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Determine Mesh Size through Monomer Mean-Square Displacement.

Ji-Xuan Hou1

  • 1School of Physics, Southeast University, Nanjing 211189, China. jxhou@seu.edu.cn.

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This study introduces a dynamic method to measure polymer entanglement length using monomer mean-square displacement. The findings suggest that measuring tube diameter offers a reliable way to determine entanglement length from microscopic data.

Keywords:
entangled polymer meltmesh sizemonomer mean-square displacementtube theory

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Area of Science:

  • Polymer Physics
  • Soft Matter Science
  • Computational Materials Science

Background:

  • Tube theory is a key concept in polymer dynamics, describing polymer chains confined within a 'tube' formed by their neighbors.
  • Determining the entanglement length is crucial for understanding the viscoelastic properties of entangled polymers.
  • Existing methods for measuring entanglement length can be complex or require extensive simulation data.

Purpose of the Study:

  • To develop a dynamic method for determining the primary parameter of tube theory, the entanglement length.
  • To establish a reliable approach for calculating tube diameter and tube step length from monomer mean-square displacement data.
  • To validate the proposed method using recent simulation data for various entangled polymer systems.

Main Methods:

  • Analyzing monomer mean-square displacement (MSD) in log-log plots to identify characteristic slopes.
  • Measuring tube step length from the intersection of slope-1/2 and slope-1/4 lines in the MSD plot.
  • Determining tube diameter by observing the time when the correlation function deviates from the slope-1/2 regime.
  • Calculating the ratio of tube step length to tube diameter.

Main Results:

  • The tube step length can be accurately determined from the characteristic slope intersections in the MSD log-log plot.
  • The tube diameter can be obtained by monitoring the onset of deviation from the initial diffusive regime in the correlation function.
  • Simulation data consistently show a ratio of approximately 2 for tube step length to tube diameter across different entangled polymer systems.
  • Measuring tube diameter is feasible even before the correlation function fully reaches the slope-1/4 regime.

Conclusions:

  • The proposed dynamic method provides a robust way to determine the entanglement length from microscopic considerations.
  • Measuring the tube diameter is identified as a potentially superior method for determining entanglement length due to its independence from reaching later dynamic regimes.
  • This approach offers a more direct and potentially simpler route to characterizing polymer entanglement compared to traditional methods.