Thompson 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... 

It is assumed that the bubble is spherical, that the liquid is incompressible, that viscosity effects may be neglected, and that the usual Thompson equation is applicable during the growth period (time from the appearance of a nucleus of size Ro, Ro = 2c/(pv — p ), to some later time). By the use of these assumptions it is possible to treat the mathematical case of a moving, spherical heat transfer boundary (L2), to combine this with the... 

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... 

During the period 1937-1940 Higuchi proposed a modified capillary condensation theory to explain the isotherms of 18 sorbates on titania gel of the same lot. The new theory proposes that in sorption phenomena vapors may be adsorbed in two ways (a) adsorption due to the surface force of solid sorbents which is usually accomplished by forming a monomolecular film in the relatively low pressure range and (b) capillary condensation of sorbates into pores whose radii are larger than ca. 10 A and covered by an adsorption film. The capillary condensation is undoubtedly due to the vapor pressure depression of the sorbate liquid described by the Thompson equation. 

The interstitial volume around contact zones of spheres which are arranged in a definite packing type are calculated as follows We assume that a sorbate condenses in the contact zones of spheres of radius R, as exhibited by the shaded zone in Fig. la. The vapor pressure, P, or relative pressure, z, of the condensed liquid of volume V is given by the Thompson equation. 

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... 

The. -matrix which defines the parameters of Table 1 are obtained by solving the Thompson equation [15], which in operator form reads... 

The Thompson equation is one among many three-dimensional reductions of the Bethe-Salpeter equation [16]. A discussion of the Bethe-Salpeter equation and several possible three-dimensional reductions can be found in Refs. [14,17]. Moreover, Tjon and co-workers [18] have compared results obtained by solving the full four-dimensional Bethe-Salpeter equation with all relevant OBE diagrams with those obtained from the Blankenbecler-Sugar (Bbs) [19] and other three-dimensional reductions. For the Bbs equation, which differs little from the Thompson equation, only small differences were found compared with the full Bethe-Salpeter equation. 

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. 

The total scattering per electron (incoherent plus coherent) is given by the classical Thompson equation. 

---