Fractional weight distributions

Horizon Fraction % weight distribution % N distribution in Amino acids Nucleic acids ... 

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. 

The basic premise of this method is that the magnitude of the detector output, as measured by hj for a particular fraction, is proportional to the weight of that component in the sample. In this sense the chromatogram itself presents a kind of picture of the molecular weight distribution. The following column entries provide additional quantification of this distribution, however. 

Column 9. Aj/Aj j gives that fraction of the area under the entire curve which has accumulated up to the Nth class. Since the curve is a weight distribution, this is equal to the weight fraction of material in the sample having M < Mj. 

The primary polymerization product ia these processes has a relatively wide molecular weight distribution, and a separate step is often used to narrow the polydispersity. Such a narrowkig step may consist of high vacuum stripping to remove volatile polymer chains, often followed by a solvent fractionation step (35,36), sometimes a solvent fractionation step alone (37,38), or a fractional precipitation from organic solvent (32). The molecular weight distribution can also be narrowed by depolymerization at elevated temperatures ia the presence of a depolymerization catalyst (217—220). 

It may be shown that M > M. The two are equal only for a monodisperse material, in which all molecules are the same sise. The ratio MI /MI is known as the polydispersity index and is a measure of the breadth of the molecular weight distribution. Values range from about 1.02 for carefully fractionated samples or certain polymers produced by anionic polymerization, to 20 or more for some commercial polyethylenes. 

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. 

Some by-product polyethylene waxes have been recently introduced. The feedstock for these materials are mixtures of low molecular weight polyethylene fractions and solvent, generaHy hexane, produced in making polyethylene plastic resin. The solvent is stripped from the mixture, and the residual material offered as polyethylene wax. The products generaHy have a wider molecular weight distribution than the polyethylene waxes synthesised directly, and are offered to markets able to tolerate that characteristic. Some of the by-product polyethylene waxes are distHled under vacuum to obtain a narrower molecular weight distribution. 

In industry and academia the need often arises to isolate portions of a polymer sample, whether it be to separate low molecular weight material from a sample or to actually fractionate the polymer across its molecular weight distribution. If gram quantities of isolated polymer are needed, true preparative chromatography equipment and techniques are usually necessary. 

Figure 2-77 shows how the weight distributions of the different molecular types vary during the fractional distillation of a naphthenic crude oil. Saturated aliphatic hydrocarbons (i.e., paraffins and naphthenes) are the predominant constituents in the light gasoline fraction. As the boiling point is raised, the paraffin content decreases, and the NSO content increases continuously. About 75 wt% of tbe residuum is composed of aromatics and NSO compounds. 

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