## 6 Effect of Surface Heterogeneity on the Transient Behaviour of IEMs  
### Modelling of Chronopotetograms for Homogeneous Membranes. Effect of Finite-Length Diffusion Layer  
When a current of density \(i\) is applied to an IEM initially in an equilibrium state with the bathing solution, the concentration profiles develop with time [12; 31; 278]. Electrolyte diffusion from the solution bulk to the membrane surface arise and the diffusion flux of counterions is added to their migration in solution, which slows down the rate of concentration changes at the interface. If the current density is not high (lower than the steady-state limiting current density, \(i_{\text{lim}}\)), the electrolyte diffusion reaches such a rate, that the difference between the counterion migration fluxes in the membrane and solution gets compensated. The system reaches a steady state whereas the main mechanism of current transfer remains electrodiffusion. However, if the current density is higher than \(i_{\text{lim}}\), at a certain time called \"transition time\" there is a change in current transfer mechanism across the membrane. At \(i>i_{\text{lim}}\), the electrolyte diffusion is not sufficient to stop the decrease of concentration at the membrane interface. When the electrolyte concentration at this interface reaches a rather small critical value [216; 277], current-induced mechanisms of overlimiting current conductance such as coupled convection (gravitational convection and electroconvection), water splitting [24; 220; 279] and others [213; 234] occur additionally to the electrodiffusion. Current-induced convection enhances the delivery of electrolyte to the membrane surface [217; 230; 232]. Since the rate of electrolyte delivery via current-induced convection increases as the current density increases, the system reaches a steady-state where its resistance is higher than that at \(i<i_{\text{lim}}\) but remains finite. The onset of these additional transport mechanisms occurs in the vicinity of the transition time \(\tau\), which corresponds to the inflection point on the chronopotetogram. The rate of increase of the PD  
\begin{table} \begin{tabular}{c c c} \hline \hline \(\gamma\) & \(\delta_{N\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \texttexttext{      }}}}}}}}}}}}}}}}} & \delta_{tot.}}\)\(\mu\)m \\ \hline
0.1 & 54 & 128 \\
0.2 & 72 & 134 \\
0.5 & 86 & 136 \\
1 & 85 & 139 \\ \hline \hline \end{tabular}  \end{table 2: Thickness of the DBL determined numerically for cross section 1 (Figure 12) passing across the centre of the conductive region at a distance of 550 \(\mu\)m from the ED channel entrance at different values of the fraction of conductive surface area, \(\gamma\). Figure 13: Concentration profiles near a heterogeneous (1–4) and a homogeneous (5) CEM. The fraction of conductive area for the heterogeneous membrane is 0.1 (**a**), 0.2 (**b**) and 0.5 (**c**). across the membrane attains its maximum. After reaching the transition state (\(t=\tau\)), the rate of PD increase slows down. Then the system reaches a steady state where the PD does not change (or slowly changes) with time. The current-induced mechanisms of ion transport result in reducing concentration polarization. Even when the current density is higher than \(i_{\text{lim}}\), the ion concentration at the interface never reaches zero and PD is not tends to infinity [239; 280]. Chronopotentiometry (CP) is a method of studying the transient behaviour of electrode and membrane systems, when a (constant) current density is applied and the response of time-dependent PD is measured. It is a powerful technique for studying interfacial ion transport and chemical reactions [15; 278; 281; 282]. The transition time is an important characteristic of time-dependent ion transport [15; 282; 283].