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# Steric Mass Action¶

The steric mass action model takes charges of the molecules into account [17] and is, thus, often used in ion-exchange chromatography. Each component has a characteristic charge $$\nu$$ that determines the number of available binding sites $$\Lambda$$ (ionic capacity) used up by a molecule. Due to the molecule’s shape, some additional binding sites (steric shielding factor $$\sigma$$) may be shielded from other molecules and are not available for binding.

\begin{aligned} \frac{\mathrm{d} q_i}{\mathrm{d} t} = k_{a,i} c_{p,i}\left( \frac{\bar{q}_0 }{q_{\text{ref}}} \right)^{\nu_i} - k_{d,i}\: q_i\: \left(\frac{c_{p,0}}{c_{\text{ref}}}\right)^{\nu_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. The number of free binding sites

\begin{aligned} \bar{q}_0 = \Lambda - \sum_{j=1}^{N_{\text{comp}} - 1} \left( \nu_j + \sigma_j \right) q_j = q_0 - \sum_{j=1}^{N_{\text{comp}} - 1} \sigma_j q_j \end{aligned}

is calculated from the number of bound counter ions $$q_0$$ by taking steric shielding into account. In turn, the number of bound counter ions $$q_0$$ (electro-neutrality condition) is given by

\begin{aligned} q_0 = \Lambda - \sum_{j=1}^{N_{\text{comp}} - 1} \nu_j q_j, \end{aligned}

which also compensates for the missing equation for $$\frac{\mathrm{d} q_0}{\mathrm{d}t}$$.

The concept of reference concentrations ($$c_{\text{ref}}$$ and $$q_{\text{ref}}$$) is explained in the respective paragraph in Section Reference concentrations.

For more information on model parameters required to define in CADET file format, see Steric Mass Action.