Dumb-bell polymers

The simplest case of comb polymer is the H-shaped structure in which two side arms of equal length are grafted onto each end of a linear cross-bar [6]. In this case the backbones may reptate, but the reptation time is proportional to the square of Mj, rather than the cube, because the drag is dominated by the dumb-bell-like frictional branch points at the chain ends [45,46]. In this case the dependence on is not a signature of Rouse motion - the relaxation spectrum itself exhibits a characteristic reptation form. The dynamic structure factor would also point to entangled rather than free motion. 

The use of. eq. (3. )) which has nothing to do with the dumb-bell model, seems justified, as eq. (5. Id) should be valid also for the subchain model. From Koyama s papers, in which use is made of the subchain model but where, unfortunately, no results suitable for a quantitative comparison with experiment are obtained, one can learn that an expression of the type of eq. (5. Id) should indeed be independent of the degree of hydrodynamic shielding of the subchain model. From these papers one can also deduce that, for the case of a non-draining polydisperse polymer, is proportional to the ratio MwjMv, where Mn is the... 

Fig. 7.9 Illustration of the dumb-bell model for the deformation of polymer coils...

Apparently, the extensional flow causes the deformation of polymer coils. The simplest dumb-bell model can be used to describe this deformatimi. As illustrated in Fig. 7.9, two beads with a distance R, and the entropic elastic recoveiy force uprni deformation of polymer coils is... 

Mechanical properties of polymer blends during elongation were determined with a Zwick 1435 instrument, according to ISO 37. Dumb-bell specimen geometry n°2 was applied. 

Further models for polymer dynamics include the incorporation of stiffness parameters for both local and collective modes, and the approach of Bird and co-workers using the finitely extensible non-linear elastic (FENE) dumb-bell. The latter has been used to reproduce the non-Newtonian viscosity observed with polymer solutions even at the 6-temperature at high shear rates (frequencies), but not given by the simple (infinitely extensible) bead spring. 

---