Surface enthalpies

Finally, the total surface enthalpy per square centimeter is... 

Ziolkowski, J. (1988). New method of calculation of surface enthalpy of solids. 

A comparison of husD and fe/M/t) values for sample 3 are particularly instructive. The heat values for the immersion of monolayer-covered samples in toluene, cyclohexane, and carbon tetrachloride are three to four times less than the heat values for the bare samples and are also significantly less than the surface enthalpies of the respective liquids. Apparently, the attractive forces of the covalent carbon atoms in the surface are highly localized. In addition, the interaction of first-layer molecules with those in the second layer is less than between the liquid molecules in adsorbed monolayer, as indicated by the 7 s (14)- The net energy of adsorption... 

The surface enthalpy hs is then obtained from the relationship G = H — TS, so that... 

Before turning to the surface enthalpy we would like to derive an important relationship between the surface entropy and the temperature dependence of the surface tension. The Helmholtz interfacial free energy is a state function. Therefore we can use the Maxwell relations and obtain directly an important equation for 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.

From the value of the liquid We measure the surface tension of the melt and rely on the fact that, close to the melting point, the free surface enthalpy of the solid is 10-20% larger. 

From the heat generated upon immersion Material in the form of a powder with an known overall surface is immersed in a liquid. The free surface enthalpy of the solid is set free as heat and can be measured with precise calorimeters. 

London dispersive components of the surface free energy and surface enthalpy... 

In Eq. (83), all terms are either known or measurable, except the quantity of interest . Moreover, it should be noted that Eq. (83) is very interesting since it takes into account a small adsorbate, i.e., —CH2— group, whose surface area and surface free energy are slightly affected by temperature. This means that the variations in area and surface entropy of an adsorbed —CH2— group are negligible with temperature. Therefore, it is possible to determine the surface enthalpy derived from the Gibbs-Helmholtz equation... 

As mentioned above, the method by using Eq. (83) can also be used to evaluate surface enthalpy, h. The values for the carbonaceous materials studied are also listed in Table 12, with 95% confidence levels. 

According to second and third observations, it is difficult to appreciate the maximum value of the surface free energy and surface enthalpy of a solid, especially in the case of microporous materials which are widely efficient adsorption properties of the surface (sample V). Therefore, for this material, more works may be needed on the adsorption isotherm, spreading pressure, isosteric heat of adsorption, and even heterogeneities of solid surfaces. They are concerned with the finite concentration technique with increasing amount adsorbed, which will be dealt to some extent in the next section. 

In the gas-solid interaction studies at infinite dilution, it is found that the surface free energy and surface enthalpy (or adsorption enthalpy including acid-base character) of a solute are strongly influenced by the most active sites on the solid surface. The surface free energy and surface enthalpy have been applied as a typical value of the surface, which can be directly related to the adhesion level [70]. 

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... 

To obtain ACp they subtracted their measured values from heat capacities of the bulk. The surface enthalpy at 298 K / 298 was taken from solubility experiments. For MgO and using /i 298 = I040 mN/m they obtained a surface tension of 957 mN/m and a surface entropy of 0.28 mNJm-lK l. 

A nanoparticle exposed to vacuum or a gas is less stable than a bulk coarse grained material. A surface free energy can be defined in terms of surface enthalpy and entropy contributions. 

These may be classified into three groups equilibrium measurements, calorimetric measurements, and computational methods. The first address surface free energy, the second surface enthalpy, and the third (usually) surface energy. 

Diakonov (1998b) argues that the surface enthalpy derived from the slope of the line relating heat of solution to surface area is apparenf rather than true. This is because the number of moles of substance does not increase linearly with surface area. The true thermodynamic surface enthalpy (or other thermodynamic function) is then argued to be 1.5 times the apparent quantity. It is not clear to me whether this argument, as presented initially by Eniistiin and Turkevitch (1960) is valid, and this point needs further clarification. 

A quantitative analysis of the heat of adsorption data enables the separation of hydration enthalpies and surface enthalpies for the two alumina polymorphs (McHale et al. 1997b). The resulting variation of enthalpy of the anhydrous material with surface area is shown in Figure 3. The enthalpy (and free energy) crossover postulated above is clearly demonstrated. 

AI2O3 or coarse a-Al203 + H2O) as a function of surface area for boehmite (circles), yAl203 (triangles), and corundum (squares). Surface enthalpy is equal to the slope of each line, shown for easier comparison in the inset. Data for anhydrous oxides from McHale et al. (1997a). (b) Surface enthalpy as a function of particle size for corundum and boehmite, assuming spherical shape of particles. [Used by permission of the editor of Clays and Clay Minerals, from Majzlan et al. (2000), Fig. 1, p. 702.]... 

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