Thompson—Gibbs equation

D. Dependence of on Lamellar Thickness (Gibbs-Thompson Equation)... 

If 8L/L0 is small, as observed experimentally, perhaps due to very slow kinetics of chain rearrangements, then the relationship between Lq and Tc is the same as the Gibbs-Thompson equation ... 

After certain duration of time, let the lamella have thickened by a factor of p so that L = LoP- According to the Gibbs-Thompson equation, Eq. (1.28), the melting temperature of the thickened lamella is... 

In a spherical nucleus, AG is associated to the supercooling, T, and the surface free energy at the crystal/ melt interface, o, through the Gibbs-Thompson equation (Eq.2) ... 

To correlate with the usual macroscopic observations, the Gibbs-Thompson equation may be Introduced to describe the dependence of the Surface free energy on parameters of the surface being analyzed U6). 

Introduction of the Gibbs-Thompson equation results in

po + 2Citr... 

The growth of the clusters is governed by the Gibbs-Thompson equation... 

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... 

This equation is also called Gibbs-Thompson equation and the effect (surface curvature, vapor pressure and chemical potential) is also called the Gibbs-Kelvin effect or Kelvin effect. 

Capillarity effects arise in physical situations where significant geometrical curvatures are present. Because of the existence of surface energy, the local chemical potential becomes a function of the local radius of curvature K according to the Gibbs-Thompson equation [93Bonl] ... 

Equation (2.24a) is referred to as the Gibbs-Thompson equation or Thompson-Freundlich equation. This equation is correct only when the effect of the interface is exerted solely on the a phase, i.e. the interface belongs only to the a phase. Therefore, when using Eq. (2.24a), Eq. (2.24b) must be simultaneously satisfied. When we express Eq. (2.24a) in terms of atom activity a. 

Figures 23.1, 23.2, 23.3 present as three selected examples the results obtained for an octene copolymer of sPP (sPPcOlS with 15% per weight of octene units), an octene copolymer of polyethylene (PEc014 with 14% per weight of octene units) and PeCL. The Gibbs-Thompson equation describes the melting point Tf of a crystalUte with thickness dc (heat of fusion Ahf, surface free energ> a c) as...

An important feature of this model is the invocation of the Gibbs-Thompson equation to describe the dependence of the Gibbs energy of LiOH (s) in the pores of the outer layer on the curvature of the internal pore surface. This analysis shows that the pore radius cannot go below a critical value, because below this critical radius LiOH precipitation is no longer spontaneous. It is for this reason that the pores remain open, but, because the concentration of LL in the pores is determined by the rates of Reactions (3) and (8), the critical radius is potential dependent, such that the radius decreases as the voltage is made more positive (Pensado-Rodriguez [1999]). 

Fakirov S and Avramova N (1982) Applicability of Gibbs-Thompson equation to Nylon 6, J Polym Sci Part C Polym Lett 20 635-641. 

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