Polymer solution length scales

On the other hand, the existence of a concentration-independent crossover probe diameter d (R, R is consistent with polymer solution models based on an assumed dominance of hydt ynatnic interactions in nondilute solution. Models such as the hydrodynamic scaling model (6.7) identify the chain radius as the primary solution length scale at all concentrations at which the model applies. With this identification, a crossover from small-probe to large-probe behavior, perhaps correlated with differential ability to interact with internal chain modes, would at all concentrations occur over the same range of d/R, or d/R, precisely as observed experimentally. 

Viscoelastic and transport properties of polymers in the liquid (solution, melt) or liquid-like (rubber) state determine their processing and application to a large extent and are of basic physical interest [1-3]. An understanding of these dynamic properties at a molecular level, therefore, is of great importance. However, this understanding is complicated by the facts that different motional processes may occur on different length scales and that the dynamics are governed by universal chain properties as well as by the special chemical structure of the monomer units [4, 5],... 

Table 5. Scaling predictions for the mean square radius of gyration and the mean square correlation lengths < 2> in the different regimes (see Fig. 38) of polymer solutions [102-104]...

Recently a very detailed study on the single chain dynamic structure factor of short chain PIB (M =3870) melts was undertaken with the aim to identify the leading effects limiting the applicability of the Rouse model toward short length scales [217]. This study was later followed by experiments on PDMS (M =6460), a polymer that has very low rotational barriers [219]. Finally, in order to access directly the intrachain relaxation mechanism experiments comparing PDMS and PIB in solution were also carried out [186]. The structural parameters for both chains were virtually identical, Rg=19.2 (21.3 A). Also their characteristic ratios C =6.73 (6.19) are very similar, i.e. the polymers have nearly equal contour length L and identical persistence lengths, thus their conformation are the same. The rotational barriers on the other hand are 3-3.5 kcal/mol for PIB and about 0.1 kcal/mol for PDMS. We first describe in some detail the study on the PIB melt compared with the PDMS melt and then discuss the results. 

The matrix polymer morphology of a collection of LDPE foams manufactured from a high-pressure nitrogen solution process was analysed at different length scales. 

Scaling theory also derives such results in another, more intuitive way, based on some heuristic picture of the internal structure of the polymer solution. Consider some piece of length nB within a chain of length n. It is natural to assume that this piece forms a subcoil, a blob1, of typical extension R, which scales like the coil radius for a polymer molecule of segments Rb nB- Thus the local density of segments due to the blob is estimated as... 

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