Split Dual Kinetics

The assumption of the Energetic Kinetic Theory (EKT) is that under nonisothermal conditions the total free energy remains that of the equilibrium at the corresponding temperature (i.e., RT In ( 2/ 7) in this example), and that there is a transfer of populations between the/and b types of bonds to render this constraint feasible. The kinetic duality between the b and/units within a closed but split statistical ensemble is the reason for the nomenclature "Split Dual Kinetics," but since the free energy remains as the driving force to determine the tme kinetic expression, we favor the expression "Energetic Kinetic Theory" to describe our new model. It will become apparent shordy that the latter expression has a more general sense. The set of equations for the new statistics... 

Note the presence of the additional term In (Njj/Nj) in the expression of the free energy. This ad hoc assumption finds its justification in the results it yields. At equilibrium, Njj=Nf = Bq/2 and therefore In (Nj/Nf) is zero the Split Dual Kinetic equation converges to classical kinetics under equilibrium conditions. 

The important point, within the scope of this paper, is that the free energy may acquire a structure, as an alternative or a complement to the Split Dual Kinetic mechanism described by eq. (6). One can easily see that the coupling of eq. (6) and eq. (8) yields more complex but probably more realistic kinetic schemes. This is not all. The same principle which regulates the coupling between eq. (6) and eq. (8), a discussion beyond the scope of this presentation, can be applied to minimize the partition function energy of the b units of the Split Dual Kinetic phase. The b units, whose number is Nj, can be divided into subsystems of units each (with cq, = NyNj, just like the Bq units in eq. 8 could be divided into N, systems. All the bb subsystems are identical and the partition function energy of the b Split Dual Kinetic phase is the energy of each bb subsystem... 

Fig. 6.14 FIA configurations with two detectors for development of kinetic methods, (a) Serial configuration (b) parallel configuration with single injection and splitting of sample (c) parallel configuration with dual injection. R, reagent C, carrier S, sample D, detector W, waste.

Fig. 11. Variation ofR = dNydt versus cooling temperature at a finite cooling rate ( = -10 K/sec) for the Dual Split Kinetic model (see text).

Fig. 12. Kinetic decrease of N), (r) as a function of time at various temperatures for a Dual Split Kinetic system obtained by nonequilibrium cooling. The equilibrium value is 50.

We have introduced so far a novel nonequilibrium statistical theory, [eq. (6)]. Although this subject might appear quite different from the objective of this paper on the possible interrelationship between the Tg, and T transitions, it is very pertinent. We will now apply the principle of the Energetic Kinetic Theory, presented above to determine the structure of the dual split, to another situation. We assume that the free energy still remains equal to the equilibrium value at the same temperature (EKT principle), but it is allowed to subdivide into (t) identical systems to render the energetic constraint feasible. Hence the total number of units, Bg, can be divided into (t) systems of (Bp/fV ) units each. We define = Bq/N, and numerically solve the following system of differential equations on a computer. 

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