Single Polymer chain in LJ Liquids

Polymer during processing reaching thermal equilibrium(50 bead polymer)

Graph of mean square end-to-end distance and radius of gyration vs different length of polymer chain

Abstract

In this project, I simulate the behavior of a polymer solution system which contains Lennard-Jones fluids and only one polymer chain. Because the parameters used in this simulation are arbitrarily chose and only one run for each case is performed, the results don't really coincide with actually data. Although everything looks unreal in this project, the trends of several properties still agree with that of the real polymer.

Introduction

The properties and behaviors of polymer melt or polymers in solution can dramatically change their usefulness. Although the behavior of polymer solution is very important, many phenomena are not able to be understood and predicted. In this project, I want to perform the molecular simulation on a single polymer chain system, and expect to get similar results with theorical prediction

Simulation

To simulate this system we use Lennard-Jones potentials between monomers and FENE spring potential between segments on the chain. The simulation is performed at constant temperature using a Nose-Hoover thermostat. The simulation steps are:First, the program is run for a small period of time to probe how much time will need to reach its equilibrium state. Then the program is rerun for more than 100 times of equilibrium period so that we can gather enough information. Finally, the data will be averaged with time to calculate properties of the polymer chain.

Data Analysis

(A)From the simulation results, the longer the polymer chain, the longer time will be needed to reach the equilibrium state.
(B)As shown on the left side,the mean square end-to-end distance and radius of gyration are getting bigger with increasing size of polymer. The figure looks not so good , but the trend is right.
(C)The results of diffusion coefficient are bad in this simulation. To do more simulations for the same case and then average their behaviors will be a better way to get accurate data.

References

1.R.G. Larson, The structure and rheology of complex fluids (Ocford University Press, New York, 1999)
2.R.B. Bird, C.F. Curtiss, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids Volume II (John-Weily& sons, 1987)