Kinetic Constants of the Flow-Equilibrium

According to this picture, some distribution of diffusion distances must exist in the gel, from which the above mentioned rediffusion into the sol is started. After forming a mean value, a mean depth of penetration, A, due to the coll diffusion, can be defined in the gel, representing some part of the gel thickness, 1, and depending both on the partition function K(P) and on its relative perturbation, 5Q(P)/K(P), by the polymer transport in the flow-equilibrium. This mean depth of penetration A and the diffusion coefficient Dg of the P-mer in the gel evidently represent the main factors contributing to the expression for the rate constant ks to be found. 

There are two interpretations of the statistical quantity A, both being closely related to the geometrical interpretation of the term phase boundary . From a purely macroscopic point of view, the gel of course represents a phase to which thermodynamical functions of state are related. Nevertheless, such a macroscopic image with a sharp boundary can hardly be correct in a PDC-column considering the range of end-to-end distances of the transported coils in the concentration profile, because the transported P-mer and the stationary gel are chemically equal in PDC. The two possible definitions of the quantity A(P) are  

Both models, (a) and (b), can formally be described by means of Fick s second law with a suitable common time boundary and the corresponding space boundaries, as shown in Fig. 16. Since the diffusion of the P-mer from the sol into the gel can be assumed as one-dimensional according to the column geometry and, in addition, the laterally diffusing macromolecules have all the same probability to reach the gel layer from the position c(0) of the sol at t = 0 (spontaneous diffusion of the P-mer from the sol into the gel), the second Fick s law 

A trivial integration of the differential Eq. (26) under the space boundaries 

There are two inconveniences connected with model (a) How to explain in such a kinetic scheme that the transported P-mer does not belong to the gel itself, although it evidently causes the concentration jump c, - c, + 5c, on the sharp boundary surface between sol and gel This dicrepancy only vanishes in the reversible-thermodynamic equilibrium where 5c, - 0 and 5Q/K - 0 for any P however, A - 0 (and not A -+ 1, as should be expected) is obtained from Eq. (27c) in this case, because ks must stay finite and positive in the reversible polymer transport. 

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T o calculate all kinetic constants of the flow-equilibrium, only the (P, T)-dependence of the rate constant ks of a spontaneous polymer diffusion from the sol into the gel must be investigated independently. The rate constant kg of the reversible rediffusion of this P-mer from the gel into the sol follows from Eqs. (16b) and (4) and from Table 2,... 

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