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# Multi Component Anti-LangmuirΒΆ

The Anti-Langmuir (or generalized Langmuir) binding model extends the Langmuir model (see Section Multi Component Langmuir). The factor \(p_j \in \{ -1, 1 \}\) determines the shape of the isotherm. For \(p_j = 1\) (standard Langmuir) the chromatograms have sharp fronts and a dispersed tail (isotherm is concave). In case of the Anti-Langmuir (\(p_j = -1\)) it is the other way around (isotherm is convex).

\[\begin{aligned}
\frac{\mathrm{d} q_i}{\mathrm{d} t} = k_{a,i} c_{p,i} q_{\text{max},i} \left( 1 - \sum_{j=0}^{N_{\text{comp}} - 1} p_j \frac{q_j}{q_{\text{max},j}} \right) - k_{d,i} q_i && i = 0, \dots, N_{\text{comp}} - 1.
\end{aligned}\]

For more information on model parameters required to define in CADET file format, see Multi Component Anti-Langmuir.