Gibbs-Thomson Equation and Chemical Potential

The Gibbs-Thomson effect is a phenomenon seen when there is variation in chemical potential or vapor pressure when examining a curved surface or interface. Chemical potential is the potential energy that may be absorbed or released during a chemical reaction, and vapor pressure occurs when the vapor exerts pressure while in equilibrium with its other phases. In essence, there will be an increase in energy required for forming small particles with a high curvature, further causing an increase in vapor pressure. Therefore, small crystals will melt at a lower temperature than large crystals. One example of this effect is that ice cream will tend to become crunchier over time. Over time, the smaller crystals will melt less easily, providing the crunchier texture of the small crystals over the larger ones.

As such, the Gibbs-Thomson equation is an extension of the effect, and it describes the effect in the case that geometry is defined, such as liquids being contained within porous media. For example, the effect may be seen in the melting behavior of materials confined in nanopores or nanotubes. Overall, the depression in the freezing point or melting point is inversely proportional to the pore size. Furthermore, the depression depends on the solid-liquid interface energy, bulk enthalpy of fusion, and the density of solid in addition to the pore size. As aforementioned, the depression occurs more for small particles when the latent heat of the phase transition is smaller than the change in the surface energy.

Because of the chemical relationship, the use of the Gibbs-Thomson equation in conjunction with experimental technique can be used to measure pore size. For the Gibbs-Thomson equation, there is also a constant pressure limitation. Generally, the sample is cooled so that it freezes with excess liquid outside of the pores then warmed so that the liquid inside the pores melts, leaving the bulk of the material frozen. In this manner, the pore size can be attained.

In addition, the Gibbs-Thomson effect can influence phase transformations, such as precipitation, and it can alter processes like coarsening during the transformations. This results from the dependence on interfacial effects. Practical approximations of the Gibbs-Thomson equation can be applied through experimentation. For example, during phase transformations, it may be necessary to take into account eh presence of interfaces, which could lead to the addition of a capillarity term. This capillarity results from the properties of interfaces, particularly the interaction of excess surface free energy and surface tension forces.

Citations:
1. Perez M., Gibbs-Thomson effects in phase transformations. Scripta Materialia. [Online] 2005, 52, 709-712.