{\beta }_2-{\alpha }_1{\beta }_2)K_{a1}[A]+{\beta }_2{K_{a1}}^2{[A]}^2\}}$	(2)
	${lim}_{[A]\to 0}\frac{1}{m_{\mathit{Lapp}}}=\frac{1}{m_L\{({\alpha }_1+{\beta }_2-{\alpha }_1{\beta }_2)K_{a1}[A]}+\frac{({\alpha }_1+{{\beta }_2}^2-{\alpha }_1{{\beta }_2}^2)}{m_L{({\alpha }_1+{\beta }_2-{\alpha }_1{\beta }_2)}^2}$	(3)
Zonal elution:
One-site direct competition 4]	$\frac{1}{k}=\frac{K_I{V}_M[I]}{K_a{m}_L}+\frac{V_M}{K_a{m}_L}$	(4)
Two-site allosteric effect [38]	$\frac{k_0}{(k_0-k)}=[\frac{1}{({\beta }_{I\to A}-1)}][1+(\frac{1}{K_{IL}[I]})]$	(5)

^aSymbols: m_Lapp, moles of applied analyte at the mean point of a breakthrough curve; [A], concentration of applied analyte; m_L, total moles of binding sites that bind to A in Eqns. (1)–(3), or moles of sites at which I and A compete in Eqn. (4); K_a1, association equilibrium constant for the highest affinity site for A in a multi-site system; α₁, fraction of all binding sites that belong to the high affinity sites for A; β₂, ratio of the association equilibrium constants for the low versus high affinity sites in a two-site system; V_M, void volume; [I], concentration of competing agent; K_a is the association equilibrium constant for the binding of A to a ligand; K_I, association equilibrium constant for I at its site of competition with A; k, retention factor for A; k₀, retention factor for A in the absence of I.