Curvature Dependent Surface Tension of Liquids Studied by Positronium Annihilation

Curvature dependent surface tension measurement for small cavities within a given liquid is an important problem for surface science and technological applications. Using positronium (Ps) annihilation studies, it has been shown that Ps (bound state of e⁺ and e^-) carves a 'bubble' in liquids due to the repulsive exchange interaction with the surrounding atoms and leads to a self trapped localized state for its centre of mass motion and finds itself in a confining potential. The zero-point motion of the positronium inside the bubble (existing in the localized state) exerts an outward pressure on the wall which is balanced by the inward contractile pressure due to the surface tension of the liquid, thus minimizing the total energy of the Ps-bubble system. Employing the pick-off annihilation characteristics of Ps in a particular liquid, and a realistic potential form (in this case Woods-Saxon potential) one can compute the depth and range of the confining cavity (bubble which is in the sub-nanometer scale). Using the Tolman's relations between effective surface tension dependent on radius of curvature and the bulk surface tension, it is possible to derive a corrected notion of surface energy for the balanced condition of the bubble which in fact gives the curvature dependent surface tension for bubbles in liquids, with sizes of several tenths of nanometers.