Configurational probabilities for monomers, dimers and trimers in fluids

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Computational Chemistry

Background:

• Molecular aggregation is crucial in various chemical and physical processes.
• Existing models often struggle to accurately capture aggregation dynamics across different temperature ranges.
• Understanding clustering behavior is key to controlling material properties.

Purpose of the Study:

• To develop a novel analytical approach for modeling molecular aggregation with nearest-neighbor attractive interactions.
• To derive exact high-temperature limit equations for clustering phenomena.
• To calculate equilibrium constants for small molecular clusters (dimers and trimers).

Main Methods:

• Treating molecular clustering as a chain reaction process.
• Employing the Ono-Kondo approach on a hexagonal lattice to determine occupation probabilities.
• Calculating configurational probabilities for i-mers (i=1, 2, 3).
• Deriving approximate analytical solutions from grand partition function calculations for monomer adsorption.

Main Results:

• The proposed analytical model accurately predicts the high-temperature limit of aggregation.
• Equilibrium constants for dimers and trimers were successfully calculated.
• The model demonstrates good agreement with Monte Carlo simulations at medium and high temperatures.
• Identified potential improvements for low-temperature predictions by incorporating more detailed site density information.

Conclusions:

• The new analytical approach provides a robust method for modeling molecular aggregation.
• The model offers valuable insights into the thermodynamics of small cluster formation.
• Further refinement is possible for low-temperature regimes, enhancing its applicability.