Four-Component Analysis and Modeling of Positron Annihilation Lifetime Parameters in AOT/Water/Isooctane Microemulsions M. F. Ferreira Marques Instituto Superior de Engenharia, 3000 Coimbra, Portugal H. D. Burrows, ² M. da Grac ¸ a Miguel, ² A. P. de Lima, ‡ and C. Lopes Gil ‡ Departamentos de Quı ´mica e de Fı ´sica da UniVersidade, 3000 Coimbra, Portugal G. Dupla ˆ tre* Centre de Recherches Nucle ´ aires, IN2P3/CNRS, Chimie Nucle ´ aire, B.P. 28, 67037, Strasbourg Cedex, France ReceiVed: September 25, 1995; In Final Form: January 8, 1996 X Reverse micelles are studied in sodium AOT/water/isooctane mixtures as functions of AOT concentration (C AOT ), water to AOT mole ratio (w 0 ) and temperature (T), from 294 to 333 K, using positron annihilation lifetime spectroscopy (LS). By four-component analysis of the spectra, it is possible to extract the LS parameters (intensities, I i , and lifetimes, τ i ) of the triplet positronium (o-Ps) present in the aqueous (I 3 , τ 3 ) and organic (I 4 , τ 4 ) phases. The latter lifetime is constant and corresponds with the value measured in pure isooctane, while τ 3 is remarkably lower than the value for pure water. This difference is attributed to the out-diffusion of o-Ps from the water cores to isooctane. The relevant rigorous diffusion equations imply two fitting parameters, the radius of the water aggregates (r 0 ) and a transmission factor (h). Fixation of r 0 ) 3.6 nm for C AOT ) 0.1 M, w 0 ) 20, and T ) 294 K, as known from previous work, allows the quantitative derivation of the r 0 values for all other conditions. The water spheres appear to present some permeability to o-Ps, with a transmission factor h ) 0.12 nm -1 . The sphere radius increases smoothly with C AOT and w 0 and, more importantly, with T. The changes with w 0 give r 0 ) 0.181w 0 and 0.186w 0 nm at 294 and 298 K, respectively, and are in excellent agreement with previous proposals. The sum of the intensities, I tot ) I 3 + I 4 , is much lower than the o-Ps intensity in pure isooctane. In particular, at C AOT > 0.04 M, I tot appears very close to the value found for pure water. The possibility of a strong inhibition of Ps formation due to the micelles, as proposed in previous work, is ruled out because of the negligible electron or positron scavenging ability of alkyl sulfonates. It is thus concluded that Ps formation occurs primarily in the aqueous part of the micelles, the water aggregates representing efficient traps for the positrons while they are slowing down in the solutions. Introduction Positronium (Ps), the bound state of a positron (e + ) with an electron (e - ), has been used increasingly in recent decades as an efficient probe of the physical and chemical properties of matter. 1 The most commonly used positron annihilation technique (PAT) is lifetime spectroscopy (LS), which allows us to obtain both the lifetimes (τ i ) and relative abundances (or intensities, I i ) of the various positron species. Normally, in order of increasing lifetimes, these are singlet Ps (p-Ps, i ) 1), free positron (i ) 2), and triplet Ps (o-Ps, i ) 3). Because of its distinct long lifetime, the latter appears to be the most useful probe. The o-Ps decay occurs with the emission of two γ-rays through the pick-off process, i.e., the annihilation of the positron with one of the (bound) electrons of the surrounding medium. Information is obtained through two distinct, independent processes, Ps formation and annihilation, both of which depend on various characteristics of the systems under investigation. In liquids, Ps formation may occur on a very short time scale (ca. picoseconds) and involves the reaction of e + with one of the electrons released by ionization at the end of the positron track in a spur containing a variety of labile, reactive species such as quasi-free electrons and holes. 2,3 The nature of the solvent, the presence of solutes (e.g., electron or hole scaven- gers), and various physicochemical parameters, such as tem- perature, can affect Ps formation. Once formed, Ps can be influenced in various ways by the medium, particularly through reactions with solutes, 4 eventually leading to a decrease in its lifetime. Although Ps has proven to be very useful in a large variety of areas, 1 particular attention has been given to the study of complex, multicomponent media 1 and, more specifically, to micellar systems. 5-8 By their nature, a detailed understanding of the structure and properties of such systems demands combined study by several techniques, among which LS appears promising. However, it must be acknowledged that, notwith- standing the intrinsic interest of the work produced so far, particularly as concerns the behavior of the probe itself, little precise quantitative information on micelles has been extracted from experimental PAT data. A major reason for this lies in the limited time resolution and counting efficiency of the LS apparatus until only recently. A medium, such as a micellar solution, containing several pseudophases is expected to result in the existence of a corresponding set of Ps states, whose respective lifetimes and intensities are difficult to extract from LS spectra without sufficient resolution and integration of counts. However, taking into account recent developments in ² Departamento de Quı ´mica da Universidade. ‡ Departamento de Fı ´sica da Universidade. X Abstract published in AdVance ACS Abstracts, April 1, 1996. 7595 J. Phys. Chem. 1996, 100, 7595-7602 S0022-3654(95)02838-3 CCC: $12.00 © 1996 American Chemical Society