Viscosity-average molecular weight distribution

Among the techniques employed to estimate the average molecular weight distribution of polymers are end-group analysis, dilute solution viscosity, reduction in vapor pressure, ebuUiometry, cryoscopy, vapor pressure osmometry, fractionation, hplc, phase distribution chromatography, field flow fractionation, and gel-permeation chromatography (gpc). For routine analysis of SBR polymers, gpc is widely accepted. Table 1 lists a number of physical properties of SBR (random) compared to natural mbber, solution polybutadiene, and SB block copolymer. 

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... 

Mark-Houwink-Sakurada constant Mass transfer coefficient around gel Fractional reduction in diffusivity within gel pores resulting from frictional effects Solute distribution coefficient Solvent viscosity nth central moment Peak skewness nth leading moment Viscosity average molecular weight Number of theoretical plates Dimensionless number... 

The second average is viscosity average molecular weight, M . This expression is obtained by using the exponent from the limiting viscosity number-molar mass relationship, a, as a power for the molecular weight of each molecule in the distribution. The formula for this average is... 

Measures of change Viscosity measurements Intrinsic viscosity Viscosity-average molecular weight Molecular weight distribution, GPC Solubility Rates Thickness changes on development... 

The intrinsic viscosities of the polymers prepared in tetrahydrofuran increased throughout the experiment. This system thus exhibits some of the aspects of living polymerization—that is, catalyst activity over an extended period, and increasing viscosity average molecular weights with added amounts of monomer. The rather broad molecular-weight distributions of these polymers, however, differentiates this system from that of the classical case in which polymerization proceeds in the complete absence of a termination process. 

The dichloride complex was used as the reference for the ethylene, see reference [ 18]. a Toluene. b Dichloromethane. c Activity, g polymer-mol Zr -lr1. d Melting point. e Polymer fraction. f Molecular weight distribution. g Viscosity average molecular weight. h Elastomer. 

Figure 8.19 Influence of molecular weight on the plateau length of narrow distribution polystyrene. The curves represent the storage relaxation modulus in the frequency domain reduced to 160°C. Viscosity-average molecular weights from left to right, xlO" 58, 51, 35, 27.5, 21.5, 16.7, 11.3, 5.9, and 4.7. (From Ref. 25.)...

The results are summarized In Table III. Narrow, monomodal distributions were seen, with Mw/Mn <1.1. The Mn correlations with Intrinsic viscosity In toluene were plotted In Figure 4. Since viscosity average molecular weight (M ) depends upon a, an Interactive procedure was used to arrive at final values of a. The following Mark-Houwlnk equations were thus derived from least squares fit ... 

For the polymer sample described in problem 7, calculate the viscosity-average molecular weight. Data for PMMA samples which are narrowly distributed show the following intrinsic viscosities in chloroform at 25 C. 

The high-temperature-vulcanizable grades have broad molecular weight distributions and high viscosity-average molecular weights. YeL they have very low viscosities in the imvulcanized state. 

See also molecular weight, molecular weight distribution, number average molecular weight, and viscosity-average molecular weight. 

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