Gibbs-Thomson relation

For liquid-vapor interfaces, the correlation length in the bulk is of t he order of atomic distance unless one is close to the critical point Hence the concept of local equilibrium is well justified in most practical circumstances For. solid surfaces above the roughening temperature, the concept also makes sense. Since the surface is rough adding (or removing) an atom to a particular part of the surface docs not disturb the local equilibrium state very much, and this sampling procedure can be used to determine the local chemical potential. This is the essence of the Gibbs-Thomson relation (1). 

Porosity Measurements via Determination of the Gibbs-Thomson Relation... 

The melting peak is simple or double according to the crystalline forms and the lamellae thickness of the spherulites using the Gibbs-Thomson relation as shown in equation 8.4. 

The relation between the chemical potential of a particle and its radius is known as the Gibbs-Thomson relation. Let /xc and /xdr) be the chemical potentials of bulk crystal and a particle with radius r, respectively. Then, their difference A/r, is... 

The used techniques for calculations of the PSD on the basis of the H NMR and TSDC spectra and modified regularization procedure applied to the integral equation based on the Gibbs-Thomson relation for the freezing point depression for confined liquids allowed us to reveal significant changes in the structure of bound and bound waters depending on the concentrations of HPF and nanosilica in their aqueous solutions. 

Water or other liquids can be frozen in narrower pores at lower temperatures that can be described by the Gibbs-Thomson relation for the freezing point depression ... 

If the nucleation is a thermally activated process, then the rate of nucleation will depend exponentially upon the free energy of formation of a nucleus of the critical size for growth to occur. The Gibbs-Thomson relation ... 

Let us assume that precipitation of the A-rich a-phase has occurred to the extent that the matrix is no longer supersaturated, and that we now have a two-phase alloy which is nearly at equilibrium. In section 7.3.2, it was assumed that the precipitate particles were all of the same size. In reality, however, there will be a range of particle sizes, since not all nuclei were formed at the same time, and also since the supply of A to a precipitate particle will be influenced by the site of the particle in the matrix. According to the Gibbs-Thomson relation, smaller particles of precipitate have a higher chemical potential for component A than do the larger particles. For spherical particles of radius r and the difference in chemical potential is ... 

Combining Equation 7.136 with (he Gibbs-Thomson relation Equation 7.126 for the boundary vacancy concentrations, we obtain an expression for the total vacancy flux in terms of the unknown B-concentration profile... 

One method that has been used to effect this separation is to invoke the Gibbs-Thomson relation. The interfacial free energy, a c, associated with the basal plane of the mature lamellar crystallite is obtained from the relation between the melting temperature and crystaUite thickness for bulk crystallized polymers. The inherent assumption is then made that a c for the mature crystallite can be identified with of the nucleus. In this manner the separation of the product of interfacial free energy can be achieved. This rather drastic assumption has not been substantiated. There is no requirement that the interfacial structure of a mature crystallite repUcates that of the initiating nucleus. In fact this situation is highly unlikely. 

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