Molar distribution technique

Table 10.6 compares the average size (DPn) and size distributions of six laboratory-purified amyloses and one commercial sample of potato amylose, which were determined by classic colorimetric and fluorescent-labeling techniques using 2-ami-nopyridine. The data by the two techniques are consistent and show that wheat and other cereal amyloses are smaller in size than those from root and tuber starches. The molar distribution technique indicated that wheat amylose contained two molecular species, compared with one for rice and com amyloses.209,210 Moreover, the molar size distributions for the cereal amyloses are much narrower than those of the tuber amyloses, and the cereal amyloses contain a preponderance of molecules of DPn < 1000 whereas the tuber amyloses contain 78-95% of molecules with DPn > 1000, and even 3-5% above DPn 10000. None of the amylose samples in Table 10.6 showed molecules with less than DPn 200, possibly because they had been purified as alcohol-inclusion complexes.209... 

Complex polymers are distributed in more than one molecular property, for example, comonomer composition, functionality, molecular topology, or molar mass. Liquid chromatographic techniques can be used to determine these properties. However, one single technique cannot provide information on the correlation of different properties. A useful approach for determining correlated properties is to combine a selective separation technique with an information-rich detector or a second selective separation technique. 

As a guide for the reader, Table 1 lists some features of the experimental techniques discussed in this chapter. For each method it is specified whether it allows the determination of an average molar mass and also of the distribution. Estimates of the molar mass range, typical sample amounts and the operating... 

SEC or gel permeation chromatography (GPC) is one of the widely used chromatographic techniques [56,57]. In contrast to the already discussed colligative and scattering methods it is not an absolute method and requires proper calibration with some known polymer standards. One obtains not only the average molar masses (M , Mw, Mz) but the complete molar mass distributions. 

Fig. 4 PIC dye nanoparticles prepared by the ion-association method. (1) Particle size distributions (determined by the dynamic light scattering technique) and the corresponding electron micrographs of the dye nanoparticles. The average diameter can be controlled by tuning the molar ratio of TPB- to PIC+ (=[TPB-]/[PIC+]. With an increase in the molar ratio, the average diameter decreased. (2) Absorption spectra of PIC nanoparticles in aqueous solution with different sizes (125 and 64 nm in diameter), exhibiting size-dependent peak shift of the 0-0 band. The spectrum of the aqueous PIC-Br monomer solution is also shown...

A second route is termed sequential anionic polymerization. More recently, also controlled radical techniques can be applied successfully for the sequential preparation of block copolymers but still with a less narrow molar mass distribution of the segments and the final product. In both cases, one starts with the polymerization of monomer A. After it is finished, monomer B is added and after this monomer is polymerized completely again monomer A is fed into the reaction mixture. This procedure is applied for the production of styrene/buta-diene/styrene and styrene/isoprene/styrene triblock copolymers on industrial scale. It can also be used for the preparation of multiblock copolymers. 

The GPC technique was used to determine gel formation. Figure 13 shows the soluble fraction of aromatic polysulfone I measured with this technique after irradiation at 30 and 150°C. The relative radiation resistance of different polymers can be obtained by comparison of the gel doses (the highest dose for complete solubility of the polymer) provided that the initial molar masses of the of the polymers are known, or from G(S) and G (X) values these can be derived from the dose dependence of the soluble fractions beyond the gel dose, using a Charlesby-Pinner, or Saito-type plot with allowance for the molar mass distribution. 

When such different techniques as in Table 1 are compared, there is always the problem of different sensitivities for different aspects of the distribution. If, for example, information about the high molar mass tail is of importance, PCS may be the method of choice. It may also be incorrect to regard the SEC distribution as the true molar mass distribution as it may suffer from calibration problems, solute-column interactions, peak broadening, and a molar mass dependence of the contrast factor d n/dc, and hence the detector sensitivity. 

While polydisperse model systems can nicely be resolved, the reconstruction of a broad and skewed molar mass distribution is only possible within certain limits. At this point, experimental techniques in which only a nonexponential time signal or some other integral quantity is measured and the underlying distribution is obtained from e.g. an inverse Laplace transform are inferior to fractionating techniques, like size exclusion chromatography or the field-flow fractionation techniques. The latter suffer, however, from other problems, like calibration or column-solute interaction. 

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. 

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