Tolman's length and limiting supersaturation of vapor

The classical Kelvin formula for the equilibrium vapor pressure over a droplet of radius R is extended to small radii and vapor non-ideality, from where the limiting supersaturation condition is obtained by relating the point R=0 to the value of limiting (spinodal) supersaturation of vapor. The analysis of different dependences of the Tolman length on radius, δ(R), obeying this condition suggests that (i) the value of δ(0) is positive and the function δ(R) decreases with increasing radius; (ii) the curvature effect (the dependence of surface tension on radius) in the nucleation region is determined by the value of δ(0). At the same time, this effect is weakly sensitive to the form of the function δ(R) and insensitive to its asymptotic value δ∞ .