Single homopolymers in the relative density representation.

Area of Science:

• Statistical mechanics
• Polymer physics
• Thermodynamics

Background:

• Homopolymers are fundamental in polymer science.
• Understanding polymer behavior under external fields is crucial.
• Grand ensemble methods provide a powerful framework for statistical systems.

Purpose of the Study:

• To study a single symmetric homopolymer within the grand ensemble.
• To represent the system as a functional of local density and fugacity.
• To explore extensions for more complex polymer interactions and environments.

Main Methods:

• Utilizing the grand ensemble of monomeric units.
• Defining the system as a functional of the local density to local fugacity ratio.
• Employing the excess grand potential as a thermodynamic generating function.
• Solving a sample case in a spherical enclosure.

Main Results:

• The system is represented as a functional of the local density to local fugacity ratio.
• A spherical enclosure case demonstrates the need for extensions to grand ensembles of polymers.
• Preliminary extensions address non-neighbor and nonsymmetric interactions.

Conclusions:

• The functional representation is effective for analyzing homopolymers.
• The study highlights the necessity of extended models for complex systems.
• The work provides a foundation for further investigations into polymer thermodynamics.