Mutually paired systems

Due to the pairing theorem, the absorption spectra and transition polarization directions of two mutually paired alternant systems should be identical, as shown in Figure 2.25 for the radical anion and the radical cation of tetra-cene. Under the same conditions (i.e., = 0 if and v are nonneighbors),... 

Smectic A phases often contain pairs of focal conics (see Fig. 7 a and b) that are well contrasted in the liquid, even in the absence of polarizers. A more common situation is the presence of arcs of conics associated in pairs (Fig. 29 d). The parallel Dupin cyclides and the associated revolution cones form three mutually orthogonal systems of surfaces [7], and therefore the lines of curvature of any surface in one system are its intersections with the surfaces of the other two systems. The toroidal shape of Dupin s... 

For systems of type II, if the mutual binary solubility (LLE) data are known for the two partially miscible pairs, and if reasonable vapor-liquid equilibrium (VLE) data are known for the miscible pair, it is relatively simple to predict the ternary equilibria. For systems of type I, which has a plait point, reliable calculations are much more difficult. However, sometimes useful quantitative predictions can be obtained for type I systems with binary data alone provided that... 

Mesomerism involving polarized and nonpolarized contributing enamine forms influences the enamine s spectral properties and chemical reactivity. For mesomerism to be present, a planar arrangement is required for the three atoms of enamine grouping and the five atoms immediately bound to this system. If this condition is not fulfilled, full interaction of the tt electrons of the double bond with the free electron pair on the nitrogen atom is impossible. Enamines in which mesomerism is inhibited do not show the properties characteristic of enamines, and only the mutual electrostatic interaction of the double bond and lone electron pair of the nitrogen atom can be observed. Such steric hindrance of mesomerism occurs mainly in polycyclic systems. 

In order to check the consistency and mutual relations of ECIs calculated by various methods, as well as to compare them with experimental data, we have performed calculations for several alloy systems, as diverse as Cu-Nl, Al-Li, Al-Ni, Ni-Pt and Pt-Rh. Here we present the results for Al-Ni, Pt-Rh and Ni-Pt alloys in some detail, because the pair interactions between the first neighbors are dominant in these alloys which makes the interpretation relatively simple. On the other hand, the pair interactions between more distant neighbors and also triplet interactions are important for Al-Li and Cu-Ni. The equilibrium atomic radii, bulk moduli and electronegativities of A1 and Ni are rather different, while Pt and Rh are quite similar in this respect. The Ni and Pt atoms differ mainly by their size. 

Mutual solubilities occur in many cases between pairs of alkali halides. The solubilities are often limited, but some are complete. There are 190 possible pairs for the set of 20 alkali halides. Only one particularly simple pair will be considered here, the KCl-KBr system. These two compounds in this system are completely soluble in each other. A few data points for the system have been determined by Armington, Posen, and Lipson (1973). See Figure 9.6. 

There is a very wide choice of pairs of liquids to act as stationary and mobile phases. It is not necessary for them to be totally immiscible, but a low mutual solubility is desirable. A hydrophilic liquid may be used as the stationary phase with a hydrophobic mobile phase or vice versa. The latter situation is sometimes referred to as a reversed phase system as it was developed later. Water, aqueous buffers and alcohols are suitable mobile phases for the separation of very polar mixtures, whilst hydrocarbons in combination with ethers, esters and chlorinated solvents would be chosen for less polar materials. 

The mutual termination of growing chains which prevails in radical polymerizations must be ruled out for all ionic systems in which the opposite ions form separate kinetic units because of the electrostatic repulsion between like ions. However, in solvents of low DC in which the growing end of the polymer chain consists of an ion pair, a mutual termination by interaction of two such ion pairs is at least conceivable. 

Chapter 18 - The determination region of solubility of methanol with gasoline of high aromatic content was investigated experimentally at temperature of 288.2 K. A type 1 liquid-liquid phase diagram was obtained for this ternary system. These results were correlated simultaneously by the UNIQUAC model. By application of this model and the experimental data the values of the interaction parameters between each pair of components in the system were determined. This revealed that the root mean square deviation (RMSD) between the observed and calculated mole percents was 3.57% for methylcyclohexane + methanol + ethylbenzene. The mutual solubility of methylcyclohexane and ethylbenzene was also demostrated by the addition of methanol at 288.2 K. 

Almost all the crystalline materials discussed earlier involve only one molecular species. The ramifications for chemical reactions are thereby limited to intramolecular and homomolecular intermolecular reactions. Clearly the scope of solid-state chemistry would be vastly increased if it were possible to incorporate any desired foreign molecule into the crystal of a given substance. Unfortunately, the mutual solubilities of most pairs of molecules in the solid are severely limited (6), and few well-defined solid solutions or mixed crystals have been studied. Such one-phase systems are characterized by a variable composition and by a more or less random occupation of the crystallographic sites by the two components, and are generally based on the crystal structure of one component (or of both, if they are isomorphous). 

For the two-component, two-phase liquid system, the question arises as to how much of each of the pure liquid components dissolves in the other at equilibrium. Indeed, some pairs of liquids are so soluble in each other that they become completely miscible with each other when mixed at any proportions. Such pairs, for example, are water and 1-propanol or benzene and carbon tetrachloride. Other pairs of liquids are practically insoluble in each other, as, for example, water and carbon tetrachloride. Finally, there are pairs of liquids that are completely miscible at certain temperatures, but not at others. For example, water and triethylamine are miscible below 18°C, but not above. Such pairs of liquids are said to have a critical solution temperature, For some pairs of liquids, there is a lower (LOST), as in the water-tiiethylamine pair, but the more common behavior is for pairs of liquids to have an upper (UCST), (Fig. 2.2) and some may even have a closed mutual solubility loop [3]. Such instances are rare in solvent extraction practice, but have been exploited in some systems, where separations have been affected by changes in the temperature. 

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