Molecular weight distribution averages

This chapter presents the definition of gels and gives some typical examples, followed by a description of their structures and fundamental properties. A statistical mechanical treatment of the chemical gels in the polycondensation reaction is developed to find the molecular weight distribution, average molecular weight, gel point, and the gel fraction. 

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

Three polystyrene samples of narrow molecular weight distribution were investigatedf for their retention in GPC columns in which the average particle size of the packing was varied. In all instances the peaks were well resolved. The following results were obtained ... 

The width of molecular weight distribution (MWD) is usually represented by the ratio of the weight—average and the number—average molecular weights, MJM. In iadustry, MWD is often represented by the value of the melt flow ratio (MER), which is calculated as a ratio of two melt indexes measured at two melt pressures that differ by a factor of 10. Most commodity-grade LLDPE resias have a narrow MWD, with the MJM ratios of 2.5—4.5 and MER values in the 20—35 range. However, LLDPE resias produced with chromium oxide-based catalysts have a broad MWD, with M.Jof 10—35 and MER of 80-200. 

Size-exclusion chromatography (sec) easily and rapidly gives the complete molecular weight distribution and any desired average (6). Thus, it has become the technique of choice for determining molecular weights despite its relatively high initial cost. 

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. 

These values are given for polymers of narrow molecular-weight distribution, with number-average molecular weights (M ) of about 20,000 prior to chlorination. Chlorination reactions are carried out under homogeneous conditions in CCl solutions at temperatures between 90 and 110°C with viscosities at about 5 Pa (50 P). 

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