Excluded-Volume Interactions in Field-Theoretic Simulations: Multiconvolutions and Model Equivalence

Area of Science:

• Computational physics
• Soft matter physics
• Statistical mechanics

Background:

• Field-theoretic simulations (FTS) of complex fluids encounter divergences in functional integrals.
• Microscopic density smearing, often with Gaussian functions, regularizes these models but alters interactions.

Purpose of the Study:

• To address fundamental issues with masking functions for delta-interactions in FTS.
• To present a novel methodology for incorporating more physically relevant interactions in FTS.
• To demonstrate the efficacy of the new framework through specific model examinations.

Main Methods:

• Resolving issues with masking functions for delta-interactions in FTS.
• Developing a new methodology based on multiconvoluted inverse potentials.
• Applying a principle of model equivalence for statistical weights.
• Examining the Gaussian-regularized Edwards model (GREM) and Yukawa potential.

Main Results:

• The new methodology accommodates more physically relevant interactions in FTS.
• The Gaussian-regularized Edwards model (GREM) is successfully applied.
• A test calculation of excess chemical potential for a polymer chain in a good solvent was performed.

Conclusions:

• The developed theoretical framework offers a powerful approach for regularizing FTS of complex fluids.
• The new methodology enhances the ability to model complex fluid systems with greater physical accuracy.
• This work advances the simulation techniques for understanding polymer solutions and other complex fluids.