Evaluation of Surface Tension and Tolman Length as a Function of Droplet Radius from Experimental Nucleation Rate and Supersaturation Ratio

Abstract

The critical embryo surface tension and Tolman length as a function of radius has determined from the experimental homogeneous nucleation rate as measured by this paper authors (Zn), and other researches (Hg, Mg, water, n-pentanol, n-nonane). The thermodynamic description of small-scale systems exhibits peculiar fea- tures with respect to the macroscopic systems. The basis for thermodynamics of small particles has its origin in the Gibbs theory of capillarity. Instead of this real system, the theory describes an imaginary system composed of a small droplet of the homogeneous phase β and another homogeneous phase α separated by the so called surface of tension of radius R S. The surface tension σ is attributed to this sur- face. The difference δ between the equimolar radius R E and the radius R S is called Tolman length. It is well known now that the surface tension is a strong function of radius for small droplets. Therefore, to describe the thermodynamics of nanoscale systems one should know both σ(R S ) and the location of the surface of tension (δ). Both σ(R S ) and δ can be evaluated from the experimentally measured homogeneous nucleation rate. To this aim two main shortcomings of the classical nucleation theory must be solved, that is, instead of the surface tension for the flat surface σ ∞ it should consider σ(R S ); besides, replacement free energy correction factor is to be taken into account properly. The long-term discussion on the "Translation-Rotation Paradox in the Theory of Nucleation" resulted to the Reiss, Kegel, and Katz (1) (RKK) correction factor. Recently Nishioka and Kusaka (2) and Debenedetti and Reiss (3) have extended the Gibbs treatment to noncritical nucleus. This formalism results in a new expression for the reversible work W of noncritical embryo forma- tion the extrema conditions for which give the Gibbs formula