🔬 applied physics

Critical study of A. Eswari and S. Sarvana kumar, "Chronoamperometric response of electrochemical reaction diffusion system: a new theoretical and numerical investigation for EC2 scheme", in J. Iran. Chem. Soc. 21(8), (2024), 2183-2199

This paper presents a critical study of a 2024 publication by A. Eswari and S. Sarvana Kumar, identifying major flaws in their theoretical and numerical investigation of the EC2 scheme, including incorrect statements, irrelevant citations, and mathematical errors that lead to invalid results when compared against the authors' own simulations.

Original authors: Dieter Britz, Jörg Strutwolf

Published 2026-05-06

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Dieter Britz, Jörg Strutwolf

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a master chef who has just published a new recipe book claiming to show the perfect way to bake a specific type of cake. Two food critics, D. Britz and J. Strutwolf, have read your book and written a scathing review. They aren't just saying the cake tastes bad; they are saying your recipe book is full of nonsense, your math is broken, and you likely never actually baked the cake at all.

Here is a breakdown of their critique in simple, everyday language:

1. The Recipe Confusion (The Introduction)

The critics say the authors of the original paper are confused about what they are even cooking.

Wrong Ingredients: The authors claim their recipe involves a "two-step electron transfer" (like using two different types of flour), but the critics say it's actually just a single step followed by a chemical reaction (like mixing one flour and letting it rise).
Wrong Oven Settings: The authors describe the experiment as "Cyclic Voltammetry," which is like baking a cake while constantly changing the oven temperature back and forth. But the critics point out that the authors actually used "Chronoamperometry," which is like setting the oven to one fixed temperature and leaving it there. The authors mixed up the instructions for two completely different cooking methods.
Padding the Book: The introduction of the paper is filled with references to other recipes that have nothing to do with this cake. It's like a chef citing a book on how to make sushi when they are trying to explain how to bake a chocolate cake.

2. The Broken Math (The Core Problem)

This is the most serious part of the critique. The critics say the authors tried to use a calculator to figure out the recipe, but they pressed the wrong buttons.

The "Square" Mistake: The authors made a fundamental math error. They tried to square a number after doing a complex calculation, instead of squaring the number before the calculation. In math, this is like saying "The square of the sum is the same as the sum of the squares." It's simply not true.
The Domino Effect: Because of this one big mistake, every single equation that followed in the paper is wrong. It's like building a house on a foundation made of jelly; no matter how pretty the paint is, the whole thing is going to collapse.
Impossible Results: The authors' math predicts that the "current" (the flow of electricity, or in our analogy, the heat of the oven) would get hotter the longer you bake the cake. In reality, it should get cooler or stabilize. The math predicts things that are physically impossible.

3. The Fake Photos (The Data and Tables)

The authors included tables of numbers and graphs claiming to show the results of their experiment and their computer simulations. The critics say these are fake.

The "Magic" Numbers: The numbers in the tables don't match the math the authors wrote down. It's as if the authors wrote a recipe for a chocolate cake but the photo shows a vanilla one.
The Broken Computer Program: The authors included a computer code (a MATLAB program) claiming it generated their "simulation" results. The critics tried to run this code, and it crashed immediately. It was like finding a "how-to" video where the camera lens was taped over.
The Coarse Grid: Even if the code worked, the critics say the computer used a very "chunky" grid to measure the results. Imagine trying to measure the thickness of a human hair using a ruler marked only in inches. You would get a very wrong answer. The authors didn't check if their measurements were accurate.

4. The Critics' Own Test (The Real Simulation)

To prove their point, the critics ran their own, highly accurate simulation of the same chemical reaction.

The Comparison: They compared their correct results (the solid line in their graph) with the authors' reported numbers (the red dots).
The Result: The authors' numbers were all over the place. They crossed over the correct line and went in the wrong direction. The critics also calculated what the authors' own broken math should have produced (the black dots), and those were even worse, showing the current increasing forever, which is impossible.

The Final Verdict

The critics conclude that the paper is a disaster. They describe it as:

Meaningless text: Filled with jargon that doesn't make sense.
Incorrect math: Based on a fundamental error.
Fake results: Numbers that don't match the math or reality.
Broken tools: A computer program that doesn't work.

The Conclusion: The critics believe the paper should be retracted (taken back and erased from the record) unless the original authors can explain how they managed to bake a cake with a recipe that says "add 5 cups of sugar" but the photo shows a cake with no sugar, and the math says the cake should be on fire.

In short: The paper claims to have solved a complex scientific puzzle, but the critics say the puzzle pieces don't fit, the picture on the box is wrong, and the person who solved it probably didn't even look at the pieces.

Based on the text provided, which is a critical study (a commentary or letter to the editor) by D. Britz and J. Strutwolf regarding the paper by A. Eswari and S. Saravana Kumar, here is a detailed technical summary.

Note: The source text is a critique of a paper, not the paper itself. Therefore, the "problem," "methodology," and "results" described below refer to the flaws identified by the critics in the original work, and the "claims" refer to the critics' own findings and their assessment of the original paper's failures.

Problem Statement

The authors of this critical study identify fundamental errors in the paper titled "Chronoamperometric response of electrochemical reaction diffusion system: a new theoretical and numerical investigation for EC2 scheme" (J. Iran. Chem. Soc. 2024). The core issues identified are:

Conceptual Misidentification: The original paper incorrectly describes the EC2 reaction mechanism as involving two electron transfers, whereas it is actually a single electron transfer followed by a homogeneous chemical dimerization.
Experimental Mismatch: The original paper claims to discuss Cyclic Voltammetry (CV) and uses scan rate ( $v$ ) for dimensionless time scaling. However, the described experiment (a potential jump at $t=0$ ) is Constant Potential Chronoamperometry, not CV. Consequently, the use of CV-specific parameters (like scan rate and reversal potential) is inappropriate.
Mathematical Errors: The derivation of key equations contains a fundamental error in Laplace transform theory (assuming the transform of a squared term equals the square of the transform). This leads to incorrect analytical solutions for concentration and current.
Numerical Failures: The MATLAB code provided in the original paper's appendix is non-functional due to incorrect parameter usage for the solvepde solver. Furthermore, the mesh resolution used is too coarse to capture the reaction layer thickness, rendering the numerical results unreliable.

Methodology

The critical study employs a three-pronged approach to validate the original paper's claims:

Theoretical Verification: The authors re-examine the mathematical derivations of the original paper, specifically checking the Laplace transform steps and the consistency of boundary conditions for the EC2 mechanism.
Code Execution and Debugging: The authors attempted to run the MATLAB program provided in the original paper's Appendix 1. They found it failed to execute. They subsequently modified the code to use the correct solver (pdepe) and fixed parameter errors to attempt a reproduction of the results.
Independent Simulation: To establish the "ground truth," the critics conducted their own high-fidelity simulations of the same EC2 system using:
- Method: Backward Implicit (BI) method.
- Linearization: The nonlinear term ( $c_R'^2$ ) was linearized as described in standard literature.
- Grid: An unequal spatial grid using damped exponential expansion to resolve the steep concentration gradients near the electrode (smallest interval $10^{-5}$ ).
- Parameters: 100 spatial intervals and 1000 time intervals.
- Boundary Conditions: The spatial domain ( $x_{lim}$ ) was set to $6\sqrt{\tau}$ to ensure the diffusion layer did not interact with the far boundary, correcting the original paper's fixed $x_{lim}=1$ .

Key Findings and Results

The critical study concludes that the results in the original paper are invalid:

Analytical Solutions: The derived equations (specifically Eq. 54 from Eq. 52) are mathematically incorrect. Consequently, the tabulated values for current and concentration derived from these equations do not match the actual physics of the system.
Current Behavior: The original paper's equation for current (Eq. 72) predicts a current that increases with time for $t > 1$ , which is physically impossible for this system. The critics' simulations show a decaying current consistent with diffusion control.
Numerical Discrepancies:
- The original paper reports finite currents at $t=0$ , ignoring the known singularity of chronoamperometry.
- The values labeled "This work" in the original tables do not match the values calculated from the authors' own equations.
- The "Simulations" column in the original paper, attributed to a non-functional MATLAB program, cannot be trusted.
- Comparison with the critics' independent simulations shows that the original paper's concentration and current values are incorrect across all tested parameters ( $\Theta = 5, 1, 0.1$ ).
Mesh Resolution: The critics demonstrate that the reaction layer thickness ( $\approx 1/\sqrt{k}$ ) is approximately 0.14 for $k=50$ , while the original paper used a grid spacing of $\delta x = 1.01$ . This coarse mesh fails to resolve the reaction layer, introducing significant numerical errors.

Significance and Conclusion

The significance of this critical study is the exposure of severe methodological and mathematical flaws in a published electrochemical study. The authors of the critique argue that:

The original paper contains "meaningless text," "irrelevant citations," and "incorrect mathematics."
The results presented in the original paper are artifacts of incorrect derivations and unverified numerical methods.
The comparison made in the original paper against "Rajendran et al." is invalid because the referenced work deals with a quasireversible case and reports no numerical data for comparison.

Final Verdict: The critical study concludes that the paper by Eswari and Kumar should be retracted unless the authors can provide a valid explanation for the mathematical errors, the non-functional code, and the discrepancy between their reported results and the physical reality of the EC2 reaction system. The study serves as a correction to the literature, ensuring that future researchers do not rely on the erroneous equations or data presented in the original work.