title: Statistical effects related to low numbers of reacting molecules analyzed for a reversible association reaction A + B = C in ideally dispersed systems: An apparent violation of the law of mass action.
abstract: Theoretical analysis and computer simulations (Monte Carlo and numerical integration of differential equations) show that the statistical effect of a small number of reacting molecules depends on a way the molecules are distributed among the small volume nano-reactors (droplets in this study). A simple reversible association A + B = C was chosen as a model reaction, enabling to observe both thermodynamic (apparent equilibrium constant) and kinetic effects of a small number of reactant molecules. When substrates are distributed uniformly among droplets, all containing the same equal number of substrate molecules, the apparent equilibrium constant of the association is higher than the chemical one (observed in a macroscopic-large volume system). The average rate of the association, being initially independent of the numbers of molecules, becomes (at higher conversions) higher than that in a macroscopic system: the lower the number of substrate molecules in a droplet, the higher is the rate. This results in the correspondingly higher apparent equilibrium constant. A quite opposite behavior is observed when reactant molecules are distributed randomly among droplets: the apparent association rate and equilibrium constants are lower than those observed in large volume systems, being the lower, the lower is the average number of reacting molecules in a droplet. The random distribution of reactant molecules corresponds to ideal (equal sizes of droplets) dispersing of a reaction mixture. Our simulations have shown that when the equilibrated large volume system is dispersed, the resulting droplet system is already at equilibrium and no changes of proportions of droplets differing in reactant compositions can be observed upon prolongation of the reaction time.
authors.affiliation: Center of Molecular and Macromolecular Studies of Polish Academy of Sciences, Sienkiewicza 112, 90-363 Lodz, Poland.
authors.forename: R
authors.initials: R
authors.lastname: Szymanski
authors.affiliation: Center of Molecular and Macromolecular Studies of Polish Academy of Sciences, Sienkiewicza 112, 90-363 Lodz, Poland.
authors.forename: S
authors.initials: S
authors.lastname: Sosnowski
authors.affiliation: Center of Molecular and Macromolecular Studies of Polish Academy of Sciences, Sienkiewicza 112, 90-363 Lodz, Poland.
authors.forename: Ł
authors.initials: Ł
authors.lastname: Maślanka