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Multimerizations, Aggregation, and Transfer Reactions of Small Numbers of Molecules.
Ronen Zangi1,2,3
1Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain.
This study introduces a new equilibrium constant expression accounting for reactant concentration cross-correlations in multimerization. This approach ensures a constant value across various conditions, unlike traditional methods that show significant variations.
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Area of Science:
- Physical Chemistry
- Chemical Physics
- Thermodynamics
Background:
- Macroscopic chemical equilibria differ from small-particle systems.
- Traditional equilibrium constant expressions neglect reactant concentration correlations.
Purpose of the Study:
- To develop and validate a new equilibrium constant expression for multimerization that includes cross-correlations.
- To demonstrate the constancy of this new expression across different conditions and system sizes.
Main Methods:
- Application of a recently proposed equilibrium constant expression for binding.
- Formulation of equilibrium constants for cluster formation (trimer, tetramer, pentamer) via series of two-body reactions.
- Molecular dynamics simulations to test the expression's validity.
Main Results:
- The new expression, including cross-correlations, yields a constant equilibrium constant value.
- Traditional expressions ignoring correlations show large variations (orders of magnitude).
- The derived relation between average particle number and fluctuations holds even with coupled reactions.
Conclusions:
- Cross-correlations are essential for accurate equilibrium constant expressions in multimerization.
- The new expression provides a robust and consistent description of chemical equilibria.
- Molecular dynamics simulations validate the theoretical framework for small systems.

