We propose a molecular dynamics method with vibration excitation, named as VEMD, to investigate the vibration effect on chain folding for polymer molecule. The VEMD method is based on the introduction of periodic force, the amplitude and frequency of which can be adjusted, and the method was applied to the folding simulation of a polyethylene chain. Simulation results show that the vibration excitation significantly affects the folding of the polyethylene, and frequency and amplitude of the vibration excitation play key roles in VEMD. Different frequencies and amplitudes will determine how and to what extent does the vibration excitation affect the folding process of the polyethylene structure.
In Feynman’s 1959 lecture named “There’s Plenty of Room at the Bottom,” he said “ultimately—in the great future—we can arrange the atoms the way we want.” However, at the time, the researchers had to accept some atomic arrangement that nature gives [
In this work, we propose a molecular dynamics method considering the effect of vibration excitation, named as VEMD, to study the behavior of polymer molecular under vibration. An important aspect of polymer morphology is chain folding, and it is an area of intense activity and debate [
Molecular dynamics (MD) simulation methods solve Newton’s equation of motion for a system of
Different wave patterns can be chosen for the vibration excitation. The sine wave is a common periodic waveform which occurs often in nature, and it will retain its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude. Therefore, a sinusoidal external periodic force is introduced in the molecular dynamics equation:
To test the effect of external excitation on the polyethylene folding, one linear polyethylene chain containing 1000 backbone carbon atoms is used in this work. The all atom OPLS-AA force field is adopted to simulate the folding process of polyethylene, and default parameters are used [
Initial structure of the polyethylene chain was in a straight line, and it was energy minimized using the conjugate gradient method. The resultant structure was then subjected to a subsequent MD simulation in vacuum for as long as 1 ns. The simulation was performed with the MD program GROMACS4.0.5 [
(a) The RMSD curve and (b) the surface area curve of the polyethylene chain during the 1 ns CMD relaxation simulation.
The final structure of the polyethylene chain after the 1 ns simulation is shown in Figure
The final structures of the polyethylene chain (a) of the 1 ns relaxation simulation and (b) of the subsequent 2 ns CMD simulation.
For investigating the influence of the vibration frequency, we firstly performed six VEMD simulations with different vibration periods: 0.2 ps, 0.4 ps, 0.8 ps, 2 ps, 4 ps, and 8 ps, and the amplitude of all the VEMD simulations was set as 500 kJ mol−1 nm−1. The orientation of the starting structure was along the
The relationship between the vibration frequency and the global structure change was firstly investigated. Surface area of a molecule is an important indicator of the level of chain folding, and its reduction means a more compact and stable folded structure. Figure
The surface area curves of the polyethylene molecule during the CMD simulation (shown in black) and six VEMD simulations with different vibration periods (shown in colors).
The final structure of the polyethylene chain after 2 ns CMD simulation is shown in Figure
The final structures derived from the VEMD simulations are shown in Figure
The final structures of the VEMD simulations with different vibration periods.
Snapshots at 400 ps, 800 ps, 1200 ps, and 1600 ps during the VEMD simulation with 8 ps vibration period.
For further evaluating the structure change caused by vibration excitation, RMSD curves of all the carbon atoms derived from the CMD and VEMD simulations are plotted and compared in Figure
The RMSD curves of the CMD and VEMD simulations.
For analyzing the influence of the external excitation on the local structure of the folded polyethylene, the carbon atom torsion angle distributions of the finally folded structure derived from the CMD and VEMD simulations are statistically analyzed and plotted in Figure
The torsion distributions of the final structures derived from the CMD and VEMD simulations.
Combining the analysis of Figures
The RMSF values of carbon atoms of the polyethylene molecule (a) and the overlaid final structures (b) of the VEMD simulations with 4 (shown in green in (b)) and 8 ps (shown in blue in (b)) vibration periods.
Natural modes indicate the structural and vibrational characteristics of molecular structure. For deeply discussing the effect of the external excitation on the polymer folding, we also analyzed the influence of the frequency of external vibration on the modes of the molecule. Normal mode analysis was firstly taken on the starting structure. As the first few principal modes often describe collective, global motions in the system, only the first six order periods are analyzed here, and the values of them for the starting structure are 9.04, 7.42, 6.14, 5.64, 5.37, and 5.11 ps, respectively. The modes of the final structures of the VEMD simulations were also calculated. Figure
The relationship between the vibration periods and the first six order nature periods of the VEMD final structures.
To have a good understanding of how much the individual molecule change during the simulation process, radius of gyration Rg curves was calculated with the tool provided in GROMACS4.0.5 package and given in Figure
Radius of gyration curves of the CMD and VEMD simulations.
Amplitude is a measure of the severity of the vibration. For evaluating the influence of the vibration magnitude to the polymer folding, we took another simulation experiment by fixing the vibration period but varying the amplitude meanwhile. In the previous chapter about vibration frequency, the 2 ps period has a significant influence on the polymer, so 2 ps is set as the fixed vibration period in this chapter. Except for the abovementioned simulation with 500 kJ mol−1 nm−1 amplitude, another five simulations were performed, and their amplitudes were 250, 750, 1000, 1250, and 1500 kJ mol−1 nm−1, respectively.
Similarly, the RMSD curves of these simulations were calculated and compared, as plotted in Figure
The RMSD curves of the VEMD simulations with varied amplitudes.
The torsion distributions of these simulations were also analyzed, as plotted in Figure
The torsion distributions of the final structures derived from the VEMD simulations with varied amplitudes.
From Figures
For evaluating the effect of vibration excitation on the folding of polymer molecule, we introduced a vibration excitation molecular dynamics simulation method, named as VEMD, and this method was applied to the folding simulation of polyethylene molecule that consisted of 1000 carbon atoms. The results show that the vibration excitation has an obvious influence on the polymer chain folding. Frequency of the vibration excitation has a key role in the simulation. When the frequency is relatively high, the vibration excitation will have stretching effect on the polyethylene structure, and with the decrease of the frequency, constraint effect will be increasingly significant. By then, the global structure of the polyethylene is constrained and stabilized referenced to the starting structure, and local structures indicated by the torsion distribution begin to be affected by the vibration excitation. With further growth of the frequency, the effect on the local structures is increasingly significant, but the constraint to the global structure is decreased, and some irregular segments begin to be reorganized by the vibration excitation. In addition, amplitude of the vibration excitation also has influence on the polyethylene folding. Through these results, it is concluded that the vibration excitation has significant effect on the polymer molecule folding, and frequency and amplitude determine the way and the extent of the effect. With appropriate choosing of frequency and amplitude, the vibration excitation will hopefully assist the polymer folding in a more organized way. Through this research, it is possible to further study the effect of vibration excitation in the polymer crystallization even the polymer molding, and this will help us to better use the vibration technology in the polymer processing.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge financial support for this work from the National Basic Research Program of China (no. 2012CB025905), the National Natural Science Funds of China (no. 11202049), and the Fundamental Research Funds for the Central Universities.