Emergent Behaviors in Lennard-Jones Systems

Now that you have gained some familiarity with the behavior of the LJ potential, you have the opportunity to explore a molecular dynamics model with a number of interacting atoms. The core of this model is the same as the previous ones: atoms calculate the force they feel due to the LJ interatomic potential with all the other atoms, are accelerated according to that force, and move based on their velocity. With multiple atoms interacting, some properties emerge that are not easy to predict without running a simulation!

An emergent property is a property of a system that doesn’t exist in the entities themselves but rather emerges from their interactions. Many of the phenomena in materials science and engineering can be seen as emergent. An example of a non-emergent phenomenon is mass. Each atom has mass, and the mass of a material is simply the sum of the masses of its constituent atoms.

With these models we make certain assumptions (these are akin to axioms in mathematics) that are not emergent and run computational experiments exploring the behavior. In our case, we assume Newtonian objects interacting according to the LJ potential. Any behaviors of the model not encoded directly in those assumptions are “emergent.”

Feel free to see if any interesting behavior emerges in Exercise 4.7.1.

Exercise 4.7.1: Emergent Behaviors
Not Currently Assigned

  1. Start the initial-config as "random" with around 25 atoms. Make sure constant-temp? is on. Then, decrease the temperature until the atoms condense. What shape do the atoms pack in and what is the maximum number of neighbors atoms have? Why is this?

  2. Change the number of atoms to 2 and the configuration to HCP. Turn constant-temp? off and set the initial temperature to 0. Press setup and go. Nothing should be moving if atom1-initial-vx is also 0.

    Now try increasing atom1-initial-vx and pressing setup and go again. What is the minimum velocity to break the bond between the atoms? (make sure to click setup again between each time).

    Now change the number of atoms to 3 and proceed. Do it again with 5. Does it take a greater or initial smaller velocity to separate particle 1? Why is this? What does this tell you about melting temperature vs the size of a particle (in terms of the number of atoms it has)?

    Note: Given the small number of atoms, we're working with nanoparticles, here. If we had enough material to model a macroscopic material, the melting temperature would not depend on size.

  3. Go back to two atoms initialized in HCP with constant-temp? turned off atom1-initial-vx set to 0. Find a temperature at which the bond between the two atoms sometimes breaks. It won’t always break at this temperature. Why does it sometimes break and sometimes not?

  4. If you start a bunch of atoms (say 28) in HCP with a low temperature, the particle maintains a approximately rectangular shape. But, if you start the atoms at random positions and then cool the system down until they solidify, they condense but often don't form a rectangular shape. Why is this?