Interactive Learning of Diffusion and the Diffusion Equation with Mathematical Software

The process of diffusion is intimately related to random
molecular
displacement and is central to many problems in chemistry. Here, we
provide an intuitive derivation of the diffusion equation based on
the analysis of the random trajectories of particles generated and
plotted by simple MATLAB and Python scripts. The codes are very simple
and profusely commented on, so they can be modified by students and
instructors with little experience with these software packages. The
codes plot the trajectories in 1D, 2D, and 3D of a number of particles
during a number of steps, both specified by the operator. Advanced
versions of the codes with animated evolution of the diffusion process
are also provided. The interactive generation and analysis of the
trajectories of the particles in different scenarios allows a faster
and more complete understanding of the effect of the number of particles,
diffusion time, or dimensionality of the system, on the basic aspects
of chemical diffusion, like mean square displacement, through the
statistical nature of the process. A series of activities for the
instructor and students was also suggested.