cui¶

poreana.diffusion.cui(link, pore_id='shape_00', z_dist=0, ax_area=[0.2, 0.8], intent='', is_fit=False, is_plot=True)¶

This function samples and calculates the diffusion coefficient of a molecule group in a pore in both axial and radial direction, as described in the paper of Cui.

The mean square displacement is sampled in function poreana.sample.Sample._diffusion_bin().

The axial diffusion is given by the Einstein relation

\[\langle\left[z(0)-z(t)\right]^2\rangle=2D_\text{axial}t\]

with axial diffusion coefficient \(D_\text{axial}\). Thus the coefficient corresponds to the slope of the axial msd

\[D_\text{axial}=\frac12\frac{\text{msd}_\text{axial}[i]-\text{msd}_\text{axial}[j]}{t_i-t_j}\]

with bin \(i>j\). The radial diffusion is given by

\[\langle\left[r(0)-r(t)\right]^2\rangle=R^2\left[1-\sum_{n=1}^\infty\frac{8}{\lambda_{1n}^2(\lambda_{1n}^2-1)}\exp\left(-\frac{\lambda_{1n}^2}{R^2}D_\text{radial}t\right)\right].\]

with radial diffusion coefficient \(D_\text{radial}\), the maximal accessible radial position \(R\) by an atom

\[R = \frac12d-0.2\]

with pore diameter \(d\), and the zeros \(\lambda_{1n}^2\) of the derivative

\[\frac{dJ_1}{dx}\]

of the first order Bessel function \(J_1\). Therefore the coefficient has to be fitted to the sampled radial msd. The author observed that the first 20 Bessel function zeros were sufficient for the function fit.

The final unit transformation is done by

\[\frac{\text{nm}^2}{\text{ps}}=10^{-2}\frac{\text{cm}^2}{\text{s}}.\]

Note that the function for the radial diffusion is obtained under the assumption that the density inside the pore is uniform.

Parameters:

linkstring: Link to hdf5 data file generated by the sample routine poreana.sample.Sample._diffusion_bin()
pore_idstring, optional: If there is more than one shape in the structure, select the shape you want the results to be.
z_distfloat, optional: Distance from pore centre to calculate the mean
ax_arealist, optional: Bin area percentage to calculate the axial diffusion coefficient
intentstring, optional: axial, radial or empty for both
is_fitbool, optional: True to plot the fitted function
is_plotbool, optional: True to create plot in this function