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Connecting the vulcanization transition to percolation.

W Peng¹, P M Goldbart, A J McKane

¹Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 3, 2001

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This study uses a field-theoretic model to show that percolation theory accurately describes the critical behavior of the vulcanization transition in liquid and critical states.

Area of Science:

Polymer Science
Statistical Mechanics
Theoretical Physics

Background:

The vulcanization transition is a critical phenomenon in polymer science.
Understanding its critical phenomenology is essential for material properties.

Purpose of the Study:

To investigate the vulcanization transition using a minimal replica-field-theoretic model.
To determine if percolation theory can describe the critical behavior of vulcanization.

Main Methods:

A minimal replica-field-theoretic model was employed.
Diagrammatic analysis of two- and three-point vertex functions was performed to all orders in perturbation theory.
Comparison with the Houghton-Reeve-Wallace field-theoretic approach to percolation.

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Main Results:

The long-wavelength behavior of vertex functions was analyzed.
A correspondence was established between the vulcanization transition and percolation critical phenomena.
Percolation theory was shown to capture the critical phenomenology of vulcanization.

Conclusions:

Percolation theory provides a valid framework for understanding the critical states of vulcanization.
The field-theoretic model successfully links vulcanization to percolation critical phenomena.