Extension of the Gibbs-Duhem Equation to the Partial Molar Surface Thermodynamic Properties of Solutions.

In this paper, the Gibbs-Duhem equation is extended to the partial molar surface thermodynamic properties of solutions. According to the surface Gibbs-Duhem equations, the sum of the mole fractions of the components in the surface region of a bulk solution multiplied by different partial molar surface quantities should equal zero if summation is taken by all components of the solution. There are four different partial molar surface quantities identified in this paper for which the surface Gibbs-Duhem equation is proven to be valid: (i) the reduced surface chemical potential, (ii) the surface chemical potential, (iii) the partial molar surface area, and (iv) the partial molar excess surface Gibbs energy = the product of partial molar surface area and the partial surface tension. The first one is known since Guggenheim (1940), but the other three are presented here for the first time. It is also demonstrated here how to apply the surface Gibbs-Duhem equations: (i) it is proven that the model equation applied by us recently for the reduced chemical potential [Adv Coll Interf Sci 2020, 283, 102212] obeys one of the surface Gibbs-Duhem equations, (ii) in contrary, it is proven that the model equation suggested by us recently for the partial molar surface area contradicts one of the surface Gibbs-Duhem equations; therefore, a new (and simpler) model equation for the partial molar surface areas of the components is suggested here that obeys the surface Gibbs-Duhem equation. It is also shown that the Butler equation obeys one of the surface Gibbs-Duhem equations. It is also concluded that surface composition in equilibrium should be one that ensures minimum surface tension.

The nano heat effect of replacing macro-particles by nano-particles in drop calorimetry: the case of core/shell metal/oxide nano-particles.

Experimental results are presented here obtained by a drop calorimetric method, in which Ni and Cu particles, both in bulk and nanosized form, were dropped into a liquid Sn-3.8Ag-0.7Cu solder alloy (in wt%). The molar enthalpies of mixing of the liquid (Sn-3.8Ag-0.7Cu)-Ni(Cu) alloys were measured. An extra exothermic heat effect is observed when dropping nano-particles instead of macro-particles. This is partly due to the loss of the large surface area and the corresponding large surface enthalpy of the nano-particles before their dissolution in the liquid alloy. However, a large additional exothermic heat effect was also found in the case of Cu-nano-particles, due to the exchange chemical reaction between the Cu2O shell of the nano-particles and liquid Sn; this is caused by the fact that the Cu-nano-particles are core-shell particles with an inner metallic Cu core and an outer Cu2O shell. This effect is less significant for Ni nano-particles which have a thinner oxide shell.

Formation of nanoparticles by ion beam irradiation of thin films.

The possibility of fabricating nanoparticles by ion bombardment was investigated by the ion bombardment of indium films on oxide covered Si and Cr surfaces. The different masses of implanting specimen ensured the different energy transfer while the same Si substrate ensured the same thermal conductivity for the In and Cr layers. Chromium served as a reference for the effect of ion bombardment and as a substrate as well. The SRIM program was used to simulate the ion surface interaction process. The nanoparticles were detected by scanning electron microscopy (SEM). We found that the melting of the In layer results in the formation of nanoparticles of 50-300 nm diameter and 5-10 nm height. This method can be promising for nanoparticle formation of materials with low melting point.

On the size and shape dependence of the solubility of nano-particles in solutions.

The general equation is derived for the equilibrium of a small solid particle and a large solution, being consistent with the thermodynamics of Gibbs. This equation can be solved in a closed form for solubility if an ideal (or an infinitely diluted) solution is considered, if the interfacial energy is independent of the composition of the solution and if all physical parameters (other than the solubility itself) are taken size independent. The solubility of the particles is found to increase with increasing its specific surface area, i.e. if non-spherical particles are applied. This simplified solution further simplifies if the shape of the solid is supposed to be spherical. This latter equation, however, is found to be in contradiction with the Ostwald-Freundlich equation, widely used in chemistry, biology and materials science to describe the size dependence of solubility of a spherical crystal. The reason for its incorrectness is shown to be due to the incorrect application of the Laplace equation. It is found that the solubility increases with decreasing the size of the dissolving phase not due to the increased curvature of the phase (Kelvin and Freundlich), but rather due to the increased specific surface area of the phase (Gibss, Ostwald). Equations are also derived for the case, when the size effect of the interfacial energy is taken into account, and when the crystal is surrounded by several planes of different interfacial energies. The role of wettability is discussed on the size dependence of solubility.