You're right to question the apparent discrepancy between the theoretical prediction of the Cottrell equation and the experimental observation of stable current densities in many electrochemical systems. Let's delve into this:

The Cottrell Equation and Its Implications:

The Cottrell equation describes the time-dependent current response to a potential step in a diffusion-controlled electrochemical system. It predicts a decrease in current over time as the concentration of the electroactive species at the electrode surface diminishes due to diffusion. This is a fundamental principle in electrochemistry.

Factors Influencing Durability and Stable Current Densities:

While the Cottrell equation is a valuable tool, it's essential to consider other factors that can influence the long-term performance and durability of electrochemical systems:

Interpreting Experimental Data:

When analyzing i-t curves, it's crucial to consider the experimental setup and conditions. While the Cottrell equation predicts a decreasing current, several factors can lead to a more stable or even increasing current:

• Steady-State Conditions: In some cases, the system may reach a steady-state condition where the rate of mass transport to the electrode balances the electrochemical reaction rate.
• Kinetic Limitations: If the reaction kinetics are slow compared to mass transport, the reaction rate may limit the current rather than diffusion.
• Electrode Degradation: Unfortunately, many electrochemical systems suffer from degradation over time due to various factors, including dissolution, passivation, or fouling. This can decrease current density, even if the mass transport and kinetic conditions remain favorable.

To accurately assess the durability of an electrochemical system, it's important to:

By carefully considering these factors and employing appropriate experimental techniques, you can gain valuable insights into the durability of electrochemical systems and develop strategies to improve their performance.