Statistical mechanics of dimerizations and its consequences for small systems.

Area of Science:

• Statistical Mechanics
• Chemical Kinetics
• Physical Chemistry

Background:

• Dimerization reactions are fundamental in chemical and biological processes.
• Existing models for equilibrium constants may not fully capture behavior in finite systems.
• Two-body correlations are increasingly recognized as critical for accurate reaction modeling.

Purpose of the Study:

• To derive a statistically mechanical expression for the equilibrium constant in dimerization reactions.
• To investigate the role of two-body correlations in (homo-)dimerizations.
• To analyze the impact of these correlations on finite systems and scaling behavior.

Main Methods:

• Derivation using a statistical mechanics framework.
• Analysis of two-body correlations and self-correlations.
• Comparison with standard textbook expressions.
• Verification through Monte Carlo and molecular dynamics simulations.

Main Results:

• A novel expression for the equilibrium constant in dimerization reactions is derived, accounting for two-body correlations.
• The derived expression differs from traditional forms, particularly in finite systems.
• The bimolecular rate for dimer formation is proportional to the squared monomer concentration.
• System properties exhibit inhomogeneous behavior when scaled below the thermodynamic limit.

Conclusions:

• Two-body correlations are essential for accurate equilibrium constant expressions in dimerization, especially for finite systems.
• The findings necessitate a revised understanding of molecular interactions at smaller scales.
• The study provides a more robust theoretical framework for analyzing dimerization dynamics.