# Glotzer:Lennard-Jones Fluid Module

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## Contents |

# Download

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# Simulation Description

This simulation consists of a single-component system of particles that interact via the Lennard-Jones Potential. The system runs NVT Brownian Dynamics. The number of particles, number density, temperature, and time step are all user-modifiable variables. The simulation outputs the radial distribution function ( RDF), mean squared displacement, kinetic and potential energy, temperature, and pressure.

## Simulation Model/Method

- Particle-particle interactions are modeled using the Lennard-Jones potential. Interactions are truncated and shifted at the standard 2.5σ, where σ, the particle diameter, is set to 1.
- This simulation uses Brownian Dynamics where the equations of motion are integrated using the Velocity Verlet integration scheme.
- Temperature is kept constant by the use of the Brownian Dynamics which by the nature of its construction acts as a non-momentum conserving thermostat.
- A brute force neighbor list routine is used to calculate particle-particle interactions, thus simulation is most suited for smaller system sizes < ~1000;
- periodic boundary conditionts are utilized.

# Instructions

## Installing

- Instructions for installing modules can be found on the Module Installation page.

## Running

A variety of system parameters can be modified as shown in the schematic below. To run at this statepoint, simply press the **Run Simulation** button. After pressing **Run Simulation** a visualizer window with the simulation will appear, as shown below. Note that the number of timesteps completed are displaced in the bottom left corner. Name of run will correspond to the directory name where data will be saved. The code will crash if there are spaces or odd characters.

The simulation can be terminated from within the visualizer window by pressing "escape", "q" or select "Quit" from the application menu. Additional functionality of the visualizer can be found on the Visualizer Controls page.

# Suggested Assignments

## Phase Behavior

The phase behavior of this system will be a function of both temperature and number density. For example, at low number density and high temperature, we would expect a gas phase, where as low temperature and high number density we would expect a solid.

### Structure

To see the differences in phase behavior, simulate this system at Number Density = 0.02, 0.7, and 1.12, for Temperature = 1.0. You should be able to visually see a difference, and your observations should be reinforced by examination of the [[softmatter:Radial Distribution Function | Radial Distribution Function (RDF or g(r)]. You may additionally refer to the MATDL Examples given below, for more information regarding the conditions at specific statepoints.

### Dynamics

You can also see a difference in phase behavior by looking at the dynamics of the system. For instance, from the Mean Squared Displacement you can calculate the diffusion coefficient ( see softmatter:Calculating_the_diffusion_coefficient). There should be a noticeable difference in diffusion coefficient between the following: Number Density = 0.02, 0.7, and 1.12 for Temperature = 1.0. Varying Temperature for a fixed Number Density = 0.7 will also yield noticeable differences in the diffusion coefficient.

## Timestep

Also important to note is the timestep. The timestep is step size used to integrate the particle positions through time. This can be thought of as the resolution of the system; a larger timestep will result in a particle translating more. If we know our diffusion coefficient, on average a particle will translate (timestep)*(diffusion coefficient). The default timestep is set to 0.01, however larger timesteps are available to select. If the time step becomes too large, particles will be strongly overlapping and may cause the system to blow up. With a fixed temperature, trying determining where this crossover occurs as a function of Number Density.

## Sample Questions

- Regarding the Radial Distribution Function, how would one differentiate between a solid, liquid, and a gas? What are the characterstics of each?
- Plot the potential energy for a solid and a gas. What factor(s) contribute to the difference in potential energy?
- How to you expect the diffusion coefficient to change as a function of temperature? Number Density? Calculate the diffusion coefficient for the gas and liquid phases from the Mean Squared Displacement. Do the results support your expectations?
- Starting at the liquid phase, can you find a temperature at which you observe two-phase coexistence?
- If you make the timestep very large, why might the system "blow up"? Where does this transition occur? Do you expect a high temperature system to "blow up" at a smaller/larger timestep than a low temperature system for a fixed Number Density?

# Examples/Links

## MATDL Examples

- Simulation snapshot and RDF of a single component Lennard-Jones gas, Full MatDL Record
- Simulation snapshot and RDF of a single component Lennard-Jones liquid, Full MatDL Record
- Simulation snapshot and RDF of a single component Lennard-Jones solid, Full MatDL Record

## Literature Examples

- SMIT B, PHASE-DIAGRAMS OF LENNARD-JONES FLUIDS , JOURNAL OF CHEMICAL PHYSICS 96 (11): 8639-8640 JUN 1 1992
- JOHNSON JK, ZOLLWEG JA, GUBBINS KE, THE LENNARD-JONES EQUATION OF STATE REVISITED, MOLECULAR PHYSICS 78 (3): 591-618 FEB 20 1993

## Related Pages

- softmatter:Basic Dynamical Simulation Methodology
- softmatter:Brownian Dynamics Simulation (BD)
- softmatter:Simulation Variables/Units
- softmatter:Periodic boundary conditions
- softmatter:Pair potential
- softmatter:The Lennard-Jones Potential
- softmatter:Radial Distribution Function
- softmatter:Mean Squared Displacement
- softmatter:Diffusion
- softmatter:Calculating_the_diffusion_coefficient
- Glotzer:modules
- Glotzer:Visualizer Controls
- Glotzer:Module_Installation