Special relationships between kinetic constants

The importance of the cocatalyst in metal-catalyzed polymerization processes can be appreciated as follows. First, to form active catalysts, catalyst precursors must be transformed into active catalysts by an effective and appropriate activating species. Second, a successful activation process requires many special cocatalyst features for constant catalyst precursor and kinetic/thermodynamic considerations of the reaction. Finally, the cocatalyst, which becomes an anion after the activation process, is the vital part of a catalytically active cation—anion ion pair and may significantly influence polymerization characteristics and polymer properties. Scheme 1 depicts the aforementioned relationships between catalyst and cocatalyst in metal-catalyzed olefin polymerization systems. 

The various gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would describe the behaviour of all gases. Gases and mixtures of gases behave in a similar way over a wide variety of physical conditions because (to a good approximation) they all consist of molecules or atoms which are widely spaced a gas is mainly empty space. The ideal gas equation can be derived from kinetic molecular theory. The gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables (pressure, volume and absolute temperature) held constant. 

This formulation is of advantage only when the constant ho (cq) is given a physical meaning (118, 119) or a supposed general linear relation between ho and /3—the so called hypercompensation effect (6)—is looked for (26, 102) or when it can be shown that ho is equal to zero (30,45, 172). Usually, or at least in kinetics, ho and Co are simply seen as intercepts without any special meaning and without a general relationship to Of course, eq. (11) can be written with interchanged variables, and in this case the intercept So can be interpreted as the so called model entropy (6). 

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