Glotzer:Polymer Scaling Module

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Simulation Description

This simulation consists of a single-component system of particles that are permanently bonded together via FENE springs. Particles either interact via the Lennard-Jones Potential or the Weeks-Chandler-Andersen Potential to model different solvent selectivity. The system runs NVT Brownian Dynamics. The length of the polymer, solvent conditions, and runtime are all user-modifiable variables. The simulation outputs the end to end distance.

Simulation Model/Method

  • Particle-particle interactions in good solvent are modeled using the Weeks-Chandler-Andersen Potential. In good solvent the bond distance between particles is set to 7σ, where σ is the diameter of a particle bead, to minimize the effect of the excluded volume interactions and better capture the behavior of a freely jointed chain.
  • Particle-particle interactions in poor solvent 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. In Poor solvent the spacing between polymer beads is set to σ
  • 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 Browniand 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.
  • periodic boundary conditionts are utilized.

Instructions

Installing

Running

A variety of system parameters can be modified as shown in the schematic below. Specifically, the following variables can be changed:

  • Number of particles: This corresponds to the number of beads in the polymer chain. The maximum number of beads supported is 50.
  • Name of Run: This corresponds to the name of the simulation run. The histogram of the end-to-end distances will be written into a folder with the corresponding name. The simulation will crash if there are spaces or odd characters in the directory name.
  • Solvent Conditions: The toggles between good and poor solvent conditions.

To run at this statepoint, simply press the Run Simulation button. After pressing Run Simulation a visualizer window with the simulation will appear and a window showing a plot of the histogram of end-to-end distances, as shown below. The visualizer window additionally outputs:

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

The histogram window displays a histogram of the End to End distance Note: the histogram of the End to End distance being plotted should be used as a guide for when the average value of the End to End distance has sufficiently converged. When you have collected enough data, the histogram should appear gaussian.

Screen snapshot showing the visualizer and runtime interface.

Suggested Assignments

Sample Questions

  • Switch between poor ( Lennard-Jones), and good ( Weeks-Chandler-Andersen) solvent conditions. What differences in behavior do you observe?
  • Consult the definition of End to End distance. Run simulations of various length polymers. Can you reproduce the proper scaling for the End to End distance of the polymer verses (number of beads -1)?
    • Note: the histogram of the End to End distance being plotted should be used as a guide for when the average value of the end to end distance has sufficiently converged. When you have collected enough data, the histogram should appear gaussian.
    • Note: as the length of the polymer is increased, the amount of time needed to collect data will increase.
    • Note: the poor solvent system will converge to faster than the good solvent case.

Examples/Links

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