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Scaling properties of maximally compact chains
1The Department of Pharmaceutical Chemistry, University of California, San Francisco, 3333 California Avenue, San Francisco, California 94118, USA. kw@maxwell.ucsf.edu
Summary
This study determines how intramolecular nonbonded contacts scale in compact homopolymers on hypercubic lattices. The findings provide insights into polymer and protein structural behavior.
Area of Science:
- Statistical physics
- Polymer science
- Computational chemistry
Background:
- Understanding polymer conformation is crucial for predicting material properties.
- Maximally compact structures represent an important conformational state for polymers.
- Lattice models simplify complex polymer systems for theoretical analysis.
Purpose of the Study:
- To determine the scaling function for intramolecular nonbonded contacts in compact homopolymers.
- To analyze the relationship between polymer size (N) and dimensionality (d) on contact formation.
- To provide a theoretical framework applicable to polymer and protein studies.
Main Methods:
- Design of a representative maximally compact linear homopolymer structure.
- Derivation of an exact recursive expression for the maximum number of contacts (m(max)).
- Development of a nonrecursive expression for asymptotic scaling analysis.
Main Results:
- The asymptotic scaling of m(max) was found to be (d-1)N - dN^((d-1)/d) + 1.
- This scaling is dependent on both the number of monomers (N) and the lattice dimension (d).
- A specific formula for contact scaling in compact homopolymers was established.
Conclusions:
- The derived scaling law offers a quantitative understanding of intramolecular contacts in compact homopolymers.
- The findings have potential implications for modeling protein folding and polymer self-assembly.
- This work contributes to the theoretical understanding of polymer physics in various dimensions.