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Frenkel-Kontarova Model

By Calvin J Mwesigwa1, Ashlie Martini1

1. Purdue University

Simulate movement of simple molecules over a 2D potential energy landscape due to external forcing using the Frenkel-Kontarova model

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Version 1.0 - published on 04 Aug 2011

doi:10.4231/D3PN8XF3C cite this

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Default Screen Molecule Viewer Movie Illustration Outputs

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Abstract

Description

This tool enables you to simulate the movement of eight simple molecules over a 2D potential energy landscape due to external forcing using the Frenkel-Kontarova model. You may specify the geometry of the molecules and the virtual surface over which they move, as well as the degree of forcing applied and the rate of energy dissipation during movement. The simple model predicts the molecule movement, relative slip, the associated energetics. Results are presented as plots and a “movie” of the molecule as it traverses the surface.

Input Parameters

The following parameters are specified by the user through the toolkit interface.

Molecular Structure
This is a drop down box that lets the user choose a model molecule. The current version of the toolkit has eight different molecule types which are illustrated below the drop down box:
* Single atom
* Two atoms linear
* Three atoms linear
* Four atoms linear
* Five atoms linear
* Six atoms linear
* Six atoms branched
* Six atom ring

Molecule Parameters
Each of the molecular structures above can be further modified using the following parameters:
* Atomic mass, m (1 to 100 amu)
* Bond length, b (1 to 5 A)

Simulation Parameters
The simulation conditions can be fully customized using this menu. The options include:
* Simulation time, tmax (10 to 100 fs)
* Time step size, Delta t (0.01 to 0.04 fs)
* Non-dimensional forcing factor, f (0.1 to 2)
* Non-dimensional friction/energy dissipation factor, Eta (0.1 to 2)

Wall Parameters
These options enable the user to change the properties of the potential energy distribution modeling a crystalline solid wall. These options are illustrated in a figure below the menu:
* Lattice constant, a (1 to 5 A)
* Angle of rotation, Phi (radians)

Simulation and Output

To begin a simulation, click the simulate button on the right side of the toolkit window. The simulation will run for about a minute and then provide the following analysis options in the drop down box labeled results.

Plot: Displacement vs time
Displacement of the centroid of the molecule as a function of time.

Plot: Bond Energy vs time
Magnitude of the bond energy as a function of time.

Plot: Angle Energy vs time
Magnitude of the bond angle energy as a function of time.

Plot: Wall Energy vs time
Magnitude of the energy due to interaction with the wall.

Illustration of Atom Movement
Animation of the movement of the atoms over the two dimensional potential energy landscape where colors from blue to red indicate regions from low to high energy respectively.

Result file: Output Parameters
This is a compilation of simulation output including the slip velocity (mean speed of the molecule) and the maximum, minimum and average values of the bond, angle, wall and total energies during the simulation.

Cite this work

Researchers should cite this work as follows:

  • Calvin J Mwesigwa; Ashlie Martini (2011), "Frenkel-Kontarova Model," https://nanohub.org/resources/fkt. (DOI: 10.4231/D3PN8XF3C).

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