Viscosity molecular weight dependence

Fox.T.G., Loshaek,S. Isothermal viscosity-molecular weight dependence for long chains. J. Appl. Phys. 26,1080-1082 (1955). 

Allen,V.R., Fox,T.G. Viscosity-molecular weight dependence for short chain polystyrenes. J. Chem. Phys. 41,337-343 (1964). 

The refinement introduced by Doi [9] who considers tube length fluctuations is more relevant to experimental scaling laws as far as the viscosity/molecular weight dependence is concerned. Following that concept, Gc(t) can be cast into the integral form ... 

Typical viscosity-molecular weight dependence for molten polymers. Xw is proportional to Ae number of backbone atoms and Mw Front Berry and Fox (1968). 

There are three major aspects of polymer viscosity discussed in this chapter. First, we shall consider the fact that most bulk polymers display shear-dependent viscosity that is, this property does not have a single value but varies with the shearing forces responsible for the flow. Second, the molecular weight dependence of polymer viscosity is examined. We may correctly expect a... 

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

The Molecular Weight Dependence of Viscosity Experimental Aspects... 

In connection with a discussion of the Eyring theory, we remarked that Newtonian viscosity is proportional to the relaxation time [Eqs. (2.29) and (2.31)]. What is needed, therefore, is an examination of the nature of the proportionality between the two. At least the molecular weight dependence of that proportionality must be examined to reach a conclusion as to the prediction of the reptation model of the molecular weight dependence of viscosity. 

The viscosity of a polymer solution is one of its most distinctive properties. Only a minimum amount of research is needed to establish the fact that [77] increases with M for those polymers which interact with the solvent to form a random coil in solution. In the next section we shall consider the theoretical foundations for the molecular weight dependence of [77], but for now we approach this topic from a purely empirical point of view. 

The intrinsic viscosity of poly(7-benzyl-L-glutamate) (Mq = 219) shows such a strong molecular weight dependence in dimethyl formamide that the polymer was suspected to exist as a helix which approximates a prolate ellipsoid of revolution in its hydrodynamic behaviorf ... 

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

The viscosity average molecular weight depends on the nature of the intrinsic viscosity-molecular weight relationship in each particular case, as represented by the exponent a of the empirical relationship (52), or (55). However, it is not very sensitive to the value of a over the range of concern. For polymers having the most probable distribution to be discussed in the next chapter, it may be shown, for example, that... 

Sato, N., Ito, S. and Yamamoto, M. (1998) Molecular weight dependence of shear viscosity of a polymer monolayer evidence for the lack of chain entanglement in the two-dimensional plane. Macromolecules, 31, 2673-2675. 

Zhu D, Haidekker MA, Lee J-S, Won Y-Y, Lee JC (2007) Application of molecular rotors to the determination of the molecular weight dependence of viscosity in polymer melts. Macromolecules 40 7730-7732... 

The intrinsic viscosity vs molecular weight dependence extracted from the SEC experiments curve of the intrinsic viscosity also often gives a straight line in the double logarithmic plot and can be described by the (KMHS) relationship ... 

This simple argument can yield the expected molecular weight dependence of both the single chain diffusion constant (in three dimensions) D and the viscosity 77. For in one reptation time the chain has moved on average one chain end-to-end distance R (N/Nj a, so... 

As known from the broad crossover phenomena observed in the macroscopic chain dynamics (such as the molecular weight dependence of the melt viscosity) very important limiting mechanisms must exist that affect the confinement limit of the reptation process. These processes increase in importance as the chain length decreases. The two main mechanisms are [62] ... 

From this information the absolute molecular weight distribution and the intrinsic viscosity-molecular weight plot can be constructed. From this plot the solvent and temperature dependent Mark-Houwink coefficients for linear polymers and information for polymer chain-branching of non-linear polymers can be obtained. 

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