Molecular Weight Distribution of Linear Polymers

As mentioned earlier, all synthetic polymers have finite MWD and the measurement of MWD is usually the first step in the characterization of polymers. SEC has been the most widely employed method for the MWD measurements of polymers. In the SEC analysis, the precision of the measurements depends on various factors in the operation of the instrument and the data reduction [1,3j. Various efforts including round robin tests to establish a standardized procedure in the SEC analysis have been made [62, 63]. However, even for linear homopolymers there is an intrinsic limitation of SEC to measure the precise MWD due to the band-broadening problem, in particular for the polymers with narrow molecular weight distribution [64]. 

The MWD of polymers prepared by living anionic polymerization is a good example [65]. According to the early theoretical work of Flory, an ideal living anionic polymerization is expected to yield a polymer with Poisson distribution of chain lengths [66]  

With the advances of new characterization techniques, the validity of the values determined by SEC has been questioned Shimpf et al. foimd much lower values for PS made by anionic polymerization from thermal field 

If the instrumental problems were correctly taken care of, light scattering detection clearly shows a narrower distribution of the polymers prepared by anionic polymerization (Fig. 5). Recently Netopilik et al. proposed a method to extract the M /M values of PS with narrow molecular weight distribution from SEC-light scattering detection results assuming a log-normal MWD [74]. 

Shortt [75] and Wyatt and Villalpando [76] used an interesting approach to measure values for PS prepared by anionic polymerization. Instead of mo- 

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Lavall6e, C. and Berker, A., More on the predictions of molecular weight distributions of linear polymers from their rheology. J. RheoL, 41(4), 851-871 (1997). 

Leonardi, R, AUal, A., Marin, G. Determination of the molecular weight distribution of linear polymers by inversion of a blending law on complex viscosities. RheoL Acta (1998) 37, pp. 199-213... 

Until recent years, there existed major barriers to the development of quantitative relationships between the molecular structure of molten polymers and their rheological behavior. First, reaction systems capable of producing polymers on an industrial scale yielded materials with complex and imprecisely controlled structures. Second, the molecular weight distributions of linear polymers tended to be broad and somewhat irreproducible. And, finally, the branching structure of long-chain branched polymers, particularly low-density polyethylene, involves multidimensional distributions that can neither be predicted nor characterized with precision. 

Galimberti and co-workers synthesized ethylene/ propylene/4-iodo-l-butene terpolymers with a V(acac)3/AlEt2X catalyst (X = Cl, I). The copolymers prepared were amorphous, having at least 35 wt % propylene content, and possessed a bimodal molecular weight distribution of high polymer (MW > 500 000) and oligomers. The preparation of crystalline copolymers of propylene with linear ft>-halo-olefins using TiCla/EtsAl has also been reported by Hoechst. ... 

D. W. Mead, Determinations of Molecular Weight Distributions of Linear Flexible Polymers from Linear Viscoelastic Material Fimctions J. Rheol. 38, 1797—1827... 

The polysilanes synthesized usually show a trimodal mass distribution containing a low molecular weight cyclic and a medium and a high molecular weight fraction of linear polymer. The oligomeric fraction can easily be separated from the other two by solvent extraction, whereas the fractionation of the medium and high molecular weight products requires more effort. 

Mathematical models for the calculation of the molecular weight distribution of linear [36] and nonlinear [37-40] polymers are available, but a detailed discussion of this issue is out of the scope of the present chapter. Instead, some simplified equations for the calculation of the molecular weights of linear polymers in the limiting cases of Smith and Ewart [28] will be presented. 

Table1.6 rilt at r/o y as a Function of Molecular Weight Distribution for Linear Polymer Melts [45]...

Marrucci G, Maffettone PL (1993) Liquid crystalline polymers. Pergamon, New York Mead DW (1994) Determination of molecular weight distributions of linear flexible polymers from linear viscoelastic material functions. J Rheol 38 1797-1827 Moldenaers P, Yanase H, Mewis J (1990) Effect of shear history on the theological behavior of lyotropic liquid crystals. Liq Cryst Polym 24(1990) 370-380 Muir MC, Porter RS (1989) Processing rheology of liquid taystal polymers a review. Mol Cryst Liq Cryst 169 83-95... 

Mead, D. W. Determination of molecular weight distributions of linear flexible polymers from linear viscoelastic material functions. / RheoL (1994) 38, pp. 1797-1827... 

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