Statistical Mechanics of Dimerizations and its Consequences for Small Systems

Utilizing a statistical mechanics framework, we derive the expression of the equilibrium constant for dimerization reactions. An important feature arising from the derivation is the necessity to include two-body correlations between reactants' concentrations, reminiscent to those recently found crucial for binding reactions. However in (homo-) dimerizations, particles of the same type associate, and therefore, self-correlations are excluded. As a result, the mathematical form of the equilibrium constant differs from the well-known expression given in textbooks. For systems with large number of particles the discrepancy is negligible, whereas, for finite systems it is significant. Rationalized by collision probability between monomers, the bimolecular rate constant for dimer formation is proportional to concentration the same way correlations are accounted for. Another consequence of these correlations, is an inhomogeneous function behavior of system's properties when scaling-down the system to a regime smaller than the thermodynamic limit. All predictions are verified by MC and MD simulations.