Surface Free Energy Measurements

The difference in etch rate between (111) and (100) surfaces was related to the bond densities on the two surfaces in the early surface kinetics models. According to Hesketh et the etch rate difference between (100) and (111) planes is due to the difference in the surface free energy of the crystal planes which is proportional to the number of bonds on the surface. The (111) plane, which has the lowest surface free energy measured in vacuum, has the lowest bond density and thus has the lowest etch rate. They postulated that the etch rate of crystal planes is a function of the total number of bonds at the surface, that is, the sum of the in-plane, lateral bonds between atoms in the plane of the surface, and surface bonds, dangling bonds. It was recognized however, that this effect alone will not cause etch rate differences of more than a factor of two. ° ... 

Schaefer et al. have developed a somewhat different method which involves measuring the shape and depth of grooves, which are formed at equilibrium when a liquid meets a grain boundary in the solid, with a small temperature gradient imposed. The curvature at each point is related to the local temperature and to the surface free energy. Measurements were... 

The rate law in Eq. (V.35) for uptake of oxygen by silver has been interpreted as follows From surface free-energy measurements at 900°C 4 6), it is known that solid silver at 900°C and po2 = 10" to 1 atm is covered nearly completely by oxygen. Suppose that at 400°C there are mostly O2 molecules lying parallel to the surface, 02( )(ad), each occupying two adjacent sites denoted by the symbol ,... 

The results of surface free energy measurements for four types of carbon fibers are summarized in Table. 1 [24]. Althou the 5 for ethylene glycol and formamide are almost equal, their interaction with the surface produces veiy different 15c values which can be explained by a difference in their electron donating capabilities.The highest average value of is obtained for 1M7, therefore its surface... 

Contact angle and surface free energy measurements offer the first insight into the potential use of the PDLC as biomaterial and also provide information about the physical interactions inside the material that determine the droplet anchoring. Usually, for a material to be considered as potentially biocompatible, the water contact angle value must be in the range of 60-90 degrees, which is considered within the domain of moderate wettability (Ikada 1994 Vasile and Pascu 2007). These values ensure an appropriate balance of hydrophobic/hydrophilic forces that will favor cellular adhesion and prevent the rejection of the implanted material. 

Table 3. Surface free energy measured at high temperature with an estimate of the temperature dependenee...

A solid, by definition, is a portion of matter that is rigid and resists stress. Although the surface of a solid must, in principle, be characterized by surface free energy, it is evident that the usual methods of capillarity are not very useful since they depend on measurements of equilibrium surface properties given by Laplace s equation (Eq. II-7). Since a solid deforms in an elastic manner, its shape will be determined more by its past history than by surface tension forces. 

It turns out to be considerably easier to obtain fairly precise measurements of a change in the surface free energy of a solid than it is to get an absolute experimental value. The procedures and methods may now be clear-cut, and the calculation has a thermodynamic basis, but there remain some questions about the physical meaning of the change. This point is discussed further in the following material and in Section X-6. 

The basic phenomenon involved is that particles of ore are carried upward and held in the froth by virtue of their being attached to an air bubble, as illustrated in the inset to Fig. XIII-4. Consider, for example, the gravity-free situation indicated in Fig. XIII-5 for the case of a spherical particle. The particle may be entirely in phase A or entirely in phase B. Alternatively, it may be located in the interface, in which case both 7sa nnd 7sb contribute to the total surface free energy of the system. Also, however, some liquid-liquid interface has been eliminated. It may be shown (see Problem XIII-12) that if there is a finite contact angle, 0sab> the stable position of the particle is at the interface, as shown in Fig. XIII-5Z>. Actual measured detachment forces are in the range of 5 to 20 dyn [60]. 

During emulsification new surfaces are created between the two phases. Such a process requires energy the surface free energy, numerically identical to the easily measured surface tension, reflects this amount. 

However, on rigid substrates, the growth of dry zones is accompanied by a rim of excess liquid with width X (Fig. 10). As the dewetting proceeds, X increases. For short times and < K, the growth of dry patches is controlled only by surface tension forces and the dewetting speed is constant. A constant dewetting speed of 8 mm-s has been measured when a liquid film of tricresyl phosphate (TCP) dewets on Teflon PFA, a hard fluoropoly-mer of low surface free energy (p. = 250 MPa, 7 = 20 mJ-m ). 

While in previous ab initio smdies the reconstructed surface was mostly simulated as Au(lll), Feng et al. [2005] have recently performed periodic density functional theory (DFT) calculations on a realistic system in which they used a (5 x 1) unit cell and added an additional atom to the first surface layer. In their calculations, the electrode potential was included by charging the slab and placing a reference electrode (with the counter charge) in the middle of the vacuum region. From the surface free energy curves, which were evaluated on the basis of experimentally measured capacities, they concluded that there is no necessity for specific ion adsorption [Bohnen and Kolb, 1998] and that the positive surface charge alone would be sufficient to lift the reconstmction. 

Electrocapillarity is the measurement of the variation of the surface tension of mercury in (usually) aqueous electrolyte with applied potential. The surface tension, y, of an interface relates to the surface free energy, C, by the expression ... 

In terms of understanding the mercury/electrolyte interface, it is clear from the above discussion that the measurement of the surface free energy (in terms of the surface tension), is central. If the clectrocapillarity technique could be applied to solid electrodes, then it is capable of supplying information extremely difficult to obtain by any other technique. Sato has indeed developed a technique to measure the surface tension of a metal electrode which he terms piezoelectric surface stress measurement and is based upon the previous work of Gokhshtein (1970). 

Perhaps the most striking result of the measurements of the ratio 7, /7S is that so many values of it are confined to the range 0.25—0.40. As a matter of fact, an earlier review50 refers to the general observation that the grain-boundary free energy is about one-third of the solid-surface free energy. Also in a latter study on UC, the ratio 71 /ys was found to vary between 0.36 and 0.41116. Because so much... 

The surface polarity of telomerized starches was determined by the contact angle technique. The surface free energy of the solid was measured from the contact angles of a drop of various probe liquids with the surface of a starch tablet (Table 16). 

The phenomenon of the orientation dependent surface free energy of metals is theoretically and experimentally well established [1-4]. An example from the experimental work of Heyraud and Metois for Pb is shown in fig. 1 [5]. Here the relative anisotropy of y(0) is derived from the ECS of Pb particles on graphite measured by scanning electron... 

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