Molecular-Weight Scaling Laws

Because of hydrodynamic interactions, the Rouse model fails in its prediction of the scaling of the low-shear viscosity, rjo, with molecular weight. Note from Eqs. (3-41) and (3-42a) that for the Rouse model we obtain 

Since the exponent a is always less than unity, Eq. (3-47b) disagrees with the Rouse prediction. For theta solvents, a is 0.5. For good solvents, polymer-solvent contacts are favorable, so the polymer coil expands to contact as many solvent molecules as possible. Hence, a for good solvents is higher than 0.5, but it is always less than around 0.8 for flexible polymers (de Gennes 1979). 

In theta solvents, experimental results confirm the scaling predicted for [rjh in the limit of dominant hydrodynamic interaction. In good solvents, the measured exponent is generally slightly less than the value, 4/5, predicted for dominant hydrodynamic interaction. The scaling law, [jyJo = for a flexible polymer in a theta solvent is often used to 

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Empirical concentration and molecular-weight scaling laws... 

Empirical Concentration and Molecular-Weight Scaling Laws... 

The divergence of the viscosity law plot from linear and subsequent decline in g for a lightly branched polyethylene is shown in Fig. 19. The work was done with an integrated GPC system that can maintain all zones at the temperature needed to keep the sample in solution. In this presentation the molecular-weight scale is high to low. This is a user preference that is chosen in the software. In addition to the degree of branching indicated by... 

We hope that this chapter on the molecular weight determination of synthetic polymers has illustrated that in the case of a complex polymer it is preferable to use several experimental methods for the molecular weight determination to obtain a full picture. Owing to the different sensitivity of the various methods some are blind for low molar masses while others are blind at low concentrations. As exemplified, often scaling laws can be utilized to compare results of different methods and different sensitivities. 

Here f(M.) is the weight fraction of molecular weight M. using equal spacing in M scale and P(K,M.) is the form factor ior the molecular weight M. at the scattering vector K, and the final expression in eq. (9) approximates the MWD as a discrete distribution. If T. is related to M. by an empirical power law (T - M D), constant. space... 

A list of various mean-square radii of gyration as function of the molecular weight is given in Table 3. In many cases this molecular weight dependence can be described by the approximation of a scaling law, i.e. 

No doubt structural differences are also responsible for the 0-36% increase in molecular volume of liquid water on going from H20 to D20. The molecular volumes of mixtures obey an ideal mixture law very closely (Kirshenbaum, 1951). However, in the main, the density difference between H20 and its mixtures with D20 is due to the change in average molecular weight. Because of this density difference, the quantitative results for thermodynamic measurements on solutions in H20-D20 mixtures are different according to the concentration scale adopted. For dilute solutions in ordinary water the difference between... 

A very considerable portion of the text has been wholly rewritten, and the entire text has been subjected to a revision and rearrangement. Specific new exercises and discussions which have been introduced include such topics as the determinations of vapor density and molecular weight, the standardization of acids and the titration of acids and bases, Faraday s law, and the use of the pH scale of hydrogen-ion concentration. Several new preparar tions have been introduced, and a few of the old ones have been discontinued. A complete list of apparatus and chemicals required in the course has been added to the Appendix. 

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