Gibbs-Thomson formula

A quantitative test of the Gibbs-Thomson formula will accordingly involve the following measurements we first determine the surface tension of a solution for a number of different concentrations, plot the [Pg.41]

In view of the fundamental importance of the Gibbs-Thomson formula, and the magnitude of the discrepancies between the figures calculated from it and the experimental results, it is of obvious interest to inquire to What causes the deviations may be due. The first point to be noticed is that the complex substances which exhibit them most markedly form, at least at higher concentrations, colloidal and not true solutions. It is, therefore, very probable that they may form gelatinous or semi-solid skins on the adsorbent surface, in which the concentration may be very great. There is a considerable amount of evidence to support this view. Thus Lewis finds that, if the thickness of the surface layer be taken as equal to the radius of molecular attraction, say 2 X io 7 cms., and the concentration calculated from the observed adsorption, it is found, for instance, for methyl orange, to be about 39%, whereas the solubility of the substance is only about 078%. The surface layer, therefore, cannot possibly consist of a more concentrated solution of the dye, which is the only case that can be dealt with theoretically, but must be formed of a semi-solid deposit. 

One of the first theoretical analyses of freezing/melting in thin pores was undertaken by Batchelor and Foster [17] on the basis of the Clausius-Clapeyron equation for solid and liquid states of substance inside the pores. From the geometric representation they derived an equation that, as shown later by Defay et al. [9], describes the shift of the triple point for the system. Since then this equation, as well as so-called Gibbs-Thomson equation - which is easily derived from Batchelor-Foster formula by assuming equality of solid and liquid densities and by replacing the... 

The last formula is a general expression of the Gibbs - Thomson equation giving the interrelation between the size c of the critical nucleus and the supersaturation Ap. 

This analysis convincingly shows that the formula (1.125) derived by means of kinetic considerations coincides with the thermodynamic Gibbs-Thomson equation (1.78). The beauty of this result is that it demonstrates in an unambiguous way the complete agreement between the purely thermodynamic and the purely kinetic approach to the equilibrium state of the small phases. Nowadays this may seem clear and even self-evident. 

The method of deduction also applies when B is a liquid, or a solid, and (6) therefore holds for these cases. The equation (6) is called Gibbs s Adsorption Formula it was deduced independently by J. J. Thomson W (1888). The present deduction is due to Milner <12> (1907). 

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