# Simulation of the Coiling of a Polymer Strand

2232 Words Feb 28th, 2013 9 Pages
Simulation of the Coiling of a polymer strand
Tsvetoslav Pavlov Department of Materials, Imperial College London, United Kingdom

27th Feb 2012

1. Abstract

This study will examine the temperature dependence of internal energy, heat capacity and R2 value (representative of the end to end distance) using a Langevin Dynamics simulation. It will also consider the dependence of the internal energy, heat capacity and R2 value with increasing polymer chain length. Internal energy has been found to be is negative at low temperatures, increases linearly with temperature and becomes positive at high temperatures. Heat capacity seems to increase linearly with a higher number of atoms in the chain due to additional atoms storing additional
The time step 0.005fs gives a mean energy error (standard deviation) of around 0.01% of the mean value. This is an acceptable level of accuracy. The hottest system has been chosen for this test because it will have the most kinetic energy and atoms will move the most. Therefore the system will be the most volatile and have the biggest uctuations from the mean energy value. Thus a time step at this high temperature will be as accurate or more at any lower temperature.

Figure 1: Graph of temperature vs. Equilibration time.

Initially there is a temperature peak which will inuence the accuracy of the data.

By choosing a time after which

temperature remains fairly constant will minimize uctuations in the rest of the data and optimize its accuracy. However, the longer the equilibration time the longer the simulation will take. Therefore an equilibration time of 700fs has been assigned. The coldest system has been used for this experiment. The colder the system the slower the atoms will move and thus the longer it will take for the polymer to reach its equilibrium state. Therefore the coldest system will give the largest equilibration time, meaning at any higher target temperature the system will take less long to equilibrate. This will ensure the data is accurate at all temperatures.

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Figure 2: T vs. To for 32 atoms.

Figure