General Thermodynamic Foundations

Electric field-induced chemical transformations in macromolecules and macromolecular organizations such as membranes cannot be analyzed satisfactorily in all cases because adequate theoretical approaches are lacking. The observed dependence of bio polymer reactions on the electric field intensity seems, however, to be very similar to that of small molecules. Therefore, it appears pertinent to introduce the analysis of field-induced macromolecular changes with relationships which are derived to describe field effects in reactions of small molecules. 

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J.W. Cahn s early contributions to elastic coherency theory were motivated by his work on spinodal decomposition. His subsequent work with F. Larche created a rigorous thermodynamic foundation for coherency theory and stressed solids in general. A single volume, The Selected Works of John W. Cohn [15], contains papers that provide background and advanced reading for many topics in this textbook. This derivation follows from one in a publication included in that collection [16]. 

Thermodynamic Foundation." "—A. single-step chemical reaction process can in a general way be formulated as... 

Pourbaix (or ErpH) diagrams are frequently used in the context of metal CMP to categorize the reactant/product surface species expected for a given slurry composition. The thermodynamic foundation of this approach follows from the Nemst equation for general redox reactions in the aqueous environment, where the components of water (H" /OH ) join the redox species to support the faradaic steps. Such a reaction has the form x(Ox) + y(H ) + ne = w(Rd) + w(H20), where Ox and Rd denote the oxidized and reduced species of the active redox couple (such as the oxidized and pure forms of a metal), respectively x, y, n, u, and w denote the mole numbers of the participating species. The Nemst equation for this reaction can be written as... 

It is an inference naturally suggested by the general increase of entropy which accompanies the changes occurring in any isolated material system that when the entropy of the system has reached a maximum, the system will be in a state of equilibrium. Although this principle has by no means escaped the attention of physicists, its importance does not seem to have been duly appreciated. Little has been done to develop the principle as a foundation for the general theory of thermodynamic equilibrium (my italics). ... 

Von Neumann18 did more than coin these words. He showed how the statistical matrix can be generalized to include the description of mixtures, and he succeeded, mainly by this device, in laying the foundation for the quantum mechanical counterpart of thermodynamics. 

The foundations of stable isotope geochemistry were laid in 1947 by Urey s classic paper on the thermodynamic properties of isotopic substances and by Nier s development of the ratio mass spectrometer. Before discussing details of the naturally occurring variations in stable isotope ratios, it is useful to describe some generalities that are pertinent to the field of non-radiogenic isotope geochemistry as a whole. 

The foundation of irreversible thermodynamics is the concept of entropy production. The consequences of entropy production in a dynamic system lead to a natural and general coupling of the driving forces and corresponding fluxes that are present in a nonequilibrium system. 

Chemists are generally more interested in the system (the reaction mixture) than the surroundings, and it s therefore convenient to restate the second law in terms of the thermodynamic properties of the system, without regard to the surroundings. For this purpose, we use the thermodynamic property called free energy, denoted by G in honor of J. Willard Gibbs (1839-1903), the American mathematical physicist who laid the foundations of chemical thermodynamics. As discussed in Section 8.14, the free energy G of a system is defined as... 

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