Immobile component, potential

Chemists and physicists must always formulate correctly the constraints which crystal structure and symmetry impose on their thermodynamic derivations. Gibbs encountered this problem when he constructed the component chemical potentials of non-hydrostatically stressed crystals. He distinguished between mobile and immobile components of a solid. The conceptual difficulties became critical when, following the classical paper of Wagner and Schottky on ordered mixed phases as discussed in chapter 1, chemical potentials of statistically relevant SE s of the crystal lattice were introduced. As with the definition of chemical potentials of ions in electrolytes, it turned out that not all the mathematical operations (9G/9n.) could be performed for SE s of kind i without violating the structural conditions of the crystal lattice. The origin of this difficulty lies in the fact that lattice sites are not the analogue of chemical species (components). 

Since the state of a crystal in equilibrium is uniquely defined, the kind and number of its SE s are fully determined. It is therefore the aim of crystal thermodynamics, and particularly of point defect thermodynamics, to calculate the kind and number of all SE s as a function of the chosen independent thermodynamic variables. Several questions arise. Since SE s are not equivalent to the chemical components of a crystalline system, is it expedient to introduce virtual chemical potentials, and how are they related to the component potentials If immobile SE s exist (e.g., the oxygen ions in dense packed oxides), can their virtual chemical potentials be defined only on the basis of local equilibration of the other mobile SE s Since mobile SE s can move in a crystal, what are the internal forces that act upon them to make them drift if thermodynamic potential differences are applied externally Can one use the gradients of the virtual chemical potentials of the SE s for this purpose ... 

Let us consider a homogeneously, but not hydrostatically, stressed solid which is deformed in the elastic regime and whose structure elements are altogether immobile. If we now isothermally and reversibly add lattice molecules to its different surfaces (with no shear stresses) from the same reservoir, the energy changes are different. This means that the chemical potential of the solid is not single valued, or, in other words, a non-hydrostatically stressed solid with only immobile components does not have a unique measurable chemical potential [J. W. Gibbs (1878)]. 

From a more fundamental point of view the difference between y and T in an elastic solid arises from the inequality for immobile components of chemical potentials. In principle, for real solids such equalization is possible, but it proceeds very slowly so that always y T in practice. 

Figure 2.69 compares the theoretical responses of an adsorption coupled reaction with the simple reaction of a dissolved redox couple, for a reversible case. Obviously, the adsorption enhances considerably the response, making the oxidation process more difficult. The forward component of reaction (2.144) is a sharp peak, with a lower peak width compared to reaction (2.157). The relative position of the peak potentials of the forward and backward components of the adsorption comph-cated reaction is inverse compared to simple reaction of a dissolved redox couple. Finally, the peak current of the stripping (forward) component of adsorption coupled reaction is lower than the backward one, the ratio being 0.816. The corresponding value for reaction of a dissolved couple is 1.84. This anomaly is a consequence of the current sampling procedure and immobilization of the reactant, as explained in the Sect. 2.5.1. 

The competition between molecular-based and molecule-substrate interactions is one of the features that make supramolecular assemblies based on the combination of molecular components and solid substrates so exciting and also potentially useful from the applications point of view. The control issue is whether can one achieve long-lived charge separation between molecular components when immobilized on a surface, and from the fundamental perspective, can the interactions between the surface and molecular components be manipulated In this section, the immobilization of molecular components consisting of at least two electroactive and/or photoactive units will be discussed. The intramolecular interactions within these dyads in solution, as well as their behavior as interfacial supramolecular triads when immobilized on nanocrystalline TiC>2, will be compared. 

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