Enhanced Chemical Synthesis at Soft Interfaces: A Universal Reaction-Adsorption Mechanism in Microcompartments

A bimolecular synthetic reaction (imine synthesis) was performed compartmentalized in micrometer-diameter emulsion droplets. The apparent equilibrium constant ($K_{\mathrm{eq}}$) and apparent forward rate constant ($k_1$) were both inversely proportional to the droplet radius. The results are explained by a noncatalytic reaction-adsorption model in which reactants adsorb to the droplet interface with relatively low binding energies of a few $k_{B}T$, react and diffuse back to the bulk. Reaction thermodynamics is therefore modified by compartmentalization at the mesoscale—without confinement on the molecular scale—leading to a universal mechanism for improving unfavorable reactions.

Figure 1

Model chemical reaction: a fluorescent imine ($AA$) is synthesized from two nonfluorescent reagents ($A$) (Supplemental Material).

Figure 2

Concentration $C$ of imine 3 product as a function of time in bulk and in droplets. Stoichiometric mixtures of amine 1 and aldehyde 2 were used at the concentrations indicated. The initial rate and equilibrium constant of the reaction are significantly increasing when the reaction occurs in droplets of decreasing sizes (from 160 to 2.5 pL; Supplemental Tables 1–3). Error bars correspond to $\pm 1$ standard deviation.

Figure 3

Equilibrium constant for the reaction in droplets (a), forward (b), and backward (c) rate constants of the reaction as a function of droplet size. The dashed lines correspond to bulk values. The dotted and dashed line correspond to a $1/R$ relationship recovered in the model [Eq. (8)]. The direct fit by linear regression of the droplet data (solid line) shows a negative intercept with the $y$ axis, which is explained by the solubility of the product in the oil phase. Error bars correspond to $\pm 1$ standard deviation. (d) Fluorescence imaging of 2.5 and 160 pL droplets, showing the increase of product in the small droplets. (e) Thermodynamics of imine formation in 2.5 pL droplets compared to bulk (Supplemental Table 2).

Figure 4

(a) Model scheme for the reaction including surface interactions. Reactants and products in bulk and at the surface are subscripted b and s, respectively. The net flux is shown by blue arrows. (b) Scheme of the diffusion process for the products towards the bulk of a droplet of radius $R$. (c,d) Concentration profiles were obtained by solving the adsorption-reaction-diffusion equation for two limiting cases $R/\xi =0.1$ (c) and $R/\xi =10$ (d) ($\xi =\sqrt{D/k_{-1}}$).