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Scaling of entropic shear rigidity.
Xiangjun Xing1, Swagatam Mukhopadhyay, Paul M Goldbart
1Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA.
Physical Review Letters
|December 17, 2004
Summary
We explored shear modulus scaling near gelation. Dense melts show sublinear chain scaling, contributing k(B)T to rigidity, resulting in a dnu shear-modulus exponent.
Area of Science:
- Polymer Physics
- Rheology
- Materials Science
Background:
- The gelation-vulcanization transition is critical for polymer network properties.
- Understanding shear modulus scaling is key to predicting material behavior.
Purpose of the Study:
- To investigate the scaling of shear modulus near the gelation-vulcanization transition.
- To differentiate scaling behaviors in dense melts versus phantom elastic networks.
Main Methods:
- Heuristic analysis of polymer chain scaling.
- Analytical exploration of shear modulus exponents.
Main Results:
- Dense melts exhibit sublinear scaling of effective chain sizes with contour length.
- Each chain contributes k(B)T to rigidity, leading to a dnu shear-modulus exponent.
- Phantom elastic networks show linear scaling, matching random resistor network conductivity exponents.
Conclusions:
- The scaling exponent of shear modulus differs between dense melts and phantom networks.
- Nondense systems exhibit crossover behavior dependent on correlation lengths.