Molecular polydispersity index

My,lM Molecular polydispersity index, MWD MWD Molecular weight distribution usually expressed as Nb Norbomyl... 

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. 

Molecular weights of polysaccharides in solution can also be measured by osmotic pressure and light scattering. Osmotic pressure yields the number average molecular weight, which can be usefully used with Mw from sedimentation equilibrium as a measure of polydispersity Preston and Wik [28] have done this for example with hyaluronic acid. The ratio Mw/Mn the polydispersity index is often given as a measure of polydispersity, and can be related to the width of a molecular weight distribution via the well-known Herdan [96] relation ... 

The micro-mixed reactor with dead-polymer model was developed to account for the large values of the polydispersity index observed experimentally. The effect of increasing the fraction of dead-polymer in the reactor feed while maintaining the same monomer conversion is to broaden the product polymer distribution and therefore to increase the polydispersity index. As illustrated in Table V, this model, with its adjustable parameter, can exactly match experiment average molecular weights and easily account for values of the polydispersity index significantly greater than 2. 

A micro-mixed, seeded reactor will produce a broad polymer distribution with a high molecular weight tail and polydispersity index that approaches 2 at large degrees of polymerization. 

Silane radical atom transfer (SRAA) was demonstrated as an efficient, metal-free method to generate polystyrene of controllable molecular weight and low polydispersity index values. (TMSlsSi radicals were generated in situ by reaction of (TMSlsSiH with thermally generated f-BuO radicals as depicted in Scheme 14. (TMSlsSi radicals in the presence of polystyrene bromide (PS -Br), effectively abstract the bromine from the chain terminus and generate macroradicals that undergo coupling reactions (Reaction 70). 

Table II shows that for SRM 706 good agreementis obtained between SEC/LALLS and conventional SEC sample My, and Rp values when the band-spreading correction was used. However, the NBS 706 polydispersity index (Ry/Rp) given by the supplier (ca. 2.1) does not agree with that 1.°) found here using the SEC/LALLS and conventional SEC techniques. Insensitivity of the LALLS detector to a small amount of low molecular weight material may account for a larger sample R however, this is not supported by the conventional SEC data. The reason for the discrepancy remains unclear.

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. 

Tab. 5.7 Polyethers from isosorbide and 1,8-dibromo- or dimesyloctane yield and distribution data for the microwave procedure (Mn and Mw are, respectively, the number average and weight average molecular weights, the ratio Mw/Mn being the polydispersity index).

The number average molecular weight (Mjj) and polydispersity index (1 /Mjj) are given in Table II for the various PS and PDMS samples prepared. 

The hydroboration/oxidation sequence does not change the molecular-weight distribution. Gel permeation chromatography (GPC) measurements in dimethyl-formamide (DMF) with the resulting polystyrene-ft-polyalcohol polymers show very similar polydispersity indexes (Table 10.2). Here, the hydroboration/oxidation sequence is clearly superior to the epoxidation reaction, which leads to a... 

The development of mass spectroscopic techniques such as matrix assisted laser desorption (MALDI) and electrospray mass spectrometry has allowed the absolute determination of dendrimer perfection [7,8], For divergent dendrimers such as PAMAM and PPI, single flaws in the chemical structure can be measured as a function of generation to genealogically define an unreacted site of or a side reaction producing a loop at a particular generation level. Mass spectromet-ric results on dendrimers, not only demonstrate the extreme sensitivity of the technique, but also demonstrate the uniformity of the molecular mass. The polydispersity index of Mw/Mn for a G6 PAMAM dendrimer can be 1.0006 which is substantially narrower than that of living polymers of the same molecular mass [7],... 

The distribution of molecular weights of each generation was determined from measurements on about 50 molecules, with results shown in Figure 12.19 (the weight fraction is the percent dendrimer in each interval of molecular weight under consideration). Based on these distributions, the polydispersity index (.MJMa) of G5 to G10 can be calculated, with results shown in Table 12.1 [39], They are all less than 1.08, which means that the particle size distribution is very uniform for each generation. 

At 24 °C and 15-60 bar ethylene, [Rh(Me)(0H)(H20)Cn] catalyzed the slow polymerization of ethylene [4], Propylene, methyl acrylate and methyl methacrylate did not react. After 90 days under 60 bar CH2=CH2 (the pressure was held constant throughout) the product was low molecular weight polyethylene with Mw =5100 and a polydispersity index of 1.6. This is certainly not a practical catalyst for ethylene polymerization (TOP 1 in a day), nevertheless the formation and further reactions of the various intermediates can be followed conveniently which may provide ideas for further catalyst design. For example, during such investigations it was established, that only the monohydroxo-monoaqua complex was a catalyst for this reaction, both [Rh(Me)3Cn] and [Rh(Me)(H20)2Cn] were found completely ineffective. The lack of catalytic activity of [Rh(Me)3Cn] is understandable since there is no free coordination site for ethylene. Such a coordination site can be provided by water dissociation from [Rh(Me)(OH)(H20)Cn] and [Rh(Me)(H20)2Cn] and the rate of this exchange is probably the lowest step of the overall reaction.The hydroxy ligand facilitates the dissociation of H2O and this leads to a slow catalysis of ethene polymerization. 

Table 14.2 Molecular weights and polydispersity indexes of polycarbosilanes 1 obtained via reactions I and II.

The degree of polymerization depends on the duration of the process. After 7 min, the molecular mass is equal to 9400 (the polydispersity index is 5.30). When the reaction is carried out for 15 min, the molecular mass of the polymer increases to 37,000 and the polydispersity index reaches 7.31 (Bauld et al. 1996). Depending on whether cation-radical centers arise at the expense of intramolecular electron transfer or in a stepwise intermolecular lengthening, polymerization can occur, respectively, through a chain or a step-growth process (Bauld and Roh 2002). In the reaction depicted in Scheme 7.17, both chain and step-growth propagations are involved. 

The hnal copolymer was obtained in 90% yield it had a molecular weight of 10,800 and polydispersity index of 2.1. In this case, Diels-Alder copolymerization dominates over the cyclobntane homopolymerization. It means that Diels-Alder addition of the dienophile cation-radical to the diene is substantially faster than the competing addition of the dienophile cation-radical to the nen-tral dienophile. 

Hence, cation-radical copolymerization leads to the formation of a polymer having a lower molecular weight and polydispersity index than the polymer got by cation-radical polymerization— homocyclobutanation. Nevertheless, copolymerization occnrs nnder very mild conditions and is regio-and stereospecihc (Bauld et al. 1998a). This reaction appears to occnr by a step-growth mechanism, rather than the more efficient cation-radical chain mechanism proposed for poly(cyclobutanation). As the authors concluded, the apparent suppression of the chain mechanism is viewed as an inherent problem with the copolymerization format of cation-radical Diels-Alder polymerization. ... 

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