HIC Unified

This model implements a unified hydrophobic interaction chromatography (HIC) isotherm as described by Jäpel et al. [16]. It combines the isotherms proposed by Mollerup [17], Deitcher [18] and the SWA isotherm by Jäpel et al. into one isotherm. In addition to the first component \(c_{p,0}\), which represents salt, the second component \(c_{p,1}\) represents another non-binding modifier (e.g., pH).

\[\begin{split}\begin{align} k_{a,i} &= k_{a,i,0} \exp\left( k_{a,i,lin} ({c_{p,1}}-{c}_{1,ref})\right)\\ \nu_i &= \nu_{i,0} + \nu_{i,lin} ({c_{p,1}}-{c}_{1,ref})\\ \beta &= \beta_0 \exp\left(\beta_1 c_{p,0}\right) \\ \frac{\mathrm{d}q_i}{\mathrm{d}t} &= k_{a,i} c_{p,i}\exp\left({k_{p,i} c_{p,i}+k_{s,i} c_{p,0}}\right)\left( 1 - \sum_j \frac{q_j}{q_{max,j}} \right)^{\nu_i} -k_{d,i} q_{p,i}(1+\epsilon q_{p,i}) \exp\left(({\rho c_{p,0}})^{\nu_i \beta} \right) \end{align}\end{split}\]

Model Assumptions and Limitations:

• Component \(c_0\) is assumed to be salt with no bound state.

• Component \(c_1\) is assumed to be a modifying component with no bound state. It is measured relative to a reference concentration of \(c_{1,ref}\), which defaults to 0.0.

• Multiple bound states are not supported.

• Components without bound state (i.e., salt and additional non-binding components) are supported.

For more information on model parameters required to define in CADET file format, see HIC Unified.