Preview - Atomic Forces And Phase Transitions

Lennard-Jones Model

Start by playing around with the model and then use it to answer the questions below.

 

Questions

Please answer the questions below.

Estimate temperature ranges when the system is clearly a solid and clearly a gas. It is hard to tell in a 2-dimensional model when the atoms are in a liquid, but try to estimate the temperature range for liquid as well.

Use your ranges to estimate the melting point and the boiling point. 

As you change the temperature, what happens to the average energy per atom? Why do you think that is?

Use some basic NetLogo commands to figure out what the maximum and minimum energies are for atoms in the model. You'll type the commands in the Command Center underneath the model.

Here are some useful commands:

  • [calc-v] of turtles: this returns a list of the energies for all the atoms
  • min(...) and max(...): you have to put a list inside the parentheses

(hint:  you shouldn't have to copy and paste anything. You just have to write the right command.)

Does the temperature affect the the maximum and minimum energies?

This is a graph of equation used to model potential energy between two atoms used in the agent based model. It is known as the Lennard-Jones potential after Sir John Edward Lennard-Jones who came up with it. The equation is:

Solve for rminin terms of ε and σ. Ask for a hint if you aren't sure how to do that.

What is the minimum potential energy between two atoms in terms of variables in the Lennard-Jones potential?

When the temperature is low enough for the atoms to solidify, how many neighbors can an atom have? Why is this?

Calculate potential energy of an atom in the configuration from the previous question, assuming all of it's neighbors are rmin distance away.

When you used Netlogo commands to find the minimum energy of atoms, did any of them have this energy? Why? (to find out what the model uses for ε, go into the Netlogo Code tab and look for where it gets set. ε is called EPS in the code.)

Add a slider to change the value ε.

To do that, click the lock button in the upper left corner that looks like this: , and it will change to authoring mode.

You can click and drag things to move them around. Right click to add a slider. Call it EPS, and set the values of the slider to what seems reasonable based on what EPS is currently set to. When you try to add the slider, you should get an error that says "There is already a global variable called EPS." So, go into the NetLogo code tab and find where the EPS variable is currently set. Either delete it, or turn it into a comment that the computer ignores by putting a semicolon in front of it. You also will need to delete EPS from the list of globals at the top of the code. 

No explore how changing your EPS slider changes the behavior of the model and describe what you find.

Notes

These notes will appear on every page in this lesson so feel free to put anything here you'd like to keep track of.