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Multifractal behavior of linear polymers in disordered media
A Ordemann1, M Porto, H E Roman
1Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany.
Summary
This study investigates polymer scaling in disordered media using self-avoiding walks on percolation clusters. Results reveal multifractal behavior and generalized exponents, suggesting a valid relation to regular lattice counterparts.
Area of Science:
- Physics
- Polymer Science
- Statistical Mechanics
Background:
- Disordered media present complex environments for polymer behavior.
- Percolation theory models the connectivity of such systems at critical points.
- Self-avoiding walks (SAWs) are crucial for understanding polymer configurations.
Purpose of the Study:
- To analyze the scaling properties of linear polymers within disordered media.
- To model polymers as SAWs on percolation cluster backbones at critical concentrations.
- To investigate multifractal characteristics and derive generalized exponents.
Main Methods:
- Exact enumeration of all SAW configurations on single backbone configurations.
- Averaging over numerous backbone configurations to study scaling behavior.
- Analysis of moments of the total number of SAWs to identify multifractality.
Main Results:
- The study confirms multifractal behavior in the scaling of SAWs on percolation clusters.
- Generalized coordination numbers (μ(q)) and enhancement exponents (γ(q)) were found to be dependent on the moment order (q).
- A key finding is the validation of the relation μ(1) = p(c)μ, linking cluster and regular lattice behavior.
Conclusions:
- Polymer scaling in disordered media exhibits multifractal properties.
- The derived generalized exponents provide deeper insight into polymer conformations.
- The results support the applicability of established scaling relations even in complex, disordered environments.