Enhancement of reaction rate in small-sized droplets: A combined analytical and simulation study

Several recent mass spectrometry experiments reveal a marked enhancement of the reaction rate of organic reactions in microdroplets. This enhancement has been tentatively attributed to the accumulation of excess charge on a surface, which in turn can give rise to a lowering of activation energy of the reaction. Here we model the reactions in droplets as a three-step process: (i) diffusion of a reactant from the core of the droplet to the surface, (ii) search by diffusion of the reactant on the surface to find a reactive partner, and finally (iii) the intrinsic reaction leading to bond breaking and product formation. We obtain analytic expressions for the mean search time (MST) to find a target located on the surface by a reactant in both two- and three-dimensional droplets. Analytical results show quantitative agreement with Brownian dynamics simulations. We find, as also reported earlier, that the MST varies as R²/D, where R is the radius of the droplet and D is the diffusion constant of the molecules in the droplet medium. We also find that a hydronium ion in the vicinity can substantially weaken the bond and hence lowers the activation barrier. We observe a similar facilitation of bond breaking in the presence of a static dipolar electric field along any of the three Cartesian axes. If the intrinsic reaction is faster compared to the mean search time involved, it becomes primarily a diffusion-controlled process; otherwise the reaction cannot be accelerated in the droplet medium. The air-droplet interface provides a different environment compared to the interior of the droplet. Hence, we might also expect a completely different mechanism and products in the case of droplet reactions.