Ruchs Model

In contrast to the tetrahedron, two of the four mirror planes of the square pyramid contain only one of five vertices and therefore fewer than n — 2 = 3 ligand sites. This skeleton therefore belongs to category b. If the transposition of the two ligands at sites a and b in Fig. 5 is also visualized as a continuous change in the diameter of the corresponding spheres, there is no point at which the model becomes achiral. The same is true of 

FIGURE 4 Conversion of an asymmetric tetrahedron (left) into its mirror image (right) along an achiral pathway. Four spheres with different but variable diameters are centered at the vertices of a regular tetrahedron. The spheres labeled a and b shrink and expand, respectively, until their diameters are switched. Along this path a point is reached at which the diameters are the same this is the achiral intermediate (center) with symmetiy. 

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Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

Ruch, E., The Stereochemical Analogy Model-A Mathematical Theory of Dynamic Stereochemistry, 4, 99. 

When equivalent components of a molecule can be altered in turn to produce stereoisomers, that component which may be associated with an atom or symmetry planes or axes is termed stereogenic.117-119 A chemical process that is stereogenic can produce several stereoisomers, in which case it is said to be stereoselective if the products are not present in equimolar amounts, and stereospecific if only one stereoisomer is produced. A detailed mathematical model for the prediction of the extent of stereoselectivity in organic syntheses has been developed by Ruch and Ugi.120... 

The importance of adsorbed polymer conformation at interfaces was first recognized by Jenkel and Rumbach in 1951. A model of adsorbed polymer conformation was proposed based on the observation that amount of polymer adsorbed per unit area of the surface corresponds to a layer more than ten molecules thick. In that model, not all the segments of a polymer are in contact with the surface. As schematically shown in Figure 7.27, those segments that are in direct contact with the surface are termed trains, those between and extending into solution are termed loops, the free ends of the polymer extending into solution are termed tails. Sato and Ruch classified the possible conformations for most situations into the six types shown in Figure 7.28. 

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