Free Energy of j-mer Formation

In the previous chapter we derived the Kelvin, or Gibbs-Thomson, equation (see (9.82) and (9.85)), 

A partial pressure less than p) S 1) indicates p, piAn this case the vapor is stable and will not condense. If the partial pressure exceeds p) (S 1), P I Pi, the /-mer will tend to grow at the vapor s expense since the system gravitates toward its lowest chemical potential. 

A transfer of / molecules from the vapor phase forms an /-mer of radius r. The accompanying free energy change is 

The free energy change of /-mer formation contains two terms. The first is the free energy increase as a result of the formation of the /-mer surface area. The second term is the free energy decrease from the change in chemical potential on going from the vapor to the condensed phase. 

The corresponding value of the number of molecules at the critical size is given by (10.35). 

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