Bimodal distributions molar mass

FIGURE 16.1 Schematic differential (—) and integral (—) representations of amount of polymer with certain molar mass present in the sample. The narrow, broad, and bimodal molar mass distributions are shown. The typical positions of weight, viscosity, number, and z-molar mass averages are depicted. 

Other important pitfalls lie again in the low selectivity of SEC, which does not allow identifying small amounts of the macromolecular admixtures that is the minor components of polymer blends. The bell-shaped chromatograms with a broad base and a slim upper part are often erroneously proclaimed to signalize the narrow molar mass distribution of sample. On the other hand, the accumulation peaks due to presence of macromolecules excluded from the packing pores (Section 16.8.1) are interpreted as the sign of sample bimodality. The absolute detectors may also contribute to erroneous conclusions concerning sample polydispersity (Section 16.8.1). 

Whereas in the example just described the sample amount was about 50 mg, a similar procedure developed by another group 129) started with 4 g polyethylene copolymer. The sample was applied as a dilute solution in xylene and precipitated by very slow cooling (1.5 K/h) onto the Chromosorb P packing of a 500 x 127 mm column. The first separation was temperature-rising elution fractionation at a flow-rate of 20 ml/min and a Unear temperature increase by 8 K/h. The MMD of the fractions was measured by SEC at 145 °C in o-dichlorobenzene at 0.7 ml/min flow rate. The column set included a pair of bimodal columns 100 A and 1000 A plus a 4000 A column. The apparatus was equipped with an IR detector. The experimental data is computed to show the distribution of short-chain branching and of molar mass simultaneously. 

Bimodal distribution Once the rate distribution P(I) and the scaling relation in Eq. (39) are known, the molar mass distribution c(M), expressed in weight fractions, is obtained for the three basic types of experiment discussed ... 

For the whole cl/ Nd range studied ( ci/ Ndv = 2 to 5) BR with a bimodal distribution is obtained with the catalyst system Nd(N(SiMe3)2)3/TIBA/ DEAC. The bimodality of the polymer is attributed to two active centers. Contrary to the previous studies a larger fraction of the high molar mass BR is found at low chlorine contents ( ci/ Nd = 2) [318]. 

In summary, the studies on the impact of nx/ Ndv-ratios on polymerization rate, molar mass, MMD and PDI support the view on the existence of several active species. The relative concentrations of the active species are governed by the molar ratios x/ Nd- Particularly the occurrence of bimodal distributions provides strong evidence for the existence of two distinct active catalyst species. 

This can be clearly seen in the comparison of viscosity functions of polystyrene 1 and polystyrene 2. If we add a very high-molecular weight component to polystyrene 2, we obtain polystyrene 3. It is therefore evident that the bimodal molar mass distribution causes the shear thinning to increase further, although not as far as the polydispersity change of the molar mass distribution between polystyrene 1 and polystyrene 2. In the case of higher shear rates, all flow curves proceed to similar viscosity functions. 

HDPE HDPE ( reactor blends ) Bimodal molar mass distributions provide rmique properties that cannot he achieved by mixing the two PE grades... 

This polymer was also characterised by SEC. Its bimodal molar mass distribution pointed to a significant contribution from the cyclic polysiloxane fraction. The dialysis of this polymer in water permitted the separation of cyclics into the lower molar mass fraction, while the linear polymer constituted the higher molar mass fraction. The gel chromatograms of both these fractions were also compared. The two-step dialysis performed for the precursor and biocidal polymer led to a narrow polydispersity of the former, MW / Mn = 1.21 [95]. 

Asua et al. [121] and Nomura and Fujita [122,123] have analysed the case of oil-soluble initiators theoretically. The latter group [124,125] has verified the conclusions experimentally for styrene with azobis-isobutyronitrile as initiator. Below the cmc of the emulsifier suspension polymerization occurs in the monomer droplets but, in the presence of emulsifier micelles many more much smaller latex particles are produced and emulsion polymerization kinetics becomes dominant. Only the portion of the initiator partitioned into the water phase is significant in the initiation of the emulsion polymerization. The molar mass distribution of the polymer obtained is bimodal initially [125]. The molar mass of the polymer produced by suspension polymerization in the droplets is the same as that produced by bulk polymerization under comparable conditions and only about one-hundredth of that of the emulsion polymer. Wth increase of conversion the contribution of the lower molar mass component to the overall molar mass distribution becomes insignificant. 

Types of molar mass distributions (a) narrow, (b) broad, (c) bimodal. 

In addition to the DB, the fractionation process is quite heavily influenced by the different chemical nature of the byproducts, and also provides the possibility of their separation and identification. One example of the chemically controlled elution fractionation was that of a hb poly(urea urethane) this was the product of a complex AA + B2B reaction between 2,4-toluylene diisocyanate (TDI) and diethanol amine (DEA), additionally end group-modified with phenylisocyanate [94]. Whilst the fractionation of this sample led to a bimodal distribution, an analysis of the fi actions (using SEC with RI detection) showed clearly that the first peak of the distribution belonged to a low-molar-mass substance, identified by NMR and MALDI-TOF as the byproduct diphenylurea (Figure 24.9) [154]. 

A similar experiment from the group of German and co-workers is shown in Figure 7. The batch emulsion copolymerization of STY and MA leads to a strong composition drift with even a bimodal CCD. Figure 7 shows a prediction and an experimental measurement of the resulting molar mass CCD (MMCCD). Such a distribution can only be measured via... 

PLAiooa initially exhibits a narrow and monomodal molar mass distribution (Fig. 2.9). After 31 weeks degradation, the molar mass of the interior becomes lower than that of the surface due to internal autocatalysis, and the molar mass distribution becomes larger. Moreover, a small shoulder is detected in the low molar mass range. After 50 weeks, the shoulder becomes a narrow peak, and the molar mass distribution becomes bimodal for both the surface and interior. Finally at 90 weeks, the narrow peak becomes predominant, in agreement with the increase of crystallinity. Thus the... 

Transesterification reactions could occur during anionic ROP of six-membered carbonates (Scheme 4.5). The intramolecular nucleophilic attack on carbonyl carbon atom (back-biting) leads to cyclic oligomers. The control of the polymerisation is rather poor, and bimodal distribution of molar masses is often observed (Matsuo et al., 1998b Pahovnik and Hadjichristidis, 2015). 

The observed bimodality of the thermomechanical curves of cured DGET testifies for the fact that the forming polymers are stnicturaDy essentially inhomogeneous. The inhomogeneity could be on a molecular or/and siqiramolecular level On a molecular level the observed bimodal thermomechanical curve could be e7q>lain6d by bimodahty of the molar mass distribution of the polymer tested. There is, however, no chemic reason to expect the molar mass distribution of the polymer formed to be bimodal in the case under consideration. 

---