You're reading an old version of this documentation. For the latest released version, please have a look at v5.0.3.

Simplified Multi-State Steric Mass Action

The simplified multi-state steric mass action is the same as the multi-state SMA model described above (see Section Multi-State Steric Mass Action), but with additional assumptions:

• Molecules are only exchanged between two adjacent states, that is, no transfer from state $q_{i,1}$ to state $q_{i,3}$ is allowed.

• Characteristic charge ${\nu }_{i,j}$ and shielding factor ${\sigma }_{i,j}$ only depend on the index of the state $j$.

Thus, the exchange parameters $k_{j\ell }^{(i)}$, the characteristic charge ${\nu }_{i,j}$, and the shielding ${\sigma }_{i,j}$ can be parameterized with few degrees of freedom. For all $i=1,\dots ,N_{\text{comp}}-1$ and $j,\ell =0,\dots ,M_i-1$ let

$$\begin{array}{r}\begin{array}{rl}{k}_{j\ell }^{(i)}& =\{\begin{array}{ll}0,& \text{for }|j-\ell |\ne 1\\ K_{ws}^{(i)}+j{K}_{ws,\text{lin}}^{(i)}-K_{ws,\text{quad}}^{(i)}j(j-M_i+2),& \text{for }\ell =j+1\\ K_{sw}^{(i)}+\ell K_{sw,\text{lin}}^{(i)}-K_{sw,\text{quad}}^{(i)}\ell (\ell -M_i+2),& \text{for }\ell =j-1,\end{array}\\ {\nu }_{i,j}& ={\nu }_{\text{min},i}+\frac{j}{M_i-1}({\nu }_{\text{max},i}-{\nu }_{\text{min},i})-{\nu }_{\text{quad},i}j(j-M_i+1),\\ {\sigma }_{i,j}& ={\sigma }_{\text{min},i}+\frac{j}{M_i-1}({\sigma }_{\text{max},i}-{\sigma }_{\text{min},i})-{\sigma }_{\text{quad},i}j(j-M_i+1).\end{array}\end{array}$$

Note that the characteristic charge ${\nu }_{i,j}$ has to be monotonically non-decreasing in the second index $j$ and all other rates and the steric factor ${\sigma }_{i,j}$ have to be non-negative.

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