The Theory of Indicators

Textbooks of analytical chemistry should be consulted for further details concerning the ionization of weak acids and bases and the theory of indicators, buffer solutions, and acid-alkali titrations. 

For the theory of indicators and the pH ranges, see Clark WM. The Determination of Hydrogen Ions. London, Balliere, Tindal Cox, 1928. 

The theory of indicators, pK values (as a measure of acid strength) and the choice of indicators for acid-base titrations is discussed in Chapter 18. 

Sherman, H. On the Theory of Indicator-Dilution Methods Under Varying Blood-Flow Conditions. Bull. Math. Biphysics 22 (1960) 417. 

Another phenomenon is so called two-side filling of one-side closed conical capillaries with liquid [5]. On the one hand the more penetrant is trapped by the defect the wider indication will appear. Contrariwise it is almost impossible to extract a penetrant from the completely filled surface defects by dry developer [6]. In this study we propose the theory of the phenomenon. Besides experimental results of the investigation of two-side filling with various penetrants of conical capillaries are presented. Practical recommendations to optimize liquid penetrant testing process are proposed. 

The indicator method is especially convenient when the pH of a weU-buffered colorless solution must be measured at room temperature with an accuracy no greater than 0.5 pH unit. Under optimum conditions an accuracy of 0.2 pH unit is obtainable. A Hst of representative acid—base indicators is given in Table 2 with the corresponding transformation ranges. A more complete listing, including the theory of the indicator color change and of the salt effect, is also available (1). 

In this book, the theory of gases and liquids and its application to surface and interfacial problems is considered. In this chapter, theories based on integral equations are reviewed. Since these theories were developed originally for bulk fluids, we will consider this case first and indicate the extension of the theories to interfaces. 

The theory of atoms in molecules defines chemical properties such as bonds between atoms and atomic charges on the basis of the topology of the electron density p, characterized in terms of p itself, its gradient Vp, and the Laplacian of the electron density V p. The theory defines an atom as the region of space enclosed by a zero-/lMx surface the surface such that Vp n=0, indicating that there is no component of the gradient of the electron density perpendicular to the surface (n is a normal vector). The nucleus within the atom is a local maximum of the electron density. 

Hydrogen was recognized as the essential element in acids by H. Davy after his work on the hydrohalic acids, and theories of acids and bases have played an important role ever since. The electrolytic dissociation theory of S. A. Arrhenius and W. Ostwald in the 1880s, the introduction of the pH scale for hydrogen-ion concentrations by S. P. L. Sprensen in 1909, the theory of acid-base titrations and indicators, and J. N. Brdnsted s fruitful concept of acids and conjugate bases as proton donors and acceptors (1923) are other land marks (see p. 48). The di.scovery of ortho- and para-hydrogen in 1924, closely followed by the discovery of heavy hydrogen (deuterium) and... 

The proposed model for the so-called sodium-potassium pump should be regarded as a first tentative attempt to stimulate the well-informed specialists in that field to investigate the details, i.e., the exact form of the sodium and potassium current-voltage curves at the inner and outer membrane surfaces to demonstrate the excitability (e.g. N, S or Z shaped) connected with changes in the conductance and ion fluxes with this model. To date, the latter is explained by the theory of Hodgkin and Huxley U1) which does not take into account the possibility of solid-state conduction and the fact that a fraction of Na+ in nerves is complexed as indicated by NMR-studies 124). As shown by Iljuschenko and Mirkin 106), the stationary-state approach also considers electron transfer reactions at semiconductors like those of ionselective membranes. It is hoped that this article may facilitate the translation of concepts from the domain of electrodes in corrosion research to membrane research. 

The first useful theory of indicator action was suggested by W. Ostwald3 based upon the concept that indicators in general use are very weak organic acids or bases. 

The theory of hydrophobic interaction [70-72] indicates that hydrophobic residues tend to associate with one another so as to minimize the surface area exposed to the aqueous phase and thereby to release a maximum number of structured water molecules. Therefore, the steric fit between the hydrophobic groups may be an important factor for the hydrophobic association. It is reasonable to consider that aromatic hydrophobic groups may undergo tighter hydrophobic self-association because planar aromatic rings would sterically fit with each other to favor the release of structured water. 

In these developments there were two distinct stages the first one, which dealt with the nearly linear oscillations, found its perfect algorithm in the theories of Poincare (both topological and analytical), which constitute the major part of this review here the discoveries were most striking as well as systematic. Numerous phenomena that had remained as riddles for many years, sometimes even for centuries, were systematically explained. We indicate in Part I of this chapter the qualitative aspect of this progress and in Part II, the quantitative one. 

The Hamiltonian (3.4) is a function of the usual spatial coordinates x, y, z or r, 0, (j)). Electrons possess the intrinsic property of spin, however, which is to be thought of as a property in an independent, or orthogonal, space (spin space). Spin is actually a consequence of the theory of relativity but we shall merely graft on the property in an ad hoc fashion. The spin, s, of an electron (don t confuse with s orbitals ) takes the value 1/2 only. The z component of spin, m, takes (25 + 1) values of ms, ranging 5, 5-l,...-s. Thus for the single electron, = +1/2 or -1/2, also labelled a or p, or indicated by t or i. 

---