Solvent viscosity, segment density

Average square end-to-end distances polymers from light scattering or intrinsic viscosity in Insolvents. In fact, according to Flory (131), (hf) should be independent of solvent power as soon as the segment density becomes uniform. 

It soon became evident that the correlation between the termination rate coefficients and viscosity was much more complex than it had seemed to be at first. This complexity arises from the fact that if one solvent is replaced by another (or, alternatively, as soon as some polymer has been formed), the thermodynamic properties of the solution change simultaneously. Poor solvents, for instance, will decrease the radii of gyration of polymer coils and hence also the segment densities of these solvated macromolecules. Consequently, the dynamics of polymer coils in general (including the translational and segmental motions) will be affected by the solvent properties. This was actually already the case in some of the MM A studies in different solvents as mentioned above [40, 66-71, 73, 77] as not all these solvents dissolve pMMA equally well [95]. 

In contrast, all the hyperbranched polystyrenes used in the current study were fractionated by precipitation, i.e., according to the interaction parameter xM, where M is the overall molar mass of the chain and x is the Flory-Huggins parameter, a constant, independent on M for a polymer in a given solvent. Therefore, hyperbranched chains in each fraction used here have a similar molar mass. In comparison with our results, some of previous computer simulations [27, 28] suggested that the molar mass dependence of intrinsic viscosity of irregular hyperbranched chains deviates from Eq. 5.2 because the segment density distribution is different from those predicted by de Gennes and Hervet. We will come back to this point later. 

The interpretation of [rj] for branched polymers and copolymers is considerably more complicated, and will not be dealt with here other than to highlight some of the additional complexities. The effect of branching is to increase the segment density within the molecular coil. Thus a branched polymer molecule has a smaller hydrodynamic volume and a lower intrinsic viscosity than a similar linear polymer of the same molar mass. For copolymers of the same molar mass, [rj] will differ according to the composition, composition distribution, sequence distribution of the different repeat units, interactions between unlike repeat units, and degree of preferential interaction of solvent molecules with one of the different types of repeat unit. 

The chemical structure of a polymer can also cause a contraction of the polymer coil compared to the unperturbed dimensions at theta-conditions. In this case the exponent a of the [ ]]-M-relationship shows values of a<0.5. A contraction of the coil occurs if the attractive intramolecular interactions between the polymer segments become larger than the interactions with the solvent molecules. In extreme cases, the solvent is forced out of the polymer coil and the chain segments start to form compact aggregates. The density of the polymer coil is then independent of the molar mass and the intrinsic viscosity is constant. In this case the exponent a is zero. An example is shown in Fig. 6.12 for compact glycogen in aqueous solution. 

Matsuoka and Cowman [32] proposed the consideration of two simple models to study the hydrodynamic properties of hyaluronan on the basis of inherent viscosity. The first model of the not freely-jointed or non-ideal coil is based on the statistical conformations of polymer chains. Under this model, the intrinsic viscosity [ /] is directly proportional to the volume occupied by mass units of the polymer segments. The volume is filled mainly with solvent and has low density of polymer segments. The second model is the freely-jointed chain model. It is assumed that the chain is more extended and its viscosity corresponds to that of the worm-like chains. The intrinsic viscosity changes as a square of the mean-squared end-to-end distance. Experimental studies of intrinsic viscosity of hyaluronan indicate that short chains act as freely-jointed chains and long chain of hyaluronan behave like the not freely-jointed chains. The molecular weight, at which these two types of behaviour co-exist, is approximately 3.75xl(yDa. The size of the polymer corresponds to a smallest coil of hyaluronan (Figure 4.6). 

The factor a is 1 for the unperturbed coil defined in this way, and is larger (or smaller) when a polymer molecule is expanded (or compressed) due to polymer-solvent interactions. Thus, for an idealized freely jointed chain in theta solvent, we have = nl, and the corresponding mean square radius of gyration = nf-/G. When one accounts for the steric effects that prevent distant chain segments from overlapping (excluded volume effect), the dependence of (r ) is predicted to be (closer to experimental observation), rather than [Eq. (5)]. This polymer coil size is much larger than that based on polymer density, and hence markedly influences the viscosity behavior of polymers. 

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