Thermodynamic work function

G is, as a thermodynamic work function, a measure of the driving force (the work-producing potential) of a redox process. For a naturally occurring process,... 

In conclusion let us recall that the position of the electrochemical potential of electrons in a semiconductor, i.e., F relative to that of vacuum, is determined by the thermodynamic work function for the semiconductor wT, and that the position of F relative to the edges of the bands Ec and v in the semiconductor bulk is given by... 

First, the level F, whose position determines the thermodynamic work function wx, is located in the case of semiconductors in the forbidden band. The energy characteristics of a semiconductor-electrolyte interface under photoemission are presented in Fig. 31, which shows, in particular, that the threshold frequency is given by the relation tiw0 = Eg + where % is the difference between the potential energy level of a delocalized electron outside... 

An alternate approach to the above is to use the thermodynamic work function (Refs. 2, 3). 

The thermodynamic work function is the Helmholtz free energy, A, where... 

Although air shock is occasionally scaled against the linear dimensions of the explosive charge (Ref 20), it is more often scaled to an equivalent weight of TNT. The TNT equivalency is based on energy of explosion obtained in various ways. The preferred method being calculation of either the hydrodynamic or the thermodynamic work function. (Recall section 26.4.) TNT weight equivalence... 

Let us recall in this connection that the thermodynamic work function is equal to w = x P Ec. Here x is the electron affinity of the semiconductor, and the position of F relative to the conduction-band bottom, Ec, in the semiconductor bulk is given by the following relations ... 

The electron chemical potential of flic electrode is the negative of the thermodynamic work function, [Pg.306]

Table 5. Some thermodynamic work. functions for Cu /Cu system. From Z.Yang, an unpublished...

It is evident from this brief description that the determinative processes of LED function are, sequentially, hole and electron injection and transport, formation of excitons, and the latter s radiative decay. Clearly, hole and electron injection must be balanced for highest efficiency, so that any currents produced are utilized for exciton production, rather tlian simply being carried between electrodes by the carrier which is in excess (whether hole or electron). The thermodynamic work function of the contact electrode thus must match that of the CP (in terms of its overall redox potential, or more specifically its ionization potential (IP) for hole... 

The energy release rate (G) represents adherence and is attributed to a multiplicative combination of interfacial and bulk effects. The interface contributions to the overall adherence are captured by the adhesion energy (Go), which is assumed to be rate-independent and equal to the thermodynamic work of adhesion (IVa)-Additional dissipation occurring within the elastomer is contained in the bulk viscoelastic loss function 0, which is dependent on the crack growth velocity (v) and on temperature (T). The function 0 is therefore substrate surface independent, but test geometry dependent. 

Thermodynamically, an average work function can be defined for a polycrystalline surface3,6 ... 

As previously noted the constancy of catalyst potential UWr during the formation of the Pt-(12xl2)-Na adlayer, followed by a rapid decrease in catalyst potential and work function when more Na is forced to adsorb on the surface, (Fig. 5.54) is thermodynamically consistent with the formation of an ordered layer whose chemical potential is independent of coverage. 

It should be noted that dissociation of surface complexes of oxygen in polar solvents on semireduced ZnO films is presumably justified from the thermodynamic point of view as oxygen adsorption heat on ZnO and electron work function are [58] 1 and approximately 5 eV respectively while the energies of affinity of oxygen molecules to electron, to solvation of superoxide ion and surface unit charge zinc dope ions are 0.87, 3.5, and higher than 3 eV, respectively [43]. 

Further progress in the study of the Cu-Ni system awaited the preparation and careful characterization of alloy films of known bulk and surface composition. The essential step was taken by Sachtler and his co-workers 28, 88, 114) who prepared Cu-Ni alloy films by successive evaporation of the component metals in UHV. After evaporation the films were homogenized by heating in vacuum at 200°C. The bulk composition of the alloys was derived from X-ray diffraction, and the photoelectric work function of the films was also measured. A thermodynamic analysis, summarized by Fig. 13, indicated that alloy films sintered at 200°C should consist, at equilibrium, of two phases, viz., phase I containing 80% Cu and phase II containing 2% Cu. Evidence was presented that alloys within the... 

To understand the role of the noble metal in modifying the photocatalysts we have to consider that the interaction between two different materials with different work functions can occur because of their different chemical potentials (see [200] and references therein). The electrons can transfer from a material with a high Fermi level to another with a lower Fermi level when they contact each other. The Fermi level of an n-type semiconductor is higher than that of the metal. Hence, the electrons can transfer from the semiconductor to the metal until thermodynamic equilibrium is established between the two when they contact each other, that is, the Fermi level of the semiconductor and metal at the interface is the same, which results in the formation of an electron-depletion region and surface upward-bent band in the semiconductor. On the contrary, the Fermi level of a p-type semiconductor is lower than that of the metal. Thus, the electrons can transfer from the metal to the semiconductor until thermodynamic equilibrium is established between the two when they contact each other, which results in the formation of a hole depletion region and surface downward-bent band in the semiconductor. Figure 12.6 shows the formation of semiconductor surface band bending when a semiconductor contacts a metal. 

Next we describe some work that is directed at the question, does the agreement with experiment of model potentials like the one in Eq. (9) imply that the models are right It seems unlikely that the answer is affirmative because of the great variety of equations which, over the years, have been reported to give precision fits to the thermodynamic excess function data apparently there is relatively little information in these data. More directly, we find that we can change some important aspects of the models within the scope of Eq. (9) and still fit the data for thermodynamic excess functions. Typical examples are given below. 

The first law of thermodynamics, which can be stated in various ways, enuciates the principle of the conservation of energy. In the present context, its most important application is in the calculation of the heat evolved or absorbed when a given chemical reaction takes place. Certain thermodynamic properties known as state functions are used to define equilibrium states and these properties depend only on the present state of the system and not on its history, that is the route by which it reached that state. The definition of a sufficient number of thermodynamic state functions serves to fix the state of a system for example, the state of a given mass of a pure gas is defined if the pressure and temperature are fixed. When a system undergoes some change from state 1 to state 2 in which a quantity of heat, Q, is absorbed and an amount of work, W, is done on the system, the first law may be written... 

The difference in electrostatic potential which exists between the inside and the outside of the metal is termed the surface potential. The related properties—the work function and the contact potential difference—respectively measure free energy changes when electrons are moved from one conductor to a vacuum and from one conductor to another. The thermodynamic basis of these properties has been reviewed by Herring and Nichols (6), and Chalmers (7) has considered the theory of contact potentials. 

The benefit of this course is that it provides all students taking the physical chemistry lecture course with the same mathematical foundation. In the physical chemistry lecture we can discuss the relationship between different thermodynamic functions without stopping to review partial derivatives. We can talk about the difference between work, heat, and energy without stopping to teach the difference between path functions and work functions. We can write... 

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