Preserving positivity in density-explicit field-theoretic simulations

Area of Science:

• Polymer physics
• Computational chemistry
• Statistical mechanics

Background:

• Field-theoretic simulations (FTS) model polymeric fluids using auxiliary field (AF) theory.
• Hubbard-Stratonovich transformations in AF theory restrict non-bonded potentials.
• A need exists for FTS methods capable of handling complex, multi-body potentials.

Purpose of the Study:

• To develop the first stable and efficient density-explicit field-theoretic simulations (DE-AF FTS).
• To overcome limitations of Hubbard-Stratonovich transformations in modeling non-bonded potentials.
• To enable the study of diverse polymer systems requiring complex potentials.

Main Methods:

• Introduced positivity-preserving schemes for stable stochastic evolution of density fields.
• Developed density-explicit auxiliary field (DE-AF) theory for polymer simulations.
• Implemented DE-AF FTS for various dense fluid systems.

Main Results:

• Achieved thermodynamically correct results for a simple fluid at high densities.
• Demonstrated applicability to dense systems: simple fluids with three-body potentials, homopolymer solutions, and diblock copolymer melts.
• Identified limitations in the dilute regime, indicating areas for future algorithm refinement.

Conclusions:

• Density-explicit field-theoretic simulations (DE-AF FTS) offer a powerful new tool for polymer physics.
• The method successfully models dense polymeric fluids with complex potentials.
• Further development is needed to extend DE-AF FTS to dilute fluid regimes.