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# Mobile Phase Modulator Langmuir¶

This model is a modified Langmuir model (see Section Multi Component Langmuir) which can be used to describe hydrophobic interaction chromatography [12, 13]. A modulator component (termed “salt”, $$c_{p,0}$$ and $$q_0$$) influences ad- and desorption processes:

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

where $$c_{p,0}$$ and $$q_0$$ denote the salt concentrations in the liquid and solid phase of the beads respectively. Salt is considered to be inert, therefore either

\begin{aligned} \frac{\mathrm{d} q_0}{\mathrm{d} t} = 0 \end{aligned}

is used if salt has one bound state, or salt can be used without a bound state. The parameter $$\gamma$$ describes the hydrophobicity and $$\beta$$ the ion-exchange characteristics.

For more information on model parameters required to define in CADET file format, see Mobile Phase Modulator Langmuir.