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Published on: December 16, 2022
Measuring Topological Constraint Relaxation in Ring-Linear Polymer Blends.
Daniel L Vigil1, Ting Ge2, Michael Rubinstein3,4
1<a href="https://ror.org/01apwpt12">Sandia National Laboratories</a>, Albuquerque, New Mexico 87185, USA.
Topological constraints in polymer blends are efficiently evaluated using the Gauss linking integral. This method reveals that in blends with more linear than ring polymers, constraint relaxation depends on linear polymer reptation.
Area of Science:
- Condensed Matter Physics
- Polymer Science
- Rheology
Background:
- Polymers offer diverse chain topologies for studying topological constraints.
- Blends of linear and ring polymers exhibit emergent rheological properties, often exceeding the viscosity of individual components.
- These emergent behaviors stem from long-lived topological constraints formed when linear polymers thread ring polymers.
Purpose of the Study:
- To demonstrate the utility of the Gauss linking integral for quantifying topological constraint relaxation in ring-linear polymer blends.
- To elucidate the relationship between polymer topology and blend rheology.
Main Methods:
- Utilized the Gauss linking integral to efficiently calculate the relaxation dynamics of topological constraints.
- Investigated ring-linear polymer blends, focusing on majority-linear compositions.
Main Results:
- The Gauss linking integral provides an efficient method for evaluating topological constraint relaxation.
- In majority-linear blends, the relaxation rate is predominantly governed by the reptation dynamics of the linear polymers.
- The diffusive time for rings (τ_{d,R}) in such blends scales with ring length (N_{R}) and linear chain length (N_{l}) as τ_{d,R}∼N_{R}^{2}N_{L}^{3.4}.
Conclusions:
- The Gauss linking integral is a powerful tool for understanding topological dynamics in polymer blends.
- The reptation of linear polymers is the primary mechanism controlling topological constraint relaxation in majority-linear blends.
- The scaling relationship provides quantitative insights into the rheological behavior of these complex polymer systems.

