Gibbs-Thompson relation

Although, for obvious reasons, classical thermod5mamics caimot provide a quantitative account of the vast variety of phenomena occurring on the nanoscale, it does make some useful semiquantitative predictions in the scalable size interval. For example, based on the Gibbs-Thompson relation, Pheth predicted that for a metal composed of small particles, the redox potential E d) of the transition... 

In Eqs. (3) and (4), v is the molecular volume, k is the Boltzmann constant, T is the absolute temperature, and S is the supersaturation. For constant temperature and pressure, the supersaturation can be defined as the ratio of ionic activity products. Thus, for a binary electrolyte, S = AP/Xjp, where AP is the ionic activity product in the supersaturated solution and is the solubility product of the respective solute. Equation (3) is known as the Gibbs-Thompson relation, and Eq. (4) was first derived by Gibbs [14] to describe the condensation of droplets from vapor. 

The Gibbs-Thompson equation relates the mean-field concentration and the mean particle size. 

Here q is the molecular volume of the adatoms. The flux of adatoms to and from a crystallite is estimated by considering local equilibrium at the surface via the Gibbs-Thompson equation and resorting to the mean-field approximation for the concentration far from the crystallites. The Gibbs-Thompson equation relates the radius of curvature of a particle with the concentration of adatoms in equilibrium with it. It is given by... 

For ideal sphCTical particles, the Gibbs-Thompson equation relates the Gibbs energy to the radius. The chemical potential per metal atom of a particle with radius rpt is given by... 

The Thompson-Gibbs equation relates the melting point of crystalline polymers to the crystal thickness. It is derived from a balance of the free energy of the crystal surface and the surface-independent contribution. By measuring Tm for a series of samples with different crystal thicknesses, /c, it is possible to obtain the equilibrium melting temperature, 7, by extrapolation to k = oo ... 

The vapor pressure of the liquid, Pv. is related to the curvature (or, equivalently, to the capillary pressure) by the Gibbs-Thompson (or Kelvin) equation,... 

Another approach avoids specifying the field of inter molecular force between solid and liquid and instead resorts to thermodynamics. The first application of thermodynamics to capillarity appears to have been made by Thompson [101,102] later came the classic and general treatment by J. Willard Gibbs [50]. Nearly 60 years had elapsed after Young s treatment before Dupre [31] introduced the reversible work of adhesion of liquid and solid, and its relation to ygv sl ... 

The Thompson-Gibbs (TG) equation (4-6) allows the melting point to be related to the lamella thickness. The change in free energy on melting (AG j) is given by... 

It is interesting to note that eqn (6.60) has an identical form to that of the Thompson Gibbs equation. Note that A// is the mass-related heat of fusion (in kg ) and that = Tm. Integration of eqn (6.58) gives the expression... 

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