Molecular mass distribution number-average

The chains of the produced polymer are lengthened by combination, but not by disproportionation. This affects the molecular mass distribution but the differences are not very large, differing by a factor of 2 at most. Due to the inaccuracies in molecular mass determinations, it is almost impossible to make estimates of the relation between termination and disproportionation from the distributions. Even labelling of the initiator and determination of the average number of its fragments in a macromolecule (one for disproportionation and two for combination) is usually unsafe because of transfer. 

The common averages of a polymer molecular mass distribution arc number (m=l viscosity (m=1 +aX weight (m=2), and z or zeta average (m=3). What molecular mass average does the following formula calculate and of what property or "weighting" of the polymer sample is it a function ... 

This distribution of molecular masses and sizes can now be routinely quantified for all soluble polymers by gel permeation chromatography (1). While this distribution is useful both in practice and in theory, many properties of the polymer sample depend on a single middle value of the distribution. There are, however, several ways to reduce the distribution to a middle value. Each of these reductions is important because they correlate with or predict a certain subset of physical or chemical properties of the polymer. The common averages of a polymer molecular mass distribution are number (m=1), viscosity (m=1 +a ), weight (m=2), and z or zeta average (m=3). These "averages" are actually ratios of the m- moment of the molecular mass distribution to the preceding moment in the above list. The moments of a distribution are fundamental properties of any distributed variable and are covered in detail in reference 2. 

Calculate the number average and weight average relative molecular mass for a sample of polystyrene made by blending eight separate fractions, each of which has a very narrow molecular mass distribution, as follows ... 

For molecular masses distributed according to Poisson distribution, the ratio of the degrees of polymerization depends only on the number average degree of polymerization and the ratio tends to unity for. They recognize that... 

High-temperature SEC finds wide application in polymerization studies, as the molecular mass distribution is an artefact of the various reactions involved in polymerization, initiation, termination, and transfer. It is diagnostic of living systems and random polymerization reactions, such as condensation and radical initiated polymerizations, for which the distributions are Poisson and normal respectively. In the polymerization of ethene and propene by Ziegler-Natta catalysts, the determination of the concentration of active centres as a function of conversion defines catalyst type. Similar studies have been made in the study of chain scission by thermal degradation or by irradiation, in defining the number of molecules produced from the inverse of the number average molecular mass and random chain scission eventually leads to a normal molecular mass distribution, with polydispersities close to 2.0. This has, of course, been widely used to produce narrow from broad molecular mass distribution samples prior to fractionation. 

The viscosity of a dilute polymer solution depends on the nature of polymer and solvent, the concentration of the polymer, its average molecular mass and molecular mass distribution, the temperature, and the shear rate. The most important characteristic quantity in a very dilute solution, at vanishing shear rate, is the limiting viscosity number, which is defined as [1]... 

An average molecular mass (viscosity average) An average molecular mass (number average) Molecular dimensions and an average molecular mass (weight average) Molecular mass distribution... 

Data such as density, melt flow rate, melting temperature, crystallinity, number-average or mass-average of molecular mass distribution and polydispersity are not yet satisfactory to fully characterise the properties of polymeric materials. The specific manufacturmg process and process-related parameters define further properties sueh as type and extent of impurities, for example eatalyst residues, low-molecular fractions and co-... 

The molecular mass distribution, its number average and mass average and the width of the molecular mass distribution belong to the key parameters of polymeric materials. Let rii be the number of molecules with the molecule mass Mi according to the distribution of the molecular masses in a certain plastic. The number average molecular mass M and the mass average molecular mass can be written as ... 

The unit of both quantities is g/mol. Occasionally, the unit Dalton = g/mol is used. Dividing M by the molecule mass of the basic module of the polyethylene chain, CH2 (14 g/mol), one obtains the dimensionless average degree of polymerisation. A measure for the range of molecular mass distribution is the relationship of the mass average to the number average, the so-called polydispersity U ... 

Zagala et al. investigated the polymerization of methacrylates in the presence of tetraphenylphosphonium (TPP) ion at ambient temperature. The polymerization appears to have living character [228]. In case of MMA number average molecular masses increase linearly with conversion and molecular mass distributions are narrow (< 1.30). Results of H, and P NMR studies indicated the presenee of phosphorylides formed by the addition of the PMMA enolate anion to one of the phenyls of the TPP cation. Muller et al. managed to synthesize another metal-free initiator, namely the salt of the tetrakis[tris(dimethylamino)-phosphoranylideneamino]phosphonium (P5) cation with the... 

Figure 2.26. Dependence of the glass transition temperature of polystyrenes of narrow molecular mass distribution on the number average molecular mass (MJM for all samples ranged between 1.01 and 1.12). Heating experiments, with heating rate of 10°C/min. (Menczel, nnpublished results.)...

It has been demonstrated both by calculations and by experiments, that polymers produced in batch or in continuous process may have a different molecular mass distribution for a given average molecular mass. The molecular mass distribution is expressed as the dispersion index D, that is the ratio of the mass (weight) average and the number average values of the molecular mass of the polymer ... 

The length of particular macromolecules is determined by the number of constituent atoms, so their molecular mass. Because the particular macromolecules differ in the length of polymer chain for their description one introduces the notion of average molecular mass (M). It spears that very often polymers prepared from the same monomer, characterized by the same average molecular mass M exhibit dificrent properties. Therefore, the notion of polydispersity of polymers was introduced. It describes the molecular mass distribution. 

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