Confinement Effect on Triple-point Temperature

If one considers the thermodynamic equilibrium between gas, liquid, and solid phases in a cylindrical pore, combination of the Clausius-Clapeyron and Kelvin equations yields 

Writing AT = Tp - T0, a serial development of Equation 10.2 in the first order yields 

Equation 10.3 is known as the Gibbs-Thomson [1] equation and is classically used experimentally to calculate r from the measurement of AT. In the case of a cylindrical pore of radius rp, Equation 10.4 can be written 

A rigorous treatment of melting in confined geometries considering the three interfaces (including the vapor phase) becomes difficult This has been discussed extensively by Defay et al. [2], 

This treatment of melting in confined geometries is obviously oversimplified and the molecular nature of the phases and interactions between the adsorbent walls and the adsorbate should be taken into account by considering not only the surface energies but also the exact nature of the solid phase (structure, crystalline orientation, crystal defects, and so on). 

---