Figure 2.05. Spherical Nucleus Gibbs Energy vs. Radius. The two colored circles represent two spherical nucleii, one with a radius (R) of 1 nm and one with a radius (R) of 2 nm. The volumes (V) and surface areas (A) of the two spheres are listed in cubic nanometers and square nanometeres, respectively. The ratio of the volume to the surface area (V/A) increases as R/3, so the ratio for the small sphere is 1/3 nm and the ratio for the larger sphere is 2/3 nm. As the radius of the sphere increases, the volume energy effects will change faster than the interfacial energy effects.

Using the listed values of the reaction Gibbs energy per unit volume (ΔG_V) and the interfacial Gibbs energy per unit area (σ_A), the Gibbs energy changes associated with the growth of a spherical nucleus are shown on a graph as a function of the radius of the spherical nucleus. The interfacial energy changes are shown with a blue line. The phase change energy changes are shown with a red line. The net Gibbs energy change (ΔG_T) with the growth of the nucleus is shown with a black line. The critical radius is the radius value at the maximum of the the black curve. Once that critical radius is achieved, any addtions to the nucleus reduce the Gibbs energy and the nucleus will grow.