Mean-Field-Theory for Polymers in Mixed Solvents Thermodynamic and Structural Properties

TL;DR

This paper develops a mean-field theoretical framework using the Edwards Hamiltonian to analyze the thermodynamic and structural behavior of polymers in mixed solvents, especially near criticality, revealing phase transitions and effective interactions.

Contribution

It introduces a novel mean-field approach to study polymers in mixed solvents, incorporating critical phenomena and effective interactions within the Edwards Hamiltonian formalism.

Findings

Polymer phase transitions depend on solvent criticality and interaction asymmetry.

Effective polymer-solvent interactions increase near solvent criticality, affecting polymer conformation.

The effective potential can be expanded as a series similar to Ornstein-Zernike expansion.

Abstract

Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approaches criticality. Both the single and the many chain problems are examined. When the pure mixed solvent is near criticality, addition of a small amount of polymers shifts the criticality towards either enhanced compatibility or induced phase separation depending upon the value of the parameter describing the interaction asymmetry of the solvents with respect to the polymer. The polymer-solvent effective interaction parameter increases strongly when the solvent mixture approaches criticality. Accordingly, the apparent excluded volume parameter decreases and may vanish or even become negative. Consequently, the polymer undergoes a phase transition from a swollen state to an unperturbed state or even take a collapsed configuration. The effective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of ternary mixtures of polymers in mixed solvents are investigated within the Edwards Hamiltonian model. It is shown that the effective potential on a test chain in strong solutions could be written as an infinite series expansion of terms describing interactions via one chain, two chains etc. This summation can be performed following a similar scheme as in the Ornstein-Zernike series expansion.