A general relation between the nucleation work and the size of the nucleus in multicomponent nucleation

We prove a general theorem that relates the variation of the work of formation of the critical nucleus with chemical potential and the size and composition of the critical nucleus. Applications are made to multicomponent nucleation and to both isothermal and nonisothermal phase transformations. We show that the excess number of molecules and the excess entropy of the critical nucleus are thus accessible to experimental determination with the help of data for the dependence of the nucleation rate on supersaturation. The results derived do not rely on classical nucleation approximations and thus apply down to the smallest nuclei of a few molecules only.