Generally, the apparent diffusion coefficient (D) can be evaluated by Cottrell equation I = nFAD1/2c0 π-1/2 t-1/2, Where c0 is the catalyst concentration (M), t is the time elapsed (s) and A is the surface area of modified electrodes. Under diffusion control, the value of D could be calculated with the slope of the linear equation of I and t-1/2. In additiom, the catalytic rate constant (k) can be evaluated by the following equation, IC/IL= π1/2 γ1/2 =π1/2 (kc0t)1/2, where IC is the catalytic current of analytes at different modified electrodes in the presence of mediator, IL is the limited current in the absence of analytes. What is the meaning of values of the apparent diffusion coefficient (D) and catalytic rate constant (k) of analytes at different modified electrodes? the D values and the k values of analytes at composite electrode was largest compared with other electrodes, what does that mean for analytes at composite electrode ? For the same analyte, in previously reported in many papers, thier calculated D values and k values are different using different materials modified electrodes,I wonder what caused these results?
When you increase the surface area by modifying electrode, diffusion constant D and k both increase. Because D is directly proportional to availability of surface area and current gets enhanced. And as diffusion rate increases, it increases K also. Because D and K has linear relationships.
Your diffusion constant, D, should not change for changing electrodes; it is a property of a specific ion in a specific solution. Cottrell equation holds for diffusion controlled current, i.e. everything at the surface reacts, and at t>0 the concentration of analyte is assumed to be near zero. At that point, your current equals to the diffusion flux of analyte from the bulk to the surface through a growing depletion region. This shouldn't have much to do with kinetics of the reaction, as long as kinetics are fast enough to deplete the analyte as it arrives to the surface. If kinetics are too sluggish for that, the Cottrell equation stops being valid.
I'm not familiar with the second equation for kinetics that you've listed. That seems like something you might want to do with Butler-Volmer.
Dear Dr.Pavel Mardilovich and Dr. Zaheer Masood
Thank you very much for your answer, For the same analyte, in previously reported in many papers, thier calculated D values and k values are different using different materials modified electrodes,I wonder what caused these results?
It seems very strange that the diffusion coefficient would change. One reason why it could actually change would be changes in solution properties, such as temperature or concentration of analyte or any supporting electrolyte. Apparent changes that come from the experimental setup could be things such as an insufficiently high potential step leads to only partial depletion of the analyte at the electrode surface, producing a lower diffusion coefficient, or if the electrode area is too small to safely assume a 1-D problem, which leads to calculation errors. It's hard to say much without looking at some of the papers that you mentioned. Maybe if someone had more experience with this, they could offer an opinion?
Dear Dr.Pavel Mardilovich
Thank you very much for your suggestion. I'm not familiar with these two equation, i also read a lot of literature, but theses difference is still not understood. (for example, Journal of Applied Electrochemistry, 2016, 46(9): 951-962) Do electrocatalytic ability or electrochemical active area of materials affect the diffusion coefficient? Could you please tell me your E-mail address ? I'd like to send some of the papers to you. Thank you again!
Dear Yangping Wen
Actually, the diffusion coefficient may change depends on the electrode area (electrochemical active area), Please refer the following link https://doi.org/10.1016/B978-044451958-0.50036-7
Dear Wen
I agree with pavel
As you know the D is the rate of diffusion of analyte from solution to the electrode and it is not relative to the surface of the electrode. About D, this value must be same for one analyte in the same solution. But changing in temperature or solution type the D value can be change. The D value is between 1E-4>>>>>OX+ne (step 1)
OX+A (ANALYTE)red>>>>>>Red+(A)OX (step 2)
the value of k is relative to second step. The rate constant between mediator and analyte.
This value is relative to the speed of this step and can be different in the different investigation. More value of k confirms better electrocatalytic interaction.
Please feel free for contact with me.
Hassan
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