Molecular mass distribution polydispersity

A measure of the breadth of the molecular mass distribution is given by the ratios of molecular mass averages. The most commonly used ratio Mw/Mn — H, is called the polydispersity index. Wiegand and Kohler discuss the determination of molecular masses (weights) and their distributions in Chapter 6. 

A characteristic of polyolefins synthesized with metallocene catalysts is their significantly lower polydispersity compared to one obtained by using heterogeneous Ziegler-Natta catalysts. Such narrower molecular mass distributions can lead to different mechanical properties of the resulting material. 

Except for biopolymers, most polymer materials are polydisperse and heterogeneous. This is already the case for the length distribution of the chain molecules (molecular mass distribution). It is continued in the polydispersity of crystalline domains (crystal size distribution), and in the heterogeneity of structural entities made from such domains (lamellar stacks, microfibrils). Although this fact is known for long time, its implications on the interpretation and analysis of scattering data are, in general, not adequately considered. 

A general principle is governing the relation between physical parameters and underlying distribution functions. Its paramount importance in the field of soft condensed matter originates from the importance of polydispersity in this field. Let us recall the principle by resorting to a very basic example molecular mass distributions of polymers and the related characteristic parameters. 

With the di-sodium salt of 1,2-dicarbomethoxyethylphosphonic acid as modifier the diethylene glycol content and the carboxyl group content is very low (Table III). These results indicate that the used modifier has also thermostabilizing properties. The integral and differential curves (Fig.2) of molecular mass distribution show that the polydispersity of modified resin is comparable to that of the un-modified. 

Summary Comprehensive investigation of the influence of nine modifiers on the properties of fluoro- and phenylsiloxane rubber was carried out. The synthesized modifiers were analyzed by DTA, TGA, and Si NMR methods. Modifiers polydispersivity was evaluated in terms of molecular-mass distribution (MMD). The modifiers were found to produce a selective effect on the performance of phenyl- and fluorosiloxane-based rubbers, and at their optimum content an improvement in most rubbCT properties was observed. The optimum amount of the introduced modifier depends on its structure. 

The MAO-activated /3-enaminoketonato complexes of Figure 62 are moderately to highly active ethylene polymerization catalysts.1186 However, molecular masses are not very high (Mn < 100000). PEs produced with the first two systems, that is, R =GF3 and R2 = Ph or 2-theonyl, show rather narrow molecular mass distribution (Mw/ Mn < 1.35), indicative of quasi-living behavior. The post-polymerization experiments indicated that the catalyst lifetime is longer than 60 min even in the absence of ethylene. On the other hand, the third system, that is, R1 = CF3 and R2 = 2-furyl, produces PEs with rather broad polydispersities, although the only difference with the 2-theonyl-based catalyst is the replacement of an S atom with an O atom. 

Chain length and molecular mass distribution have of course also strong implications for the performance of modified cellulose. For ethers, the degree of polymerization, DP, is usually between 50 and 2000 (300 for esters), as compared with 100 to 3000 for cotton cellulose and 600 to 1000 for wood cellulose. The relatively high polydispersity of the molecular mass originates from the starting material. 

To obtain samples with small polydispersion, from a sample whose molecular mass distribution is relatively broad, fractionation may be useful. Two main methods can be used precipitation fractionation and exclusion chromatography. 

The samples with great molecular mass are liable to be rather strongly polydisperse, and this polydispersion varies from one sample to another. It will be necessary to account for this. Now, the observable quantities Rq,z and Mw are different averages of the molecular mass distribution in the sample. In order to relate these quantities to each other, let us choose as a reference system a set of monodisperse polymers with molecular mass equal to Mw. In this way... 

Active centres of lanthanide catalyst probably differ in reactivity. This conclusion was made on the basis that polydienes obtained with lanthanide catalysts have a broad molecular mass distribution [50, 55], the polydispersity index being in the order of three even when the reactions of chain termination and transfer do not occur [57]. 

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. 

MALDI-MS is a powerful tool for polymer characterization. Compared with analytical techniques currently used for polymer analysis, it provides several unique features. In MALDI-MS, molecular mass and molecular mass distribution information can be obtained for polymers of narrow polydispersity with both precision and speed. The accuracy, though difficult to determine due to the lack of well-characterized standards, also appears to be good [150]. The MALDI analysis of polymers does not require the use of polymer standards for mass caUbration. Furthermore, this technique uses a minimum amount of solvents and other consumables, which translates into low operational costs. MALDI-MS can also provide structural information, if the instrumental resolution is sufficient to resolve oligomers. In this case, monomer and end-group masses can be deduced from the accurate measurement of the mass of individual oligomers. This is particularly true when a FT-ICR MS is used for polymer analysis. With the use of MALDI-MS/ MS, stmctural characterization can be facilitated. Finally, impurities, byproducts, and subtle changes in polymer distributions can often be detected even for relatively complex polymeric systems such as copolymers. 

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 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 ... 

Table 3). In case of polymerization of ethyl (EM A) and -butyl ( -BuMA) methacrylates under the same conditions, a bimodal molecular mass distribution was observed. The similar isotacticity in both fractions, indicates the existence of two types of active species [169]. The addition of (CH3)3A1 to the polymerization of EMA recently has been found to have the beneficial effect of allowing the synthesis of highly isotactic PEMA with low polydispersity [167]. 

In contrast, the extension of this promising polymerization process to acrylates proved to be more challenging than expected. Indeed, synthesis of random copolymers of styrene and low amounts of -butyl acrylate provided high yields and narrow molecular mass distributions, but increasing the level of acrylate resulted in higher polydispersities and a lowering of conversion (Table 7). Additionally to random copolymerization, this method was applied for the synthesis of a poly(styrene- )-(styrene-cu-n-butyl methacrylate) block copolymer [265],... 

Innovations to mass spectrometry (MS) ionization sources and mass analyzers have helped usher in a new era in polymer chemistry in which the mass spectrometer is viewed as an essential tool that complements classical methods of polymer characterization. MS can be employed for the direct characterization of individual molecules, enabling not only determination of molecular mass and molecular mass distributions, but also determination of structural aspects of polymers such as end-group composition, repeat unit composition and sequence, and the presence of impurities and unintended side products. Here, we review some particular challenges faced for polymer characterization by MS. Synthetic polymers are polydisperse and require fractionation to reduce the complexity of samples analyzed by MS. Different approaches integrating gel permeation chromatography (GPC) with MS analysis for this application are compared and discussed. Next, several different MS... 

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