PDC-Effect and Flow-Equilibrium

The pronounced discrepancy between the measured dynamic 15 °C-elution curve and its extrapolated reversible-thermodynamic part, shown in Fig. 7, represents a direct proof of the inadequacy of the reversible Eq. (3) in the dynamic region of the column (PDC-effect). Moreover, the experiment shows immediately that the polymer of the mobile phase has to dissolve in the gel layer within the transport zone to a considerably higher extent than is allowed by the partition function (4) in a reversible-thermodynamic equilibrium between the gel and the sol at the same column temperature. As a consequence, a steady state, i.e. a flow-equilibrium, must be assumed in the system sol/gel within the considered transport zone, governing the polymer trans- 

It is well known that a flow-equilibrium must be treated by the methods of irreversible thermodynamics. In the case of the PDC-column, principally three flows have to be considered within the transport zone (1) the mass flow of the transported P-mer from the sol into the gel (2) the mass flow of this P-mer from the gel into the sol and (3) the flow of free energy from the column liquid into the gel layer required for the maintenance of the flow-equilibrium. If these flows and the corresponding potentials could be expressed analytically by means of molecular parameters, the flow-equilibrium 18) could be calculated by the usual methods 19). However, such a direct way would doubtless be very cumbersome because the system is very complicated (cf. above). These difficulties can be avoided in a purely phenomenological theory, based on perturbation calculus applied to the integrated transport Eq. (3 b) of the PDC-column in a reversible-thermodynamic equilibrium. 

The concentration c depends on the shape of the concentration profile in the transport zone of Fig. 13. If the perturbation calculus (see Sect. 3.2.2) is applied to the reversible-thermodynamic equilibrium in the zone, and if further the spreading of the zone remains small, then c = vcs with v 1 is approximately valid. 

It is clear that the system of Eqs. (14) is not complete because the third flow leading to the retarded rediffusion (that of the free energy) was not described explicitely. 

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