Molecular mass distribution of the product

Macromolecules of unequal length are usually generated by polymerization. Some idea of the relative contents of chains of various size in the studied polymer sample can be obtained by fractionation. The results are represented graphically as distribution curves of molecular mass (or degree 

The fraction of molecules, of degree of polymerization n (or some other 

The number of monomeric units in one average macromolecule of a polymer sample in which the chain length distribution is represented by the function 

According to the statistical nomenclature, fi is regarded as the moment fi, a quantity from a more general set of parameters which can be assigned to the given distribution. Other moments of this kind of distribution (moments with respect to 0) can be defined as 

Another kind of important moment, represented by dispersion variance, are moments referred to the centre. They are defined by 

Chromatography, in the form of gel permeation chromatography (GPC), can also be used. 

The fraction of molecules, Xn, of degree of polymerization n (or some other chain length characteristics) can be defined by some function n 

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Cationic polymerization of comb LCPs was first reported by Percec who used the Lewis acid boron trifluoride etherate as initiator. This approach, illustrated in Fig. 7.22, gave useful solution preparations of polyvinylethers (R = H) and polypropenylethers (R = CH3). Recently Sagane and Lenz demonstrated that the use of the cationic initiator system HI/U brought about living polymerizations of similar monomers and greatly improved the molecular mass distribution of the products. 

Effect of transfer constant values C and ktrP/kp on the character of the molecular mass distribution in the product... 

Two versions of the slurry process are most frequently applied. In the autoclave or Hoechst process (named after the former company Hoechst that introduced this version of the slurry process) the reaction temperature is 80-90 °C. Typical ethene pressures in the polymerization reactor are 5-10 bar, allowing the application of very large reactors (typically 100 m ). The catalyst compound and the aluminum alkyl activator are premixed in the catalyst preparation vessel with the diluent hexane. This mixture is fed to the polymerization reactor. Figure 6.20.3 shows a schematic view of the process with one polymerization reactor, but cascades of two or more polymerization reactors are also frequently found (allowing additional freedom in achieving specific molecular mass distributions of the PE product - see also picture at the beginning of the section, Hostalen ACP technology). 

Example CE-CI allows for the direct determination of the molecular weight distributions of the major aromatic components in liquid fuels and other petroleum products. [49,51,62] The approach involves selective CE between CeHsCE and the substituted benzenes and naphthalenes in the sample. In this application, chlorobenzene also serves as the solvent for the fuel to avoid interferences with residual solvent. Thus, the paraffinic components present in the fuel can be suppressed in the resulting CE-CI mass spectra (Fig. 7.10). [51]... 

Size-exclusion chromatography has been recently applied, with success, to the analysis of biopolymers derived from biomass, as it is used for the determination of molecular mass distributions of polymeric compounds in general, because of its short analysis time, high reproducibility, and accuracy. This application of SEC has permitted the separation and further detection of polymeric and monomeric residues of biopolymers, as well as the estimation of the degree of polymerization and eventual uses of namral products as additives, not only in... 

It is reiharkable that the molecular mass distribution of products obtained is very narrow, for example the dispersion index for diheptylsubstituted PV oligomers synthesized in toluene is 1.08 [5]. 

Herod, A.A., Zhang, S.-E, Johnson, B.R., Bartle, K.D., Kandiyoti, R. (1996) Solubility limitations in the determination of molecular mass distributions of coal liquefaction and hydrocracking products l-methyl-2-pyrrolidinone as mobile phase in size exclusion chromatography. Energy Fuels, 10,743-750. 

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