Quantitative determination of a sodium dodecyl sulfate micellar radius through positron annihilation lifetime spectroscopy

Rigorous equations are established to describe the lifetime decay spectrum expected for positronium (Ps) atoms reacting with a solute by diffusion, taking into account the time dependence of the encounter rate coefficient. To assess the validity of the equations, these are applied to the case of Ps trapping into sodium dodecyl sulfate micellar aggregates in water studied by positron annihilation lifetime spectroscopy (LS). The LS spectra are satisfactorily analysed either on this new basis or in a conventional way, in terms of simple decaying exponentials. Several hypotheses are examined to derive the radius of the micelles from the data, by considering furthermore that the Ps atoms exist in the solution either in a quasi-free or in a bubble state. In complete accordance with the theoretical expectations, the combination of a time dependent encounter rate coefficient together with the bubble state assumption leads to a very good agreement between the radius thus determined (1.72 nm) and the micellar hydrophobic radius known from other techniques (about 1.84 nm).