Do equilibrium and rate constants of intramicellar reactions depend on micelle size?

Abstract

We have studied the combined static and dynamic quenching of pyrene by methyl viologen in sodium alkyl sulfate micelles varying in volume by a factor of more than 4. Size controls were the temperature T (283 K–333 K) and the alkyl chain length n (9–14) as well as, with n = 12 only, added NaCl (up to 9 times the surfactant weight-in concentration). At high [NaCl], up to 40% of the viologen resides in the aqueous bulk and quenches dynamically across the micelle–water interface with a rate limited by its diffusion-controlled attachment to the micelle. The micellar aggregation numbers depend linearly both on n and on the difference between T and the Krafft temperature; we have derived interpolation formulas for them as well as for the associated molar volumes of the micelles; the aggregation numbers at the critical micelle concentration are also linear functions of T, and the exponent relating them to the aggregation numbers at other concentrations is temperature independent. At given T, the volume-based quenching rate constants for different n or [NaCl] are very similar, and the same holds true for the equilibrium constants of the static quenching. Arrhenius plots identify the microviscosity inside the micelles as octanol-like; van't Hoff plots give virtually the same reaction enthalpies and entropies as in homogeneous methanolic solution; and the underlying kinetic and thermodynamic parameters are not modified by the micelle size.