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Effective propagators for quenched disorder in linear polymers.

A Fernández¹, H Rabitz

¹Frick Laboratory, Princeton University, Princeton, NJ 08544, USA.

Biophysical Chemistry

|November 1, 1987

Summary

This study uses path integral theory to analyze disordered polymer chains. We found quenched randomness affects intra-chain interactions, altering large chain behavior compared to homogeneous polymers.

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Area of Science:

Polymer Physics
Statistical Mechanics
Computational Chemistry

Background:

Understanding polymer behavior is crucial in materials science and biophysics.
Inhomogeneous polymers with random monomer sequences present unique statistical challenges.
Existing theories often simplify polymer structures, limiting applicability to complex systems.

Purpose of the Study:

To develop a theoretical framework for analyzing inhomogeneous polymers with quenched disorder.
To investigate the impact of random monomer sequences on polymer chain statistics.
To determine the asymptotic behavior of these polymers in the thermodynamic limit.

Main Methods:

Implementation of a chain conformation space path integral theory.
Application of a replica approach to average over quenched randomness.
Perturbative analysis using mixed propagators for effective interactions.

Main Results:

The quenched disorder significantly influences intra-chain interactions.
The asymptotic behavior of inhomogeneous polymer chains was calculated.
A comparison was made between the effective Gibbs measure and homogeneous polymer systems.

Conclusions:

The developed theory provides insights into the statistical mechanics of disordered polymers.
Quenched disorder leads to deviations from homogeneous polymer behavior, especially for large chains.
This work offers a method to predict polymer properties based on monomer sequence randomness.