Deformation Concept in PDC

To answer the questions stated above, a typical value for the entropy of deformation, ASdef, caused by the stress related to the velocity gradient in the gel front , must be estimated. To do so, Eqs. (17c) with AGdd = —T ASdef 0 and (18a) are applied under the assumption of rubber-elasticity in the deformed chain. They yield the relationship 

The results are shown in Table 7. It can be seen that the considered entropy diminution of R/2, caused by the deformation of the sorbed structure due to the stress related to the velocity gradient near the gel front (X,llo) and along it (Xiso), can be attained the more easily the more contacts are formed between each coil and the segments of the gel phase4. However, it will be shown below that only few contacts between P-mer 

4 But this does not take place at a constant tensile stress (38) because G depends linearly on n according to Eq. (39), whereas the dependence of X on n is nonlinear in Eq. (40) at the constant entropy —R/2 

It must be said that there are some hypothetical presumptions in this part of the theory, all originating in the simplified mathematical treatment of a complicated hydrodynamic problem. Nevertheless, these simplifications lead to reasonable results, as is shown below. 

As can be seen, the entropies at both sides of Table 9 agree well in all cases if, on average, about n = 1 contact between each coil and the gel phase is assumed for the 353-mer, and about n = 2 and n = 3 contacts are assumed for the 1082-mer and the 2444-mer, respectively. Hence, Table 9 strongly supports the idea of the flow-equilibrium as a basis for the resolution of the PDC-column, thus completing the evidence given by the three Figs. 14, 15 and 20. 

---