Determine Mesh Size through Monomer Mean-Square Displacement

• Main Author: Ji-Xuan Hou
• Format: Article
• Language: English
• Published: MDPI AG 2019-08-01
• Series: Polymers
• Subjects: entangled polymer melt; tube theory; monomer mean-square displacement; mesh size
• Online Access: https://www.mdpi.com/2073-4360/11/9/1405

A dynamic method to determine the main parameter of the tube theory through monomer mean-square displacement is discussed in this paper. The tube step length can be measured from the intersection of the slope-<inline-formula> <math display="inline"> <semantics> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </semantics> </math> </inline-formula> line and the slope-<inline-formula> <math display="inline"> <semantics> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </semantics> </math> </inline-formula> line in log-log plot, and the tube diameter can be obtained by recording the time at which <inline-formula> <math display="inline"> <semantics> <msub> <mi>g</mi> <mn>1</mn> </msub> </semantics> </math> </inline-formula> data start to leave the slope-<inline-formula> <math display="inline"> <semantics> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </semantics> </math> </inline-formula> regime. According to recent simulation data, the ratio of the tube step length to the tube diameter was found to be about 2 for different entangled polymer systems. Since measuring the tube diameter does not require <inline-formula> <math display="inline"> <semantics> <msub> <mi>g</mi> <mn>1</mn> </msub> </semantics> </math> </inline-formula> data to reach the slope-<inline-formula> <math display="inline"> <semantics> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </semantics> </math> </inline-formula> regime, this could be the best way to find the entanglement length from microscopic consideration.