Density functional theory for polymeric systems in 2D.

Area of Science:

• Soft Matter Physics
• Polymer Physics
• Statistical Mechanics

Background:

• Density functional theory (DFT) is a powerful tool for studying fluids.
• Thermodynamic perturbation theory (TPT) provides a framework for incorporating molecular structure.
• Previous DFT models for polymers have limitations in describing complex systems.

Purpose of the Study:

• To develop a novel density functional theory for polymeric fluids in two dimensions.
• To apply the theory to model density profiles of hard-disk polymers near hard walls.
• To assess the accuracy of the proposed theory by comparing with simulation data.

Main Methods:

• Utilizing Wertheim's first-order thermodynamic perturbation theory (TPT).
• Building upon the density functional theory for polymers developed by Yu and Wu.
• Performing Monte Carlo simulations to generate benchmark data for comparison.

Main Results:

• The proposed DFT accurately predicts density profiles for short polymer chains.
• Agreement between theory and simulations decreases for longer polymer chains.
• Recasting the theory using self-consistent field theory formalism improves performance, especially at low densities.

Conclusions:

• The developed DFT provides a promising approach for modeling 2D polymeric fluids.
• Further refinements, including going beyond first-order TPT and incorporating self-avoiding statistics, are necessary for improved accuracy with longer chains.
• The study highlights the potential of DFT in understanding polymer behavior in confined geometries.