.. _extended_mobile_phase_modulator_langmuir_model: Extended Mobile Phase Modulator Langmuir ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This model is an extension of the mobile phase modulator Langmuir model (see Section :ref:multi_component_langmuir_model), which allows linear binding of some selected components. A modifier component :math:c_{p,\mathrm{mod}} is selected and the remaining components are divided into the index sets :math:\mathcal{I}_{\mathrm{lin}} and :math:\mathcal{I}_{\mathrm{lang}}. .. math:: \begin{aligned} \frac{\mathrm{d} q_i}{\mathrm{d} t} &= k_{a,i} e^{\gamma_i c_{p,\mathrm{mod}}} 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,\mathrm{mod}}^{\beta_i} \: q_i && i \in \mathcal{I}_{\mathrm{lang}}, \\ \frac{\mathrm{d} q_i}{\mathrm{d} t} &= k_{a,i} c_{p,i} - k_{d,i} \: q_i && i \in \mathcal{I}_{\mathrm{lin}}. \end{aligned} The modifier component is considered to be inert, therefore either .. math:: \frac{\mathrm{d} q_{\mathrm{mod}}}{\mathrm{d} t} = 0 is used if the modifier component has a bound state, or it can be used without a bound state. The model can also be used without a modifier component. In this case, the equations are given by .. math:: \begin{aligned} \frac{\mathrm{d} q_i}{\mathrm{d} t} &= k_{a,i} 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} \: q_i && i \in \mathcal{I}_{\mathrm{lang}}, \\ \frac{\mathrm{d} q_i}{\mathrm{d} t} &= k_{a,i} c_{p,i} - k_{d,i} \: q_i && i \in \mathcal{I}_{\mathrm{lin}}. \end{aligned} For more information on model parameters required to define in CADET file format, see :ref:extended_mobile_phase_modulator_langmuir_config.