Viscosity-molecular weight relationship

A comparison of the expressions giving the molecular-weight dependence of the Staudinger index shows that the relationships can be generalized for all macromolecular types in the form of the modified Staudinger equation [ ] = (see also Table 9-7). Both K and are usually 

Rods Same as above, but with rotational diffusion 1.7 

Coils Unbranched free draining no excluded volume 1 

Coils Unbranched none draining excluded volume 0.51-0.9 

Spheres Constant density, unsolvated or uniformly solvated 0 

Values obtained for and a for a number of polymer-solvent pairs are given in Table XXX. It will be observed that the exponent a varies with both the polymer and the solvent. It does not fall below 0.50 in any case and seldom exceeds about 0.80. Once K and a have been established for a given polymer series in a given solvent at a specified temperature, molecular weights may be computed from intrinsic viscosities of subsequent samples without recourse to a more laborious absolute method. 

It should be emphasized that Eq. (52) is empirical in origin. However, the more complicated theoretical expressions to be discussed in Chapter XIV can be approximated quite closely by this simple equation over ranges of as much as a hundredfold in M. The convenience of application of the empirical relationship assures its continued use for correlating intrinsic viscosities and molecular weights. 

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The dilute solution properties of copolymers are similar to those of the homopolymer. The intrinsic viscosity—molecular weight relationship for a VDC—AN copolymer (9 wt % AN) is [77] = 1.06 x 10 (83). The characteristic ratio is 8.8 for this copolymer. 

Intrinsic viscosity—molecular weight relationships have been obtained for copolymers in methyl ethyl ketone. The value for a 15 wt % ethyl acrylate (EA) copolymer is [77] = 2.88 x 10 . ... 

Fig. 50.—Intrinsic viscosity-molecular weight relationship for polyisobutylene in diisobutylene (DIB) at 20° and in cyclohexane at 30°C. Open circles from Ref. 7 filled circles, Ref. 8.

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... 

We, therefore, propose an indirect method for obtaining the variation of the intrinsic viscosity and number average molecular weight across the chromatogram. First the intrinsic viscosity-molecular weight relationship for a polymer with long chain branching (LCB) is assumed to be expressable in a form similar to that used by Ram and Milts (6),... 

Kurata, M., Tsunashima, Y., Iwama, M., and Kamada, K., Viscosity-molecular weight relationships and unperturbed dimensions of linear chain molecules, in Polymer Handbook, 2nd ed., Brandrup, J. and Immergut, E. H., Eds, John Wiley Sons, New York, 1975, iv, 1-60. 

Fig Intrinsic viscosity-Molecular weight relationships for polyisobutylene in disobutylene and cyclohexane. 

The original poly(vinyl alcohol) was studied in both aqueous and DMSO solutions. Viscosity-molecular weight relationships have been reported for each of these solutions at 30°C as shown in Equations 19 and 20 (3). 

Intrinsic viscosity molecular weight relationship. The values of two constants appearing in the above relation, determined when fractions of a polymer of molecular weights 34000, 61000 and 130000 dissolved in an organic solvent gave the intrinsic viscosities as 1.02,1.60 and 2.75 respectively at 25°C... 

A more appropriate equation (3) for CTPB viscosity-molecular weight relationship which appears to apply over a wider molecular weight range is ... 

Fig. 24. Intrinsic viscosity-molecular weight relationships for typical polypeptides in helicogenic solvents (O) PELG in TFE (57), ( ) PBLA in m-cresol at 15° C (22% (3) PCBL in DMF at 25° C (23% ( ) PCBL in DMF at 20° C (58)...

Gupta,D., Forsman,W.C. Newtonian viscosity-molecular weight relationship for concentrated solutions of monodisperse polystyrene. Macromolecules 2, 304-306... 

The polydispersity factor p is evaluated with the aid of any of the well-known viscosity-molecular weight relationships. From eq. (3.60) a proportionality of the intrinsic viscosity to the half power of the molecular weight is expected, as this theory holds for 0-solvents. However, based on the conclusion of Section 3.5, viz. that the reduced steady-state compliance of a monodisperse polymer is insensitive to the excluded... 

However, the square root of this denominator controls the viscosity-molecular weight relationship [cf. eq. (3.37)]. This means that any increase of JeR corresponds to a decrease of the viscosity below the value... 

As the scope of the present chapter is to stress limits and background for the Gaussian theory, a discussion of the said viscosity-molecular weight relationships is omitted. Some general remarks will be made in the discussion of the next section. 

Intrinsic Viscosity—Molecular Weight Relationship for PMMA in TFE. The intrinsic viscosities of the PMMA preparative GPC fractions and whole polymers in TFE at 50 °C and in benzene at 30 °C are shown in Table III and plotted in Figure 4. A least-squares analysis of the data plotted in Figure 4 yields the relation... 

Clearly, much more information is needed about the behaviour of these two monomers and oxacyclobutane is perhaps the more favorable for further study because of its clearer catalyst-co-catalyst relationship and the absence of vinyl ether formation. The particular information needed about oxacyclobutane reactions at the present time are (a) knowledge of the fate of the catalyst, (b) viscosity-molecular weight relationship, (c) much more information about the variation of molecular weight with the reaction variables, and (d) information about the reaction of both monomer and polymer with oxonium ions and about the ease of formation of oxonium ions by oxacyclobutane. 

G. Ajrodi, G. Marchionni, and G. Pezzin, The viscosity-molecular weight relationships for diolic perfluoropolyethers, Polymer 40, 4163 4-164 (1999). 

Robinson, G., Ross-Murphy, S. B., and Morris, E. R. (1982). Viscosity-molecular weight relationships, intrinsic chain flexibility, and dynamic solution properties of guar galactomannan. Carbohydr. Res. 107 17-32. 

K4 Kinsinger, J. B., and R.E. Hughes Intrinsic viscosity-molecular weight relationships for isotactic and atactic polypropylene. J. Phys. Chem. 63, 2002 (1959). 

M 25 -— and B. M. TidsWELL Viscosity molecular weight relationships for cellulose acetate. J. Appl. Chem. (London) 8, 232 (1958). 

There are relatively few data available for the synthetic polyamides. From the studies of Schaefgen and Flory (224) on 6-Nylon in sulfuric acid and those of Howard (127) on 66-Nylon in formic acid-sodium formate we derive identical values of A and of isomeric polymers is also shown in the work of Batzer and Moschle (32 f), who found that both of these Nylons and their copolymers obeyed the same viscosity-molecular weight relationship. 

Finally, we return to a practical problem, i. e., the chain conformation of stereo-specific polymers. Since Danusso and Moraglio (73), it has been repeatedly reported that the isotactic and atactic species of a given polymer show the same viscosity-molecular weight relationship but different second virial coefficients. This statement may be readily confirmed... 

CR, cryoscopic method DV, diffusion constant and intrinsic viscosity EB, ebullioscopic method EG, end-group titration IV, intrinsic viscosity-molecular weight relationship in other solvents LS, light scattering MV, melt viscosity-molecular weight relationship OS, osmotic pressure PR, analysis of polymerization rate SD, sedimentation and diffusion constants SE, sedimentation equilibrium (Archibald s method) SV, sedimentation constant and intrinsic viscosity [see Eq. (72)]. 

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