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Dynamic scaling in entangled mean-field gelation polymers
Chinmay Das1, Daniel J Read, Mark A Kelmanson
1Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK.
We developed a reaction kinetics model for branched polymer synthesis, matching experimental structural data. Our model reveals rheological properties, with viscosity discrepancies at high molecular weights potentially due to mean-field behavior near gelation.
Area of Science:
- Polymer Science
- Chemical Kinetics
- Rheology
Background:
- Vulcanization class polymers exhibit complex branching.
- Experimental studies by Lusignan et al. (1999) produced randomly branched polymers.
- Understanding polymer structure-property relationships is crucial.
Purpose of the Study:
- To present a reaction kinetics model for polymer synthesis.
- To compare model predictions with experimental structural and rheological data.
- To investigate rheological properties near the gelation transition.
Main Methods:
- Numerical solution of reaction rate equations.
- Generation of a numerical ensemble of polymer molecules.
- Application of a tube model for polymer melt rheology calculations.
Main Results:
- Quantitative agreement between model and experimental structural data across molecular weights.
- Discrepancies in estimated linear segment length and zero-shear viscosity for high molecular weight polymers.
- Identification of mean-field behavior at the limit of gelation transition.
Conclusions:
- The model accurately predicts polymer structure but shows deviations in rheology at high molecular weights.
- Mean-field behavior near gelation may explain viscosity disagreements.
- Tube theory with dynamical dilation predicts Rouse-like viscosity exponents close to the gelation limit.
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