Molar mass polydispersity index

Figure 8.1 The first example of a living cationic polymerization of isobutene using cumyl acetate as initiator and BCI3 as activator in dichloromethane at —30°C. Number-average molar mass, polydispersity index (numbers in the plot), and number of polymer chains (inset) are reported as a function of the mass of PIB obtained. Source Reprinted with permission from Faust R, Kennedy JP. J Polym Sci A Polym Chem 1987 25 1847 [28]. Copyright 1987 John Wiley and Sons, Inc.

In Table 1 the experimental data (weight average of molar mass, polydispersity index, decomposition temperature and heat of decompositioiO of polymers with varius add groups — OR (see equ.l) and different stereochemistry are listed. It can be seen, that the decomposition temperature decreases from ca. 390 °C for poly(emfo,endo-2,3-diacetoxy-5-norbomene), polymer 1 b, down to ca. 270 C for poly(e >,exo 5-norbomene-23-bis(methylcarbonate)), pofymer 3 a. As erqpected, the polymers from the exo,eco-isomers decomposed at lower temperatures as the endo,endo- sova.cK because the thermal elimination reaction is a typical syn-elimination ... 

These observations require a detailed explanation. After several unsuccessful attempts a satisfying answer was finally found. A first step was made by the ingenious derivation of the molar mass distributions of randomly branched or randomly cross-linked materials [14]. The equation, that was later rederived by Elory [13], will be given in the next section. Here it suffices to point out that the width of the distribution, or the polydispersity index MJM , increases asymptotically with the weight average degree of polymerization... 

All these limitations were overcome by implementing a third approach based on the ROP of lactones [7, 8]. Indeed, many examples of living or/and controlled polymerization with fast initiation are reported using this technique. High molar mass aliphatic polyesters with low polydispersity indexes can be thus be synthesized. In terms of the availability of the monomers, this approach occupies... 

Because of these side reactions, the molar mass distribution of UP prepolymers is larger than expected, with a polydispersity index that can be 10 or more (Fig. 2.1). 

A chromatographic technique frequently used in polymer and dendrimer analysis is size exclusion chromatography (SEC) [13], which is often also called gel permeation chromatography (GPC). It is a straightforward method of determining the relative molar mass, the molar mass distribution, and the polydispersity index (PDI) with compatively modest consumption of material and time. 

Fig. 3 Dissolving kinetics (in terms of average hydrodynamic radius Rh) of collapsed single-chain PNIPAM globules, where t is the standing time after the solution temperature was quenched from 33.02 to 30.02 °C and the dashed line represents a stable average value of Rh of individual PNIPAM random coils at 30.02 °C. The weight-average molar mass (Mw) of the PNIPAM sample used is 1.08 x 107g/mol with a polydispersity index (Mw/Mn) less than 1.1 [32]...

The ratio Mw/ Mn must by definition be greater than unity for a polydisperse polymer and is known as the polydispersity or heterogeneity index. Its value often is used as a measure of the breadth of the molar mass distribution, though it is a poor substitute for knowledge of the complete distribution curve. Typically Mw/ Mn is in the range 1.5-2, though there are many polymers which have smaller or very much larger values of polydispersity index. A perfectly monodisperse polymer would have Mw/ Mn = 1.00. 

By SEC, we observed that the fnU distribution of PDMS chains shifted to large molar masses, thus proving the good initiation efficiency of snch macroinifator. The final polydispersity index (M /M =1.25) is smaller than the polydispersity index of the PDMS macroinitiator (1.49), another evidence that all PDMS chains were fnnc-tionalized. The final molecular weight obtained by SEC for the triblock copolymer... 

As mentioned, in addition to the MMD and PSD, various average molar masses, particle sizes, and polydispersity indexes can be calculated from the FFF frac-tograms. If the detector response, h, is proportional to the mass of the macromolecules or particles, the mass-average molar mass or mass average particle diameter can be calculated from... 

The polydispersity index is defined as the ratio of the weight-average and number-average molar masses Monodisperse samples with... 

Consider a mixture containing number fraction nx= jl of the protein gelatin with molar mass A/a = lO gi ior and number fraction b= 1-Ha =1/2 of gelatin dimers with molar mass Mb = 2x lO gmoU. What are the number- and weight-average molar masses of this sample and its polydispersity index ... 

This polydispersity index is larger than for the binary mixture in Example 1. Note that the arithmetic average of and (1.5 x 10 gmol ) is the number-average molar mass for Example 1 with equal number fractions and is the weight-average molar mass for Example 2 with equal weight fractions. ... 

The weight-average molar mass for linear condensation polymers also diverges as the extent of reaction p—> 1 (see Fig. 1.19). The polydispersity index of the linear condensation polymers,... 

Many addition polymerization reactions with very low concentrations of impurities have propagation rates much faster than initiation rates and have essentially no termination. Such reactions produce narrow molar mass distributions that can be approximated by the Poisson distribution. Comparison of the polydispersity index of anionically polymerized butadiene with Eq. (1.69) is shown in Fig. 1.20. 

X lO gmol and 20% by weight of dimer with molar mass lO gmol Calculate M , M, and polydispersity index. ... 

Prove that the weight-average molar mass is never smaller than the number-average molar mass and therefore the polydispersity index is never less than unity ... 

The number-average molar mass stays finite at the gel point and therefore the polydispersity index of the sol diverges at the gel point proportional to Ww. 

Mono-disperse fractions of molar masses 200000 and 400000 g mol are added to the polymer of example 3.1 so that the ratios of the numbers of chains, in order of increasing M, become 1 1 2 1 Calculate the number-average and weight-average molar masses of the resulting polymer and hence show that the polydispersity index has increased. 

Assuming that a polymer has a molar-mass distribution defined by (m) = ae ", where n m)Am represents the fraction of molecules with molar masses between m and m + Am, show that a = b and calculate (i) the number- and weight-average molar masses, and hence the polydispersity index and (ii) the molar mass at the mode (maximum) of the distribution function. 

Hence the polydispersity index is 2. The molar mass that contributes most is the one corresponding to the maximum in the curve of weight fraction against M and therefore to the maximum in w = ame " . However, dw/dm - a — so that the maximum is when... 

The molar mass distribution was analysed by means of GPC giving Mn= 172000 g/mol and Mw=298800 g/mol with a polydispersity index Mw / Mn of 1,74 respectively. The molar mass distribution is typically unimodal. 

The width of a molecular weight distribution can, because of Equation (8-47), always be described by the ratio of two molecular weight averages. The molar mass ratio ( polydispersity index ) Q is given as... 

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