Magic triangle

These three interrelated properties are sometimes assigned to a so-called magic triangle (Figure 32.2). In recent years, the world s leading carbon black manufacmrers have come with innovative grades to meet conflicting demands. ... 

Use of highly dispersible silica together with silanes and high vinyl S-SBR has met all critical magic triangle requirements like good dry and wet traction, reduction in tread wear, and low RR. 

FIGURE 16.15 The principle of the magic triangle [261] that depicts the desirable symmetricity of the SEC system. The symmetric example (------) polystyrene-co-divinylbenzene (PS/DVB) column packing, poly-... 

The magic triangle behind the second law. The relation between results from classical, engineering, and irreversible thermodynamics (see Chapter 4). 

This equation expresses the fact that in a process with the various flow rates /, work is continuously dissipated to overcome the barriers, the resistance, or the friction that all the processing such as heat and mass transfer and chemical conversion introduce. In Chapter 5, we refer to this as the result of the "magic triangle." There is no clearer way to illustrate the origin of the process s energy bill, nor a better way to calculate it. This relation also defines the challenge that in order to keep the energy bill as low as possible one should find, as Bejan calls it, "the path of least resistance" [6]. 

The magic triangle relating classical, engineering, and irreversible thermodynamics. 

Figure 1. Magic triangle speed vs. resolution vs. capacity in preparative-scale chromatography (Pescar, 1971).

Supply security is of utmost importance for the European Union (EU) and its member states, in economic, technical, and political terms. Secure energy supply is a cornerstone of the magic triangle of energy policy, the two others being competition and sustainability. And in times of rising geopolitical conflicts, supply security has also increased in importance in the external relations of the EU. 

The Latin word qualitas expresses the description of the character, consistence, composition or condition of an entity or product. In production and industrial engineering this concept turned into an applicable quantity that should be recognizable, measureable and controllable. The progress in industrialization and the influence of scientific and theoretical models in production technology mainly stressed the putative magic triangle of time, costs and quality, in which... 

FIGURE 11 MAGIC TRIANGLE —the role ofpolaiity of eluent, column packing, and analyzed polymer in SEC. For detailed explanation, see the text. 

A proper SEC experiment has to be balanced with respect to polarities. In order to obtain a true and pure SEC separation, the polarity of stationary phase (column material), the polarity of eluent, and the polarity of sample have to be matched. This is visualized by the magic triangle (Fig. 9.6). Dominance of size separation is only maintained in the center of the triangle (bright area), where the overall systan is balanced. Otherwise, specific interactions will occur, which will overlay with the normal SEC elution behavior. 

Figure 9.8 Magic triangle choice of synthetic path depends on three main...

In summary, automated methodologies may help to speed up the process but have more or less no effect on the other parameters of the magic triangle . 

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