# Reactions at the Solid/Solution Interface

The aim of this lecture course is to enable the audience to gain an understanding and appreciation of how we can mathematically model interfacial reactions occurring at the solid/solution interface, accounting for the role of mass-transport in determining the overall reaction rate. Having identified how to model the system the focus will be on discover how we can use finite difference methods to numerically solve the resulting mathematical problems. Throughout the lecture series the programming language Python will be used to demonstrate and exemplify how these calculations can be made. A brief introduction to programming and the use of the Python programming language will be provided and example scripts and code will be used throughout the course to practically show how the calculations are made. No prior coding experience will be assumed but some knowledge may be beneficial for following the provided examples.

On this page you will find copies of the lecture handouts and links to the relevant literature. The example python scripts used in the course can be found here.

In lecture 1, I mentioned that Nernst was the first to recognise that near surfaces convective flows are damped and that "under certain conditions reaction rates in heterogeneous systems can be traced back to diffusion rates". The original paper making this observation is Nernst, W. (1904). Zeitschrift für physikalische Chemie, 47(1), 52-55. However, it is interesting that Nernst notes that he had earlier outlined his theory in his textbook. Experimental evidence for these obseravtions seem to have been provided by studying the dissolution rates of particles in solutions!

### Lecture 1

- An Introduction to Python
- Mass-Transport
- The Diffusion Equation
- Diffusion to a sphere

### Lecture 2

- Size Effects
- Finite Difference Methods
- Explicit vs Implicit
- Simulation Walk-through

### Lecture 3

- Convergence and Testing
- Improving the Simulation
- 2D Simulation
- Heterogeneous Surfaces

### Lecture 4

- Adsorption & Thin-Layers
- Modified Electrodes
- Electrocatalysis
- Advanced Methods