# Molecular Dynamics Simulation: Diffusion

## Diffusion

In a sample of air at room temperature, the nitrogen molecules, which make up nearly 80% of the air, are moving at a speed of 511 m/sec or 1143 mph (root-mean-square speed).

One would therefore expect that a nitrogen molecule on the far side of a room would travel to the opposite end of the room (even a very large room) in a fraction of a second.

Test this prediction using the simulation below. All of the molecules in the simulation are the same, but one molecule is red (rather than blue) and will be used as a tracer. The red molecule is initially at the center of the system, at x = 0.0 and y = 0.0. As the simulation runs, the red molecule will move away from its initial position. As the simulation progresses, the displacement of the red molecule from its initial position will be recorded and displayed on the graph with a red line.

The average speed of the red molecule is 500 m/sec. The displacement expected for the red molecule if it travels at a constant speed of 500 m/sec in a straight line is shown by the black line on the graph.

Compare the black and red lines shown on the graph. Why are the two different?

Also note the time scale and the distance scale. The simulation takes less than 200 psec. There are 1012 or 1000 billion picoseconds in a second. The distance scale is nm. There are 109 or one billion nanometers in a meter.

## Random Walk

The motion of a particle undergoing diffusion is sometimes described as a random walk.

Run the simulation shown below and observe the path of the red molecule as plotted on the graph at the right. The graph shows the x-y position of the red molecule as it moves through the system.

Does the red molecule follow straight-line motion? Why is the motion called a "random walk"?

Use the Reset button to run the simulation several times. Does the red particle always follow the same path?

Molecular Dynamics - Diffusion (version 3.0)
© 2001, 2014, 2023 David N. Blauch