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Related Experiment Video

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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Structural crossover of polymers in disordered media.

Roni Parshani¹, Lidia A Braunstein, Shlomo Havlin

¹Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan, Israel.

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

|June 13, 2009

Summary

Small polymers are more compact than large ones in disordered substrates, exhibiting strong disorder behavior. Large polymers show weak disorder behavior, with crossover length depending on disorder broadness and correlation length.

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Area of Science:

Polymer physics
Statistical mechanics
Condensed matter physics

Background:

Polymers in disordered media exhibit complex structural behaviors.
Optimal polymer configuration minimizes monomer-substrate interaction energies.
Previous studies noted differing fractal dimensions in strong disorder (SD) vs. weak disorder (WD) limits.

Purpose of the Study:

Develop a unified scaling theory for polymer structural behavior in disordered energy substrates.
Investigate the crossover phenomena between WD and SD limits.
Analyze how polymer size influences structural properties within the same disordered substrate.

Main Methods:

Theoretical scaling analysis.
Mathematical modeling of polymer-substrate interactions.
Analysis of fractal dimensions in different disorder regimes.

Main Results:

Introduced a scaling theory for the crossover between WD and SD limits.
Demonstrated that small polymers (N<>N*) behave as in WD.
Showed that crossover effects are observable within a single polymer configuration, with smaller segments exhibiting higher fractal dimensions.

Conclusions:

Polymer size dictates its structural behavior (compactness and fractal dimension) in a disordered substrate.
The crossover length (N*) is determined by the percolation correlation length exponent (nu) and disorder broadness parameter (a).
Findings reveal size-dependent structural transitions and implications for polymer self-assembly and function in complex environments.