Energy internal surface

Until now we have considered the total energy quantities of the system. Now we turn to the interfacial excess quantities. We start with the internal interfacial or internal surface energy... 

For pure liquids the description becomes much simpler. We start by asking, how is the surface tension related to the surface excess quantities, in particular to the internal surface energy and the surface entropy ... 

This is the heat per unit area absorbed by the system during an isothermal increase in the surface. Since d y/dT is mostly negative the system usually takes up heat when the surface area is increased. Table 3.1 lists the surface tension, surface entropy, surface enthalpy, and internal surface energy of some liquids at 25°C. 

Table 3.1 Surface tension, surface entropy, surface enthalpy, and internal surface energy of some liquids at 25°C.

Determining surface energy parameters such as the surface tension, the surface stress, the internal surface energy, etc., is a difficult task. This is partially due to the fact that different... 

Table 8.2 Internal surface energies u of noble gas crystals. A range is given because of different crystal orientations which lead to different surface energies.

It involves the change of the internal surface energy upon adsorption of an infinitesimal amount of gas at constant temperature and total surface area. 

Surface stress — The surface area A of a solid electrode can be varied in two ways In a plastic deformation, such as cleavage, the number of surface atoms is changed, while in an elastic deformation, such as stretching, the number of surface atoms is constant. Therefore, the differential dUs of the internal surface energy, at constant entropy and composition, is given by dUs = ydAp + A m g m denm, where y is the interfacial tension, dAp is the change in area due to a plastic deformation, gnm is the surface stress, and enm the surface strain caused by an elastic deformation. Surface stress and strain are tensors, and the indices denote the directions of space. From this follows the generalized Lippmann equation for a solid electrode ... 

When dealing with surfaces, the Gibbs-Duhem relation is an important equation of chemical thermodynamics. It can be derived in the following way [24.25.16.26], The differential of the internal surface energy. dUn. can be expressed as... 

Ms and Msl are the internal surface energies per unit area for the bare and the immersed surface, respectively. Hence from measuring the heat of immersion one can obtain information about the internal surface energy, but it is not possible to measure the surface tension directly. 

The total surface area needs to be known to determine the change of internal surface energy from the heat of immersion. This is often done by adsorption measurements [94,83]. An alternative method was suggested by Harkins and Jura 92. They proposed not to immerse a clean solid but to expose the solid first to the vapor of the liquid. If the liquid wets the solid at the saturating vapor... 

TABLE 6 Internal Surface Energies at 25 C (in It) 1 N/m) from Heats of Solution for Various Solids... 

A variation of the technique is to measure the internal surface energies from the heat of solution. When the solid interface is destroyed, as by dissolving, the internal surface energy appears as an extra heat of solution. With accurate calorimetric experiments it is possible to measure the small difference between the heat of solution of coarse and of finely crystalline material (Table 6). The calorimetric measurements need to be done with high precision, since there is only a few joules per mole difference between the heats of solution of coarse and those of finely divided material. A typical example is NaCI. For large crystals the heat of solution in water is 4046 J/mol. Lipsett et al. [951 measured with finely divided NaCI (specific surface area of 125 nr/mol) a heat of solution that was 51 J/mol smaller. 

Another method to determine the surface enthalpy and entropy and the internal surface energy was devised by Jura and Garland 96. They measured the heat capacity for a powder versus temperature. The surface enthalpy per unit area is... 

TABLE 11 Summary of Methods for Measuring the Surface Stress T, the Surface Tension y. the Internal Surface Energies of the Solid Surface i/ or of the Solid-Liquid Interface. and Changes in Surface Stress AT... 

Their Tammann temperatures are low. As a consequence, these lattices are in a metastable state, near these temperatures. If two structures are closely related, as we shall see in the next section, the two solids will be able to form either coherent interfaces or solid solutions. In these cases, "hybrid crystals, in which microdomains of both phases coexist, can be formed according to UBBELOHDE s theory (43), which considers strain energy E and internal surface energy ri (44). The free enthalpy of a domain (1) in a matrix of structure (2) is given by ... 

Here, S = 5 gj is the surface stress, f r the external body force per unit mass of material surface, Sa- the specific internal surface energy, q . = q a the surface heat flux vector, rjg. the surface entropy density, So- = i a the surface entropy flux vector, and h /d the surface entropy production. 

In this chapter, the assumption wdl he made that the material interface is in a state which can he characterized, locally, hy physical and thermodynamic quantities, as can the media in contact with that interface. Thus, in the absence of fields, we had, for the internal surface energy e =eg[ Sg, lper unit mass (see Chapter 3 of [PRU 12]) ... 

Table 8.1 Internal surface energies u° of noble gas crystals.

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