Free Energy for Formation of Nucleus of Critical Size via Heterogeneous Nucleation. When nucleation occurs heterogeneously, the free energy for a nucleus of a critical size (ΔG^*hetero) is given by 

which is the free energy for homogeneous nucleation of a nucleus of a critical size. If the contact angle (θ) of the phase that is nucleating on the pre-existing surface is 180°, there is no wetting, and the value of the function f (θ) is 1. The free energy of forming a nucleus of a critical radius is the same as that for homogeneous nucleation. If the nucleating phase wets the solid completely (i.e., θ 5 0), then f(θ) = 0, and there is no barrier for nucleation. Write a computer program that will ask the user to provide the values of parameters needed to calculate the free energy for formation of a nucleus via homogeneous nucleation. The program should then calculate the value of ΔG^*hetero as a function of the contact angle (θ) ranging from 0 to 180°. Examine the variation of the free energy values as a function of contact angle.

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AG*hetero = AG*homo f(0) nof(0), where (2 + cos 0) (1 - cos 0)² 4 16πƠ 3AG' and AG homo is given by.