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Loop statistics in polymers in crowded environment.
1Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine.
This study investigates polymer loop formation in disordered environments. Structural defects in the polymer chain
Area of Science:
- Polymer Physics
- Statistical Mechanics
- Materials Science
Background:
- Understanding polymer chain behavior in disordered environments is crucial for materials science.
- The formation of loops within polymer chains influences their macroscopic properties.
- Previous studies often simplified environmental disorder or focused on short chains.
Purpose of the Study:
- To analyze the probability of forming a single loop in a flexible polymer chain within a disordered environment.
- To investigate the impact of correlated structural defects on loop formation probability.
- To determine how loop position and length scale with chain properties in d dimensions.
Main Methods:
- Utilized a continuous chain model for polymer representation.
- Applied the direct polymer renormalization group scheme for analysis.
- Calculated critical exponents governing loop formation probabilities.
Main Results:
- Quantified the scaling of loop formation probability with loop length.
- Determined the influence of correlated structural defects on loop statistics.
- Established a power-law relationship for defect correlation (∼r⁻ᵃ).
Conclusions:
- The presence of structural defects significantly decreases the probability of loop formation in polymer macromolecules.
- Results provide quantitative insights into polymer self-assembly in complex media.
- Findings are relevant for designing polymers with specific conformational properties.

