A Thermodynamic Resolution of Molecular Clustering: Eliminating Sticking Efficiency

In gas-phase chemistry, forward and reverse rates are governed by Gibbs free energy to ensure equilibrium. Yet in molecular clustering models, particularly for low or negative $\Delta G$ associations, reverse rates are often neglected and replaced with an empirical “sticking efficiency” $\eta$. This substitution violates thermodynamic consistency. We present a parameter-free framework in which equilibrium and dynamics emerge from microscopic reversibility and statistical mechanics. Applied to argon dimer formation—a chemically inert system with no free parameters, the model reproduces both transient and equilibrium behavior without approximation. Post hoc computation of $\eta$ reveals that it becomes negative and collapses to zero at equilibrium, exposing a structural failure in the parameter when reversibility is restored. This result is not merely theoretical. Climate models rely on molecular clustering to simulate black carbon and secondary organic aerosol formation, key drivers of radiative forcing. Models using $\eta$ inherit its inconsistencies. This framework offers a thermodynamically grounded and general replacement.