Methodical evaluation of Boyle temperatures using Mayer sampling Monte Carlo with application to polymers in implicit...

Area of Science:

• Polymer Physics
• Computational Chemistry
• Statistical Mechanics

Background:

• The Boyle temperature (TB) is crucial for polymer solutions, marking where the second osmotic virial coefficient (A2) is zero.
• TB is linked to polymer condensation critical temperature, especially for long polymer chains (n → ∞).
• Existing experimental and computational methods for TB can be complex or require specific conditions.

Purpose of the Study:

• To present and evaluate two novel Mayer-sampling Monte Carlo (MSMC) based computational approaches for calculating polymer Boyle temperatures (TB).
• To compute TB as a function of polymer model parameters, specifically chain stiffness.
• To compare TB with the temperature Tθ, where polymer size scales as random walk chains.

Main Methods:

• Developed two MSMC-based methods: one using temperature derivatives of A2 to guide TB search, and another using numerical integration of an ODE for TB variation.
• Applied these methods to off-lattice linear Lennard-Jones polymers with chain lengths from 2 to 512 monomers.
• Calculated single-molecule radius of gyration (Rg) to determine Tθ.

Main Results:

• Successfully computed TB lines for polymers as a function of chain stiffness.
• The new methods avoid the need for reference states or special averages often required for direct A2 computation.
• Found that Tθ and TB appear to differ by approximately 6% in the infinite chain length limit (n → ∞).

Conclusions:

• The presented MSMC adaptations offer efficient and unbiased computational routes to determine polymer Boyle temperatures (TB).
• The observed difference between Tθ and TB suggests distinct physical behaviors or potential systematic errors in extrapolation.
• Further investigation is needed to resolve the discrepancy between Tθ and TB in the long polymer limit.