Effect of particle size on melting temperature

It is becoming increasingly more popular to prepare sub-micrometre sized artificially engineered structures with new properties. In particular, the tailoring of 

Here M/p is the molar volume of the substance. At equilibrium, the chemical potential of the liquid and solid droplet are equal  

The equilibrium conditions require equal temperatures but different pressures due to the curvature. Using eq. (6.66) for both phases, the equilibrium condition, eq. (6.67), yields 

Here ps and p are the density of the solid and liquid and ps and pl the pressures inside the solid and liquid droplets, respectively. Rearrangement of eq. (6.68) yields 

The difference in curvature between the liquid (r ) and the solid (r ) particles can be found since they are related by pjT1 = psVs andT = 7t(rl )3 which gives 

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