Surface forces worked example

The common example of real potential is the electronic work ftmction of the condensed phase, which is a negative value of af. This term, which is usually used for electrons in metals and semiconductors, is defined as the work of electron transfer from the condensed phase x to a point in a vacuum in close proximity to the surface of the phase, hut heyond the action range of purely surface forces, including image interactions. This point just outside of the phase is about 1 pm in a vacuum. In other dielectric media, it is nearer to the phase by e times, where e is the dielectric constant. 

One may consider another example to describe surface energy. Let us imagine that a liquid fills a container of the shape of a funnel. In the funnel, if one moves the liquid upwards, then there will be an increase in surface area. This requires that some molecules from the bulk phase have to move into the surface area and create extra surface The work required to do so will be (force x area) y As. This work is reversible at constant temperature and pressure, and thus gives the increase in free energy of the system ... 

A two-dimensional analog of PV work can be recognized in fluid films that exhibit surface tension (tendency of the film surface to contract against an opposing spreading force). The surface tension work wsurf (of, for example, a soap film) can be measured by a rectangular wire-frame device with moveable edge, as shown in Fig. 3.5. 

The capillary force works in the opposite direction for nrai-wetting liquids The level of the liquid is lowered and it displays a convex surface. In this case, one speaks of a capillary depression (Example mercury in a glass tube as in thermometers and barometers). 

In addition to the tendency for liquids to form spherical droplets in order to minimize their surface area, it can be easily demonstrated that liquid surfaces have other properties that can be traced back to the concept of the work necessary to form new surface area. For example, if one takes a clean needle and carefully places it on the surface of pure distilled water, the needle will float, even though it has a density many times that of the water. In order for the needle to sink, it must penetrate the surface of the water. Penetration of the liquid surface involves increasing the water interfacial area with respect to both the vapor phase and the needle. The force causing the needle to sink, of course, is its mass times the acceleration due to gravity. Opposing it is the surface tension of the water. 

Results using this technique are better for force helds made to describe geometries away from equilibrium. For example, it is better to use Morse potentials than harmonic potentials to describe bond stretching. Some researchers have created force helds for a specihc reaction. These are made by htting to the potential energy surface obtained from ah initio calculations. This is useful for examining dynamics on the surface, but it is much more work than simply using ah initio methods to hnd a transition structure. 

Figure 4.28 shows an example where STM recognizes the individual metal atoms in an alloy, thus revealing highly important structural information on the atomic level. The technique does not require a vacuum, and can in principle be applied under in situ conditions (even in liquids). Unfortunately, STM only works on well-defined, planar, and conducting surfaces such as metals and semiconductors, and not on oxide-supported catalysts. For the latter surfaces, atomic force microscopy offers better perspectives. 

However, the question must always be asked as to whether these processes could have taken place on the primordial Earth in its archaic state. The answer requires considerable fundamental consideration. Strictly speaking, most of the experiments carried out on prebiotic chemistry cannot be carried out under prebiotic conditions , since we do not know exactly what these were. In spite of the large amount of work done, physical parameters such as temperature, composition and pressure of the primeval atmosphere, extent and results of asteroid impacts, the nature of the Earth s surface, the state of the primeval ocean etc. have not so far been established or even extrapolated. It is not even sure that this will be possible in the future. In spite of these difficulties, attempts are being made to define and study the synthetic possibilities, on the basis of the assumed scenario on the primeval Earth. Thus, for example, in the case of the SPREAD process, we can assume that the surface at which the reactions occur could not have been an SH-containing thiosepharose, but a mineral structure of similar activity which could have carried out the necessary functions just as well. The separation of the copy of the matrix could have been driven by a periodic temperature change (e.g., diurnal variation). For his models, H. Kuhn has assumed that similar periodic processes are the driving force for some prebiotic reactions (see Sect. 8.3). 

The deposition of metals has also been studied by a large number of electrochemical techniques. For the deposition of Cu2+, for example, it is reasonable to ask whether both electrons are transported essentially simultaneously or whether an intermediate such as Cu+ is formed in solution. Such questions, like those of the ECE problem discussed above, have usually been investigated by forced convection techniques, since the rate of flow of reactant to and away from the electrode surface gives us an important additional kinetic handle. In addition, by using a second separate electrode placed downstream from the main working electrode, reasonably long-lived intermediates can be transported by the convection flow of the electrolyte to this second electrode and detected electrochemically. 

---