# Experimental Setup and Graphical User Interface for Zero-Length Column Chromatography
## 7 Case Study II: Methane and Ethane Diffusion in Zeolite 5A and Basolite(r) C300  
To determine the diffusion control in the system, experiments were performed at different desorption fluxes. According to the ZLC mathematical model, one way to verify this condition is by a semi-log plot of normalized concentration vs. \(Ft\) (flux rate per time). For equilibrium-controlled processes, the response curves should be independent of flow rate, which implies an overlapping of the curves, whereas for a kinetically controlled process the curves diverge. In the diffusion-controlled regime, in the long time region, a log-linear plot of \(C/C_{0}\) vs. \(t\) the long time, asymptote approximates a straight line, therefore, from the slope and the intercept \(L\) and \(D/R^{2}\) can be extracted [38]. To validate the diffusion time constant extracted with this approach (long time analysis), experiments with different flow rates are needed. The resulting response curves will be characterized by similar slopes of the long time asymptote, but different intersections due to different values of the \(L\) parameter (flow dependent). ZLC experiments were conducted using \(7.5\,\mathrm{mg}\) of zeolite 5A at flow rate of \(20\,\mathrm{sccm}\). The resulting desorption curves for ethane at \(298\,\mathrm{K}\) are shown in Figure 8. Both desorption curves at the same temperature have similar slopes over time, ensuring that the system is controlled by kinetics. Semi-logarithmic plots of \(C/C_{0}\) vs. \(Ft\) for Basolite(r) C300 are shown in Figure 9. The representative response curves at four different purge rates cross each other and are divergent, confirming non-equilibrium conditions. The diffusivities and \(L\) parameters for ethane and methane on both adsorbents were determined from the desorption curves under kinetic conditions. Considering the \(L\) values obtained (Table 2) it can be concluded that diffusion is the controlling step and that the transport process is controlled by intra-particle diffusion rather than equilibrium [39]. All \(L\) values obtained from the fits are significantly greater than 10, which explains the non-linearity in the curves [14]. Figure 7: Bicomponent ZLC desorption curves of methane an ethane on zeolite 5A at \(298\,\mathrm{K}\) and flow rate of \(5\,\mathrm{sccm}\). The simulated curves using Equation (1) are represented by lines while the experimental data are represented by symbols. The diffusivity data reported in this work using ZLC agree with measurements made using other techniques. The results obtained are summarized in Table 2. It should be noted that our \(D\) values in some cases are much lower and in others higher than the values reported in the literature, but all remain in the same order of magnitude. These small differences in diffusivity could be due to unequal crystal sizes, which can lead to subtle differences in diffusivity. Another point that could be discussed is that the investigations were not carried out with identical materials and coatings, such a discrepancy could occur, if there was a strong dependence of concentration and/or cation content on diffusion. Considering these facts the results obtained by the ZLC setup are consistent with what has been reported [26; 44; 45; 46; 47].