## Molecular Dynamics Simulation: Effect of Temperature

 Statistical mechanics envisions matter as being composed of a large number of small particles in rapid motions. A simulation of this behavior is provided below. This simulation, called Molecular Dynamics, applies Newton's laws of motion to predict the paths of individual particles (molecules). The forces that operate on the particles are described by the Lennard-Jones potential, which is graphed at the right. The graph shows how the potential energy (PE) between two particles varies with the distance between the particles (r). When the molecules are far apart, the PE is essentially zero. As the molecules get closer, there is an attractive force between the particles, which lowers the PE. The particles need to be fairly close together for this attraction to be relevant. In the simulation, the particle diameter is σ. Examination of the graph shows that the particles need to be within about two diameters (2 σ ) for a significant attractive force to exist. If the molecules get too close (within one diameter), however, the PE increases rapidly. This strong repulsive force drives particles away from each other and is the reason why the particle "bounce" off each other. The depth of the Lennard-Jones energy well is ε which is equal to 1.000 kJ/mol in this simulation. The pressure (P) of the system is also displayed. The units N/m are consistent with a two-dimensional system. For a simulation in three dimensions, the units of pressure would be N/m2 (pascal).

### Simulation Control

• Enter the desired temperature (between 0 and 1000 K) and select the Set button.
• Start the simulation with the Start button. This button can also be used to pause the simulation.

• After an initialization time, statistics for the collection of particles will be displayed. For low temperatures, it may take a minute or longer for the statistics to appear.

• < KE > is the average kinetic energy per particle. (Bear in mind this is a 2D not 3D simulation. Each degree of freedom should have 1⁄2 R T of energy.)
• < PE > is the average potential energy per particle.

• For the purposes of comparison, the value of R T and the Lennard-Jones well depth ε are provided.

• A histogram shows the distribution of particle speeds or < KE > obtained from the molecular dynamics simulation. The blue curve is the theoretical prediction for the distribution.

### Exercises

1. Run the simulation at 1000. K.
1. Do all the particles move at the same speed?
2. How does < PE > compare with - ε ?
3. Do any of the particles stick together? Explain this observation.

2. Run the simulation at 1000. K and at 200. K and compare the two behaviors.
1. What is the effect of changing the temperature on the behavior of the particles?
2. How does < KE > compare with R T ?
3. This simulation occurs in two dimensions. What would < KE > be in three dimensions?
4. How does < PE > change with temperature? Explain this behavior.

3. Run the simulation at 100. K.
1. How does < PE > compare with - ε ?
2. Do any of the particles stick together? How does your answer compare with that for Question I.3?
3. In what phase (solid, liquid or gas) do the particles exist?

4. Run the simulation at 50. K.
1. In what phase do the particles exist? Is there a single phase?
2. Explain the term vapor pressure in terms of your observations of how the particles behave.

5. Run the simulation at 20. K.
1. In what phase do the particles exist? Is there a single phase?
2. Explain the value for < PE >.
3. What is the lowest possible value for < PE >?
4. Why is this lowest value for < PE > not exactly observed in this simulation?
5. Would the lowest value of < PE > be different in a 3D simulation? Why?

 < KE > kJ/mol < PE > kJ/mol R T kJ/mol - ε kJ/mol < P > N/m

Temperature
K

Simulation
Control

Reset
Statistics

Virtual Chemistry Experiments

Conditions of Use
This web page is part of Virtual Chemistry Experiments and may be used and redistributed for non-commerical purposes without requesting permission from the author. Derivative works and publications whose results are obtained with these resources should contain the following attribution: "Virtual Chemistry Experiments, David N. Blauch."

Disclaimer
This simulation is intended solely for educational purposes. The author is not responsible for any losses or damages suffered directly or indirectly from the use of this simulation. By using this simulation, you assume all risks associated with its use.

Molecular Dynamics - Effect of Temperature (MD-Temperature.html, version 1.0)