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On the Applications of Discontinuous Bessel Integrals to Chronoamperometry
William T Yap1, Richard A Durst2
1National Institute of Standards and Technology, Gaithersburg, MD 20899-0001.
Summary
Discontinuous Bessel integrals solve chronoamperometry problems, providing current functions with long-time series and short-time expansions for electrochemical analysis.
Area of Science:
- Electrochemistry
- Applied Mathematics
- Physical Chemistry
Background:
- Chronoamperometry is a key electrochemical technique.
- Boundary value problems are essential for modeling electrochemical systems.
- Discontinuous Bessel integrals offer a novel mathematical approach.
Purpose of the Study:
- To apply discontinuous Bessel integrals to a chronoamperometry boundary value problem.
- To derive current functions for electrochemical analysis.
- To provide analytical expansions for different time regimes.
Main Methods:
- Utilizing discontinuous Bessel integrals for mathematical modeling.
- Solving a boundary value problem with specific boundary conditions.
- Deriving series expansion for long-time behavior.
- Developing asymptotic expansion for short-time behavior.
Main Results:
- Successfully derived current functions for the chronoamperometry problem.
- Obtained series expansion for long-time analysis.
- Developed asymptotic expansion for short-time analysis.
- Presented numerical calculations and plots of current functions.
Conclusions:
- Discontinuous Bessel integrals are effective for solving chronoamperometry boundary value problems.
- The derived analytical expansions facilitate understanding of electrochemical behavior across time scales.
- Numerical results validate the theoretical framework.
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