Dilute solution molecular-weight, dependence

Gundert F, Wolf BA (1986) Viscosity of dilute polymer solutions molecular weight dependence of the Huggins coefficient Makromol Chem 187 2969... 

The viscosity of a dilute solution of polymer depends on the molecular weight of the polymer. This gives us a simple method for measuring molecular weight based on viscosity, which is readily measured. 

Considering the development of the theory of melt viscosity, one notices a similar kind of evolution as with the intrinsic viscosity of dilute solutions. In both cases starting points were formed by empirical relations describing the respective molecular weight dependencies. Only afterwards, the relations are interpreted on more fundamental grounds. 

The aim of the theories developed for polymer solutions has been to explain experimental observations such as deviations from Raoult s law and the molecular weight dependence of solubility at any given temperature. Indeed, it is necessary to account for the phase diagram for polymer solutions in general. The more recent theories deal with semi-dilute and concentrated solutions. No single theory currently explains ail the experimental observations for polymer solutions. Some of the more significant are [8-16] ... 

This equation is valid both in dilute and semidilute solutions. Unlike with dilute solutions, the scaling argument does not predict molecular weight dependence explicitly. (This must be so since one can derive the same formula for the self-diffusion constant Dq. Further information is needed to distinguish the functional form of D pp from that of Dc-) If one assumes that is independent of the molecular weight, then one has... 

The zero shear viscosity scales with Nf" to contrast Af dependence for isotropic polymers [20] So far, we have examined the dynamics of rod-Uke macromolecules in isotropic semi-dilute solution. For anisotropic LCP solutions in which the rods are oriented in a certain direction, the diffusion constant increases, and the viscosity decreases, but their scaling behavior with the molecular weight is expected to be unchanged [2,17], Little experimental work has been reported on this subject. The dynamics of thermotropic liquid crystalline polymer melts may be considered as a special case of the concentrated solution with no solvent. Many experimental results [16-18] showed the strong molecular weight dependence of the melt viscosity as predicted by the Doi-Edwards theory. However, the complex rheological behaviors of TLCPs have not been well theorized. 

The limiting flux behaviour can also be described by this model. By increasing the pressure difference the flux increase on and hence the concentration at the tiKinbrane surface, c , will also increases. This leads to an increase in the osmotic pressure and hence the pressure increase is (partly) counterbalanced by the osmotic pressure increase. The phenomenon of osmotic pressure has been described in a previous section of this chapter. Thus, for dilute low molecular weight solutions, a linear relationship, the so-called van t Hoff relationship, exists between the osmotic pressure and the concentration. However, the dependence of the osmotic pressure of a macromolecular solution on the concentration is generally exponential rather than linear and can be described by... 

Finally Dill and Zimm have designed a new rheological instrument that can not only perform steady shear, but also measure transient responses, e.g., both stress relaxation and strain relaxation (creep recovery) experiments for dilute solutions. They have investigated the properties of T2 DNA, and studied, for example, the concentration dependence of Results are consistent with the theory of Muthukumar and Freed, and from the value of r, at infinite dilution the molecular weight of the DNA may be determined. 

MO1 Morimoto, S., Calorimetric investigations on polymer solutions. IV. Heats of dilution of polystyrene solutions and their molecular weight dependence, Bull. Res. Inst. Polym. Textil., 90(3), 38, 1970. 

The effects of molecular weight on separation has been shown to be negligible over a wide molecular weight range of linear polyethylenes [119]. The reason the separation is not molecular weight dependent has been ascribed to a very controlled crystallization process from dilute solution. By using a very slow and controlled decrease in temperature (in some cases over the course of days), the crystallization process is more thermodynamically controlled and the kinetic effect of chain length on crystallization is diminished. 

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